adaptive time delay compensator (atdc) design for wide-area power system stabilizer

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Adaptive Time Delay Compensator (ATDC) Designfor Wide-Area Power System Stabilizer

Lin Cheng, Member, IEEE, Gang Chen, Wenzhong Gao, Senior Member, IEEE,Fang Zhang, Student Member, IEEE, and Gan Li

Abstract—Wide-area power system stabilizer (WPSS) is one ofthe most potentially effective approaches to damp interarea lowfrequency oscillations in power systems. When WPSS is imple-mented in a real project, emphasis should be put on feedbacksignal delay problem. In order to intensively study the delay ofphasor measurement unit data, field tests have been carried outin Guizhou power grid (GZPG), and results show that, in thelong-term, the delay might change remarkably under some cir-cumstances, such as when route switches or communication loadincreases. Therefore, this paper proposes an adaptive time delaycompensation method to deal with such kind of delay. Boundedrandom delay is divided into several intervals and compensatorsare designed for each delay interval. Then appropriate compen-sators will be selected according to the delay measured online,based on the switching rules that is also demonstrated in thispaper. The delay used here is the average delay before the com-pensator switching. The proposed compensator is demonstratedin a two area power system. Numerical simulation results showthe effectiveness and feasibility of the proposed adaptive compen-sator. A comparison with conventional methods is also presented.Finally, the proposed method is validated on GZPG based onreal-time digital simulations.

Index Terms—Adaptive, phasor measurement units (PMUs),power system stabilizer (PSS), real-time digitalsimulation (RTDS), time delay, wide-area measurementsystem (WAMS).

I. INTRODUCTION

LOW FREQUENCY oscillation is one of the most severeproblems of power systems. Traditional fixed-parameters

local power system stabilizer (LPSSs), in which local sig-nals are used as feedback signals, perform reasonably well indamping out low frequency oscillations if they have been prop-erly tuned [1]. Even after great changes in system structure and

Manuscript received October 27, 2013; revised March 10, 2014 andJune 11, 2014; accepted August 1, 2014. This work was supportedin part by the National High-Technology Research and DevelopmentProgram (863 Program) of China under Grant 2014AA051901; and inpart by the State Key Laboratory of Power System, Tsinghua University.Paper no. TSG-00814-2013.

L. Cheng and F. Zhang are with the State Key Laboratory of Power Systems,Department of Electrical Engineering, Tsinghua University, Beijing 100084,China (e-mail: [email protected]; [email protected]).

G. Chen and G. Li are with the State Grid Sichuan Electric PowerResearch Institute, Chengdu 610072, China (e-mail: [email protected];[email protected]).

W. Gao is with the Department of Electrical and ComputerEngineering, University of Denver, Denver, CO 80208 USA (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TSG.2014.2347401

operating mode, these LPSSs can also achieve reasonable per-formance by online retuning of their parameters [2]. However,their effects are limited in damping interarea oscillations due tothe use of local feedback signals. With the interconnection oflarge regional power grids, the interarea low frequency oscilla-tion becomes a very serious issue, which threatens the stabilityand security of the interconnected power systems and also lim-its the power flow of tie-lines. With the rapid advancementsin synchronized phasor measurement technologies, developingnovel wide-area damping controllers for interarea oscillationshas become a hot topic in recent years [3]–[6]. The wide-areapower system stabilizer (WPSS) has been proved to be oneof the most potentially effective approaches to damp interareaoscillation.

In wide-area damping control, data measured by phasormeasurement units (PMUs) are transmitted to remote controlcenter through communication channels. Thus, network timedelay is unavoidable. Such kind of delay varies from tens toseveral hundred milliseconds. Several experiments, reportedin [7]–[9], have been carried out to measure the time delay.As even a very small delay can result in loss of power systemstability [10], input delay cannot be neglected in controllerdesign. For wide-area damping control, once the control loca-tion and feedback signal are selected, the path and mode ofsignal transmission are also fixed. Usually, this transmissionpath will not change in the short-term, so that WPSS inputdelay becomes stable. Thus, the delay can be modeled as aconstant delay in controller design. Smith predictor [11] andPade approximation [12] are two effective approaches to dealwith this kind of constant time delay problem. Reference [13]modeled the closed-loop power system as a networked controlsystem, and designed a state feedback controller by solvinglinear matrix equations considering delays. However, it shouldbe noted that only delay compensators with fixed parameterscan be obtained with these methods. Such compensators per-form “acceptably” over a range of delays, but cannot track thelarge variation of delays and tend to be conservative [14], [15].

