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IEEE TRANSACTIONS ON POWER SYSTEMS 1

Robust ESS-Based Stabilizer Design for DampingInter-Area Oscillations in Multimachine

Power SystemsLinjun Shi, Member, IEEE, Kwang Y. Lee, Life Fellow, IEEE, and Feng Wu

Abstract—In this paper, a robust approach to the energy storagesystem (ESS)-based stabilizer is proposed to select its installationlocation, feedback signals, and damping control loop, and to tunethe stabilizer parameters. Based on the linearized model of thepower system with ESS and application of damping torque anal-ysis (DTA), the maximum of all minimum damping torque indices(DTIs) under multi-operational conditions is used as the index forselecting ESS installation locations, feedback signals and dampingcontrol loops. The operational condition for theminimumDTI pro-vides the condition for tuning the ESS-based stabilizer parame-ters for robust operation. And a proper compensation angle is se-lected by a robust method to design the ESS-based stabilizer pa-rameters. The eigenvalue analysis and non-linear simulation re-sults of a four-machine power system and New England ten-ma-chine power system with ESS show that power system oscillationsare suppressed effectively and robustly by the ESS-based stabi-lizer.Index Terms—Damping torque indices (DTIs), energy storage

system (ESS), inter-area oscillations, multimachine power systems,robust stabilizer.

I. INTRODUCTION

D AMPING inter-area low-frequency oscillations in largescale power systems has been one of the most important

research topics for several decades [1]–[4]. Power systemstabilizers (PSSs) have been proven to be effective in dampinglocal-area oscillation. While PSSs have limited effectivenessfor inter-area damping control, inter-area oscillation still re-mains a critical challenge in today's power systems [5]. Manyother approaches have been proposed for damping inter-arealow-frequency oscillations. For example, a comprehensive re-view is presented in [6] on the research and developments in thepower system stability enhancement using flexible alternativecurrent transmission systems (FACTS) damping controllers.

Manuscript received October 11, 2014; revised January 12, 2015; acceptedApril 07, 2015. This work was supported in part by the National Natural Sci-ence Foundation of China (NSFC) under Grant 51422701, 51137002. Paper no.TPWRS-01399-2014.L. Shi and F. Wu are with the College of Energy and Electrical Engineering,

Hohai University, Nanjing, Jiangsu 210098, China (e-mail: [email protected];[email protected]).K. Y. Lee is with the Department of Electrical and Computer En-

gineering, Baylor University, Waco, TX 76798-7356 USA (e-mail:[email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TPWRS.2015.2422797

However, it is shown that interactions occur between stabilizersin multimachine power systems, where the stabilizers beingPSSs, FACTS device stabilizers or both [7]. In [8], a novelalgorithm is presented for simultaneous coordinated design ofPSSs and a thyristor-controlled series capacitor (TCSC) in amultimachine power system for damping power system oscilla-tions. In [9], different input–output controllability analyses areused to assess the most appropriate input signals for the staticvar compensators (SVCs), the static synchronous compensator(SSSC), and the unified power-flow controller (UPFC) forachieving good damping of inter-area oscillations. Takingadvantages of the FACTS devices depends largely on howthese devices are placed in the power system, namely, on theirlocation and size. In [10], power system stability is used as anindex for optimal allocation of the controllers. After placing theSVCs based on their primary functions, the most appropriateinput signal supplementary controller is also selected.With the advancement of energy storage technologies in re-

cent years, energy storage systems (ESSs) are applied in powersystems widely [11]–[14], such as to improve system stability[15], [16], power quality [17], and reliability of supply [18].Since the inter-area oscillation between two connected powersystems is the oscillation of active power, damping oscillationwith ESSs by exchanging active power directly can be a moreefficient and effective way than PSSs or FACTS [19]. And sinceselecting installation location for ESSs is more flexible thanfor PSSs, there have been a growing interest in the applica-tion of ESSs on damping low frequency inter-area oscillations[20]–[22]. For example, a battery energy storage system (BESS)is used for damping inter-area oscillations in a multimachinepower system [20], a candidate energy storage system basedon ultra-capacitor technology is evaluated for damping controlapplications in real power systems [21], and the flywheel en-ergy storage system (FESS) is proposed for damping powersystem oscillations in a single-machine infinite-bus power sys-tems [22]. In [20], it is explained how and why the ESS-basedstabilizer can suppress the inter-area oscillation. In [21], an ana-lytical method for ensuring proper stability margins is provided.In [22], the principle of the complex torque coefficient (CTC)method is applied to analyze the use of FESS for damping os-cillation in a single-machine infinite-bus system. However, allof these ESS-based stabilizers do not consider the robustness is-sues as a whole in damping power system oscillations, such asselection of the ESS installation locations, feedback signals anddamping control loops, and tuning of the stabilizer parameters.

