advanced power electronic for wind-power generation buffering (th., alejandro montenegro león)

8/7/2019 Advanced Power Electronic for Wind-Power Generation Buffering (th., Alejandro Montenegro Len)

1/194

ADVANCED POWER ELECTRONIC FORWIND-POWER GENERATION BUFFERING

By

ALEJANDRO MONTENEGRO LEN

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL

OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2005


2/194

Copyright 2005

by

Alejandro Montenegro Len


3/194

To my brother


4/194

iv

ACKNOWLEDGMENTS

I would like to first express my gratitude to Charles Edwards, the principle

engineer at S&C Electric Co. (Chicago, IL) for his patience and the knowledge he shared

throughout the project. I would also like to acknowledge Kenneth Mattern (manager at

S&C Electric Co., Power Quality Division) for his constant encouragement and

confidence in my ability. I am grateful to S&C Electric Company in general for all of

their contribution and concern.

Additionally, I would like to thank Alexander Domijan (my supervisory committee

chair) for his funding during my graduate studies. My gratitude also goes to my

supervisory committee (Dr. Ngo, Dr. Arroyo, and Dr. Goswami) for all of their time and

effort.

I would furthermore like to acknowledge my family in Spain, for supporting me

and believing in me throughout my stay in the United States. I would finally like to

express my love and gratitude to my girlfriend, Andrea Victoriano, for her help with the

proofreading and for always being the shoulder I could lean on throughout the project


5/194

v

TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ................................................................................................. iv

LIST OF TABLES........................................................................................................... viii

LIST OF FIGURES ........................................................................................................... ix

ABSTRACT.................................................................................................................... xvii

CHAPTER1 INTRODUCTION........................................................................................................ 1

Wind-Energy Outlook .................................................................................................. 1Electrical Issues ............................................................................................................ 3Solutions to Wind-Power Fluctuations.........................................................................9State of the Art.............................................................................................................. 9Objective..................................................................................................................... 11

2 SYSTEM DESIGN.....................................................................................................14

Introduction................................................................................................................. 14Control Scheme .......................................................................................................... 14

Positive Sequence Calculation ............................................................................14Real Power Calculation Using dq Components ..................................................20Phase Locked Loop .............................................................................................21Control Algorithm Design...................................................................................26

Inner regulators ............................................................................................27Outer regulators............................................................................................35

Per-Unit System Model ..............................................................................................56Inverter Output-Filter Design..............................................................................56

Harmonic content .........................................................................................57

Switching frequency.....................................................................................60Passive filter design......................................................................................61Passive filter damping..................................................................................65

Direct-Current Link Capacitor Design ................................................................68Energy Storage Design........................................................................................69Chopper Inductor Design ....................................................................................71Per-Unit System Model Summary.......................................................................72

Simulated Model......................................................................................................... 73


6/194

vi

3 SYSTEM DESCRIPTION..........................................................................................78

System Overview........................................................................................................ 78Electrical Network Model...........................................................................................80

Synchronous Machine .........................................................................................80Voltage regulation ...............................................................................................81Prime Mover ........................................................................................................ 81Synchronous Machine Control Algorithm ..........................................................83

Wind-Farm Model ...................................................................................................... 87Wind-Farm Control Algorithm............................................................................90Wind-Farm Power-Factor Correction..................................................................90Wind-Farm Soft-Start System.............................................................................94

Power Stabilizer.......................................................................................................... 97Power-Stabilizer Hardware Description..............................................................97

Interface board..............................................................................................99Digital signal processor..............................................................................105Field-programmable gate array..................................................................106Intelligent power module ...........................................................................107Isolation interface circuit............................................................................108

Power Stabilizer Software Description .............................................................108Description of DSP program......................................................................109FPGA program description ........................................................................114

4 SYSTEM PERFORMANCE....................................................................................121

System Data .............................................................................................................. 121Power Stabilizer Transient Response .......................................................................121

Direct-Current Link Voltage Control................................................................121

Reactive Current Control...................................................................................123Passive Filter Performance .......................................................................................126Voltage Regulation ...................................................................................................127System Losses........................................................................................................... 128Power Limiter Results ..............................................................................................130

Power Limiter 1 (High Pass Filter) ...................................................................131Power Limiter 1 (Adaptive High Pass Filter)....................................................136Power Limiter 2.................................................................................................138

Power Limiters Comparison Study...........................................................................145

5 SUMMARY.............................................................................................................. 148

Conclusions............................................................................................................... 148Further Work ............................................................................................................ 150

APPENDIX

A MATHEMATICAL TRANSFORMATIONS..........................................................151

B MATLAB CODES ...................................................................................................158


7/194

vii

C POWER STABILIZER CONTROL MODULES ....................................................168

LIST OF REFERENCES.................................................................................................172

BIOGRAPHICAL SKETCH ...........................................................................................176


8/194

viii

LIST OF TABLES

Table page

1-1 Technical specifications of IEC and IEEE................................................................4

1-2 Wind-farm output-power requirements.....................................................................8

1-3 Large-scale wind-power output-leveling projects...................................................10

1-4 Conceptual wind-power filtering projects...............................................................12

1-5 Basic system configurations....................................................................................13

2-1 Outer regulator assignation .....................................................................................35

2-2 Rate-of-change limits or PPA for a 10 MW wind farm ..........................................47

2-3 Generalized Harmonics of line-to-line voltage .......................................................59

2-4 L filter vs. LCL filter...............................................................................................61

2-5 LCL filter design ..................................................................................................... 64

2-6 LCL equivalent impedance with damping resistance .............................................65

2-7 Per-unit system........................................................................................................ 65

2-8 Per-unit system parameters .....................................................................................73

2-9 Designed system results and simulated system results comparison........................76

3-1 Synchronous machine output voltage profile at rated speed...................................82

3-2 Alternatives for the power stabilizer controller.....................................................106

3-3 FPGA code words .................................................................................................120

4-1 System parameters................................................................................................. 122

A-1 Mathematical transformations summary...............................................................157

C-1 Control Modules....................................................................................................168


9/194

ix

LIST OF FIGURES

Figure page

1-1 Wind-power output for two wind farms during one month. .....................................5

1-2 Power fluctuation comparison...................................................................................6

1-3 Typical power curve of a wind turbine. ....................................................................6

1-4 Wind-farm output power vs system frequency. ........................................................7

1-5 Control strategies along the power curve..................................................................8

1-6 Wind-farm generation buffering concept ................................................................13

2-1 Unbalanced system..................................................................................................15

2-2 Space vector trajectory of an unbalanced system in the d-q-o plane ......................16

2-3 Space vector trajectory projection over the d-q plane.............................................16

2-4 Direct and quadrature components of an unbalanced system .................................17

2-5 Representation of an unbalanced system in the frequency domain.........................17

2-6 Positive-sequence extraction algorithm ..................................................................19

2-7 Voltage waveforms for an unbalanced fault event..................................................19

2-8 Response of the positive-sequence extraction algorithm ........................................20

2-9 Distortion of phase angle due to a negative sequence component ..........................22

2-10 PLL diagram............................................................................................................ 23

2-11 PLL simplified model..............................................................................................24

2-12 PLL system step response .......................................................................................25

2-13 Root locus for two different regulator gains ...........................................................25

2-14 PLL system response to an unbalanced system condition ......................................26


