Transient Stability of Distributed Generators in thePresence of Energy Storage Devices

Mohammed Benidris, Student Member, IEEE, Salem Elsaiah, Student Member, IEEE,Samer Sulaeman, Student Member, IEEE and Joydeep Mitra, Senior Member, IEEE

Department of Electrical and Computer EngineeringMichigan State University

East Lansing, Michigan 48824, USA(benidris@msu.edu, elsaiahs@msu, samersul@msu and mitraj@msu.edu)

Abstract—Several small-scale distributed generators DGs havebeen recently used in power and distribution systems. Placementof such small-generators to the power grid has numerous econom-ical and environmental advantages. However, high penetrationlevel of these devices could also have a significant impact onthe voltage and angle stability limits of the system. This canbe partly attributed to the fact that most DGs are inertia-lessgenerators or sometimes having small inertia. Therefore, in non-conventional power systems where DGs are present, the overallsystem inertia will significantly decrease. Such low inertia maylead to loss of synchronism during abnormal fault conditionsand large disturbances. One method to compensate for thereduced system inertia is to connect short-term energy storageto the DG bus. The entire unit is termed as virtual inertiaor Virtual Synchronous Generator VSG. This paper introducesa methodology for stability enhancement of non-conventionalpower systems. The method utilizes the concept of virtual inertiato account for the transients that usually take place on powersystem. A control algorithm was integrated to the storage devicethat is connected to the DG bus through bidirectional DC-DCconverter and DC-AC converter. The method was demonstratedon a 5-bus power system.

Index Terms—kinetic energy, transient stability, storage ele-ments, virtual inertia.

I. INTRODUCTION

Electric power distribution systems have been operated ina vertical and centralized manner for many years. In recentyears, however, due to certain environmental, economical,and, political concerns, small-scale resources of energy wereintroduced into distribution systems to support the main grid.Such energy sources are commonly denoted as Dispersed orDistributed Generators DGs [1]. Distributed Generators areable to operate in grid-connected or stand-alone mode ofoperation and can be located at or even near the end user node.Despite the fact that DG installation on power system hasseveral advantages, the introduction of such energy resourcesbrings up a number of technological and operational issuessince the distribution system can no longer be considered asa single-source passive network.

One of the major problems associated with DG installationis the noticeable reduction in the total system inertia whichis needed during abnormal system conditions. For example,in conventional power systems, stability can be traditionally

maintained by regulating the large-inertia synchronous gener-ators to keep the system in normal operating state [2]- [3].Conversely, in the deregulated power and distribution systemswhen DGs participate in power generation and control, theamount of inertia provided by such small-scale generatorsmight not be adequate to accommodate every disturbanceoccurred in the system. This can be attributed, in part, to thefollowing,

• Most of nowadays rotating DGs such as micro turbinesare interfaced with power electronic converters, whichhide their inertia.

• Certain types of DGs such as Photovoltaic (PV) andFuel Cells (FCs) do not initially have rotating masses.Therefore, their contribution to the entire system rotatingkinetic energy is omitted.

• As of now, the vast majority of Wind-Turbine InductionGenerators (WTIG) being installed in medium and lowvoltage distribution systems are characterized by bothsmall-size and low-rating, thus there influence on theoverall system inertia is relatively small.

The aforementioned DGs characteristics combined with thefact that not all synchronous generators are being in service allthe time, a practical meaning that compensates for the reducedinertia and increases the stability limit becomes necessary.

One method to extend the stability limit of the non-conventional power systems can be achieved by the meaning ofVirtual Synchronous Generators VSGs or just virtual Inertia VI[4]- [6]. The idea behind the VSG is relatively novel and wasactually proposed to compensate for the relatively low inertiapower systems in which DGs are dominant. Consequently,VSG can be considered as a control strategy in which theelectronically-interfaced distributed generator will behave as aconventional generator system that uses prime-mover as wellas synchronous machine. Therefore, additional inertia can beprovided to the non-conventional power systems by addingshort-term energy storage devices to the bus at which the DGis located. The combined unit will act as a VSG which hasthe ability to supply short-term energy during transients anddisturbances.