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2 IEEE TRANSACTIONS ON POWER SYSTEMS

Damping torque analysis (DTA) was introduced in [2] on thebasis of the Phillips–Heffron model [23] for a single-machineinfinite-bus power system. It was further developed in [24] intothe well-known phase compensation method for the design ofa PSS. Since the 1980s, there has been much effort to extendthe phase compensation method to design PSSs [25]–[27], andFACTS stabilizers [28], [29] in a multimachine power system.In our paper, both the DTA and phase compensation methodbased on linearized model will be applied to design a robustESS-based stabilizer in damping inter-area oscillations in mul-timachine power systems since a linearized model is well ac-cepted for studying power system oscillations [3], [13].As a candidate energy storage system, an ESS based on the

flywheel storage technology consisting of a doubly-fed induc-tion machine (DFIM) is considered to demonstrate the robustselection of the ESS installation locations, feedback signals anddamping control loops, and the robust tuning of the parametersof the ESS-based stabilizer. Based on the linearizedmodel of thepower system with ESS and application of DTA, the maximumof all minimum damping torque indices (DTIs) under multi-op-erational conditions, as far as the inter-area mode of power os-cillation is concerned, is found to be the index for the best se-lection of ESS installation locations, damping control loops andfeedback signals. And the operation condition for the minimumchange of the real parts of eigenvalues provides the conditionfor tuning the ESS-based stabilizer parameters for robust op-eration in multi-operational conditions. The eigenvalue anal-ysis and nonlinear simulation results of a four-machine powersystem and New England ten-machine power system with ESSshow that power system oscillations are suppressed effectivelyby the robust ESS-based stabilizer.

II. FLYWHEEL ENERGY STORAGE SYSTEM

The FESS consisting of DFIM has several advantages. Forexample, it can exchange relatively larger amounts of energycompared with a battery or ultra-capacitor and it has quick en-ergy release and storage capability; therefore, it is very fittingfor large-scale power system stability control. Moreover, the re-quired capacity of a power electronics component for the DFIMis in a range from one-fifth to one-seventh as small as the ca-pacity of the machine [30]. Therefore, it is cheaper to installand operate [30]. The ESS can release and absorb active power.Inter-area oscillation is the oscillation of active power betweentwo connected power systems. The ESS can be controlled to bal-ance the power oscillation, damping the inter-area modes of os-cillations quickly. This paper’s main work is to ensure the ESSreleasing and absorbing power correctly through phase compen-sation.In the ESS based on the flywheel storage technology con-

sisting of DFIM, the energy is stored in the rotation of therotor. The configuration of a FESS based on DFIM is shownin Fig. 1 [30]. Regulating the speed of the flywheel and energyexchange between ESS and the power system can be realizedthrough the DFIM.The ESS connected to a power system is shown in Fig. 2.In Fig. 2, is the terminal voltage of the ESS, is the

negative current which is injected to the power system, and

Fig. 1. Configuration of FESS based on DFIM.

Fig. 2. ESS connected to a power system.

and are, respectively, the currents of the stator and the rotorof the ESS.

A. ESS Nonlinear ModelThe third-order model of DFIM is adequate for oscillations

studies [31]. The ESS based on DFIM has been represented bya third-order nonlinear model [32] as follows.1) Stator Voltage Equation:

(1)

where and are transient electric potential in the -axis,, , , and are, respectively, the stator voltage and

current in the -axis, is stator resistance, and is the tran-sient reactance equal to , withand , where is stator winding self-induc-tance, is rotor winding self-inductance, and is the mutualinductance between stator and rotor windings.2) Dynamic Equation: Transient electric potential dynamic

equation can be obtained as

(2)

where is the slip of DFIM, is the rotor open circuit timeconstant, and is synchronous speed. Similar to synchronousgenerator, the swing equation is given by

(3)

where is inertia constant, is the electromagnetic torqueequal to , and is the mechanical torque.For ESS, .Thus ESS based on DFIM can be represented by the third-

order dynamic model in (2), (3).3) Decoupled Control Loops: Based on the orientated con-

trol strategy of stator magnetic field, the ESS can be realizedwith the active and reactive power decoupled control [33], [34].