10/194

x

2-15 PLL system response to a frequency excursion ......................................................26

2-16 System description ..................................................................................................27

2-17 Simplified system model .........................................................................................28

2-18 Electrical representation of the dq components ......................................................30

2-19 System model block diagram ..................................................................................30

2-20 Inverter current regulator-system model block diagram .........................................31

2-21 Inverter current regulator-system model simplified block diagram........................32

2-22 Simplified current control diagram .........................................................................32

2-23 Current regulator step response...............................................................................33

2-24 Chopper equivalent system .....................................................................................34

2-25 Chopper current controller ......................................................................................35

2-26 Powers' definition.................................................................................................... 36

2-27 System model .......................................................................................................... 37

2-28 DC link equivalent system block diagram ..............................................................37

2-29 DC link simplified system block diagram...............................................................38

2-30 DC link voltage regulator step response .................................................................38

2-31 Simplified system model .........................................................................................40

2-32 Source impedance voltage drop ..............................................................................41

2-33 Transfer functions of inverters quadrature current component..............................42

2-34 Transfer functions of inverters direct current component......................................42

2-35 Voltage regulator system block diagram.................................................................44

2-36 Positive sequence extraction algorithm equivalent system.....................................44

2- 37 Voltage regulator detailed block diagram ...............................................................45

2- 38 Voltage regulator simplified control diagram .........................................................45

2- 39 System response to a 5% change in voltage reference............................................45


11/194

xi

2-40 Adaptive control scheme.........................................................................................46

2-41 Power Regulator general control scheme................................................................47

2-42 Power limiter 1. Control block diagram..................................................................48

2-43 Power limiter 1. Performance using different cut-off frequencies (unlimitedpower and energy)....................................................................................................49

2-44 Power limiter 1. Performance using different cut-off frequencies (Pinverter=1.0MW and Einverter=8.5 MJ) .......................................................................................49

2-45 Power limiter 2. Limiters details .............................................................................50


2-47 Power limiter 2. Compensation performance.........................................................51

2-48 Power limiter 2. Inverter response for a sampling time of 2 seconds .....................52

2-49 Power limiter 2. Inverter response for different power ratings. Sampling time 2seconds ..................................................................................................................... 53

2-50 Power limiter 2. Inverter response for different ESS sizes. Sampling time 2seconds ..................................................................................................................... 53


2-52 Power limiter 3. Compensation performance.........................................................55

2-53 Power limiter 3. Inverter response for a sampling time of 2 seconds .....................55

2-54 Inverter topology ...................................................................................................... 57

2-55 Line-to-line and line-to-neutral voltage of a three phase inverter...........................57

2-56 RMS Line-to-line voltage harmonic spectrum........................................................58

2-57 Static Synchronous Generator diagram...................................................................59

2-58 LCL filter topology .................................................................................................61

2-59 LCL equivalent block diagram................................................................................62

2-60 Single phase equivalent filter model at the fundamental frequency .......................62

2-61 Single phase equivalent filter model at the hth harmonic ........................................63

2-62 LCL equivalent impedance with damping resistance .............................................66


12/194

xii

2-63 Single phase harmonic generator equivalent circuits ..............................................66

2-64 LCL gain frequency response .................................................................................67

2-65 Inverter frequency analysis .....................................................................................67

2-66 Capacitor Voltage vs. Energy Storage ....................................................................70

2-67 ESS-Chopper topology............................................................................................71

2-68 Equivalent circuit for maximum current ripple calculation ....................................72

2-69 System overview ..................................................................................................... 74

2-70 Per-unit electric system model ................................................................................74

2-71 Power Stabilizer Control Scheme ...........................................................................75

3-1 Equivalent system model ........................................................................................79

3-2 DC gen-set............................................................................................................... 83

3-3 Two single quadrant chopper circuit .......................................................................83

3-4 Synchronous generator control system ...................................................................84

3-5 Frequency deviation ................................................................................................85

3-6 DC-GEN set control scheme ...................................................................................85

3-7 System frequency response forf=-1Hz ................................................................86

3-8 Frequency control equivalent system......................................................................87

3-9 Equivalent model frequency response forf= - 0.01666 pu ..................................88

3-10 Dynamic model used for transient studies ..............................................................88

3-11 Static model used for steady-state studies...............................................................88

3-12 Wind-farm model ....................................................................................................89

3-13 Wind-farm controller...............................................................................................90

3-14 Wind-farm power regulator & current regulator step response (P=100%) ..........91

3-15 Induction generator PQ curve .................................................................................92

3-16 Wind-farm PF correction capacitor bank ................................................................93


13/194

xiii

3-17 PF correction capacitor bank current waveforms....................................................93

3-18 Capacitor bank impedance frequency scan .............................................................94

3-19 Machine control scheme operating states................................................................95

3-20 Electric power system start-up ................................................................................96

3-21 Detail of the transition from start-up mode to run mode.........................................96

3-22 Power Stabilizer system overview ..........................................................................97

3-23 Interface board overview.......................................................................................100

3-24 AC voltage scaling circuit (input [-1000+1000V], output [0 +3V]) .....................101

3-25 DC voltage scaling circuit (input [0 +1000V], output [0 +3V]) ...........................101

3-26 CT current scaling circuit (input [-5 +5A], output [0 +3V]).................................101

3-27 LEM current scaling circuit (input [-0.36 +0.36A], output [0 +3V])....................101

3-28 Power supplies voltage monitoring......................................................................102

3-29 Systems critical signals during turn on ................................................................103

3-30 Systems critical signals during turn off ...............................................................103

3-31 Darlington drivers .................................................................................................104

3-32 IPM status signals interface circuitry ...................................................................104

3-33 DAC circuit ........................................................................................................... 105

3-34 DSP built-in PWM output performance vs. FPGA...............................................107

3-35 IMP power circuit configuration ...........................................................................108

3-36 Isolated interface board .........................................................................................109

3-38 Power stabilizer control algorithm sampling rates................................................110

3-37 Interconnections between the different sub-systems of the power stabilizer........111

3-39 Power stabilizer control stages..............................................................................113

3- 40 Power stabilizer start-up sequence ........................................................................113

3-41 FPGA system overview.........................................................................................116


14/194

xiv

3-42 Up/Down counter. .................................................................................................117

3-43 PWM generator ..................................................................................................... 117

3-44 One phase dead-time generator detailed diagram .................................................119

3-45 Dead-time generators waveforms ........................................................................119

3-46 Watchdog logic .....................................................................................................120

4-1 DC link voltage response for different Kp gains...................................................121

4-2 DC link voltage response for different Ki gains ...................................................122

4-3 Iqrefcommand step change from -0.5 to 0.5 A per unit. Integral gain effect ........123

4-4 Iqrefcommand step change from -0.5 to 0.5 A per unit. Proportional gain

effect....................................................................................................................... 1244-5 Iq current regulator output for different Kp ..........................................................124

4-6 Iqref command step change from -0.5 to 0.5 and back to -0.5 A per unit ............124

4-7 Power stabilizer harmonic injection response for Ki=18 and Kp=1 .....................125

4-8 Current regulator frequency response ...................................................................126

4-9 Front-end inverter current waveform ....................................................................126

4-10 Frequency spectrum of the LCL currents..............................................................1274-11 Simplified system description ...............................................................................127

4-12 Power stabilizer voltage regulation performance..................................................128

