modeling, stability analysis and control of...
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MODELING, STABILITY ANALYSIS AND CONTROL OF MICROGRID.
A Thesis submitted in Partial Fulfilment of the Requirement for the
Degree of
Doctor of Philosophy
Ritwik Majumder
M.Sc (Engg), B.E (Electrical engineering)
Faulty of Build and Environment Engineering
School of Engineering Systems
Queensland University of Technology
Queensland, Australia
February 2010
KEYWORDS
Microgrid Distributed Generators Islanding Resynchronization Voltage Source Converter Converter Structure and Control Voltage Control State Feedback Control Power Sharing Droop Control Frequency Droop Angle Droop Power Quality Back to Back Converters Stability Rural Distributed Generation Modified Droop Control Web Based Communication
ABSTRACT
With the increase in the level of global warming, renewable energy based
distributed generators (DGs) will increasingly play a dominant role in electricity
production. Distributed generation based on solar energy (photovoltaic and solar
thermal), wind, biomass, mini-hydro along with use of fuel cells and micro turbines
will gain considerable momentum in the near future. A microgrid consists of clusters
of load and distributed generators that operate as a single controllable system. The
interconnection of the DG to the utility/grid through power electronic converters has
raised concern about safe operation and protection of the equipments.
Many innovative control techniques have been used for enhancing the
stability of microgrid as for proper load sharing. The most common method is the use
of droop characteristics for decentralized load sharing. Parallel converters have been
controlled to deliver desired real power (and reactive power) to the system. Local
signals are used as feedback to control converters, since in a real system, the distance
between the converters may make the inter-communication impractical. The real and
reactive power sharing can be achieved by controlling two independent quantities,
frequency and fundamental voltage magnitude.
In this thesis, an angle droop controller is proposed to share power amongst
converter interfaced DGs in a microgrid. As the angle of the output voltage can be
changed instantaneously in a voltage source converter (VSC), controlling the angle
to control the real power is always beneficial for quick attainment of steady state.
Thus in converter based DGs, load sharing can be performed by drooping the
converter output voltage magnitude and its angle instead of frequency. The angle
control results in much lesser frequency variation compared to that with frequency
droop.
An enhanced frequency droop controller is proposed for better dynamic
response and smooth transition between grid connected and islanded modes of
operation. A modular controller structure with modified control loop is proposed for
better load sharing between the parallel connected converters in a distributed
generation system. Moreover, a method for smooth transition between grid
connected and islanded modes is proposed.
Power quality enhanced operation of a microgrid in presence of unbalanced
and non-linear loads is also addressed in which the DGs act as compensators. The
compensator can perform load balancing, harmonic compensation and reactive
power control while supplying real power to the grid
A frequency and voltage isolation technique between microgrid and utility is
proposed by using a back-to-back converter. As utility and microgrid are totally
isolated, the voltage or frequency fluctuations in the utility side do not affect the
microgrid loads and vice versa. Another advantage of this scheme is that a
bidirectional regulated power flow can be achieved by the back-to-back converter
structure.
For accurate load sharing, the droop gains have to be high, which has the
potential of making the system unstable. Therefore the choice of droop gains is often
a tradeoff between power sharing and stability. To improve this situation, a
supplementary droop controller is proposed. A small signal model of the system is
developed, based on which the parameters of the supplementary controller are
designed.
Two methods are proposed for load sharing in an autonomous microgrid in
rural network with high R/X ratio lines. The first method proposes power sharing
without any communication between the DGs. The feedback quantities and the gain
matrixes are transformed with a transformation matrix based on the line R/X ratio.
The second method involves minimal communication among the DGs. The converter
output voltage angle reference is modified based on the active and reactive power
flow in the line connected at point of common coupling (PCC). It is shown that a
more economical and proper power sharing solution is possible with the web based
communication of the power flow quantities.
All the proposed methods are verified through PSCAD simulations. The
converters are modeled with IGBT switches and anti parallel diodes with associated
snubber circuits. All the rotating machines are modeled in detail including their
dynamics.
CONTENTS
List of Figures xv
List of Tables xix
List of Principle Symbols xxi
1 Introduction 1 1.1 Power Sharing In Distributed Generation 2
1.2 Microgrid And Its Autonomous Control 2
1.2.1 Controls for Grid and Island Operation 4
1.3 Power Quality And Reliability 4
1.4 System Stability 6
1.5 Power Sharing In Rural Network 7
1.6 Objectives of the Thesis and Specific Contributions 8
1.6.1 Objectives of the Thesis 8
1.6.2 Specific Contributions of the Thesis 9
1.7 Thesis Organization 10
2 Power Sharing with Converter Interfaced Sources 13 2.1 Control Of Parallel Converters For Load Sharing With
Frequency Droop 13
2.1.1 Frequency Control 14
2.1.2 Modular Control Structure 14
2.1.3 Converter Voltage Angle Calculation 15
2.1.4 Reference Generation 15
2.2 Angle Droop Control 17
2.2.1 Angle Droop Control And Power Sharing 18
2.3 Angle Droop And Frequency Droop Controller 20
2.4 Simulation Studies 22 2.4.1 Frequency Droop Controller 22
2.4.2 Angle Droop Controller 23 2.4.3 Comparison Of Frequency Droop And Angle Droop 23 2.4.4 Angle Droop In Multi DG System 25
2.5 Conclusions 27
3 Load Frequency Control in Microgrid 28 3.1 Seamless Transfer between Grid Connected and Islanded Modes 28 3.2 Proposed Control 29
3.3 Simulation Studies 30
x
3.3.1 Islanded Mode 30
3.3.2 Grid Connected Mode 32
3.3.3 Seamless Transfer Between Grid Connected
and Islanded Modes 33
3.4 Microgrid with Inertial and Non Inertial DGs 37
3.4.1 System Structure 38
3.4.2 Micro Source Model 38
3.4.2.1 Fuel Cell 38
3.4.2.2 Photo Voltaic Cell (PV) 39
3.4.2.3 Battery 39
3.4.3 Simulation Studies 40
3.4.3.1 Case 1: Grid Connected and Autonomous Operating Modes 40
3.4.3.2 Case 2: Power Sharing In Autonomous Mode 40
3.4.3.3 Case 3: Source Inertia And System Damping 41
3.5 Conclusions 42
4 Power Quality Enhanced Operation of a Microgrid 44 4.1 System Structure 45
4.2 Reference Generation And Compensator Control 46
4.2.1 Compensator Reference Generation in Grid
Connected Mode 46
4.2.2 Compensator Control 50
4.2.3 Compensator Reference Generation in Islanded Mode 51
4.2.4 DG Coordination for Sharing the Common Load 52
4.3 Simulation Studies 54
4.3.1 Sharing the Local Load with Utility 54
4.3.2 Sharing the Common Load by The DGs 56
4.3.3 Sharing a Common Induction Motor Load 57
4.3.4 DG-1 Supplying the Entire Common Load during Islanding 58
4.4 Discussions 59
4.5 Conclusions 60
5 Power Flow Control with Back-to Back Converters in a Utility Connected Microgrid 65 5.1 System Structure and Operation 65
5.2 Converter Structure And Control 68
5.3 Back-To-Back Converter Reference Generation 68
5.3.1 VSC-1 Reference Generation 68
xi
5.3.2 VSC-2 Reference Generation in Mode-1 69
5.3.3 VSC-2 Reference Generation in Mode-2 69
5.4 Reference Generation for DG Sources 70
5.4.1 Mode-1 70
5.4.2 Mode-2 71
5.5 Relay and Circuit Breaker Coordination during Islanding and Resynchronization 72
5.6 Simulation Studies 74
5.6.1 Case-1: Load Sharing of the DGs with Utility 74
5.6.2 Case-2: Change in Power Supply from Utility 76
5.6.3 Case-3: Power Supply from Microgrid to Utility 77
5.6.4 Case-4: Load Sharing with Motor Load 78
5.6.5 Case-5: Change in Utility Voltage and Frequency 79
5.6.6 Case-6: Islanding and Resynchronization 81
5.6.7 Case-7: Variable Power Supply from Utility 81
5.6.8 Case-8: DC Voltage Fluctuation and Loss of A DG 83
5.7 Microgrid Containing Multiple DGs 84
5.8 Conclusions 85
6 Stability Analysis of Multiple Converter Based Autonomous Microgrid 87 6.1 Converter Structure and Control 87
6.2 Droop Control and DG Reference Generation 88
6.2.1 Droop Control 88
6.2.2 DG Reference Generation 88
6.3 State Space Model of Autonomous Microgrid 89
6.3.1 Converter Model 90
6.3.2 Droop Controller 93
6.3.3 Combined Converter-Droop Control Model 94
6.3.4 Transformation to Common Reference Frame 95
6.3.5 Network and Load Modeling 97
6.3.6 Complete Microgrid Model 98
6.4 System Structure and Model of Autonomous Microgrid Example 99
6.5 Eigenvalue Analysis of Microgrid 101
6.6 Simulation Studies 104
6.6.1 Case 1: Full System of Fig. 6.2 (3 DG And 3 Loads) 105
6.6.2 Case 2: The Effect of System Reduction 105
6.7 Improvement in Stability with Supplementary Droop Control 107
6.7.1 Test System 110
6.7.2 Simulation Studies with Supplementary Droop Controller 110
xii
6.7.2.1 Case 1: Full System Of Fig. 6 With Lower Droop Gains 110
6.7.2.2 Case 2: Reduced System with Lower Droop Gains 111
6.7.2.3 Case 3: System Stability with High Droop Gain 112
6.7.2.4 Case 4: Power Sharing with The Proposed Supplementary Controller 113
6.7.2.5 Case 5: Power Sharing with the Proposed Controller in Reduced System 113
6.8 Conclusions 115
7 Droop Control of Converter Interfaced Micro Sources in Rural Distributed Generation 117 7.1 Power Sharing with Angle Droop and Proposed Droop Control 117
7.1.1 Proposed Controller-1 without Communication 119
7.1.2 Proposed Controller-2 with Minimum Communication 121
7.1.3 Multiple DG System 122
7.1.4 Web Based Communication 124
7.2 Converter Structure and Control 125
7.2.1 Converter Control 125
7.2.2 DG Reference Generation 126
7.3 Simulation Studies 128
7.3.1 Case 1: Load_3 and Load_4 Connected to Microgrid 128
7.3.2 Case 2: DG-1 and DG-3 Supply Load_1 and Load_2 130
7.3.3 Case 3: Induction Motor Loads 131
7.3.4 Case 4: Load Sharing with Advanced Communication System 132
7.3.5 Case 5: Load Sharing with Conventional Droop Controller 133
7.3.6 Case 6: Load Sharing With Conventional Droop Controller 134
7.4 Conclusions 134
8 Conclusions 137 8.1 General Conclusions 137
8.2 Scope for Future Work 138
Appendix-A: Converter Structure and Control 139 A.1 Converter Structure 139
A.2 Converter Control 139
A.3 Output Feedback Voltage Controller 140
A.4 State Feedback Controller 142
Appendix-B: List of Publication 145
xiii
References 149
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xv
LIST OF FIGURES
2.1. Microgrid system under consideration
2.2. The modular control structure
2.3. Voltage angle control loop
2.4. Converter structure
2.5. Equivalent circuit of one phase of the converter
2.6. Source angle extraction from rotating angle
2.7 DG connection to microgrid
2.8 System stability as function of frequency droop gain
2.9 System stability as function of angle droop gain
2.10 DG power output with frequency droop control
2.11 DG power output with angle droop control
2.12 Frequency variation with frequency droop control
2.13 Frequency variation with angle droop control
2.14 Angle variation with angle droop control
2.15 Microgrid Structure with multiple DGs
2.16 Real Power Sharing of the DGs
2.17 Real Power Sharing of the DG-1 and DG-4
3.1 Microgrid system under consideration
3.2 System response with impedance load in islanded mode
3.3 System response with motor load in islanded mode
3.4 System response with impedance load in grid connected mode
3.5 System response with induction motor load in grid connected mode
3.6 System response with synchronous motor load in grid connected mode
3.7 System response during islanding and resynchronization with impedance load
3.8 PCC voltage during islanding and resynchronization with impedance load
3.9 System response during islanding and resynchronization with motor load
3.10 PCC voltage during islanding and resynchronization with motor load
3.11 DG connection to microgrid
3.12 Microgrid system
3.13 Single-phase equivalent circuit of VSC
3.14 System stability as function of frequency droop gain
3.5 System stability as function of angle droop gain
3.6 DG power output with angle droop control
3.7 Frequency variation with angle droop control
3.8 DG power output with frequency droop control
3.9 Frequency variation with frequency droop control
3.10. Microgrid structure under consideration
3.11 Fuel cell modeled equivalent circuit
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3.12 Equivalent circuit of PV and boost chopper based on MPPT
3.13 MPPT control flowchart for PV
3.14 Islanding and resynchronization
3.15 Real power sharing of the DGs
3.16 Current output of the micro sources
3.17 Real power sharing of the DGs
3.18 Real power sharing of the DGs
4.1 The microgrid and utility system under consideration
4.2 Equivalent circuit of one phase of the converter
4.3 Real and reactive power sharing in DG-1and DG-2
4.4 Voltages at the PCC1 and PCC2
4.5 Power sharing and DG-1current and PCC1 voltages
4.6 Real power sharing by DG-1 and DG-2
4.7 Common load sharing between DG-1 and DG-2
4.8 Real power sharing of the DGs and voltages at PCC1 and PCC2
4.9 Microgrid structure with large number of DGs and loads
5.1 The microgrid and utility system under consideration
5.2 Angle controller for VSC-1
5.3 Schematic diagram of VSC-2 connection to microgrid
5.4 Power flow from DG-1 to microgrid
5.5 Logic for breaker operation and converter blocking
5.6 Breakers and converter blocking timing diagram
5.7 Real and reactive power sharing for Case-1
5.8 Voltage tracking of DG-1 Case-1.
5.9 Capacitor voltage and angle controller output for Case-1
5.10 Real and reactive power sharing for Case-2
5.11 Three phase PCC voltage and injected current for Case-2
5.12 Real and reactive power sharing during power reversal (Case-3)
5.13 PCC voltage and injected current for Case-3
5.14 Real and reactive power sharing with motor load (Case-4)
5.15 Real and reactive power during frequency fluctuation (Case-5)
5.16 Real and reactive power during voltage sag (Case-5)
5.17 DC capacitor voltage and angle controller output during voltage sag
5.18 Location of the single line to ground fault
5.19 DC capacitor voltage and angle controller output during islanding and resynchronization (Case-6)
5.20 Real and reactive power during islanding and resynchronization (Case-6)
5.21 Real power sharing during power limit and mode change (Case-7)
5.22 DC voltage fluctuation in DG-1 and its tripping (Case-8)
5.23 Microgrid structure with large number of DGs and loads
xvii
5.24 Real power sharing with four DGs
6.1 Interconnection diagram of the complete microgrid system
6.2 Microgrid system under consideration
6.3 Eigenvalues for nominal operating condition
6.4 Eigenvalue locus with real power droop gain change
6.5 Eigenvalue locus with reactive power droop gain change
6.6 Eigenvalue locus without DG-3
6.7. Real and reactive power during a change in load 1
6.8 Unstable operation with m = 8.18×10−5 rad/W
6.9 Marginally stable operation with n = 2.5×10−3 V/VAr
6.10 System response 3 and 2 DGs for m = 6.18×10−5 rad/W
6.11 System response for different system configuration
6.12 . Supplementary Droop Controller Configuration
6.13 Supplementary controller structure
6.14 Microgrid system under consideration
6.15 Real and reactive power during a change in load 1
6.16 Power sharing with reduced system
6.17 System stability with high droop gain
6.18 Power sharing with proposed controller
6.19 Droop controller and supplementary controller output
6.20 System response for different system configuration
6.21 Power sharing in reduced system
7.1 Power sharing with angle droop
7.2 Power sharing in resistive-inductive line
7.3 Multiple DG connected to microgrid
7.4 (a) Web based PQ monitoring scheme and (b) web based communication for DG-1
7.5 Power sharing with conventional controller (Case 1)
7.6 Power sharing with Controller-1 (Case 1)
7.7 Power sharing with Cntroller-2 (Case 1)
7.8 Power sharing with conventional controller (Case 2)
7.9 Power sharing with Controller-1 (Case 2)
7.10 Power sharing with Controller-2 (Case 2)
7.11 Power sharing with conventional controller (Case 3)
7.12 Power sharing with Controller-1 (Case 3)
7.13 Power sharing with Controller-2 (Case 3)
7.14 Power sharing with high bandwidth communication (Case 4)
7.15 Error in power sharing with different control techniques
7.16 Frequency droop and angle droop
7.17. Power sharing with frequency droop Case 1
7.18. Frequency dependent load
xviii
xix
LIST OF TABLES
2.1 System and Controller Parameters
2.2 Microgrid System and Controller Parameters
3.1 System Parameters
4.1 System Parameters
4.2 Numerical Results
5.1 System and controller parameters
6.1 Nominal System Parameters
6.2 Mode participation factors
6.3 Parameters of the supplementary droop control loop
6.4 Nominal System Parameters
7.1 Nominal System Parameters
7.2 Simulation Results
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LIST OF PRINCIPLE SYMBOLS vsa, vsb, vsc Source voltages of phases a, b, and c respectively
isa, isb, isc Source current of phases a, b, and c respectively
vPCCa, vPCCb, vPCCC PCC voltages of phases a, b, and c respectively
i1a, i1b, isc Converter current of phases a, b, and c respectively
Rs, Ls Feeder resistance and inductance respectively in utility
XD Line reactance
RD Line resistance
Cf Filter capacitance
L1, L2, L3 Filter inductance
Lf Transformer leakage reactance
Rf Transformer and VSC losses
VDC1, VDC2, VDC3 DC voltage source of the Distributed Generators
u Converter switching function
ωs Synchronous frequency
V Magnitude of converter output voltage
Angle of converter output voltage
VP Magnitude of PCC voltage
P Angle of PCC voltage
vcf Voltage across filter Capacitor
icf Current through filter Capacitor
ω Operating frequency
ωS Cut off frequency of low pass filter
P1, P2 Real power injected by DGs to microgrid
Q1, Q2 Reactive power injected by DGs to microgrid
Prated, Qrated Real and reactive power rating of the DG
Pg Real power injected by utility to microgrid
Qg Reactive power injected by utility to microgrid
PL, QL Real and reactive load power
PLC, QLC Real and reactive power of common load
1P, 1Q Real and reactive power sharing ratio with utility
m, n Droop coefficients
K State feedback controller gain
S, R Polynomials in pole shift controller
Pole shift factor
Z-1 Delay operator
h Hysteresis band
KP, KI Proportional and integral gain constant
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STATEMENT OF ORIGINAL AUTHORSHIP
The work contained in this thesis has not been previously submitted to meet requirements for an award at this or any other higher education institution. To the best of my knowledge and belief, the thesis contains no material previously published or written except where due reference is made.
Signature ___ ______________________________ Date________________06.06.2010_______________
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ACKNOWLEDGEMENT
First and foremost I offer my gratitude to my supervisors, Prof. Arindam Ghosh, Prof. Gerard Ledwich and A/Prof. Firuz Zare, who have supported me throughout my doctoral research. It was a great honor for me to pursue my research under their supervision.
I would like to thank Australia for giving me the opportunity of doctoral research here. I thank Queensland University of Technology and Australia Research Council (ARC) for the financial support.
I thank Saikat da, Rajat, Sachin, Ali, Arash, Jaffar, Manjula and all for the technical and much needed non technical discussions. Rajat gave me a warm welcome to Australia and without his presence, this Ph.d in QUT would not have started.
With many other staff in QUT, I would like to thank our research office (Diane and her team), theme coordinator (Christine), School Office (Noelene) for all the support and help.
Life has been always bigger than science. I thank Kie for showing me the power of simplicity and honesty in life. I thank my parents for their support and unconditional love.
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1
CHAPTER 1
The concern for climate change is driving major changes in electricity generation and
consumption patterns. Various countries have set a target of 20 % greenhouse gas reduction by the
year 2020.
Large scale changes in both transmission and distribution levels are expected to occur in the
near future. Transmission systems will be bolstered to transmit power generated from large windfarm,
geothermal and solar thermal generations.
In distribution levels, many smaller renewable generators (e.g. photovoltaic, fuel cells, micro
hydro etc.) will be connected to the networks. These are called distributed generators (DGs) or
distributed energy resources (DERS). Their integration into distributions systems disturbs the radial
nature of power flow through distribution feeders.
The interconnection of DG to the utility/grid through power electronic converters has raised
concern about safety and protection. IEEE P1547 standard [1] provides the technical requirement for
the interconnection of the distributed resources (DR) units to the electric power system. The current
IEEE recommended industry practice is to isolate all distributed energy resources (DERs, e.g., PV and
wind) from the grid in the event of a fault in the grid. This approach is adequate when the total
capacity of the DERs is not significant and they can be removed without major impact on the system.
However it is expected that the penetration level of grid-connected DERs will increase substantially
over the next few decades. In addition, the number of Plug-in Hybrid Electric Vehicles (PHEVs) will
increase in the near future and microgrids will become popular in rural communities and commercial
buildings. The cumulative effect of these innovations will be a change in the power flow patterns in
power distribution systems.
1.1 MICROGRID AND DISTRIBUTED GENERATION
A microgrid is a cluster of loads and microsources operating as a single controllable system that
provides power to its local area. To the utility, the microgrid can be thought of as a single controllable
load that can respond in seconds to meet the needs of the transmission system. To the customer, the
microgrid can meet their special needs; such as, enhancing local reliability, reducing feeder losses,
2
supporting local voltages, providing increased efficiency through the use of waste heat, voltage sag
correction or providing uninterruptible power supply functions to name a few [2]. In ref [3], the focus
is on systems of distributed resources that can switch from grid connection to island operation without
causing problems for critical loads. Different microgrid control strategy and power management
techniques are discussed in [4-8] Premium power is a concept based on the use of power electronic
equipment (such as custom power devices and active filters), multi utility feeders and uninterruptible
power supplies to provide power to users having sensitive loads. This power must have a higher level
of reliability and power quality than normally supplied by the utility. These technologies require
power electronics to interface with the power network and its loads. In many of the cases, there is a dc
voltage source (e.g. PV), which must be converted to an ac voltage at the required frequency,
magnitude and phase angle. In these cases, the conversion will be performed using a voltage source
converter, using a possible pulse width modulation to provide fast control of voltage magnitude. The
reliability, economic operations and planning of microgrid are investigated in [9-11]. Some of the
basic issues that need to be addressed are:
• Control: A major issue in distributed generation is the technical difficulties related to control
of a significant number of microsources.
• Operation and investment: The economy of scale favors larger DG units over microsources.
For a micro source, the cost of the interconnection protection can add as much as 50% to the
cost of the system [6]. DG units with a rating of three to five times that of a microsource have
a connection cost much less per kW since the protection cost remains essentially fixed. The
microgrid concept allows for the same cost advantage of large DG units by placing many
microsources to a single dc bus with single voltage source converter interface.
• Power quality/Power Management/Reliability: DG has the potential to increase system
reliability and power quality due to the decentralization of supply. Increase in reliability
levels can be obtained if DG is allowed to operate autonomously in transient conditions [6].
1.2 POWER SHARING IN DISTRIBUTED GENERATION
Parallel converters have been controlled so as to deliver desired power (and reactive power) to the
system. Local signals are used as feedback to control converters, since in a real system, the distance
3
between the converters may make the communication impractical. A common approach for real and
reactive power sharing is droop control of two independent quantities – the frequency and the
fundamental voltage magnitude [12-22]. In this, the real power controls the system frequency, while
the reactive power controls the voltage magnitude. In [12] real and reactive power management
strategies of electronically interfaced distributed generation (DG) units in the context of a multiple-
DG microgrid system are addressed, where emphasis is primarily on electronically interfaced DG (EI-
DG) units. Robust voltage regulation with harmonic elimination under island and decoupled active
and reactive power flow control under grid-connected mode is proposed in [13]. The impact of
distributed generation technology and the penetration level on the dynamics of a test system is
investigated in [15]. The pre-planned switching events and the fault events that lead to islanding of a
microgrid are explored in [17] with the desired power sharing. The slow and oscillating nature of the
load sharing with a conventional droop control is overcome by introducing power derivative integral
terms [23], where a better controllability of the system is obtained and improvement in transient
performance is achieved. A transient droop characteristic [23] achieves a steady state invariant
frequency and good current balance. Sometimes an additional faster loop is added to program the
output impedance. Both inductive and resistive output has been investigated. In the resistive output,
the active power is controlled by terminal voltage where the reactive power is controlled by the source
angle. Karimi et al [24] developed a dynamic model and a control system for autonomous operation of
a stand-alone DG, which includes an electronically interfaced distributed resource and a local load.
The DG is represented by a DC voltage source in series with a three phase voltage-sourced converter
and an RL filter. The local load is modeled by a parallel RLC network. A state-space dynamic model is
developed for the DR (distributed resources) including the RLC network. A controller is designed to
maintain stability and control voltage and frequency of the stand-alone DG based on dynamic model
of the DG.
It is always desired in a microgrid that all the DGs respond to any load change in a similar rate to
avoid the overloading of a lagging or leading DG. In the presence of both inertial and non inertial
DGs, the response time for each DG to any change in load power demand will be different. A
converter interfaced DG can control its output voltage instantaneously and so the change in the power
demand can be picked up quickly, while in an inertial DG, the rate of change in power output is
4
limited by the machine inertia. To ensure that a load change is picked up by all the DGs in same rate,
the rate of change in converter interfaced DGs is to be limited.
1.2.1 CONTROLS FOR GRID AND ISLAND OPERATION
Power electronic interfaces introduce new control issues and possibilities. It is necessary to create
a power electronic interface, which allows large clusters of micro generators to operate in both an
island mode and as a satellite to the power grid while providing a high quality of power at a minimum
equipment cost. Basic requirements of the power electronic interface are:
• To provide fixed power and local voltage regulation
• To facilitate DG fast load tracking using storage
• To incorporate “frequency droop” methods to insure load sharing between micro-sources in
islanded operation without communications
Keyhani et all [25] propose the use of a low-bandwidth data communication system along with
locally measurable feedback signal for each DG. This is achieved by combining two control methods:
droop control method and average power control. The average power method with a slow update rate
is used in order to overcome sensitivity voltage and current measurement errors. In addition, a
harmonic droop scheme for sharing harmonic content of the load currents is also proposed. But the
communication between DGs may not be always possible in reality due to the physical distance
between them. The application of adaptive control or robust control in distributed generation is shown
in [26-27]. A strategic analysis and optimal voltage control technique for distributed generation are
proposed in [28 and 29].
1.3 POWER QUALITY AND RELIABILITY
A microgrid may contain non linear unbalanced loads. Moreover the voltage source converter
(VSC) connecting the DGs are themselves sources of harmonic generation. Therefore, it is important
to ensure a compensator configuration that is suitable for supplying electrical power to the microgrid,
while at the same time compensating for the non linearity/unbalance.
5
Power quality is always been a major concern and different filtering techniques are proposed in [30,
31, 32]. Determination of allowable penetration levels of distributed generation resources based on
harmonic limit consideration has been addressed in [33]. Many optimization methods are also been
proposed for planning and energy loss reduction [34, 35 and 36].
The authors of [37] propose a single-phase high-frequency ac (HFAC) microgrid as a solution
towards integrating renewable energy sources in a distributed generation system. For a better
performance of the DGs and more efficient power management system, it is important to achieve
control over the power flow between the grid and the microgrid. With a bidirectional control on the
power flow, it is possible not only to specify the exact amount of power supplied by the utility but
also the fed back power from microgrid to utility during lesser power demand in the microgrid.
Reliability is also a major issue in microgrid operation. Frequent load change, DG location and
change in DG power output always challenge the power management system and system reliability.
From the reliability point of view, frequency isolation between a microgrid and utility may be
desirable.
With number of DGs and loads connected over a wide span of the microgrid, isolation between the
grid and the microgrid will ensure a safe operation, in most cases.. Any voltage or frequency
fluctuation in the utility side has direct impact on the load voltage and power oscillation in the
microgrid side. For a safe operation of any sensitive load, it is not desirable to have any sudden
change in the system voltage and frequency. The isolation between the grid and microgrid not only
ensures safe operation of the microgrid load, it also prevents direct impact of microgrid load change or
change in DG output voltage on the utility side.