In the long run, transmission path might change withthe changes of communication systems, such as when routeswitches and communication load increases, resulting ina remarkable delay variation. In addition, the change offiltering algorithm in PMUs also results in delay varia-tion. In order to guarantee the performance in time-varyingdelay and reduce the conservativeness, adaptive time delaycompensators (ATDCs) are proposed. A gain-scheduling con-troller was designed in [14], which could be considered as an

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adaptive process as the time delay may be variable. However,continuous compensation of time-varying delay is hard toachieve because a large number of predesigned controllershave to be required for switching from one to another depend-ing on actual delay [15]. In [15], an adaptive phasor poweroscillation damping controller was designed. The time delayis compensated by a forward rotation of the phasor in thetime domain. The signal with delay is compensated before thedamping controller receives the input signal. In [16], anotheradaptive damping control scheme was presented, in whichthe structure and parameters of damping controllers are tunedonline once an oscillation is detected, and then a delay com-pensator is designed at the controller location. However, thiskind of online designing method might miss the best controltime. Reference [17] presented an adaptive damping con-troller, comprising several phase compensators. The controllerswitches among these compensators based on the measuredinstantaneous delay. The upper bound delay was used as thecompensated delay for an entire delay interval. In other words,delay is overcompensated in every interval, which deterioratesthe performance of the compensator. Moreover, the way toobtain the delay intervals, especially the number of intervalsthat should be selected, was not taken into consideration.

This paper aims to improve the idea of ATDC in [17] con-sidering engineering application. In this paper, an ATDC isproposed to deal with time-varying delay for WPSS. Boundedrandom delay is divided into several delay intervals and com-pensators are designed for each interval. The ATDC willselect an appropriate interval compensator according to theactual delay measured online. The delay used for selecting thedelay interval is the average of delay before the compensatorswitching. Methods for dividing delay intervals and switchingrules of the compensator are also presented. This method isa middle way between the fixed compensation and continu-ous compensation, reducing the conservativeness of the fixedcompensation and avoiding switching among a large numberof predesigned controllers.

This paper is arranged as follows. Section II analyses thecomponents of delay in closed loop control and presents a wayto measure PMU data delay online. Based on the measurementmethod, field tests of time delay are carried out. Section IIIproposes a detailed design procedure of ATDC, putting empha-sis on dividing delay interval and switching rules. Section IVgives a case study on a two-area power system, including com-parisons with conventional methods. The proposed method isvalidated through real-time digital simulation (RTDS) on anactual power grid in Section V. Further discussion about mer-its and shortcomings of the proposed method, and conclusionsare described in Sections VI and VII, respectively.

II. PMU DATA DELAY

In this section, the components of PMU data delay are ana-lyzed, and then measurement of delay is deduced. After that,field tests are carried out to measure the delay in a real-powersystem.

Nowadays, PMUs are widely distributed in power systems,providing signals with time-stamp of real powers, reactive

Fig. 1. PMU data communication path and delay.

powers, generator rotor speeds, power angles, frequencies,voltages, and currents. In wide-area damping control, remotesignals measured by PMUs are sent to the damping con-troller through communication system. A typical hierarchicalarchitecture is shown in Fig. 1, where the wide-area damp-ing controller is placed at the same location as the phasordata concentrator (PDC). This centralized control structurehas significant advantages in terms of reliability and opera-tional flexibility, and has been proved to be cost-effective fordamping interarea oscillations and adopted in many controllerdesigns [18]–[19].