4-13 Energy storage charge/discharge cycle .................................................................129

4-14 Control scheme with a losses compensation term.................................................129

4-15 Power stabilizer equivalent system .......................................................................130

4-16 Wind-power conditions under study .....................................................................1304-17 Measured and modeled high pass filter results for Kc=0.0064 W/J,

fcut_off=0.005 Hz......................................................................................................132

4-19 Measured high pass filter performance for different cut-off frequencies. Systemparameters Kc=0.0064 W/J.....................................................................................134


15/194

xv

4-20 Modeled high pass filter performance for different cut-off frequencies. Systemparameters Kc=0.0064 W/J.....................................................................................135

4-21 Measured high pass filter performance for different energy storage sizes.System parameters, Kc=0.0064 W/J, fcut-off=0.005 Hz. ..........................................135

4-22 Cut-off frequency trajectory of the adaptive high pass filter for a given energydeviation................................................................................................................. 136

4-23 Measured adaptive high pass filter performance for different Kfs. Systemparameters, Kc=0.0064 W/J, fcut-off-origin=0.005 Hz.................................................137

4-24 Measured adaptive high pass filter performance for different energy storagesizes........................................................................................................................ 137

4-25 Multiple sampling concept. ...................................................................................139

4-26. Measured and modeled power limiter 2 results for Kc=0.0064, RR=2MW/minute, A=0.3 MW/minute, I=1MW/2 seconds fcut-off=0.005 Hz. ................140

4-27 Measured power indexes activity. System parameters: Kc=0.0064 W/J, RR=2MW/minute, A=0.3 MW/minute, I=1 MW/2 seconds, and fs=10Hz.....................141

4-28 Measured power limiter 2 response to different Kc . System parameters: RR=2MW/minute, A=0.3 MW/minute, I=1MW/2 seconds, and fs=10Hz......................142

4-29 Measured power limiter 2 response to different ramp rate limits. ........................142

4-30 Measured power limiter 2 response to different average power fluctuation

limits....................................................................................................................... 143

4-31 Effect of linear interpolation on the average power fluctuation index activity.The sampling time of the original wind-power data is 2 seconds.... ......................144

4-32 Measured power limiter 2 response to different instantaneous power fluctuationlimits....................................................................................................................... 144

4-33 Measured power limiter 2 response to different sampling frequencies.................145

4-34 Measured synchronous machine output power for the different power limiter

control schemes......................................................................................................1464-35 Measured synchronous machine output power for the different power limiter

control schemes. .....................................................................................................147

4-36 Frequency regulator output for the different power limiters.................................147

A-1 Relationships among ds-qs, and abc axes .............................................................153


16/194

xvi

A-2 Stationary ds-qs components in the time domain.....................................................153

A- 3 Relationship among ds-qs and dr-qraxes ...............................................................154

A-4 Direct and quadrature components........................................................................155

A-5 Time domain representation of abc and d-q components .....................................156


17/194

xvii

Abstract of Dissertation Presented to the Graduate Schoolof the University of Florida in Partial Fulfillment of theRequirements for the Degree of Doctor of Philosophy

ADVANCED POWER ELECTRONIC FORWIND-POWER GENERATION BUFFERING

By

Alejandro Montenegro Len

May 2005Chair: Alexander Domijan, JrMajor Department: Electrical and Computer Engineering

As the cost of installing and operating wind generators has dropped, and the cost of

conventional fossil-fuel-based generation has risen, the economics and political

desirability of more wind-based energy production has increased. High wind-power

penetration levels are thus expected to augment in the near future raising the need for

additional spinning reserve to counteract the effects of wind variations. This solution is

technologically viable, but it has high associated costs. Our study presents a different

solution to short-term wind-power variability, using advanced power electronic devices

combined with energy-storage systems. New control schemes (designed to filter power

swings with a minimum of energy) were designed, modeled and verified through

experimental tests. We also determined the procedure to extract the corresponding per-

unit model parameters for simulations and test purposes.


18/194

xviii

We first reviewed D-Q transformations with emphasis on modeling of the system

and control algorithm. System components were then designed using criteria similar to

those used to design medium-voltage power products.

We tested a proof-of-concept for performance of the power converter in a scaled-

down isolated system using real wind-power data. Tests were conducted under realistic

system conditions of wind-penetration level and energy-storage levels, to better

characterized the impacts and benefits of the Power Stabilizer. We described the scaled-

down isolated electric power system used in the testing. We also analyzed the

performance of the wind-farm model and the synchronous machines governor to gain aninsight into the model systems limitations.

Simulation results carried out in Mathematical Laboratory (MATLAB) and Power

Systems Computer Aided Design (PSCAD) were compared to experimental data to verify

the performance of the power converter under different system conditions and algorithms.

Power limiters were also contrasted and evaluated for frequency deviations and

attenuated power fluctuations.

In summary we can say that, among all the power limiters considered in our study,

the adaptive high pass filter presented the best performance in terms of system robustness

and effectiveness.


19/194

1

CHAPTER 1INTRODUCTION

Wind-Energy Outlook

Wind power has been used for at least 3000 years, mainly for milling grain,

pumping water, or driving various types of machines. However, the first attempt to use

wind turbines for producing electricity date back to the 19th century. In 1891, Poul La

Cour in Demark built an experimental wind turbine driving a dynamo. The oil crisis of

the 1970s revived interest in wind turbines. Nowadays, the power is the fastest growing

source of energy in the world and its growth rates have exceeded 30% annually over the

past decade [1]. Cumulative global wind-energy generating capacity approached 40,000

MW by the end of 2003 [2]-[3]. The main drivers for developing of the wind industry in

the United States are

Federal Renewable Energy Policies, particularly the Production Tax Credit (PTC)that provides a 1.5 cent per kilowatt-hour credit for electricity produced from awind farm during the first 10 years of operation. This wind energy PTC expiredDecember 31, 2003 but will be reinstated through 2005 as part of a major taxpackage (H.R. 1308).

State-level renewable energy initiatives, such as the Renewable Portfolio Standard,or green pricing.

The Database of State Incentive for Renewable Energy [4] gives more information

on incentives. These government initiatives, together with technological advances, plus

the need for a new source of energy capable of meeting the worlds growing power

demand and the rising prices of conventional fossil fuel-based generation, make the wind

power one of the most promising industries in the future.


20/194

2

According to the European Wind Energy Association and Greenpeace, no barriers

exist for wind to provide 12% of the worlds electricity by 2020. The American Wind

Energy Association forecasts that wind power will provide 6% of the USs electricity by

2020 if the wind industry maintains an annual growth rate of 18%.

The positive effects of using such types of renewable resources are well known.

However, wind-power plants, like all other energy technology, have some drawbacks that

should be mentioned. These problems can be divided into major groups: environmental

issues and interconnection issues.

Environmental issues. Most significant among these are the following: Sound from turbines: Some wind turbines built in the early 1980s were very

noisy. However, manufactures have been working on making the turbines quieter.Today, an operating wind farm at a distance of 750 to 1,000 feet is no noisier than amoderately quiet room. Research in aero-acoustics is still being carried out tofurther reduce noise from wind on the blades.

Bird death: Wind turbines are often mentioned as a risk to birds, and severalinternational tests have been performed. The general conclusion is that birds areseldom bothered by wind turbines. Studies show that for example, overhead powerpole lines are far more hazardous for birds than wind turbines [2].

