Edf Experience With Co-Ordinated Avr+Pss Tuning

7/27/2019 Edf Experience With Co-Ordinated Avr+Pss Tuning

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EDF EXPERIENCE WITH CO-ORDINATED AVR+PSS TUNINGT. Margotin*, H. Bourl&s**,Senior Member, IEEE

* Electricitt de France, Division Recherche &Dtveloppement, 1 aven ue du GCnCral de Gaulle, 92141 Clamart, France** Scientific consultant for ED F and Professor at the C onservatoire National des A rts et Metiers, Paris, FranceAbstract - tate feedback voltage controllers including both activepower and rotor speed stabilizing loops have been successfully used formany years on the F rench power system: the "Four L oop Regulator"(FLR) is currently installed on most of the French biggest power plants.It will be replaced in the next years by a robust coordinated AVR+PSS,called the "D esensitized Four Loop regulator" (DFLR), having a goodperformance in terms of transient and small signal stability. It is shownhere that the DFLR can be tuned with few design parameters, using asystematic procedure. The opportunity to transform the specificstructure of this controller into standard IEEE AVR+PSS structures hasbeen proved. A two step method is therefore proposed for tuning theparameters of a standard IEEE AVR+PSS: (i) design a DFL R, (U) makethe above-mentioned conversion, which depends on the type of theexcitation system. The AVR+PSS obtained in this manner are efficientfor damping all kinds of electromechanical oscillations of a large scalepower system (including inter-area oscillations). This approach shouldbe combined with modal analysis techniques to determine the bestlocation of the AVR+PSS to be installed or retuned. Its efficiency hasbeen verified on several large scale systems and is illustrated here on amodified version of the New England system. The obtained AVR+P SSshave a good robustness against significant changes in thecharacteristic s of the network.Keywords- VR , PSS, Line ar q uadr a t ic cont ro l , Desens i tiv ity ,Inter-ar ea oscillat ions .

I. INTRODUCTIONEDF has a long experience in designing and tuning automatic

voltage regulators (AVR) and power system stabilizers (PSS). TheFour Loop Regulator (FLR) has been implemented on almost allFrench nuclear power plants since the beginning of the 80's. Thiscontroller was designed using a state space approach (poleplacement) [6].Compared with classical AVR+PSS, this controllerallows to stabilize a power plant that feeds very long lines. Suc h aperformance (concerning both small-signal and transient stability) isa need for the French power system where several power plants arelocated far from consumption centers [2].As was shown in the ~ O ' S ,his controller is not optimal in caseof large variations of the network frequency. It induces indeed alarge coupling between frequency and terminal voltage. In order to

overcome this problem, the Desensitized Four Loop Regulator(DFLR) was then designed [SI. The design method, also based onthe state space representation, uses optimal control and robustnesstheory. DFLR enjoys the same performance as FLR when feedinglong lines, but its behavior is globally better, as the above-mentioned coupling between frequency and terminal voltage hasbeen much decreased and made very reasonable. As the FLR, itprovides good transient stability performance, as the increase of the

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rotor speed generates, du e to its positive feedback, an overexcitationduring and immediatelv after a three phase fault. DFLR will beimplemented in place of FLR i n the next years.More recently, it was shown that DFLR is a concept to beexported outside France. Although its structure is not classic, as it is

a state feedback control, it can be put in several classic AVR+PSSstructures: IEEE STlA+PSSIA [4], E E E D C I A + P S S I A [IO] ndother ones. In this manner, the structure of the obtained controller isclassic (and, therefore, it can b e easily implemented), but so is notthe tuning of the parameters. It has indeed several features:- Due to the design method, the AVR and the PSS have acoordinated action.- The PSS has a large gain, a fact which is also related to thecoordination. This makes it possible to stabilize the powersystem in very different situations, due to the robustness o f theobtained controller.- A price to pay fo r this robustness could be a poor behavior incase of, e.g., islanding. The usual limitation of the PSS canindeed be insufficient. This is why at ED F DFLR iscomplemented by protections like disconnection of the PSS incase of islanding, or terminal voltage limiter. With thesecautions, the large gain of the PSS is definitively an advantage,as fa r as the power system stability is concerned.- As explained in the sequel, due to the fact that DFLR has agood performance in case of a generator feeding a long line, it isalso efficient for damping low frequency inter-area oscillations[4, O], lthough its main function is to da mp out local ones.The paper is organized as follows: the DFLR is presented inSection 11, where the main ideas of [SI are recalled: the designmethod is described and an example applying the method ispresented. In Section 111, it is shown how the DFLR can beconverted to standard AVR+PSS structures and the performance ofthe resulting controller in terms of small signal stability is illustrated

by simulation results in the case of the modified New England testsystem affected by an inter-area mode. Section IV is devoted toconcluding remarks.

