contiollable and observable in the generator's local signals as the local modes. We inve5tigate wing gZobuZ signals obtained remote from the controller to damp ...
IEEE Transactions on Power Systems, Vol. 11, No. 2,May 1996 DAMPIN(;
CONTROLLER DESIGN FOR POWER SYSTEM OSCILLATIONS USIN(; G L O B A L SIGN A L S
A.A. Sallam Student Member, B E E Senior Member, IEEE Suez canal University Egypt
Magdy E. Aboul-Ela
Abstract: This paper describes a new power system stabilizer (PSS) design for damping power system oscillations focusing o n interarea modes The input to the PSS consists of two signals The first signal is mainly to damp the local mode in the ruea where I'SS i\ located using the generator rotor speed as an input \ignaI The \econd is an additional global signal for damping interarea modes Two glohal signals are suggested, the tie-lme active power and speed difference signals The choice of PSS location, input signals and tuning 15 based on modal analy\is and frequency response information. These two signals can also be used to enhance damping of interarea modes using SVC located i n the middle of the transmission circuit connecting the two oscillating groups. The effectiveness and robustne5s of the new design are tested on a 19-generator \ystem having characteristics and structure similar to the Western North American grid.
Keywords: Interarea owllation, PSS design, stability 1 INTRODUCTION The \tability ot electro-mechanical oscillations between interwnneLted synchronous generators is necessary for secure qy\tem opelation The oscillations of one or tnore generatois in an area with repect to the rest of the system are called ZocuZ m o d e s , while those associated with groups of generators in difteient rueas oscillating against each other are called interureu triodes [ I ] Local modes are largely deteimined and influenced by local area states Inteiarea modes are more difficult tu study as they iequire detailed representation of the entne interconnected sy\tem and a e influenced by global state\ of larger areas of the power network [2] This has led to an increased interere\t in the nntuie of these mode, and m method\ (if contiolling them. We are motivated to investigate more effective control rchemes in order to incredse transmission capability for systems limited by oscillatory instability The most cominon control measures in use today for this problem employ power system stabilizers (PSS5) with local rotor speed as input. These PSSs are effective in ctarnping local modes, and if carefully tuned [ 3 ] may also be effective in damping interarea modes up to a certain transini\sion loading. The effectiveness in damping interarea modes is limited because interarea modes are not as highly contiollable and observable in the generator's local signals as the local modes. We inve5tigate wing gZobuZ signals obtained remote from the controller to damp interarea modes The global ugnals studied A paper recommended and approved 95 SM 520-7 PWRS by the IEEE Power System Engineering Committee of the IEEE Power Engineering Society for presentation at the 1995 IEEE/PES Summer Meeting, July 23-27, 1995, Portland, OR. Manuscript submitted December 28, 1994; made available for printing June 5, 1995.
James D. McCalley
A.A. Fouad Fellow, IEEE
Member, IEEE
Iowa SLite University US A are (1) difference between two generators speed deviation (2) tie line active power flow. Although control obtained remotely requires additional cominunic equipment, it is likely that the cost of such equipment WO offset by the additional operating flexibility gained h control. In addition, we note that recent advances in the fi phasor measurements may enable use of remote s transmitted via satellite for control purposes [4]. This paper extends investigation of using g signals reported in [5,6] via development of control strategies utilizing these signals The first \t utilizes a two-level PSS controller where the first lev control 15 derived from local signals and is desi effectively deal with the local modes. The second control is supplied from a coordinator using selecte states to deal with the poorly damped interearea modes The second strategy utilizes a static var compens enhance damping of interarea modes Although S often applied for the purpose of voltage support, be used to increase damping of oscillations. We 1 that an SVC using local bus voltage inputs does n contiibute significantly to system damping significant contribution to system damping can when an SVC is controlled by an appropriately ch signal superimposed over the voltage control loop
2 DAMPING OF SYSTEM MODES
N
i= AX+ Bu = Ax+ YJ
=
C/r
Blilj J=
1
where B , and CJ are the colutnn-vector input matrix
function residues [8]
2.1 Location of PSS Using PF
0885-8950/96/$05.00 Q 1995 IEEE
768 Theretore, the machines with highest PF m the mode of interest are good candidates for applying control via PSS.
2.2
Therefore, the P residue for the i-
Location of PSS Using Residues
The open-loop transfer function for a certain input/output of the Ith generator of the system is
It can also he expiessed in terms of the modes and residues as
where R , i\the residue associated with ith mode and the jth trander function (iJ It i s given by
Rzj = Slim -tX, ( s - X % ) G ~ ( ~ ) The residue
I\
(6)
selected generators, conventional PSSs modes under stresse is required particular approach focusing o
(7)
capable of damping all next section.
also given hy [ 6 ] .
