Analysis of inter-area mode oscillations using a PSS for Variable Speed Wind Power Converter and Modal decomposition.

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1 Analyss of nter-area mode oscllatons usng a PSS for Varable Speed Wnd Power Converter and Modal decomposton. C. GALLARDO and P. LEDESMA Electrcal Engneerng department Carlos III Unversty of Madrd Butarque 5, 89 Leganes SPAIN Abstract: Ths paper shows a smple approach to dampng nter-area oscllatons usng a PPS for a varablespeed wnd power converter. The proposed control s evaluated performng several smulatons on modfed verson of 0-generator, 39-bus New England power system. The smulaton represent a three-phase shortcrcut, and the dampng control system s appled wth dfferent gans. The selecton of the varable-speed wnd power converter s gan s carred out through modal decomposton and the effectveness of the proposed approach s demonstrated for a fault at bus 4. Key-Words: Lnearzaton, crtcal mode, egenvalues, Wnd Power Converter, dampng, nter-area oscllatons, partcpaton factor, modal decomposton, ampltude rato. Introducton Large scale wnd power ntegraton has a sgnfcant mpact on the operaton of power systems, ncludng on level of oscllatons dampng []. It has been demonstrated that wnd generaton has some mpacts on the dampng levels of a power system, and the nature of the mpacts depend on factors lke wnd generator converson technology such as varablespeed or fxed-speed wnd power converters, and also network confguraton []. Power system stablzer (PSS) s stll one of the most cost effectve solutons capable of provdng supplementary dampng. However, wth hgh penetraton of the system n wnd, these devces may no longer be able to provde the necessary addtonal dampng. PSS for Varable-speed wnd power converter can be used to mprove the overall dampng. It s the objectve of ths research to analyze the contrbuton of varablespeed turbne to the problem of the stablty and to take advantages of the control strateges that employ the flexblty provded by these machnes to ncrease the dampng of oscllatons. The study was conducted usng modal analyss, partcpaton factor and modal decomposton usng PSS/E software package. Test System The 0-generator, 39-bus New England power system shown n fgure has been modelled; ths system ncludes 0 generators and 3 Wnd Parks, and comprses 07 states varables. Models were mplemented n the PSS/E software package. The NE 0-generator, 39-bus system has some adjustment n loadng and generaton n order to create a crtcal case. Nne generators are represented by the two-axs model and one generator (generator number 0) s modelled by classcal model. The generators are round rotor wth d and q axs transent and subtransent effects represented. The excters are IEEE type. For transent stablty smulatons, the real and reactve power portons of the load are typcally modelled as constant current and constant admttance. The real power portons of the loads are modelled as 60% constant admttance and 40% constant current; the reactve power portons of the loads are modelled as 50% constant admttance and 50% constant current Fgure. 0-generator, 39-bus New England Power System ISBN: ISSN

2 Wnd Speed. Control desgn of the PSS for varablespeed wnd power converter (WPSS). The modellng of the varable-speed wnd turbne s depcted n fgure. The wnd turbne model ncludes a block whch mplements an actuator dsk model. Its nput varables are the wnd speed, the mechancal rotor speed and the ptch angle, and ts output varable s the mechancal power. Besdes, there are a number of addtonal blocks such as: A ptch angle controller, a rotor speed controller, wnd speed model, and PSS for varable-speed wnd power converter [4]. The proposed control s based on the ablty of varable speed wnd turbnes to perform an actve power control whch s decoupled from reactve power control and from rotor mechancal speed. Fgure. Wnd Power Converter Model Usually, actve power reference s provded by a wnd turbne speed control loop, and t s used to track the operaton