tate pace Analysis of Power ystem tability Enhancement with Use the ACOM M. Mahavian () - G. hahgholian () () Department of Electrical Engineering, Islamic Aza University, Naein Branch, Esfahan, Iran () Department of Electrical Engineering, Islamic Aza University, Najaf Aba Branch, Esfahan, Iran Abstract- FAC evices can regulate the active an reactive as well as -magnitue. tatic synchronous compensator (ACOM) is taking place as of the new generation FAC evices. he effects of ACOM using eigenvalues analysis on systems small signal stability presente in this paper. he simulation of system ynamic behavior is mainly one in the following two cases: classical moel an classical flux-ecay moel equippe with automatic regulator (AVR). I. INRODUCION With the increasing electric eman, systems can reach stresse conitions, resulting in unesirable an frequency conitions. Power system is a non-linear object an its stability epens on the type, location an uration of a isturbance. hunts FAC evices such as VC an AC- OM are use for controlling transmission, flow, reucing reactive loss, an amping of system oscillations for high transfer levels. he ACOM can offer a number of performance avantages for reactive control applications over the conventional VC because of its greater reactive current output at epresse, faster response, better control stability, lower harmonics an smaller size []. Power systems are experiencing low frequency oscillation (LFO) ue to isturbances. Main causes of LFO are: (i) A long istance from loa center of generator, (ii) Lack of transmission lines compare to loa growth, (iii) Use of high reactance electric equipment, (iv) Use of a high gain exciter to compensate synchronous stability reuction, an (v) 0.-.0 Hz low frequency oscillation ue to lack of brake torque. Application of ACOM an several control strategies for stability improvement has been iscusse in the literature [-3]. An aaptive fuzzy is incorporate into the supplementary control of a ACOM to enhance the amping of an interarea oscillation exhibite by a two-area four-machine interconnecte system presente in [4]. A current injection moel of FAC s is aopte for stuying ynamic stability of system which can be easily applie to the linear an the nonlinear analysis, an aopt any kin of VI type FAC s regarless of moel types, propose in [5]. his paper presents a stuy of the effect of a ACOM on system low frequency oscillations amping. he simulation of system ynamic behavior is mainly one in the following two cases: classical moel [moel (0,0)] an thir-orer moel [moel (,0)] equippe with AVR. Moreover, the effect of the system loaing on system amping is also explore. II. MAHEMAICAL MODEL OF HE UDY YEM he system moeling plays an important role in the small signal stability problem of systems. In this stuy, a single machine infinite bus (MIB) system as shown in Figure is consiere. he generator is equippe with an excitation system an the system has a ACOM installe. he transmission line has parameters of A L B L C L D L an A L B L C L D L for the first an the secon sections respectively. In principle, a ACOM is a shunt-connecte evice which injects reactive current into the AC system. he ACOM has only two possible steay-state operating moes: lagging (inuctive) an leaing (capacitive), therefore it is not possible to significantly impact both active an reactive simultaneously. he ACOM here is moele as a first-orer shunt controllable reactive current source with time elay ( A ). he approximate moel of the ACOM is show in Figure. In the phasor iagram shown in Figure 3, the rotor angle δ is the angle by which the q-axis leas the infinite bus the [6]. Figure. ACOM installe in MIB system Figure. Mathematical moel of ACOM When the ACOM operates in capacitive moe, the injecte current can be expresse as: π j( θ ) I I e ()
