A NEW APPROACH FOR INVESTIGATION OF MULTI MACHINE STABILITY IN A POWER SYSTEM

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1 ISSN: (Online) A NEW APPROACH FOR INVESTIGATION OF MULTI MACHINE STABILITY IN A POWER SYSTEM MEENAKSHI DE a, G. DAS b AND K. K. MANDAL c abc Department of Power Engineering, Jadavpr Univerity ABSTRACT MATLAB oftware package ha been developed by MathWork Inc., which i a very compatible tool for power ytem tability analyi and cientific nmerical comptation. Power ytem tability tdie are carried ot from the view point of electrical machine, power tranmiion, protection, atomation and voltage control. Here a elf fficient MATLAB/Simlink baed mlti-machine model ha been tdied to carry ot tranient tability analyi of power ytem. KEYWORDS: MATLAB, Power Sytem Stability, Tranient Stability, Mlti Machine Power Sytem. Modern electrical power ytem are highly complex in natre, mainly de to increaing interconnection, extra high voltage tie line etc. In ch perpective, the tability of power ytem contine to be of major concern and deerve tmot importance in ytem operation. Moreover, ever expanding ytem and intallation of large generating nit have caed power ytem engineer to dedicate more foc to increaing tranient condition. Tranient tability refer to capacity of power ytem to keep ynchronim when bjected to a evere tranient ditrbance, which may be in the form of falt on tranmiion facilitie, dden lo of generation, or may be lo of large load. In thi cae, there are occrrence of large excrion of generator rotor angle and other ytem variable. It i major importance that while teady tate tability i a related to operating condition, tranient tability i related to operating condition and ditrbance [Kndr, 994]. Repeated analyi i reqired for different ditrbance that that are to be conidered. In tranient tability, ditrbance may be the hort circit. The three phae hort circit cae maximm acceleration of the connected machine [Nagrath and Kothari, 00]. Tranient phenomenon i an aperiodic fnction of time and i of very hort dration. Yet they are of coniderable importance becae it can eventally cae blackot in a city, htdown of a plant etc [Wadhwa, 00]. The electrical tranient tability analyi can be carried ot by vario analyi tool ch a MATLAB, Electrical Tranient Analyi Program (ETAP), by ing Electromagnetic Tranient program (EMTP) or the alternative tranient program (ATP) etc [Patel et. al., 00]. MATLAB/Simlink i an important oftware ed for high performance data analyi and vialization, developed by MathWork Inc. It provide the correct combination of featre like analyi capabilitie, flexibility and powerfl graphic which make it an optimm platform to carry ot power ytem tdie/tability analyi. In thi paper, MATLAB/Simlink i ed to carry ot a implified, yet effective approach to tdy the tranient tability performance of a tet ytem. ILLUSTRATIVE SYSTEM EXAMPLE Sytem Detail We conider here a 50Hz, 0kV tranmiion line ytem with two generator and an infinite b [Nagrath and Kothari, 00] a hown in Fig..A three phae falt occr near b 4 at end of line 4-5.The falt i cleared by opening line 4-5. Figre : Mlti-machine tet ytem nder conideration. Sytem Modeling Load admittance, along with tranient reactance are ed with the line and tranformer admittance to form the pre-falt agmented b admittance matrix which contain the tranient reactance of the machine. Since the falt i near b 4, the Yb dring falt condition wold be obtained by deleting 4 th row and 4 th colmn from the pre-falt Y b matrix. Redced falt matrix i obtained by ing the relationhip a in eqation : Y = Y Y Y Y () kj( new) kj( kn( nj( / nn( Correponding athor

2 The load at be 4 and 5 are repreented by the admittance calclated a Y L4 and Y L5 repectively. Once the falt i cleared by opening the circit breaker at both end of the line between be 4 and 5, the pre-falt Y b ha to be modified again by btitting Y 45 =Y 54 = 0. MATHEMATICAL MODELING Dring Pre-falt condition:- Y 4 = Y 4 () Y = = (3) 4 Y4, Y35 Y53 B4 B45 Y44 = YL 4+ Y4+ Y Y4 (4) B54 B5 Y55 = YL 5+ Y54+ Y Y35 (5) Dring falt condition:- P e = 0 (6) 3 = G33+ Y3 3 θ3 P e (7) Pot falt condition:- = E G+ E Y θ P e (8) 3 = G33+ Y3 3 θ3 P e (9) The power into the network at node i which i the electrical power otpt of machine i i given by N ei = Ei G33 + j= ; j i P E i E j Y ( δ θ ) The wing eqation are then given a follow: d δ dt 80f = H ( ) P m P e MATLAB/SIMULINK SOFTWARE (0) () The complete ytem given in Figre () ha been imlated a a ingle integral model in Simlink. The mathematical model given above give the tranfer fnction of different block. Figre () how the complete block diagram of the ytem for tranient tability tdy. The bytem hown in Figre (3) are meant to calclate the vale of electrical power otpt for different generator. The model alo facilitate the choice of imlation parameter ch a tart and top time etc. The model can be rn either directly or from MATLAB command line or from an m-file program. In the preent tdy, the falt clearing time, the initial vale of parameter a well a the change in network de to falt are controlled throgh m-file program in MATLAB. The key featre [Patel et. al., 00] of MATLAB/Simlink baed model are: Interactive imlation with live diplay; A comprehenive block library for creating linear/nonlinear, dicrete, hybrid mlti-inpt/otpt ytem; Mak facility for creating ctom block and block librarie. The amption in Mlti machine tability analyi made are:. The aynchrono power hall be neglected.. Each ynchrono machine i repreented by a contant voltage orce. 3. Governor action i neglected and the inpt power are amed to remain contant. 4. Uing the pre-falt b data, all load are converted to eqivalent admittance to grond and are amed to remain contant. 5. The mechanical rotor angle of machine coincide with the angle of voltage behind the machine reactance. 6. Machine belonging to ame tation wing together which are aid to be coherent. Grop of coherent machine are conidered a one eqivalent machine. SIMULATION RESULTS Cae Stdy And Relt The ytem repone can be hown from the above model. Figre (4) how the repone of both generator with falt clearing time of Here machine i ntable while machine 3 i table, machine i reference. Figre (5) how ytem repone with falt clearing time of Here machine ha large anglar wing. Tranient tability depend on both the initial operating tate of the ytem and everity of ditrbance.

