Wide-area measurement signal-based stabiliser for large-scale photovoltaic plants with high...

www.ietdl.org

6©

Published in IET Renewable Power GenerationReceived on 15th February 2013Accepted on 20th April 2013doi: 10.1049/iet-rpg.2013.0046

14The Institution of Engineering and Technology 2013

ISSN 1752-1416

Wide-area measurement signal-based stabiliser forlarge-scale photovoltaic plants with high variabilityand uncertaintyRakibuzzaman Shah1, Nadarajah Mithulananthan1, Kwang Y. Lee2, Ramesh C. Bansal3

1School of Information Technology and Electrical Engineering, The University of Queensland, Australia2Department of Electrical and Computer Engineering, Baylor University, WACO, TX, USA3Department of Electrical, Electronic and Computing Engineering, University of Petoria, South Africa

E-mail: [email protected]

Abstract: In this study, norm bounded linear quadratic Gaussian controller synthesis method is utilised to design a wide-areameasurement signal (WAMS)-based power oscillation damping controller at photovoltaics (PV) plants. The uncertaintiesassociated with the system are confined by the system matrices which are the affine functions of parameters belong to aconvex polytopic region. A hybrid method based on Hankel singular value (HSV) and right-half-plane zeros (RHP-zeros) isutilised to assess and select the optimal feedback signal for the PV wide-area damping controller. First, the HSVs of thedelayed subsystems are employed to preselect the candidate signals for damping the target mode. Then, the RHP-zeros andthe modal interaction measures of the candidate signals are evaluated. Finally, the signal with minimum variance in HSV andmodal interaction over the wide range of operating conditions is selected as the optimal feedback signal for the controllerdesign. The wide range of operating conditions is obtained by the probabilistic distribution of loads, synchronous generatorsand PVs. The approach has been tested on a large 16 machine, 68 bus test system as compared to geometric measures ofcontrollability/observability method and has shown improved performance.

1 Introduction

Worldwide capacity of grid connected photovoltaic (PV)power plants has increased significantly over the last tenyears [1, 2]. Even the current installation is nearly 1%, thepresent growth suggest that a 15–20% level might be seenin foreseeable future [3]. Furthermore, among theseinstalled capacity, 33% are centralised grid-connected PVsystem [4]. A significant number of large-scale PV plantsare already in operation around many utilities, such asplants in Ontario (100 MW) in Canada, Briest (91 MW) inGermany, Montalto di Castro (84.2 MW) in Italy, Lopburi(73 MW) in Thailand, and so on. Moreover, PV plants over100 MW size are recently being commissioned around theglobe, such as plants in Sonoran Desert, AZ (150 MW) inUSA, Golmud (200 MW) in China, Yuma County, AZ(250 MW) in USA, and so on [2].Low frequency electromechanical oscillations of 0.1–2 Hz

frequency range have adversely affected many power gridsworldwide [5]. The increased penetration of stochasticgenerators like PV units leads to a long distance powertransfer and the maximum use of the existing network,resulting in smaller stability margin [6–8]. In [6, 7, 9]advocate that because of the integration of large-scale PVs,the inter-area mode of the system could adversely beaffected. Therefore the proliferation of such generations onpower systems has imposed the requirement that theyshould also contribute to the network support through

damping control of inter-area oscillations, which could addadditional technical value of the PV to the power system.The research effort in [10] proposed a damping controllerbased on robust control technique in the PV plant.However, the controller was designed on a naïve systemwithout considering signal latency (time delay) and thestochastic nature of the power grid.Rapid development of phasor measurement units (PMUs)

and data communication techniques enable utilities toemploy remote/wide-area measurement signals for effectivepower oscillation damping (POD) [11]. So far numerousfeedback signal selection methods have been reported inliteratures. The most frequently used one is the residuetechnique based on modal analysis [12]. Other feedbacksignal selection methods are also proposed based ongeometric measures of modal controllability/observability(GMCO), the minimum singular value (MSV), and theHankel singular value (HSV) in [13–15]. Nguyen-Duc et al.[16] have proposed a hybrid method of wide-area signalselection based on GMCO, loop to mode measures andphase compensation conflict. However, all these controlsignal selection methods are based on the nominal operatingcondition and the controller is intended to obtain therequired damping performance under the worst caseoperating scenario.High variability and uncertainty in power system is

inevitable in future power grid because of the proliferationof stochastic generations and changing nature of consumer