SHI et al.: ROBUST ESS-BASED STABILIZER DESIGN FOR DAMPING INTER-AREA OSCILLATIONS IN MULTIMACHINE POWER SYSTEMS 3

Fig. 3. Block diagram of active control loop.

Fig. 4. Block diagram of reactive control loop.

Fig. 5. ESS-based stabilizer superimposed on the decoupled control loop.

The block diagrams of the control loops for the active and reac-tive power controls are shown in Fig. 3 and Fig. 4, respectively.In the figures, , , and are, respectively, the rotor

power, stator power, and reference power, , , andare, respectively, the rotor voltages in the -axis, andthe stator voltage reference in the -axis, and , ,

, and are the coefficients of the respective PIcontrollers.4) ESS-Based Stabilizer: In order to damp power system

low-frequency oscillations, the structure of PSSs [24] orFACTS-based stabilizers [7], [28] can be superimposed uponthe active power or reactive power control loop of ESS, calledESS-based stabilizer. Without loss of generality, the transferfunction model of the stabilizer [2], [3], [20], [24] is given inFig. 5, where is either or , depending on the real orreactive control loop. If the input signal has information ofsystem oscillation, the output signal of the ESS-based stabilizer,, acts on the ESS through the control loop, and the power

system oscillation can be suppressed quickly by storing orreleasing energy to or from the ESS.In the figure, , , , , and are time constants, is

gain, , , and are intermediate variables, and is thetransfer function of the ESS-based stabilizer.

B. Full System Linearized Model

According to Fig. 2, and applying the bulk current injectionmethod [35], [36], can be expressed by all ESS’s state vari-ables and bus voltages; meanwhile, is a branch current ofthe power system network. Thus, ESS can be integrated into thepower system. Since analysis and control of power system os-cillation stability is mainly based on the linearized model of a

Fig. 6. Block diagram of linearized power systems with ESS.

power system [3], [13], details of deriving the linearized powersystem model with ESS is given in Appendix A. Rearranging(A15), the linearized power system with ESS is

(4)where is the deviation of generator power angle, is thedeviation of generator speed, are all state variables exceptfor the power angle and generator speed variables, is thedeviation of damping signal added to ESS output from ESS-based stabilizer, and is the transfer function matrix from

to state variables.The output can be expressed as

(5)

where is the coefficient matrix from state variable to .Output of the stabilizer is given as

(6)

Thus, (4)–(6) are made up of the linearized model of a multi-machine power system with the ESS. The block diagram of thelinearized system is shown in Fig. 6.In Fig. 6, is an identity matrix, and is the differential op-

erator.

III. ROBUSTNESS ISSUES OF ESS-BASED STABILIZER

A. Damping Torque Index

From (4) and Fig. 6, the forward path of the output controlsignal of the ESS-based stabilizer to the electromechanical os-cillation loop can be obtained as

(7)



and the output can be restructured by rotor speed as [37]

(8)

where is restructuring function. In Appendix B, the detailof deriving of is given. Thus

(9)

From Fig. 6, (7), and (9), the damping torque [2] providedby the ESS-based stabilizer to the electromechanical oscillationloop of the th generator in the power system is

(10a)(10b)

(10c)

where is the inter-area oscillation mode of interest at an op-erating condition, is the th element of in (7), ,and is the number of generators; ,and .From (10a) and (10b), we know that the damping torque con-

tributed by the ESS-based stabilizer is changed in the variationsof system operating conditions and it is acted on every gen-erator through a single forward channel . So there aretotal channels through which the ESS-based stabilizer pro-vides all generators with the damping torque. However, if theESS-based stabilizer for a generator provides a damping torquewhich results in little improvement of the damping of an oscil-lation mode, the generator is not really participating in dampingthe oscillation mode. Thus, for an oscillation mode , we candefine the sensitivity of with respect to an addition of thedamping torque with the th generator as .Thus, the total improvement of the damping of the oscillation

mode due to the addition of a damping torque with all gener-ators is

(11a)