A method for power system stability improvement by virtual

978-1-4673-2308-6/12/$31.00 ©2012 IEEE

Energy Storage Device

DG

Grid

Fig. 1. Interfacing of the VSG unit to the Grid

kinetic storage has been proposed in [7]. A short-term energystorage was added to the system to form a virtual synchronousgenerator. The rotor angle and the clearing time were used asindicators for system performance evaluation. A double-layercapacitor bank has to be used as a provider for short-termenergy so that the instability of the rotor angle is mitigated.In [8], an approach in which distribution static compensator(DSTATCOM) is implemented for power system stability en-hancement. This method used droop control through a parallelconnected converter to produce the required real and reactivepower by controlling voltage magnitude and angle. A largecapacitor bank was used to provide a short-term power. Thesize of the capacitor, however, has to be chosen carefully inorder to ban the low frequency oscillations. Vu Van Thonget al. presented a method to demonstrate the operation ofthe VSG on practical distribution systems [9]. A small-scaleVSG rated at 5-10 KW is firstly developed. It was mainlyconsisting of a power electronic conversion circuit, an energy-storage device, and a VSG control algorithm. A flexible powerelectronic conversion circuit was used to validate the numericalsolutions obtained in the theoretical phase of simulations.

In this paper, a method for stability enhancement for non-conventional power systems is presented. The method utilizesthe concept of virtual inertia or Virtual Synchronous Gener-ators to account for the transients that usually take place onpower system. In this research, virtual inertia is realized byconnecting a short-term energy storage device “such as ultra-capacitor”, in parallel, to the bus at which the DG is located.Then, the whole unit, which comprises the storage and theDG, is interfaced to the grid by suitable converter circuit asshown in Fig. 1. A method to estimate and model the storagedevice rating has also been implemented in a previous work[10]. Though the work presented here can be considered asan extension to what is done in [10], the key objective hereis to develop a control strategy to compensate for the low-inertia system. The method is based on linearizing the swingequation around the machine operating point that producesthe amount of power required to stabilize the machine duringthe disturbances. This amount of power is used to producea reference current for the power electronic converter thatconnects the energy storage device to the DG bus.

This paper is organized as follows: section II presents

modeling aspects. The control strategy of the storage devices isexplained in section III. Short-Term Energy Storage Devicesand Transient Stability Calculations is illustrated in sectionIV. A case study is demonstrated in section V. A conclusionis given in section VI.

II. MODELING ASPECTS

This section briefly discusses the modeling aspects whichare employed during the simulation phase.

A. Synchronous Machine Model

The equation of motion of a synchronous machine rotorconnected to an infinite bus and neglecting the damping powercan be written as,

2H

ωsω̇ = Pm − Pe = Pa p.u. (1)

Where H is the inertia constant, ωs is the system ratedfrequency, Pm is the mechanical power, Pe is the electricalpower, Pa is the accelerating power and ω is the angularvelocity of the rotating magnetic field.

Neglecting the losses, the difference between the mechani-cal and electrical powers gives the net accelerating power Pa,which is equal to zero in steady-state conditions.

Now, by neglecting the stator winding resistance, the electricpower Pe delivered by a rotational machine can be given as,

Pe =|Ea||Vt|

Xssin δ (2)

where Ea is the machine internal voltage, Vt is the terminalvoltage, Xs is the synchronous reactance and δ is the torqueangle.

For transient stability studies, the mechanical power for thefirst swing can be assumed constant [2]. There are several rea-sons for disturbances that take place on power system and thesynchronous machine will behave accordingly. For instance,if a large amount of load is connected to the system, themachine will decelerate and certain control actions should beperformed to keep the system frequency within predeterminedlimits, hence maintaining the system stability. On the otherhand, if a large amount of load removed from the systemdue to abnormal fault conditions, the machine acceleratesconsequently and a control action has to be performed too, inorder to preserve the stability limits. Such control actions canbe done by means of power system stabilizers in conventionalpower systems. In non-conventional systems, however, dis-tributed generators are not equipped with such control devicesfor several economical and operational reasons. Moreover, asit was mentioned before, most DGs are inertia-less or just havesmall inertia according to their sizes. As a result, for powersystems when the inertia-less distributed generators are used,the kinetic energy of the DG can be increased or decreased byconnecting a short-term energy storage to the DG bus. Thisconnection will form a virtual inertia unit that can be used toenhance the system stability and extend its limits. The problemof sizing of the storage devices is described in the followingsection. A solution methodology was also described and thenimplemented.