IET Renew. Power Gener., 2013, Vol. 7, Iss. 6, pp. 614–622doi: 10.1049/iet-rpg.2013.0046

www.ietdl.org
demands, which could result in large variations of ‘modalobservability’ of the signal considered for damping control.In some operating conditions modal observability of theselected signal could be poor for the target mode, whereasthat for other modes are good, resulting in poor controllerperformance or even destabilisation of some modes. Thus, acontrol signal has been sought that has minimum variationof performance over different operating conditions [17–19].In this work, along with modal controllability (MC)/observability other aspects of control signal selection areemployed, such as right-half-plane (RHP) zeros and modalinteraction. It has been pointed out in certain cases thatMC/observability does not properly reflect the effect offeedback controls on oscillations, because of RHP-zerosand modal interactions. Moreover, time delays associatedwith wide-area signals could introduce RHP-zeros to thesystem [16]. On the other hand, reduced order models arewidely used in controller design, which could simplify theinteractions among different modes, resulting in thedamping control to perform in an unpredictable manner.Therefore along with the MC/observability, it is vitallyimportant to consider other aspects of signal selection forwide-area control.In this paper, a systematic design procedure of PV
wide-area damping controller (PV-WADC) is presented bycombining a stabilising signal selection procedure androbust controller design based on the norm bounded linearquadratic Gaussian (LQG) criterion, with particularattention to robust performance evaluation of the controlleron multiple operating conditions. The paper is organised asfollows: following this section, mathematical backgroundon signal selection methods and the generation ofprobabilistic operating conditions are illustrated in Section2. Section 3 briefly illustrates the theoretical background ofnorm bounded LQG control synthesis. In Section 4, optimalsignal selection procedure is described in 16 machine 68bus test system. Application example of the proposedcontroller along with performance evaluation is depicted inSection 5. Finally, conclusions are drawn in Section 6.

2 Mathematical background

2.1 Delayed power system model

The general form of the power system linearised model foroscillation study is as follows

Dx = ADx+ BDu (1)

Dy = CDx+ DDu (2)

where Δx, Δy and Δu are the state, output and input deviationsof the system, whereas A, B, C and D are the linearisedmatrices.Often the remote/wide-area measurement signals provide

greater observability to the inter-area oscillation mode [11].Hence, PV-POD is synthesised here by utilising suchsignal. However, time delays are involved in wide-areasignals which could deteriorate the performance of theclosed-loop system [20]. Therefore the delays correspondingto such signal need to be considered for controllersynthesis. The time delay operator e−sT can be transformedinto a rational transfer function by Padé approximation [21].


The mth order approximation of e−sT can be expressed as

e−sT ≃ N (s) = Nm(s)

Nm(− s)

Nm(s) =∑ml=0

(2m− l)!(− sT )l

l!(m− l)!

(3)

where T is the delay time. A better match between the givenfunction e−sT and its approximation N(s) is guaranteed byincreasing the order m. The order to choose for the Padéapproximation depends on the system dynamics, and foundthat the second-order approximation satisfies the demandsof inter-area oscillations quite well. The rational transferfunction of second-order Padé approximation can betransformed to the state-space representation as follows

Dxd = AdDxd + BdDud (4)

Dyd = CdDxd + DdDud (5)

where Δxd is the state vector, Δud input vector and Δyd is theoutput vector of delay state-space model, whereas Ad, Bd, Cd

and Dd are the state-space realisation of the Padéapproximation. By connecting (4) and (5) in cascade withthe delay-free system (1) and (2), the time-delayed model isobtained with the following system matrices

AD = A 0

BdC Ad

[ ], BD = B

BdD

[ ]

CD = [DdC Cd ]

(6)

The delay of 80–100 ms (delay between measurement unitand controller) [22] is considered in this research forobtaining delayed power system model.

2.2 Modal controllability (MC)

Suppose a modal analysis of a system matrix A produces theeigenvalues λi (assumed distinct for i = 1, …, n) and thecorresponding matrix of left eigenvectors, F = [ f1, f2, …,fn]. The MC associated with mode i and kth input (Bk) is [5,12]

MCi = fiBk (7)

If MCi = 0, then the mode i is uncontrollable from the selectedinput k. The higher the value of the MC is, the better thecontroller to control the target mode.