11. A ROBUST COORDINATED AVR+PSS: THE DFLRThe aim of this section is to describe the design method of

DFLR. It is based on the single machine-infinite bus model in statespace form. This model is augmented for obtaining a control lawwith integral term. The desensitivity method is then applied. Weexplain first this theory, then how the designer should adjust thedesign parameters based on the table of robustness margins, andfinally an example of design is presented.


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A. Basic linear modelThe model which is considered for the design is the classical

system "single machine, infinite bus". This model is linearizedaround an operating point defined by specific values P, V, q' and Xof the active power, the terminal voltage, the reactive power and theexternal reactance, respectively. That model is reduced to order 3using the balanced realization technique, which can be viewed as aprincipal compone nt analysis method for dynamic systems [9]. Forany signal 5, le t 6( denote the deviation of ( rom its steady-statevalue (when it exists). Th e state is chos en as being z = [SV 6P

where o s the rotor speed; the control U is &E,. Note that forthe design of DFLR, the ex citer is supposed to b e com pensated (onthe French power system AC type exciters are compensated by alead network). The variable to be controlled can be written

6V =C z, with C =[ l 0 01.Se t 0 =[P V q XIT; the matrices of the linearized model depen don 0 , .e . , the differential equation of the linearized sy stem aroundthe operating point 8 is of the form

(1)It is assumed that the vector of parameters 0 is constant withrespect to time and unknown (thus, it is a considered as randomvector) but belongs to a known domain 9, alled the "admissible

parametric dom ain".

z =F ( 0 ) z +G(0)U

B. Augmented model and control structureLet V, be the terminal voltage reference (which is assumed to

be constant). In order to satisfy the steady -state objective, the plantmodel (1 ) is augmented with the additional state e defined by

e = V - V , (2)With the control syn thesized below, e(t) tends to a constant as ttends to infinity, thus the regulation error V(t) - V, tends to zero; as

a result, the steady-state value of V(t) is Vc, so that 6V =V - Vc. Inaddition, as e is defined up to a constant, one can set 6e =e.x = A ( @ ) x +B ( 0 ) U

The "augmented state" is x =[zT elT. Equations (I), (2 ) yield(3)

where (A(@), B (0) ) is controllable and is defined byA ( @ ) = [ F ( 0 ) 0 ] B ( O ) = [ GT']

The control law is constrained to be a classic state feedbacku = - K x (4)

and therefore its scheme is the one presented in Fig. 1.Notice that the active power P has been replaced by the

"accelerating power" P - Pm, where P, denotes the m echanicalpower supplied by the turbine (in practice it is estimated from thefirst stage pressure).

The block-diagram in Fig. 1 clearly shows that the DFLR can beviewed as a coordinated AVR+PSS; U can be viewed as anadditional stabilizing signal. Th e gains K,, Kn, K, an d K, ar econstant.

C. DesensitivityDesensitivity is a method for designing a robust controllerwith respect to param etric uncertainties, i.e.,a controller stabilizing

system (3) with a suitable level of performance, not only when 0has its nominal value O0,ut for every 0 in 1). In order to clarifythe main idea of desensitivity, it is assu med in this section that 0 is ascalar parameter (this is generally not true for the AVR+PSS designproblem).

1 ) The state x is a funct ion o f t and 0,nd so is also the controlU by (4),.e .

x =x(t, e), =u(t, 0 )Le t O0 e a nominal value of 0. Desensitivity consists in

minimizing a quadratic index invo lving x$t) =x(t, 0 ), U (t) =u(t,02, and also the partial derivatives to(t) =&x(t, 8) and po(t) =deu(t, 02 (where de denotes the partial derivative with respect to0 ) ; $t) and p$t) are called the "sensitivities".This index is defined by

0 0

where d s the variance of 0 (in case when 0 is a vector, it shouldbe replaced by a c ovariance matrix [5] ) .The minimization of sensitivities ensures that the "perturbed

trajectories" x(t, 0 ) and u(t, 0 ) remain close to the "nominaltrajectories" x$t) a nd u,(t) wh en the curren t parameter value 0 isslightly different (and, in practice, rather different) from 0,. In thismanner, a good robustness of the performance is obtained. Thelarger is (3, the more weighted are the sensitivities, and the moreimproved is the robustness. Th e price to pay for this improvement,however, is a deterioration of the performance, so that a goodcomprom ise should be found.

