The Principle of Effect of the Transient Gain Reduction and Its Effect on Tuning Power System Stabilizer

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1 he Principle of Effect of the ransient Gain Reuction an Its Effect on uning Power System Stabilizer Ghazanfar Shahgholian 1, Mehi Mehavian 2, Manijeh Azaeh 2, Saee Farazpey 2, Mohammareza Janghorbani 3 1 Department of Electrical Engineering, Najafaba Branch, Islamic Aza University Najafaba, Isfahan, Iran, shahgholian@iaun.ac.ir 2 Department of Electrical Engineering, Naein Branch, Islamic Aza University Naein, Isfahan, Iran, meh_mahavian@yahoo.com 3 Young Researchers an Elite lub, entral ehran Branch, Islamic Aza University, ehran, Iran Abstract he main operation of power system stabilizer (PSS) is to provie optimal amping which is in phase with the rotor oscillation. In this paper the effect of the transient gain reuction (R) on the amping performance an the electromechanical torque components in power system with PSS is prove. he tuning of PSS parameters are compute using phase compensation (P). Several simulations have been one to show the effect of the R on the small signal stability uner operating at ifferent loaing conitions. Keywors power system stabilizer; power system stability; small signal moel. I. INRODUION Nowaays, with the expansion of the transmission system an increase power transfer through the transmission lines, maintain the ynamic stability of the power system is important [1, 2]. Dynamic instability ue to imbalance between the mechanical power input an electrical power output an lack of amping torque is achieve [3, 4]. here are several ifferent ways how to suppressing the low-frequency oscillation of the power system to improve the ynamic stability in a power system [5, 6]. Generally, there are two kins of power oscillation amping controllers in power systems: PSS an flexible ac transmission systems (FAS) controllers [7, 8]. PSS is wiely use in moern power systems amping the low frequency oscillations in orer to the enhancement of the ynamic stability of power systems [9, 10]. Different methos have been use for the esign of PSS parameters. A computational for the phase shaping of the PSS in a power system to improve the amping of the generator rotor oscillations is presente in [11]. he amping scale is propose in [12] an formulate to obtain a set of optimal PSS parameters as an objective function to increase system amping after the system unergoes a isturbance. he optimal esign of settings of PSS parameters that shift the system eigenvalues associate with the electromechanical moes to the left in the s-plane using evolutionary programming optimization is presente in [13]. By using the flexible structure of linear matrix inequalities (LMI), an algorithm that minimizes the norm of the controllers gain matrix while it guarantees the amping factor specifie for the close loop system is presente in [14]. In [15], a hybri for tuning an placement of PSS in power systems is provie to improving power system ynamic stability with wie range of changes in system parameters an operating point of the system. An aaptive fuzzy PSS base on robust synergetic control theory an terminal attractor s is evelope in [16], which fuzzy logic systems are use to approximate the unknown power system ynamic functions without calling upon usual moel linearization an simplifications. Rotor angle stability is results of a balance between the amping torque (in phase with rotor angle change) an the synchronizing torque (in phase with the spee eviation change). In general, the angle instability may happen ue to lack of amping torque (oscillatory instability) or insufficient synchronizing torque (non-oscillatory instability) [17]. In this paper, the effects of R using eigenvalues analysis on PSS parameters an rotor angle stability in power system is presente. he phase compensation is use to PSS parameters settings. Eigenvalues analysis an time omain simulation show the effectiveness of the R uner ifferent propose cases. II. POWER SYSEM MODEL he block iagram of the linearize small perturbation of the single-machine infinite-bus (SMIB) power system with PSS an R is show in Fig. 1, in which case the generator rotor spee eviation is use as the only stabilizing signal. he transfer functions of PSS, R an exciter system are G P (s), G (s) an G V (s), respectively. Fig. 1. ontrol structure for a single-machine infinite-bus power system with R an PSS /16/$ IEEE