2.3 HSV and modal interaction measures

The system shown in (6) can be transformed to a balancedrealisation [23]. Let (Ab, Bb, Cb, Db) be a minimalrealisation of a transfer function G(s), then (Ab, Bb, Cb, Db)is called ‘balanced’ if the solution of the followingLyapunov equations

AbP + PATb + BbB

Tb = 0 (8)

ATbQ+ QAb + CT

b Cb = 0 (9)

are such that P =Q = diag(σ1, σ2, …, σn), where σi are theHSV such that, σ1≥ σ2≥ , …, σn, and P and Q are,

615© The Institution of Engineering and Technology 2013

www.ietdl.org
respectively, controllability and observability Gramians.Once the HSV are found for a single input/output pair, the‘total contribution’ of a mode (λk) to the candidate input/output pair is [16]
Ck =∑ni=1

s2i pi lk

( )(10)

where pi(λk) is the participation factor of the ith statevariable to mode λk [12]. Ideally, Ck need to be high inorder to obtain the best signal for controller design. The‘modal interaction’ for the particular mode λk can beobtained by dividing its contribution and the totalcontribution of all other modes [16]

Ik =Ck∑

lj[L Cj(11)

where Cj =∑n

i=1 s2i pi

(lj). From (11), it is evident that Ik

resolves how the other modes would be affected if onetries to control mode λk from the selected input/outputpair. Thus, Ik is defined as the interaction measuresbetween controller and the modes. For a wide-areacontroller, an input/output pair with Ik close to 1 is betterfor the controller design [16].

2.4 Generation of probabilistic operating condition

With the proliferation of intermittent renewable energy andchange in demand patterns, power system has encounteredincreasing uncertainty and variability in operatingconditions [18]. This section depicts a method of obtainingvarious operating conditions for the purpose of assessingthe variations of modal observability and the interaction ofthe feedback signals as well as the robust performanceevaluation of the controller.

2.4.1 Variability of demand and conventionalgenerator output: The uncertainty of generators andloads are modeled by Gaussian distribution functions.The output and demand of the generators and loads atnominal operating condition are considered as the mean(μ) for the distribution. The standard deviation of thecorresponding load and generator are obtained byconsidering certain percentage of coefficient of variation(CV) around μ. A ± 3σ variations around the mean isemployed to cover 99.73% area of the Gaussiandistribution curve, and the standard deviation of thedistribution can be obtained as

si =miCV(%)

3× 100(12)

f PPV

( ) = C ktu − (1/2) a+ a′( )( )−ktuAchT

′a′ el/2

0,

⎧⎨⎩

f PPV

( ) = C ktu − (1/2) a− a′( )( )−ktuAchT

′a′ el/2

0,

⎧⎨⎩


2.4.2 Variation of PV output: The output power of PVcan be expressed as [24]

PPV = AchIb = Ach ktT − k2t T′( )

(13)

where Ac is the array surface area (m2), η is the efficiency ofthe PV panel, T and T/ are the parameters that depend oninclination, declination, reflection of ground, latitude, hourangle, sunset hour angle, and kt is the hourly clearnessindex. If the probability density function (PDF) of thehourly clearness index is known, one can obtain the PDF ofPPV. PDF of PPV depends on the sign T and T/, can beexpressed as [24] (see (14))For T > 0 and T/ < 0, and (see (15))For T > 0 and T/ > 0.Where ktu represents the upper bound of kt, C is the

parameter of the PDF, and

a = T

T ′ , a′ =��a2 − 4

PPV

hT ′Ac

√(16)

Line contingency is also considered in generating multipleoperating conditions. Transmission lines are selected by thecontingency ranking index based on Hopf-bifurcation (HB)[25], and feasible operating conditions for each linecontingency are generated.

