Kolchanova, Veronika Andreevna

Tarasenko, S. S.

Electronic archive of Tomsk Polytechnic University

203 MODEL OF SYNCHRONOUS GENERATOR FOR REMOTE PERTURBATION  V.A. Kolchanova, S.S. Tarasenko National research Tomsk Polytechnic University  Introduction  The model of the synchronous generator with damper windings is described with the system of six differential equations. Two first are writ-ten for direct and quadrature stator windings. Three next equations are writ-ten for the rotor windings. Direct and quadrature damper windings and ex-citation winding are included into the rotor windings. Sixth, the differential equation is nonlinear. This equation describes the relationship of inertia, electromagnetic and mechanical torques acting on the rotor shaft. The solu-tion of these equations is not an easy task. However, the art of modelling is not the ability to solve complex equations, but the ability to lossless main, the main features of the phenomenon to transform the original complex system into a simpler, guided by the conditions faced by the system under study. Therefore, the aim of this paper is to study the model of the genera-tor in an environment where the original complex system can be simplified, but without losing the basic characteristics of the model. If the point of application of the disturbance is far from the genera-tor, the generator is allowed in the equations do not take into account the electromagnetic transients in the damping circuits. Because damping cir-cuits shorted and, consequently, their currents are only free - aperiodic component which decays rapidly, without having to wait for the disturb-ance. Due to the large inertia of the rotor speed of the rotor changes slowly, so we can assume that there is no slip . And equations to describe the tran-sient generator take the form [1, 3]: 1;0 0;0( ) ;dEx di qd dRi x i ud q q ddt dtx diq qx i Ri E ud d q q qdtdT x x i E E er d d d q q rdt                 (1) Here Eq  – quadrature-axis synchronous voltage is proportional to the excitation current i f . This value is to be determined. Tr  – time con-stant of the circuit excitation closed loop circuit of the stator. ,i iq d  – direct 204 and quadrature токи статора. /e U x xr f ad f  – electromotive force pro-portional to the stator voltage. , , ,x x x rq d d  – the main technical data of the machine: synchronous reactance in the direct and quadrature axes, direct axis transient reactance, resistance of the stator winding, respectively. When the solution of differential equations (1) it is more convenient to use the continuously changing value Eq – quadrature-axis transient elec-tromotive force. It is proportional to flux linkage f of the exciting circuit. And to determine changes abruptly synchronous electromotive force Eq  to use a ratio [4, 5]: E i x E i x uq d d q d d q          It also can ignore the transients in the stator windings of the genera-tor, considering that the appearance of the disturbance in the stator wind-ings originated steady state. On the rotor of the generator is only one path - the excitation winding, oriented along the axis d (direct-axis of the rotor), and the equation becomes: ;;( ) .0x i Ri uq q d dE x i Ri uq d d q qdEqT E i x x Ed q q d d qedt           (2) Thus, the system of algebraic and differential equations describes the assumptions made transients in salient-pole synchronous generator without damping circuits. . Algebraic equations are obtained from the steady state of the system (2) by equating to zero the derivatives of the equation d / dt = 0. The solution is divided into 3 stages 1. Determine the dependence of stator currents ,i iq d  от on the sta-tor voltage ,u uq d  and transient electromotive force Eq  22x u E r u rd d q qiqx x rd qx E x u u rd q q q didx x rd q          (3) 2. Next, find the values Eq пр  in the steady state, substituting instead of the current id  its current expression (4)  205   2E i x x Eq d d d qeE x x u u rq q q q dE x x Eq d d qex x rd q            The result is:  22x u x x u x u x r u x r E x x E rq q d q q d d d d d qe q d qeEq прx x rd q        Solve differential equations to determine the transition EMF ( )E tqпри известных напряжения статора. under certain stator voltage. Pre present equation to normal form      22 200 0r x x E x x u r u xq d qdE E d d d q qq qedt T dT r x x T r x xd q d d q d         From the last equation it follows that the time constant of the transi-tion process is equal to the value of the expression;   202T r x xd q dTr x xq d, This expression, neglecting the stator resistance is converted to a known relation: 00T xd dT dxd   3. The third stage is solution of the system of differential equations. The construction of plots and interpretation of results [2]. To solve the system (6) we use MathCAD program using function rkfixed() – Runge-Kutta method of order 4. With the help of the inverse trans-form Park - Gorev phase stator currents will be obtained [5, 6]  Conclusions Models of synchronous generators proposed in the work lead to do the following conclusions: If the place of application disturbance is in a remote location of a synchronous generator we can ignore fast transients occurring in the damp-ing circuits and the contours of the stator.  Calculations of the transient processes of the synchronous generator on the proposed model show that after restart may be that repeated short-206 circuit conditions are more difficult as initial conditions, that is, the current during the second circuit achieves greater value. If the place of application disturbance is at a point close to the syn-chronous generator, than by the calculation mode in the generator model the transients in the stator windings should be taken into account. The proposed model is in good agreement with the known fact that at the initial stage of the transient stator currents have doubled frequency harmonics. The use of models is possible in networks containing synchronous generators and for the design of objects containing generators.  REFERENCES:  1. P.S. Zhdanov, Questions stability of electric power systems, M:, En-ergy, 1979, -536 p. 2. Y.N. Isaev, A.M. Kupzov, Practice in usage of MathCAD in calcula-tions of electric and magnetic circuit, M:, SOLON –PRESS, 2013, -180 p. 3. М.L. Levinstein, Operational calculus in problems of electrical engi-neering, Leningrad:, Energy, 1972, -358 p. 4. G.G. Pivnyak, V.N. Vinoslavsky, A.Y. Rybalko, L.I. Nesen, Transi-ents in power systems, M:, Energoatomizdat, 2003, -540 p. 5. S.A. Ulyanov, Electromagnetic transients, M:, ООО «ТID «ARIS», 2010, -519 p.  V.A. Kolchanova, PhD, associate professor, National research Tomsk Polytechnic University.   

Model of synchronous generator for remote perturbation

Abstract

Similar works

Full text

Available Versions

Electronic archive of Tomsk Polytechnic University