Wind-tower shadow effect: Wind turbines, like other tall structures cast a shadowon the neighboring area when the sun is visible. It may be irritating if the rotorblades chop the sunlight, causing a flickering effect while the rotor is in motion,especially when the sun is low in the sky.

Interconnection issues. Connecting wind turbine to operate in parallel with the

electric power system influences the system operating point (load flow, nodal voltages,

power losses, etc). These changes in the electric power system state bring up new system-

integration issues that system operators and power quality engineers must take into

account. These interconnection issues can be divided into operational issues and electrical

issues.

Operational Issues: These include unit commitment and spinning reserve.


21/194

3

The unit commitment problem is to schedule specific or availablegenerators (on or off) on the utility system to meet the required loads at aminimum cost, subject to system constraints. The most conservativeapproach to unit commitment and economic dispatch is to discount anycontribution from interconnected wind resources because of wind

variability. Operating reserve is further defined to be a spinning or non- spinning

reserve. Any probable load or generation variations that cannot beforecasted, such as wind power, have to be considered when determiningthe amount of operating reserve to carry out.

Electrical issues: These factors are considered in the next section.

Electrical Issues

Wind-turbine generator-system operation has some negative influence on power

systems. This influence on the electric power system depends on wind variations and on

wind-turbine technology. Impacts on the electric power system can be grouped as

follows:

Power quality: Voltage variations, flicker, harmonics, power-flow variations Voltage and angle stability Protection and control

The IEEE 1547 [5] and the IEC 61400-21 [6] standards are the bases to evaluating

the impact of such wind-turbine generation systems on the electric power system.

According to the IEEE 1547 [5, page 2] abstract,

This standard focuses on the technical specifications for, and testing of, theinterconnection itself. It provides requirements relevant to the performance,operation, testing, safety considerations, and maintenance of the interconnection. Itincludes general requirements, response to abnormal conditions, power quality,islanding, and test specifications and requirements for design, production,

installation evaluation, commissioning, and periodic tests. The stated requirementsare universally needed for interconnection of distributed resources (DR), includingsynchronous machines, induction machines, or power inverters/converters and willbe sufficient for most installations. The criteria and requirements are applicable toall DR technologies, with aggregate capacity of 10 MVA or less at the point ofcommon coupling, interconnected to electric power systems at typical primaryand/or secondary distribution voltages.


22/194

4

According to the IEC 61400-21 [6, page 9] abstract,

The purpose of this part of IEC 61400 is to provide a uniform methodology thatwill ensure consistency and accuracy in the measurement and assessment of powerquality characteristics of grid connected wind turbines (WTs). In this respect the

term power quality includes those electric characteristics of the WT that influencethe voltage quality of the grid to which the WT is connected.

This standard provides recommendations for preparing the measurements andassessment of power quality characteristics of grid connected WTs.

Table 1-1 shows technical specifications for interconnection and power assessment

covered in both standards.

Table 1-1. Technical specifications of IEC and IEEEInterconnection systemresponse to excursions Power quality assessment

IEEE VoltageFrequency

IEC VoltageFrequency

Voltage fluctuations:Continuous operationSwitching operation

Harmonics

As shown in Table 1-1, both standards overlooked one of the most significant

characteristics of wind farms: its variability (i.e., power fluctuations) [7], the mostimportant ones being

Gusty wind variations having a spectrum of frequencies from 1-10 Hz.

Shadow effect having a spectrum of frequencies from 1-2 Hz and producing torquevariations up to 30%.

Complex oscillations of the turbine tower, rotor shaft, gear box, and blades withspectrum frequencies from 2-100 Hz, and creating torque variations up to 10%.

Figure 1-1 shows actual output power data collected by NREL from two large

wind-power plants in the United States. The small wind farm has a capacity of about 35

MW, and the large one has a capacity of 150 MW.


23/194

5

0 0.5 1 1.5 2 2.5 3

x 106

0

10

20

30

40

Power(MW)

Time (s)

0 0.5 1 1.5 2 2.5 3

x 106

0

50

100

150

Trent Mesa Project. Wind power output May 2003

Power(MW)

Time (s)

Figure 1-1. Wind-power output for two wind farms during one month (May 2003). A)

Nominal capacity 35 MW. B) Nominal capacity 150 MW.

Even though the technology used in constructing the small wind farm is more than

a decade older than the large one, power fluctuations keep being an issue. Figure 1-2 is a

close-up ofFigure 1-1 and shows the magnitude of these power fluctuations.

Wind turbine manufactures usually provide power curves (Figure 1-3) to

developers to determine the amount of power that will be transferred into the grid for a

single turbine, given the wind speed. However, those figures represent only the mean

values, since a series of stochastic values cannot be controlled, and create additional

power fluctuations.

Wind-output power fluctuations can have different effects on the electric power

system, but the most significant ones are voltage variation and frequency variation in

small or isolated systems.

A

B


24/194

6

0 1 2 3 4 5 6 7 8

x 104

0

10

20

30

40

.

Power(MW)

Time (s)

0 1 2 3 4 5 6 7 80

50

100

150

Trent Mesa Project. Wind power output May 2003

Power(MW)

0 1 2 3 4 5 6 7 8

x 104

0

10

20

30

40

Power(MW)

Time (s)

0 1 2 3 4 5 6 7 8

x 104

40

50

60

70

80Trent Mesa Project. Wind power output May 2003

Power(MW)

Time (s)

Figure 1-2. Power fluctuation comparison. A) Nominal capacity 35 MW. B) Nominalcapacity 150 MW.

Figure 1-3. Typical power curve of a wind turbine.

As the power fluctuates, the reactive power required by the turbines changes as

well, and therefore voltage variations are expected, especially when the wind farm is

A

B


25/194

7

located at weak points in the system. To compensate for such voltage variations and keep

the voltage close to its rated value, several solutions are available: simple capacitor

banks, static voltage compensator (SVC), or static compensators (STATCOM).

A different approach must be taken for frequency variations due to power

fluctuations. Normally, wind farms connected to big systems do not present a major

problem in terms of frequency variations, because of the stiffness of the system.

However, with small or isolated systems that contain slow or no automatic generation

controls, a mismatch between generated and absorbed power can significantly affect

system frequency unless spinning reserves are significant. Figure 1-4 shows the effect ofwind-power fluctuation on an isolated system with a wind penetration level of 1%.

To counter these negative effects, countries and small isolated systems with high

wind-penetration factors developed special purchase power agreement (PPA)

requirements or indexes for wind-farm developers (Table 1-2).

Figure 1-4. Wind-farm output power vs system frequency.


26/194

8

Table 1-2. Wind-farm output-power requirements

Ramp Rate dP/dt InstantaneousAverage (maxvariation)

Netherlands


27/194

9

Solutions to Wind-Power Fluctuations

To reduce the effects of wind-power variations and meet the PPA requirements for

electric utilities, two solutions can be considered:

Higher spinning reserves Wind farm buffer

Increasing spinning reserves is a costly solution. A better approach would be to use

an energy-storage system that could deliver the required power when needed.

Work has been done in developing large-scale energy storage systems that have

overcome these issues by absorbing undesirable power fluctuations and providing firm,

dependable peaking capacity [8]. However, a less costly solution should be explored

based exclusively on power-fluctuation indexes (such as ramp rate indexes or

instantaneous fluctuation indexes).