A. Measurement of PMU Data Delay

The global positioning system (GPS) provides precise timestamps to PMU data and control signals, as well as PDC,controller and actuator. In general, as shown in Fig. 1,the delay from remote signals to control actuator can beexpressed by

τ = �τm + �τup + �τsyn + �τdown + �τa (1)

where �τm is the delay caused by PMU, including the time forsynchrophasor sampling, calculation and packaging, as wellas sending jitter delay. Once filtering algorithm is selected,this part of delay is fixed and can be taken into considera-tion directly. �τup is the delay for transmitting measurementdata from PMU to PDC through feedback channels. The PDCsynchronizes PMU data from all substations. Therefore, �τupis the delay in the channel with the most delay. �τsyn is thesum of delay required by PDC to synchronize the PMU dataand generate a desired damping controller input signal, and thetime for the controller to obtain a control signal. �τdown is thedelay for transmitting the control signal from the controller tothe actuator through forward channel. �τa is the time betweenwhen the actuator receives a control signal and when excita-tion system is effected on. Usually, �τa is less than 5 ms andrelatively fixed, thus it can also be taken into considerationdirectly in controller design.

Using GPS, data packages uploaded by PMUs are taggedwith a time stamp tm; by comparing the current time stamp taat the actuator, the delay for each PMU data package can bemeasured online

τ = ta − tm + �τm + �τa (2)


CHENG et al.: ATDC DESIGN FOR WPSS 3

Fig. 2. Delays of transmitting data in different package sizes in the same2 Mb/s private channel.

Fig. 3. Delays of transmitting the same data in different channels.

where �τm and �τa are the fixed delay components asmentioned above. Given the delay, compensator can be easilydesigned to eliminate the influence of time delay.

B. Field Tests of PMU Data Delay

In order to study the distribution characteristics of the PMUdata delay in real-power systems, field tests have been care-fully conducted to measure the delays of feedback channels inWAMS of Guizhou power Grid (GZPG). Figs. 2 and 3 showthe test results between Siling (SL) PMU substation andthe Guiyang (GY) PMU center station, where the PDC islocated.

It can be seen from Fig. 2 that the average delay is about20 ms when the size of each package is 500 bytes. When thesize increases to 1500 bytes, the delay also increases to about37 ms. One thing should be noted is that the communicationchannel in Fig. 2 is a 2 Mb/s private channel. Fig. 3 showsthat for the same package size, the delay of most packagestransmitted in an existing public channel is almost the sameas the delay in a private channel, except for a few spikesin delays. Therefore, it can be concluded that the delay inWAMS varies in a range and has some random characteristics.If the communication channels changes, the delay might haveremarkable change. In the tests above, we only tested the delayin the feedback channel. If the forward channel and routingswitching are taken into consideration, the delay might havemore significant changes.

Traditional fixed compensator cannot handle such situationwhen there is significant variation in the delay, especially whenthe average of delay changes remarkably. Therefore, the nextsection proposes an ATDC method, aiming to deal with thedelay with remarkable change.

III. ATDC DESIGN

This section presents a design method of the ATDC. Firstly,the delay is divided into several delay intervals. Thencompensators are designed for each delay interval. Afterthe implementation, the ATDC will select an appropri-ate interval compensator according to the delay measuredonline. The proposed approach resolves the problem that theWPSS input delay might remarkably change when the tra-ditional fixed delay compensation method fails, so that thelong-term stable operation of the WPSS can be ensured.Moreover, the method avoids controller’s frequent actioncaused by continuously tracking of the delay compensa-tion, which might result in the risk of system instability.Therefore, our method will also help ensure short-term stableoperation.

A. Dividing of Time Delay

The reason why the feedback signal delay of wide-areacontroller affects the control effect is because the delay willintroduce phase deviation at the input signal. Usually, foran oscillation mode with frequency of f , the phase lag ϕ

introduced by delay τ can be obtained by

ϕ = 360 f τ. (3)

For example, when the dominant frequency of a WPSSis 0.5 Hz, a delay of 100 ms will introduce a phase lag of360◦ × 0.5 × 0.1 = 18◦. It can be seen from (3) that thephase lag introduced by delay is determined by both the delayitself and the oscillation frequency. For the same delay, thecorresponding phase lag is larger with the higher frequency,and vice versa. In other words, for the same bounded delay,the higher oscillation frequency is, the more intervals will beobtained.