3 Norm bounded LQG control

To facilitate the norm bounded LQG controller design theperformance function J expressed in (17) needs to beminimised

J = limT�1

1

TE

∫T0

xTQrx+ uTRru( )

dt (17)

where Qr = QTr ≥ 0, Rr = RT

r . 0 and E is the expectationoperator. The controller which minimised performancefunction J can be expressed as [26]

Ac = A− BR−1r BTPr − PfC

TR−1f C (18)

Bc = PfCTR−1

f ; Cc = R−1r BTPr (19)

Here, Pr and Pf are symmetric positive definite solutions ofthe following control algebraic Riccati equation and filteralgebraic Riccati equation

PrA+ ATPr − PrBR−1r BTPr + Qr = 0 (20)

PfAT + APf − PfC

TR−1f CPf + Qf = 0 (21)

If there is ς(p) uncertain system with a matrix P (symmetric

a+ a′( ), if Ppv [ 0, Ppv ktu

( )[ ]otherwise

(14)

a− a′( ), if Ppv [ 0, Ppv ktu

( )[ ]otherwise

(15)


www.ietdl.org
positive definite) and a scalar α > 0 such that [26]
A(p)TP + PA(p)+ C(p)TC(p) PB(p)B(p)TP −aI

[ ]≤ 0 (22)

To minimise α, one must find P = PT > 0 such that α isminimised subject to above LMI constraint. If (22) issatisfied for all ς(p) system, then

G(p, s)∥∥ ∥∥

1≤ g := ��a

√

Now, for the nominal system G(s)∥∥ ∥∥

1≤ g, if there is a matrixP (symmetric positive-definite) such that the following LMI issatisfied

ATP + PA+ CTC PBBTP −g2I

[ ]≤ 0 (23)

Let, the infinity norm of the LQG controller is bounded by μwhere 0 < μ < 1/γ [26], and

Gc(s)∥∥ ∥∥1≤ m

Assumed that Γ∈ Rn × n is a square root of P, and P = ΓTΓ.By using coordinate transform (ξ = Γx), the system becomes

j = Aj+ Bu

y = Cj

where A = GAG−1, B = GB and C = CG−1. Pre-multiplying(23) by diag(T− T, I) and post-multiplying by its transpose, thefollowing expression can be obtained

AT + A+ C

TC B

BT −g2I

[ ]≤ 0 (24)

Hence, from (24) it is evident that without losing thegeneralisation, (23) is satisfied with P = I which reveals that

Fig. 1 Sixteen machine 68 bus test system


the LQG controller is also gain bounded. The designed LQGcontroller is said to be norm bounded by μ (0 < μ < 1/γ) if itsatisfies

Rr ≥ I

Qr . m−2PrCTR−2f CPr − C

TR−1f CPr − PrC

TR−1f C

Qf = − A+ AT

( )+ C

TR−1f C

(25)

4 Optimal signal selection

The test system used in the paper is 16 machine 68 busnetwork shown in Fig. 1 [27]. It is an interconnected testsystem of New England (NEST) and New York powersystem (NYPS) with five areas, where G1–G13 represent thegenerators of NEST and NYPS whereas G14–G16 are thedynamic equivalents of the three neighbouring areasconnected to NYPS. The sixth-order synchronous generatormodel is considered for all the 16 generators. Thegenerators G1–G8 are equipped with slow excitation system(IEEE-DC1A), whereas G9 is equipped with fast actingstatic excitation system (IEEE-STI1) [27]. The aggregatedsystem load is PL = 17 620.65 MW, QL = 1,971.76 MVAr,and generation PG = 18 408.00 MW. The system andgenerator data are given in [27]. PVs are considered at bus16, 30, 38 and 48. The instantaneous penetration of 6% isconsidered for the analysis. The load sharing of theconventional generators is changed in the same proportionto accommodate the PV generator to the system. It isassumed that PV plants are operating at 60% of their ratedcapacity in the nominal system operating condition. For theanalysis generic model of the PV is used [28]. The detailabout this generic model can be found in [28, 29].Modal analysis has been performed to assess the low

frequency oscillatory stability of the system with thelarge-scale PV plants. Table 1 shows the two lightlydamped inter-area modes of the system. Between the twomodes, mode 1 is more critical as the damping of the mode


Table 1 Dominant inter-area modes with large-scale PVpenetration

Mode no. Eigenvalue f, Hz % ζ Generatorparticipation

mode 1 −0.0824 ±j3.5165

0.589 2.34 G1–G13, againstG14–G16 (areas 4 and5 against areas 1–3)

mode 2 −0.3672 ±j4.502

0.716 8.129 G15 against G14,G16 (area 2 againstareas 1 and 3)

Table 2 Wide-area signal candidates to the dominantinter-area mode

Candidate signalno.

Line betweenbuses

Lineno.