when it operates at full capacitive rating (I I max ) an at full inuctive rating (I -I min ). Figure 3. Voltage phasor iagram he angles between the infinite bus with the terminal an ACOM are δ an δ M, respectively: Figure 4. Reactive supplie by the ACOM X U sin δ tgδ M tg( δ θ) () X U cosδ + X U where the magnitue of the generator terminal an the infinite bus is represente by U an U B, respectively. X an X represents the equivalent reactance of the line for two sections. hat is the ACOM current oes not change the angle of the at bus M. he magnitue at bus M can be expresse as: B XX I + X U cos( δ δm ) + XU B cos δm U M (3) X + X XX U M I X + X + (XU B ) + (X U ) + XX U U B cos δ (4) X + X Here the angle of at bus M is efine as the angle between the ACOM bus an the internal an is given by: X (X X ) (U sin X sin ) + X + X + q B δ + θ tgθ X X X + + q X E q + (X + X )(U B cos δ + X cos θ) (5) where E q is the proportional to the -axis flux linkages, X is the irect axis reactance, X is the irect axis transient reactance an X q is the quarature reactance. hat is the magnitue of bus M epens on the ACOM current, but the angle at bus M is inepenent of AC- OM current. ACOM can control the terminal without influence of the at the installation bus. A lossless ACOM oes not supply or absorb any active. he reactive supplie by the ACOM is given by: Q U I (6) A M Figure 5. Amplitue of ACOM bus Basic linear ifferential equations escribing ynamics of the single machine infinite bus system with installe A- COM are: Δδ ω o Δω K D K K K E Δ ω Δω Δδ ΔE q ΔI + ΔPM (8) J J J J J Δ Eq [ ΔE F ΔEq + (X X ) Δi ] o (9) K A Δ E F ΔE F + ( ΔU R ΔU ) A A (0) Δ I ( ΔI + KA ΔU ) () A where J an K D are respectively the inertia coefficient an amping coefficient, P M enotes the mechanical input, P E the electrical output, E F the stator which correspons to the generator fiel an o the fiel open circuit time constant, U R the reference, A the transient time constant for AVR, K A the transient gain for AVR. (7) Figures 4 an 5 shows the variation of reactive supplie by the ACOM an the magnitue at bus M
III. DYNAMIC PERFORMANCE ANALYI Dynamic control of generator output is the key point in improving amping of a system. Performances of ynamical systems are usually efine with their transient responses. With the help of a FAC evice, the output electrical of the machine can ynamically be controlle to improve the ynamic performance of the system. he approximate continuous time moel typically employe for ynamic analysis is summarize in this section. he ynamic response of a linear system is governe by the magnitue an location of its eigenvalues, or poles. For oscillation amping, the shoul be locate to efficiently bring the critical eigenvalues into the open left half plane. he ynamic analysis is verifie by transfer function simulation using Matlab an time omain simulation of the supply system. he ynamic characteristics of the system for low frequency oscillation stuies are expresse by the block iagram shown in Figure 6 with the sensitivity constants. he resulting linear moel is expresse in terms of the sensitivity parameters which are epenent upon the operating point consiere. Constant K, K an K E are erive from the electric torque expression, K 3, K 4 an K EI from the fiel wining circuit equation, K 5, K 6 an K V from the generator terminal magnitue, K UD, K U an K UE from the ACOM bus magnitue, K D, K an K E from the ACOM bus angle, K ID, K I an K IE, K DD, K D an K DE, K QD, K Q an K QQ from the generator terminal current an q components. K U an K W are proportional coefficient of PID in the an spee loops respectively. IV. IMULAION REUL imulation stuies for the evaluation of amping effects by the ACOM an the propose control schemes have been performe on a MIB system. he ata use in this stuy are given in able I. he loaing in a system is never constant. he four cases (liste in able II) were simulate. Nominal parameters of the system for the initial q current an components an torque angle for loaing ifferent conition are shown in able III. By varying the operating point, the sensitivity parameter values also vary. ables IV an V summarize the value of the sensitivity constant of moel system for ifferent loa conitions for without an with ACOM, respectively. he system moes for ifferent loaing conition are shown in ables VI an VII. his confirms the well-known facts that ACOM have little effect on electromechanical oscillations at light loa an leaing factor. he amping ratio, corresponing to the electromechanical moe of oscillations, increase from 0.04 (without ACOM) to 0.4 (with A- COM) for the system with normal loa, an increase from 0.053 (without ACOM) to 