(11b)

(11c)

where .The transfer function of the stabilizer in Fig. 5 can be ex-

pressed as:

(12)

From (11c) and (12), we know stabilizer affects the real part ofthe as:

(13a)(13b)

From (11b) and (11c), we know that is changed by theESS-based stabilizer. The range of change can be described byDTI defined as follows:

(14)

The DTI is defined as the effects of the ESS-based stabilizeron the real part of the eigenvalue. Therefore, if the value ofthe DTI is higher, the ESS-based stabilizer can provide moredamping torque which results in more improvement of thedamping of the oscillation mode, that is, (14) shows the effectof the ESS-based stabilizer, which can be used for selectionof the best installation location, damping control loop, and thefeedback signal.

B. Robust Selection MethodA conventional method for selecting ESS installation loca-

tion, control loop, and the feedback signal is to use

(15)

where is the collection of all candidates of installation loca-tions, control loops, and the feedback signals, is the result ofthe choice, , and is a typical operating condition.However, the DTI will change under different operating con-

ditions even if in the same installation location, control loop andwith the feedback signal. Therefore, (15) is not always the bestchoice under a typical operating condition.In this paper, an alternative method of selecting ESS instal-

lation location, control loop, and feedback signal is defined asfollows:

(16)

where is a collection of given operating conditions whichoften include load condition from light to heavy load accordingto inter-area modes of power oscillation concerned. There isa minimum value of DTI under different operating conditionsfor every element of . Then choose an operating condition

which has maximum of all the minimum values ofDTI. And is the result of selecting the ESS installationlocation, control loop and the feedback signal under selected op-erating condition . Equation (16) shows that the selection re-sult is the least effective in damping the th oscillation modeat the operating condition . Thus, if we choose asthe operating condition to design the ESS-based stabilizer, aneffective design of the ESS-based stabilizer at can ensure itseffectiveness for all other operating conditions in . There-fore, (16) is a robust method for selecting the ESS installationlocation, control loop and the feedback signals.

C. Robust Tuning of ESS-based Stabilizer ParametersUsing the phase compensation method [24], [29], the param-

eters of the ESS-based stabilizer can be tuned, which shouldensure that the power systems oscillations can be suppressedeffectively under various operating conditions.If

(17)



where , then (17) shows that the least effectivedamping of the th oscillation mode is provided at the operatingcondition . If we choose as the operating condi-tion to tune the ESS-based stabilizer parameters, more effectivedamping will be obtained at all other operating conditions in

. Thus, is the robust operating condition for tuning theESS-based stabilizer parameters.From (13b), if a compensation angle causes moving left-

ward, the system damping of the oscillation is increased. Thus,the key problem is how to select a proper compensation angleto ensure moving leftward maximally at all operating con-

ditions.Since the robust operating condition is selected by (17),

the process of selecting the compensation angle is given here.1) In order to ensure is moving leftward at all operating

conditions and provide positive synchronous torque [2],[37], the range is

(18)

2) For any in (18), calculate through (13b) for all operatingconditions included in . Then, there exists a minimumvalue given by

(19)

where , is the number of included in(18).

3) Define. Then, there exists

(20)

(21)

From above, we can know that can change the max-imum in all minimum changes of the real part of eigenvalues inoperating condition selected by (17), that is, it canprovide maximum DTI to all operating conditions in at

when designing the stabilizer. Thus, is the propercompensation angle to provide maximum damping for all oper-ating conditions in .Therefore, having obtained a proper compensation angle in

an operating condition, the robustness in the design of an ESS-based stabilizer to the variations of power system operating con-ditions is achieved. The stabilizer parameters can be tuned by(12)–(13b) according to [24].

IV. CASE STUDY I: FOUR-MACHINE SYSTEMAn example of a four-machine power system is shown in

Fig. 7 [38]. The collection of different operating conditionsis 400 MW 420 MW , whereis represented for the active power transferred along thedouble-circuit line 7–8. The typical collection of different op-erating conditions is 420 MW250 MW 125 MW150 MW 250 MW 400 MW .Parameters of an example of ESS based on flywheel are as

follows [30]: capacity is 70 MVA, is 0.0013 p.u.,is 2.9 p.u., is 2.6 p.u., and is 3.4 s. The active

Fig. 7. Four-machine power system with an ESS.