Ck Ik

1 1–2 1 0.835 0.62822 8–9 16 0.863 0.79903 9–36 48 0.856 0.83074 9–36 49 0.856 0.83075 36–37 50 0.889 0.80466 37–65 82 1.000 0.7652

Table 3 Mean absolute error of Ck and Ik

Candidate signal no. MAE of Ck MAE of Ik

1 0.044 0.02472 0.092 0.09765 0.0187 0.0284

Fig. 3 Grid of system operating conditions

Fig. 2 Control overview of 16 machine 68 bus test system

www.ietdl.org

is very low (% ζ = 2.34), suggesting a remedial measure needsto be taken to enhance the damping of the mode. Damping ofthe other mode is greater than 5%, settling in 12 s. From thetable, it can be seen that mode 1 represents the inter-areaoscillation of Areas 4 and 5 against Areas 1–3.Before selecting the feedback signals, suitable location for

POD in the PV needs to be selected. MC measure is used toselect the location. MC results reveal that the PV-1 is the bestlocation for plugging in a POD to damp out the criticalinter-area mode. In this study, the real power throughtransmission lines is considered as an initial set of feedbacksignals. A prescreening of this set is carried out based onCk (10) under nominal operating condition. As the locationof the controller is fixed at PV-1 (invariant B), Ck dependson the output matrix C. The real power signals havingnormalised magnitude of Ck≥ 70% are chosen as the set ofpotential feedback signals. Then the modal interactionmeasures Ik (11) for the set of potential feedback signals areevaluated. For the clarity of presentation, the potentialsignals with Ck and Ik are listed in Table 2. It is evidentfrom Table 2 that the candidate signal 6 which has high Ck

value has an adverse effect on other modes of the system.The candidate signals 3 and 4 seem to be the best signals asthey have fairly good modal observability and lowinteraction to other modes of the system at nominaloperating condition. However, analysis of RHP-zerosreveals that the system with candidate signals 3, 4 and 6has RHP-zeros. Hence, these signals have been discardedfrom further analysis.The final signal selection is done by evaluating Ck and Ik

for various operating conditions. Wide range of operatingscenarios is obtained by the probability distribution ofloads, conventional generators, and PV plants as describedin Section 2. The histograms of the system load, PV plants,and synchronous generator outputs for all scenarios areshown in appendix (Figs. 9i and ii). Total of 250 feasibleoperating conditions are generated to evaluate the variationsof the Ck and Ik under multi-operating conditions. Signalswith minimum mean absolute error (MAE) of Ck and Ik isthe optimal choice for the control signal.


Table 3 depicts the MAE of Ck and Ik for candidate signals.The results in Table 3 reveal that the candidate signal 5 hasthe minimum MAE of Ck, whereas signal 1 has theminimum MAE of Ik. The MAE of Ik for candidate signals1 and 5 is very close. Hence, the candidate signal 5 isselected as the optimal control signal for the PV-WADC.

5 Controller design and performanceevaluation

5.1 Controller design

The norm bounded LQG design scheme has been used in thispaper as described in Section 3. Two PODs have beendesigned; namely, Controller 1 (with signal selected by theproposed method), and Controller 2 (with signal selected bythe GMCO) for comparison. Ruan et al. [30] shown thatpower system damping can be achieved through themodulations of either real and/or reactive power of voltagesource converters. Reactive power modulation at the


Fig. 5 System EM modes with and without controllers

www.ietdl.org
converter of the PV is used here for the oscillation damping.Fig. 2 shows the control overview of the 16 machine 68 bustest system. Step-by-step controller design procedure isdescribed below:
Step 1. Obtain the region of interest for the variation of systemloads and PV generations as depicted in Fig. 3.Step 2. Find γ of the uncertain system such that (22) issatisfied.Step 3. Obtain P to the LMI of (23) for the nominal systemand get the transformed system matrices.Step 4. Chose LQR weighting matrices based on theperformance requirement and obtain Pr and Pf.Step 5. Solve (18) and (19) to obtain the required controller.