pont at whch maxmum power s absorbed from the wnd or to lmt the blades speed durng hgh wnds. In order to dam power system oscllatons, a control sgnal proportonal to the devaton of the frequency s added to the actve power reference: P = P ( k D ) ( ) ref Wnd power system stablzer Extracted power from the wnd w Pm + + w f - - Ptch angle X P w P pssw [ P P ( + P )] Speed control dω r = ( ) m ref pssw dt H Where the WPSS gan K w s an mportant factor as the dampng provded by the WPSS ncreases n proporton to an ncrease n the gan up to a certan crtcal gan value, D f s the devaton of the frequency n per unt, P pssw s the proposed control sgnal, Pw s the actve power reference as provded by the turbne usual control, and P ref s the new actve power reference. Ths control s ntended to be performed n wnd power converters wth voltage-dp rde through capablty, and wll actuate only durng transent oscllatons. Durng normal operaton, when frequency devaton s null, the control sgnal P pssw wll be zero. Reactve power reference Q ref s supposed to be zero, ths s, wnd turbne s operatng at unt power factor. K w D f /HS Blade ptch angle control w r Frequency devaton P e + P pssw Grd Although dfferent control strateges may be used here, there s no reason to suppose that they would have major effects on the results of the study. It should also be noted that ths control technque uses only local varables, so that t does not nvolve any telecommuncaton ssue. 3 Problem Formulaton 3. State Space Model To model the behavor of dynamc systems [7], qute often a set of n frst order nonlnear ordnary dfferental equatons are used. Ths set commonly has the form: x& = f (x, x,., x n ; u, u,.,u r ; t) =,.,n ( 3) Where n s the order of the system and r s the number of nputs. If the dervatves of the state varables are not explct functons of the tme, equaton (3) may then be reduced to: x & = f(x,u) ( 4) Where n s the order of the system, r s the number of nputs and x, u and f denote column vectors of the form: x u f x u f x = u = f = ( 5) x n u n f n The state vector x contans the state varables of the power system; the vector u contans the system nputs and x& encompasses the dervatves of the state varables wth respect to tme. The equaton relatng the outputs to the nputs and the state varable can be wrtten as: y = g(x, u) ( 6) The state concept may be llustrated by expressng the swng equaton of a generator n per-unt torque as follows: Hd δ = Tm Te K D ω r ( 7) ωodt Where H s the nerta constant at the synchronous speed ω o, t s tme, δ s the rotor angle, T m and T e are the per-unt mechancal and electrcal torque, respectvely, K D s the dampng coeffcent on the rotor and ω r s the per-unt speed devaton. Now, expressng (7) as two-frst-order dfferental equatons yelds: d ωr = (Tm Te K D ω r ) ( 8) dt H dδ = ωo ωr ( 9) dt ISBN: ISSN

3 3. Lnearzaton Small sgnal stablty s the ablty of the power system to mantan synchronsm when subjected to small dsturbances. In ths context, a dsturbance s consdered to be small f the equatons that descrbe the resultng response of the system may be lnearzed [8]. For the general state space system, the lnearzaton of (4) and (6) about operatng pont x o and uo yelds the lnearzed state space system gven by: x& = A x+ B u (0) y = C x+ D u () Here, x s the n state vector ncrement, y s the m output vector ncrement, u s the r nput vector ncrement, A s the nxn state matrx, B s the nxr nput matrx, C s the mxn output matrx and D s the mxr feed-forward matrx: Specfcally, x = x xo, y = y y o and u = u uo. As an example, (8) and (9) are lnearzed about the operatng pont (δ o, ω o ), yeldng: d ωr = ( Tm K S δ K D ωr ) () dt H d δ = ω ω (3) o r dt Where K S s the synchronzng torque coeffcent 3.3 Egenvalues and Stablty Analyss Once the state space system for the power system s wrtten n the general form gven by (0) and (), the small-sgnal stablty of the system can be calculated and analyzed [9]. The analyss performed follows tradtonal root-locus (or root-loc) methods usng PSS/E software package. Frst the