0.463 (with ACOM) for the system with light loa. mechanical ACOM current mechanical KW spee statcom current KE KE machine ynamics J.s+D q-axis transient KEE machine J.s+D output ACOM KA A.s+ KED KUE KA po.s+k3 file circuit A.s+ statcom KED KU PID KEI relative spee spee wo s PID exciter KE E.s+ relative spee regulator K6 K wo s K4 KU ACOM KU K5 KUD (a) Classical moel for synchronous machine angle rotor angle rotor KUD reference statcom bus (b) Classical flux-ecay moel for synchronous machine Figure 6. Mathematical moel of MIB system with ACOM in imulink/matlab ABLE I DAA OF HE MIB YEM Components Item Value X q.66 X.68 X 0.3 Generator J 4.6 K D 4 o 4 f 60 ransmission line X 0.3 0.3 X U o P Eo Q Eo K A A I o K W K U K E E Loaing 0.8 normal 0.6 ACOM 0.0 00 Controller 0 30 AVR 0.05
ABLE II IMULAION CAE Case Loa conition P Eo Q Eo U o A Normal 0.8 0.6 B Heavy 0. C Light 0.6-0.3 ABLE III EADY AE OPERAING POIN OF MODEL POWER YEM Parameter A B C U o 0.5539 0.7800 0.8930 U qo 0.836 0.658 0.450 U Bo 0.8000.065.337 I o 0.947 0.905 0.4008 I qo 0.3337 0.4699 0.5379 θ o 50.44 67.3 7.83 δ o 70.5 85.54 80. (a) Loa angle ABLE IV ENIIVIY CONAN OF MODEL POWER YEM WIHOU ACOM Constant A B C K 0.6497 0.8046.0560 K 0.897.54.35 K 3.4783.4783.4783 K 4.48.5697.797 K 5-0.098-0.837-0.058 K 6 0.5430 0.408 0.935 ABLE V ENIIVIY CONAN OF MODEL POWER YEM WIH ACOM Constant A B C K.883.708.04 K.45.6775.900 K 3.488.0884.0983 K 4.5754.334.444 K 5-0.0953-0.754-0.037 K 6 0.536 0.404 0.87 K EI -0.368-0.94-0.479 K V 0.008 0.455 0.700 K ID.694.446.96 K I -0.769-0.0483 0.076 K IE 0.769 0.6878 0.4543 (b) Relative spee rotor Figure 7. tep response for light loa uring a step change in the mechanical ABLE VI EIGENVALUE OF LINEAR MODEL FOR DIFFEREN LOADING CONDIION WIHOU ACOM Loa Electrical moe Mechanical moe Control moe A -9.6599±j 4.9674 -.87±j7.50-48.3390 B -9.839±j 9.307 -.96±j6.700-47.374 C -5.5466±j 3.83-5.004±j 9.638-50.764 Figure 7, the step response of system with ACOM uring a step change in the mechanical using the classical moel (ot line), the thir orer moel (soli line) an without ACOM (ash line) for light loaing is shown. Also the Boe iagram of loa angle is shown in Figure 8. he step response of the system for normal loa conition is shown in Figures 9 an 0. Figure 8. Boe iagram of loa angle for light loa Figure show the reactive elivere eviation an output current of ACOM accoring to loa angle for ifferent loa conitions in the system.
(a) Normal loa (a) Loa angle (b) Light loa (b) Relative spee rotor Figure 9. tep response for normal loa uring a step change in the mechanical (c) Heavy loa Figure. Reactive an output current of ACOM accoring to loa angle REFERENCE Figure 0. Boe iagram of loa angle for normal loa V. CONCLUION Electromechanical oscillations have been observe in many systems worlwie. hat is generally stuie by moal analysis of a linearize system moel. his paper has examine the effects of the ACOM using eigenvalues analysis on amping systems electromechanical oscillations. [] P.R. harma, A. Kumar, N. Kumar, "Optimal location for shunt connecte FAC evices in a series compensate long transmission line, urk J Elec Engin, Vol.5, No.3, pp.3-38, 007. [] G. hahgholian, "Development of state space moel an control of the ACOM for improvement of amping in a single-machine infinitebus", Inter. Rev. of Elec. Engi.(IREE), Vol.4, No.6, pp.367-375, Nov./Dec. 009. [3] D. Murali, M. Rajaram, ransient energy analysis for ACOM an C applications, Inter. Jour. of Elec. An Pow. Engin., No.3, pp.9-97, 009. [4] W. Chao, Z. Yao, Approach on nonlinear control theory for esigning ACOM, IEEE/ICGI, pp.87-875, Nov. 007. [5] M. Mahavian, G. hahgholian, N.Rasti, Moeling an amping esign for static synchronous compensator, IEEE/ECI-CON, pp. 300-304, May 009. [6]. Qu, C. chen, Low frequency oscillations amping by ACOM with a fuzzy supplementary, IEEE/ICP, Vol., pp.67-70, Oct. 00. [7] J. Park, G. Jang, K.M. on, Moeling an control of VI type FAC s for system ynamic stability using the current injection metho, Inte. Jou. of Con., Aut., an ys., Vol. 6, No.4, pp.495-505, Aug. 008. [8] G. hahgholian, P. hafaghi,. Moalem, M. Mahavian, Damping system oscillations in single-machine infinite-bus system using a ACOM, IEEE/ICCEE, pp.30-34, Dece. 009.