TABLE IVALUE OF DTI UNDER DIFFERENT OPERATING CONDITIONS

and reactive power controls parameters are: ,, , , and

[39].

A. Robust Parameter Tuning of ESS-Based Stabilizer

An ESS is installed at bus 7, and the oscillation power on line7–8 is taken as the feedback signal, which is applied to the activepower control loop.The value of DTI in different operating conditions is shown

in Table I.From Table I, it can be seen that DTI of

has the minimum DTI value. Thus, is the robust op-erating condition for the design of the ESS-based stabilizer ac-cording to (17).The next step is to select a proper compensation angle .

Based on (18), the range of is, that is, .

From Table I, is from 83.091 to 87.792 . The range ofis relatively narrow. According to (19) and (20), if com-

pensation angle deviates 180 too much, the value ofwill be too small to find . Thus, in order to simplify

calculation, assume , such that a given can-didate is in

. Ac-cording to (19), for any , there exists a minimum value,

. So the is. The re-

sults are also shown in Table I. When ,there exists . Thus,is the proper compensation angle for providing the maximumdamping to all operating conditions in .The ESS-based stabilizer parameters are tuned by the phase

compensation. Consider the following settings: target dampingratio is 0.1, is 5 s, and lag-lead time constant are 0.05s. Then, the robust ESS-based stabilizer parameters are tuned as

, by the phase compensationmethod [28]. In order to verify the damping effect, the results



TABLE IIEIGENVALUES UNDER DIFFERENT OPERATING CONDITIONS

Fig. 8. Damping effects under different operating conditions.

of eigenvalue and nonlinear simulation are respectively shownin Table II and Fig. 8.In Table II, damping ratios at all operating conditions are

better than that at . In Fig. 8, the oscillations are triggeredby a three-phase short circuit occurring at the end of line 9–10at 0.1 s and removed after 100 ms. Nonlinear simulation resultsalso show that all system oscillations are suppressed effectivelyat all other operating conditions with the ESS-based stabilizerdesigned at the operating condition . Table II and Fig. 8 bothshow that this is a robust stabilizer. Therefore, the method pro-posed provides a robust method of tuning the ESS-based stabi-lizer parameters.

B. Robust Selection of Installation Location, Feedback Signaland Control Loop

The candidate group is selected as follows.• Candidate ESS locations: bus 7, bus 8 and bus 9.• Candidate stabilizer feedback signals: between gener-ator 1 and generator 3, and power oscillations on line 7–8.

• Candidate stabilizer control loops: active power controlloop and reactive power control loop.

The general method of selection is based on a typical oper-ating condition, such as . The values of DTI are shown inTable III under the operating condition .From Table III, maximum DTI is 0.231 at . According to

(15), candidate is the best choice by the conventional method,that is, the ESS installation location is at bus 7, feedback signal

TABLE IIIVALUES OF DTI IN

Fig. 9. DTI of various candidates in different operating conditions.

is , and stabilizer control loop is a voltage control loop, i.e.,a reactive power control loop.For the robust selection method proposed in this paper, the

values of DTI should be calculated first for all candidates inthe group in different operating conditions. The results areshown in Fig. 9.In Fig. 9, every curve delegates the DTI values of a candidate

in in different operating conditions. And the colored dotrepresents the minimum DTI value of the candidate for eachoperating conditions. From Table III and Fig. 9, we observe thefollowing.1) is the robust selection among all candidates in . Be-

cause the minimum DTI value of candidate is the max-imum in all minimum DTI values of candidates in .Thus, according to (16), candidate is the best choice,that is, the ESS should be installed at bus 7, the feedbacksignal should be , and the stabilizer control loop is theactive power control loop.

2) Feedback signal is better than feedback signal .3) The ESS installed at bus 7 and bus 9 is better than that at

bus 8. This shows that ESS installed at a terminal of the



TABLE IVVALUE OF DTI UNDER DIFFERENT OPERATING CONDITIONS AT

TABLE VPARAMETERS OF TWO STABILIZERS

transmission line is better than one installed in the middleof the line.