Protection of the devices both in utility and microgrid sides during any fault is always a major
concern [38-42]. Of the many schemes that have been proposed, [38] explores the effect of high DG
penetration on protective device coordination and suggests an adaptive protection scheme as a
solution to the problems. In [39], a method has been proposed for determining the coordination of the
rate of change of frequency (ROCOF) and under/over-frequency relays for distributed generation
protection considering islanding detection and frequency-tripping requirements. The method is based
on the concept of application region, which defines a region in the trigger time versus active power
imbalance space where frequency-based relays can be adjusted to satisfy the anti-islanding and
frequency-tripping requirements simultaneously.
6
1.4 SYSTEM STABILITY
The system stability during load sharing has been explored by many researchers [13, 15, and 43].
The Transient stability of the power system with high penetration level of power electronics interfaced
(converter connected) distributed generation is explored in [13]. But the study is based on presence of
an infinite bus. The other important issue, with isolated operation of the power system network has
been overlooked in the study. A scheme for controlling parallel connected converter in a standalone ac
system is presented in [44]. A modular structure of the controller is presented. The structure can be
modified to meet the control requirement for any other ac system. The scheme proposed a P-I
regulator to determine the set points for generator angle and flux. The dynamic performance of the
system can be substantially improved by using other advanced control technique. Similar to the small-
signal stability of conventional power system, [45] establishes how the control scheme gives rise to
the oscillatory modes with poor damping. To identify the possible feedback signals for controllers, a
sensitivity analysis is carried out. The low frequency stability problem with change in power demand
is investigated in [46]. It is shown that with the change in power demand, the movement of the low
frequency oscillations to new location affects the relative stability of the system. The decentralized
control strategies for parallel converters are shown in [47 and 48].
The robust stability of a voltage and current control solution for a stand-alone distributed generation
(DG) unit is analyzed in [49] using structured singular values. This results in a discrete-time sliding
mode current controller. In [50], small-signal stability analysis of the combined droop and average
power method for load sharing control of multiple distributed generation systems in a stand-alone ac
supply mode is discussed. A small-signal model is developed and its accuracy is verified from
simulations of the original nonlinear model.
Modeling and analysis of autonomous operation of converter-based microgrid is presented in [20,
51], in which the converters are controlled based on voltage and frequency droop. Each sub-module of
the system is modeled in state-space form and all the modules are then combined together on a
common reference frame. The model captures the detail of the control loops of the converter but not
the switching action. Normal PI controllers are used for voltage and current control.
7
1.5 POWER SHARING IN RURAL NETWORK
Rural electrification should ensure the availability of electricity irrespective of the technologies,
sources and forms of generation, but many cannot afford it due to a shortage of resources. Distributed
generation is one of the best available solutions for rural microgrids. However the locations of the
micro sources are very important. The success or failure of the rural electrification activities in a
developing country invariably depends on the extent to which the relevant issues have been
systematically analyzed and addressed. Power electronic converter solution is introduced that is
capable of providing rural electrification at a fraction of the current electrification cost. For weaker
networks, this inevitably leads to poor voltage regulation.
A highly resistive line, typical of low or medium voltage rural networks, challenges the power
sharing controller efficacy. The strong coupling of real and reactive power in the network leads to an
inaccurate load frequency control. High values of droop gains are required to ensure proper load
sharing, especially under weak system conditions. However, high droop gains have a negative impact
on the overall stability of the system. Moreover, proper load sharing cannot be ensured even with a
high gain if the lines are highly resistive. In such cases, the main assumption of the droop control that
active and reactive powers are decoupled is violated and the conventional droop control [43] is not
able to provide an acceptable power sharing among the DGs.
The decoupling of the real and reactive power is achieved in [52] for a high R/X line with
frequency droop control. It is shown that a modification of the droop equation can accommodate the
effect of line impedance. However, the choice of droop gains for rating based sharing of power has
not been addressed in [52].
As discussed previously, in the case of voltage source converter (VSC) based DGs, the output
angle can be changed instantaneously and so drooping the angle is a better way to share load [53].
Frequency regulation constraint limits the allowable range of frequency droop gain, which in turn,
may lead to chattering during frequent load changes in a microgrid. In [54], it is assumed the lines are
mainly resistive and conventional droop can work with real power controlled by voltage and reactive
8
power by angle. But in a rural network a high R/X ratio is common. With a strong coupling of real
and reactive power, they cannot be controlled independently with either frequency or voltage and so
the droop equations need to be modified. The real power droop coefficients can be chosen depending
on the load sharing ratio.
It is often difficult to install extensive distribution network, especially since the customer density in
the rural areas can be sparse. Distributed generation is one of the best available solutions for such a
predicament. Planning of a typical medium-voltage rural distribution system in different loading
conditions is discussed in [55-57]. The bottom up approach through an evaluation of autonomous or
non-autonomous modified microgrid concept to provide electricity to local residents is proposed in
[56].
The policy and prospective planning achievements for rural electrification are hindered in many
countries are described in [58-69]. Electrification in Africa, Uganda, Nepal or India has their own site
specific requirements [63, 65, 66 and 68]. The general rural electrification is described in [61].
Planned islanding in rural distribution system is demonstrated in [69].
The off grid renewable connection at Anangu Solar Station of South Australia [70], where 220 kW
power is distributed covering 10,000 square km among number of communities up to 500 people or
minigrid connection at Hermannsburg in central Australia [70], where three communities each with
several hundred households with 720 kW total power consumption are the examples of the scenario
where the converter interfaced micro sources and loads are geographically far from each other in a
low voltage network.
1.6 OBJECTIVES OF THE THESIS AND SPECIFIC CONTRIBUTIONS
The objectives of the thesis and the specific contributions are discussed in this section.
1.6.1 OBJECTIVES OF THE THESIS
Based on gaps in the literature, the objectives of the research are set as,
• To improve power sharing techniques in a microgrid with converter interfaced sources.
9
• To facilitate load frequency control of the microgrid and a smooth transition between grid
connected and islanded mode.
• To enhance power quality in a microgrid which may contain unbalanced and non linear loads.
• To improve power management system and reliability of the microgrid:
• To perform stability analysis and enhancement in stability with supplementary controller
• To achieve superior power sharing in rural network with high R/X lines.
1.6.2 SPECIFIC CONTRIBUTIONS OF THE THESIS
Based on the above objectives, the specific contributions of this thesis are
1. An angle droop controller is proposed to share power amongst converter interfaced DGs in a
microgrid. As the angle of output voltage can be changed instantaneously in a voltage source
converter (VSC), controlling the angle to control the real power is beneficial for quick
attainment of steady state. Thus converter based DGs, load sharing can be done by drooping
the converter output voltage magnitude and its angle instead of system frequency. The angle
control results in much lesser frequency variation compared to the frequency variation with
frequency droop.
2. An enhanced frequency droop controller is proposed for better dynamic response and smooth
transition between grid connected and islanded mode of operation. A modular controller
structure with modified control loop is proposed for better load sharing between the parallel
connected converters in a distributed generation system. The integral control in the voltage
angle loop helps to influence the close loop dynamics without affecting the steady state
frequency regulation. Moreover, a smooth transition between grid connected mode and
islanded mode is very important to ensure a superior system performance.
3. Power quality enhanced operation of a microgrid with unbalanced and non linear loads is
addressed. The proposed controllers are capable of compensating the local unbalanced and
non linear loads. The local loads can be shared with utility in any desired ratio. The common
loads which are normally supplied by the utility in grid connected mode, shared among the
DGs proportional to their rating in the islanded mode.
4. An isolation technique between microgrid and utility, for better reliability, is proposed by
using a back-to-back converter. As utility and microgrid are totally isolated, the voltage or
10
frequency fluctuations in the utility side do not affect the microgrid loads. Proper switching
of the breaker and other power electronics switches has been proposed during islanding and
resynchronization process. With a bidirectional power flow, it is possible to control the
power flow to and from the utility and microgrid.
5. A linearized state space model of an autonomous microgrid supplied by all converter based
DGs and connected to number of passive loads is formed. The proposed generalized model is
valid even when the network is complex containing any number of DGs and loads. The
model is utilized for eigenvalue analysis around a nominal operating point. A supplementary
loop is proposed around the primary droop control loop of each DG converter to stabilize the
system despite having high gains that are required for better load sharing. The control loops
are based on local power measurement that modulates of the d-axis voltage reference of each
converter. The coordinated design of supplementary control loops for each DG is formulated
as a parameter optimization problem and is solved using an evolutionary technique.
6. Two methods are proposed for load sharing in an autonomous microgrid in rural network
with high R/X ratio lines. The first method proposes power sharing without any
communication between the DGs. The feedback quantities and the gain matrices are
transformed with a transformation matrix based on the line resistance-reactance ratio. The
second method is with minimal communication based output feedback controller. The
converter output voltage angle reference is modified based on the active and reactive power
flow in the line connected at PCC. It is shown that a more economical and proper power
sharing solution is possible with the web based communication of the power flow quantities.
Publications covering the contribution of this thesis are given in Appendix B.
1.7 THESIS ORGANIZATION
The thesis has been organized in seven chapters. This chapter presents the relevant literature
survey and sets the motivation for the research work carried out in this thesis.
11
Chapter 2 compares the performance of angle and frequency droops in an autonomous microgrid
that only contains voltage source converter (VSC) interfaced distributed generators. As a VSC can
instantaneously change output voltage waveform, power sharing in a microgrid is possible by
controlling the output voltage angle of the DGs through droop. The angle droop is able to provide
proper load sharing among the DGs without a significant steady state frequency drop in the system. It
is shown that the frequency variation with the frequency droop controller is significantly higher than
that with the angle droop controller.
In Chapter 3, the control methods for proper load sharing between parallel converters connected
to microgrid supplied by distributed generators is described. A control strategy is proposed to improve
the system performance through seamless transfer between islanded and grid connected modes. The
smooth transition between the grid connected and off grid mode is achieved by changing the control
mode from voltage control in islanded mode to state feedback control in grid connected mode. Its
efficacy has been validated through simulation for various operating conditions.
A control strategy is proposed in Chapter 4 to improve power quality and proper load sharing in
both islanded and grid connected modes. It is assumed that each of the DGs has a local load connected
to it, which can be unbalanced and/or nonlinear. The DGs compensate the effects of imbalance and
nonlinearity of the local loads. Common loads are also connected to the microgrid, which are supplied
by the utility grid under normal conditions. However during islanding, each of the DGs supplies its
local load and shares the common load through droop characteristics.
Chapter 5 proposes a method for power flow control between utility and microgrid through
back-to-back converters, which facilitates isolation and desired controlled real and reactive power
flow between utility and microgrid. In the proposed control strategy, the system can run in two
different modes depending on the power requirement in the microgrid. In mode-1, specified amounts
of real and reactive power are shared between the utility and microgrid through the back-to-back
converters. Mode-2 is invoked when the power that can be supplied by the DGs in the microgrid
reaches its maximum limit. In such a case, the rest of the power demand of the microgrid has to be
supplied by the utility.
The problem of appropriate load sharing in an autonomous microgrid is investigated in chapter 6.
High gain angle droop control ensures proper load sharing, especially under weak system conditions.
However it has a negative impact on the overall stability. Frequency domain modeling, eigenvalue
12
analysis and time domain simulations are used to demonstrate this conflict. A supplementary loop is
proposed around the conventional droop control of each DG converter to stabilize the system while
using high angle droop gains. The control loops are based on local power measurement that
modulation of the d-axis voltage reference of each converter.
Chapter 7 proposes new droop control methods for load sharing in a rural area with distributed
generation. To overcome the conflict between higher feedback gain for better power sharing and
system stability in angle droop, two control methods have been proposed. The first method considers
no communication among the distributed generators (DGs) and regulates the converter output voltage
and angle ensuring proper sharing of load in a system having strong coupling between real and
reactive power due to high line resistance. The second method, based on a smattering of
communication, modifies the reference output voltage angle of the DGs depending on the active and
reactive power flow in the lines connected to point of common coupling (PCC).
The general conclusions and scope for future works are given in Chapter 8. Appendix A
discussed the converter structure and control methods used in the thesis.
13
CHAPTER 2
POWER SHARING WITH CONVERTER INTERFACED SOURCES
With the growth of distributed generation and its operation in tandem with utility power supply,
the interconnection of distributed generators (DGs) to the utility grid through power electronic
converters has raised concern about system control and power sharing among the DGs. Control of the
DG system is important and system regulation such as frequency deviation and voltage drop becomes
very crucial during the decentralized power sharing through droop control.
This chapter presents, the power sharing in microgrid with converter interfaced sources. The
conventional frequency droop control is first demonstrated. As the sources are converter interfaced, it
is possible to control the output voltage angles instantaneously. The proposed angle droop control is
derived from load flow analysis and demonstrated in a similar system to compare the performance of
both the droop controllers.
2.1 CONTROL OF PARALLEL CONVERTERS FOR LOAD SHARING WITH
FREQUENCY DROOP
The basic power system model with two DG sources connected to the load at the point of common
coupling (PCC) is shown in Fig. 2.1. The load can be a constant impedance load or a motor load. The
converter output voltages are denoted by V1∠δ1 and V2∠δ2 and are connected to the microgrid with
output filter of inductance L1.and L2. . P1, P2 and Q1, Q2 represent the real and reactive power supplied
by the DGs while PL and QL are respectively the real and reactive power demand of the load. The line
resistances are denoted by R1 and R2 while Lline1 and Lline2 represent the line inductances.
14
Fig. 2.1. Microgrid system under consideration.
2.1.1 FREQUENCY CONTROL
The conventional droop control method is given by [43]
nQVV
mPs
−=
−=∗
ωω (2.1)
where m and n are the droop coefficients, ωs is the synchronous frequency, V is the magnitude of the
converter output voltage and ω is its frequency, while P and Q respectively denote the active and
reactive power supplied by the converter. Thus the frequency and the voltage are being controlled by
the active and reactive power output of the DG sources.
2.1.2 MODULAR CONTROL STRUCTURE
A modification to the conventional droop controller is proposed here. This is shown in Fig. 2.2
for DG-1 only. A similar structure is also used for DG-2. The output voltage V1∠δ1 and output current
I1 of the converter are used for calculating the real power (P1) and reactive power (Q1) injected by
DG-1. These are then used in (2.1) to calculate ωs and V1*. The quantity ωs and the angle of the PCC
voltage δPCC are then used to calculate the reference angle δ1*. This is described in Section 2.1.3. The
reference magnitude V1* and its angle δ1
* are then used to generate the instantaneous reference
voltages of the three phases which are then compared with the measured instantaneous phase voltages
of V1. The resultant error is used in the feedback control to generate the firing pulses (u) of VSC-1.
The feedback control and converter structure are discussed in Appendix-A. In islanded mode state
feedback control (A.4) is used while voltage control (A.3) is employed in the grid connected
operation.
15
Fig. 2.2. The modular control structure
2.1.3 CONVERTER VOLTAGE ANGLE CALCULATION
The converter voltage angle control loop is shown in Fig. 2.3. The frequency ω1 is calculated from
the droop given in (2.1) and is then compared with the frequency (ωPCC) of the PCC voltage. The error
is passed through an integrator with a gain of KI and is then added with the integral of ωPCC to obtain
φ1*. The angle φ1
* rotates at the synchronous speed ωs making an angle δ1* with the reference.
Changing the value of KI, we can influence the close loop dynamics without affecting the steady state
frequency regulation.
Fig. 2.3. Voltage angle control loop.
2.1.4 REFERENCE GENERATION
With respect to Fig. A.3 in Appendix A, a state vector is defined as
[ ]1iivx cfcfT = (2.2)
The reference for vcf is v1*, as mentioned in the previous sub-section. Given V1
* and φ1*, the phasor
current through the capacitor Cf is given by
16
( )°+∠= ∗∗∗ 9011 δω VCI fcf (2.3)
The reference icf* is obtained from the instantaneous value of Icf
*.
The reference for i1 is derived through its phasor quantity I1*. Fig. 2.1 identifies that if the
references are strictly followed
*1
*1
*111 )( IVjQP ×−∠=− δ (2.4)
It is to be noted that in this section * denote reference quantities and not conjugate functions.
Let us define I1* = I1p
* + j I1q*. Then from 2.4,
[ ][ ]∗∗
∗∗
∗∗∗
∗
−=
+=
11111
1
11111
1
cossin1
sincos1
δδ
δδ
QPV
I
QPV
I
q
p
(2.5)
Therefore the phasor reference is given by
+= ∗
∗−∗∗∗
p
qqp
I
IIII
1
11111 tan (2.6)
The voltage angle controller of Fig. 2.3 generates a rotating angle φ1*, which is equal to ωst + δ1
*.
The angle φ1* is reset after every 2π. Fig. 2.6 shows the variation along with the reference ωst. From
this figure, we can write
∗+== 110 2 δωπω tt ss
Therefore
( )011 tts −=∗ ωδ (2.7)
Fig. 2.6. Source angle extraction from rotating angle.
17
Once the references for the state vector are obtained, the control law is computed as shown in
Appendix-A with the state feedback controller (A.4).
2.2 ANGLE DROOP CONTROL
The DGs have the potential to deliver reliable power when their locations are strategically planned.
However, for large scale application of DGs, the commercial and regulatory challenges have to be
considered before their benefits can be realized [71]. One of the most significant aspects is the change
in system frequency. As discussed in [12-14], DG real power output is controlled by dropping the
system frequency. Depending on the stiffness of the power-frequency curve, the steady state
frequency will change with the changes in system loads.
It is not desirable to operate the system in a much lower frequency and a complimentary frequency
restoration strategy is proposed in [43]. The reference powers of the DGs are modified to restore the
frequency which is equivalent to shifting the power-frequency curve vertically. The process can be
controlled in a slow, coordinated manner by a master controller, using a slow communication channel
between the converters [43]. In conversational frequency droop, the frequency deviation signal is used
to set the power output of the converter. The limitations of the use of frequency deviation alone have
been established for many years [72]. Nevertheless, the conventional droop method has several
drawbacks that limit its application, such as: slow transient response, frequency and amplitude
deviations, imbalanced harmonic current sharing, and high dependency on converter output-
impedance [73]. High frequency signals are injected to overcome the imbalance reactive power flow.
Since the power balance and the system stability rely on these signals, the application of such signal
increases system complexity and reduces reliability.
It is possible for a VSC to instantaneously change its output voltage waveform and power sharing
in a microgrid by controlling the output voltage angle of the DGs through droop. Let us consider same
microgrid system as shown in Fig. 2.1 is considered. First, the load sharing with angle droop is
derived using the DC load flow method. It is possible to share power among the DGs proportional to
their rating by dropping the output voltage angles.
The angle droop control strategy is applied to all the DGs in the system. It is assumed that the total
power demand in the microgrid can be supplied by the DGs such that no load shedding is required.
18
The output voltages of the converters are controlled to share the load proportional to the rating of the
DGs. As an output inductance is connected to each of the VSCs, the real and reactive power injection
from the DG source to the microgrid can be controlled by changing voltage magnitude and its angle
[12-14]. Fig. 2.7 shows the power flow from a DG to the microgrid where the RMS values of the
voltages and current are shown and the output impedance is denoted by jXf. It is to be noted that real
and reactive power (P and Q) shown in the figure are average values.
Fig. 2.7. DG connection to microgrid.
2.2.1. ANGLE DROOP CONTROL AND POWER SHARING
The average real power is denoted by P and the reactive power by Q. These powers, from the DG to
the microgrid, can then be calculated as
( )
( )f
tt
f
tt
X
VVVQ
XVV
P
δδ
δδ
−×−=
−×=
cos
sin
2 (2.8)
These instantaneous powers are passed through a low pass filter to obtain the average real and
reactive power P and Q. It is to be noted that the VSC does not have any direct control over the
microgrid voltage at the bus Vt∠δt (see Fig. 2.7). Therefore from (2.8), it is obvious that if the angle
difference ( − t) is small, real power can be controlled by controlling , while the reactive power can
be controlled by controlling voltage magnitude. Thus the power requirement can be distributed among
the DGs, similar to a conventional droop by dropping the voltage magnitude and angle as
( )( )ratedrated
ratedrated
QQnVV
PPm
−×−=−×−= δδ
(2.9)
19
where Vrated and rated are the rated voltage magnitude and angle respectively of the DG, when it is
supplying the load to its rated power levels of Prated and Qrated. The coefficients m and n respectively
indicate the voltage angle drop vis-à-vis the real power output and the voltage magnitude drop vis-à-
vis the reactive power output. These values are chosen to meet the voltage regulation requirement in
the microgrid.
To derive power sharing with angle droop, a simple system of Fig. 2.1 with two machines and a
load is considered. Applying DC load flow with all the necessary assumptions we get,
2222
1111
)(
)(
PXX
PXX
L
L
+=−
+=−
δδδδ
(2.10)
where X1 = L1/(V1V) , XL1 = LLine1/(V1V), X2 = L2/(V2V) and XL2 = LLine2/(V2V).
From (2.9), the angle droop equations of the two DGs are given by
( )( )ratedrated
ratedrated
PPm
PPm
22222
11111
−×−=−×−=
δδδδ
(2.11)
The offsets in the angle droop are such that when DG output power is zero, the DG source angle is
zero. Therefore the rated droop angles are taken as 1rated = m1P1rated and 2rated = m2P2rated. Then from
(2.11) we get
221121 PmPm −=−δδ (2.12)
Similarly from (2.10) we get
22211121 )()( PXXPXX LL +−+=−δδ (2.13)
Assuming the system to be lossless (as normally used in DC load flow), we get,
LLL
L
LLLL
PmXXmXX
mXXP
PPmPmPPXXPXX
111222
2221
1211122111 )())(()(
+++++++=
−−=−+−+ (2.14)
Similarly P2 can be calculated as
LLL
L PmXXmXX
mXXP
111222
1112 +++++
++= (2.15)
From (2.14) and (2.15), the ratio of the output power is calculated as,
20
111
222
2
1
mXXmXX
PP
L
L
++++= (2.16)
It is to be noted that the value of X1 and X2 are very small compared to the value of m1 and m2.
Moreover if the microgrid line is considered to be mainly resistive with low line inductance and the
DG output inductance is much larger, we can write
222111 and LL XXmXXm >>>>>>>>
Therefore from (2.16), it is evident that the droop coefficients play the dominant role in the power
sharing. Since the droop coefficients are taken as inversely proportional to the DG rating, from (2.16)
we can write
rated
rated
PP
mm
PP
2
1
1
2
2
1 =≈ (2.17)
The above approximation can incorporate little error in power sharing ratios depending on the
droop gain and inductances values. The error is further reduced by taking the output inductance (L1
and L2) of the DGs inversely proportional to power rating of the DGs. If the microgrid line is
inductive in nature and of high value, then knowledge about the network is needed.
2.3 ANGLE DROOP AND FREQUENCY DROOP CONTROLLER
The converter structure is given in Appendix A (A.1). Both the angle and frequency droop
controllers are modeled separately from their droop equations (2.9) and (2.1) respectively. The droop
controller model is then combined with the converter model. All the combined converter and
controller models are converted to a common reference frame and then connected to the network to
derive the entire microgrid model as shown in [51]. The microgrid model is used to select the
parameters of the droop controllers through eigenvalue analysis. The detail converter model with
droop equation is given in Chapter 6.
The droop controllers are designed based on the composite model discussed above. The system
parameters considered for the study are given in Table-2.1. The eigenvalue trajectory is plotted by
varying either the angle droop or frequency droop gain. The voltage droop gain is held constant. Fig.
2.8 shows one of the dominant complex conjugate eigenvalue trajectories with the angle droop
21
controller. It can be seen that, the complex pole crosses the imaginary axis, for a droop controller gain
of 0.00045 rad/kW. Similarly Fig. 2.9 shows the corresponding eigenvalue trajectory as function of
frequency droop controller gain.
Fig.2.8. System stability as function of frequency droop gain.
Fig. 2.9. System stability as function of angle droop gain.
To compare the results of the two droop controllers, the nominal values of the controller gain are
chosen at 75% of the gain at which the system becomes unstable. This implies that the gain with the
angle droop controller is m = 0.00034 rad/kW and with the frequency droop controller is mω =
0.000375 rad/s/kW.
22
TABLE-2.1: SYSTEM AND CONTROLLER PARAMETERS
System Quantities Values
Systems frequency 50 Hz
Load ratings
Load
2.8 kW to 3.1 kW
DG ratings (nominal)
DG-1
DG-2
1.0kW
1.33kW
Output inductances
LG1
LG2
75 mH
56.4 mH
DGs and VSCs
DC voltages (Vdc1 to Vdc4)
Transformer rating
VSC losses (Rf)
Filter capacitance (Cf)
Hysteresis constant (h)
0.5kV
0.415kV/0.415 kV, 0.25 MVA, 2.5% Lf
0.1 Ω
50 µF
10-5
Angle Droop Controller
m1 0.000340 rad/kW
m2 0.000255 rad/kW
Frequency Droop Controller
mw1 0.000375 rad/s/kW
mw2 0.000281rad/s/kW
2.4 SIMULATION STUDIES
Simulation studies are conducted with different types of load and operating conditions to check the
system response and controller action. Some of the results are discussed below. The system data used
is given in Table 2.1.
2.4.1 FREQUENCY DROOP CONTROLLER
The frequency droop controller is employed to share power in this case. The output impedances of
the two sources are chosen in a ratio of DG-1: DG-2 = 1:1.33 and the power rating of these DGs are
also chosen in the ratio of 1.33:1. To investigate the power sharing in a constant load changing
situation, the load conductance is chosen as the integral of a Gaussian white noise with zero mean and
a standard deviation of 0.01 Mho. The system parameters and the controller gains are shown in Table-
2.1.The power outputs of the DGs are shown in Fig. 2.10.
23
Fig. 2.10. DG power output with frequency droop control.
2.4.2 ANGLE DROOP CONTROLLER
The same system is used to investigate the angle droop controllers. Fig. 2.11 shows the power
output of the DGs in case of the angle droop controller. It can be seen that the constant deviation in
power output from the DGs are always in the desired ratio and the fluctuation in output power is
almost 10% as per the load change.
Fig. 2.11. DG power output with angle droop control.
24
2.4.3 COMPARISON OF FREQUENCY DROOP AND ANGLE DROOP
To compare the performance of the controllers, the frequency deviation is presented for
both cases. The frequency deviation of the DG sources is shown in Fig. 2.12. It is evident that the
frequency variation with the frequency droop controller is significantly high.
The standard deviation with the frequency droop controller is 0.4081 rad/s and 0.4082 rad/s for the
two DGs. It can also be seen that the mean frequency deviation is large.
Fig. 2.12. Frequency variation with frequency droop control
Fig. 2.13 shows the frequency deviation with the angle droop control. The steady state frequency
deviation is zero-mean and the standard deviation of the frequency deviation is 0.01695 rad/s and
0.01705 rad/s respectively for DG-1 and DG-2. The deviation in the frequency is small and the angle
droop controller is able to share load in the desired ratio despite the random change in the load
demand. This demonstrates that the angle droop controller generates a substantially smaller frequency
variation than the conventional frequency droop controller. Fig. 2.14 shows the angle deviation with
the angle droop. It can be seen that the nature of angle deviation is similar to the frequency deviation
with the frequency droop.
25
Fig. 2.13. Frequency variation with angle droop control.
Fig. 2.14. Angle variation with angle droop control.
2.4.4 ANGLE DROOP IN MULTI DG SYSTEM
To investigate the efficacy of the angle droop controller in a microgrid with multiple DGs and
loads, angle droop controllers are designed for the system shown in Fig. 2.15 with system parameter
shown in Table-2.2. It has four DGs and five loads as shown. It is desired that DG-1 to DG-4 share the
load in 1.0:2.0:1.5:1.5 ratio (to share power proportional to the DG rating). With the system running at
steady state, the loads Ld2 and Ld3 are disconnected at 0.2 s. The power sharing among the DGs is
shown in Fig. 2.16.
26
Fig. 2.15. Microgrid Structure with multiple DGs.