B. Modeling and Sizing of Short-term Energy Storage Devices

Referring to equation (1), the difference between the me-chanical and electrical power gives the net accelerating powerPa. This accelerating power is equivalent to zero in steady-state. Therefore, the stability limit of the given system can beextended if a certain amount of power is added to/or subtractedfrom the accelerating power term according to the systemstatus, acceleration or deceleration. This amount of power canbe assumed constant since it is supplied as a short-term energy.In doing so, the equation of motion of the machine can be nowexpressed as,

2H

ωsω̇ = Pm − Pe ± Ps = Pa ± Ps p.u. (3)

where Ps is the power supplied or absorbed by the storagedevice.

It is worthy to say here that the sign of Ps is positive duringdeceleration, but it is made negative during acceleration periodto maintain equilibrium.

From [10], with the assumptions that the input mechanicalpower is constant for transient stability study, ignoring damp-ing coefficient and linearizing around the operating point; thesize of the energy storage devices can be estimated.

If equation (1) is linearized with ΔPm = 0, we get thefollowing result,

2H

ωs

d2Δδ

dt2= −KΔδ (4)

where K is the synchronizing power coefficient.

K =dPe

dδ=

|Ea||Vt|Xs

cos δ0 (5)

From (1) and (4), to keep the machine running in a balancedcondition, Pa has to be close to zero. Therefore, if this poweris provided or absorbed by an energy storage device duringthe disturbances, the machine will maintain its stability.

Therefore, the storage energy device should provide powerequal to the right hand side of equation (4).

PE =|Ea||Vt|

Xscos δ0Δδ (6)

where PE is the required power to maintain system stability.Equation (6) presents a general formula for estimating the

size of the energy device which is required with combinationwith control systems in maintaining stability of power systems.However, the rated values of the internal voltage, terminalvoltage and power angle are provided by the manufactures.Also, power angle deviation can be linearized in a piecewisemanner. Therefore, by linearization, the size of these devicescan be estimated.

In this study, the energy storage devices are utilized toenhance transient stability of systems with high level ofDGs penetration. Having said that, the protective devices areassumed not to operate during this transient period.

=

3-Phase ConverterBidirectionalConverter

Energy StorageDevice

DC-DCConverter

To theAC

System

Fig. 2. Connection of the energy storage device to the DG bus

III. CONTROL STRATEGY OF THE STORAGE DEVICES

In some applications, the energy storage devices are con-nected to the DGs side to smooth the output power. Forinstance, in Photovoltaic systems, a storage device is requiredto provide short-term power in case of presence of cloudsand to recharge in case of excess power. In such applications,the controller switches between charging and discharging onthe time horizon of minutes or even hours. However, in caseof transients the controller is required to act in time horizonof milliseconds to seconds. Therefore, if the controller issomehow designed to inject power from the storage deviceto the system or vice versa, which equal to the synchronizingpower coefficient times the change in the power angle, thesystem can be stabilized.

Fig. 2 shows one way to connect the storage device tothe DG bus. The bidirectional DC-DC converter is used toadjust the voltage across the DC-AC converter since energystorage devices voltages usually fluctuate and to transfer powerin both directions. Also, the bidirectional converter can boostthe storage device voltage so that no need to connect so manyenergy storage devices to get the desired voltage. Furthermore,bidirectional converters can have separate control scheme toadjust the voltage across the DC-AC converter leg.