Since time delay affects the performance of the dampingcontroller by phase lag, the phase lag introduced by delay isadopted to select the time intervals. As the compensator for aspecific delay usually has robustness in a certain range, herethe delay causing phase lag ϕ0 is selected as the bound ofdelay intervals. ϕ0 could be set as a parameter and selectedby power system operators, according to actual situation. Inother words, for a bounded random delay τ ∈ (0, τM], whereτM is the maximum delay considered, the upper bound τi ofthe ith interval is

τi = ϕ0 × i

360 × f(4)

where τi is also the lower bound of the (i + 1)th interval. Thenumber of intervals is determined by the maximum delay τM .Assuming there are m intervals, thus the upper bound of the(m −1)th interval τm−1, which is also the lower bound of themth interval, is the largest bound delay that is smaller than τM

τm−1 = max

{τi < τM|τi = ϕ0 × i

360 × f

}. (5)

Therefore, the mth interval is (τm−1, τM] .



TABLE IINTERVAL COMPENSATION OF TIME DELAY

Fig. 4. Architecture of the proposed ATDC.

B. Implementation of ATDC

Usually, a time delay compensator can be implemented withone stage of phase compensation, that is

Hc(s, τ ) = Kc(τ )1 + sTc1(τ )

1 + sTc2(τ ). (6)

In (6), the parameters Kc(τ ),Tc1(τ ), and Tc2(τ ) are depen-dent on delay τ , which can be expressed by Table I.

In Table I, m is the number of intervals, τci is the compen-sated delay for each delay interval, which is selected as themiddle point of the delay interval. For an interarea oscilla-tion mode with eigenvalue λ = σ + jω, the phase lag andgain change caused by time delay τci are ϕ = ωτci andγ = e−στci , respectively. To eliminate the influence causedby delay τci, the parameters of compensator can be obtainedusing the following [20]:⎧⎪⎨

⎪⎩Tc1 (τci) = tan ϕ + Tc2 (τci) ω

ω − Tc2 (τci) ω2 tan ϕ

Kc (τci) = 1

|(Tc1 (τci) · jω + 1) (Tc2 (τci) · jω + 1)| .(7)

In (7), usually, Tc2(τci) can be selected between0.05 and 0.1 s according to dynamic response speed. Afterobtaining compensators for each delay interval, the ATDC isimplemented as Table I. Based on the switching rules that willbe illustrated in the next subsection, the ATDC can compensatetime-varying delay well.

C. Switching Rules of ATDC

The architecture of the proposed ATDC is shown in Fig. 4.There are three important components of this adaptive con-troller. The first component is to continuously monitor thedelay of the arriving PMU data using (2) based on the GPSsignal. The second component is to select a delay intervalfrom the intervals divided by (4) and (5). The last compo-nent is the action of the compensator switching between thecompensators in Table I, according to the following rules.

Assuming that the switching interval of the proposed ATDCis �T , this means that the ATDC runs the switching rule in

Fig. 5. Relationship of �T and �t.

Fig. 6. Sketch of time delay with interval compensation.

Fig. 7. Sketch of compensate delay larger than the upper bound.

every �T time. As the delay stays stable in the short-term,there is no need to change the controller delay for every PMUdata package. Moreover, in order to avoid constantly switch-ing between the compensators, which would cause transientsin the controller itself, a delay is required in the switching ofthe compensator [17]. At each time the rule runs, the ATDCuses a delay to select a proper interval, and then makes acorresponding switching. In this paper, we choose the averagedelay τav in �t before the switching time as the delay to deter-mine the compensator interval, avoid incorrect action causedby the delay spikes. Usually �t is chosen to be smaller than�T . The relationship of �T and �t is shown in Fig. 5.

The interval compensation of time delay can be illustratedin Fig. 6. In Fig. 6, τi and τi−1 is the upper bound and lowerbound of the ith delay interval, respectively; τci is the com-pensated delay of the ith interval. As mentioned above, τci isthe middle point of delay interval.

Assuming that at t = Tk, where t is current time delay τci

is used to set the compensator. In other words, the currentdelay belongs to interval (τi−1, τi]. According to the delaymeasured online for every PMU data point, the average delayτav in [Tk +�T −�t, Tk +�T] can be obtained. Therefore, atthe next switching time t = Tk+�T , the ATDC runs accordingto the following rules.

1) If τ > τi, τmin is the minimum bound in all the boundslarger than τ , as shown in Fig. 7

τmin = min{τj ≥ τav| j = 1, . . . , m}. (8)

The compensator should switch to interval(τmin −1, τmin], and the compensated delay isτc = (τmin −1 + τmin)

/2.