The ‘Balanced Reduction Method’ available ‘in RobustControl Toolbox’ [31] has been used to reduce the order ofthe power system to design the PV-WADC effectively. Theopen-loop system is reduced from 172 to 11 orders. TheLMI associated with the control design method has beensolved in YALMIP [32]. The order of the designedcontrollers is equal to the reduced order model of the powersystem which is relatively high for the implementation.Hence, the model reduction has been executed again toreduce the order of the design controllers without losing theeffectiveness on the frequency of interest. Fig. 4 showsthe frequency response of full- and reduced ordercontrollers. From the results in Fig. 4 it is clear that the

Fig. 4 Frequency response of full-and reduced order controller

a Controller 1b Controller 2


sixth order controllers have the indistinguishable controlcharacteristics for the frequency range of interest (0.1–2Hz). Electromechanical (EM) modes are shown in Fig. 5 forthe system with and without controllers. Fig. 5 depicts thatboth controllers move the target mode (mode 1) further leftin the s-plane. It is also noticeable from the figure that theController 2 has an adverse effect on inter-area mode 4 ofthe system since it has shifted the mode 4 to the right.Transient response has been analysed to verify the linear

analysis results. Three phase self-clearing fault aresimulated at bus 36 for 100 ms. The nonlinear simulation


Fig. 6 Dynamic response following a three-phase fault at bus 36

www.ietdl.org

has been carried out for 20 s. The results concerning thedynamic response of the power flow in tie-line betweenbuses 1 and 27 is shown in Fig. 6. It can be seen from thisthat the POD performance of Controllers 1 and 2 is almostthe same for the nominal operating condition as describedin Section 4, but Controller 1 has slightly better response.

5.2 Controller performance evaluation

The uncertainties in power system encompass not only thevariation of operating conditions because of load demands,generation outputs and network topologies, but alsouncertainties in the load characteristics and variations intime delays of the wide-area signals. This section depictsthe robust performance assessment of the designedcontrollers under different operating conditions, loadcharacteristics and time delays. Fig. 7 shows the percentage

Fig. 8 Damping of other inter-area modes under multipleoperating conditions

a Controller 1b Controller 2

Fig. 7 Damping of inter-area mode under multiple operatingconditions

a No line outageb With line outage


of the damping factor for the target inter-area mode ofoscillation under different operating conditions, whereasFig. 8 shows the percentage of damping of other inter-areamodes under the same operating conditions. Robustperformance assessment results in Fig. 7 depict that theperformance of Controller 1 is better than that of theController 2 under the wide range of operating conditionsand contingencies tested. For the vast majority of casesinvestigated (including outage contingencies) for bothcontrollers, there are some operating regions in whichdamping performance of the controllers is reducedsignificantly. However, the variations in dampingperformance are less for Controller 1 than for Controller2. From the results in Fig. 8 it can be seen that the dampingof other inter-area modes varies less with Controller 1 ascompared to Controller 2.The robust performance of the damping controller is further

evaluated under different load characteristics since the changeof load characteristics is quite common, and difficult topredict [33]. Table 4 shows the damping of the targetinter-area mode for different load characteristics. From thetable, it can be seen that the damping performance of theController 1 is more robust as compared to Controller 2 fordifferent load characteristics. It is worthwhile to note thatthe system with Controller 2 will experience morevariations in oscillation frequency on the target inter-areamode.The effect of time-delay variations of feedback signal on

controller performance is demonstrated in Table 5. From thetable it is evident that the damping performance of the bothcontrollers is gradually declined as the time delay of thefeedback signal is increased. However, the deterioration ofController 2 damping performance is more significant ascompared to Controller 1.

Table 5 Damping of critical inter-area mode for time-delayvariation

Time-delay, ms Controller 1 Controller 2

% ζ f, Hz % ζ f, Hz

150 13.0 0.5840 11.58 0.610200 12.09 0.5872 9.67 0.604250 10.80 0.5900 8.74 0.615300 9.08 0.5904 7.34 0.588350 8.13 0.5904 6.30 0.6127400 7.30 0.5852 5.25 0.59