TABLE-2.2: MICROGRID SYSTEM AND CONTROLLER PARAMETERS
System Quantities Values
Systems frequency 50 Hz
Feeder impedance
Z12 = Z23 = Z34 = Z45 = Z45 = Z56 =
Z67 = Z78 = Z89
0.1 + j 0.6 Ω
Load ratings
Ld1
Ld2
Ld3
Ld4
Ld5
1.8 kW and 1.6 kVAr
0.8kW and 0.6 kVAr
0.8 kW and 0.6 kVAr
0.8 kW and 0.6 kVAr
1.8 kW and 1.6 kVAr
DG ratings (nominal)
DG-1
DG-2
DG-3
DG-4
1.0kW
2.0kW
1.5 kW
1.5 kW
Output inductances
LG1
LG2
LG3
LG4
75 Mh
37.5 mH
50 mH
50mH
DGs and VSCs
DC voltages (Vdc1 to Vdc4)
Transformer rating
VSC losses (Rf)
Filter capacitance (Cf)
Hysteresis constant (h)
0.5kV
0.415kV/0.415 kV, 0.25 MVA,
2.5% Lf
0.1 Ω
50 µF
10-5
Angle Droop Controller
in multi machine
m1 0.1 rad/MW
m2 0.05 rad/MW
m3 0.075 rad/MW
m4 0.075 rad/MW
The efficacy of the angle droop is further verified by sharing power only between DG-1 and DG-4,
when DG-2 and DG-3 are disconnected from the system. Let us assume that the system is running in
the steady state supplying the loads Ld1, Ld2 and Ld4. At 0.2 s, the load Ld4 is disconnected. The
27
system response is shown in Fig. 2.17. This test studies the controller response when the power
generation and load demand is not evenly distributed along the microgrid. It can be seen that after 0.2
s, the sharing is not very accurate. Choosing a higher droop controller gain, we can assure better
sharing in such situations. However, a very high value of droop gain can lead the system to instability
as shown in eigenvalue trajectory of Fig. 2.9. The choice of controller gain is thus a trade off between
system stability and system response.
Fig. 2.16. Real Power Sharing of the DGs.
Fig.2.17. Real Power Sharing of the DG-1 and DG-4.
2.5 CONCLUSIONS
A modular controller structure with modified voltage angle control loop is proposed for better load
sharing between the parallel connected converters in a distributed generation system. The integral
28
control in the voltage angle loop helps to influence the close loop dynamics without effecting the
steady state frequency regulation. The efficacy of angle droop over frequency droop in a voltage
source converter based autonomous microgrid is also demonstrated in this chapter. The power sharing
of the DG sources with angle droop is derived first. A frequency droop controller and an angle droop
controller are designed to ensure the same stability margin in a two DG system. It is shown that the
frequency variation with the frequency droop controller is significantly higher than that with the angle
droop controller. The efficacy of the angle droop controller is further verified in a microgrid with
moderate number of DGs and loads. It is to be noted that, angle droop requires measurement of angle
with respect to a common reference frame and GPS phasor measurement can be used for this purpose.
Frequency droop does not require any GPS measurement. Moreover, with the presence of inertial DGs
(synchronous machine), it is easier to share power with the frequency droop controller. In the next
chapter, the frequency droop controller is discussed for a smooth transfer between grid connected and
islanded operations.
29
CHAPTER 3
LOAD FREQUENCY CONTROL IN MICROGRID
A smooth transfer between the grid connected and standalone modes is essential for a reliable
operation in a microgrid. Control of the DG system is important in both the grid connected and
islanded mode and system stability becomes very crucial during the transfer between grid connected
and islanded mode. A seamless transfer can ensure a smooth operation with proper load sharing and
quick attainment of steady state.
In this chapter a scheme for controlling parallel connected converters in islanded and grid
connected mode are presented. The control techniques for a smooth transfer between these two modes
are also shown. A modular structure of the controller is used as described in Chapter 2. Later the
frequency droop controller strategy is applied to a microgrid containing both inertial and inertia-less
DGs. To investigate the operation of all the micro-sources together, a microgrid is planned at
Queensland University of Technology (QUT) where the main issue is decentralized power sharing and
system stability. As mentioned in Chapter 2, a converter interfaced DG can control its output voltage
instantaneously and so the change in the power demand can be picked up quickly, while in an inertial
DG, the rate of change in power output is limited by the machine inertia. To ensure that a load change
is picked up by all the DGs at the same rate, the rate of change in converter interfaced DGs needs to
be limited. To investigate the system response with the dynamics of the DG units, the sources and all
the power electronic interfaces are modeled in detail.
3.1 SEAMLESS TRANSFER BETWEEN GRID CONNECTED AND ISLANDED
MODES
The basic power system model with two DG sources connected to the load at the point of common
coupling (PCC) is shown in Fig. 3.1. In this, the system runs in islanded mode when the circuit
breaker (CB) is open; otherwise it runs in grid connected mode. The load can be a constant impedance
30
load or a motor load. In Fig. 3.1, the voltage source VS is the utility voltage that is connected to the
PCC with a feeder of impedance RS + jXS. The current drawn from the utility is denoted by Ig, while Pg
and Qg are respectively the real and reactive power supplied by the grid. It is assumed that the DGs are
constant dc voltage sources Vdc1 and Vdc2. The converter output voltages are denoted by V1∠δ1 and
V2∠δ2 and they are connected to the PCC through reactances jX1 and jX2 respectively. P1, P2 and Q1,
Q2 represent the real and reactive power supplied by the DGs.
Fig. 3.1. Microgrid system under consideration.
3.1.1 PROPOSED CONTROL
The frequency droop controller described in Chapter 2 has been employed here. The detail
converter structure is also the same as given in Appendix A (A.1).
1. As discussed in the last chapter the voltage regulation is a problem with frequency droop when
the load changes frequently. In this chapter it is shown that better load sharing and a rapid steady
state attainment are achieved when the voltage control is used in the islanded mode, while the
state feedback ensures better response in the grid connected mode (Detail converter control
techniques are discussed in Appendix A). A seamless transfer between these two modes is
proposed by changing state feedback to voltage control and vice versa. Ordinarily, in the grid
connected mode, the DGs operate under the state feedback control. When an islanding is
detected, the DGs are switched to the voltage control mode. These are switched back to the state
feedback control mode after resynchronization.
31
3.1.2 SIMULATION STUDIES
Simulation studies are carried out with different type loads and operating conditions to check the
system response and controller action. Some of the results are discussed below. The system data used
are given in Table 3.1.
3.1.2.1 ISLANDED MODE
In the islanded mode, the VSCs are operated in voltage control mode through output feedback. In
this mode, the grid is not available and the total power demand of the load is supplied by the DGs.
The frequency is also not fixed and is calculated from the modified droop to meet the active and
reactive power requirements. With any load change, the active and reactive power requirements
change and the VSC reference voltage magnitude and angle must change to meet the new load
requirement. Two types of load are considered here – constant impedance type load and motor load.
Fig. 3.2 shows the response with impedance load, where the values of the load impedances are
doubled at 1 s. The load is changed back to its nominal value at 1.5 s. It can be seen that DG-1 shares
more load than DG-2 in accordance with their droop characteristics, while the grid does not supply
any power.
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7-0.5
0
0.5
1
1.5
Act
ive
pow
er (M
W)
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7-0.2
00.20.40.6
Rea
ctiv
e p
ower
(M
VAR
)
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7-0.1
0
0.1
Time(s)
Cu
rren
t-ph
ase
a (k
A)
DG1DG2Grid
DG1DG2Grid
DG1DG2Grid
Fig.3.2 System response with impedance load in islanded mode.
Fig. 3.3 shows the results when the inductor motor is connected in parallel with the passive load at
2 s and disconnected at 2.75 s. The motor is operated in speed control mode. The change in active
32
power supplied by the DGs and output current of the converters show proper load sharing with a quick
steady state attainment. The zero power and zero current from the grid confirm the islanded condition.
TABLE 3.1. SYSTEM PARAMETERS
System Quantities Values
Systems Frequency (ωs) 100π rad/s
Source voltage (Vs) 11 kV rms (L-L)
Feeder impedance (Rs + jXs) 3.025 + j12.095
DG-1
DC voltage (Vdc1)
Transformer rating
VSC losses
Source inductance (L1)
Filter Capacitance (Cf)
Frequency droop coefficient (m)
Voltage droop coefficient (n)
3.5 kV
3 kV/11 kV, 0.5 MVA, 2.5%
reactance (Lf)
1.5 Ω
0.0578 H
30 µF
0.005 rad/s/kW
0.2045 kV/kVAr
DG-2
DC voltage (Vdc1)
Transformer rating
VSC losses
Source inductance (L1)
Filter Capacitance (Cf)
Frequency droop coefficient (m)
Voltage droop coefficient (n)
3.5 kV
3 kV/11 kV, 0.5 MVA, 2.5%
reactance (Lf)
1.5 Ω
0.0722 H
30 µF
0.00625 rad/s/kW
0.2727 kV/kVAr
Passive load The load is varied between
4.84 + j30.25 Ω and
102.85 + j157.3 Ω
Motor load (synchronous)
Rated rms voltage (L-N)
Rated rms line current
Inertia constant
Iron loss resistance
6 kV
5 kA
1 s
300 pu
Motor load (induction)
Rated rms voltage (L-N)
Rated rms line current
Rated power
6 kV
0.11 kA
50 hp
3.1.2.2 GRID CONNECTED MODE
In the grid connected mode, the steady state system frequency is fixed to the utility frequency. It is
assumed that the distributed generators supply their rated power at rated frequency. When the load
requirement is less than the total rated power of the DGs, the excess power flows from DGs go to the
33
grid.For a motor load, even a slight transient in voltage causes large power swing. Therefore the PCC
voltage should not deviate much from its nominal value and the VSCs must supply the change in the
power demand as quickly as possible. To accomplish this, relying only on a voltage control may not
be sufficient. It is desirable that a current controller is added with the voltage controller to ensure
better power tracking. Therefore the control is changed to a state feedback control which uses the
feedback of DG output voltage; output current and the current through the filter capacitor (see
Appendix A).
1.8 2 2.2 2.4 2.6 2.8 3 3.2
0
0.5
1
1.5
2
Act
ive
pow
er (
MW
)
1.8 2 2.2 2.4 2.6 2.8 3 3.2-0.6
-0.4
-0.2
0
0.2
0.4
Time (s)
Cur
rent
-pha
se a
(kA
)
DG1DG2Grid
DG1DG2Grid
Fig .3.3. System response with motor load in islanded mode.
The reference voltage magnitude and angle are calculated from the droop similar to the islanded
mode. However the steady state frequency is fixed to the grid frequency and the power output of the
DGs are equal to their rated power. Thus the active and reactive power requirements for an individual
DG are calculated based on their rating. The output current reference is calculated from the power and
voltage reference. The reference for the filter capacitor current is calculated from the voltage reference
(Appendix A).
Fig. 3.4 shows the system response during change of load in the grid connected mode. In this mode,
any change in load is picked up by the grid as the DGs always provide the rated power (or the
maximum available power). The change in grid current with active power demand ensures a stable
operation.
Fig. 3.5 shows the results when an induction motor gets connected at 2 s and disconnected at 2.75 s
while the passive load remains connected all the time. It is obvious that the additional power required
by the motor is coming from the grid as the DGs supply the rated power.
34
Fig. 3.6 shows the results when a synchronous motor is connected in parallel with impedance load.
With the motor and impedance operating in the steady state, the motor is disconnected at 1.5 s and
reconnected at 3 s. It can be seen that the powers supplied by the DGs remain constant during both the
transients and the oscillations in the grid current die out within 1 s.
1.2 1.4 1.6 1.8 2 2.2 2.4-0.5
0
0.5
1
1.5
Act
ive
pow
er (M
W)
1.2 1.4 1.6 1.8 2 2.2 2.4-0.2
-0.1
0
0.1
0.2
Time(s)
Gri
d C
urr
ent -
pha
se a
(kA
)
DG1DG2Grid
Fig. 3.4. System response with impedance load in grid connected mode.
1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.20
1
2
3
Act
ive
pow
er (
MW
)
1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2-0.4
-0.2
0
0.2
0.4
Time(s)
Gri
d c
urr
ent -
pha
se-a
(kA
)
DG1DG2Grid
Fig.3.5. System response with induction motor load in grid connected mode.
3.1.2.3 SEAMLESS TRANSFER BETWEEN GRID CONNECTED AND ISLANDED
MODES
The results simulated so far show that a better load sharing and a quick steady state attainment are
achieved with the voltage control in the islanded mode, while the state feedback ensures better
response in the grid connected mode. A seamless transfer between these two modes is proposed by
changing state feedback to voltage control and vice versa. Ordinarily, in the grid connected mode, the
35
DGs operate under the state feedback control. When an islanding is detected, the DGs are switched to
the voltage control mode. These are switched back to the state feedback control mode after
resynchronization. The sequence of control from a grid connected operation to islanded mode and
then again back to grid connected is given in Fig. 3.7.
1 1.5 2 2.5 3 3.5 4 4.5
0
0.5
1
Act
ive
pow
er (
MW
)
1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3-0.04
-0.02
0
0.02
0.04G
rid
cur
rent
(kA
)
2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4-0.04
-0.02
0
0.02
0.04
Time (s)
Gri
d cu
rren
t(k
A)
DG1DG2Grid
Fig.3.6. System response with synchronous motor load in grid connected mode.
Figs. 3.8 and 3.9 show the response of the system during islanding and resynchronization with the
impedance load. The islanding occurs at 1.5 s and the resynchronization occurs at 2 s. Fig. 3.8 shows
the power sharing and currents, while the PCC voltages are shown in Fig. 3.9.
An impedance load is an infinite sink as it can absorb any change in instantaneous real and reactive
power with a change in the supply voltage. This however is not true for an inertial load such as motor.
Thus any change in the terminal voltage will result in large oscillation in the real and reactive powers.
So damping becomes a major issue during islanding with inertial load. Since the voltage control is a
slow process, a re-initialization in the reference value is required to force the system to a new steady
state quickly.
For this analysis it is assumed that an online load flow study is always performed in background
with the microgrid load and generation. At the instant of islanding, the values obtained from the load
flow are used to determine the new voltage reference. The new reference ensures minimal change in
the load voltage after islanding and proper sharing of the loads among the DGs. These new values are
assigned as the new reference for the controllers.
36
Fig.3.7. Control sequence from a grid connected operation to islanded mode
Fig. 3.8, System response during islanding and resynchronization with impedance load.
37
Fig. 3.9. PCC voltage during islanding and resynchronization with impedance load
Fig. 3.10 shows the active power sharing during islanding and resynchronization with a motor load.
An induction motor is used here. The active power input to the motor load is also shown in this figure.
It can be seen that this power remains constant during islanding and resynchronization, validating a
seamless transfer between the two modes. Phase-a of the DG output currents along with the grid
currents are shown separately during islanding and resynchronization in Fig. 3.11. It can be seen that
all the currents reach their steady state values with 0.2 s, both during islanding and resynchronization.
0.5 1 1.5 2 2.5 3 3.5
0
0.5
1
1.5
2
2.5
Act
ive
pow
er (M
W)
0.5 1 1.5 2 2.5 3 3.50.5
1
1.5
2
2.5
Time (s)
Act
ive
pow
er o
f M
oto
r L
oad
(MW
)
DG1DG2Grid
Fig. 3.10. System response during islanding and resynchronization with motor load.
3.2 MICROGRID WITH INERTIAL AND NON INERTIAL DGS
A microgrid should appear as a single controllable load that responds to changes
in the distribution system. Different micro-sources can be connected to the
microgrid, such as inertial sources like diesel generators and converter interfaced
sources such as fuel cells or photovoltaics (PV). A diesel generator set (genset)
38
consists of an internal combustion (IC) engine and a synchronous generator mounted
on the same shaft. Such systems are widely used as backup or emergency power in
commercial as well as industrial installations. Diesel gensets are also heavily used in
remote locations where it is impractical or prohibitively expensive to connect to
utility power [73]. Over the last few decades, there has been a growing interest in
fuel cell systems for power generation. These has been identified as a suitable
solution for distributed generation [74].
Fig. 3.11. PCC voltage during islanding and resynchronization with motor load.
Other than fuel cell, the use of new efficient photovoltaic solar cells (PVs) has emerged as an
alternative source of renewable green power, energy conservation and demand side management. [75].
To investigate the operation of all the micro-sources together, a microgrid is planned at QUT where
the main issue is decentralized power sharing and system stability. It is desired that in a microgrid all
the DGs respond to any load change in a similar rate to avoid the overloading of a lagging or leading
DG. In the presence of both inertial and non inertial DGs, the response time for each DG to any
change in load power demand will be different. A converter interfaced DG can control its output
voltage instantaneously and so the change in the power demand can be picked up quickly, while in an
inertial DG, the rate of change in power output is limited by the machine inertia. To ensure that a load
change is picked up by all the DGs in same rate, the rate of change in converter interfaced DGs needs
to be limited.
39
3.2.1 SYSTEM STRUCTURE
The microgrid system under consideration is shown in Fig. 3.12. There are four DGs as shown;
one of them is an inertial DG (diesel generator) while the others are converter interfaced DGs (the PV,
fuel cell and battery). There are five resistive heater loads and six induction motors. The parameters of
the grid, DGs, loads and controllers are given in Appendix A. The microgrid can run both in grid
connected, as well as, autonomous mode of operation.
Fig.3.12 Microgrid structure under consideration
To increase the system damping and to restrict the rate of change in power output in non inertial
DGs, the droop equations are modified as
dtdQ
nQQnVV
dtdP
mPPm
drated
drateds
+−−=
+−−=
∗ )(
)(ωω (3.1)
3.2.2 MODEL OF MICRO SOURCE
As mentioned before there are four DGs in the microgrid. The diesel generator is modeled as [73]
and not shown in this chapter. The other three DG models and associated power electronic controllers
are discussed below.
3.2.2.1. FUEL CELL
Various methods have been introduced for modeling of fuel cells; however a simplified empirical
model, introduced in [74], is used here. The output voltage-current characteristic of the fuel cell is
given in (3.2). An open loop boost chopper is used at fuel cell output for regulating the necessary DC
voltage VC across the capacitor. The schematic diagram of the simulated model with the output
chopper is shown in Fig. 3.13.
40
ieiiiV 025.02242.02195.0)log(38.123.371)( −−−= (3.2)
Fig. 3.13. Fuel cell modelled equivalent circuit
3.2.2.2. PHOTOVOLTAIC CELL (PV)
PV arrays are built with combination of series and parallel PV cells which are usually
represented by a simplified equivalent circuit as shown in Fig. 3.14. PV cell output voltage is a
function of the output current while the current is a function of load current, ambient temperature and
radiation level. The output chopper controls the voltage VC across the capacitor. The reference voltage
of the chopper is set by a Maximum Power Point Tracking (MPPT) method for getting the maximum
power from the PV based on the load or ambient condition changes. The MPPT algorithm used as
shown in Fig. 3.15 [75]. The chopper uses a PI controller in order to achieve the desired reference
voltage set by the MPPT.
Fig. 3.14. Equivalent circuit of PV and boost chopper based on MPPT
3.2.2.3. BATTERY
The battery is modeled as a constant dc source voltage with series internal resistance where the VSC
is connected to its output. The battery has a limitation on the duration of its generated power and
depends on the amount of current supplied by it.
3.2.3. SIMULATION STUDIES
The system is simulated for various operating conditions with different load demand in the
microgrid. The simulation results are discussed below.
41
Fig. 3.15. MPPT control flowchart for PV
3.2.3.1. CASE 1: GRID CONNECTED AND AUTONOMOUS OPERATING MODES
In this case, the microgrid operation has been simulated during grid connected and autonomous
modes. In grid connected mode, each DG will generate its rated power and the extra load demand will
be supplied by the grid. In autonomous mode total power demand is shared among the DGs
proportional to their rating. Fig. 3.16 shows the system response where the grid is disconnected at 0.5
sec. and resynchronized at 1.5 sec. A smooth resynchronization can be achieved as shown in this
figure. It can be seen that the system reaches steady state within 10 cycles in either case.
3.2.3.2. CASE 2: POWER SHARING IN AUTONOMOUS MODE
The response of the power sharing controller in accordance with load changes in autonomous
mode is investigated in this subsection. In this case, it is assumed the system is operating in steady
state while all the micro sources are connected and supplying the three 1.5 kW fan heater load. At 0.5
sec all inductions motors get connected to the microgrid and the system response is shown in Fig.3.17.
It can be seen the system reaches to the steady state condition within 5-6 cycles and the extra power
requirement is picked up by all the DGs. The micro sources output currents are shown in Fig. 3.18.
For converter interfaced DGs, the change in output current are achieved within 1 cycle. The delay in
change of power in the power output is due to the micro source dynamics (fuel cell and PV).
42
Fig. 3.16. Islanding and resynchronization
Fig.3.17 Real power sharing of the DGs
0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6 0.62-30
-20
-10
0
10
20
30
40
Time (s)
Cu
rren
t (A
)
Current Output of DG Units
IFC IPV IBat ISynGen
Fig.3.18 Current output of the micro sources
3.2.3.3. CASE 3: SOURCE INERTIA AND SYSTEM DAMPING
In the previous section it is noted that there is a finite difference in the rate of change in output
current and power between the inertial and non inertial sources. As mentioned before it is always
43
desired that all the DGs respond to any load change in a similar rate to avoid the overloading of a
lagging or leading DG. In this case, it is assumed that synchronous generator, battery and fuel cell are
supplying the entire network load while at 0.5 sec. the PV is also connected to the system. The total
power demand is shared by all the DGs. The system response is shown in Fig. 3.19. The inertia of the
diesel generator and dynamics of the PV result in a large overshoot.
To limit the rate of change in power output, the proposed derivative feedback [76] in the power
sharing controller is used. System response with the derivative feedback is shown in Fig. 3.20. It is
apparent that derivative feedback has decreased the overshoot and improved the dynamic response of
the system.
Fig.3.19 Real power sharing of the DGs
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
1
2
3
4
5
6
7
8
9
10
Time (s)
Act
ive
Po
wer
(kW
)
Active Power Sharing of DG Units
PBat
PSynGen
PPV PFC
Fig.3.20 Real power sharing of the DGs
44
3.2.4 CONCLUSIONS
A modular controller structure with modified voltage angle control loop is proposed for
better load sharing between the parallel connected converters in a distributed generation system. The
integral control in the voltage angle loop help to influence the close loop dynamics without affecting
the steady state frequency regulation. By switching the control action of the DGs from state feedback
in grid connected mode to voltage control in islanded mode, a seamless transfer is achieved. A step by
step control method is proposed for a smooth transition during islanding and resynchronization. The
efficacy of the controller is verified with impedance as well with motor loads. The decentralized
control of a microgrid in presence of inertial and non inertial DGs is achieved and the system stability
is enhanced with a derivative feedback. Inclusion of the micro source model ensures proposed power
electronic control can work in tandem with the associated dynamics of micro sources.
45
CHAPTER 4
POWER QUALITY ENHANCED OPERATION OF A MICROGRID
Power quality and proper load sharing between different DGs and the grid is one of most
important issues that need to be investigated in a microgrid. Concerning the interfacing of a microgrid
to the utility system, an important area of study is to investigate the overall system performance with
unbalanced and non linear loads. Such loads are common and distributed through distribution feeders.
A common practice is to isolate the microgrid from the utility grid by an isolator if the voltage is
seriously unbalanced [46]. However when the voltages are not critically unbalanced, the isolator will
remain closed, subjecting the microgrid to sustained unbalanced voltages at the point of common
coupling (PCC), if no compensating action is taken. Unbalance voltages can cause abnormal operation
particularly for sensitive loads and increased losses in motor loads.
Many innovative control techniques have been used for power quality enhanced operation as
well as for load sharing [46]. A microgrid that supplies to a rural area is widely spread and connected
to many loads and distributed generators at different locations. In general, a DG may have local loads
which are very close to it. There may be loads which are not near to any of the DGs and they must be
shared by the DGs and the utility. These are termed as common load in this chapter.
In this chapter a control algorithm for power electronics interfaced microgrid containing
distributed generators is developed. It is assumed that the common load is supplied solely by the
utility in the grid connected mode. However, when an islanding occurs, this load will be shared by the
DGs through traditional droop method. Furthermore, each DG will supply part of its local load in grid
connected mode, while at the same time, compensating for their unbalance and nonlinearities.
However in the islanded mode, each of the DGs supplies its local load and shares the common load
through droop characteristics.
46
4.1 SYSTEM STRUCTURE
A basic power system model with two DGs is shown in Fig. 4.1 in which the real and
reactive power drawn/supplied is denoted by P and Q respectively. The microgrid is connected to the
utility grid at PCC. Both DG-1 and DG-2 are connected directly to the microgrid through circuit
breaker CB-3 and CB-4 respectively. As mentioned, both the DGs have local loads which may be
unbalanced and nonlinear. In addition, the microgrid may also have a common load, which is assumed
to be balanced and linear and further away from any of the DGs. One of the functions of the DGs is to
correct for the unbalance and nonlinearity of its local load. In the grid connected mode, the DGs share
a percentage of its local load with the utility, while the common load is supplied entirely by the utility.
During islanding, each DG supplies its local load and shares common load with the other DG. The
complex powers drawn by the local loads are PL1 + jQL1 and PL2 + jQL2. The common load draws a
current iLC and a complex power of PLC + jQLC. The local loads are connected to the DGs at PCC1 and
PCC2 with voltages of vp1 and vp2 respectively. The real and reactive powers supplied by the DGs are
denoted by P1, Q1 and P2, Q2. It is assumed that the microgrid is mostly resistive, being in the
distribution level, with line impedances of RD1 and RD2. The utility supply is denoted by vs and the
feeder resistance and inductance are denoted respectively by Rs and Ls. The utility supplies PG and QG
to the microgrid and the balance Ps − PG and Qs − QG are supplied to the utility load. The breakers
CB-1 can isolate the microgrid from the utility supply.
The structure of the VSCs connecting DG-1 and DG-2 to the microgrid is similar to as shown
in Appendix A, Fig. A.1. But the output filter is not present. Equivalent one phase of the converter is
shown in Fig. A.2 (b).
4.2 REFERENCE GENERATION AND COMPENSATOR CONTROL
In this chapter, the reference generation for the DG with compensator is presented. The
control strategy for both the compensators is same. Here description is given only for DG-1 and its
compensator.
47
Fig.4.1. The microgrid and utility system under consideration.
4.2.1. COMPENSATOR REFERENCE GENERATION IN GRID CONNECTED
MODE
It is assumed, for the time being, that the common load and DG-2 are not connected (i.e., CB-
2 and CB-4 are open), while DG-1 is supplying part of its local load only. The main aim of the
compensator is to cancel the effects of unbalanced and harmonic components of the local load, while
supplying pre-specified amount of real and reactive powers to the load. If it is successful in its aim,
then current ig1 will be balanced and so will be the voltage vp1 provided that vs is balanced. Let us
denote the three phases by the subscripts a, b and c. Therefore since ig1 is balanced we have
0111 =++ cgbgag iii (4.1)
From Fig. 4.1, the Kirchoff’s current law (KCL) at vp1 gives
cbakiii kLkgk ,,,111 ==+ (4.2)
48
Therefore combining (4.1) and (4.2) by adding the currents of the all the three phases together, we get
cLbLaLcba iiiiii 111111 ++=++ (4.3)
Since ig1 is balanced due to the action of the compensator, the voltage vp1 will also become
balanced. Hence the instantaneous real powers PG1 will be equal to its average component. Therefore
we can write
1111111 Gcgcpbgbpagap Piviviv =++ (4.4)
From the KCL of (4.2), (4.4) can be written as
( ) ( ) ( ) 1111111111 GccLcpbbLbpaaLap Piiviiviiv =−+−+− (4.5)
Similarly the reactive powers QG will be equal to its instantaneous component, i.e.,
( ) ( ) ( ) 1111111111 3 Gcgbpapbgapcpagcpbp Qivvivvivv ×=−+−+− (4.6)
Using the KCL of (4.2), (4.6) can be rewritten as
( )( ) ( )( ) ( )( ) 1111111111111 3 GccLbpapbbLapcpaaLcpbp Qiivviivviivv =−−+−−+−− (4.7)
Equations (4.3), (4.5) and (4.7) form the basis of the algorithm. From these three, the
following can be written
−−+
=
1
1
1
1
1
1
1
1
3
0
G
G
cL
bL
aL
c
b
a
Q
P
i
ii
A
i
ii
A (4.8)
49
where
−−−=
bpapapcpcpbp
cpbpap
vvvvvv
vvvA
111111
111
111
The determinant of the matrix A is given by
( ) ( ) ( )cpapbpcpbpcpapbpapbpcpap vvvvvvvvvvvvA 111111111111 222 −++−++−+= (4.9)
If vp1 is balanced, then the following is true
0111 =++ cpbpap vvv (4.10)
Substituting (4.10) in (4.9), we get |A| = − K, where
( )21
21
213 cpbpap vvvK ++= (4.11)
Then the solution of (4.8) is given as
( )( )( )
−+−+−+
−
=
bpapGcpG
apcpGbpG
cpbpGapG
cL
bL
aL
c
b
a
vvQvP
vvQvP
vvQvP
Ki
ii
i
ii
11111
11111
11111
1
1
1
1
1
1
333333
1 (4.12)
As we have stipulated that DG-1 supplies a fraction of the average real and reactive power
demanded by the local load, we can write
avLQ
avLP
PP
111
111
×=×=
λλ
(4.13)
50
where PL1av and QL1av are respectively the average real and reactive power demanded by the local load
and λ1P and λ1Q are respectively the real and reactive power fractions supplied by DG-1. It is to be
noted that both the active and reactive powers will have double frequency and distorted components
over the average components [87]. DG-1 will supply the double frequency and distorted component to
cancel out the unbalance and harmonics. Then, as a consequence, the active (PG1) and reactive (QG1)
power supplied by the grid will not contain any double frequency and distortion components.