2) If τ ≤ τi−1, τmax is the largest bound in all the boundssmaller than τ , as shown in Fig. 8

τmax = max{τj < τv| j = 1, . . . , m

}. (9)

The compensator should switch to interval(τmax, τmax +1], and the compensated delay isτc = (τmax + τmax +1)

/2.



Fig. 8. Sketch of compensate delay smaller than the lower bound.

Fig. 9. Two-area power system.

3) Or else, the delay is still in the interval (τi−1, τi], andthe same controller continues to be used.

As time proceeds t = t + �T , steps 1), 2), 3) are repeated.Note that for online application, �t and �T should be set

to be adjustable parameters, which are selected by operatorsfor actual power systems accordingly.

IV. CASE STUDY I: TWO-AREA POWER SYSTEM

A. System Introduction

A classical two-area power system [21] is shown in Fig. 9.The system is modeled in Simulink/MATLAB, and all param-eters are the same as in [21]. To improve the load voltageprofile, additional 187 Mvars of capacitors are installed in eacharea at bus 7 and 9, respectively.

The system is stressed by increasing the length of line7–9 from 220 to 280 km and the power transmitted betweenthe two areas from 400 to 500 MW. Moreover, the inertiaconstants of G1∼G4 are set to be 3.5, 3.5, 6.175, and 4.175,respectively. While there is no LPSS, the system is unstablewith negative mode. LPSSs are installed to G1∼G4 with thefollowing transfer functions:

HG1(s) = 1010s

1 + 10s

(1 + 0.174s

1 + 0.106s

)2

(10)

HG3(s) = 1010s

1 + 10s

(1 + 0.173s

1 + 0.111s

)2

(11)

HG2(s) = HG4(s) = 1010s

1 + 10s

(1 + 0.02s

1 + 0.05s

)(1 + 3.5s

1 + 5.4s

).

(12)

After deploying the LPSSs, the damping ratio of the twolocal modes increases to about 22.30%, which is enough forsystem stability operation. The frequency and damping ratio ofthe interarea mode are 0.4345 Hz and 2.92%, respectively. Thisweakly damped mode threatens system operation. Therefore,in this case study, a WPSS is designed to increase the damping.

B. Implementation of WPSS

The designing of WPSS is not the key point of this paper,thus existing methods are used to design the WPSS.

Fig. 10. Active power of tie-line responses under three-phase to ground faultat Bus 8 for 0.4 s duration.

The geometric approach is adopted as it is one of the mosteffective approaches to select the most effective stabilizing sig-nals and control locations [18], [22]. According to the resultsfrom the geometric approach, the generator with the most con-trollability is selected as the control location for WPSS. Thesignal with the maximum observability is ω12, which denotesthe interarea relative rotor speed, which is

ω12 =∑2

i=1 Hiωi∑2i=1 Hi

−∑4

i=3 Hiωi∑4i=3 Hi

(13)

where ωi and Hi are the rotor speed and inertia constant ofgenerator i, respectively. Given the feedback signal and con-troller location, the transfer function of WPSS can be obtainedusing the residue phase compensation method [4]

HWPSS(s) = 510s

1 + 10s

(1 + 1.032s

1 + 0.694s

)2

. (14)

After deploying the obtained WPSS to G1, the dampingratio of the interarea mode increases from 2.92% to 11.16%.In order to evaluate the effectiveness of the designed WPSS,we simulate the system response under a fault scenario inwhich a three-phase short-circuit fault happens at bus 8 for0.4 s duration before fault-clearance. The simulation resultsare plotted in Fig. 10. It can be seen from Fig. 10 that theWPSS performs reasonable well, if there is no delay at theinput signal.

C. Implementation of Proposed ATDC

Now, assuming a delay of 100 ms at WPSS input, whichintroduces a phase lag of about 15.64◦ at the interarea oscilla-tion frequency of 0.4345 Hz, without compensation, the phaselag has a negative impact on the damping effect, as indicatedby the dashed line in Fig. 11. But it can be compensated forby a lead-lag block of 100 ms delay, as shown by the solidline in Fig. 11. When the compensated delay is equal to thedelay at the WPSS input, the compensation performance isalmost the same as that of WPSS with no delay, as shown bythe dotted line in Fig. 11.