' This notation is not classic, but it allows one to avoid a confusion with thestate weighting matrix (see ( 5 ) ) .

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2) Differentiating (4) with respect to 8 yields F&t) =- K {Jt).Now, differentiating (3) with respect to 8 and using the latterequation and as well as (3) one obtains

x, = e , [ x i e,.] (7)where the expressions of A,,B ,,C, can be easily determined; thetwo former matrices depend on K. Thus, assuming that K is known,a controller can be synthesized for system ( 6 ) , (7) using the LQGtheory [I].

However, K is the controller gain matrix we want to calculate,hence iterations should be used.

At step 0, a first gain matrix KO s calculated, such that (4)stabilizes the nominal system (3) (with 0 =02. For this, theclassical LQ method [l] is used: the quadratic index (5) isminimized with CJ =0; the matrix Q is chosen diagonal; KO s thegain of the non-desensitized LO regulator.

At ste p 1, sensitivities are for the first time taken into account bychoosing CJ >O. The resulting quadratic index is minimized forsystem (6 ) , 7) with K replaced by KO, sing LQG theory; the orderof the LQG controller then obtained in nonzero, hence it is reducedto order zero using, e.g., the method developed in [7]*. In thismanner, a first desensitized controller with gain matrix K, isobtained.

Step 1 can now be repeated with KO eplaced by K,, etc. In thismanner a sequence of gain matrices (K) is determined. Theprocedure ends when KO=Kn+,o within the tolerance. T he numberof iterations does not generally exceed about 10.

D. Table of robustness margins and their use for adjusting thedesign parameters

margins at representative operating conditions.margins are considered:Of paramount importance for the design are the robustness

Two types ofThose calculated from the open loop: the delay margin andmodulus margin [3].The dam ping of the closed loop system.

--

GeneratorInfinite bu s+Exciter Stabilizingsignals

F~ Where the loop should be opened

According to the authorsexperience, that reduction to order zero does notsignificantly disturb the closed loop dynamics, as far as AVR+PSS design isconcerned. However, in [5], that reduction to order zero is made at the finalstep only. The latter method is more accurate.The reduction to order zero isassumed to be made at each step here for the sake of simplicity.

Fo r a correct calculation of the open loop margins, the loopshould be open at the suitable place, wh ich is the input of the controlsystem, indicated by a cross in the scheme in Fig. 2. The modelerrors can indeed be assum ed to be gathered at this place. Note thatthe resulting open loop system is then a mono-input-mono-outputone, hence having a scalar transfer function, whose usual Bode andNyquist plots can be considered.The delay margin is the ratio of the phase margin (expressed inrad.) by the cutoff frequency (expressed in rad s) assuming that the

latter is unique. It is the maxim um delay which can be inserted atthe place indicated by the cross in the closed loop system withoutdestabilizing the latter. Thi s margin characterizes robustness againstsampling delay and unmo delled dynamics.The m odulus margin is the distance between the Nyquist plot ofthe open loop transfer function and the critical point -1. Asufficient modulus margin ensures a good robustness againstuncertainties on gains and against neglected non-linearities.The closed loo p system g enerally has several pairs of complexpoles, each of them hav ing a da mping ratio. In the tables presentedin the sequel, the damping of the closed loop system is defined asthe worst of these ratios. Generally speaking, this damping is verysignificant as fa r as small sign al stability is concerned.The table gathering these margins at various operatingconditions is a key tool for the design, as shown by the followingexample.E. Example1)In what follows, all quantities are expressed in p.u. except for w

which is in rad/s; X inclu des the reactance of the transformer. Letthe admissible p arametric domain 1)be:

Parametric dom ain an d design Doint

P =1 (Pn ase),0.95I 5 1.05(Vm ase),-1 I I 1 (4. base),

0.2 5 X 5 1(Snbase)In the tables below, the variations of q are not presented due tothe lack of place. No tice that 1) s very large and that V and X are

the key parameters. The design point is chosen as 00:=POVO o&IT =[l 0.95 1 O.6lT; Vo has been chosen at its lowest valuebecause it is the most co nstraining situation, X, s the mean of X.Recall that the state is x = [SV 6P 6w elT and that the input isU =6E,.