Additionally DG-1 will also supply a part of the average component.
Therefore the active and reactive power supplied by the grid is given by using the KCL of
(4.2) as
( )( )QavLavLQavLG
PavLavLPavLG
QQQQ
PPPP
111111
111111
1
1
λλλλ−=×−=
−=×−= (4.14)
We can then modify (4.12) as to get the following reference currents for i1
( ) ( )( )( ) ( )( )( ) ( )( )
−−+−−−+−−−+−
−
=
bpapQavLcpPavL
apcpQavLbpPavL
cpbpQavLapPavL
cL
bL
aL
c
b
a
vvQvP
vvQvP
vvQvP
Ki
i
i
i
i
i
1111111
1111111
1111111
1
1
1
1
1
1
1313
1313
13131
λλλλλλ
(4.15)
In a similar way, the current references for DG-2 can be calculated and are given by
( ) ( )( )( ) ( )( )( ) ( )( )
−−+−−−+−−−+−
−
=
bpapQavLcpPavL
apcpQavLbpPavL
cpbpQavLapPavL
cL
bL
aL
c
b
a
vvQvP
vvQvP
vvQvP
Ki
ii
i
ii
2222222
2222222
2222222
2
2
2
2
2
2
1313
1313
13131
λλλλλλ
(4.16)
Equations (4.15) and (4.16) will remain valid so long as DG-1 and DG-2 are supplying a part of their
local loads and neither of the DGs is supplying the common load. When they will be required to
supply the common load during islanding, (4.15) and (4.16) will be suitably modified to accommodate
this. This will be discussed later in Section 4.2.3.
51
4.2.2. COMPENSATOR CONTROL
The equivalent circuit of one phase of the converter is shown in Fig. A. 2 (b). The following
state vector is chosen
[ ]pcccfT viix 1= (4.17)
where the PCC voltage vpcc is the same as the voltage across the filter capacitor vcf, i.e., vcf = vpcc.
The state feedback control shown in appendix (A.4) is used to track the references. In exactly
a similar fashion, DG-2 VSCs are controlled and its reference states are computed.
4.2.3. COMPENSATOR REFERENCE GENERATION IN ISLANDED MODE
In Section 4.2.1, it has been assumed that the DGs are not required to supply the common
load as it will be supplied by the utility. In case of an islanding, however, each of the DGs will have to
supply its local load entirely. In addition, they must also share the real (PLC) and reactive (QLC) power
demand of the common load. Therefore in this mode, λ1P = λ1Q = λ2P = λ2Q = 1. Also PG1, QG1, ig1,
PG2, QG2 and ig2 will be negative with respect to the directions shown in Fig. 4.1. If DG-1 supplies the
local load PL1, QL1 and inject power − PG1, − QG1 to the microgrid to share the common load then the
total real and reactive power generated by the DG-1 are P1 = PL1 − PG1 and Q1 = QL1 −
QG1.respectively. Similarly the total real and reactive power generated by the DG-2 are P2 = PL2 − PG2
and Q2 = QL2 − QG2.respectively.
Note from (4.15) and (4.16) that when λ1P = λ1Q = λ2P = λ2Q = 1, and the DGs also supply the
grid currents, we have
+
=
cg
bg
ag
cL
bL
aL
c
b
a
i
i
i
i
i
i
i
i
i
1
1
1
1
1
1
1
1
1
and
+
=
cg
bg
ag
cL
bL
aL
c
b
a
i
i
i
i
i
i
i
i
i
2
2
2
2
2
2
2
2
2
(4.18)
Following the derivations presented in (4.1) to (4.12) the injected currents are computed as
52
( )( )( )
−+−+−+
−=
bpapGcpG
apcpGbpG
cpbpGapG
cg
bg
ag
vvQvP
vvQvP
vvQvP
Ki
i
i
11111
11111
11111
1
1
1
33
33
331
and
( )( )( )
−+−+−+
−=
bpapGcpG
apcpGbpG
cpbpGapG
cg
bg
ag
vvQvP
vvQvP
vvQvP
Ki
i
i
22122
22122
22222
2
2
2
33
33
331
(4.19)
Therefore combining (4.18) and (4.19) we get the references for the islanded mode as
( )( )( )
−+−+−+
−
=
bpapGcpG
apcpGbpG
cpbpGapG
cL
bL
aL
c
b
a
vvQvP
vvQvP
vvQvP
Ki
ii
i
ii
11111
11111
11111
1
1
1
1
1
1
33
33
331
(4.20)
( )( )( )
−+−+−+
−
=
bpapGcpG
apcpGbpG
cpbpGapG
cL
bL
aL
c
b
a
vvQvP
vvQvP
vvQvP
Ki
i
i
i
i
i
22122
22122
22222
2
2
2
2
2
2
33
33
331
(4.21)
The generalized form for the reference currents of DG-1 can be given from (4.15) and (4.20)
as
( ) ( )( )( ) ( )( )( ) ( )( )
( ) ( )( )( ) ( )( )( ) ( )( )
−−+−−−+−−−+−
−
−−+−−−+−−−+−
−
=
bpapQGGcpPGG
apcpQGGbpPGG
cpbpQGGapPGG
bpapQLavcpPLav
apcpQLavbpPLav
cpbpQLavapPLav
cL
bL
aL
c
b
a
vvQvP
vvQvP
vvQvP
K
vvQvP
vvQvP
vvQvP
Ki
i
i
i
i
i
1111111
111111
1111111
1111111
1111111
1111111
1
1
1
1
1
1
1313
13113
13131
1313
1313
13131
λλλλλλ
λλλλλλ
(4.22)
In the above equation, 1P = 1Q = 1 and 1PG = 1QG = 0 while sharing the common in the islanded
mode, which will result in (4.20). However in the grid connected mode, when the local load is shared
by the DG-1 and the grid, we have 0 < 1P ≤ 1 and 0 < 1Q ≤ 1 and 1PG = 1QG = 1. A similar
expression as (4.22) can also be written for DG-2.
53
4.2.4. DG COORDINATION FOR SHARING THE COMMON LOAD
From Fig. 4.1, it is clear that the total power demand from the common load PLC, QLC is
shared only by the DGs in the islanded mode. The KCL at PCC gives the following expression
21 ggLC iii −−= (4.23)
Assuming that the microgrid is (almost) resistive, the active power balance equation at PCC is given
from Fig. 4.1 by
22
212
121 DgDgGGLC RIRIPPP ++−−= (4.24)
where |Ig1| and |Ig2| are the rms values of ig1 and ig2 respectively. The reactive power balance equation
at PCC is
21 GGLC QQQ −−= (4.25)
With respect to Fig. 4.1, let us define the rms voltage of the PCC as |Vp|∠δp and that of the
PCC1 as |Vp1|∠δp1.The real and reactive power flow from vp1 to vp is then given as
( ) *
1
1111
∠−∠×∠=−−
D
ppppppGG R
VVVjQP
δδδ
From the above equation, the real and reactive power is calculated as
1
111
1
112
1
)sin(
)cos(
D
PPppG
D
pppppG
R
VVQ
R
VVVP
δδ
δδ
−=−
−+−=−
(4.26)
54
When the angle difference δp − δp1 is small (4.26) can be rewritten as
( )
( )111
111
111
12
1
)(PPG
D
PPppG
ppGD
pppG
QR
VVQ
VVPR
VVVP
δδδδ
−∝−−
=−
−∝−+−
=− (4.27)
Equation (4.27) gives us approximate relationships, which clearly indicate that the real and reactive
power can be controlled by controlling the voltage magnitude (|Vp| − |Vp1|) and angle δp1. Therefore the
real and reactive power output to the microgrid from the DG-1 can be controlled using their respective
droop relations with the voltage magnitude and angle respectively. Since the voltage |Vp| is not locally
measurable, these are given by
( )( )∗∗
∗∗
−×−=
−×−=
11111
11111
GGpp
GGpp
PPnVV
QQmδδ (4.28)
where |Vp1|∗, δp1∗, PG1
∗ and QG1∗ respectively are the rated values of the voltage magnitude, angle, real
and reactive power. The coefficients m1 and n1 denote respectively the voltage magnitude and angle
drop with real and reactive power output. These values are chosen to meet the voltage regulation
requirement at point PCC1. In a similar way, the droop characteristics of DG-2 are given by
( )( )∗∗
∗∗
−×−=
−×−=
22222
22222
GGpp
GGpp
PPnVV
QQmδδ (4.29)
In grid connected mode, the droop is inactive. Hence the reference voltage is set from the
positive sequence fundamental component of the PCC1 (or PCC2) voltage. However, when the DGs
are operating in the islanded mode, the magnitude and angle of the reference voltage are derived from
the droop equations (4.28-4.29) given above. These are then used in the state feedback controller.
Hence the positive sequence voltage extraction is unnecessary in this case and the nominal value
before the islanding can be used in the droop equations. Once the voltage magnitude and angle from
55
equations (4.28) and (4.29) are calculated, the current references are obtained from (4.20) and (4.21)
respectively. Noting that each DG will have to supply its local load, the droop coefficients are chosen
based on the ratings of the DGs. Neglecting the resistive drops across the microgrid, these are given
by
( ) ( )( ) ( )max_2_22max_1_11
max_2_22max_1_11
LratedLrated
LratedLrated
QQmQQm
PPnPPn
−×=−×
−×=−× (4.30)
4.3 SIMULATION STUDIES
Simulation studies are carried out in PSCAD/EMTDC (version 4.2) in which different
configurations of load and its sharing is considered. The DGs are considered to be ideal dc sources.
The system data are given in Table 4.1. The numerical results of all the simulation studies are
summarized and listed in Table 4.2 for better clarity.
4.3.1. SHARING THE LOCAL LOAD WITH UTILITY
In this section, the sharing of the local load by the DGs with utility is shown. In this case the current
references of the DG compensators are calculated from (4.22) with 1PG = 1QG = 1 and 2PG = 2QG = 1
such that the DGs do not share the common load. It is desired that DG-1 shares 20% of both real and
reactive power of its local load, while DG-2 shares 50% of the real power and 70% of the reactive
power requirement of its own local load. So in this case 1P = 0.2, 1Q = 0.2 and 2P = 0.5, 2Q = 0.7.
The common load is totally supplied by the utility. At 0.5 s, the common load impedance is made half
of its initial value. Fig. 4.2 shows the power sharing of DG-1 and DG-2. The voltages of PCC1, PCC2
are shown in Fig. 4.3. The power sharing in same desired ratio and balanced voltages even after
change in the common load indicate a stable operation.
To investigate the controller response in the islanded mode, with the same value of local and common
loads, system is islanded at 0.4 s and, at the same time, the common load is also disconnected. As the
island is detected, the each DG reference is changed to supply its total local load. A rapid island
56
detecting scheme is introduced. The instantaneous power pG injected by the grid is computed from the
following relation
Fig.4.2. Real and reactive power sharing in DG-1and DG-2
Fig.4.3. Voltages at the PCC1 and PCC2
gcpcgbpbgapaG ivivivp ++= (4.31)
Once this power falls below a threshold value, an islanding signal is generated. This instantaneous
power pG is used to detect the resynchronization when it rises above the threshold value. Fig. 4.4 (a)
and (b) show the real and reactive power sharing of DG-1. Fig. 4.4 (c) and (d) show DG-1 current and
voltages at PCC1. As soon as the islanding is detected at 0.4 s, the compensator current increases to
deliver the total local load demand. A balanced voltage at PCC1 ensures proper functioning of the
controller even after islanding. DG-2 also behaves in a similar fashion and its plots are not shown
here.
57
Fig.4.4. Power sharing and DG-1current and PCC1 voltages
4.3.2. SHARING THE COMMON LOAD BY THE DGs
If the common load exists in the islanded mode, it is shared among the DGs proportional to
their rating. It is desired to supply the real and reactive power from the DGs to their local load as
before (as shown in Fig.4. 2). An islanding occurs at 0.3 s, where the common load remains
connected. It is desired now that the local loads are totally supplied by the individual DGs and they
share the common load as per (4.30). The droop coefficients of the DGs are taken such that they share
the common load in 1:2 ratio in which DG-2 supplies 2/3rd of the load. Fig. 4.5 shows the real power
sharing of DG-1 and DG-2. At the onset of the islanding, both PCC1 and PCC2 voltage drop, causing
a slight drop in PL1 and PL2. However both P1 and P2 increase to supply the common load, as indicated
by negative power flow in PG1 and PG2. At 1.0 s, the utility is reconnected and the power sharing goes
back to the initial values.
4.3.3. SHARING A COMMON INDUCTION MOTOR LOAD
An impedance load can absorb a sudden change in instantaneous real and reactive power like
a infinite sink. However in case of a motor load, a sudden change in the terminal voltage gives large
oscillation in real and reactive power level. To investigate the system response with the motor load,
the common load shown in Fig. 4.1 is now replaced with an induction motor and the power sharing is
58
observed by islanding and resynchronization the utility. Fig. 4.6 shows the results. The islanding and
resynchronization occur at 0.2 s and 0.7 s respectively. During islanding it is desired that the motor
load is shared between DGs in 1:2 ratio. The absolute value of common load supplied by the DGs
along with the total motor load during islanded mode is indicated in Fig. 4.6. The system reaches
steady state within 0.2 s after islanding and 0.3 s after resynchronization.
Fig.4.5. Real power sharing by DG-1 and DG-2.
Fig. 4.6. Common load sharing between DG-1 and DG-2
4.3.4. DG-1 SUPPLYING THE ENTIRE COMMON LOAD DURING ISLANDING
Let us now assume that DG-2 is capable of supplying only its local load. Hence during an
islanding, DG-1 must supply both its local load and the entire requirement of the common load. To
investigate this operation an islanding is created at 0.25 s. Before islanding the following λ’s are
chosen:
59
1P = 0.2, 1Q = 0.2 and 2P = 1.0, 2Q = 1.0
1PG = 1QG = 2PG = 2QG = 1.0
Once the islanding occurs, the following λ’s are chosen:
1P = 1.0, 1Q = 1.0, 2P = 1.0, 2Q = 1.0
1PG = 1QG = 0 and 2PG = 2QG = 1.0
The system response is shown in Fig. 4.7. Once the islanding occurs, there is a slight voltage
drop in both PCC1 and PCC2, causing PL1 and PL2 to drop. DG-1 supplies its local and common load
causing a rise in P1 and negative PG1. However DG-2 supplies only its local load, thereby maintaining
PG2 to nearly zero.
Fig.4.7. Real power sharing of the DGs and voltages at PCC1 and PCC2
4.4 DISCUSSIONS
In the studies presented in this chapter, it has been assumed that only two DGs and a common
load are connected to the microgrid. In general, however, there might be several DGs and loads
connected to the microgrid as shown in Fig. 4.8. In this case a total number of n common loads and m
60
DGs, with the compensators and local load are considered. The one way communication needed to
broadcast the CB_grid status to the DG compensator is shown in Fig. 4.8. The total active and reactive
powers consumed by the common loads are given by
LCnLCLCLC
LCnLCLCLC
QQQQ
PPPP
+++=+++=
21
21 (4.32)
This total power will be supplied by the grid alone. However in islanded mode this power will be
shared among the DGs. The power can be shared depending on the DG rating. Coefficient of the
droop characteristics of the DGs should be chosen by
( ) ( ) ( )( ) ( ) ( )max__max_2_22max_1_11
max__max_2_22max_1_11
LmratedmmLratedLrated
LmratedmmLratedLrated
QQmQQmQQm
PPnPPnPPn
−×=−×=−×
−×=−×=−× (4.33)
However, similar to conventional droop method, the different line impedance between the load
connection points throughout the microgrid will have impact on the load sharing. As the line
impedances are not purely resistive or inductive, control of the active and reactive powers are not
totally decoupled in nature. The detail impact of the line impedance on droop control is discussed in
[77 and 78].
Fig.4.8. Microgrid structure with large number of DGs and loads.
61
4.5 CONCLUSIONS
In this chapter a local load sharing technique is proposed for a distributed microgrid. The controllers
are capable of compensating the local unbalanced and non linear loads. The local loads can be shared
with utility in any desired ratio. The common loads which are normally supplied by the utility in grid
connected mode, shared among the DGs proportional to their rating in the islanded mode. A smooth
transfer between the islanded and grid connected mode assures a stable operation of the system. The
controller efficacy is checked both with impedance and motor loads. The application is mainly aimed
at rural area where unbalanced load is common and wire less communication is always desirable due
to the large network size. Similar to any droop control method, the distance among the load and DG
determine the line impedance between them and that impedance has impact on the load sharing.
However load sharing can be made more accurate by incorporating the line impedance values in the
power reference calculation.
62
TABLE-4.1: SYSTEM PARAMETERS
System Quantities Values
Systems frequency 50 Hz
Source voltage (Vs) 11 kV rms (L-L)
Feeder impedance Rs = 1.025 Ω, Ls = 57.75 mH
DG-1 Local Unbalanced load RLa = 48.4 Ω, LLa = 192.6 mH
RLb = 24.4 Ω, LLb = 100.0 mH
RLc = 96.4 Ω, LLc = 300.0 mH
DG-1 Local Nonlinear load A three-phase rectifier supplying an
RL load with R = 200 Ω, L = 100 mH
DG-2 Local Unbalanced load RLa = 48.4 Ω, LLa = 192.6 mH
RLb = 24.4 Ω, LLb = 100.0 mH
RLc = 96.4 Ω, LLc = 300.0 mH
DG-2 Local Nonlinear load A three-phase rectifier supplying an
RL load with R = 200 Ω, L = 100 mH
Common Impedance Load RLa = 24.4 Ω, LLa = 100.0 mH
RLb = 24.4 Ω, LLb = 100.0 mH
RLc = 24.4 Ω, LLc = 100.0 mH
Common Motor Load (M) Induction motor rated 40 hp, 11 kV
rms (L-L).
Microgrid Line Impedance RD1=RD2=0.2 Ω
DGs and Compensators
DC voltage (Vdc1)
Transformer rating
VSC losses
Filter Capacitance (Cf)
3.5 kV
3 kV/11 kV, 0.5 MVA,
2.5% reactance (Lf)
1.5 Ω
50 µF
Droop Coefficients
m1
m2
n1
n2
- 0.1 rad/MVAr
- 0.05 rad/MVAr
0.12 kV/MW
0.06 kV/MW
63
TABLE-4.2: NUMERICAL RESULTS
Case-I Active
Power
Initial
value
(MW)
Final value
(MW) Reactive Power
Initial
value
(MVAr)
Final value
(MVAr)
Section 4.3.1
Sharing the Local
Load with Utility
Fig.4.2
P1 0.275 0.274 Q1 0.28 0.28
PG1 1.125 1.125 QG1 1.12 1.12
PL1 1.4 1.39 QL1 1.4 1.4
P2 0.71 0.69 Q2 0.42 0.41
PG2 0.69 0.69 QG2 0.18 0.17
PL2 1.4 1.38 QL2 0.6 0.58
Fig.4.3
Voltage drop at PCC1 (%) Voltage drop at PCC2 (%)
3.15% 3.38%
Fig.4.4
Active
Power
Initial
value
(MW)
Final
value
(MW)
Reactive
Power
Initial
value
(MVAr)
Final value
(MVAr)
P1 0.142 0.71 Q1 0.09 0.43
PG1 0.568 0.0 QG1 0.36 0.0
PL1 0.71 0.69 QL1 0.45 0.43
Case-II
Active
Power
Initial
value
(MW)
Intermediate value
(In Islanded Mode)
(MW)
Final value
(After resynchronization)
(MW)
Section 4.3.2
Sharing the
Common Load
by the DGs
Fig.4.5
P1 0.142 0.78 0.142
PG1 0.568 -0.13 0.568
PL1 0.71 0.65 0.71
P2 0.35 0.91 0.35
PG2 0.35 -0.31 0.35
PL2 0.70 0.60 0.70
Case-III
Active
And
Reactive
Power
Initial value
(Active power in
MW and
reactive power
in MVAr)
Intermediate value
(In Islanded Mode)
(Active power in MW and
reactive power in MVAr)
Final value
(After
resynchronization)
(Active power in MW
and reactive power in
MVAr)
Section 4.3.3
Sharing a
Common
Induction Motor
Load
Fig.4.6
PG1 0.95 -.081 0.95
PG2 0.60 -0.157 0.60
PLC 0.238 0.238 0.238
QG1 0.59 -0.039 0.59
QG2 0.21 -0.076 0.21
QLC 0.115 0.115 0.115
Case-IV
Active
Power
Initial value
(MW)
Final value
(In Islanded Mode)
(MW)
Section 4.3.4 Fig.4.7 P1 0.34 1.86
64
DG-1 Supplying
the Entire
Common Load
During Islanding
PG1 1.50 -0.28
PL1 1.83 1.58
P2 1.825 1.625
PG2 0.01 -0.025
PL2 1.835 1.6
Voltage Drop at PCC1 (%) Voltage Drop at PCC2 (%)
4.3% 5.8%
65
CHAPTER 5
POWER FLOW CONTROL WITH BACK-TO BACK CONVERTERS IN A UTILITY
CONNECTED MICROGRID
In general, a microgrid is interfaced to the main power system by a fast semiconductor switching
system called the static switch (SS). It is essential to protect a microgrid in both the grid-connected
and the islanded modes of operation against all faults. Converter fault currents are limited by the
ratings of the silicon devices to around 2 per unit rated current. Fault currents in islanded converter
based microgrids may not have adequate magnitudes to use traditional overcurrent protection
techniques [40]. To overcome this problem, a reliable and fast fault detection method is proposed in
[41].
The aim of this chapter is to set up power electronics interfaced to the microgrid containing
distributed generators, connected to the utility through back-to-back converters. Bidirectional power
flow control between the utility and microgrid is achieved by controlling both the converters. The
back-to-back converters provide the much needed frequency and power quality isolation between the
utility and the microgrid. A proper relay breaker co-ordination is proposed for protection during fault.
The scheme not only ensures a quick and safe islanding at inception of the fault, but also a seamless
resynchronization once the fault is cleared. This application of back-to-back converters in distributed
generation would facilitate:
controlled power flow between microgrid and utility which can be used in case of any contractual
arrangement.
reliable power quality due to the isolation of the microgrid system from utility.
5.1 SYSTEM STRUCTURE AND OPERATION
A simple power system model with back to back converters, one microgrid load and two DG
sources is shown in Fig. 5.1. A more complex case is considered in Section 5.7. In Fig. 5.1, the real
66
and reactive power drawn/supplied are denoted by P and Q respectively. The back to back converters
are connected to the microgrid at the point of common coupling (PCC) and to the utility grid at point
A as shown in Fig. 5.1. Both the converters (VSC-1 and VSC-2) are supplied by a common dc bus
capacitor with voltage of VC. The converters can be blocked with their corresponding signal input
BLK1 and BLK2. DG-1 and DG-2 are connected through voltage source converters to the microgrid.
The output inductances of the DGs are indicated by inductance L1 and L2 respectively. The real and
reactive powers supplied by the DGs are denoted by P1, Q1 and P2, Q2. While the real and reactive
power demand from the load is denoted by PL, QL. It is assumed that the microgrid is in distribution
level with mostly resistive lines, whose resistances are denoted by RD1 and RD2.
The utility supply is denoted by vs and the feeder resistance and inductance are denoted respectively
by Rs and Ls. The utility supplies PG and QG to the back-to-back converters and the balance amounts
Ps − PG and Qs − QG are supplied to the utility load. The breakers CB-1 and CB-2 can isolate the
microgrid from the utility supply. The power supplied from the utility side to microgrid at PCC is
denoted by PT, QT, where the differences PG − PT and QG − QT represent the loss and reactive power
requirement of the back-to-back converter and their dc side capacitor.
The system can run in two different modes depending on the power requirement in the microgrid.
In mode-1, a specified amount of real and reactive power can be supplied from the utility to the
microgrid through the back-to- back converters. Rest of the load demand is supplied by the DGs. The
power requirements are shared proportionally among the DGs based on their ratings. When the total
power generation by the DGs is more than the load requirement, the excess power is fed back to the
utility. This mode provides a smooth operation in a contractual arrangement, where the amount of
power consumed from or delivered to the utility is pre-specified.
67
Fig. 5.1. The microgrid and utility system under consideration.
When the power requirement in the microgrid is more than the combined maximum available
generation capacity of the DGs (e.g. when cloud reduces generation from PV), a pre-specified power
flow from the utility to the microgrid may not be viable. The utility will then supply the remaining
power requirement in the microgrid under mode-2 control, while the DGs are operated at maximum
power mode. Once all the DGs reach their available power limits, the operation of the microgrid is
changed from mode-1 to mode-2. While mode-1 provides a safe contractual agreement with the
utility, mode-2 provides more reliable power supply and can handle large load and generation
uncertainty. The rating requirement of the back to back converters will depend on the maximum
power flowing through them. The maximum power flow will occur when
the load demand in the microgrid is maximum and minimum power is generated by the DGs
(power flow from utility to microgrid)
maximum power is generated by DGs, while the load demand in the microgrid is minimum
(power flow from microgrid to utility).
The rating issue has to be determined a priori. The microgrid cannot supply/absorb more power than
the pre-specified maximum limit.
68
5.2 CONVERTER STRUCTURE AND CONTROL
The converter structure for VSC-3 is shown in appendix-A and converter contains three H-bridges
(with output inductance). They are controlled in output feedback control as shown in Appendix-A.
All the four VSCs are controlled using the same control strategy. Hence, all these controllers
require their instantaneous reference voltages. These are discussed in the next two sections.
5.3 BACK-TO-BACK CONVERTER REFERENCE GENERATION
This section describe the reference generation for the back-to-back VSCs. Both the VSCs are
supplied from a common capacitor of voltage VC as shown in Fig. 5.1. Depending on the power
requirement in the microgrid; there are two modes of operation as discussed previously. However the
reference generation for VSC-1 is common for both these modes. This is discussed next.
5.3.1. VSC-1 REFERENCE GENERATION
Reference angle for VSC-1 is generated as shown in Fig. 5.2. First the measured capacitor voltage
VC is passed through a low pass filter to obtain VCav. This is then compared with the reference
capacitor voltage VCref. The error is fed to a PI controller to generate the reference angle ref. VSC-1
reference voltage magnitude is kept constant, while angle is the output of the PI controller. The
instantaneous voltages of the three phases are derived from them.
Fig. 5.2. Angle controller for VSC-1.
The two modes of VSC-2 reference generation are discussed next.
69
5.3.2. VSC-2 REFERENCE GENERATION IN MODE-1
VSC-2, which is connected with PCC through an output inductance LG, controls the real and
reactive power flow between the utility and the microgrid. Fig. 5.3 shows the schematic diagram of
this part of the circuit, where the voltages and current are shown by their phasor values.
Fig. 5.3. Schematic diagram of VSC-2 connection to microgrid.
Let us assume, that in mode-1 the references for the real and reactive power be PTref and QTref
respectively and the VSC-2 output voltage be denoted by VT∠δT and the PCC voltage by VP∠δP. Then
the reference VSC-2 voltage magnitude and its can be calculated as
( )PTP
GTrefPT V
XQVV
δδ −+
=cos
2
(5.1)
PGTrefP
GTrefT
XQV
XPδδ +
+= −
21tan (5.2)
Depending on the real and reactive power demand, these references are calculated, based on which the
instantaneous reference VSC-2 voltages for the three phases are computed. It is to be noted that, sign
of the active and reactive power references are taken as negative when it is desired to supply the
power from the microgrid to the utility side.
5.3.3 VSC-2 REFERENCE GENERATION IN MODE-2
In mode-2, the utility supplies any deficit in the power requirement through back-to-back
converters while the DGs supply their maximum available power. Let the maximum rating of the
70
back-to-back converters are given by PTmax, QTmax. Then the voltage magnitude and angle reference of
VSC-2 is generated as
( )( )TTTTT
TTTTT
QQnVV
PPm
−×−=−×−=
maxmax
maxmaxδδ (5.3)
where VTmax and Tmax are the voltage magnitude and angle, respectively, when it is supplying the
maximum load. The VSC-2 droop coefficient mT and nT are chosen such that the voltage regulation is
within acceptable limit from maximum to minimum power supply.
5.4 REFERENCE GENERATION FOR DG SOURCES
In this section, the reference generation for the DGs is presented. It is to be noted that the reference
generations of the DGs are different from reference generation of the back-to-back converters. The
control strategy for both the DGs is the same and hence only DG-1 reference generation is discussed
here.