State of the Art

Storing wind power is not a new concept; in fact, back in 1900, the father of the

modern wind turbine, Poul La Cour, tackled for the first time the problem of energy

storage. He used the electricity from the wind turbines for electrolysis and to store energy

in the form of hydrogen. However, with time, system requirements, energy storage

systems, and wind turbine ratings have changed.

Nowadays, the average wind turbine installed is around 1 MW, according to the

European Wind Energy Association, and wind-power farms usually consists of ten to

several tens of wind-turbine generators of rated power up to 2 MW. Thus, the amount of

energy storage needed to stabilize the power output change in the short term has

increased. Table 1-3 shows some recent projects dealing with output leveling of wind-

energy conversion.


28/194

Table 1-3. Large-scale wind-power output-leveling projects

Project name Wind farm size Energy storage systemActive power refercontrol scheme

Subaru Project [9].Tomamae wind-powerstation.

1.65 MW *16(Vestas).1.5 MW * 5(Enercon).

Total Capacity30.6 MW

VanadiumRedox Flow Battery

PVRB nominal =4.000kWEVRB=6.000kWhS inverter=6.000kVA

Moving Average odetermined as

Pbattery=Pwind average ((fort=8 seconds t

King Island [10]. Energy-storage system providedby Pinnacle VRB

250 kW*3850 kW*2


VanadiumRedox Flow Battery

PVRB nominal=200kWPVRB short-term ( 5 minutes)=300kWPVRB short-term (10 seconds)=400kWEVRB =1100kWh

Isochronous frequepower range.

Speed droop characand short-term loa

Oki project by FujiElectric

600 kW *3


Flywheel

E flywheel = 100 kW - 90 secP inverter flywheel side= 110kVAP inverter power system side= 150kVA

Power ramp rate lim


29/194

11

However, small-scale concepts and technical/economic feasibility studies have

been proposed (Table 1-4). Each of these projects has a different objective (frequency

control, power smoothing, load leveling, etc.). However, they all end up using one of the

topologies and energy-storage systems shown in Table 1-5, where the flywheel or

capacitors may be replaced by some other energy-storage medium. Tables 1-3 and 1-4

show that the amount of energy needed for wind-power balancing using current

technology and current pricing is so significant, that a more flexible and integrated

approach is needed.

Our study focused on developing new power smoothing control algorithms. Thenew integrated approach used a shunt-connected voltage-source converter with added

storage included on the DC link bus. The system can

Exchange active power with the system. Regulate voltage at the point of common coupling Increase power quality and system stability

Objective

Our purpose was to develop, simulate, and implement a proof-of-concept prototype

advanced-power electronic device capable of controlling and smoothing the power

fluctuations of a wind farm using an optimal amount of energy. The wind-power

generation buffering concept is shown in Figure 1-6. The Power Stabilizer was designed

to store excess power during periods of increased wind-power generation and release

stored energy during periods of decreased generation due to wind fluctuations.

We tested the performance of the advanced electronic device on

DC-synchronous machine set Passive load DC-asynchronous machine set Wind-farm buffer or also called Power Stabilizer


30/194

Table 1-4. Conceptual wind-power filtering projectsWind farm size Energy storage system Active power reference control scheme 20 MW Zinc-bromide battery

PZBB nominal (charge) =-750kWPZBB nominal (discharge)=1500kWEZBB =1500 kWh

Limiting instantaneous power fluctuations basedon a 2 seconds intervalPinstantaneous (t=2 seconds) = 1.3 MWAverage power levels over a 2 hour windowPaverage(t- t=2hours)= 200 kW

Maximum poweroscillation 2.5 MW

Super-conducting magneticenergy storage (SMES)

Active power reference is chosen to controlsystem frequency

300kW Electric double layercapacitorP ECS =100 kWE ECS =1.1 kWh

ESS active power reference is determined bydetection power oscillation components using ahigh pass filter

6GW Redox-flow battery(Regenesys )E=62004 MWhP=255MW

Power balancing

45KW FlywheelE flywheel= 12MJP drive=45kW

The active power demand is extracted via a 2ndorder Butterworth high pass filter, with a 5mHzbandwidth

55kW Lead Acid BatteryE battery=35kWhP converter=50kVA

Power smoothing


31/194

13

A

B

C

A

B

C 0.69

#2 #1

12.47

?L1

L2

L3

Vestas

VRCCV47

VnaS

NAS

VnbS

NBS

VncS

NCS

A

B

C

A

B

C0.48

#2#1

12.47

?

g1

g2

g3

g4

g5

g6

2

1

300.0

2

3

2

5

2

4

2

6

2

2

dcCur

gc12

5

gc22

5

1.0

ChopperReactor

1.0

EnergyStorageCapacitor

A

B

C

A

B

C 12.47

#2 #1

69.0

?

INVERTER

WIND FARM

0 20 40 60 80 100 1208800

9000

9200

9400

9600

9800

10000

10200

10400

10600

10800Wind Power Output

Power(W)

Time (s)

0 20 40 60 80 100 120-1000

-800

-600

-400

-200

0

200

400

600Power Stabilier Power Output

Power(W)

Time (s)

0 20 40 60 80 100 1208800

9000

9200

9400

9600

9800

10000

10200

10400

10600

10800Wind Power Output

Power(W)

Time (s)

Wind power + Wind farm buffer Power

Figure 1-6. Wind-farm generation buffering concept

Table 1-5. Basic system configurations

System configuration

Voltage source inverterESS connected at the DC link side [19]-[21]-[24]

SynchronousMachine

Voltage Source

Inverter

ESS (flywheel)

Electric SystemWind Turbine

DClink

ESS connected at the AC side [18]-[20]-[22]-[23]-[25]

InductionMachine

Voltage Source

Inverter ESS (flywheel)


DClink

Current source inverter (shunt connected) [13]

InductionMachine

Current Source

Inverter ESS (capacitors)


Chopper(DC/DCconverter)

ECS

Energy storage system

Available options [26] Compressed air energy storage Battery storage Electro-chemical flow cell systems Fuel cell/electrolyser/hydrogen systems Kinetic energy (flywheel) storage Pumping water


32/194


33/194

15

=

=

=

240

120

0

0.1

0.1

5.0

c

b

a

V

V

V

(2-1)

Figure 2-1 shows the time domain representation of this three-phase unbalanced system.

Figure 2-1. Unbalanced system

If we now calculate the symmetrical components of this unbalanced system, we obtain

=

=

=

1800

1802

01

167.0

167.0

833.0

V

V

V

(2-2)

The symmetrical components transformation is a good tool to determine the type of

distortion or asymmetry the system has. However, it has the drawback of having to use

phasors as input instead of time domain signals. Therefore a different transformation was

needed in order to extract the positive sequence component out of the rotating space

vector.Figure 2-2 shows the trajectory followed by the rotating space vector of the

unbalanced system in the d-q-o plane using Clarkes transformation. This trajectory is


34/194

16

clearly distorted from the ideal one, and the space vector no longer follows a circular path

(Figure 2-3).

Figure 2-2. Space vector trajectory of an unbalanced system in the d-q-o plane

Figure 2-3. Space vector trajectory projection over the d-q plane

Figure 2-4 shows the Vdrand Vqrcomponents (Parks transformation) of the

unbalanced system in the time domain for= 0.