The input voltage of the DC-AC converter which is equalto the output voltage of the bidirecational converter can beexpressed as [11],

v̂in =d

1− dvb (7)

Where, v̂in is peak DC voltage across the DC-AC converter,d is the duty cycle (i.e., interval ratio) and vb is the energystorage device voltage. In some applications, instead of bidi-rectional converter with switches, they use Z-source invertersuch as the one used in the HEV [12].

The control scheme of the bidirectional DC-DC converteris assumed to maintain its output voltage constant.

The DC-AC converter plays the most important role incontrolling the amount of the output power. By controllingthe modulation index M of the converter, which is the theratio of the magnitude of the reference waveform and the

triangular waveform, the amount power injected to the systemcan be controlled [11]. The peak output voltage of the DC-ACconverter to the load side can be expressed as [11],

v̂ac = M.v̂in2

(8)

By assuming unity power factor, the output power from theDC-AC converter can be expressed as [11],

Pout =3√2v̂ac (9)

Where I is the rms current that can be injected to/or withdrawnfrom the DG bus.

IV. SHORT-TERM ENERGY STORAGE DEVICES AND

TRANSIENT STABILITY CALCULATIONS

For the first swing in the transient stability analysis, asimplified model can be utilized without compromising theresults. This simplified model is characterized as follows [2]:

1) Mechanical power input is constant.2) Damping or asynchronous power is negligible.3) Constant-voltage-behind-transient-reactance model for

the synchronous machines is valid.4) The mechanical rotor angle of a machine coincides with

the angle of the voltage.5) Loads are represented by passive impedances.

The stability calculation procedures for multi-machine systemsis well documented in the literature and only the flowchart isprovided in this work for illustration and is shown in Fig. 2.

The only modification for conventional power system tran-sient stability analysis algorithm, is injecting or absorbingsome power by the energy storage devices to balance theacceleration and the deceleration dynamics. After calculatingthe final estimate of the power angle and speed deviation,the difference in accelerating and decelerating power can bebalanced.

The simulation time is equally divided into N time stepswith time length h second for every step. At every time step,after calculating the final estimate of the power angle andspeed deviation, the amount of power required to stabilize thesystem is calculated according to equation (6). This amount ofpower is then sent to DC-AC converter controller to calculatethe reference current and then transfers the required powerfrom the energy storage device to the DG bus. The transferedpower is used in the next time step before calculating thefinal estimate of the power angle and speed deviation. Thissequence is repeated until the simulation time ends. It shouldbe noted that, for the DC-AC converter, the current was takenas a reference because the voltage of the DG bus which isconnected to the grid is assumed constant. Also, the timeto provide or absorb power is assumed to be too small incomparison to the oscillation time and can be neglected.

Start

Read System data

Initialization and Program Settings

Perform Load Flow prior to disturbance

Modify network data for new representation

Calculate Machine Currents

Calculate voltages behind machine equivalents

Solve network Performance equations

Plot results

Advance t by

Calculate final estimates of power Angles and machine speeds at

Calculate final estimates of voltages behindmachine impedances at

Solve network Performance equations

Calculate final estimates of power anglesand machine speeds at

Calculate final estimates of voltages behindmachine impedances at

tΔ

clearingtt < ) ( faultduringYY busbus =

) ( faultAfterYY busbus =

tt Δ+

tt Δ+

tt Δ+

tt Δ+

?limtt ≤

No

Yes

No

Yes

Fig. 3. Transient Stability Calculation Flowchart

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−20

0

20

40

60

80

100 D

egre

e

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.97

0.98

0.99

1

1.01

1.02

1.03

1.04

Time,sec

p.u

.

G1G2

G1G2

Fig. 4. Angle and speed deviation for the original system for a fault at bus3 for 100 ms and no change in system configuration after clearing the fault

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−500

0

500

1000

1500

2000

Deg

ree

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.8

1

1.2

1.4

1.6

1.8

2

Time,sec

p.u

.