2) Non desensitized L O controller de si m ( CJ =0)The state weighting matrix is chosen as Q =diag (4000, 0, 0,1000). The idea leading to this choice is the following: only thestates 6V -the varia ble to be controlled- and e -the outp ut of theintegrator- are weighted, in order to obtain a good PI controller for

the voltage regulation (i.e., a good proportional and integralcontroller). The controlle r gain matrix is

K,,= [ 74.7 35.4 -5.28 31.6 ]The robustness of this controller is not sufficient, because thesystem is not stabilized in the whole admissible parametric domain

1). as shown in Table 1.

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Notice that a poorly damped closed loo p system is obtained forlarge values of X. Even if the "real" equivalent reactanceconnecting the generator to the rest Of the power system (calculatedfrom the short circuit Power) is not large, the behavior of thecontroller should be improved for large values of x, s it concernsthe low frequency domain. Therefore, this controller should bedesensitized with respect to this parameter.

3) Desensitized controller desirrnThe standard deviation (J is increased until satisfying damping isobtained for all values ofxX. Choosing ax=O.Syields the resultsgiven in Table 2.

considered operatingconditions. Therefore it is not necessary to desensitize the controller

Good stability margins are obtained at

Table. 1 Robustness margins with the non desensitized controller

Table. 2 Robustness margins with the desensitized controller

with respect to critical parame ter V in this particular case. Note thatthe described procedure is very systematic.

The following controller gain matrix is obtained:AK = [ 7 6 . 2 64.3 -10.1 2 9 . 8 1 = [Kv K, K, K, ] (8 )Basically, the gains of both stabilizing signals P and o havebeen increased.

111 CONVERSION OF THE DFLR TO A STANDARDA m +Pss STRUCTURE

A. Analysis of the structure of DFLR

From Fig 1, the control law of the DFL R can be w rittenU =U,, +U ( 9 )A V R i ( s )=K , +e (10)

where U,, is generated by a PI controller with transfer functionKS

and where U,,& is an additional stabilizing inputU & d = - K m W + K p P a

Assuming that the mechanical power slowly varies, this signal canbe seen as the output of a PI controller feeded by the active power,due to the equation1

2 HW ( t )=-1 Pa t )dtwhere Pa = P , - P denotes the accelerating power. The transferfunction of this controller is

K,PSS,(S) K, --2 H sTherefore, DFLR can be converted to standard P-input .AVR+PSSstructures.B. Example: IEEE DC lA +P S S l A

In case of a static excitation system, it has been detailed in[4 ] how the DFL R can be con verted, using suitable approximations,to the IEEE STlA +PS SIA structure. I t is shown in [l o] that theidea used in [3] is quite general and can be applied in other cases.To illustrate this, a DC excitation system is considered, and morespecifically the DC lA AVR below. The calculations are detailed in[lo]. The structure of IEEE DClA +PSS IA is shown in Fig. 3.

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V

The Bode diagrams of AVR(s) an d AVR,(s), defined by ( l o ) ,have the shape shown in Fig. 4. Therefore,AVR(s) can be viewed asthe approximation of AVR,(s) on the suitable frequency range

1. A similar rationale can be m ade for the PSS on the sameI[%* sfrequency range.

A V R ( s )+Fig. 3c: Structure of IEEE P S S l A + D C l A

Iv. APPLICATIONXAMPLE: THE MODIFIED NE WENGLANDSYSTEM

A. System description

-Fig. 3b: Block diagram of AVR(s1

U--+

Fig. 3c: Block diagram of PSS(s1

gain (dB)

The New England test system is classic (see, e.g., [ l l ] ) and isshown in Fig. 5 (it is a constant impedance load model, and loadsare connected to un derlined buses).

A 0.26Hz inter-area oscillation has to be damped. From the smallsignal stability analysis , a P SS should be installed on machine 9.For this machine, a DFLR has been designed and then convertedto D C l A + P S S l A structure. Th e performance of the obtainedcontroller is illustrated by the simu lation below. It has been madeusing the time simulation software EUROSTA G [SI.

A 50 ms three phase fault has been made on line 3-18 , which isthen disconnected. The voltage at bus 18 and the active power inthe inter-area link are sh own in Fig. 6. Note that the power systemis well damped with the PSS , although the topology of the networkhas changed. This is also true when significant changes are made inother parameters of the power system (such as load characteristics).This proves that the PSSs have a good robustness.-nter-areamode- nter-machinemode

i.---..;

Fig. 4: AsymDtotic Bode Diagrams of AVR an d AVR, Fig. 5: New En gland test system

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PU1.14 ,.-;... . . . . . .