35/194

17

Figure 2-4. Direct and quadrature components of an unbalanced system

It is clear that the Vdrcomponent is not constant any more, and it contains a 2nd

harmonic due to the negative sequence. This effect can also be explained in the frequency

domain as shown in Figure 2-5. The rotating reference frame aligns with the fundamental

frequency, w=2f, and therefore

a negative sequence (-w) appears as a 2nd harmonic a dc component appears as a 1st harmonic a positive sequence (w) has a constant value.

abcaxis

drq

raxis

0.167

0.833

-w wdcw

dc-w-2w

Figure 2-5. Representation of an unbalanced system in the frequency domain


36/194

18

Thus, it can be concluded that Clarkes and Parks transformations do not provide

suitable components that can be used in a voltage regulation control algorithm. It is

therefore necessary then to redefine the transformations in order to extract the desired

components.

Assuming the three-phase electric system has positive and negative sequence

components

)34

cos()34

cos(

)3

2cos()

3

2cos(

)cos()cos(

++=

++=

+=

wtVwtVV

wtVwtVV

wtVwtVV

npc

npb

npa

(2-3)

Clarkes transformation can be used to obtain

+

+

+==

+=+=

qsqsnpqs

dsdsnpds

VVwtVwtVV

VVwtVwtVV

)sin()sin(

)cos()cos((2-4)

where+ds

V and+qs

V are the d-q components of the positive sequence, whileds

V andqs

V

are the d-q components of the negative sequence.If we now assume that the symmetrical components remained constant for at least a

quarter of cycle, the equations can be rewritten as

( ) ( )

( ) ( )

( ) ( )

( ) ( )

=

+=

+

=

=

+

+

ttt

ttt

ttt

ttt

qsdsqs

qsdsds

qsdsqs

qsdsds

V2

V2

1V

2VV

21V

V2

V2

1V

2VV

2

1V

(2-5)


37/194

19

These components can now be transformed using the rotating reference frame in

order to obtain the positive sequence component. Figure 2-6 shows the block diagram of

the algorithm used to extract the positive-sequence component. The same concept could

be used if the negative sequence magnitude is needed.

abd

dsq

s

Vds

Vqs

Delay (1/f/4)

+

+

0.5

Delay (1/f/4)

_

+

0.5

Vds+

Vqs+

dsqs

drq

r

x+

+

+

Vdr+

Vqr+

x Vmagnitudepositive sequence

Vdr

Vqr

VaVbV

c

dsq

s

drqr

Filter

Sliding windowfilter

Figure 2-6. Positive-sequence extraction algorithm

Figure 2-8 shows the algorithm performance when an unbalanced fault condition

takes place at t=0.02 sec (Figure 2-7). The data used for this example is given by

Equation 2-2.

Figure 2-7. Voltage waveforms for an unbalanced fault event


38/194

20

Figure 2-8. Response of the positive-sequence extraction algorithm. A) Positive sequenceusing and 1 cycle filters. B) Positive sequence using Vdrwith 1 cycle filter

The meaning of the different plotted variables is the following:

Vpositive-sequence magnitude is the output of the positive-sequence extraction algorithm. Asexpected, its time response is only one quarter of a cycle. However, the transientresponse is very abrupt an uneven.

Vpositive-sequence magnitude (1/2 cycle filter) is the filtered signal of Vpositive-sequence magnitude usinga half cycle sliding window filter.

Vpositive-sequence magnitude (1 cycle filter) is the filtered signal of Vpositive-sequence magnitude using aone-cycle sliding window filter. Its transient response is the slowest but at the sametime the smoothest among the three signals.

Vdr filtered is the filtered signal of Vdr . The one cycle sliding window filter (alsocalled moving average) rejects all harmonics. Therefore there is no need to use theVds+ and Vqs+ calculator to extract the positive sequence. However its transientresponse is not as smooth as the Vpositive-sequence magnitude (1 cycle filter) one.

Real Power Calculation Using dq Components

As shown in Appendix A Parks transformation matrix is not unitary

( [ ] [ ] 1 dqot

dqo TT ) and therefore is not power invariant.

The total instantaneous power in abc quantities can be transformed into q-d-o

quantities as shown in Equation 2-6.

A B


39/194

21

This relationship between dqo quantities and the instantaneous power is later used

in the control system to determine the amount of direct-current component ( drI ) needed

to meet the power fluctuation requirements.

[ ] [ ]

[ ] [ ][ ] [ ]

[ ]

( )ooqrqrdrdr

o

qr

dr

oqrdr

o

qr

dr

dqo

t

dqooqrdr

o

qr

dr

dqo

t

o

qr

dr

dqo

c

b

a

t

c

b

a

ccbbaaabc

IVIVIV

I

I

I

VVV

II

I

TTVVV

I

I

I

T

V

V

V

T

I

I

I

V

V

V

IVIVIVP

++=

=

=

=

=++=

3

1

2

3

3

100

02

30

002

3

11

11

(2-6)

Phase Locked Loop

The phase angle of the utility voltage () is of vital importance for the operation of

most of the advanced power electronic devices connected to the electric utility, since it

has a direct effect on their control algorithms.

A simple and fast method to obtain the phase angle of the utility voltage is to use

Clarkes transformation as shown in Equation 2-7.

=

=

ds

qs

c

b

a

qs

ds

X

X

X

X

X

X

Xarctan

2

3

2

30

2

1

2

11

3

2 (2-7)


40/194

22

However, this approach is not robust since it is very sensitive to system

disturbances. The phase angle distorts as the utilitys voltage becomes affected by

different power quality events, such as voltage unbalance, voltage sags, frequency

variations, etc.

Figure 2-9 shows the voltages phase angle under unbalanced conditions using

Equation 2-7. The angle distortion is due to the negative sequence component of the

unbalanced three-phase system.

Figure 2-9. Distortion of phase angle due to a negative sequence component

In order to lock the phase angle of the utility voltage in a robust way, a phase

locked loop (PLL) was used.

Assuming a balanced three phase system, the control model of the PLL was

obtained using Parks transformation as shown in Equation 2-8.

=

=

=

)240cos(

)120cos(

)cos(

21

21

21

)240sin()120sin()sin(

)240cos()120cos()cos(

3

2

21

21

21



32

***

***

***

***

wtV

wtV

wtV

V

V

V

V

V

V

c

b

a

o

qr

dr

(2-8)


41/194

23

Where * is the PLL phase angle output, is the utilitys phase angle, anddt

dw = .

Thus, if(t=0)=0, we can substitute wt for(t) and obtain

=

)240cos(

)120cos()cos(

21

21

21

)240sin()120sin()sin()240cos()120cos()cos(

3

2 ***

***

V

VV

V

VV

o

qr

dr

(2-9)

Using trigonometric identities, Equation 2-9 results in

=

=

0

)sin(

)cos(

0

)sin(

)cos(*

*

VV

V

V

V

o

qr

dr

(2-10)

Where is the error between the utility angle and the PLL output. If the is set to

zero, Vdr=V and Vqr=0. Therefore, it is possible to lock the utility angle by regulating Vqr

to zero without needing any information regarding the magnitude of the utility voltage.

Figure 2-10 shows the details of the PLL algorithm used in our study. The limits of

the controller integrator and the limiter were 30 rad/sec. Thus, the PLL was able to track

the system frequency as long as this was within 26030 rad/sec or 55 to 65 Hz range.