G1G2G4

G1G2G4

Fig. 5. Angle and speed deviation for the modified system for a fault at bus3 for 100 ms and no change in system configuration after clearing the fault

V. CASE STUDY

The control strategy for short term storage devices is appliedon a small five bus system which is taken from [13] andis shown in Fig. 3. System data are given in the appendix.The system is modified to examine the effect of total rotatinginertia. For the modified system, the inertia of generator 2was adjusted to be 30% of the original value and its powercapacity was divided by 2. Also, a new generating unit isadded at bus 4 which has the same parameters as generator 2after modification.

Fig. 4 shows the angle and speed deviation for the originalsystem for a fault at bus 3 for 100 ms and no change in systemconfiguration after clearing the fault. Fig. 5 shows the angleand speed deviation for the modified system for the same faultconditions and without the energy storage devices.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−40

−20

0

20

40

60

80

Tor

que

Ang

le D

evia

tion,

(D

egre

e)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.95

1

1.05

Time,sec

Spe

ed D

evia

tion,

(p.

u.)

G1G2G4

G1G2G4

Fig. 6. Angle and speed deviation for the modified system for a fault at bus3 for 100 ms and no change in system configuration after clearing the faultwith utilizing the energy storage devices

Fig. 6 shows the angle and speed deviation for the modifiedsystem for the same fault conditions with utilizing the energystorage devices. The energy storage devices is assumed to beconnected to the DG bus via bidirectional DC-DC converterand DC-AC converter. The control scheme of the bidirectionalDC-DC converter is assumed to maintain the input voltage ofthe DC-AC converter constant. The size of the energy storagedevice is estimated according to equation (6) with determiningthe values of |Ea|, |Vt| and δ0 from the pre-fault load flowanalysis. Also, Δδ is linearized around the operating point bypiecewise technique. The energy storage device is estimated tobe approximately 100 KW. The DC-DC and DC-AC convertersare set to handle 100 KW.

The DC-AC converter controller is set to track the amountof power that is required to stabilize the system which is equalto the synchronizing power coefficient times the change in thepower angle. The simulation time step is set to 0.0001 seconds.At every time step the required power to stabilize the systemis calculated and then is sent as a control signal to the DC-ACconverter. The output power from the DC-AC converter is thensent back to be used in the next time step. This sequence ofsteps is repeated until the time reached the simulation time.Fig. 7 shows the required power to stabilize generator 2. Fig.8 shows the output power, current and modulation index ofthe DC-AC converter connected to bus 2.

VI. CONCLUSION

When distributed generators are introduced into power sys-tem networks, they provided controllability and flexibility forpower system operation. However, as the penetration level ofthe distributed generators increases in power system networks,the total rotational inertia decreases significantly. This decreasemay cause the system to operate at stability limit borders orlose its stability under certain fault conditions.

To increase system stability margin, a short-term power

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−100

−50

0

50

100

Time, (sec)

Pow

er, (

KW

)

Fig. 7. The required power to stabilize generator 2 which is the synchronizingpower coefficient times the change in power angle

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−100

−50

0

50

100

Pow

er, (

KW

)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−200

−100

0

100

200

Time, (sec.)

Cur

rent

, (A

)

Fig. 8. Output power, current and modulation index of the DC-AC converterconnected to bus 2

is supplied to/or absorbed from the system at the time ofdisturbances by utilizing energy storage devices as virtualinertia. The utilization of the energy storage devices as virtualinertia can maintain system stability and increase systemstrength during transient stability.

This paper used the concept of virtual inertia to accountfor the transients that usually occur on power systems. Virtualinertia is realized by connecting a short-term energy storagedevice at the DG bus. The entire unit is then interfaced to thegrid by a suitable converter. The method is demonstrated on 5-bus system. The results show that stability limits are expandedwhen the virtual inertia is introduced to the system.

REFERENCES

[1] Ackermann, T., Andersson, G. and Soder, L., “Distributed Generation: Adefinition,”Electric Power Systems Research, 2001, Vol. 57, pp.195-204.

[2] Anderson, P. and Fouad, A., “Power System Control and Stability,”2ndedition, A JOHN WlLEY and SONS 2003, ch. 2.