Table 4 Damping of inter-area mode for different loadcharacteristicsa

Type of load Controller 1 Controller 2

% ζ f, Hz % ζ f, Hz

ZIP 12.83 0.598 12.14 0.6063Z 13.15 0.5908 12.56 0.613I 12.81 0.598 11.89 0.614P 13.05 0.584 13.0 0.610real I; reactive Z 11.02 0.589 11.05 0.588real Z; reactive P 11.91 0.592 8.02 0.623real P; reactive I 9.84 0.592 7.56 0.593dynamic 12.64 0.584 12.20 0.527

aZIP, polynomial; I, constant current; P, constant power; Z,constant impedance


www.ietdl.org
6 Conclusions
This paper presents a reactive-power modulation-basedWADC at utility scale PV plants for stabilising theinter-area oscillation mode in an interconnected powersystem. High variability and uncertainties related togenerations and loads have been considered in designingsuch controller. A norm bounded LQG controller hasdesigned for the class of uncertain systems with systemmatrices which are the affine functions of parametersbelong to convex polytopic region. An appropriatepolytopic region for the test network is formed based on theuncertainty range of the system loads and PV outputs.Hybrid signal selection method for delayed system isproposed utilising the concepts of HSV-based MC/observability, RHP zeros, and mode to loop interactions.The final selection of the signal is achieved by checking theminimum variances of modal observability and interactionto ensure the robust performance of the controller for awide range of system operating conditions. A detailedrobust performance assessment has been carried out over awide range of operating conditions obtained from theprobabilistic distribution of loads, generators and PV plants.From the analyses it is apparent that the designed controllerbased on the proposed method provides better robustperformance than the controller designed by the geometricmeasures of MC/observability.

7 References

1 Delfino, F., Procopio, R., Rossi, M., Ronda, G.: ‘Integration oflarge-scale photovoltaic systems into distribution grids; a P-Q chartapproach to assess reactive support capability’, IET Renew. PowerGener., 2010, 4, (4), pp. 329–340

2 Top 50 large-scale photovoltaic power plants, [Online]. Available athttp://www.pvresources.com

3 Whitaker, C., Newmiller, J., Ropp, M., Norris, B.: ‘Distributedphotovoltaic systems design and technology requirements’ (SandiaNational Labs., Albuquerque, NM, Sandia, 2008)

4 Photovoltaic power systems programme, ‘Trends in photovoltaicapplications – Survey Report of selected IEA Countries between 1992and 2008’, International Energy Agency, 2009, IEA-PVPS T1–18: 2009

5 Pal, B., Chaudhuri, B.: ‘Robust control in power systems’ (Springer,New York, 2005)

6 Shah, R., Mithulananthan, N., Bansal, R.C.: ‘Oscillatory stabilityanalysis with high penetrations of large-scale photovoltaic generation’,Energy Convers. Manage., 2013, 65, pp. 420–429

7 Shah, R., Mithulananthan, N., Bansal, R.C.: ‘Damping performanceanalysis of battery energy storage system, ultracapacitor and shuntcapacitor with large-scale photovoltaic plants’, Appl. Energy, 2012,99, pp. 235–244

8 Du, W., Wang, H.F., Xiao, L.-Y.: ‘Power system small-signal stability asaffected by grid-connected photovoltaic generation’, Eur. Trans. Electr.Power, 2011, 21, (5), pp. 688–703

9 Shah, R., Mithulananthan, N., Lee, K.Y.: ‘Contribution of PV systemswith ultracapacitor energy storage on inter-area oscillation’. IEEEPower and Energy Society General Meeting, Detroit, Michigan, USA,24–28 July 2011

10 Shah, R., Mithulananthan, N., Lee, K.Y.: ‘Design of robust poweroscillation damping controller for large-scale PV plant’. IEEE Powerand Energy Society General Meeting, San Diego, CA, USA, 22–26July 2012

11 Dotta, D., Silva, A.S.E., Decker, I.C.: ‘Wide-area measurement- basedtwo-level control design considering signal transmission delay’, IEEETrans. Power Syst., 2009, 24, (1), pp. 208–216


12 Kundur, P.: ‘Power system stability and control’ (McGraw-Hill Inc.,New York, 1994)

13 Heniche, A., Kamwa, I.: ‘Assessment of two methods to selectwide-area signals for power system damping control’, IEEE Trans.Power Syst., 2008, 23, (2), pp. 572–581

14 Farsangi, M.M., Song, Y.H., Lee, K.Y.: ‘Choice of FACTS devicecontrol inputs for damping interarea oscillations’, IEEE Trans. PowerSyst., 2004, 19, (2), pp. 1135–1143

15 Farsangi, M.M., Nezamabadi-pour, H., Song, Y.H., Lee, K.Y.:‘Placement of SVCs and selection of stabilizing signals in powersystems’, IEEE Trans. Power Syst., 2007, 22, (3), pp. 1061–1071