egenvalues λ are calculated for the A-matrx, whch are the non-trval solutons of the equaton AΦ = λφ (4) Where Φ s an nxl vector. Rearrangng (4) to solve for λ yelds: Det(A-λI) = 0 (5) The n solutons of (5) are the egenvalues (λ,λ,, λ n ) of the nxn matrx A. These egenvalues may be real or complex and are of the form σ±jω. If A s real, the complex egenvalues always occur n conjugate pars. The stablty of the operatng pont (δ o, ω o ), may be analyzed by studyng the egenvalues. The operatng pont s stable f all the egenvalues are on the left-hand sde of the magnary axs of the complex plane; otherwse t s unstable, fgure 3. If any of the egenvalues appear on or to the rght of ths axs, the correspondng modes are sad to be unstable, as s the system. Ths stablty s confrmed by lookng at the tme dependent characterstc of the oscllatory modes correspondng to each egenvalues λ, gven by e tλ. The latter shows that a real egenvalue corresponds to a non-oscllatory mode. If the real egenvalues s negatve, the mode decays over tme. The magntude s related to the tme of decay: the larger magntude, the qucker the decay. If the real egenvalue s postve, the mode s sad to have aperodc nstablty [0]. Fgure 3. egenvalues and assocated response For ω = 0, σ < 0 damped undrectonal response For ω 0, σ < 0 damped oscllatory response For ω 0, σ = 0 oscllaton response of constant wdth For ω 0, σ > 0 oscllatory response wth the oscllaton grows wthout lmt For ω = 0, σ > 0 undrectonal response from growng monotonous. On the other hand, the conjugate-par complex egenvalues (σ±jω) each correspond to an oscllatory mode. A par wth a postve σ represents an unstable oscllatory mode snce these egenvalues yeld an unstable tme response of the system. In contrast, a par wth a negatve σ represents a desred stable oscllatory mode. Egenvalues assocated wth an unstable or poorly damped oscllatory mode are also called domnant modes snce ther contrbuton domnates the tme response of the system. It s qute obvous that he desred state of the system s for all of the egenvalues to be n the left-hand sde of the complex plane. Other nformaton that can be determned from the egenvalues s the oscllatory frequency and the dampng factor. The damped frequency of the oscllaton n Hertz s gven by: ω f = (6) π And the dampng factor (or dampng rato) s gven by: σ ξ = (7) σ + ω 3.4 Egenvectors and Modal Matrces Gven any egenvalue λ, the n-column vector whch satsfes AΦ = λ Φ (8) Φ ISBN: ISSN

4 Is called the rght egenvector of A assocated wth the egenvalue λ. Qute smlarly, the n-row vector Ψ A = λ Ψ (9) Is called the left egenvector assocated wth the egenvalue λ. For convenence, t s assumed here that the egenvectors are normalzed so that: Ψ Φ = ( 0) To contnue the egenanalyss of the matrx A, the followng modal matrces are ntroduced: Φ = Φ Φ ( ) [ Φn ] T T T [ Ψ Ψ ] T Ψ = Ψ ( ) n Λ = Dagonal matrx wth egenvalues as dagonal elements ( 3) The relatonshps (8) and (0) can be wrtten n a compact form as: AΦ = ΦΛ ( 4) ΨΦ =, yeldng Ψ = Φ ( 5) Once the oscllatory modes have been dentfed and the modal matrces constructed, an analyss s performed to fnd the specfc rotor-angle modes. These modes provde the largest contrbuton to the low frequency oscllatons, the rotor-angle modes can be dentfed by analyzng the rght and left egenvectors n conjuncton wth the partcpaton factors 3.5 Orgnally proposed n [8], a matrx called the partcpaton matrx, denoted by P, provdes a measure of assocaton between the states varables and the oscllatory modes. It s defned as: P = [ p p ] ( 6) p n Wth p ΦΨ p = Φ Ψ p = ( 7) p n Φ nψn The element p = Φ Ψ s called the partcpaton k k k factor, and gves a measure of the partcpaton of the kth state varable n the th mode, and vce versa. The use of the partcpaton factor wll be presented n the analyss of the oscllaton profle of the Power System. 