Obviously, the selection result is different for the conven-tional selection method (15) and the robust method proposed(16). The result of the robust method is while the result of theconventional method is . Then, the question is: “which selec-tion result is better?” These can be validated through eigenvalueanalysis and nonlinear simulation.The robust tuning method was discussed in Section III to tune

the ESS-based stabilizer parameters for two selection resultsand . In order to compare in the same condition, there must bethe same gain of the stabilizer in (12) for the two selectionresults, and . In the result of in Section III, the value ofDTI in different operating conditions has been shown in Table I,and operating condition is the robust operating condition fortuning the ESS-based stabilizer parameters, where

is the proper compensation angle.In the result of , the values of DTI under different operating

conditions are shown in Table IV.From Table IV it can be seen that DTI of

has the minimum value. So is the robust operation condi-tion for the design of ESS-based stabilizer according to (17).Also, from Table IV, it can be seen that when

, there exists the . Thusis the proper compensation angle in providing

maximum damping for all operating conditions in .The two ESS-based stabilizers parameters are tuned by the

phase compensation method. And they have the same . Ifis 1.407 and 0.05 s, 5 s, the results of

other parameters of the two stabilizers are shown in Table V.Eigenvalues are shown in Table VI under different operating

conditions.From Table VI, although the two stabilizers have the same

gain, the damping ratio of the selection result by the conven-tional method is worse than the selection result by the ro-bust method proposed in this paper. In , damping ratio meets

TABLE VIEIGENVALUES IN OPERATIONS AND

the design requirement only under operation condition and; while in , damping ratio meets the design requirement

under all operating conditions. Obviously, higher stabilizer gainis needed in to meet the requirement under all other operatingconditions. Thus, control cost will be increased at . Thus,is a better choice.Nonlinear simulation also is used to compare the two selec-

tion methods. Simulation condition is a three-phase short cir-cuit occurring at the end of line 9–10 at 0.1 s and removed after100 ms. The results of the simulation are shown in Figs. 10 and11.From Figs. 10 and 11, damping effect of is better than

that of , and thus is a better choice. From Table VI andFigs. 10 and 11, it is validated that the selection method pro-posed in this paper is effective and robust.

V. CASE STUDY II: TEN-MACHINE SYSTEMIn order to further verify the validity and generality of the

proposed robust method, a larger sample of the New Englandten-machine system is given. The system connection diagram isshown in Fig. 12. Parameters of the system are given in [40].The parameters of FESS are same as those in Section IV.The New England ten-machine system is a typical intercon-

nected system and has been widely used for studying the lowfrequency oscillation [4]. The governor dynamics are neglectedwhile each generator is equipped with an IEEE DC1A excita-tion system except generator 10 which is an equivalent gener-ator, and the loads are modeled as constant impedances. Theinitial load condition is 120 MW, and there exists aninter-area oscillation mode [4]. Thetypical collection of different operating conditions is

120 MW160 MW 200 MW according to different loadconditions from light to heavy load.

A. Robust Parameter Tuning of ESS-based StabilizerFor suppressing the poor inter-area power oscillation mode

, anESS-based stabilizer is installed at bus 2. And the oscillation



Fig. 10. Nonlinear simulation of and in .

Fig. 11. Nonlinear simulation of and in .

Fig. 12. Ten-machine power system with an ESS.

TABLE VIIVALUE OF DTI UNDER DIFFERENT OPERATING CONDITIONS

TABLE VIIIEIGENVALUES UNDER DIFFERENT OPERATING CONDITIONS

power on line 2 to 1 is taken as the feedback signal, which isapplied to the active power control loop.The value of DTI in different operating conditions is shown

in Table VII (other oscillation modes are not listed).From Table VII, we know is the robust operating con-

dition for the design of the ESS-based stabilizer according to(17), and is the proper compensation angle forproviding the maximum damping to all operating conditionsin based on (18). Then, the robust ESS-based stabilizerparameters are tuned as , ,

10 s, 0.5 s for target damping ratio to 0.1by the phase compensation method [24]. Modal analysis of thesystem shows that damping ratios at all operating conditions aresuppressed and better than the one at in Table VIII.General method of tuning parameters is based on an oper-

ating condition. For example, in , the compensation angleis , the ESS-based stabilizer parameters are tuned as

, , 10 s,0.5 s for target damping ratio to 0.1 by the phase compensa-tion method [24]. Eigenvalue analysis in vary operating condi-tions with the ESS-based stabilizer shows in Table VIII. FromTable VIII, we know that damping ratio meets the design re-quirement only at operating condition .Therefore, the method proposed provides a robust method of

tuning the ESS-based stabilizer parameters.