5.4.1. MODE-1
It is assumed that in mode-1 the utility supplies a part of the load demand through the back-to-back
converters and rest of the power demand in the microgrid is supplied and regulated by the DGs. The
output voltages of the converters are controlled to share this load proportional to the rating of the
DGs. As the output impedance of the DG sources is inductive, the real and reactive power injection
from the source to microgrid can be controlled by changing voltage magnitude and its angle [43]. Fig.
5.4 shows the power flow from DG-1 to microgrid where the voltages and current are shown in rms
values and the output impedance is denoted by jX1.
Fig. 5.4. Power flow from DG-1 to microgrid.
71
As mentioned before, the power requirement can be distributed among the DGs, similar to
conventional droop [43] by dropping the voltage magnitude and angle as (2.9) and can be represented
as,
( )( )ratedrated
ratedrated
QQnVV
PPm
11111
11111
−×−=−×−= δδ
(5.4)
where V1rated and 1rated are the rated voltage magnitude and angle respectively of DG-1, when it is
supplying the load to its rated power levels of P1rated and Q1rated.
So DG-1 can supply the desired power if the output voltage of VSC-3 has magnitude and angle as
given in (5.4). From the rms quantities the instantaneous reference voltages of the three phases are
obtained. In a similar way, the instantaneous reference voltages for VSC-4 are also obtained. This
method of load sharing is based only on local measurements and does not need intercommunication
between the DGs. For the determination of the phase angles, a common reference is used.
5.4.2. MODE-2
In mode-2, the DGs supply their maximum available power. The reference generation for the DGs
in mode-2 is similar to the reference generation of VSC-2 of back-to-back converter in mode-1 as
given in (5.1) and (5.2). Let us denote the available active power as P1avail. Then based on this and the
current rating of the DG, the reactive power availability Q1avail of the DG can be determined. Based on
these quantities, the voltage references as shown in Fig. 5.4 is calculated as
( )PPP
availP
VXQV
Vδδ −
+=11
112
11 cos
(5.5)
111
21
1111 tan P
availP
avail
XQV
XP δδ +
+= − (5.6)
The references for the other DGs are generated in a similar way.
72
5.5 RELAY AND CIRCUIT BREAKER COORDINATION DURING ISLANDING
AND RESYNCHRONIZATION
The reference generations described in the previous section for DGs and back-to-back converters
are totally independent of each other. In mode-1, once the desired value of real and reactive power
flow through the back-to-back converters is set, the rest of the required power will automatically be
shared amongst the DGs. In mode-2, the DGs supply their maximum available power while the extra
power requirement from the utility is supplied through the back-to-back converter. When a DG
reaches its maximum available signal, it broadcasts it to VSC-2 control center. The mode change is
initiated when all the DGs their available limits. Note that other than the broadcast signals, no other
communication is needed between the back-to-back converters and the DGs Even during islanding
and resynchronization, no communication is needed. But proper relay breaker coordination, along
with converter blocking, will be required to maintain the voltage of the dc capacitor during islanding
and resynchronization. Fig. 5.5 shows the logic diagram used for this purpose, where Trip_Signal
initiates the tripping of CB-2 (Fig. 5.1) and the signal BLK1 blocks VSC-1. The same logic is also
used for the tripping CB-1 and the blocking of VSC-2. The rate of rise of current ig is monitored by
the protection scheme. When it exceeds a threshold value in response to a fault in the utility grid, the
output of the Protection Scheme (Fig. 5.5) becomes high. This output is used to set all the RS flip
flops. The upper flip flop (F/F-1) generates the trip signal. This flip flop is reset by the Fault_Clear
signal. The lower two flip flops, F/F-2 and F/F-3 generate BLK1 and BLK2 signals respectively. The
blocking deactivation is initiated when the fault is cleared and Fault_Clear signal is set high
manually. The converter VSC-1 is deblocked by resetting F/F-2 when the breaker CB-2 is closed, as
indicated by Br_Status signal. The AND gate insures that no false deblocking occurs till both these
signals are high. VSC-2 is deblocked after VSC-1 is deblocked. This is why Fault_Clear signal is
passed through a time delay circuit to generate the reset signal for F/F-3.
73
Fig. 5.5. Logic for breaker operation and converter blocking.
Fig. 5.6 shows the timing diagram of the breakers and converter blocking during islanding and
resynchronization process. If a breaker is closed, the signal Br_Status is high and it goes low when the
breaker opens. As evident from Fig. 5.5, the output of the Protection Scheme triggers the RS flip
flops, which simultaneously generates both the trip and block signals. The block signals blocks both
VSC-1 and VSC-2 simultaneously. Once the trip signals goes high, the breakers CB-1 and CB-2 open
after a finite time delay (t_op) as indicated in Fig. 5.6. Unless the two VSCs are blocked, the dc
capacitor voltage collapses due to the sudden increase in power requirement on the utility side. Also to
prevent the angle reference δref from diverging during the contingency, the angle controller of Fig. 5.2
is bypassed and the reference is held at the pre-fault value. Note that, once a breaker opens, the
Protection Scheme output goes low causing the set input of the flip flops of Fig. 5.5 to become 0.
During islanding, breakers CB-1 and CB-2 are opened simultaneously. However during
resynchronization, CB-2 is closed and VSC-1 is deblocked first connecting this to the utility. This will
cause the dc capacitor voltage to rise taking a finite time depending on the capacitor voltage drop
during islanding. Once the capacitor voltage settles to its reference value and the angle controller of
Fig. 5.2 settles, CB-1 is closed and VSC-2 is deblocked.
Once the fault is cleared, Fault_Clear signal is set high manually. This signal is the same as
Br_Close signal of CB-2. The Fault_Clear signal also resets Trip_signal, used both by CB-1 and CB-
2. With a finite time delay (t_cl) from the initiation of Br_Close signal, CB-2 closes, making the
Br_Status signal for CB-2 high. This resets F/F-2 and deactivates BLK1 signal causing switching
devices of VSC-1 to start conducting. As mentioned earlier and shown in Fig. 5.5 that Br_Close signal
for CB-1 is generated after a time delay from the Fault_Clear signal. Once this signal is generated,
74
CB-1 closes after a time delay t_cl. This then resets F/F-3 and VSC-2 starts conducting. To even
further safeguard the dc capacitor voltage, the power flow reference for VSC-2 is switched to zero
during islanding and brought back to its previous value after resynchronization. This step by step
process ensures a seamless resynchronization.
Fig. 5.6. Breakers and converter blocking timing diagram.
5.6 SIMULATION STUDIES
Different configurations of load and its sharing are considered. The DGs are considered as inertia-
less dc source supplied through a VSC. The system data are given in Table 5.1. The droop coefficients
are chosen such that both active and reactive powers of the load are divided in 1:1.25 ratios between
DG-1 and DG-2.
5.6.1 CASE-1: LOAD SHARING OF THE DGS WITH UTILITY
If the power requirement of the load in microgrid is more than the power generated by the DGs, the
balance power is supplied by the utility through the back-to-back converters. The desired power flow
from the utility to the microgrid is controlled by (5.1) and (5.2), while droop equation (5.4) controls
the sharing of the remaining power. It is desired that 50% of the load is supplied by the utility and rest
of the load is shared by DG-1 and DG-2. The impedance load of Table 5.1 is considered for this case.
Fig. 5.7 shows the real and reactive power sharing between utility and the DGs. Fig. 5.8 (a) shows the
phase-a reference and output voltage, whereas three phase voltage tracking error is shown in Fig. 5.8
(b). It can be seen that the tracking error is less than 0.2%. Fig. 5.9 shows the capacitor voltage and
75
the output of the angle controller. At 0.1 s, the impedance of the load is halved and at 0.35 s, it is
changed back to its nominal value. It can be seen that the system goes through minimal transient and
reaches its steady state within 5 cycles (100 ms) for both the transients.
TABLE 5.1. SYSTEM AND CONTROLLER PARAMETERS
System Quantities Values
Systems frequency 50 Hz
Source voltage (Vs) 11 kV rms (L-L)
Feeder impedance Rs = 3.025 Ω, Ls = 57.75 mH
Load
Impedance (Balanced)
or
Induction motor
RL = 100.0 Ω, LL = 300.0 mH
Rated 40 hp, 11 kV rms (L-L)
DGs and VSCs
DC voltage (Vdc1, Vdc2)
Transformer rating
VSC losses (Rf)
Filter capacitance (Cf)
Inductances (L1, L2)
Inductances (LG)
Hysteresis constant (h)
3.5 kV
3 kV/11 kV, 0.5 MVA, 2.5% reactance (Lf)
1.5 Ω
50 µF
20 mH and 16.0 mH
28.86 mH
10-5
Angle Controller
Proportional gain (Kp)
Integral gain (KI)
− 0.2
− 5.0
Droop Coefficients
Power−−−−angle
m1
m2
Voltage−−−−Q
n1
n2
0.3 rad/MW
0.24 rad/MW
0.15 kV/MVAr
0.12 Kv/MVAr
Fig. 5.7. Real and reactive power sharing for Case-1.
76
Fig. 5.8. Voltage tracking of DG-1 Case-1.
Fig. 5.9. Capacitor voltage and angle controller output for Case-1.
5.6.2 CASE-2: CHANGE IN POWER SUPPLY FROM UTILITY
If the power flow from the utility to the microgrid is changed by changing the power flow
references for VSC-2, the extra power requirement is automatically picked up by the DGs. Fig. 5.10
shows the real and reactive power sharing, where at 0.1 s the power flow from the utility is changed to
20% of the total load from the initial value of 50% as considered in Case-1. It can be seen that the
DGs pick up the balance load demand and share it proportionally as desired. The unchanged real and
reactive load power during the change over proves the efficacy of the controller for smooth transition.
Fig. 5.11 shows the PCC voltage and change in current injection at PCC from utility. It can be seen
that the PCC voltage remained balanced and transient-free, while the injected currents reach steady
state within 4 cycles.
77
Fig. 5.10. Real and reactive power sharing for Case-2.
5.6.3 CASE-3: POWER SUPPLY FROM MICROGRID TO UTILITY
When the power generation of the DGs is more than the power requirement of the load, excess
power can be fed back to the utility through the back-to-back converters. It is desired the utility
supplies 50% of the microgrid load initially. At 0.1 s, however, the same amount of power is fed back
to the utility by changing the sign of the power flow reference for the back-to-back converters. The
DG output increases automatically to supply the total load power and power to the utility, as evident
from Fig. 5.12.
Fig. 5.11. Three phase PCC voltage and injected current for Case-2.
78
Fig. 5.12. Real and reactive power sharing during power reversal (Case-3).
Fig.5.13 (a) shows the phase-a voltage at PCC and phase-a current injected from the utility to the
microgrid, where current is scaled up 30 times. The change in the power flow direction is indicated by
the sudden change in phase of the injected current phase at 0.1 s vis-à-vis that of the voltage. Fig.5.13
(b) shows the three phase current injected by the utility to the microgrid. It reaches steady state within
3 cycles. Apart from the phase reversal, the magnitude of the currents remain the same indicating that
the same amount of power flow is taking place, albeit in opposite direction.
Fig. 5.13. PCC voltage and injected current for Case-3.
5.6.4. CASE-4: LOAD SHARING WITH MOTOR LOAD
In this section, load sharing with the induction motor load, given in Table 5.1, is investigated. An
impedance load is an infinite sink as it can absorb any change in the instantaneous real and reactive
power. However an inertial load such as motor is not capable of that. Thus any sudden big change in
79
the terminal voltage results in large oscillation in the real and reactive power. At the beginning it is
assumed that the utility supplies 0.2 MW of real power and 0.5 MVAr of reactive power to the
microgrid. Then at 0.05 s, the power reference is changed such that the utility supplies 0.3 MVAR of
reactive power and no real power. The power sharing results for this case is shown in Fig. 5.14.
Fig. 5.14. Real and reactive power sharing with motor load (Case-4).
5.6.5 CASE-5: CHANGE IN UTILITY VOLTAGE AND FREQUENCY
One of the major advantages of the back-to-back converter connection is that it can provide
isolation between the utility and the microgrid, both for voltage and frequency fluctuations. Fig. 5.15
shows the system response for frequency fluctuation in the utility side from 0.05 s to 0.25 s. At 0.05 s,
the utility frequency dropped by 0.5%, and at 0.25 s, it comes back to its initial value of 50 Hz. The
real and reactive power injections from utility to VSC-1 are shown as PG and QG respectively. It can
be seen that while PG and QG fluctuate, the load power (PL, QL) and the injected power to the
microgrid (PT, QT) remain constant.
Fig. 5.15. Real and reactive power during frequency fluctuation (Case-5).
80
Fig. 5.16. Real and reactive power during voltage sag (Case-5).
With the system operating in steady state, a 50% balanced sag in the source voltage occurs in 0.1 s.
The sag is removed after 0.5 s. Fig. 5.16 shows the power and the reactive power during this
condition. It can be seen that the load power (PL, QL) and the injected power to the microgrid (PT, QT)
remain almost undisturbed. The real power drawn from the grid (PG), barring transients at the
inception and removal of the sag, is maintained at the steady state level in order to supply power to the
microgrid. The reactive power (QG) however reverses sign as the utility voltage drop causing it to
absorb reactive power. During the sag, the dc capacitor supplies reactive power to the utility. The dc
capacitor voltage and the output of the angle controller are shown in Fig. 5.17. It can be seen that
while the dc capacitor voltage is maintained at its pre-specified value, the angle drops in sympathy
with the source voltage drop to maintain the injected power constant. The angle returns to its pre-sag
value once the sag is removed.
Fig. 5.17. DC capacitor voltage and angle controller output during voltage sag.
81
5.6.6. CASE-6: ISLANDING AND RESYNCHRONIZATION
In this section the system response during a fault in the utility is investigated. Let us assume a
single-line to ground fault occurs at point F, which is half way between the utility source and point A,
as shown in Fig. 5.18. As the fault occurs, the trip signal for the breakers CB-1 and CB-2 are initiated
by the protection scheme which measure the rate of rise of current ig. But breakers need a finite time
to physically open the contact. During this time, the back to back converters start feeding the fault as
shown by PG, QG in Fig. 5.18, which will result in the collapse of the capacitor voltage VC. As
explained in Section 5.5 , the coordination of breaker tripping and VSC blocking is required to avoid
the voltage collapse.
Fig. 5.18. Location of the single line to ground fault.
With the system is operating in steady state, the single-line to ground fault in phase-a occurs at 0.05
s and the fault is cleared at 0.1 s. The resynchronization process starts at 0.25 s when the Br_Close
signal of CB-2 is generated. Subsequently, at 0.35 s, the Br-Close signal of CB-1 is generated. The dc
capacitor voltage and the angle controller output are shown in Fig. 5.19 in which the angle controller
output is kept constant to its pre-fault value between 0.05 s to 0.25 s. Fig. 5.20 shows real and reactive
power sharing, which are in accordance to the desired objective to keep microgrid load power
constant.
5.6.7. CASE-7: VARIABLE POWER SUPPLY FROM UTILITY
In cases presented above, it has been assumed that the system is running in mode-1 where DGs can
supply the balance of the load requirement once the pre-specified amount of power is drawn from the
utility. The following example shows the switch from mode-1 to mode-2 when the maximum
82
available power that can be supplied by the DGs is reached. Initially the microgrid is running in mode
1. At 0.1 s, the input power from DG-1 (P1avail) suddenly reduces to 60 KW. DG-2 then supplies the
shortfall as can be seen in Fig. 5.21. The load power and that supplied by the utility remain
unchanged. Subsequent to this, suddenly the load changes at 0.35 s in which the power demand in the
microgrid increases from 0.53 MW to 0.64 MW. However, the maximum power that can be supplied
by DG-2 is set at 300 kW. This implies that both the DGs together can supply 360 KW. Moreover, the
utility grid was supplying 200 kW before this event. Therefore an additional 80 KW power is required
from the utility grid and hence a mode change is inevitable. This mode change is initiated with VSC-2
droop gains of mT = 0.03 rad/MW and nT = 0.02 kV/MVAr. The results are shown in Fig. 5.21. It can
be seen that there is no appreciable overshoot in the active powers supplied by the DGs. The utility
power (PT) rises sharply in order to supply the load demand. The system settles in 5 cycles.
Fig. 5.19. DC capacitor voltage and angle controller output during islanding and resynchronization (Case-6).
Fig. 5.20. Real and reactive power during islanding and resynchronization (Case-6).
83
Fig. 5.21. Real power sharing during power limit and mode change (Case-7).
5.6.8 CASE-8: DC VOLTAGE FLUCTUATION AND LOSS OF A DG
Photovoltaic (PV) cells are the most common form of converter interfaced DGs. The power output
from these cells may vary during the day and may also have fluctuations depending on the
atmospheric conditions. However so long at the DC voltage remains above a threshold, the converter
tracks the output voltage reference. If the voltage falls below this threshold, the converter is switched
off and the utility and the other DGs will have to share the microgrid load. To prove this point, a
simulation is carried out in which it is assumed that DG-2 is capable of supplying the excess load
demand, while the utility supplies the pre-specified amount of power in mode-1. If this is not possible,
a switch to mode-2 will be necessary, which is not shown here.
Fig. 5.22. DC voltage fluctuation in DG-1 and its tripping (Case-8).
84
The simulation results for this case are shown in Fig. 5.22. The dc voltage of DG-1 has a sinusoidal
fluctuation of 3% and at 0.05s, it starts ramping down as in Fig. 5.22 (a). The 500 Hz fluctuation is
shown in the inset. At 0.3 s, when the dc voltage falls below 2.25 kV, this DG is isolated from the
system. Since the other DG picks up the load, any appreciable drop in vp1 (Fig. 5.4) does not occur as
evident from Fig. 5.22 (b). Fig 5.22 (c) and (d) show the real and reactive powers respectively. It can
be seen that there is a slight drop in the load power indicating a slight microgrid voltage drop.
However the utility power remains unchanged and that supplied by DG-2 increases.
5.7 MICROGRID CONTAINING MULTIPLE DGS
In the studies presented so far, it has been assumed that only two DGs and a load are connected to
the microgrid. In general, however, there might be several DGs and loads connected to it, as shown in
Fig. 5.23. It is assumed that there are a total number of n loads and m DGs. The total active and
reactive powers consumed by the loads are given by
LnLLL
LnLLL
QQQQ
PPPP
+++=+++=
21
21 (5.7)
The required power will be shared by DGs depending on their rating, given by
mratedmratedrated
mratedmratedrated
QnQnQn
PmPmPm
×==×=××==×=×
2211
2211 (5.8)
However, like any droop method, the different line impedance between the load connection points,
throughout the microgrid will have slight impact on the load sharing. The reference generation for the
DGs will remain the same as before.
To validate a proper load sharing with multiple DGs, two more DGs are connected to the microgrid.
The DG parameters, output impedance, converter structure and controller are the same as those used
for DG-1 and DG-2. The droop coefficients for the four DGs are chosen such that they share both real
and reactive power in the ratio of DG-1: DG-2: DG-3: DG-4 is 1:1.25:1.55:1.72. The load is also
distributed in three different places to achieve a microgrid structure similar as shown in Fig. 5.23 with
m = 4 and n = 3. Fig. 5.24 shows the real power sharing, where the load power demand is doubled at
0.3 s, and brought back to initial value at 0.8s. It is evident from the figure that a proper load sharing
occurs in the desired ratio.
85
Fig. 5.23. Microgrid structure with large number of DGs and loads.
Fig. 5.24. Real power sharing with four DGs.
5.8 CONCLUSIONS
In this chapter, a load sharing and power flow control technique is proposed for a utility
connected microgrid. The utility distribution system is connected to the microgrid through a set of
back-to-back converters. In mode-1, the real and reactive power flow between utility and microgrid
can be controlled by setting the specified reference power flow for back-to-back converters module.
Rest of the power requirement in the microgrid is shared by the DGs proportional to their rating. In
case of high power demand in the microgrid, the DGs supply their maximum power while rest of the
power demand is supplied by utility through back-to-back converters (mode-2). A broadcast signal
can be used by the DGs to indicate their mode change. However only locally measured data are used
by the DGs and no communication is needed for the load sharing. The utility and microgrid are totally
isolated, and hence, the voltage or frequency fluctuations in the utility side do not affect the microgrid
86
loads. Proper switching of the breaker and other power electronics switches has been proposed during
islanding and resynchronization process.
87
CHAPTER 6
STABILITY ANALYSIS OF MULTIPLE CONVERTER BASED AUTONOMOUS
MICROGRID
In an autonomous microgrid, all the DGs are responsible for maintaining the system voltage and
frequency while sharing the power and reactive power.
In this chapter, stability of multiple converter based autonomous microgrid is studied through
the eigenvalue analysis. The VSC of each DG with its state feedback and droop controllers are
modeled in the state space domain. Each DG is referred to a common reference frame. The network
and loads are also modeled separately. As the converters operate in high frequency mode, the network
dynamics are not neglected [79]. Hence the overall system is represented in differential equation form
rather than differential-algebraic form. The models of the DGs, loads and network are connected
together to get complete generalized model of an autonomous microgrid. A detail eigenvalue analysis
is carried out to identify the trajectory of the eigenvalues with respect to the droop control parameters.
Also the effect of droop control parameters on system stability is investigated when system
configuration changes. A sensitivity analysis is also performed to detect the modes participation to
state variables. The eigenvalue analysis results are verified through simulation studies using
PSCAD/EMTDC. It has been shown that the stability predicted by the eigenvalue analysis is fairly
accurate.
6.1 CONVERTER STRUCTURE AND CONTROL
All the DGs are assumed to be an ideal dc voltage source supplying a voltage of Vdc to the VSC. The
structure of the VSC is as shown in Appendix A.
The following state vector is chosen
[ ]cfcfT viix 2= (6.1)
where converter output voltage is the same as the voltage across the filter capacitor vcf.
88
The control action results in perfect tracking when the error is within limit [80].
6.2 DROOP CONTROL AND DG REFERENCE GENERATION
The same control strategy, as discussed in this section, is applied to all the DGs. It is assumed total
power demand in the microgrid can be supplied by the DGs and no load shedding is required. The
output voltages of the converters are controlled to share this load proportional to the rating of the
DGs. As an output inductance is connected to each of the VSCs, the real and reactive power injection
from the DG source to the microgrid can be controlled by changing voltage magnitude and its angle
[53]. Fig. 3.1 shows the power flow from a DG to the microgrid where the rms values of the voltages
and current are shown and the output impedance is denoted by jXf. It is to be noted that real and
reactive power (P and Q) shown in the figure are average values.
6.2.1. DROOP CONTROL
The power sharing among the converter interfaced sources is achieved through angle droop
control as discussed in Section 2.2 of Chapter 2.
6.2.2 DG REFERENCE GENERATION
It is evident that the reference for all the elements of the states, given in (6.1), is required for state
feedback. Since V and δ are obtained from the droop equation, the reference for the capacitor voltage
and current are given by
( )δω += tVvcfref cos (6.2)
( )δωω += tCVi fcfref sin (6.3)
The reference for the current i2 can be calculated as
f
tcfref jX
vvi
−=2
89
The above calculation will need a phase shifter for the instantaneous current reference. This may not
be desirable. Hence the measured values of the average real and reactive power output of the VSC can
be used to find the magnitude and phase angle of the reference rms current. From Fig. 3.1, it can be
seen that
( )PQIV
QPI ref
cfref /tanand 1
2
22
2−−=∠
+= δ
Hence the current reference can be given as
( )refrefref ItIi 222 cos ∠+= ω (6.4)
6.3 STATE SPACE MODEL OF AUTONOMOUS MICROGRID
The stability of a microgrid needs to be studied through the analysis of state-space models, and so
suitable models of converters are needed to complement the well-established models of rotating
machines. As machine models include features such as automatic voltage regulators and wash-out
functions, the converter model should also include the internal control loops [51]. In an autonomous
microgrid that contains converter based DGs only, the fast switching action can influence the network
dynamics [51]. Hence the network is modeled by differential equations rather than algebraic equations
for stability investigation. So far we have presented the single-phase control of the converter.
However, for the analysis of the total microgrid system, a common reference frame is chosen and the
system voltages and currents are converted in a DQ reference frame.
Fig. 6.1 shows the block diagram of the complete microgrid system containing Z number of DGs. It
is assumed that the model of each of DGs is same. This includes the VSC with its state feedback
controller, droop controller and the interface block that connects the converter to the network. The
system equations are nonlinear and thus they are linearized to perform eigenvalue analysis. The linear
quantities are denoted by the prefix ∆. The measured real and reactive power output (P, Q) of
converter is fed to the droop controller, while voltage reference (vcfref, ref), set by droop controller,
is fed back to the converter. The DGs are connected to the network through the interface block which
convert the input/output signal from DG reference frame to the common reference frame and vice
versa. Each DG block has, current output to the network, which is converter output current (i2D,
90
i2Q) and network voltage as input (vtD, vtQ). Similarly, the input to the load model is the network
voltage at the connected nodes (vtD, vtQ) and its output is the load current (iLoadDQ). The state space
equations of the DG-VSC, load and network are derived separately in a modular fashion. These are
then combined together depending on the network structure to get the overall microgrid system model.
Fig. 6.1. Interconnection diagram of the complete microgrid system.
6.3.1 CONVERTER MODEL
From equivalent circuit shown in Fig.A.4 of Appendix-A, the following equations are obtained for
each of the phases of the three-phase system
( )T
dccf
T
T
L
Vuvi
LR
dtdi .
11 +−
+−= (6.5)
( )f
cf
Cii
dt
dv 21 −= (6.6)
dtdi
Lvv ftcf2=− (6.7)
Equations (6.5-6.7) are translated into a d-q reference frame of converter output voltages, rotating at
system frequency , where a-b-c to d-q transformation matrix P is given by
91
( )
( )
+−
−−−
+
−
=
21
21
21
32
sin3
2sinsin
32
cos3
2coscos
32 πωπωω
πωπωω
ttt
ttt
P
Defining a state vector as
Tcfqcfdqdqdi vviiiix ][ 2211=
the state equation in the d-q frame is given by
tdqcdqiii vBuBxAx 21 ++= (6.8)
In (6.8), the matrices are
−−
−
−
−−−
−−
=
01
01
0
001
01
10000
01
000
1000
01
00
ω
ω
ω
ω
ω
ω
ff
ff
f
f
TT
T
TT
T
i
CC
CC
L
L
LLR
LLR
A
−
−
=
=
0000
10
01
0000
and0
0000000
0
0
21
f
fT
dc
T
dc
L
LB
LV
LV
B
It is assumed here that the tracking is perfect and hence, in the limit, u can be represented by uc. ucdq
can be expressed as
( ) ( )( )
( )cfrefdqcfrefdq
refdqcfdqdqdq
cfrefdqcfdq
cfrefdqdqdqrefdqdqcdq
vkik
ikvkikkik
vvk
iiikiiku
32
21321212
3
212221
−−
−−−+−=
−−
−−−−−=
(6.9)
92
The above equation can be written in matrix form as
refdqiiiq
d yHxGu
u+=
(6.10)
where,
( )( )
−−−−−−
=3122
3122
000
000
kkkk
kkkkGi
−−−−−−
=321
321
000
000
kkk
kkkH i
Tcfrefqcfrefdcfrefqcfrefdrefqrefdrefdq vviiiiy ][ 22=
Substituting (6.9) into (6.10) we get
( ) tdqrefdqiiii vByHBxGBAx 2111 +++= (6.11)
Since Vdc is assumed to be constant, the linearization of (6.11) will not alter B1. This linearization
results in
tdqrefdqCONViCONVi vByBxAx ∆+∆+∆=∆ 2 (6.12)
where , ACONV = Ai + B1Gi and BCONV = BiHi.
The current references can be expressed in terms of the voltage reference as
∆∆
−=
∆∆
cfrefq
cfrefd
f
f
cfrefq
cfrefd
v
v
C
C
ii
00
ωω
(6.13)
∆∆
−+
∆∆
−=
∆∆
tq
td
f
f
cfrefq
cfrefd
f
f
refq
refd
vv
L
Lvv
L
L
i
i
01
10
01
10
2
2
ω
ω
ω
ω (6.14)
Combining (6.13) and (6.14), the reference vector is given as
tdqcfrefdqrefdq vMvMy ∆+∆= 21 (6.15)
where
93
−
=
−
−
=
00
00
00
00
01
10
and
10
01
0
0
01
10
21f
f
f
f
f
f
L
L
M
C
CL
L
Mω
ω
ωω
ω
ω
Combing (6.12) and (6.15) we get the converter model as
tdqBUScfrefdqTiCONVi vBvBxAx ∆+∆+∆=∆ (6.16)
where BT = BCONVM1 and BBUS = BCONV (M2 + B2).