To use linear control techniques for the design and tuning of PLL controller, it was

assumed that:

For small values of, the term sin () behaved linearly, i.e., sin() . Wref was assumed to be a constant perturbation. Limiters behave linearly for small control actions, and therefore can be removed.

abd

dsq

s

Vds

Vqs

dsq

s

drq

r

Vdr

Vqr

Va

Vb

Vc

Ki

Kp +

+

30

-30

s

1

30

-30

+

+

Wref

=2f

s

1

Figure 2-10. PLL diagram


42/194

24

Figure 2-11 shows the PLL control loop after eliminating the non-lineal terms.

Ki

Kp +

+

s1

s

1

-

+

PLL controller Plant transfer

Function

Control

action

Figure 2-11. PLL simplified model

The closed loop transfer function ofFigure 2-11 determines the dynamic

characteristics and stability of the system, and can be expressed as

Ip

Ip

KsKsKsKH++

+==2

*

(2-11)

The control system (Kp and Ki) was designed to satisfy two performance

objectives

< 10% overshoot Settling time inside the 2% band error lower than 2 secs

The criterion to select the settling time was a tradeoff between high distortion

rejection and tracking of normal system frequency variations.

The PLL closed loop transfer function was compared to a standard second order

transfer function to determine the regulators gains. The obtained values were

485.27.022

1.827.0

44

sec2t

)overshoot5%for(7.0

22

2

s

===

=

=

==

=

=

np

s

nI

K

tK

Figure 2-12 shows the systems closed-loop step response for two different PI

regulators.


43/194

25

The originally designed regulator did not meet the system requirements due to the

effect of the zero introduced by the PLL regulator. This additional zero increased the

overshoot, but it had very little influence on the settling time. Thus, it was necessary to

tune the original regulator gains in order to meet the system requirements.

Figure 2-12. PLL system step response

Figure 2-13 shows the root locus of the single-input single output PLL system for

the two regulators.

Figure 2-13. Root locus for two different regulator gains


44/194

26

Figures 2-14 and 2-15 show the PLL system response to a negative sequence

condition (V2=16.6%) and a system frequency excursion (w=260+30 rad/sec).

Figure 2-14. PLL system response to an unbalanced system condition

Figure 2-15. PLL system response to a frequency excursion. A) Angle. B) PLL error.

Control Algorithm Design

Parks transformation was used to model the systems equations to facilitate the

design of the control system. The usage of a rotating reference frame had the following

advantages:

Improvement of the steady-state performance of the current controllers:Sinusoidal signals were transformed into dc components, and accordingly it ispossible to achieve small signal errors.

High bandwidth current controllers: Feedback signals and reference signalswere not sinusoidal, but dc.

A B


45/194

27

Decoupling of active and reactive power: This was very useful when trying tocontrol voltage at the point of coupling while meeting the system requirements interms of power fluctuations.

Figure 2-16 shows the overall system topology as well as the sign notation that was

used in the control system design. In general, power flowing out of the inverter will be

considered to be positive. The objective was to smooth out wind-power fluctuations using

the power stabilizer as a buffer. The energy-storage voltage was expected to change in

order to accommodate for those changes in wind power.

Iwind

Vpcc

Vf

Iinv Vinv

VdcVchopper Vstorage

IchopperCdcLfLxfrm

Cf

WIND

FARM

UTILITY

SYSTEM

Xsource

Transformer

equivalent impedance

Filter

Inverter DC link bus Chopper

ESS

P + Figure 2-16. System description

Inner regulators

Inverter system model. For the following set of equations, it was assumed that the

inverter behaved as an ideal controllable voltage source, neglecting the effects of the

current harmonics. Systems non-linearities, such as saturation or dead-time effects were

taken into consideration later on in the design.

The capacitor filter was neglected in the analysis, since the filter current

represented a small portion of the inverters current.

The system can then be represented as shown in Figure 2-17.


46/194

28

Vpcc a R L Vinv a

VDC LINKC

Vpcc b R L Vinv b

Vpcc c R L Vinv c

Iinv a

Iinv b

Iinv c

Figure 2-17. Simplified system model

The system equations for the simplified model are

+

+

=

pcca

pcca

pcca

invc

invb

inva

invc

invb

inva

invc

invb

inva

V

V

V

I

I

I

dtdL

I

I

I

R

V

V

V

(2-12)

Applying Parks transformation we get

[ ] [ ] [ ] [ ]

+

+

=

opcc

qrpcc

drpcc

dqo

oinv

qrinv

drinv

dqo

oinv

qrinv

drinv

dqo

oinv

qrinv

drinv

dqo

V

V

V

T

I

I

I

Tdt

dL

I

I

I

TR

V

V

V

T1111 (2-13)

[ ] [ ] [ ] [ ] [ ] [ ]

+

+

=

opcc

qrpcc

drpcc

dqodqo

oinv

qrinv

drinv

dqodqo

oinv

qrinv

drinv

dqodqo

oinv

qrinv

drinv

V

V

V

TT

I

I

I

Tdt

dLT

I

I

I

TRT

V

V

V111 (2-14)

[ ][ ]

[ ]

+

+

+

=

opcc

qrpcc

drpcc

oinv

qrinv

drinv

dqo

oinv

qrinv

drinv

dqo

dqo

oinv

qrinv

drinv

oinv

qrinv

drinv

V

V

V

I

I

I

dt

dT

I

I

I

dt

TdTL

I

I

I

R

V

V

V1

1

(2-15)

[ ][ ]

[ ] [ ]

+

+

+

=

opcc

qrpcc

drpcc

oinv

qrinv

drinv

dqodqo

oinv

qrinv

drinv

dqo

dqo

oinv

qrinv

drinv

oinv

qrinv

drinv

V

V

V

I

I

I

dt

dTTL

I

I

I

dt

TdTL

I

I

I

R

V

V

V1

1

(2-16)


47/194

29

[ ][ ]

+

+

+

=

opcc

qrpcc

drpcc

oinv

qrinv

drinv

oinv

qrinv

drinv

dqo

dqo

oinv

qrinv

drinv

oinv

qrinv

drinv

V

V

V

I

I

I

dt

dL

I

I

I

dt

TdTL

I

I

I

R

V

V

V 1

(2-17)

Where

[ ]

dt

d

dt

d

dt

d

dt

Td dqo

=

=

=

0)240cos()240sin(

0)120cos()120sin(

0)cos()sin(

1)240sin()240cos(

1)120sin()120cos(

1)sin()cos(1

(2-18)

It can be shown that

[ ] [ ]

=

=

=

=

000

00

00

000

001

010

0)240cos()240sin(

0)120cos()120sin(

0)cos()sin(

21

21

21



3

2 ***

***

1

dt

TdT

dqo

dqo

(2-19)

Thus, the equations for the simplified model in the d-q plane are

+

+

+

=

opcc

qrpcc

drpcc

oinv

qrinv

drinv

oinv

qrinv

drinv

oinv

qrinv

drinv

oinv

qrinv

drinv

V

V

V

I

I

I

dt

dL

I

I

I

L

I

I

I

R

V

V

V

000

00

00

(2-20)

The zero-sequence component can be removed, since the system is a three-phase

three-wire inverter with the DC link bus isolated from the AC side (the DC link mid-

point will not be tapped to neutral). Removing the zero sequence we obtain

drinvqrpcc

qrinv

qrinvqrinv

qrinvdrpcc

drinv

drinvdrinv

ILVdt

dILIRV

ILVdt

dILIRV

+++=

++=

(2-21)


48/194

30

Equation 2-21 can be represented as a coupled electrical system as shown in Figure

2-18.