4 Modal decomposton The man dea behnd modal decomposton s that any lnear system response can be decomposed nto a summaton of terms lke the followng: Output ( ) ( ) σ t σ jt A e + B je cos( w jt+ ) = j φ ( 8 ) That s, a summaton of exponental and damped (or undamped) snusodal terms. Each exponental component s assocated wth one real egenvalue σ. Smlarly, each snusodal term s assocated wth two complex conjugate egenvalues, of real and magnary σ j and +/-w j parts, respectvely. Partcpaton and phase of each term s dctated by ts respectve A, or Bj and φ coeffcent. The larger a partcular A or Bj coeffcent s relatve to those of other modes, the more domnant mode s the partcular mode. The less negatve (or more postve) the assocated σ j or σ j exponent s, the longer the mode wll lnger relatve to other better damped modes. The order of the system s defned as the sum of the number of egenvalues, real and complex, whch descrbe ts response. Lnear systems theory ndcates that there are many roots or egenvalues as there are states n the dynamc model. For large dynamc models, ths would result n tens of thousand s of terms n Equaton (8). However, the theory also says that due to pole-zero cancellatons, only a few of those roots are excted by a partcular dsturbance, and even fewer are observable on any partcular output sgnal. In other words, for the majorty of modes, A or Bj are ether zero or neglgble. Further, of the remanng modes, most are well damped and te out quckly. As a consequence, t s common to observe that well nto a smulaton, only a few modes subsst, showng ether a sngle lghtly damped oscllaton (two complex conjugate modes), or, n some nstances, two or more oscllaton modes (normally ndcated by the presence of beatng). It s those few remanng modes that these analyss technques are ntended to capture. It s ther assocated A and σ or B j,, σ, w j and φ factors that the technques wll produce. Two alternatve algorthms are offered n the program; one employng Prony analyss technques; the other utlzng least-square approxmatons. Prony technques have been descrbed n a number of techncal publcatons []. They are characterzed by provdng an exact model (barrng numercal mprecsons) of the smulaton results under consderaton. Ths precson however can prove to be a hndrance when analyzng nonlnear cases. Consder, for example, a case wth a sngle lghtly damped oscllaton mode whose frequency changes slghtly wthn the tme wndow of nterest. Because t s desgned to exactly ft the smulaton results wth a lnear model, Prony technques wll go to great lengths to derve modes of smlar frequences, some of whch domnatng the ntal part of the tme wndow, whle others domnatng the later parts of the wndow. The result n such cases can be qute confusng and may requre sgnfcant judgment n ther nterpretaton. j j ISBN: ISSN

5 For case where Prony analyss fals to render the expected results, least square technques are an attractve alternatve. Under the least square mode of operaton, the analyst would typcally select a relatvely low model order n to descrbe the system. The algorthm would then ntalze by exactly fttng the frst n ponts n the selected tme wndow. Followng ntalzaton, t analyzes the remanng data by recursvely adjustng the ntal model so as to render an n th order least-square approxmaton of the tme wndow of nterest. Executon tme can be sgnfcantly larger than for the Prony technques, partcularly when hgh-order models are requred and /or when a large number of tme steps are selected. Two optons are gven under least square analyses. In one opton, only egenvalues are determned wth least squares, whle egenvectors are calculated by Prony analyss to ft the ntal n ponts. Ths opton s the faster of the two and wll render more exact egenvector calculatons at ntal tme. Under the second least-square opton, both egenvalues and egenvectors are calculated wth least squares. Ths opton s more tme consumng but wll render a better ft throughout the tme wndow of nterest. Whatever technque s employed, two ndces and graphcal technques are provded to assess the adequacy of the model. The two ndces are: Percent error: Calculated as the rato (multpled by 00), throughout the tme wndow, of the summaton of absolute values of dfferences between actual data and the frst and the frst actual pont. In other words, t s the absolute value of error, n percentage of the average devaton relatve to the frst data pont. Sgnal/Nose Rato: The Square of dfferences between actual data and frst data pont (sgnal) and between model and actual data (nose) are summated throughout the tme wndow. The square root of the rato s calculated and expressed n decbels (0 tmes the decmal logarthm). 