6.3.2 DROOP CONTROLLER
The droop controller set the references for converter output voltage magnitude and its angle. The
output voltage of the converter is equal to voltage across the capacitor Cf. The measured instantaneous
real and reactive power are passed through two lowpass filters to obtain the average values of P and Q
respectively. These can be expressed as
( )
( )dcfqqcfdC
C
C
C
qcfqdcfdC
C
C
C
ivivs
Qs
Q
ivivs
Ps
P
22
22
ˆ
ˆ
−+
=+
=
++
=+
=
ωω
ωω
ωω
ωω
(6.17)
where c is cut-off frequency of the filter. Linearizing equation (6.17) we get,
∆∆
+
∆∆
−−
=
∆∆
dq
cfdqP
C
C
i
vB
QP
QP
20
0
ωω
(6.18)
where,
−−=
000202
000202
cfdCcfdCdCqC
cfqCcfdCqCdCP VVII
VVIIB
ωωωωωωωω
and 0 indicates the nominal values.
Let us now define the three-phase reference filter capacitor voltages as
94
+
−=
)3
2cos(
)3
2cos(
)cos(
πω
πω
ω
tV
tV
tV
v
v
v
cfref
cfref
cfref
c
b
a
(6.19)
Then using the transformation matrix P we get
−−+−−=
−+++=
)3
42sin()
34
2sin()2sin(3
)3
2(cos)
32
(cos)(cos3
2 222
πωπωω
πωπωω
tttV
v
tttV
v
cfrefcfrefq
cfrefcfrefd
From the above equation we get
0 and == cfrefqcfrefcfrefd vVv (6.20)
It can be seen from Fig. 3.3 that vcf is the converter output voltage. Hence from the droop equation and
(6.20), we can write the voltage droop equation as
( )ratedratedcfrefcfrefd QQnVVv −−== (6.21)
Linearizing and combining the droop equation angle droop (Section 2.2 of Chapter 2) and (6.21) them
we get the droop controller model as
∆∆∆
−−
=
∆∆∆
Q
Pn
m
v
v
cfrefq
cfrefd
ref δδ
00000
00 (6.22)
6.3.3 COMBINED CONVERTER-DROOP CONTROL MODEL
Let us now substitute Vcfrefdq from (6.22) in the converter model of (6.16). This gives
tdqBUSGiCONVi vBQP
BxAx ∆+
∆∆
+∆=∆ (6.23)
where,
−=
000 n
BB TG .
Combining the converter and droop controller state vectors together an extended state vector is
formed as
95
[ ]TcfqcfdqdqdCONV vviiiiQPx 2211=
The combined state equation is then written as
tdqcCONVcCONV vBxAx ∆+∆=∆ (6.24)
where
Ο=
= ×
BUSc
CONVG
ccc B
BAB
AAA 221211 and
where Oi×j represents null matrix of dimension i×j and
−−
=C
CcA
ωω0
011
−−=
020200
02020012 00
00
dCqCcfdCcfqC
qCdCcfqCcfdCc IIVV
IIVVA ωωωω
ωωωω
6.3.4 TRANSFORMATION TO COMMON REFERENCE FRAME
Since all the converters are modeled individually with their own d-q axis reference, they need to be
transformed into common reference D-Q frame. The small signal output current of the converter in D-
Q frame is
δ∆+∆=∆ CdqSDQ TiTi 22 (6.25)
where
−−−
=
−=
020020
020020
00
00
sincoscossin
cossinsincos
δδδδ
δδδδ
qd
qdCS II
IITT
Similarly the input to the converter from the network, the network voltage can be expressed in as,
δ∆+∆=∆ −− 11VtDQStdq TvTV (6.26)
where
−−+−
=−
0000
00001
sincoscossin
δδδδ
QtDt
QtDtV VV
VVT
96
Substituting equation (6.26) in (6.24) we get
δ∆+∆+∆=∆ 1PtDQLCONVcCONV BvBxAx (6.27)
where BL = BC TS−1 and BP1 = BC TV
−1
It is to be noted that in equation (6.27) can be expressed as the droop controller output equation
in terms of P. It is assumed that the change in angle in the converters is instantaneous such that the
converter produces the demanded angle (ref). The state equation (6.27) can be written as
tDQLCONVLCONV vBxAx ∆+∆=∆ (6.28)
where [ ]781 ×Ο−= PcL BmAA .
Similarly (6.25) is expressed as
CONVPDQ XCi ∆=∆ 2 (6.29)
where
−=
00cossin000
00sincos000
0021
0011
δδδδ
C
CCP and
)sincos(
)cossin(
02002021
02002011
δδδδ
qd
qd
IImC
IImC
−−=
+=
Let us assume that the microgrid has Z number of DGs with their state space and output equations
being given by
ZiXCi
vBxAx
CONViPiDQi
tDQiLiCONViLiCONVi ,,1,2
=
∆=∆∆+∆=∆
(6.30)
Then the combined state space equation including all the converters in the system is written as
ZZZ
tZZZZZ
xCi
vBxAx
∆=∆∆+∆=∆
2
(6.31)
where AZ, BZ and CZ are block diagonal matrices, given by
( )( )( )PZPPZ
LZLLZ
LZLLZ
CCCC
BBBB
AAAA
21
21
21
diag
diagdiag
===
The input, output and state vectors of the state space equations are defined as
97
∆
∆∆
=∆
∆
∆∆
=∆
∆
∆∆
=∆
CONVZ
CONV
CONV
Z
DQZ
DQ
DQ
Z
tDQZ
tDQ
tDQ
tZ
x
x
x
x
i
i
i
i
v
v
v
v
2
1
2
22
12
22
1
6.3.5 NETWORK AND LOAD MODELING
The network and the loads are modeled as shown in [51]. We have assumed that there are L number
of loads, N number of network nodes and LN number of lines. The state space equation of the ith load
connected at jth node is given by
tDQiLoadiLoadDQiLoadiLoadDQi vBiAi ∆+∆=∆ (6.32)
where
=
−−
−=
Loadi
LoadiLoadi
Loadi
Loadi
Loadi
Loadi
Loadi
L
LB
LR
LR
A1
0
01
ω
ω
Combining the total of L number of loads together, we get
tLoadLoadLoadLoadLoad vBiAi ∆+∆=∆ (6.33)
where ALoad and BLoad are block diagonal matrices and
∆
∆∆
=∆
∆
∆∆
=∆
tDQL
tDQ
tDQ
tLoad
LoadL
Load
Load
Load
v
v
v
v
i
i
i
i
2
1
2
1
In a similar way the state space equation for the network is written as
tLNLNLNDQLNLN vBiAi ∆+∆=∆ (6.34)
where ALN and BLN are block diagonal matrices containing the
individual state matrices for the ith line connected between jth and kth node. These matrices are given
by
98
LNi
LR
LR
A
Linei
Linei
Linei
Linei
Ni ,,1, =
−−
−=
ω
ω
−
−=
...1
0...1
0...
...01
...01
...
LinekLinej
LinekLinejNi
LL
LLB
It can be seen that the matrix BNi contains elements only pertaining to nodes j and k.
6.3.6. COMPLETE MICROGRID MODEL
Once the converters, network and loads are modeled, they are combined to get the complete model
of the microgrid. Between each network node and ground a virtual resistance (rN) of large magnitude
( 1000 ) is chosen to ensure a well defined node voltage [51]. Suppose node i contains both a
converter and a load. Then the node voltage can be written in terms of the three currents, e.g.,
converter output currents, load currents and line currents in the network as
( )LineDQiLoadDQiDQiNtDQi iiirv ∆+∆−∆=∆ 2 (6.35)
Therefore the node voltage equation for the complete microgrid can be written as
( )LineNETLoadLOADZCONVNtM iMiMiMRv ∆+∆+∆=∆ 2 (6.36)
where, the matrix RN is defined as the 2N×2N matrix with diagonal elements equal to rN. The MCONV is
a 2N×2Z matrix. Let us assume that the ith converter is connected with the jth node. Then the (j,i)
element of the matrix is 1, all other element in the row is 0. Similarly MNET is 2N×2LN matrix, whose
(j,i) element will be + 1 or − 1, depending on whether the current entering or leaving the node, if the
ith line is connected to the jth node. MLOAD is the 2N×2L matrix with an entry of − 1 for the nodes
where the loads are connected.
It is to be noted that in (6.31) the state space equation for DGs, is derived for the network nodes
where the DGs are connected. Similarly the state space equation for load and lines are derived for the
point of load and line connection in the network. To derive a general equation for the DGs taking all
the network nodes into account, (6.31) can be written as
99
ZZZ
tMZZZZ
xCi
vBxAx
∆=∆∆+∆=∆
2
1 (6.37)
where vtM represents the complete network voltage vector, considering all the network nodes. BZ1 can
be derived from BZ where the diagonal terms are zero if no DG is connected to that node and BLi for
the ith node if a DG is connected to that node.
Similarly the load and line equations (6.33) and (6.34) can be represented in terms of all the
network nodes as
tMLoadLoadLoadLoad vBiAi ∆+∆=∆ 1 (6.38)
tMLNLNDQLNLN vBiAi ∆+∆=∆ 1 (6.39)
The total microgrid model is then derived by combining equation (6.36), (6.37), (6.38) and (6.39)
∆∆∆
=
∆∆∆
Load
LN
Z
MG
Load
LN
Z
i
i
x
A
i
i
x
(6.40)
The state matrix of the whole microgrid AMG is given
++
+=
LOADNLOADLOADNETNLOADZCONVNLOAD
LOADNLNNETNLNLNZCONVNLN
LOADNZNETNZZCONVNZZ
MG
MRBAMRBCMRB
MRBMRBACMRB
MRBMRBCMRBA
A
111
111
111
(6.41)
6.4 SYSTEM STRUCTURE AND MODEL OF AUTONOMOUS MICROGRID
EXAMPLE
The structure of the study system is shown in Fig.6.2. The real and reactive powers supplied
by the DGs are denoted by Pi, Qi, i = 1, …, 3. The real and reactive power demand from the loads are
denoted by PLi, QLi, i = 1, …, 3. The load and line impedances are also shown in the figure.
100
Fig. 6.2. Microgrid system under consideration.
For the system shown in Fig. 6.2, Z = 3. Then the matrices defined in the previous section are given
below.
DG:
=
=
=
3
2
1
3
2
1
3
2
1
00
0000
,
00
00
00
,
00
00
00
P
P
P
Z
L
L
L
Z
L
L
L
Z
C
CC
C
B
B
B
B
A
A
A
A
Line:
=
=
2
1
2
1 ,0
0
N
NLN
N
NLN B
BB
A
AA
Load:
=
=
3
2
1
3
2
1
,
00
00
00
Load
Load
Load
Load
Load
Load
Load
Load
B
B
B
B
A
A
A
A
These three M matrixes in (6.43) are calculated for the given example as
6IMCONV =
where I6 is a 6×6 identity matrix and
−−
−−
−−
=
001000
000100100000
010000
000010000001
LOADM
101
−−
−−
=
1000
01001010
0101
00100001
NETM
The matrix AMG is then derived from these matrices for eigenvalue analysis.
6.5 EIGENVALUE ANALYSIS OF MICROGRID
The parameters chosen for the system shown in Fig. 6.2 are listed in Table-6.1. When the system
operates with the parameters given in Table-6.1, it is assumed to be operating in the nominal operating
condition. The eigenvalues of the system for this nominal operating condition are shown in Fig. 6.3. It
can be seen that the eigenvalues, based on their damping (real component), are placed on four
different clusters. It will be shown that the dominant eigenvalues of cluster 1 are sensitive to the
changes in the droop controller parameters. The eigenvalues of clusters 2, 3 and 4 are sensitive to the
other parameters, like filter, state feedback controller, load etc., and their effects are not investigated
here.
TABLE-6.1: NOMINAL SYSTEM PARAMETERS
System Quantities Values
Systems frequency 50 Hz
Source voltage (Vs) 11 kV rms (L-L)
Line impedance Line-1: RLine1=3.83Ω, LLine1 =0.0053 H (R/X>2)
Line-2: RLine2=5.83Ω, LLine2 =0.0308 H (R/X<1)
Load
RLOAD1 = 420.0 Ω, LLOAD1 = 0.5 mH
RLOAD2 = 333.0 Ω, LLOAD2 = 0.5 mH
RLOAD3 = 420.0 Ω, LLOAD3 = 0.5 mH
DGs and Controller
DC voltage (Vdc1, Vdc2, Vdc3)
Transformer rating
VSC losses (Rf)
Filter capacitance (Cf)
Filter Inductances (Lf)
3.5 kV
3 kV/11 kV, 0.5 MVA, 2.5%
1.5 Ω
185 µF
20 mh
State Feedback
Controller (K)
[1.6963 0.3449 1.6959]
Droop Coefficients
m1 = m2 = m3 = m
n1 = n2 = n3 = n
4.18×10−5 rad/W
2.272×10−4 V/Var
Low pass Filter cut-off C 31.4 rad/sec
102
Fig. 6.3. Eigenvalues for nominal operating condition.
Table-6.2 lists the modes of the eigenvalues of cluster 1 and their participation factor on the real
and reactive power state variable of the three DGs. In this table, mode Q-1-2 indicates that this mode
is sensitive to the reactive powers of DG-1 and DG-2. In a similar way, all the other modes are
defined.
TABLE-6.2: MODE PARTICIPATION FACTORS.
Dominant Modes
Mode Q-1-2 Mode Q-1-2-3 Mode PQ-1-2-3
State Participation State Participation State Participation
P1 0.0008 P1 0.0006 P1 0.1689
Q1 0.4600 Q1 0.2216 Q1 0.1600
P2 0.0010 P2 0.0003 P2 0.1683
Q2 0.5385 Q2 0.1366 Q2 0.164
P3 0.0000 P3 0.0000 P3 0.1679
Q3 0.0035 Q3 0.6428 Q3 0.1804
Not Dominant Modes
Mode P-1-2 Mode P-1-3
P1 0.1929 P1 0.1199
Q1 0.0005 Q1 0.0005
P2 0.2357 P3 0.2291
Q2 0.0007 Q3 0.0005
For example, PQ-1-2-3 is sensitive to real and reactive power of all three DGs. This strong real and
reactive coupling is due to highly resistive lines in the network. It can also be seen that the modes P-1-
2 and P-1-3 are not very sensitive. However the DG real powers have some influence on them
103
Fig. 6.4 shows the locus of the eigenvalues of cluster 1 as the droop controller real power coefficient
m changes. It can be seen that for a very high value of m (6.18×10−5), a complex conjugate pair the
eigenvalues almost reaches the imaginary axis indicating a low system stability. For m = 8.18×10−5,
the above pair crosses the imaginary axis and three more eigenvalues reach the imaginary axis,
indicating an unstable operation
Fig. 6.5 shows the locus of the eigenvalues of cluster 1 as the droop controller reactive power
coefficient n changes. It can be seen that this coefficient also has significant effect on system stability.
It can be seen that a complex conjugate pair of eigenvalues of cluster 1 reaches the imaginary axis
Fig. 6.4. Eigenvalue locus with real power droop gain change.
Fig. 6.5. Eigenvalue locus with reactive power droop gain change.
104
Fig. 6.6. Eigenvalue locus without DG-3.
when n = 2.5×10−3. The results of the eigenvalue analysis will be validated through simulation studies
in the next section, where the effect of these droop controller parameters will be clearly shown.
Fig. 6.6 shows the eigenvalue locus as a function of the real power coefficient when DG-3 removed
from the system, with the loads reaming the same. It can be seen that the eigenvalues remain stable
even with m = 8.18×10−5, for which the 3-DG system was unstable (Fig. 6.4). The effect of reduction
of the size of the microgrid is further investigated through simulation studies in the next section.
It is to be mentioned here that the gains of the state feedback controllers have no adverse effects on
the system stability. The controllers are designed using LQR, which is very robust. This has been
observed by changing the cost function in the LQR design and the results are not shown here.
6.6 SIMULATION STUDIES
Simulation studies are carried out in PSCAD/EMTDC (version 4.2). Different configurations of load
and its sharing are considered. The DGs are considered as inertia less dc source supplied through a
VSC. The system data used for eigenvalue analysis (Table-6.1) are also used here. It is to be noted
that R/L value of Line-1 in Fig. 6.2 is very high. Hence there is a strong real and reactive power
coupling present in the system. The power sharing accuracy will improve further with inductive line
where the real and reactive power coupling is much weaker. The nominal values of the droop
controller parameter are chosen such that there is 3% voltage drop with the maximum reactive power
output.
105
6.6.1 CASE 1: FULL SYSTEM OF FIG. 6.2 (3 DG AND 3 LOADS)
In this case it is assumed that all the DGs and loads are connected in the system shown in Fig.6.2.
The nominal values of controller parameters, given in Table-6.1, are considered here. With the system
operating in the steady state, load 1 is increased by 0.45 MW at 0.1 s. The results are shown in Fig.
6.7. The system takes around 5-6 cycles to reach steady state.
From Fig. 6.4, it can be seen that the system becomes unstable when m = 8.18×10−5 rad/W. With
the system operating in the steady state with the nominal value of m, which is suddenly changed to
8.18×10−5 at 0.05 s. The unstable system response is shown in Fig. 6.8.
Similarly for n = 2.5×10−3, the dominant eigenvalues are oscillatory. This can be observed from Fig.
6.9, where n is changed to this value from the nominal value at 0.1 s. Figs. 6.8 and 6.9 validate the
eigenvalue study.
6.6.2 CASE 2: THE EFFECT OF SYSTEM REDUCTION
In this section, we shall investigate the effect of the reduction of loads, lines and DGs on the system
stability. From Fig. 6.4, it can be seen that the full system is oscillatory for m = 6.18×10−5. This is also
evident from Fig. 6.10 (a), where a sustained oscillation can be observed following a small (0.15 MW)
change in load 1 at 0.1 s. The response for the same load change is shown in Fig. 6.10 (b), when DG-3
is not operational. From the eigenvalue locus of Fig. 6.6, it can be seen that the system remains stable
for this condition. This is also evident from Fig. 6.10 (b).
With same value of m and load change as above, the system is simulated first with DG-3 and line 2
removed. This implies that DG-1, DG-2 and load-1 and load-3 remain in the system. Fig. 6.11 (a)
shows the real power sharing. Even with high value of m, the system remains stable. In Fig.6.11 (b),
the real power sharing is shown when only DG-1, DG-3 and load 3 remain in the system. Though high
line impedance between the DG-1 and DG-3 makes the load sharing less accurate, the system reaches
much quickly than when 2 DGs and 2 loads are present. (Fig. 6.11 (a)).
106
Fig. 6.7. Real and reactive power during a change in load 1.
Fig. 6.8. Unstable operation with m = 8.18×10−5 rad/W.
Fig. 6.9. Marginally stable operation with n = 2.5×10−3 V/VAr.
107
Fig. 6.10. System response 3 and 2 DGs for m = 6.18×10−5 rad/W.
Fig. 6.11. System response for different system configuration.
6.7 IMPROVEMENT IN STABILITY WITH SUPPLEMENTARY DROOP
CONTROL
The schematic layout of the supplementary loop around the conventional droop control is shown in
Fig. 6.12. The real power output Pi, of the ith converter is fed through a high pass washout circuit (with
0.05 s time constant) to capture the oscillatory behavior, eliminating the dc component, ∆Pi about the
steady-state value Pi. The supplementary control signal, ∆vdrefi, modulates the output of the droop
controller to generate a modified d-axis voltage reference, vdrefi´ for each converter. The droop
equation is then modified for the ith converter as
( )( ) iiratediiratediii
iiratediiratediii
VQQnVVVV
PPm
∆+−×−=∆+=
∆+−×−=∆+=*
* δδδδδ (6.42)
108
where ∆Vi and ∆i are the voltage magnitude and voltage angle correction by the supplementary
controller signal ∆Vdrefi. The resultant voltage reference for the converter is
qrefidrefiii VjVV ∗+=∠ ** δ (6.43)
Fig. 6.12. Supplementary Droop Controller Configuration
When the DGs are supplying rated power, the angle of the converter output voltage is rated. As the
irated = miPirated, the rated angles for all the DGs are 0.1 rad,. It is to be noted that the rated angles are
chosen so that when the output power of the DGs are zero, the reference output voltage angle is zero.
The test system considered for this study has three critical oscillatory modes with frequencies in the
vicinity of 50 Hz which require stability enhancement. To ensure adequate controllability and
observability of these modes, each of the four converters were equipped with a separate
supplementary control loop. The structure of each controller was fixed a priori and is comprised of
three lead-lag blocks and a gain as shown in Fig. 6.13 for the ith converter. The calculation of these
unknown gains, Ki, i=1,2,3,4, and the time constants Tij, i =1,2,3,4; j = 1,2,..,6, are formulated as a
parameter optimization problem with the constraint on stability of the closed-loop over a range of
operating conditions. A lower limit of 0.01 and an upper limit of 100 were imposed on the search
space of the denominator time constants to ensure stable poles and fast enough controller response.
Simultaneous design of the four decentralized controllers eliminates possible interactions and ensures
overall stability due to their combined action.
Fig. 6.13. Supplementary controller structure
It is not straight forward to solve the above parameter optimization problems using analytical
techniques [80, 81], one of the reasons being lack of proper choice of initial guess. Hence, swarm
optimization [82] – one of the standard evolutionary techniques – was employed here. The optimum
gains and time constants obtained are shown in Table 6.3. Parameters of the supplementary controllers
109
are tuned simultaneously to eliminate possible interactions. No constraint on gain of the controller and
lead time constant of each lead-lag compensator block have been imposed during the optimization
stage to allow more search space. This has resulted in one negative gain and a few right half plane
zeros in the compensator. If the phase compensation required is less than zero, it is more effective (in
terms of the number of lead-lag blocks required) to use a negative feedback (180 degrees) and to
compensate for only the difference between 180 degrees and original phase compensation. For the
first channel with negative gain (K1) this turned out to be the case. Also a non minimum phase
feedback controller does not imply a non minimum phase closed loop system. The step responses did
not show any evidence of non minimum phase behavior. Constraining feedback to be minimum phase
for this problem with a wide range of droop gains resulted in no feasible solution. Permitting non
minimum phase feedback enabled a feasible solution to be found. If there were less onerous
requirement on the range of gain then a feasible solution become possible with a minimum phase
constraint. However we placed the major emphasis in accurate sharing and the optimization process
results in right half plane zeros as mentioned above.
A standard lead lag compensation structure, which is most widely adopted and easily
implementable structure of different kind of supplementary controllers in power system application
such as PSS (Power System Stabilizer), is adopted during control design.
Table-6.3: PARAMETERS OF THE SUPPLEMENTARY DROOP CONTROL LOOP
Parameters Conv 1
Conv 2
Conv 3
Conv 4
Ki -13.8409 4.8089 12.3064 12.4806
Ti1 13.1384 -12.805 14.6033 14.8943 Ti2 8.6429 12.4003 13.9471 1.0895 Ti3 15.6881 16.1046 -1.1439 -14.482 Ti4 0.3669 0.01 6.1067 0.01 Ti5 3.8954 5.2054 0.01 0.4818 Ti6 0.2475 0.4223 0.01 5.9059
As high droop gains are needed for proper load sharing, the proposed supplementary controller is
aimed to guarantee the system stability even with high droop gains. Note that the controller gains were
optimized to obtain a good performance over a range of operating conditions despite the requirement
of stabilizing a family of a number of unstable plants with a fixed structure low order compensator.
This has resulted in the change of frequencies of the dominant eigenvalues. However, as the
frequencies did not migrate either up to the switching range or down to the low oscillatory frequency
range, it was not necessary to modify the performance index to avoid the frequency shift.
110
6.7.1 TEST SYSTEM
The structure of the study system is shown in Fig. 6.14. The real and reactive powers supplied by
the DGs are denoted by Pi, Qi, i = 1, …, 4. The real and reactive power demand from the loads are
denoted by PLi, QLi, i = 1, …, 5. The line impedances are denoted by Z12-Z89 in the figure. The system
matrix AT is derived with all the parameter shown in Table-6.4 for eigenvalue analysis.
Fig. 6.14. Microgrid system under consideration.
6.7.2 SIMULATION STUDIES WITH SUPPLEMENTARY DROOP CONTROLLER Different configurations of load and power sharing of the DGs are considered to ensure that the
propose controller provide a stable operation in all the situations . The DGs are considered as inertia
less dc source supplied through a VSC.
6.7.2.1 CASE 1: FULL SYSTEM OF FIG. 6 WITH LOWER DROOP GAINS
In this case, it is assumed that all the DGs and loads are connected to the microgrid as shown in Fig.
6. The lower droop gains values of controller parameters, given in Table-6.4, are considered here.
With the system operating in the steady state, Ld1 changed to 155 kW from 100 kW at 0.25 s. Fig.
6.15 (a) shows the real power sharing while Fig. 6.15 (b) shows the three phase terminal voltages of
DG-1. It can be seen that the controller provides proper load sharing with stable system operation.
6.7.2.2 CASE 2: REDUCED SYSTEM WITH LOWER DROOP GAINS
To investigate the load sharing with reduced system, DG-2 and DG-3 are disconnected at 0.25 s and
the total power is shared by DG-1 and DG-4 as shown in Fig. 6.16. At 1.3 s, Ld2 Ld3, Ld4 and Ld5 are
also disconnected. The two DGs connected to the microgrid supply the 100 kW load, Ld1. It can be
seen that system operation is stable. However due to weak system condition, as the DGs are located
geographically far from each other, they can not share load in the desired ratio of 1:1.33
111
Fig. 6.15. Real and reactive power during a change in load 1.
Fig. 6.16.Power sharing with reduced system
6.7.2.3. CASE 3: SYSTEM STABILITY WITH HIGH DROOP GAIN
As discussed before, the power sharing can be made independent of the system condition and the
converter output reactance by choosing high droop controller gains. The eigenvalue analysis, on the
other hand, predicted system instability for such gains. To investigated the system stability with high
droop gain, the full system (Case-1) is operated first with lower value of droop gain and at 0.2 s, the
droop gains are changed to higher values as mentioned in Table-I. Fig. 6.17 (a) shows the system
response with only droop controller while Fig. 6.17 (b) shows system response with proposed
supplementary droop controller.
112
Fig. 6.17. System stability with high droop gain.
6.7.2.4. CASE 4: POWER SHARING WITH THE PROPOSED SUPPLEMENTARY CONTROLLER
In this section, we shall investigate the load sharing capability with proposed supplementary
controller and the system stability. All the simulations are done with high droop controller gain as
mentioned in Table-6.4. With the system running in steady state and supplying power to all the loads,
Ld5 is disconnected from the microgrid at 0.25 s. Fig. 6.18 shows the system response. The power
output of all the converters reduces proportionally and system attains steady state within 8-10 cycles.
The droop controller converter output voltage reference angle and supplementary controller d-axis
voltage modulation is shown in Fig. 6.19, which clearly shows a damping type controller with 90°
phase shift during transients.
Fig. 6.18. Power sharing with proposed controller.
113
Fig. 6.19.Droop controller and supplementary controller output.
6.7.2.5. CASE 5: POWER SHARING WITH THE PROPOSED CONTROLLER IN REDUCED SYSTEM
The power sharing with the proposed controller in the reduced system is investigated in this section.
DG-1 is disconnected first at 0.25 s when system is running in steady state. Fig. 6.20 shows the
response and it can be seen that the other three DGs supply the extra power requirement. Ld5 is
disconnected at 1.3 s and the DG outputs reduce proportionally. From the system response and
numerical values (Appendix-A) it can be concluded that the DGs share the loads as desired while
ensuring stable operation of the system.
Fig. 6.20. System response for different system configuration.
To validate the performance of the supplementary proposed controller, the microgrid is operated
similar situation as described in Case 2 with reduced system. Fig. 6.21 shows the system response.
114
Fig. 6.21. Power sharing in reduced system.