Voltage at bus 18 Time (s.)

26. 30. 46. 51 .5 0 . ' '16 .Active power in the inter- area link Time(s.)

Fig. 6: 50 ms three ohase fault on line 3-18IV. CON CLUDING REMARKS

The Desensitized Four Loop Regulator which design method ispresented in section I1 of this paper, has a good performance interms of transient and small signal stability. As sho wn in section111, approximations allow to convert the particular structure of theDFLR to standard IEEE structures as the AClA+PSSlA,DC lA+PS SlA, ST lA+P SSlA . This conversion lead to a similarbehavior of the converted controller and of the DFLR on a suitablefrequency range. The controller resulting from the conversion hasthe same ability as the DFLR to improve the damping of an inter-area mode, as fa r as the concerned machine has a sufficientparticipation to the mode. A reason for this is that the DFLR isdesigned to be ab le to stabilize the closed loop system, even in thecase of a large value of the external reactance connecting the singlemachine to the infinite bus in the design model (the frequency of theelectromechanical mode of the machine is then low). T h s property,obtained by desensitizing the controller with respect to X, leads to astabilizing behavior in case of inter-area mode, as confirmed by thesimu lations presented in section 111.

REFERENCES[l ] B. D. 0. Anderson, J. B. Moore, Optimal Control: LinearQuadratic Methods. Englewood Cliffs, NJ: Prentice-Hall, 1989.[2] R. BCnCjean, P. Blanchet, J. P. Meyer, P. Hugoud, " A NewVoltage Regulator for Large French Alternators", CIGRE Conf.,[3] H. Bourlb, F. Aioun, "Approche H, et p-synthkse", in Larobustesse -Analyse et synthPse de commandes robustes, A.Ousta loup, Edt., Paris: Hermks, pp. 1 63-23 5, 1994.[4] H. Bourlks, S. Peres, T. Margotin, M.P. Houry, "Analysis andDesign of a Robust Coordinated AVRP SS", IEEE Trans. on PowerSystems, vol. 13, n"2, pp. 568-575, 1998 .[ 5 ] A. Heniche, H. BourlBs, M. P. Houry, "A DesensitizedController for Voltage Regulation of Power Sy stems", IEEE Trans.on Power Systems, vol. PWRS-10, pp. 146 1-1466, 1995.161 E. Irving, J.P. Barret, C. Charcossey, J.P. Monville, "ImprovingPower Network Stability and Unit Stress with Adaptive GeneratorControl", Automatica, vol. 15 , pp. 31-46 , 1979.[7] D. Kavranoglu, "Zeroth Order H, Norm Approximation ofMultivariable Systems", Numer. F unct. Anal. and Optimiz . ,vol. 14,[8] B. Meyer, M. Stubbe, "EUROSTAG, a Single Tool for PowerSystem Simulation", Transmission & Distribution International,March 1992.[9] B. C. Moore, "Principal Component Analysis in Linear System:Controllability, Observability, and M odel R eduction", IEEE Trans.Automat. Contr., vol. AC-26, pp. 17-31, 1981.[lo] H. Quinot, H. Bourlb, T. Margotin, "Robust CoordinatedAVR+PSS for Damping Large Scale Power Systems", IEEE PE-[ l l ] D. Wong, G. Rogers, B. Porreta, P. Kundur, "EigenvalueAnalysis of Very Large Power Systems", IEEE Trans. on PowerSystems, vol. PWRS-3, pp. 472-480, 1988 .

BIOGRAPHIES

vol. 32-13, 1982.

pp. 89-101, 1993.

455-PWRS-0-12- 1998.

Thibault Margotin received his Engineering Degree from EcoleCentrale de Nantes (France) in 1994. He is a Research Engineer atthe EDF Research and Development Division located in Clamart,France. e-mail: [email protected] Bourlss received his Engineering D egree from Ecole Centralede Paris (France) in 1977 and his Ph. D. from the Institut NationalPolytechnique d e Grenoble (France) in 1982. He worked at the EDFResearch and Development Division as Senior Research Engineeruntil 1997. He is currently a scientific consultant for EDF. On theother hand, he is Professor of the Chair of Automatic Control at theConservatoire National des Arts et MCtiers where he is also theDirector of the Laboratoire dAutom atique des Arts et M Ctiers, Paris,France. e-mail: [email protected] .

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Edf Experience With Co-Ordinated Avr+Pss Tuning