I? i j = Cif
1
V j Bj
the residue can be expressed in, terms of mode y and observability Mode Controllahilitv The controllabihty of mode i from the jth generator is given by ('OIZt
Lj
=I
vi Bj I
(8)
Mode Observahilitv. The tneasure of mode observability of a certan niode 1 froin machine j ctan be defined as
ohsv,=/ c,tJ
Equation (14) indicates that maximum; therefore the chosen as input to the must be directed towards can be done by shaping
(9)
Fiom Equations (7),(8) and (9), it is clear that
1 I?, 1 =I qtl"&,I=
cmt
* obsvLI,
(10)
The residue associated with an eigenvalue AL and a feedback transfei funLtion f/(s&,) , where K , 15 the constant gain of the contio1ler, are ielnted by [SI
AA, = AGi + j A W i =K Pssj Equation (16) shows of the i-th mode, due to the real and imagin
Figuie 1 shows a PSS at the jth generatoi having a transfer function H p , ~ . \ ~ ( s given ) by
H P S S J ( S ) = K PHS iS(~$ )
(12)
Then, replacing f;(sKI)in Equation (11) by HPSS/(S), and f o r small value\ of gain, it giveq
g the feedback to the system will cause a change in the i-th eigenvalue given by
For local modes, the
Using Equations (12) & (13), this change is
AAl =I? H p s s J ( a L )
(14)
with the highest obse the generator with the hi the highert observabili
69 ccimhining information from different areas rather than being a \ingle \tate of one generator. Therefore, iit will he called globul signul, and it may be remotely transmitted. This signal will be used as input to a two-level PSS controller, described in Section 4, and also to an SVC controller, described in Section 5.
where,
T2j= -, T l j = ~T2j j
copq
4 PROPOSED TWO-LEVEL PSS DESIGN The new PSS design aims to enhance the damping of poorly damped local and interarea modes. This design provides a control signal which is a sum of two component control signals. The firut control signal U’ is to provide damping for local mode\ using the local generator rotor speed signal as a PSS input. The angle of compensation is computed at the local mode frequency, and the controller time constants are chosen accordingly. Thus, the local mode will be very highly damped. This pwt of the controller is called PSSl and can he considered as a first-level controller i n a two-level control scheme as shown in Figure 3. Each generator is considered as a subsystem. The interaction between subsystems. represented in the interarea modes, is neglected in this stage. The beconcl control signal is to provide damping for the interarea modes, controlled from the selected machines using a global input signal . The angle of compensation is computed at the interarea mode frequency, with PSSl in service, and the controller time constants are chosen to give this angle This part of the controller is called PSS2. It is the second-level controller or the coordinator as shown i n Figure 3 . The job of thi\ controller is to obtiun the measurements characterizing the global signals and send a control signal in terms of these measurements to the selected machines for controlling the interarea modes. Therefore the total control signal for the jth machine is U, =U:
+
I
U;
Coordinator
and m is the number of compensating blocks, T is a wash It is the frequency If time constant (usually 5-10 sec.), and the local mode in rad/sec. The gam K I is taken as one-third e instability gain Kinst , i.e. K I = Kinst/-?.