2 he state variables are angle loa (δ), fiel voltage (E ), output of R (E F ), angular velocity (ω) an voltage proportional to irect axis flux linkages (E q ), an the inputs signals are mechanical torque input (P M ) an reference voltage (U R ) [18]. A. ransient Gain Reuction R is use to reuce high frequency gain of the exciter system. he block of the R sets after exciter system, so its output signal is F. By using the lea-lag network, the transfer function of R is given by [19]: 1+ B s G ( s ) = 1 + s (1) where B an are transient constant time an steay state constant time, respectively. Usually their values are 1s an 10 s. he phase characteristics of the R is show in Fig. 2. he figure shows that the maximum phase lagging of the R is approximately -55 egree at 0.3 ra/s. Fig. 3. Block iagram of the conventional PSS he ynamic equations of the SMIB power system through an external reactance (X E ) can be written as [24, 25]: (a) n=1 Fig. 2. Phase characteristics of the R B. Power System Stabilizer he transfer function of PSS as shown in Fig. 3 is given by [20, 21]: W s 1+ D s n G P ( s ) = K P ( ) D > (2) 1+ W s 1+ s where K P is the stabilizer gain, W is the washout filter time constant, D is the phase-lea time constants, G is the phaselag time constants an n is the number of lea-lag stages [22]. he parameters of lea-lag PSS to be optimize are K P an D. he phase characteristics of the PSS for ifferent values of D is show in Fig. 4. he figure shows that the maximum phase lagging of the PSS is between 8 an 55 egree for n=1 an between 10 an 78 egree for n=2.. State Space Equation In this section, IEEE moel (1.0) is assume for synchronous generator by neglecting amper winings with high gain, low time constant static exciter [23]. he 8th orer state variables are expresse as: q EF E U UW U P US ] X = [ δ ω E (3) (b) n=2 Fig. 4. Phase characteristics of the PSS ofr ifeernet vlaues of the n ( G =0.05 an W =10) 4 o Δδ = ω Δω (4) b K KD K2 1 Δω = 1 Δδ Δω q JM JM J M JM ΔPM (5) K 1 1 q = Δδ q + K F (6) K K K 3 o K K o A A 6 A = ΔU R 5 Δδ q A A (7) A A 1 1 Δ E F = F + + B 1 (8)

3 1 ΔU W = ΔU W + K P Δω (9) W 1 1 D Δ U P = ΔU P + ΔUW + ΔU W (10) 1 1 D Δ U S = ΔU S + ΔU P + ΔU P (11) K 1 an K 2 are the constant erive from electrical torque, K 3 an K 4 are the constant erive from fiel voltage equation, an K 5 an K 6 are the constant erive from terminal voltage magnitue. By varying the operating at loaing conitions, the parameter values K 1 -K 6 also vary [26]. Also, J M is the generator inertia constant, K D is the inherent amping constant, o is the -axis open circuit transient time constant, an ω b is the base electrical angular velocity. K A an A are the gain an time constant of the excitation system respectively. he nominal parameters of the power system an the various loaing conitions are given in able 1. able 2 summarizes the value of the K constant uner normal loa operation an heavy loa operation. he steay state operating points of the moel power system as a function loa conitions is shown in able 3. III. DESIGN OF PSS USING PHASE OMPENSAION EHNIQUE he change in the electrical torque eviation can be expresse in terms of rotor angle an voltage reference eviations: Δ E q ( s ) = K Δδ K ( s ) K Δ δ + H ( s ) Δδ = 1 + H P ( s )Δδ + G ( s ) ΔU ( s ) (12) where H Q (s) is the control transfer function (between the output electrical torque an loa angle), G E (s) is the electrical loop transfer function (between exciter input an the output electrical torque) an H P (s) is the PSS transfer function (between the output electrical torque Δ E2 an input signal of PSS). he block iagram representing the small signal stability moel can be simplifie as shown in Fig. 5. he expression for the transfer function of electrical loop as shown in Fig. 6 is given by (without PSS): E R Q ABLE I. SYSEM PARAMEERS AND DAA Generator J M =10, X =1.6, X =0.32, X q =1.55, o =6 s, f=50 Hz IEEE type-d1 excitation system K A =50, A =0.05 s normal loa operation P=0.8, Q=0.6, U =1 heavy loa operation P=1.5, Q=1.1, U =1 transient gain reuction B =1, =10 lea-lag PSS W =10 s, 2 = 4 =0.05 s transmission line reactance X E =0.4 un-ampe natural frequency ω n = ra/s ABLE II. PARAMEERS K VALUES (PU) onstants Normal loa operation Heavy loa operation K K K K K K ABLE III. SEADY SAE POIN (PU) Item Normal loa operation Heavy loa operation U o U qo I o I qo E qo δ o o G E ( Fig. 5. Block iagram of SMIB power system s ) = K 2 ΔU q R K 2G F ( s )GV ( s )G ( = 1+ K G ( s )G ( s )G 6 F V s ) ( s ) (13) he electrical transfer function is epenent to parameters K 2, K 3 an K 6. Parameter K 3 is inepenent of the loa change, but K 2 an K 6 have slowly change for changes in the loa. herefore there is no effect on response frequency transfer function G E (s). he effect of the R on phase lagging characteristics of the G E (s) is show in Fig. 7 uner normal loa operation. he figure shows that the maximum phase lagging of the system without R an with R are approximately -28 an -93 egree at 2 ra/s, respectively. he transfer function ue the PSS is given by: s H P( s ) = GE( s )GP( s ) (14) ω b he phase of the electrical loop transfer function is negative but the phase of the PSS is positive. In the phase compensation, the amplitue of synchronizing torque component ue of the PSS is minimum. Also the phase of the transfer function of the PSS is compensate with the phase of the electrical loop transfer function [27]. herefor the real of the H P (jω) in the electromechanical moe natural frequency of