5 Fndng a operatng pont suffcently small-sgnal stable In case of a sustaned oscllaton, there s typcally a power system equlbrum nearby that s oscllatory unstable. The objectve s to stablze ths equlbrum by modfyng the power system lnearzaton at the equlbrum, whch s now a stable operatng pont. Ths s a lkely outcome, but other transent behavours are possble. These work methods seek to stablze the equlbrum to obtan an operatng pont that s suffcently small sgnal stable and do not attempt to make more extensve changes to the system dynamcs [0]. 5. Effect of the gan n the egenvalues Startng from the case wth an operatng pont suffcently small sgnal stable, the effect of ncreasng the wnd power converter's gan has been analyzed. It s observed that the gan has small effect n a few egenvalues of the system, but the operatng pont s stll suffcently small-sgnal stable, and then the egenvalues of the New England power System at each gan are computed, fgures 4 and 5. Fgure 4 Operatng Pont suffcently small-sgnal stable Fgure 5 Effect of the gan n the egenvalues 5. Partcpaton factor calculatons Fgure 6 shows the man egenvalues of the smulatons, when varyng the gan, these egenvalues have oscllaton frequency among 0. and Hz, they are known as nter-area oscllatons and fgures 7 to show the partcpaton factors. Imagnary Part Imagnary Part -00, 0 Imagnary Part -00, 0 Operatng pont suffcently small-sgnal stable -95, , , , , , ,0-3 -5,0 - -5,0 - -5,0 5,0-00, 0 Real Part Egenvalues -95, , , , , , ,0-3 -5,0 - -5,0 - -5,0 5,0 Real Part Egenvalues -95, , , , , , ,0-3 -5,0 - -5,0 - -5,0 5,0 Real Part Fgure 6 Interarea mode oscllatons G0 G0 G30 G35 G0 G0 G30 G35 5,0-5,0-5,0-5,0-5,0-5,0 - ISBN: ISSN

6 Gen 3 (k+4) Gen 3 (k+5) Gen 5 (k+4) Mode 3 Gen (k+4) Gen (k+5) Gen 6 (k+4) Gen 6 (k+5) Gan = 0 Gan = 0 Gan = 30 Gan = 35 Fgure 7 s of Mode 3 Gen 5 (k+4) Mode 5 Gen 4 (k+4) Gen 4 (k+5) Gan = 0 Gan = 0 Gan = 30 Gan = 35 Fgure 8 s of Mode 5 Gen 5 (k+) Gen 5 (k+3) Gen 5 (k+) Mode 7 Gen 4 (k+) Gen 4 (k+3) Gen 5 (k) Gen 4 (k+) Gen 5 (k+4) Gan = 0 Gan = 0 Gan = 30 Gan = 35 Fgure 9 s of Mode 7 Mode 9 Gen 5 (k+4) Mode 9 Gen 6 (k+4) Gen 6 (k+5) Gan = 30 Gan = 35 Fgure 0 s of Mode 9 Gen 9 (k) Mode Gen (k+4) Gen (k+5) Gen 7 (k) Gen 7 (k+4) Gen 7 (k+5) Gen 9 (k+) Gan = 0 Gan = 0 Gan = 30 Gan = 35 Fgure s of Mode Gen 7 (k+) Mode 3 Gen 7 (k+) Gen 6 (k+) Gan = 0 Gan = 0 Mode 3 Gen 8 (k+) Gen 9 (k) Gen (k+) Gen (k+3) Gen 8 (k+) Gen 8 (k+) Gen 8 (k+) Gen 9 (k) Gen 8 (k+) Gen 0 (k+) Gen 6 (k+3) Gan = 0 Gan = 0 Gan = 30 Gan = 35 Fgure s of Mode 3 Mode 5 Gen 7 (k+) Gen 7 (k+) Gen 6 (k+) Gen 8 (k+) Gen 9 (k) Gan = 0 Gan = 0 ISBN: ISSN

7 Gen (k+4) Gen (k+5) Mode 35 Gen (k+) Gen 9 (k+3) Gen 9 (k) Gen 0 (k+4) Gen 0 (k+5) Fgure 7 shows the actve power producton of the wnd park. Ths producton remans bascally constant, because the actve power reference at the wnd park s ndependent from the grd condtons. Only durng, and mmedately after the fault, actve power output decreases as a result of voltage decay, because of current lmtaton n the electronc converters. Gan = 0 Gan = 30 Gan = 35 Fgure 3 s of Mode 35 Mode 45 Gen (k+5) Gen (k+4) Gen 4 (k+3) Gen 4 (k+4) Gen 4 (k) Gen 8 (k+3) Gen 6 (k+5) Gen 3 (k+5) Gan = 0 Fgure 4 s of Mode 45 Gen 7 (k+) Gen 8 (k+) Gen 7 (k+) Mode 5 Gen 6 (k+) Gen 8 (k+) Gen 5 (k+) Gan = 30 Fgure 5 s of Mode 5 6 Smulatons n PSS/E 6. Smulatons results wth no dampng control A three-phase short-crcut at bus 4 has been smulated, wth a duraton of 50 ms. The topology of the grd before and after the fault are the same. Fgure 6 shows the actve power flow between buses 39-9, 