When the delay at WPSS input increases, the performanceof the same lead-lag block of 100 ms delay will deteriorate.Under the same scenario, the active power responses with thesame lead-lag block of 100 ms under conditions of differentdelays are plotted in Fig. 12. It can be seen that the perfor-mance is getting worse with the increased delay. Especially,



Fig. 11. Active power of tie-line responses with and without compensationfor 100 ms delay at WPSS input.

Fig. 12. Active power of tie-line responses with the same lead-lag block of100 ms for different delays.

TABLE IIDAMPING RATIOS WITH DIFFERENT CONTROL MODES

compared with the dotted line shown in Fig. 10, when thedelay increases up to 400 ms, the system damping is almostthe same as the case when there is no WPSS. Damping ratiosof lines in Figs. 10–12 are identified by the standard Pronymethod [23], [24] and summarized in Table II, which furtherconfirms the conclusions of the previous analysis.

According to the above analysis, the conclusion can bedrawn that conventional fixed delay compensation blockcannot perform well while delay has a significant varia-tion compared to the original compensated delay. Therefore,we propose an ADTC. Assuming that the maximum delayτM = 350 ms, the bound of delay interval ϕ0 = 10◦, usingthe ATDC implementation method illustrated in Section III,the adaptive parameters could be obtained and summarizedin Table III.

Bode diagrams of compensators for different delay intervalsare plotted in Fig. 13. In Fig. 13, all the amplitude frequencyresponses intersect with the frequency of 0.435 Hz, which isthe dominant frequency of the interarea mode. Furthermore,the magnitude at the intersection is almost 0 dB, which meansthat the designed compensators for each delay interval do

TABLE IIIDAMPING RATIOS WITH DIFFERENT CONTROL MODES

Fig. 13. Bode diagrams of compensators for different delay intervals.

TABLE IVPARAMETERS OF THE DESIGNED RANDOM DELAY

not change the original gain of the WPSS at the dominantfrequency. Moreover, it can be seen from the phase fre-quency responses that the phases of each compensator at thedominant frequency are 5◦, 15◦, 25◦, 35◦, 45◦, and 52.4◦,respectively, which are just the phase lags introduced by thecompensated delays of each interval. In other words, thedesigned compensator for each delay interval can compen-sate the compensated delay of the interval itself perfectly atthe dominant frequency without changing the original gain ofthe WPSS.

D. Evaluation of Proposed ATDC

Random delay x with the normal distribution is modeled toevaluate the proposed ATDC. Its probability density functionis given by

f (x) = 1√2πσ

exp

(− (x − μ)2

2σ 2

)(15)

where σ and μ are the standard deviation and mean of the ran-dom delay, respectively. Obviously, once σ and μ are specifiedthe delay is completely determined. Therefore, the designeddelay can be determined by Table IV.



Fig. 14. Simulated random delay and compensated delay (�T = 5s).

Fig. 15. WPSS output signal responses under open-loop simulation.

Fig. 16. Active power of tie-line responses under closed-loop simulations.

The designed delay in Table IV is plotted in Fig. 14. Themean and the corresponding compensated delay of ATDC,while �T is 5 s and �t is 1 s, are also plotted in Fig. 14.

When this random delay is added to the input of WPSS,open loop simulations are carried out and the output signalsof WPSS are plotted in Fig. 15. It can be seen that the solidline almost coincides with the dotted line, except within thedurations 2 to 5 s and 7 to 10 s. Compared with Fig. 14, it canbe found that the reason is that the compensated delay doesnot follow the mean of the random delay well at durations2∼5 s and 7∼10 s.

After adding the output signal of WPSS to the exciter ofG1, results of closed loop simulations can be obtained. Withoutcompensation, the random delay deteriorates the damping, asshown by the dashed line in Fig. 16, which needs more cir-cles to damp oscillation. With the compensation of the ATDC,oscillation is damped in three circles, as indicated by the solidline in Fig. 16. It should be noted that the solid line withcompensation does not coincide with the dotted line, whichrepresents the ideal WPSS with no delay. This is consistentwith the conclusion from the open-loop simulations that theATDC does not provide an ideal compensation while �T = 5s.

As the proposed ATDC cannot provide an ideal com-pensation, �T is reduced from 5 to 1 s. At this time, thecompensated delay is shown as the dotted line in Fig. 17.

Fig. 17. Designed random delay and compensated delay (�T = 1s).

Fig. 18. Closed-loop simulation performance of the proposed ATDC withdifferent switching times.