16 Nguyen-Duc, H., Dessaint, L.-A., Okou, A.F., Kamwa, I.: ‘Selection ofinput/output for wide area control loops’. IEEE Power and EnergySociety General Meeting, Minneapolis, MN, USA, 25–29 July 2010

17 Wang, H.F.: ‘Selection of robust installing locations and feedbacksignals for FACTS-based stabilizers in multi-machine power systems’,IEEE Trans. Power Syst., 1999, 14, (2), pp. 569–574

18 Juárez, C.A., Rueda, J.L., Erlich, I., Colomé, D.G.: ‘Probabilisticapproach based wide-area damping controller for small signal stabilityenhancement of wind thermal power system’. IEEE Power and EnergySociety General Meeting, Detroit, Michigan, USA, 24–28 July 2011

19 Kunjumuhammed, L.P., Singh, R., Pal, B.C.: ‘Probability based controlsignal selection for inter-area oscillations using TCSC’. IEEE Power andEnergy Society General Meeting, Minneapolis, MN, USA, 25–29 July2010

20 Wu, H., Hui, N., Heydt, G.T.: ‘The impact of time delay on robustcontrol design in power systems’, IEEE Power Eng. Soc. WinterMeeting, 2002, 2, pp. 1511–1516

21 Philipp, L., Mahmood, A., Philipp, B.: ‘An improved refinable rationalapproximation to the ideal time delays’, IEEE Trans. Circuit Syst. I,Fundam. Theory Appl., 1999, 46, (5), pp. 637–640

22 Xie, X., Xin, Y., Xiao, J., Wu, J., Han, Y.: ‘WAMS application inChinese power systems’. IEEE Power and Energy Magazine, January/February 2006, pp. 54–63

23 Skogestad, S., Postlethwaite, I.: ‘Multivariable feedback control:analysis and design’ (John Wiley, Hoboken, NJ, 2005, 2nd edn.)

24 Conti, S., Rati, S.: ‘Probabilistic load flow using Monte Carlo techniquesfor distribution networks with photovoltaic generators’, Solar Energy,2007, 81, pp. 1473–1481

25 Mithulananthan, N., Shah, R., Nam, D.H.: ‘Contingency rankingmethodology for low frequency oscillations in power systems’.Australasian Universities Power Engineering Conf. (AUPEC), Bali,Indonesia, 25–28 September 2012

26 Joshi, S.M., Kelkar, A.G.: ‘Design of norm-bounded and sector boundedLQG controllers for uncertain systems’, J. Optim. Theory Appl., 2002,113, (2), pp. 269–282

27 Rogers, G.: ‘Power system oscillations’ (Boston: Kluwer AcademicPublishers, 2000)

28 NERC: ‘Standard models for variable generation’ (NERC SpecialReport, Atlanta, GA, 2010)

29 Clark, K., Miller, M.W., Walling, R.: ‘Modeling of GE solarphotovoltaic plants for grid studies’. General Electric InternationalInc., Schenectady, NY 12345, USA, 2009

30 Ruan, S.-Y., Li, G.-J., Ooi, B.-T., Sun, Y.-Z.: ‘Power system dampingfrom real and reactive power modulations of voltage source converterstation’, IET Gener. Transm. Distrib., 2008, 2, (3), pp. 311–320

31 Balas, G., Chiang, A.,, Packard, A., Safonov, M.: ‘Robust controltoolbox for Matlab’, 2005

32 Lofberg, J.: ‘YALMIP: A toolbox for modeling and optimization inMatlab’. IEEE Int. Symp. on Computer Aided Control SystemsDesign, Taipei, Taiwan, 2–4 September 2004

33 Mithulananthan, N.: ‘Hopf bifurcation control and indices for powersystem with interacting generator and FACTS controllers’. PhDdissertation, Department of Electrical and Computer Engineering, TheUniversity of Waterloo, Ontario, Canada, 2010

8 Appendix

See Fig. 9.


Fig. 9 Histograms of system load, synchronous generator outputs and PV plants

i Histogram: (a) system load (GW), (b) synchronous generator outputs (GW)ii Histogram of PV generator outputs (pu)

www.ietdl.org



Wide-area measurement signal-based stabiliser for large-scale photovoltaic plants with high...

Documents

Transcript of Wide-area measurement signal-based stabiliser for large-scale photovoltaic plants with high...