7-6, 7-6, 6-9, 4-4, and 4-3. It can be seen three nterarea mode oscllatons, poorly damped oscllatons. Gen 4 (k+) Gen 0 (k+) Fgure 7 Wnd output, no dampng from wnd energy converter, gan = Smulatons results wth dampng control Fgures 8, 9, 0 and show nter-area power flow, the control loop gan, whch s 35, 60, 0 and 40 respectvely. It can be seen how nter-area power oscllatons are damped by the proposed control. Fgure 8 Inter-area power flow, wnd power converter dampng control wth gan = 35 Fgure 6 Inter-area power flow, no dampng from wnd power converter, gan = 0 Fgure 9 Inter-area power flow, wnd power converter dampng control wth gan = 60 ISBN: ISSN

8 = 35 Fgure 0 Inter-area power flow, wnd power converter dampng control wth gan = 0 Fgure 3 Wnd output, wnd power converter wth gan = 60 Fgure Inter-area power flow, wnd power converter dampng control wth gan = 40 Fgures, 3, 4 and 5 show the actve power producton of the wnd park under the same crcumstances. It can be seen at fgure 8 whch corresponds to a gan K= 60, how wnd power producton s modfed after the fault n order to damp power system oscllatons. The varaton n the power producton s not very large compared to the total producton, and could be performed by modern wnd energy converters. Fgure 9 whch corresponds to a gan K = 0, shows larger oscllatons n power producton, whch represent an addtonal effort to the wn power converter control. However, t can be seen that, mmedately after the fault, the wnd power producton always decrease, whch wll result n a slght ncrease n rotor speed and, consequently, n the knetc energy stored n the rotor and the blades. Thus, the wndmll wll be able to use ths knetc energy to perform the requred actve power control. Fgure 4 Wnd output, wnd power converter wth gan = 0 Fgure 5 Wnd output, wnd power converter wth gan = 40 Fgures 6, 7, 8 and 9 show the modal components of lne 39-9 power flow, only nter-area mode oscllatons are shown. Fgure Wnd output, wnd power converter wth gan ISBN: ISSN

9 Fgure 6 Power flow lne 39-9, gan = 0 Fgure 7 Power flow lne 39-9, gan = 35 Fgure 8 Power flow lne 39-9, gan = 60 Fgure 9 Power flow lne 39-9, gan = 0 [] IEEE Power Engneerng Socety System Oscllatons workng group, nter-area Oscllatons n Power Systems, IEEE Publcaton 95 TP 0, October 994 [3] P.M. Anderson, A.A. Fouad, Power System Control and Stablty, Iowa State Unvesrty Press, Ames Iowa, 977. [4] P.W. Sauer, M.A. Pa, Power System Dynamcs and Stablty, Pretnce-Hall, Englewood Clffs NJ, 988. [5] J.G. Slootweg, S.W.H. de Haan, H. Polnder, W.L. Klng, Aggregated modellng of wnd parks wth varable-speed wnd turbnes n power system dynamc smulatons, 4 th Power Systems Computaton Conference, Sevlla, 4-8 June 00. [6] LEDESMA, P.;CARLOS FABIAN GALLARDO QUINGATUÑA, Voltage dp model n PSS/E, 5 th WSEAS/IASME Internatonal Conference on Electrcal Power Systems, Hgh Voltages and Electrc Machnes, SANTA CRUZ DE TENERIFE, ESPAÑA 005. [7] P. Kundur, Power System Stablty and Control, McGraw-Hll, NY, 993 [8] IEEE Power Engneerng Socety Systems oscllatons workng group, Inter-area Oscllatons n Power Systems, IEEE Publcaton 95TP 0, October 994. [9] I.J. Perez-Arraga, G.C Verghese and F.C. Schweppe, Selectve modal analyss wth applcatons to electrc power systems, Part I and II, IEEE transactons on power Apparatus and Systems, vol. PAS 0, no 9, 98, pp [0] IEEE Power System engneerng commttees Egenanalyss and frequency doman methods for system dynamc performance, IEEE Publcaton 90 TH 09-3-PWR, 989. [] K. Km, H. Schattler, V. Venkatasubramanan, J. Zaborsky, P. Hrsch, Methods for calculatng Oscllatons n large power systems, IEEE Transactons on power systems, vol, no4, November 997, pp Concluson It has been shown how wnd power converter can damp oscllatons by means of a smple control loop. It should be noted that ths control technque uses only local varables, so that t does nvolve any telecommuncaton ssue. References: [] P.M. Anderson, A.A. Fouad, Power System Control and Stablty, Iowa State Unversty Press, Ames Iowa, 977 ISBN: ISSN