Fig. 19. Compensated delay of fixed compensation method (�T = 5s).

Compared with Fig. 14, it can be found that the compen-sated delay is closer to the mean of the designed delay, whichdemonstrates that the ATDC cannot provide an ideal compen-sation only within the durations 2 to 3 s and 7 to 8 s. Therefore,the performance of the compensator whose switching time�T = 1 s is better than that with �T = 5 s, as plotted inFig. 18. As there are only two shorter time windows in whichthe compensated delay cannot follow the random delay, theperformance of the proposed compensator is almost the sameas that of no delay, as indicated by the dashed line and dottedline in Fig. 18, respectively.

E. Comparison With Fixed Compensation Method

A fixed compensation method [12] performs reasonable wellwhile the delay is stable without time-varying. A comparisonbetween fixed compensation method and proposed method isshown in Figs. 19 and 20.

It can be seen from Fig. 19 that the compensated delay ofthe fixed compensation method cannot follow the variation ofdelay. Therefore, the performance of the proposed adaptivemethod is better than that of the fixed compensation methodwhile the average of delay changes significant, which is shownin Fig. 20.




Fig. 21. Compensated delay of Chow’s method (�T = 5s).


F. Comparison With Chow’s Method

Chow and Ghiocel [17] presented an adaptive damping con-troller, comprising several phase compensators. In Chow’smethod, the upper bound delay was used as the compen-sated delay for an entire delay interval, which might dete-riorate the performance of the compensator. A comparisonbetween Chow’s method and the proposed method is shownin Figs. 21 and 22.

It can be seen from Fig. 21 that Chow’s method overcom-pensates the delay in almost every interval. Fig. 22 suggeststhat the proposed method performs better than Chow’s method.Comparing Figs. 22 and 20, it should be noted that Chow’smethod is better than fixed compensation method.

V. CASE STUDY II: GZPG

GZPG is a large interconnected power system in SouthwestChina, comprising of area A, B, C, and D, which is shownin [2, Fig. 23]. GZPG is connected with YN, GX, and GDpower grid with AC and DC lines.

In GZPG, most of the main generators have been installedwith LPSSs to increase system damping. However, low fre-quency oscillations still occur frequently. The recent two

Fig. 23. Structure diagram of GZPG in the year 2013.

Fig. 24. Delay and compensated delay in RTDS simulation.

accidents are recorded by Guizhou WAMS, which took placein HJD and DL on Nov. 9, 2008 and SL on Jul. 22, 2010,respectively [2], [23].

Eigenvalue analysis of GZPG reveals that there is an inter-area oscillation between area A and area D. SL has themaximum controllability over the oscillation mode, and WJXhas the maximum observability. In this case study, WPSS isdesigned to improve the damping ratio of the mode betweenarea A and D. According to the results of controllabilityand observability analysis, WPSS is installed at SL, and thefeedback signal is the rotor angle difference between SLand WJX.

In order to study the stability of GZPG, an equivalent sys-tem as shown in Fig. 23 is built in RTDS, which contains39 generators, 104 buses, and 174 lines. Eight racks are usedto simulate such a bulk power system.

Normally distributed random delay with a mean varyingbetween 65 and 170 ms is simulated and plotted in Fig. 24.Simulation results under a three-phase to ground fault at BusYXB for 0.1 s duration are plotted in Fig. 25.

Both relative speed and rotor angle difference responsesin Fig. 25 shows that the proposed adaptive compensatorcompensates the random delay well. After compensation, therelative speed and rotor angle difference traces are almost thesame as those of WPSS with no delay. Therefore, the simula-tion results of GZPG in RTDS verify the effectiveness of theproposed delay compensation method.



Fig. 25. Simulation results of delay compensation in RTDS.

VI. FURTHER DISCUSSION

The case studies in Sections IV and V verify the proposedmethod for compensating a time-varying delay. In this sec-tion, the merits and shortcomings of the proposed method arefurther discussed.

The proposed approach resolves the problem that the WPSSinput delay might remarkably change when the traditionalfixed delay compensation method fails, so the long-term stableoperation of the WPSS can be ensured. On the other hand, theproposed method avoids controller’s frequent action caused bycontinuously tracking of the delay compensation, which mightresult in the risk of system instability, so that it can also ensurethe short-term stable operation of WPSS. Above all, the pro-posed method is suitable for the situation in which the delaykeeps stable in a short period but changes remarkably in along period.