TABLE-6.4: NOMINAL SYSTEM PARAMETERS
System Quantities Values
Systems frequency 50 Hz Feeder impedance
Z12 = Z23 = Z34 = Z45 = Z45 = Z56 = Z67 = Z78 = Z89
1.03 + j 4.71 Ω
Load ratings Ld1 Ld2 Ld3 Ld4 Ld5
100 kW and 90 kVAr 120 kW and 110 kVAr 80 kW and 68 kVAr 80 kW and 68 kVAr 90 kW and 70 kVAr
DG ratings (nominal) DG-1 DG-2 DG-3 DG-4
100 kW 200 kW 150 kW 150 kW
Output inductances L1 L2 L3 L4
75 mH 37.5mH 56.4 mH 56.4Mh
System Quantities Values
DGs and VSCs DC voltages (Vdc1 to Vdc4) Transformer rating VSC losses (Rf) Filter capacitance (Cf) Hysteresis constant (h)
3.5 kV 3 kV/11 kV, 0.5 MVA, 2.5% Lf 1.5 Ω 50 µF 10-5
Droop Coefficients Power−−−−angle
(Lower Droop Gains) m1 m2 m3 m4
Power−−−−angle (Higher Droop Gains)
m1 m2 m3 m4
Voltage−−−−Q n1 n2 n3 n4
0.1 rad/MW 0.05 rad/MW 0.075 rad/MW 0.075 rad/MW 1.0 rad/MW 0.5 rad/MW 0.75 rad/MW 0.75 rad/MW 0.04 kV/MVAr 0.02 Kv/MVAr 0.03 Kv/MVAr 0.03 Kv/MVAr
115
6.8 CONCLUSIONS
In this chapter, a linearized state space model of an autonomous microgrid supplied by all converter
based DGs and connected to number of passive loads is formed. The proposed generalized model is
valid even when the network is complex containing any number of DGs and loads. The model is
utilized for eigenvalue analysis around a nominal operating point. A sensitivity analysis is carried out
to indicate the eigenvalue participation on the state variables. It has been shown that real power modes
get affected with the real power droop coefficients, while the reactive power modes are sensitive to
reactive power droop coefficients. Extensive simulation studies are carried out to validate the results
of the eigenvalue analysis. It has been shown that both the results agree with each other.
High gain angle droop control ensures proper load sharing, especially under weak system
conditions, but has a negative impact on the overall stability. This is illustrated through frequency
domain modeling, eigenvalue analysis and time domain simulations. A supplementary loop is
proposed around the primary droop control loop of each DG converter to stabilize the system despite
having high gains that are required for better load sharing. The control loops are based on local power
measurement and modulation of the d-axis voltage reference of each converter. The coordinated
design of supplementary control loops for each DG is formulated as a parameter optimization problem
and is solved using an evolutionary technique. The use of the supplementary droop control loop is
shown to stabilize the system for a range of operating conditions while ensuring satisfactory load
sharing.
116
117
CHAPTER 7
DROOP CONTROL OF CONVERTER INTERFACED MICRO SOURCES IN
RURAL DISTRIBUTED GENERATION
Two methods have been proposed in this chapter for power sharing with VSC connected DGs in a
rural distributed generation. In first method, decentralized operation of DGs without any
communication is investigated. A transformation matrix is derived for control parameters and
feedback gains taking into consideration the R-by-X ratios of the lines. In second method, the angle
droop power sharing controller is modified to accommodate the highly resistive line. The reference
angle of each converter output voltage is modified based on the desired active and reactive power flow
and the line impedances. A minimum amount of communication is needed among the DGs for the
change in reference angle of the output voltage. We have assumed a low-cost web-based
communication system [83-85] for this purpose.
The main focus of this chapter is the development of a graduated set of control algorithms to deal
with different levels of communication infrastructure to support the microgrid with particular
emphasis on highly resistive lines. The accuracy of the controllers is shown in different weak system
conditions where the conventional angle droop fails to share the power as desired due to high coupling
between the real and reactive power. Mathematical derivations and time domain simulations are used
to illustrate the methodologies.
7.1 POWER SHARING WITH ANGLE DROOP AND PROPOSED DROOP
CONTROL
The power sharing with angle droop in a system with two DGs and a load as shown in Fig. 7.1 is
shown in Section 2.2 as
118
rated
rated
PP
mm
PP
2
1
1
2
2
1 =≈ (7.1)
It is evident from (7.1) that the droop coefficients should be inversely proportional to the DG rating
and also the droop coefficients play the dominant role in the power sharing. The error is further
reduced by taking the output inductance (Lf1, Lf2) of the DGs inversely proportional to power rating of
the DGs. The comparison between the performance of this angle droop and a conventional frequency
droop [12] is shown in Section 2.3.
The simple system shown in Fig. 7.1 is used to show the power sharing. In a real system with
number of DGs and loads in different location line impedance will have an impact on the load sharing.
But for a microgrid within a small geographical area, the line inductance will never be very high.
Moreover a high droop coefficient will always play a dominant role and share the power as desired
with a very small deviation.
Fig. 7.1. Power sharing with angle droop.
To control power flow explicitly from any of the DGs to the local bus (e.g., DG-1 and the bus with
voltage V11∠δ11), an output inductance (e.g., Lf1) is required. This output inductance enables us to
decouple the real and reactive power injection. We shall use this structure for controlling power flow
with communication (the 2nd proposed method). However, in the 1st proposed method, the output
inductance is assumed to be zero. In this control method, we do not require a decoupling of real and
reactive power as will be explained in the next sub-section. Also this control is based on the R/X ratio
of the line and therefore the inclusion of output inductance will require the knowledge of the line
length. Note that the output inductance can be taken as zero depending on the converter output filter
structure, discussed in Appendix.
119
7.1.1 PROPOSED CONTROLLER-1 WITHOUT COMMUNICATION
As discussed before, in the rural distribution system, at the medium or low voltage level the lines
are mostly resistive and the values of the line impedances are not negligible. In that case (7.1) is not
valid. In this case we have assumed that the DGs do not have any output inductance, in which case,
Fig.7.1 is redrawn as shown in Fig. 7.2. Here the line reactance (ωLD) value is chosen to be the same
as line resistance value RD.
Fig. 7.2. Power sharing in resistive-inductive line.
The power flow from DG-1 for system shown in Fig.7.2 as
( )[ ]( )[ ]δδδδη
δδδδη−−+−−=
−+−−=
111111111
111111111
cos()sin(
)sin(cos(
VVXVRQ
VXVVRP
DD
DD
where ( )12
12
11 DD XRV +=η . From the above equation, multiplying Q1 by RD1 and subtracting the
product from the multiplication of P1 and XD1 we get
)sin( 11111111 δδ −=− VVQRPX DD (7.2)
In a similar way, we also get
)cos( 11112
111111 δδ −−=+ VVVQXPR DD (7.3)
It is to be noted that DG-1 does not have any control over the load voltage magnitude and angle.
Thus the linearization of (7.2) and (7.3) around the nominal values of V110 and δ110 results in
( ) 11110111101111 )()( VVVVQRPX DD ∆+∆−∆=∆−∆ δδδ (7.4)
111101111 )2( VVVQXPR DD ∆−=∆+∆ (7.5)
where ∆ indicates the perturbed value. From (7.4) and (7.5), the output voltage magnitude and angle
of a DG-1 can be written in terms of real and reactive power as,
120
∆∆
=
∆∆
−=
∆∆−∆
1
1
1
1
1
1
1
1
1
1
1
1
11
11 )()(Q
PTVK
Q
P
ZR
ZX
ZR
ZX
VKV DD
DDδδ
(7.6)
where the impedance Z1 and the matrix K(V) are given by
1
110
1101101
21
211 20
)(−
−=+=
VV
VVVZVKXRZ DD
δ
Defining pseudo real and reactive power as
∆∆
=
′∆′∆
1
1
1
1
Q
PT
Q
P
From equation (7.6) the control strategy can be chosen as
( )
′∆′∆
=
∆∆
1
1
11
11 1Q
PK
V
δ (7.7)
The above equation forms the basis of modified droop sharing where the matrix K(V) is approximated
as K(1) with the assumption that bus voltage is constant at 1 per unit, giving an error in the control
gain of less than 5%. This will have no significant effect on the power sharing. The load bus angle δ is
not measurable at the DG end. The chosen control (7.7) will automatically correct for changes in δ,
while retaining the desired decoupling property.
The droop control equation for DG-1 is then written as
( )( )ratedrated
ratedrated
QQnVV
PPm
1111111
1111111
′−′×′−=′−′×′−= δδ
(7.8)
where the rated powers (P′1rated, Q′1rated) are also represented after multiplying the conversion matrix
[T]. Similar transformation is also used for the rated powers of DG-2 as well. The droop gains of the
both the DGs are also transformed by the matrix T and are given by as
=
′′
=
′′
2
2
2
2
1
1
1
1 and n
mT
n
m
n
mT
n
m (7.9)
where the real and reactive power droop coefficients are
121
rated
rated
rated
rated
nn
andPP
mm
2
1
1
2
2
1
1
2 == (7.10)
Then droop equation (7.8) can be expressed as,
′−′′−′
−
=
rated
rated
rated
rated
PP
n
mT
VV 11
11
1
1
11
11
11
11 δδ (7.11)
This modified angle droop control not only ensures decoupling of the real and reactive power in a
high R/X line, but also provide a rating based power sharing. The control of the output angle results in
a much lower frequency deviation compared to frequency droop as shown in Section 2.3.
7.1.2 PROPOSED CONTROLLER-2 WITH MINIMAL COMMUNICATION
In this sub-section, a droop control is proposed that requires minimal communication. The system
in Fig. 7.1 is considered here and the DGs are connected to the microgrid with their output
inductances.
For small angle difference between the DGs and their respective local buses shown in Fig. 7.1, the
power flow equations of the DGs are given by
22222
11111
PX
PX
=−=−
δδδδ
(7.12)
Both the active and reactive power flow in a highly resistive line are determined by angle difference in
the terminal voltages. The power flow equations over the line for small angle differences can be
written as
222222
111111
PXQR
PXQR
L
L
+−=−
+−=−
δδδδ
(7.13)
where R1= RD1/(V11V), R2 = RD2/(V22V), XL1 = LD1/(V11V) and XL2 = LD2/(V22V).
From (7.13) and (7.14) we get,
2222222
1111111
PXQRPX
PXQRPX
L
L
+−=−
+−=−
δδδδ
(7.14)
The difference between δ1 and δ2 is derived from (7.14) as
122
22222211111121 PXQRPXPXQRPX LL −+−+−=− δδ (7.15)
Again from (2.11) we get,
( )( )rated
ratedratedrated
PPm
PPm
222
1112121
−×+−×−−=− δδδδ
(7.16)
Since the ratio of the droop gains m2:m1 is chosen as the ratio of the rated power P1rated:P2rated, from the
above equation we get
22112121 PmPmratedrated +−−=− δδδδ (7.17)
Equating (7.15) and (7.17) we get,
221121
222222111111
PmPm
PXQRPXPXQRPX
ratedrated
LL
+−−=++−+−
δδ (7.18)
The rated values of the converter output voltage angles are selected with active and reactive power
output of the converter as
2222222
1111111
PXQRPX
PXQRPX
Lrated
Lrated
+−=+−=
δδ
Substituting these values in (7.), we get
rated
rated
PP
mm
PP
PmPm2
1
1
2
2
12211 === (7.19)
It can be seen that the power sharing of the DGs are proportional to their rating. This control
technique shown with above simple example can be extended to multiple DG system. This is
discussed below.
7.1.3 MULTIPLE DG SYSTEM
Fig. 7.3 shows a multiple DG system where three DGs are connected at different location of the
microgrid. The four loads that are connected to the microgrid are shown as Load_1, Load_2, Load_3
and Load_4. The real and reactive power supply from the DGs are denoted by Pi, Qi, i = 1,…, 3. The
real and reactive power flow for different line sections and load demand are shown in Fig. 7.3. The
123
line impedances are denoted as ZDi (= RDi + jXDi), i = 1,…,6. Each of the DG controllers needs to
measure its local quantities only and hence, the real and reactive power flow measurements into and
out of the DG local bus are required. It is to be noted all the line impedances and loads are assumed to
be lumped.
From the power output of DG-3 we can write,
RLRL PXQRPX 36363343 +−=−δδ (7.20)
where R6= RD6/(V33VL4) and XL6= XD6/(V33VL4). Similarly from the DG-2 power output we can write,
RLRL PXQRPX 24242232 +−=− δδ (7.21)
The angle difference between the loads can be represented as,
RLRLLLLL PXQRPXQR 3636353543 +−+−=− δδ (7.22)
From (7.21) and (7.22) we get,
RLR
LLLRLRL
PXQR
PXQRPXQRPX
3636
353524242242
+−+−+−=− δδ
(7.23)
Similarly the power output of DG-1 can be expressed as,
LLRLLLRLR
LLLRLRL
PXQRPXQRPXQR
PXQRPXQRPX
363635352424
232312121141
+−+−+−
+−+−=−δδ (7.24)
It is to be noted that in (7.23) and (7.24), all the active and reactive power quantities, except the first
term, are not locally measureable. The angle difference shown in (7.22) can be measured by DG-3 and
then communicated to DG-2 and DG-1. As these quantities only modify the reference angle to ensure
better load sharing, updates can be done using longer sample rates and a much slower communication
process can achieve that. Furthermore, the first term in (7.23) and (7.24) indicates the primary output
feedback loop that is based on the locally measurable power output of the DG. This control action is
instantaneous and ensures initial load sharing among the DGs. We can write (7.24) as
131211141 δδδδδδ +++=− pL (7.25)
where
124
LLRLLL
RLRLLL
RLRp
PXQRPXQR
PXQRPXQR
PXQRPX
3636353513
2424232312
121211111 ,
+−+−=
+−+−=
+−==
δ
δ
δδ
(7.26)
Fig. 7.3. Multiple DG connected to microgrid.
The longer updates can be made using a web based communication [84] that is discussed below. It is
to be noted that in this proposed method, there is a requirement of site specific tuning of the
parameters for the reference angle generation. This tuning is required to improve the performance of
the site independent decentralized control of Controller-1.
7.1.4 WEB BASED COMMUNICATION
The web based measurement system is shown in Fig. 7.4. The real and reactive power (P and Q)
measured at each DG unit is communicated to a dedicated website or company intranet with the help
of a modem. Assuming that the PQ measurement units are already installed at each DG location, the
equipment needed for each DG unit are a computer to collect the measurements from local and remote
units, and a modem to transmit the measurements to the dedicated website, or to download remote
measurements from it. Fig. 7.4 (a) shows the web connection of all the DGs, while the communication
in each DG is shown in Fig. 7.4 (b). The power monitoring unit sends the real and reactive power
measurement to the computer to calculate 11 as shown in (7.31). The other angle component 12 and
13 are received by the modem and communicated to the DG control unit through the computer. As
mentioned before the main load sharing term δ1p in (7.30) is based on local measurement and so even
in case of communication failure, a rough load sharing is ensured among the DGs. As the DGs are
125
interfaced through converters, the structure and control of the converters are very important for the
power sharing. They are discussed in the next section.
(a)
(b)
Fig. 7.4 (a) Web based PQ monitoring scheme and (b) web based communication for DG-1.
7.2 CONVERTER STRUCTURE AND CONTROL
All the DGs are assumed to be an ideal dc voltage source supplying a voltage of Vdc to the VSC. The
structure of the VSC is same as discussed in Section 2.3 of Chapter 2.
7.2.1 CONVERTER CONTROL
The converters are controlled in state feedback control as described in Appendix A. To facilitate
this, we define set of state vectors as
[ ]cfcT viix 2= (7.27)
126
This control strategy is applied to all the DGs, when operating with the web based communication of
Section 7.1.2. The control law discussed so far is for the system in which the DGs have an output
inductor. This implies the converter output stage has LCL (or T) filter structure. Alternatively, when
the DGs do not have an output inductance, the inductance Lfi is removed and the output filter is a
simple LC filter. The system states are then modified as
[ ]cfcfT vix = (7.28)
However the control law and switching logic remain the same. This control strategy is applied to all
the DGs, when operating without any communication of Section 7.1.1.
It is assumed the total power demand in the microgrid can be supplied by the DGs and no load
shedding is required. The output voltages of the converters are controlled to share this load
proportional to the rating of the DGs as discussed in different droop control methods.
7.2.2. DG REFERENCE GENERATION
It is evident from (7.27) and (7.28) that references for all the elements of the states are required for
state feedback. Since V and δ are obtained from the droop equation, the reference for the capacitor
voltage and current are given by
( )δω += tVvcfref sin (7.29)
( )°++= 90sin δωω tCVi fcfref (7.30)
For the LCL filter, the reference for the current i2 can be calculated as
( )refrefref tIi 222 sin δω += (7.31)
Where,
( )PQV
QPI ref
cfref /tanand 1
2
22
2−−=
+= δδ
127
TABLE-7.1: NOMINAL SYSTEM PARAMETERS
System Quantities Values
Systems frequency 50 Hz
Feeder impedance
ZD1
ZD2
ZD3
ZD3
ZD3
1.0 + j 1.0 Ω
0.4 + j 0.4 Ω
0.5 + j 0.5 Ω
0.4 + j 0.4 Ω
0.4 + j 0.4 Ω
Load ratings
Load1
Load2
Load3
Load4
13.3 Kw and 7.75 kVAr
11.2 kW and 6.60 kVAr
27.0 kW and 7.0 kVAr
23.2 kW and 6.1 kVAr
DG ratings (nominal)
DG-1
DG-2
DG-3
30 kW
20 kW
20 kW
Output inductances
L1
L2
L3
0.75 mH
1.125mH
1.125mH
DGs and VSCs
DC voltages (Vdc1 to Vdc4)
Transformer rating
VSC losses (Rf)
Filter capacitance (Cf)
Hysteresis constant (h)
0.220 kV
0.220 kV/0.440 kV, 0.5
MVA, 2.5% Lf
1.5 Ω
50 µF
10-5
Droop Coefficients
Power−−−−angle
m1
m2
m3
Voltage−−−−Q
n1
n2
n3
7.5 rad/MW
11.25 rad/MW
11.25 rad/MW
0.001 kV/MVAr
0.0015 Kv/MVAr
0.0015 Kv/MVAr
128
7.3. SIMULATION STUDIES
Simulation studies are carried out in PSCAD/EMTDC (version 4.2). Different configurations of load
and power sharing of the DGs are considered. To consider the web based communication, a delay of 5
ms is incorporated in the control signals which are not locally measureable. As only one measurement
is taken in one main cycle, a 100 byte/s communication is needed, which is a very low speed
communication compared to any of the high bandwidth communication. The system parameters are
shown in Table-7.1. For clarity, the numerical values of power sharing ratios obtained from all the
simulation are given in Table-7.2.
7.3.1 CASE 1: LOAD_3 AND LOAD_4 CONNECTED TO MICROGRID
In this case, all the three DGs are connected to the microgrid and supplying only Load_3 and
Load_4. While the system in steady state, Load_3 is disconnected at 0.5 s. Fig. 7.5 (a) shows the
power output of the DGs and Fig. 7.5 (b) shows the power sharing ratios with conventional angle
controller given by (7.2). In Fig. 7.5 (b), Pratio-ij indicates Pi:Pj. It can be seen that due to high line
impedance, the power sharing of the DGs are not as desired (see Table-7.2). Fig. 7.6 shows the system
response with proposed Controller-1. The error in power sharing is reduced. Fig. 7.7 shows the system
response with proposed Controller-2. The power sharing ratio of the DGs are much closer to the
desired sharing and the system reaches steady state within 4-5 cycles as in the case with the
conventional controller.
The results of this case with a conventional frequency droop controller are discussed in Section
7.3.5.
129
Fig. 7.5. Power sharing with conventional controller (Case 1).
Fig. 7.6. Power sharing with Controller-1 (Case 1).
Fig. 7.7.Power sharing with Controller-2 (Case 1).
130
7.3.2 CASE 2: DG-1 AND DG-3 SUPPLY LOAD_1 AND LOAD_2
It is assumed that only two DG, DG-1 and DG-3 are connected to the microgrid and they are
supplying Load_1 and Load_2. The system response shown in Fig 7.8 is with the conventional
controller (7.2). Load_2 is disconnected at 0.5s and the two DGs, connected at the two ends of the
microgrid supply only Load_1. Figs.7.9 and 7.10 show the response with the proposed controllers. It
can be seen that a closer to desired power sharing is achieved with these controllers. High line
impedance (and high R/X ratio) between the DGs and load makes the power sharing difficult and the
power sharing with conventional controller shown in Fig. 7.8 is not acceptable.
Fig. 7.8. Power sharing with conventional controller (Case 2).
Fig. 7.9. Power sharing with Controller-1 (Case 2).
131
Fig.7.10. Power sharing with Controller-2 (Case 2).
7.3.3 CASE 3: INDUCTION MOTOR LOADS
To investigate the system response with induction motors connected to the microgrid, a 30 hp
motor is connected as Load_3, while Load_4 constitutes a 50 hp motor. With the system running in
steady state, DG-2 is disconnected at 0.25s. The simulation results are shown in Figs. 7.11 to 7.13 for
the conventional controller and the two proposed controllers. After DG-2 is disconnected, DG-1 and
DG-3 supply the total power demand and it can be seen that system takes around 0.3 s to reach the
steady state. Due to the high impedance of the line, conventional angle controller fails to share the
power as desired (error is almost 20%). Controller-1 reduces the error to some extent but not able to
share as desired (Fig. 7.12 (b)). However, Controller- 2 is able to share the induction machine load
almost in the desired ratio (error is less than 2%).
Fig. 7.11. Power sharing with conventional controller (Case 3).
132
7.3.4 CASE 4: LOAD SHARING WITH ADVANCED COMMUNICATION SYSTEM
In this section it is assumed that the system has advanced high bandwidth communication among all
the DGs and loads and all the control parameters are measurable without any significant time delay.
With the same induction motor load as in Case 3, the simulations are carried out considering all the
measured variables are accessible to all the DGs. In this case, the droop sharing becomes redundant.
Fig. 7.14 shows the system response. It can be seen that an accurate power sharing is achieved. The
error is less than 0.5%. However the cost involved in a high bandwidth communication is much larger
compared to the proposed no-communication or web based minimum communication control. From
this perspective, either Controller-1 or Controller-2 can provide an acceptable power sharing in a rural
area with potentially a much lower cost.
Fig. 7.12. Power sharing with Controller-1 (Case 3).
Fig. 7.13. Power sharing with Controller-2 (Case 3).
133
Fig. 7.14. Power sharing with high bandwidth communication (Case 4).
Fig. 7.15 shows the mean percentage error in the different control techniques for the cases
discussed above. The operating cases were chosen for weak system conditions, where the micro
sources and loads are not symmetrically distributed through out the network. These results in high
values of power sharing error but it can be seen that with the proposed control methods, the error can
be reduced significantly. While the first proposed method (Controller-1) can reduce the error below
10%, the web based minimum communication method (Controller-2) has an error around 3.5%.
Though the error in case with an advanced communication system is much lower, the cost involved is
likely to be high.
The decentralized droop sharing control has also been studied when the loads are voltage and
frequency dependent. The results are discussed in Section 7.3.6.
7.3.5 CASE 5: LOAD SHARING WITH CONVENTIONAL DROOP CONTROLLER
The performance of the conventional frequency droop controller for the high R/X system of Case 1
is shown in Fig. 7.16. It can be seen, as is in the case of the conventional angle droop performance
seen in Fig. 7.5, the power sharing with this frequency droop is far from desired.
134
Fig. 7.16. Power sharing with frequency droop Case 1.
7.3.6 CASE 5: LOAD SHARING WITH CONVENTIONAL DROOP CONTROLLER
To investigate the angle control performance with a frequency (F) and voltage (V) dependent load,
a system as shown in Fig. 7.1 is chosen with a continuous load perturbation. The dependent load
characteristic [86] is given by
( )dFKVV
PP PF
NP
+
= 1
00 (7.A.1)
where NP (0.95) and KPF (2.0) are the voltage and frequency dependent coefficients. The system is
initially running with a continuous varying impedance load. Then the dependent load described by
(7.A.1) is connected at 0.4s. The power sharing is shown in Fig. 7.17 (a). The system frequency and
the power demand from the frequency dependent load is shown in Fig. 7.17 (b-c). It can be seen that
the power sharing is as desired. However the droop gains may need to be reduced as the frequency
dependence of the loads can be destabilizing.
7.4 CONCLUSIONS
Load sharing in an autonomous microgrid through angle droop control is investigated in this chapter
with special emphasis on highly resistive lines. Two control methods are proposed. The first method
proposes power sharing without any communication between the DGs. The feedback quantities and
135
the gain matrixes are transformed with a transformation matrix based on the line resistance-reactance
ratio. The second method is with minimal communication based output feedback controller. The
converter output voltage angle reference is modified based on the active and reactive power flow in
the line connected at PCC. It is shown that a more economical and proper power sharing solution is
possible with the web based communication of the power flow quantities. In many scenarios, the
difference in error margin between proposed control schemes and a costly high bandwidth based
communication system does not justify considering the increase in cost. This section proposes and
demonstrates low cost control methods to ensure acceptable power sharing in a weak system condition
and highly resistive network for rural distribution networks.
Fig. 7.17. Frequency dependent load
Percentage Error in Power Sharing
18.24
9.98
3.54
0.5
0
2
4
6
8
10
12
14
16
18
20
1
% e
rror
Conventional
Controller-1
Controller-2
Full_comm
Fig. 7.15. Error in power sharing with different control techniques
136
TABLE-7.2: SIMULATION RESULTS
Ca
se
Controller Power Sharing Ratio
P1 /P2 P1 /P3 P2 /P3
Initia
l
Final Initia
l
Final Initia
l
Final
1 Desired Values 1.5 1.5 1.5 1.5 1.0 1.0
Conventional 1.32 1.3 1.22 1.2 0.62 0.59
Controller-1 1.39 1.41 1.31 1.37 0.71 0.72
Controller-2 1.59 1.6 1.53 1.54 1.02 1.03
2 Desired Values − − 1.5 1.5 − −
Conventional − − 1.60 1.69 − −
Controller-1 − − 1.55 1.58 − −
Controller-2 − − 1.48 1.46 − −
3
&
4
Desired Values − − 1.5 1.5 1.0 0.0
Conventional − − 1.22 1.25 0.97 0.0
Controller-1 − − 1.39 1.42 1.10 0.0
Controller-2 − − 1.52 1.51 1.02 0.0
Full comm − − 1.51 1.51 0.99 0.0
137
CHAPTER 8
CONCLUSIONS
The general conclusions of the thesis and future scope of the work are presented in this chapter.
The conclusions are based on the work carried out and reported in the earlier chapters.
8.1 GENERAL CONCLUSIONS
The summarized conclusions of the thesis are
1. In case of converter interfaced sources, power sharing can be achieved with drooping the
output voltage angles of the converters. Angle droop controllers provide desirable power
sharing with much lower frequency deviations compared to that of frequency droop
controller.
2. The system response can be improved significantly by changing the state feedback
controller in grid connected mode to voltage control in islanded mode of operation. A
change in control algorithm also ensures a smooth transition of a microgrid between the
modes.
3. Power quality of distributed generation can be improved significantly by proper reference
generation for the DGs. In this the compensating DG can perform load balancing,
harmonic filtering and reactive power compensation while supplying real power. This is
not possible by a DSTATCOM.
4. The reliability in a microgrid can be improved with the application of back-to-back
converters for bidirectional power flow and voltage and frequency isolation between the
microgrid and the utility.
5. High droop gains can improve power sharing. However it can also have detrimental effect
on system stability. A supplementary controller, which takes real power as input, can
improve the system stability significantly.
6. In the rural network, with high R/X line, the droop equation has to be modified to
improve decentralized operation. A low band width communication can also improve the
power sharing significantly.
138
8.2 SCOPE FOR FUTURE WORK
Some areas for future work are listed below.
1. The angle droop control scheme can be modified to share power in a microgrid with inertial
and non inertial DG.
2. Protection of back-to-back converters in case of fault in utility or microgrid faults can be
investigated.
3. Improvement in supplementary droop control for enhanced system damping under weak
operating conditions. The improvement can be achieved by selection of more appropriate
input signals or controller gains.
4. A modified droop control can be derived for frequency dependent loads.
5. Improvement and further application of the low bandwidth communication (100 byte/s) can
be performed in distributed generation. Communication can be used to correct the reference
quantities or communicating the load measurements.
139
APPENDIX-A
The converter structure and control used in this thesis from existing publication by other
authors are presented in this appendix. All the inertia less DGs are connected to the microgrid through
interfacing converters. The converter structure and control is described in this appendix. Depending
on the requirement, three phase or single phase converters are used. The converter is connected to
microgrid with an output filter. Either LCL to LC filter has been used based on requirements. The
converter control strategies adopted in this thesis are state feedback control or voltage control based
on application and requirement.
A.1 CONVERTER STRUCTURE
The converter structure is shown in Fig. A.1. This contains three H-bridge converters that are
connected to the DG sources, denoted by Vdc1. The outputs of the H-bridges are connected to three
single-phase transformers that are connected in wye for required isolation and voltage boosting [87].