3 Ually the ditrbance alter the ytem ch that pot ditrbance teady tate operation will be different from that prior to ditrbance. Intability i in the form of a drift de to infficient ynchronizing torqe and it i referred to a firt wing tability. In large power ytem, tranient intability may not alway occr a firt wing intability aociated a a ingle mode; it cold be a a relt of increaed peak deviation caed by perpoition of everal mode of ocillation caing large excrion of rotor angle beyond the firt wing [Nallagalva et. al., 0]. In thi paper firt tability of machine ytem i analyzed and then tranient tability of mlti machine ytem i done for vario falt clearing time. Before analyzing tability, vario comptation are done:. All ytem data are compted on common bae-00 MVA.. All load are converted a contant eqivalent impedance. 3. Voltage behind the tranient reactance i calclated. 3.5 Pm - Pa Gain Ot Scope Integrator 3 Ot 3 Integrator del rtd Gain 3 9 Ot 9 Scope 5 Ot 5 Scope 3.03 E.0 0 Contant del E del E_ Sbytem del E del Clock Clock3 Switch Switch3 Trigonometric Fnction Prodct Re() Complex to Real -Imag 7 Ot7 Scope 4 E_.0 Pm 3 Scope Ot 4 Ot 4 del 3 Integrator 3 - Pa3 Gain Integrator rtd Gain 4 0 Ot0 Scope 6 6 Ot 6 Sbytem 3 del E del _ Sbytem3 del 3 E del Clock Clock Switch Switch4 Trigonometric Fnction Re() Complex to Prodct Real -Imag 8 Ot 8 Scope 5 _ Sbytem4 Figre : Complete block diagram of the ytem for tranient tability tdy.

4 del Magnitde -Angle to Complex Prodct E_ The line and tranformer data i given in Table. B data of the ytem i provided in Table. Table : Line and tranformer data 5 3 E 4 del 6 del 3 Yaf(,) Y Magnitde -Angle to Complex Yaf(,) Y Magnitde -Angle to Complex Yaf(,3) Prodct Prodct Add B to b Reitance (p.) Reactance (p.) Sceptance (p.) Line Line Line Tran: Tran: Y3 Figre 3: Sbytem. Sytem repone are hown in figre (4) and figre (5):- B no. Voltage Table : B data B Voltage Generation Load type Real Imag P e f g Q g P l Q l 0 lack PV PV PQ PQ CONCLUSION Figre 4: Swing crve for machine and 3; machine i reference (infinite b). A we know, tranient tability refer to the condition of tability in repone to dden change of large magnitde. Steady tate tability limit i imple for analyi and can be calclated accrately, bt tranient tability limit i leer than the former and i therefore the deciding factor for normal power tranfer [Rao, 00]. Here a complete model for tranient tability tdy of a mlti-machine power ytem wa developed ing MATLAB/Simlink which i not only bet ited for analytical prpoe bt alo poee interactive capacity for a detailed tranient tability tdy which facilitated fat and precie oltion of non linear differential eqation i.e. the wing eqation. De to thee advantage, thi tdy can be tilized for initiating rapid falt clearing and immediate retorative action to maintain normal power flow. REFERENCES Kndr P., 994. Power Sytem Stability and Control, EPRI Power Sytem Engineering Serie Mc Graw-Hill, New York. Figre 5: Swing crve for machine for a falt clearing time of 0.08ec. Nagrath I. J. and Kothari D. P., 00. Power Sytem Engineering, Tata Mc Graw-Hill, New Delhi, 994, ninth reprint.

5 Wadhwa C. L., 00. Electrical Power Sytem, New Age International Pbliher, ixth edition. Patel R., Bhatti T.S. and Kothari D.P., 00. MATLAB/Simlink- baed tranient tability analyi of a mltimachine power ytem, International Jornal of Electrical Engineering Edcation, 39(4): Nallagalva S.K., Kirar M.K. and Agnihotri G., 0. Tranient Stability Analyi of the IEEE 9 B Electric Power Sytem, International Jornal of Scientific Engineering and Technology, (3):6-66, ISSN: Rao S. S., 00. Switchgear Protection and Power Sytem, Khanna Pbliher, ISBN No