However, with the proposed method, the compensators alsoneed to be designed offline, and the controller switches themonline. If the average delay changes more frequently, accord-ingly, the compensators need to be switched more frequently,which might causes instability. Another situation in which theproposed method might lose effectiveness is when the delaychanges remarkably during switching time �T . It means thatwithin �T the ADTC cannot compensate the delay or mayeven deteriorate the damping. Once the �T is too long, insta-bility might occur. At this time, the whole WPSS with ATDCshould be taken out of service.

In this paper, only one interarea mode is taken into consid-eration. To avoid the situation that a WPSS for one mode hasan adverse effect on the other modes, the modal decomposi-tion method presented in [25] can be used. In [25], WPSSs aretuned with its effect on other modes minimized by weakeningthe interactions among different modes.

VII. CONCLUSION

This paper presents a powerful and practical ATDC thatis specifically aimed at compensating time delays. The maincontribution of the proposed compensation strategy is to dealwith the problem of input signal delay by dividing the delayinto several intervals. The corresponding compensators aredesigned for each delay interval. PMU data delay is measuredonline and then the average delay is calculated. An appropriate

compensator is selected based on the obtained average delay,according to switching rules. The WPSS is taken as an exam-ple to illustrate the control strategy design, and other dampingcontrollers can also be easily designed in a similar way.

The proposed method has been demonstrated by simulationof a two-area power system. The results verify the effec-tiveness and practicability of the proposed ATDC strategy.Comparison studies with the conventional fixed method andChow’s method show the advantages of the method. The sec-ond case study for GZPG by RTDS shows its application in anactual complex system, which further validates the proposedmethod.

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Lin Cheng (M’05) was born in 1973. He receivedthe B.S. degree in electrical engineering from TianjinUniversity, Tianjin, China, in 1996, and the Ph.D.degree in electrical engineering from TsinghuaUniversity, Beijing, China, in 2001.

He is currently an Associate Professor with theState Key Laboratory of Power Systems, Departmentof Electrical Engineering, Tsinghua University. Hiscurrent research interests include power system reli-ability and planning, power system dynamics andcontrol, as well as voltage stability and control.

Gang Chen was born in 1985. He received theB.S. degree in electrical engineering from TianjinUniversity, Tianjin, China, in 2008, and the Ph.D.degree in electrical engineering from TsinghuaUniversity, Beijing, China, in 2013.

He is currently an Engineer with the State GridSichuan Electric Power Research Institute, Chengdu,China. His current research interests include powersystem dynamic monitoring and control based onwide-area signals.

Wenzhong Gao (S’00–M’02–SM’03) received theM.S. and the Ph.D. degrees in electrical and com-puter engineering specializing in electric power engi-neering from the Georgia Institute of Technology,Atlanta, GA, USA, in 1999 and 2002, respectively.

His current research interests include renewableenergy and distributed generation, smart grid, powerdelivery, power electronics application, power sys-tem protection, power system restructuring, andhybrid electric propulsion systems.

Dr. Gao is a member of the Power and EnergyEducation Committee of the IEEE Power and Energy Society. He is an Editorof the IEEE TRANSACTIONS ON SUSTAINABLE ENERGY and an AssociateEditor of the IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN

POWER ELECTRONICS.

Fang Zhang (S’13) received the B.S. degree in elec-trical engineering from Tsinghua University, Beijing,China, in 2010. He is currently pursuing the Ph.D.degree in electrical engineering with the State KeyLaboratory of Control and Simulation of PowerSystems and Generation Equipment, Department ofElectrical Engineering, Tsinghua University.

His current research interests include power sys-tem dynamic control based on wide-area measure-

ment system.

Gan Li received the B.S. degree in electricalengineering from Xi’an Jiaotong University, Xi’an,China, in 2005, and the Ph.D. degree in elec-tronic, electrical, and computer engineering from theUniversity of Birmingham, Birmingham, U.K., in2012.

He is currently with the State Grid SichuanElectric Power Research Institute, Chengdu, China.His current research interests include static securityanalysis and integration of renewable energy intopower systems.

adaptive time delay compensator (atdc) design for wide-area power system stabilizer

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