134
4.2
PSSZ Design Using Tie-Line Power Signal
Interarea modes typically have high observability in the act power of tie-lines between areas involved in these intera oscillations. Therefore, the tie-line active power can he used a stabilizing signal for damping the interarea modes associa with this tie-line. The selection of the controlled machine j : the tie-line signal x is such that the transfer funct Ptie,/Vrefj has the largest residue magnitude for the intera mode of interest. From Equation (6), this is given by:
e a S
d d n a
where j is the jth machine, and x is the tie-line number. The modal analysis is performed with all PSSls included, the residues associated with the lightly datnped interarea tno and several tie-lines are computed at the machines with highest controllability. These tie-lines are the heavily loat ties connecting the areas the generatois of which are swing against each other. The PSS2j transfer function is given by:
d S
le d g
I where T is the washout time constant, and Z l , 22 are compensating network time constants. The time constants found using the same method described in Section 4.1. To stl the effect of this controller on system modes using EPKI Sn Signal Stability Program (SSSP), a user defined block simulation of this controller is built [lo]. The gain Ki chosen to provide sufficient damping to the interarea mode concern.
le .e Y
11 )r 1s
If
From Equation (17) the total control signal (as shown in Fig .e
4) is given by:
V sj =H p s s l j * A w j
Figure 3: Pioposed Two-Level PSS Design
+H ps~2j*APtie
(20)
PSSZ Design Using Speed Difference Signal
4.1 Design of First-Level Controller, PSSl
4.3
Since PSSl is intended for damping local modes of the controlled machines, a PSSl is located at each machine with a poorly damped local mode. In this work, the amount of phaselead required to shift the mode to the LHP is computed from Equation (15) which is based on full system representation. The parameters of the lead/lag network are calculated frotn:
The residue Rij, corresponding to the speed deviation signa >f generator j to control mode i, may not he large enougl- 0 achieve satisfactory dampmg. To increase the residue magnit le either the observability or the controllability of these mode at particular machines must be increased, according to Equa in
770 (10) Controllability can he increased by increasing the exciter foiward gain, hut thic is not always good practice, as it can reduce the \tability margm for the local mode. We have observed that the right eigenvector elements corre\ponding to the speed, and hence the observability vectors of two machines J and k in generator groups oscillating against each other (in an inteiarea mode), are always about 180 degrees apart This suggests that the observability of this mode from these two machines speed difference signal will be larger in magnitude than each of the individual observabllities. If inteiaiea mode i is controlled from machine j using speed difference signal of machines 1 and k then:
controller
IS
where 'Is
given b
'
' 2 s
are the
The transfer function between
P
Ami GEN i 10s (1+TIs) K 1 l G s (1+T 3,s)2
+
Figure4 New PSS Design AW,L = AWj - AWk
index for the i
(21)
The ohseivability index for this signal is given by
ohsv(dWjk)= c j V i - ckVi=(Cj-Ck)VI
(22)
and the total contiol signal becomes
Vs,=Hps,slj*AWj +Hpss2j*AWjk
signal is given by:
(23)
Vs = H svc AUjk
5 APPLICATION TO STATIC VAR
COMPENSATOR (SVC) The damping ohtaineii depends on SVC location in the system and its control signal It has been found that the mid-point of the tiansmisrion ciicuit, connecting the two oscillating groups of- machines in the mterarea mode, IS the best SVC location for damping enhancement [ 2 ] .An SVC can alter the P-6 curve by changing its output Bsv(7 (SVC suceptance) in such a way that damping is increased. For example, for a one machine infinite n, if the speed deviation of the machine is fed back as iary signal to the SVC input, then Bsvc and subsequently the P-6 curve, will be altered such that the speed deviation I \ d e c r c a d , and theiefore, damping can be increased. This control stiategy has been called "Am-Control" ill]. We u\e either tie-line active power signal or speed difference signal as input to the SVC for dampmg interarea modes.
5.1
Tie-Line Power
Signal to SVC
The SVC i s assumed to be located in the middle of a tie-line connecting two areas oscillatmg against each other in a lightly darnped interarea mode. This interarea mode will be highly olhservable in such a tie line Therefore, the tie-line power of ine is u r d as a stabihzing signal. A controller i s designed der to compensate the phase lag of the system at the frequency of interarea mode of interest. This SVC stabilizing
Similarly, the transfer function -
4.1.
In
North
power 'ys
71 designed controller. This will he numerically shown for the test system in Section 9.