The resistance Rf represents the switching and transformer losses, while the inductance Lf represents
the leakage reactance of the transformers. The filter capacitor Cf is connected to the output of the
transformers to bypass switching harmonics. The inductance L1 is added to provide the output
impedance of the DG source. The advantage of this structure is that power flow can be controlled
independently in the three phases and the phases are magnetically decoupled from each other.
Fig. A.1. Three Phase converter structure.
140
The above structure is used for all the three phase DGs with LCL type of filter. If the DGs output filter
is LC type, the output inductance L1 shown in Fig. A.1 is not present. For single phase DGs, the
converter structure is shown in Fig. A.2.
A.2 CONVERTER CONTROL
The equivalent circuit of one phase of the converter is shown in Fig. A.3. In this, u⋅Vdc1 represents
the converter output voltage, where u = ± 1. The main aim of the converter control is to generate u.
Fig. A.2 Single phase converter structure
(a) Ouput filter LCL type (b) Output filter LC type
141
Fig. A.3. Equivalent circuit of one phase of the converter.
From Fig. A.3 (a), state space description of the system can be given as
PCCc vBuBAxx 2111 ++= (A.1)
While the state space equation for Fig. A.3 (b) can be given as,
cuBAxx 122 += (A.2)
where uc is the continuous time version of switching function u. Based on this model and a suitable
feedback control law, uc(k) is computed.
The equivalent circuit of one phase of the converter is shown in Fig. A.4. The choice of states
depends on the converter output filter type. In case of LCL filter the state vector is chosen from the
circuit of Fig. A.4, as
[ ]cfT viix 211 = (A.3)
While in case of LC filter, the states are
[ ]cfT vix 12 = (A.4)
Fig. A.4. Single-phase equivalent circuit of VSC (LCL filter).
The switching function u is then generated as
1 then elseif1 then If
−=−<+=>uhu
uhu
c
c (A.5)
where h is a small number. Two types of feedback controllers are used here. They are discussed
below.
142
A.3 OUTPUT FEEDBACK VOLTAGE CONTROLLER
Let the output of the system given in (A.2) be vcf. Let the reference for this voltage is given in terms
of the magnitude of the rms voltage V1* and its rotating angle φ1
*. From this the instantaneous voltage
reference v1* for the three phases are generated. Neglecting the PCC voltage since it is a disturbance
input, the input-output relationship of the system in can be written in discrete form as
( )( )
( )( )1
1
−
−
=zNzM
zu
zv
c
cf (A.6)
The control is computed from
( ) ( )( ) ( ) ( ) zvzvzRzS
u cfc −= ∗−
−
11
1
z (A.7)
Then the closed-loop transfer function of the system is given by
( )( )
( ) ( )( ) ( ) ( ) ( )1111
11
1−−−−
−−
∗ +=
zSzMzRzNzSzM
zv
zvcf (A.8)
The coefficients of the polynomials S and R can be chosen based on a pole placement strategy [88].
Once uc is computed, the switching function u can be generated from (A.5).
A.4 STATE FEEDBACK CONTROLLER
In state feedback controller, the chosen states of the system are compared with their reference
quantities to generate the converter switching. It is easy to generate references for the output voltage
vcf and current i2 from power flow condition. However, the same cannot be said about the reference for
the current i1.
To facilitate this, we define a new set of state vectors as
[ ]cfcT viix 21 = (A.9)
We then have the following state transformation matrix
143
11
100010011
xCxx P=
−= (A.10)
The transformed state space equation is then given by combining (A.9) and (A.10) as
PCCpcppp CvCBuCxACCx ++= −1
11 (A.10)
The control law is given by
( ) ( ) ( )[ ]kxkxKku refc 11 −−= (A.11)
where K is a gain matrix and xref is the reference vector. The gain matrix is obtained using discrete
time linear quadratic regulator (LQR) with a state weighting matrix of Q and a control penalty of r.
The control law discussed so far is for the system in which the DGs have an output inductor.
Alternatively, when the DGs do not have an output inductance, the inductance L1 is removed and the
output filter is a simple LC filter. The system states are then modified as
[ ]cfcfT vix =2 (A.12)
However the state space is similar to (A.10) and the control law (A.11) and switching logic remain the
same.
144
145
APPENDIX-B
LIST OF PUBLICATIONS
The following papers are published (or under publication process) from the work described in this
thesis.
Journal papers:
1. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Load sharing and power quality
enhanced operation of a distributed microgrid,” IET Renewable Power Generation, Vol-2,
No-3, pp 109-119, June, 2009.
2. Ritwik. Majumder, B. Chaudhuri, A. Ghosh, Rajat. Majumder, G. Ledwich and F. Zare,
“Improvement of Stability and Load Sharing in an Autonomous Microgrid Using
Supplementary Droop Control Loop,” Accepted to appear in IEEE Trans. in power system,
September, 2009.
3. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Power Management and Power Flow
Control with Back-to-Back Converters in a Utility Connected Microgrid,” Accepted to
appear in IEEE Trans. in power system, October, 2009.
4. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Load Frequency Control of Rural
Distributed Generation”, accepted in Electric Power Components and Systems, October,
2009.
5. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Enhancing the Stability of an
Autonomous Microgrid using DSTATCOM”, Accepted to appear in International Journal of
Emerging Electric Power Systems.
6. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Enhancing Stability of an Autonomous
Microgrid using a Gain Scheduled Angle Droop Controller with Derivative Feedback”,
Accepted to appear in International Journal of Emerging Electric Power Systems.
7. R. Majumder, G. Ledwich, A. Ghosh, and F. Zare “Droop Control of Converter Interfaced
Micro Sources in Rural Distributed Generation”, IEEE Trans. in power delivery, accepted.
146
8. R. Majumder, M. Dewadasa, G. Ledwich, A. Ghosh, and F. Zare “Control and Protection of
a Microgrid Connected to Utility through Back-to-Back Converters”, IET Generation
Transmission and Distribution, under minor revision.
9. F. Shahnia, R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Operation and Control of a
Hybrid Microgrid Containing Unbalanced and Nonlinear Loads”, EPSR, Accepted.
Conference Papers:
1. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Control of parallel converters for load
sharing with seamless transfer between grid connected and islanded modes”, IEEE Power
and Energy Society General Meeting, Pittsburgh, USA, 20-24 July 2008.
2. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Angle droop versus frequency droop in
a voltage source converter based autonomous microgrid: IEEE Power Engineering Society
General Meeting 2009, 26-30 July 2009, Calgary Telus Conventional Centre, Calgary,
Canada.
3. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Operation and Control of Single Phase
Micro-Sources in a Utility Connected Grid” IEEE Power Engineering Society General
Meeting 2009, 26-30 July 2009, Calgary Telus Conventional Centre, Calgary, Canada.
4. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Power System Stability and Load
Sharing in Distributed Generation” .In Proceedings POWERCON2008 & 2008 IEEE Power
India Conference, New Delhi, India.
5. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Enhancing the Stability of an
Autonomous Microgrid using DSTATCOM”, National Power System Conference (NPSC),
Mumbai, India, 2008
6. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Stability Analysis and Control of
Multiple Converter Based Autonomous Microgrid”, IEEE International Conference in
Control and Automation (ICCA), Christchurch, New Zealand, 2009.
7. A. Ghosh, R. Majumder, G. Ledwich and F. Zare, “Power Quality Enhanced Operation and
Control of a Microgrid based Custom Power Park”, IEEE International Conference in
Control and Automation (ICCA), Christchurch, New Zealand, 2009.
147
8. R. Majumder, Farhad Shahnia, A. Ghosh, G. Ledwich, Michael Wishart and F. Zare,
“Operation and Control of a Microgrid Containing Inertial and Non-Inertial Micro Sources”,
IEEE TENCON, Singapore, 2009.
9. R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Power Sharing and Stability
Enhancement of an Autonomous Microgrid with Inertial and Non-inertial DGs with
DSTATCOM”, IEEE International Conference in Power System (ICPS)-2009, Kharagpur,
India.
10. M. Dewadasa, R. Majumder, A. Ghosh, G. Ledwich, “Control and Protection of a
Microgrid with Converter Interfaced Micro Sources”, IEEE International Conference in
Power System (ICPS)-2009, Kharagpur, India.
11. R. Majumder, A. Ghosh, G. Ledwich, S. Chakraborti and F. Zare, “Improved Power
Sharing among Distributed Gen-erators using Web Based Communication”, Accepted to
appear in IEEE PES General Meeting, July 26 - July 29, 2010, Minneapolis, Minnesota,
USA.
148
149
REFERENCES
[1] IEEE Standard for Interconnecting Distributed Resources with Electric Power Systems," IEEE
Std 1547-2003 , vol., no., pp.0_1-16,
2003URL:http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1225051&isnumber=27496
[2] R. H. Lasseter, "MicroGrids," in Power Engineering Society Winter Meeting, 2002. IEEE, 2002,
pp. 305-308, vol.1.
[3] M. Milosevic, P. Rosa, M. Portmann, and G. Andersson, "Generation Control with Modified
Maximum Power Point Tracking in Small Isolated Power Network with Photovoltaic Source," in
Power Engineering Society General Meeting, 2007. IEEE, 2007, pp. 1-8.
[4] A.M. Salamah, S.J. Finney, B.W.Williams, "Autonomous controller for improved dynamic
performance of AC grid, parallel-connected, single-phase inverters," Generation, Transmission &
Distribution, IET, vol.2, no.2, pp.209-218, 2008.
[5] Y. W. Li, C. “An Accurate Power Control Strategy for Power Electronics Interfaced Distributed
Generation Units Operating In a Low Voltage Multibus Microgrid”. This paper appears in: Power
Electronics, IEEE Transactions on Accepted for future publication Digital Object Identifier:
10.1109/TPEL.2009.2022828.
[6] H. Nikkhajoei, H.; R. H. Lasseter, "Distributed Generation Interface to the CERTS Microgrid,"
Power Delivery, IEEE Transactions on , vol.24, no.3, pp.1598-1608, July 2009.
[7] C. K. Sao, P.W. Lehn, "Control and Power Management of Converter Fed Microgrids," Power
Systems, IEEE Transactions on , vol.23, no.3, pp.1088-1098,. 2008.
[8] M. Shahabi; M.R. Haghifam, M. Mohamadian, S. A. Nabavi-Niaki, "Microgrid Dynamic
Performance Improvement Using a Doubly Fed Induction Wind Generator," Energy Conversion,
IEEE Transactions on , vol.24, no.1, pp.137-145, 2009.
[9] I. Bae; J. Kim, "Reliability Evaluation of Distributed Generation Based on Operation Mode,"
Power Systems, IEEE Transactions on, vol.22, no.2, pp.785-790, May 2007.
[10] H. A. Gil, G. Joos, G., "Models for Quantifying the Economic Benefits of Distributed
Generation," Power Systems, IEEE Transactions on, vol.23, no.2, pp.327-335, 2008.
150
[11] S. Haffner, L.F.A. Pereira, L.A. Pereira, L. S. Barreto, "Multistage Model for Distribution
Expansion Planning With Distributed Generation—Part I: Problem Formulation," Power
Delivery, IEEE Transactions on , vol.23, no.2, pp.915-923, April 2008.
[12] F. Katiraei and M. R. Iravani, "Power Management Strategies for a Microgrid With Multiple
Distributed Generation Units," Power Systems, IEEE Transactions on, vol. 21, pp. 1821-1831,
2006.
[13] M. Reza, D. Sudarmadi, F. A. Viawan, W. L. Kling, and L. Van Der Sluis, "Dynamic Stability of
Power Systems with Power Electronic Interfaced DG," in Power Systems Conference and
Exposition, 2006. PSCE '06. 2006 IEEE PES, 2006, pp. 1423-1428.
[14] M. Dai, M. N. Marwali, J. W. Jung, and A. Keyhani, "Power flow control of a single distributed
generation unit with nonlinear local load," in Power Systems Conference and Exposition, 2004.
IEEE PES, 2004, pp. 398-403, vol.1.
[15] J. G. Slootweg and W. L. Kling, "Impacts of distributed generation on power system transient
stability," in Power Engineering Society Summer Meeting, 2002 IEEE, 2002, pp. 862-867, vol.2.
[16] P. Piagi and R. H. Lasseter, "Autonomous control of microgrids," in Power Engineering Society
General Meeting, 2006. IEEE, 2006, No of Pages-8.
[17] F. Katiraei, M. R. Iravani, and P. Lehn, "Microgrid autonomous operation during and subsequent
to islanding process," in Power Engineering Society General Meeting, 2004. IEEE, 2004, p. 2175,
Vol.2.
[18] D. K. Nichols, Stevens, J., Lasseter, R.H., Eto, J.H., Vollkommer, H.T., "Validation of the
CERTS microgrid concept the CEC/CERTS microgrid testbed," in Power Engineering Society
General Meeting, 2006. IEEE.
[19] S. K. Mishra, "Design-Oriented Analysis of Modern Active Droop-Controlled Power Supplies,"
Industrial Electronics, IEEE Transactions on , vol.56, no.9, pp.3704-3708, 2009
[20] N. Pogaku, M. Prodanovic, C. Hernandez-Aramburo, T. C. Green, "Energy Management in
Autonomous Microgrid Using Stability-Constrained Droop Control of Inverters," Power
Electronics, IEEE Transactions on , vol.23, no.5, pp.2346-2352, 2008.
[21] E. C. Furtado, L.A. Aguirre, L.A.B.Torres, "UPS Parallel Balanced Operation Without Explicit
Estimation of Reactive Power—A Simpler Scheme," Circuits and Systems II: Express Briefs,
IEEE Transactions on , vol.55, no.10, pp.1061-1065, 2008.
151
[22] X. Shangyang, Q. Weihong; G. Miller, T.X.Wu, I. Batarseh, "Adaptive Modulation Control for
Multiple-Phase Voltage Regulators," Power Electronics, IEEE Transactions on , vol.23, no.1,
pp.495-499, Jan. 2008.
[23] J. M. Guerrero, L. G. de Vicuna, J. Matas, M. Castilla, and J. Miret, "A wireless controller to
enhance dynamic performance of parallel inverters in distributed generation systems," Power
Electronics, IEEE Transactions on, vol. 19, pp. 1205-1213, 2004.
[24] H. Karimi, H. Nikkhajoei, and R. Iravani, "A Linear Quadratic Gaussian Controller for a Stand-
alone Distributed Resource Unit-Simulation Case Studies," in Power Engineering Society
General Meeting, 2007. IEEE, 2007, pp. 1-6.
[25] M. N. Marwali and A. Keyhani, "Control of distributed generation systems-Part I: Voltages and
currents control," Power Electronics, IEEE Transactions on, vol. 19, pp. 1541-1550, 2004
[26] D. Salomonsson, L. Soder, A. Sannino, "An Adaptive Control System for a DC Microgrid for
Data Centers," Industry Applications, IEEE Transactions on, vol.44, no.6, pp.1910-1917, 2008.
[27] Y. Li; D. M. Vilathgamuwa, P. C. Loh, "Robust Control Scheme for a Microgrid With PFC
Capacitor Connected," Industry Applications, IEEE Transactions on , vol.43, no.5, pp.1172-1182,
2007.
[28] G. W. Ault, J. R. McDonald, G. M. Burt, "Strategic analysis framework for evaluating distributed
generation and utility strategies," Generation, Transmission and Distribution, IEE Proceedings- ,
vol.150, no.4, pp. 475-481, 2003.
[29] T. Senjyu, Y. Miyazato, A. Yona, N. Urasaki, T. Funabashi, "Optimal Distribution Voltage
Control and Coordination With Distributed Generation," Power Delivery, IEEE Transactions on ,
vol.23, no.2, pp.1236-1242, April 2008.
[30] T. Lee; P. Cheng, "Design of a New Cooperative Harmonic Filtering Strategy for Distributed
Generation Interface Converters in an Islanding Network," Power Electronics, IEEE Transactions
on, vol.22, no.5, pp.1919-1927, 2007.
[31] T. Lee; P. Cheng; H. Akagi, H. Fujita, "A Dynamic Tuning Method for Distributed Active Filter
Systems," Industry Applications, IEEE Transactions on , vol.44, no.2, pp.612-623, 2008.
[32] T. Lee; P. Cheng, "Design of a New Cooperative Harmonic Filtering Strategy for Distributed
Generation Interface Converters in an Islanding Network," Power Electronics, IEEE Transactions
on, vol.22, no.5, pp.1919-1927, 2007.
152
[33] A. Bhowmik, A. Maitra, S. M. Halpin, J. E. Schatz, "Determination of Allowable Penetration
Levels of Distributed Generation Resources Based on Harmonic Limit Consideration," Power
Engineering Review, IEEE, vol.22, no.4, pp.79-79, April 2002.
[34] M.E.H.; Golshan, S. A. Arefifar, "Distributed generation, reactive sources and network-
configuration planning for power and energy-loss reduction," Generation, Transmission and
Distribution, IEE Proceedings- , vol.153, no.2, pp. 127-136, 16 March 2006.
[35] H. M. Khodr, Z. A. Vale, C. Ramos, "A Benders Decomposition and Fuzzy Multicriteria
Approach for Distribution Networks Remuneration Considering DG," Power Systems, IEEE
Transactions on , vol.24, no.2, pp.1091-1101, 2009.
[36] W. El-Khattam, Y. G. Hegazy, M. M. A. Salama, "An integrated distributed generation
optimization model for distribution system planning," Power Systems, IEEE Transactions on ,
vol.20, no.2, pp. 1158-1165, May 2005.
[37] H. B. Puttgen, P. R. MacGregor, F. C. Lambert, "Distributed generation: Semantic hype or the
dawn of a new era?," Power and Energy Magazine, IEEE , vol.1, no.1, pp. 22-29, 2003.
[38] S. M. Brahma, and A. A. Girgis, “Development of adaptive protection scheme for distribution
systems with high penetration of distributed generation,” IEEE Trans. On Power Delivery, Vol.
19, No. 1, pp. 56-63, 2004.
[39] C. M. Vieira, W. Freitas, W. Xu and A. Morelato, “Efficient coordination of ROCOF and
frequency relays for distributed generation protection by using the application region,” IEEE
Trans. on Power Delivery, Vol. 21, No. 4, pp. 1878-1884, 2006.
[40] H. Nikkhajoei and R. H. Lasseter, “Microgrid protection,” IEEE Power Engineering Society
General Meeting, Tampa, 2007.
[41] H. Al-Nasseri, M. A. Redfern, and R. O’Gorman, “Protecting micro-grid systems containing
solid-state converter generation,” International Conference on Future Power Systems, 2005.
[42] H. Nikkhajoei and R. H. Lasseter, "Microgrid Protection," in Power Engineering Society General
Meeting, 2007. IEEE, 2007, pp. 1-6.
[43] M. C. Chandorkar, D. M. Divan and R. Adapa, "Control of Parallel Connected Inverters in
Standalone ac Supply Systems" IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL.
29, NO. 1, JANUARYIFEBRUAKY 1993.
153
[44] M. N. Marwali, J. Jin-Woo, and A. Keyhani, "Control of distributed generation systems - Part II:
Load sharing control," Power Electronics, IEEE Transactions on, vol. 19, pp. 1551-1561, 2004.
[45] M. Lopez, L. G. de Vicuna, M. Castilla, J. Matas, and O. Lopez, "Control loop design of parallel
connected converters using sliding mode and linear control techniques," in Power Electronics
Specialists Conference, 2000. PESC 00. 2000 IEEE 31st Annual, 2000, pp. 390-394, vol. 1.
[46] D. M. Vilathgamuwa, P. C. Loh, and Y. Li, "Protection of Microgrids During Utility Voltage
Sags," Industrial Electronics, IEEE Transactions on, vol. 53, pp. 1427-1436, 2006.
[47] J. M. Guerrero, J. Matas, V. Luis Garcia de, M. Castilla, and J. Miret, "Decentralized Control for
Parallel Operation of Distributed Generation Inverters Using Resistive Output Impedance,"
Industrial Electronics, IEEE Transactions on, vol. 54, pp. 994-1004, 2007.
[48] J. M. Guerrero, J. Matas, L. Garcia De Vicunagarcia De Vicuna, M. Castilla, and J. Miret,
"Wireless-Control Strategy for Parallel Operation of Distributed-Generation Inverters," Industrial
Electronics, IEEE Transactions on, vol. 53, pp. 1461-1470, 2006.
[49] M. N. Marwali, M. Dai; A. Keyhani, “Robust stability analysis of voltage and current control for
distributed generation systems” IEEE Trans. on Energy Conversion, Vol. 21, Issue-2, pp. 516-
526, 2006.
[50] M. N. Marwali, M. Dai; A. Keyhani, “Stability Analysis of Load Sharing Control for Distributed
Generation Systems,” IEEE Trans. on Energy Conversion, Vol. 22, Issue-3, pp. 737-745, 2007.
[51] N. Pogaku, M. Prodanovic, T. C. Green, “Modeling, Analysis and Testing of Autonomous
Operation of an Inverter-Based Microgrid,” IEEE Trans. on Power Electronics, Vol. 22, Issue-2,
pp. 613-625, 2007.
[52] K. D. Brabandere, B. Bolsens, J. V. Keybus, A. Woyte, j. driesen and R. Belmans, “A Voltage
and Frequency Droop Control Method for Parallel Inverters”, IEEE Trans. Power Electronics,
Vol. 22, No. 4, pp. 1107-1115, Oct. 2008.
[53] R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Angle droop versus frequency droop in a
voltage source converter based autonomous microgrid: IEEE Power Engineering Society General
Meeting 2009, 26-30 July 2009, Calgary Telus Conventional Centre, Calgary, Canada.
[54] R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Load sharing and power quality enhanced
operation of a distributed microgrid,” IET Renewable Power Generation, Vol-2, No-3, pp 109-
119, June, 2009.
154
[55] A.P. Agalgaonkar; S.V. Kulkarni, S.A. Khaparde, “Evaluation of configuration plans for DGs in
developing countries using advanced planning techniques,” IEEE Trans. on Power Electronics,
Vol. 21, No. 2, pp. 973-981, 2006.
[56] B. K. Blyden and W.J. Lee, “Modified Microgrid Concept for Rural Electrification in Africa”,
Power Engineering Society General Meeting, pp. 1-5, 2006.
[57] K. D. Brabandere, B. Bolsens, J. V. Keybus, A. Woyte, j. driesen and R. Belmans, “A Voltage
and Frequency Droop Control Method for Parallel Inverters”, IEEE Trans. Power Electronics,
Vol. 22, No. 4, pp. 1107-1115, Oct. 2008.
[58] E. L. Owen, "Rural electrification: the long struggle," Industry Applications Magazine, IEEE ,
vol.4, no.3, pp.6, 8, 10-17, May/Jun 1998.
[59] P. Lewis, "Rural electrification in Nicaragua," Technology and Society Magazine, IEEE , vol.16,
no.2, pp.6-13, 32, Summer 1997.
[60] M. Munasinghe, "Rural electrification in the Third World," Power Engineering Journal , vol.4,
no.4, pp.189-202, Jul 1990.
[61] G. C. Neff, "Rural Electrification," American Institute of Electrical Engineers, Transactions of
the , vol.XLV, no., pp.511-514, Jan. 1926.
[62] M. M. Samuels, "Specific Engineering Problems in Rural Electrification and Electroagriculture,"
American Institute of Electrical Engineers, Transactions of the , vol.65, no.12, pp.1065-1073,
Dec. 1946.
[63] A. Applewhite, "Africa becomes electric," Spectrum, IEEE , vol.39, no.8, pp. 54-56, Aug 2002.
[64] B.S.Townsend, "Distribution: the years of change," Generation, Transmission and Distribution,
IEE Proceedings C , vol.132, no.1, pp.1-7, January 1985.
[65] D. Downer, "Rural electrification scheme in Uganda," Power Engineering Journal , vol.15, no.4,
pp.185-192, Aug 2001.
[66] L. Mackay, "Rural electrification in Nepal: new techniques for affordable power ," Power
Engineering Journal , vol.4, no.5, pp.223-231, Sep 1990.
[67] J. Balakrishnan, "Renewable Energy and Distributed Generation in Rural Villages," Industrial
and Information Systems, First International Conference on , vol., no., pp.190-195, 8-11 Aug.
2006.
155
[68] S. Mukhopadhyay, B. Singh, "Distributed generation — Basic policy, perspective planning, and
achievement so far in india," Power & Energy Society General Meeting, 2009. PES '09. IEEE ,
vol., no., pp.1-7, 26-30 July 2009.
[69] F. Katiraei, C. Abbey, C.; S. Tang,, M. Gauthier, "Planned islanding on rural feeders — utility
perspective," Power and Energy Society General Meeting - Conversion and Delivery of Electrical
Energy in the 21st Century, 2008 IEEE , vol., no., pp.1-6, 20-24 July 2008
[70] Australian Business Council Sustainable Energy, web http://www.bcse.org.au/home.asp.
[71] D. Pudjianto, G. Strbac, F. Van Overbeeke, A. I. Androutsos, Z. Larrabe, J. Tome Saraiva,
“Investigation of Regulatory, Commercial, Economic and Environmental Issues in MicroGrids”,
Future Power Systems, International Conference on future power system, pp. 1-6, 16-18 Nov.
2005
[72] Digital Control of Dynamic Systems GF Franklin, ML Workman, D Powell - 1997 - Addison-
Wesley Longman Publishing Co., Inc. Boston, MA, USA
[73] S. Krishnamurthy, T.M. Jahns, R.H. Lasseter, “The Operation of Diesel Gensets in a CERTS
Microgrid”, IEEE Power and Energy Society General Meeting- Conversion and Delivery of
Electrical Energy in the 21st Century, pp. 1-8, July 2008.
[74] Y. Hou, G. Wan, W. Jiang, M. Zhuang, “Steady State Performance Modelling of a Fuel Cell
Engine”, IEEE Int. Conf. on Vehicular Electronics and Safety (ICVES), pp. 424-427, Dec.
2006.
[75] I.H. Altas, A.M. Sharaf, “A Novel Photovoltaic On-Line Search Algorithm for Maximum Energy
Utilization”, Int. Conf. on Communication, Computer and Power (ICCCP), Feb. 2007.
[76] R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Power System Stability and Load Sharing in
Distributed Generation” .In Proceedings POWERCON2008 & 2008 IEEE Power India
Conference, New Delhi, India.
[77] A. Tuladhar, H. Jin, T. Unger, and K. Mauch, “Parallel operation of single phase inverters with
no control interconnections,” Proc. IEEE APEC’97, Vol. 1, pp. 94-100, 1997.
[78] A. Tuladhar, H. Jin, T. Unger, and K. Mauch, “Control of Parallel Inverters in Distributed AC
Power Systems with Consideration of Line Impedance Effect,” IEEE Trans. on Industry
Applications, Vol. 36, Issue 1, pp. 131-138, 2000.
156
[79] R. Majumder, A. Ghosh, G. Ledwich and F. Zare, “Stability Analysis and Control of Multiple
Converter Based Autonomous Microgrid”, IEEE International Conference in Control and
Automation (ICCA), Christchurch, New Zealand, 2009.
[80] C.Geromel, J. Bernussou ,"Decentralized control through parameter space optimization."
Automatica,1994 30(10): pp 1565-1578.
[81] A. L. B Do Bomfim,. G. N. Taranto (). "Simultaneous tuning of power system damping
controllers using genetic algorithms." IEEE Transactions on Power Systems, 15(1), 2000: pp 163-
169.
[82] J. Kennedy and R. Eberhart. “Particle swarm optimization,”. Proceedings of IEEE International
Conference on Neural Networks, 1995.
[83] B. Qiu and H. Gooi, “Web-based SCADA display system (WSDS) for access via Internet,” IEEE
Trans. Power Systems, Vol. 15, pp. 681-686, May 2000.
[84] N. Liu, J. Zhang, and W. Liu, “A security mechanism of web services-based communication for
wind power plants,” IEEE Trans. Power Delivery, Vol. 23, pp. 1930-1938, Oct. 2008.
[85] S.-J. S. Tsai and C. C. Luo, “Synchronized Power-Quality Measurement Network With LAMP,”
IEEE Trans. Power Delivery, Vol. 24, No. 1, pp. 484-485, Jan. 2009.
[86] Power System Load Flow Analysis, Lynn Powell, ISBN13: 9780071447799, McGraw-Hill
Professional Publishing, November 2004
[87] A. Ghosh and A. Joshi, “A new approach to load balancing and power factor correction in power
distribution system,” IEEE Transactions on Power Delivery, Vol. 15, No. 1, pp. 417-422, 2000.
[88] A. Ghosh, “Performance study of two different compensating devices in a custom power park,”
Proceedings of the IEE − Generation, Transmission & Distribution, Vol. 152, No. 4, pp. 521-528,
2005.