[3] Prabha Kundur, Neal J. Balu, Mark G. Lauby, “Power system stabilityand control,”- McGraw-Hill 1994

[4] Vu Van, T., Woyte, A., Albu, M., van Hest, M., Bozelie, J., Diaz,J., Loix, T., Stanculescu, D. and Visscher, K., “Virtual SynchronousGenerator: Laboratory Scale Results and Field Demonstration,”in PowerTech Conference Proceedings, IEEE Bucharest, Romania, June 28th - July2nd, 2009, pp. 1- 6.

[5] Vu Van, T., Visscher, K., Diaz, J., Karapanos, V., Albu, M., Bozelie,J., Loix, T. and Federenciuc, D., “Virtual Synchronous Generator: anelement of future grid,”in IEEE PES Innovative Smart Grid TechnologiesConference Europe (ISGT Europe), 2010, pp. 1- 7.

[6] Driesen, J. and Visscher, K., “Virtual Synchronous Generators, ”in Powerand Energy Society General Meeting - Conversion and Delivery ofElectrical Energy in the 21st Century, 2008, pp. 1-3.

[7] Torres M. and Lopes, L.A.C, “Virtual Synchronous Generator Control inAutonomous Wind-Diesel Power Systems,”in IEEE Electrical Power &Energy Conference (EPEC), 2009, pp. 1-6.

[8] Wesenbeeck, M., Hann, S., Varela, P. and Visscher, K., “Grid tied con-verter with virtual kinetic storage,”in Power Tech Conference Proceedings,IEEE Bucharest, Romania, June 28th - July 2nd, 2009, pp. 1- 7.

[9] Majumder, R., Ghosh, A., Ledwich G. and Zarem F. , “Power Sharingand Stability Enhancement of an Autonomous Microgrid with Inertial andNon-inertial DGs with DSTATCOM,”IEEE, Third International Confer-ence on Power Systems, Kharagpur, INDIA December 27-29, 2009, pp.1-6.

[10] Benidris, M. and Mitra, J., “Enhancing stability performance of renew-able energy generators by utilizing virtual inertia,”accepted, to appear inProceedings of the IEEE PES General Meeting, 2012, San Diego, CA,USA.

[11] Peng, F., Shen, M. and Holland, K., “Application of Z-Source Inverterfor Traction Drive of Fuel CellBattery Hybrid Electric Vehicles,”IEEETrans. Power Electron., vol. 22, no. 3, pp. 10541061, May 2007.

[12] Fang Zheng Peng, “Z-Source Inverter,”IEEE Trans. Power Electron., vol.39, no. 2, pp. 504510, April 2003.

[13] Stagg, Glenn W., “Computer methods in power system analysis,”NewYork, McGraw-Hill 1968, ch. 13.

APPENDIX

System data for the base case and after modification areshown as follows:

TABLE ILINE DATA

From To R (p.u.) X (p.u.) B/2 (p.u.)1 2 0.02 0.06 0.0301 3 0.08 0.24 0.0252 3 0.06 0.18 0.0202 4 0.06 0.18 0.0202 5 0.04 0.12 0.0153 4 0.01 0.03 0.0104 5 0.08 0.24 0.025

TABLE IIGENERATION DATA FOR THE ORIGINAL SYSTEM

Gen. Voltage Real Power Reactive Power R Xs HNo. (p.u.) MW MVar (p.u.) (p.u.) s1 1.06 Inf. Bus Inf. Bus 0.0 0.25 502 1.00 40 30 0.0 1.5 1

TABLE IIIGENERATION DATA FOR THE MODIFIED SYSTEM

Gen. Voltage Real Power Reactive Power R Xs HNo. (p.u.) MW MVar (p.u.) (p.u.) s1 1.06 Inf. Bus Inf. Bus 0.0 0.25 502 1.00 20 15 0.0 1.5 0.34 1.00 20 15 0.0 1.5 0.3

TABLE IVLOAD DATA

Bus Real Power Reactive PowerNo. (MW) (MVar)1 0 02 20 103 45 154 40 55 60 10