7 ROBUSTNESS OF THE DESIGNED
CONTROLLERS A rohust controller is expected to perform satisfactorily at various operating conditions. HoweveI, since the propored controller has been designed usmg linear analysis of the power system, it i q important to check that it performs satisfactorily when disturbances occur. The robustness of the controller is evaluated in two different ways. The f m t is to evaluate the system performance and damping ratio of critical modes of the system under a heavily stressed operating condition compared to the original operating condition. The second way is to evaluate the system response to various disturbances using tune domain simulation of the nonlinear power system model. 8 CASE STUDY Figure 5: The T a t System The single line diagram of the test system is shown in Figure 5. This system has characteristics and structure similar to the North American Western grid (WSCC) [12]. It consists of 46 bures and 19 machines in 7 areas Each area contains two or three machines, one of which is represented hy the classical model while the other one or two are represented hy a detailed model (two-axis model with IEEE Type AC4 exciter, no governor, and a damping coefficient of 1 Opu). Eigenanalyus, using the Small Signal Stability Program (SSSP), of the open-loop system with no PSSs included indicates there are 13 local and 5 intermea modes, all of which are poorly damped (Table 1). It is seen that all machines are participating in local modes Therefore, a PSSl is located at each ot the 11 detailed machines It 15 noted that modes 12 & 17 helong to two equivalent machines and are not of concern. The control parameters of PSSls are computed and given in Table 2 With F’SSls included (the conventional case) the 5 interarea modes are still hghtly damped By adding PSS2s (proposed
control) to the selected machines having the largest resid1 the damping is enhanced for all modes as shown in Tablt when using either the tie-line active power or the sp difference signals as input signals The control parameter.: PSS2s are given in Tahle 3. The controllers’ performance robustness are tested by using the Extended Transient and b term Stability Program (ETMSP). From Figure 6, it is clear I system datnping is significantly improved. To check controller robustness and then ability to stabilize system, the system with all PSSls included has heen stres until it is unstable by increasing the transfer in the major 11 and changing the load model to constant power. Figure 7 shc the time simulation of this unstable point compared to the L when PSS2s are applied, using speed difference signal I clear that the addition of the PSS25 has stabillzed the sysl under this unstable operating condition. Figure 8 illustrates expansion of the secure operating region for the two in; flows of the system due to the addition o f PSS2
Table 1: The Low Frequency Modes Of Oscillation With And Without Controllers I PSSl I PSSl+PSS2 I PSSl+PSS2
I
1 f i t
:d ZS VS
se 1s m le or
772 Tahle 2 The Fir\t-Level Controller\ Design (PSS 1) Local M ( d e Controllel F’arameter\ GEN (PSS1)
Time R e s p o n s e o f R e a l p o w e r f l o w o f t i e l i n e 2 8 - 2 0 t o 0 . 0 1 s e c F a u l t a t Bus t7n .__,
_ _- _ - PSSl 5
10
15
20
25
30
I
1
35
40
Time (Sec.)
Figuie 7. Stahilizatlon effect of PSS2
Secure Regions With PSSl Case and PSSI-PSSZCase Time Response o f
t i e - l i n e 2 8 - 2 0 r e a l power Lo 0.01 s e c F a u l t a t B u s t 7 n
Northwest to Northern California flow, MW (Line 2627)
Figuic 8 : Expiuided opcratlng legion clue to PSS2
In addition, an SVC controller was designed, using tie-line active power signal as input, to enhance damping of interarea I----9 4 B I2 rnudes of the system. This controller was built in SSSP using 16 20 24 ZB 32 Time (Sec.) user tlefiried hlocks as this is a non standard controller. Figure 6 : Time siniulation coinparison for tie-line 28-20 power TwcI ptrtential locations are studied for the SVC : Middle of line 28-20 (between Arizona and South California areas) and signal from Ptie 28-20 (SVCI) At B u d 2 2 (North California) and signal from F’tie 22-26 (SVC2) Tahle 4 lists the residues for the interarea rnodes at SVCl and SVC2. SVCl is chosen as it has much higher residues for mocles #1,3,4,5. The effect of S V C l on darnping of these modes, compared to PSS2 (of both types), is shown in Tahle 1. Figure 10 shows the hlock diagram of SVCl and its stahilizing controller. _______
NoConhol
1.0. Q C/ Q L
10 - Q c / Q L
~ ~ ~ & - , B ~ v c ~ , u ~ PWRS, pp1076-1083, NOV. 1990. 1+ sT5 PaK-QL,[ 111 K.P.Padiyw, et al.," Damping Torque Analysis of Static May 1991. U,,, or
(4A9) Figure 9: Block diagram of proposed SVCl controller
Kansas, Sept., 1994.