B. Robust Selection of Installation Location, Feedback Signaland Control Loop

For simplicity, the candidate group is selected asfollows.• Candidate ESS locations: bus 2, bus 9.• Candidate stabilizer feedback signals: between gener-ator 2 and generator 10, and power oscillations on line 2-1.

• Candidate stabilizer control loops: active power controlloop and reactive power control loop.

Application of the robust selection method proposed in thissection, the minimum DTI values of the candidate for each op-erating conditions are shown in Table IX.



TABLE IXVALUES OF MINIMUM DTI UNDER DIFFERENT OPERATING CONDITIONS

TABLE XVALUE OF DTI UNDER DIFFERENT OPERATING CONDITIONS AT

TABLE XIPARAMETERS OF TWO STABILIZERS

In order to compare, all DTI values are also calculated underthe operating condition . The results are shown in Table IX.From Table IX, the result (location: bus 2, feedback signal:, control loop: active power control loop) is selected based

on the robust selection method proposed in the paper, while theresult (location: bus 2, feedback signal: , control loop:voltage control loop) is selected in operating condition , andeigenvalue analysis and nonlinear simulation are used to vali-date which selection result is better.In order to compare, the ESS-based stabilizers for two selec-

tion results and are both tuned in the same condition bythe robust tuningmethod proposed in the paper. Both ESS-basedstabilizers have the same gain in (12). In the selection result, the ESS-based stabilizer tuned by the robust tuning method

has .In the selection result , the values of DTI in different oper-

ating conditions are shown in Table X.From Table X, we know is the robust operating condition

for the design of the ESS-based stabilizer at according to(17). And is the proper compensation angle forproviding the maximum damping torque to all operating con-ditions in based on (18). The two ESS-based stabilizersparameters are tuned by the phase compensation method. Andthey have the same . If is 1.36 and 10 s, the resultsof other parameters of the two stabilizers are shown at Table V.The results of other parameters of the two stabilizers are shownin Table XI.Eigenvalues are shown in Table XII under different operating

conditions at and .

TABLE XIIEIGENVALUES IN OPERATIONS AND

Fig. 13. Nonlinear simulation of and in and .

Fig. 14. Nonlinear simulation of and in and .

From Table XII, although the two stabilizers have the samegain, the damping ratio of the selection result by the conven-tional method is worse than the selection result by the robustmethod proposed in this paper.Nonlinear simulation also is used to compare the two selec-

tion results. Simulation condition is a three-phase short circuitoccurring at Bus 16 and removed after 100 ms. The results ofthe simulation are shown in Figs. 13 and 14.From Figs. 13 and 14, the damping effect of is better than

that of , and thus is a better choice.



Fig. 15. Orientated control strategy of stator magnetic field.

From Table XII and Figs. 13and 14, it is demonstrated that theselection method proposed in this paper is effective and robustfor a large-scale power system.

VI. CONCLUSIONThis paper presents a robust design procedure of the ESS-

based stabilizer for damping power systems inter-area oscilla-tions. It includes a robust selection procedure of the installationlocation, feedback signal, and control loop of the EES-basedstabilizer and a robust tuning procedure of the ESS-based sta-bilizer parameters. The paper presents the concept of DTI asa measure of robust selection criteria for selecting installationlocation, feedback signal, and control loop of the EES-basedstabilizer. The minimum DTI under different operating condi-tions combined with the improved phase compensation methodfor proper compensation angle is presented as a robust tuningmethod.The robust design procedure for the EES-based stabilizer is

demonstrated in two example power systems and its effective-ness and robustness are verified by eigenvalue calculation andnonlinear simulation, for both small and large-scale power sys-tems.Further studies will focus on coordinating design and tuning

of ESS-based stabilizer and PSS for dampingmultiple inter-areaand local-area oscillation modes.