R LV

pcc drV

inv dr

Iinv dr

LIinv qr

R L

Vpcc qr

Vinv qr

Iinv qr

LIinv dr

Figure 2-18. Electrical representation of the dq components. A) Direct circuit. B)Quadrature circuit.

Using Laplaces transformation we can re-write the equations as Equation 2-22.

( )

( ) )()()()(

)()()()(

sILsVsILsRsV

sILsVsILsRsV

drinvqrpccqrinvqrinv

qrinvdrpccdrinvdrinv

+++=

++=

(2-22)

Thus, the block diagram of the system is represented in Figure 2-19.

Vpcc dr

Vinv dr

Iinv dr

LsR +

1+

-

L

L

Vinv qr

Iinv qr

LsR +

1+

-

Vpcc qr

+

-

Figure 2-19. System model block diagram

A

B


49/194

31

The inverters critical control variable was the inverters current. This was due to

the fact the outer control loops, such voltage regulators, power regulators, etc, were based

on the inner current regulators. That was why the current controllers were designed to

meet two basic requirements, which were high accuracy and high bandwidth.

The inverters terminal-voltage needed to generate the desired inverter current can

be determined as

drinvqrpccdropdrinvqrpcc

qrinv

qrinvqrinv

qrinvdrpccdropqrinvdrpcc

drinv

drinvdrinv

ILVVILVdt

dILIRV

ILVVILVdt

dILIRV

qr

dr

++=+++=

+=++=

(2-23)

The voltage drop due to the filter inductance was compensated using a PI

controller. Figure 2-20 shows the inveters current controller implementation for the

system given in Equation 2-23.

Vpcc dr

Vinv dr

Iinv dr

LsR +

1+

-

L

L

Vinv qr

Iinv qr

LsR +

1+

-

Vpcc qr

+

-

SYSTEM MODEL

+

-+

Vdrop dr

++

+

Vdrop qr

Ki

Kp +

+

s1

+

-

Ki

Kp +

+

s

1

+

-

Iinv dr

Iinv qr

Iinv dr ref

Iinv qr ref

L

L

CURRENT REGULATORS

drpccV

qrpccV

Figure 2-20. Inverter current regulator-system model block diagram

The character ^ over a constant or variable indicates that the quantity is estimated,

and therefore subject to measurement errors.


50/194

32

To design the current regulator gains, cross-coupling factors were assumed to

cancel each other out. Under these conditions, the simplified current regulator block

diagram is shown in Figure 2-21.

Iinv dr

LsR +

1

Iinv qr

LsR +

1

SYSTEM MODEL

Ki

Kp +

+

s

1

+

-

Ki

Kp +

+

s

1

+

-

Iinv dr

Iinv qr

Iinv dr ref

Iinv qr ref

CURRENT REGULATORS

Figure 2-21. Inverter current regulator-system model simplified block diagram

Figure 2-21 shows that:

The system behaves linearly, and therefore linear control techniques can be used to

determine the regulators gains. Both regulators are identical.

Only an estimation of L and R (filter inductance + transformer equivalentimpedance) are needed to design the current regulator.

Given the filter/transformer characteristics in p.u., the closed-loop transfer function

ofFigure 2-22 is shown in Equation 2-24.

Ki

Kp +

+

s

1

+

-

Iref

LsR +

1 IControl Action

Figure 2-22. Simplified current control diagram


51/194

33

( )Ip

Ip

ref KsKRLs

KsK

I

IsH

+++

+==

2)( (2-24)

Using the following system data, the transfer function is given in Equation 2-25.

X=Xtransfomer+Xfilter=5%+10% = 0.15 L= 400 H X/R=10 R=0.015 Note: More on the system parameters can be found in the per-unit mode section.

( )Ip

Ip

KsKs

KsKsH

+++

+=

015.00004.0)(

2(2-25)

The Figure 2-23 shows the system step response for two different current regulator

gains.

Figure 2-23. Current regulator step response

Even though the current regulator with the highest gains had a faster settling time,

the control action required to obtain such a response doubled the regulator with the

lowest gains. To avoid possible system saturations the control action was kept below 1

pu.

The best PI controller performance was achieved when the plants dominant pole

was cancelled by the controller (Equation 2-26). Thus, the zero at -p

I

K

K was assigned to

the time constant of the plant, which was,L

R

K

K

p

I = .


52/194

34

s

K

KsK

s

KKPI

p

Ip

Ip

+

=+= (2-26)

The synthesis was done by selecting the integral time constant of the PI equal tothat of the load. For our study the selected values were

1

5.37

=

==

p

I

K

L

RK

Chopper system model. The analysis of the chopper system was less complex than

the inverter one, since no transformations were involved. Again, it was assumed that the

chopper behaved as an ideal controllable voltage source and therefore the effects of the

current harmonics were neglected.

Vchopper Vstorage

Ichopper

Figure 2-24. Chopper equivalent system

The system equations for the chopper equivalent circuit (Figure 2-24) are given in

Equaion 2-27.

dt

dILVV

Vdt

dILV

chopper

storagechopper

chopper

chopper

storage

=

+=

(2-27)

The choppers terminals voltage needed to generate the desired chopper current

can be determined as

dropstoragechopper VVV = (2-28)


53/194

35

The voltage drop due to the chopper inductance was compensated using a simple P

controller. The gain of the controller was found by converting the continuous system into

discrete time system as shown in Equation 2-29.

t

LKIKVV

dt

IILV

dt

ILVV

LchopperLstoragechopper

chopperchopper

storage

chopper

storagechopper

ref

==

=

=

where

)(

(2-29)

Where KL is the regulators gain and t is half of the sampling time period.

Figure 2-25 shows the implementation of the choppers current regulator.

Ichopper

+-

KL

Vstorage

-+

Ichopper ref

Vchopper

Figure 2-25. Chopper current controller

Outer regulators

There were a total ofthree controllable currents, which consisted of Ichopper_ref,

Iinvdr_ref, and Iinvqr_ref.. However, there werefourvariables that needed to be controlled,

which were voltage at the dc link bus, voltage at the point of common coupling, voltage

at the energy storage system, and wind farm power fluctuation. Table 2-1 shows how

these variables were assigned to the respective current regulators.

Table 2-1. Outer regulator assignationInner current

regulator

Variable to be

controlled CommentsIinv dr ref Vstorage, Pwind The direct current component will be responsible

for controlling the state of charge of the ESSand for smoothing the wind farm output power

Iinv qr ref Vpcc The quadrature current component will bedeployed for voltage regulation purposes

Ichopper ref Vdc link The chopper current will regulate the DC link busvoltage.


54/194

36

DC link Voltage regulator. The DC link bus was the bridge between the energy

storage system (chopper) and the inverter. Therefore, it was a critical variable in the

overall system. Poor DC voltage regulation could bring the system down, since the

inverter and chopper would not be able to meet their respective voltage requirements.

The DC link system can be mode

advanced power electronic for wind-power generation buffering (th., alejandro montenegro león)

Documents