BIOGRAPHIES
10 CONCLUSIONS
In this paper, a two-level control scheme for PSS design has been proposed. The first level control is to provide damping for the local modes using the local speed signal as an input to the PSS. The second level is to enhance damping of interarea modes using global signals as additional inputs to the PSS. The proposed global signals are either the tie-line active power or the speed difference signal. With proper choice of these signals an increased residue magnitude for the interarea modes is obtained, and hence these modes are effectively damped. The proposed control scheme has been compared to the conventional techniques using a 19Generator system. The results show that the proposed controller is more effective and robust. These global signals have also been applied to SVC in older to damp the interarea oscillations, and the damping was significantly increased.
10 REFERENCES [ l ] M. Klein, G. J. Rogers, and P. Kiindur, "A Fundamental Study of Inter-Area Oscillations in Power Systems", IEEE Truns. PWRS, Vol. 6, No.3, Aug 1991, pp 914-921. [2] Yakout Mansour, "Application of ]Eigenvalue Analysis to the Western North Americain Power System", Eigenunulysis und Frequency Donmin Methods for System Dynumic P erfiormunce, IEEE 901'H0292-3PWR, pp 97104, 1989. [7] M. Klein, G. J. Kogers, S. Moorty, P. Kundur, "Analytical Investigation of Factors Influencing Powei System Stabilizers Performance", IEEE Truns. PWRS, Vol. EC-7, Sept 1992, pp 382-388. [ 4 ] Working Group H-7 of the Relaying Channel, "Synchronized Sampling and P h a o r Measurements for Relaying and Control", 93 WM 039-8 PWRS. [SI X . Yang and A. Feliachi, "Statdization of Inter-area Oscillation Modes through Excitation Systems," IEEE Trans. on Power Systems, Vol. 9, No. 1, Feb. 1994, pp. 494-502. [h] X. Yang, A. Feliachi, and K. Adapa,"Damping Enhancement in the Wertern US Power System: A Case Study," SM94198 [7] A E. Hatnmad, "Analysis of Power System Stability Enhancement by Static Var Compensators", IEEE Trans.PWRS ,Vol.l, No.4, Nov. 1986. [8] F. L. Pagola, I. J. Perez-Arriaga , G. C. Verghese, "On Sensitivities, Residues and participation. Application to Oscillatory Stability Analysis and Control", IEEE Truns. P W R S , V o l 4 , No 1, Feh.1989, p p 278-285 [9] D. R. Ostojic, "Stabilization of Multi-modal Electromechanical Oscillation by Coordinated Application of Power System Stabilizers", IEEE Truns. PWKS-6, pp 14'39-1445, 1991. [IO] F'.Kundur, G.J. Rogers, D.Y.Wong , L. Wang, M.G. Lauhy,
the R.S. in Electrical Engineering (1950) at the Univers Cairo; M.S. (1953) from the University of Iowa; and the (1956) from Iowa State University. He is the 1990 t Marston Distinguished Professor of Engineering at Iowa University, and he is a Fellow of the IEEE. James D. McCalley is Assistant Professor of Electrica Computer Engineering Department at Iowa State Univc where he has been employed since 1992. He worked for I. Gas and Electric Company from 1986 to 1990. Dr. Mc( received the R.S. (1982), M.S. (1986), and Ph.D ( degrees in Electrical Engineering from Georgia Tech. HI registered professional engineer in California and a meml the IEEE. A.A. Sallam was born i n Mehalla El-Kobra, Egypt in He received the RS, MS, and Ph.D. from Cairo Univt Egypt in 1967, 1972, and 1976, respectively. He has employed with the Ministry of Industry, and the El-Nasr 1 and Finishing Co., Department of Electrical Substa Mehalla El-Kohra, Egypt. In 1979, he jomed the Departm Electrical Engineering, Suez Canal University, as a le^ From 1981-1983 he was a visiting tnember of staff i Department of Electrical and Electronics Engine1 University of Newcastle upon Tyne, UK. Since 1983 h been workmg in the Depa tment of Electrical Engineering, Canal University, where he is now a Professor He is a tnember of the IEEE.
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