4 oscillation (ω n ) is zero. he amping torque component is occurre by PSS is: K ( PSS ωb ( ω ) = Im[ H P( jω )] (15) ω ) ABLE IV ±j SYSEM EIGENVALUES WIHOU R FOR NORMAL LOAD (K P =26.97, 1 =0.19) ±j ±j (K P =38.65, 1 =0.11) ±j ±j Fig. 6. Block iagram of the electrical loop ABLE V ±j SYSEM EIGENVALUES WIHOU R FOR HEAVY LOAD (K P =26.97, 1 =0.19) ±j ±j (K P =38.65, 1 =0.11) ±j ±j Fig. 7. Effect of R on phase lagging characteristics of the electrical transfer function uner normal loa operation IV. SIMULAION RESULS In this section two types of system have been consiere for analysis: the power system without R an the power system quippe with R. he metho for the PSS esign parameters is base on the phase compensation. he results are compare with integral of square error (ISE) in [19]. he system eigenvalues without the R for nominal an heavy loaing conitions are given in able 4 an able 5 respectively. he real part an the imaginary part of the eigenvalue represent the amping moe an the ampe natural frequency of oscillation respectively. It is observe that the electromechanical moe for the open-loop system without R which are characterize by the eigenvalues ±j an ± are poorly ampe. he system eigenvalues with the R for nominal an heavy loaing conitions are given in able 6 an able 7 respectively. A comparison of the rotor angle eviation an angular spee eviation of the SMIB power system without R an equippe with PSS is shown in Fig. 8. he system eigenvalues with the R for nominal loaing an heavy loaing conition are given in able 8 an able 9 respectively. A comparison of the rotor angle eviation an electrical torque eviation of the SMIB power system with R an equippe with PSS for normal loa is shown in Fig. 9. ABLE VI ±j ±j ABLE VII ±j ±j SYSEM EIGENVALUES WIH R FOR NORMAL LOAD (K P =35.25, 1 =0.45) ±j ±j ±j (K P =35.50, 1 =0.12) ±j ±j ±j SYSEM EIGENVALUES WIH R FOR HEAVY LOAD (K P =35.25, 1 =0.45) ±j ±j ±j (K P =35.50, 1 =0.12) ±j ±j ±j V. ONLUSIONS Power system stability is one of the most important problems in power system operation an control. PSS is use to improve the ynamic stability of power systems. In this paper, the metho for the PSS esign parameters is base on the phase compensation. he linearize moel of single-machine infinite-bus power system which inclues the effect of R an PSS has been aopte. he effects of R using eigenvalues analysis an simulation on power systems small signal stability is shown.

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