APPENDIX

A. Full System Linearized Model

According to Fig. 2, the current injection of the ESS to thepower system is

(A1)

Ignoring the dynamics of the stator magnetic field and theESS loss and based on the orientated control strategy of thestator magnetic field, the -axis of the ESS is located at (seeFig. 15), where the angle between the -axis of the ESS and the-axis of the system is [34].From Fig. 15, the transformation matrix from the

axis to the axis can be obtained as

(A2)

Thus, ,, where and are the current, and and

are the voltage in the -axis. Then, from the linearizedequation (1), we can have

(A3)

where is deviation symbol, ,, is the ESS state variable equal to

, and and are the coefficient matrices.From Fig. 2, if PWM is ideal and power factor is unity, thenhas the same phase with in the -axis. Thus, can

be expressed as

(A4)where is rotor active power, is stator active power, and

.Linearizing (A4) in -axis yields

(A5)

where , and , are the currents in-axis, and and are the coefficient matrices.From (A1), (A3), and (A5), the linearized current of the ESS

connected to power system is

(A6)

where and are the coefficient matrices, with, . Equation (A6) shows that the current

injection of the ESS to power system can be expressed in termsof the ESS state variables and the port voltage of the ESS.According to Figs. 3, 4, and 6, the dynamic equations of ESS,

(2) and (3), are linearized as

(A7)

where and are coefficient matrices.For the whole power system, the network equation is

(A8)

where is admittance matrix, is the nodal current injection,and is the nodal voltage. Rearranging (A8) yields

(A9)

where is the current of synchronous generators into thesystem, is the port voltage of the synchronous generators,and is the nodal load voltage.The injection current of synchronous generators is linearized

as

(A10)

where is synchronous generator state variables equalto , with as the other state variables of



synchronous generators, and and are coefficient ma-trices. From (A6), (A10), and (A9), it can be seen that

(A11)

Rearranging (A11), we have

(A12)

where , , and

Synchronous generator dynamic equations [36] are linearizedas

(A13)

where and are coefficient matrices. From (A7) and(A13), it can be seen that

(A14)

where and are coefficient matrices. From (A12) and(A14), we conclude that

(A15)

where .

B. Output Restructuring Method

From (4) and Fig. 6, and not considering damping signal ,it can be seen that

(B1)

where is differential operator. Thus, can be obtained as

(B2)

Because of

(B3)

(B2) becomes

(B4)

where .

From (5), (B3), and (B4), it can be seen that

(B5)

(B6)

where , and .

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Linjun Shi (M'11) received the B.S. and M.S. de-grees fromHohai University, Nanjing, China, in 1999and 2003, respectively, and the Ph.D. degree fromSoutheast University, Nanjing, China, in 2010, all inelectrical engineering.He is currently an Associate Professor with the

College of Energy and Electrical Engineering, HohaiUniversity, Nanjing, China. He is also a VisitingScholar with the Department of Electrical and Com-puter Engineering, Baylor University, Waco, TX,USA. His research interests include power system

analysis and control, new energy and energy storages applications to powersystems.

Kwang Y. Lee (F'01–LF’08) received the B.S.degree in electrical engineering from Seoul NationalUniversity, Seoul, Korea, in 1964, the M.S. degreein electrical engineering from North Dakota StateUniversity, Fargo, ND, USA, in 1968, and thePh.D. degree in system science from Michigan StateUniversity, East Lansing, MI, USA, in 1971.He has been on the faculties of Michigan State,

Oregon State, Houston, the Pennsylvania StateUniversity, and Baylor University, Waco, TX, USA,where he is currently a Professor and Chair of the

Electrical and Computer Engineering and Director of the Power and EnergySystems Laboratory. His research interests are power systems control, oper-ation and planning, and intelligent systems applications to power plant andpower systems control.Dr. Lee has served as an editor of the IEEE TRANSACTIONS ON ENERGY

CONVERSION and an associate editor of the IEEE TRANSACTIONS ON NEURALNETWORKS. He is currently serving as Chair of the IEEE Working Group onModern Heuristic Optimization and Chair of the IFAC Technical Committee,TC 6.3—Power and Energy Systems.

Feng Wu received the B.Eng. and M.Sc. degrees from Hohai University, Nan-jing, China, in 1998 and 2002, respectively, and the Ph.D. degree from the Uni-versity of Birmingham, Birmingham, U.K., in 2008.He is currently a Professor with the College of Energy and Electrical Engi-

neering, Hohai University, Nanjing, China. His research interest is power systemmodeling and control.

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