Small Signal Stability Analysis of Synchronous Generators Connected to Infinite Bus

A synchronous generator may sometimes be able to withstand a large impact but it may fail to retain synchronism under a small impact due to growing oscillations, leading to instability. This is called dynamic instability. It occurs for specific operating conditions and network configurations, particularly in presence of fastacting excitation control. The paper presents techniques of small signal stability assessment of a turbo generator connected to a grid system while a small perturbation is injected externally. The infinite bus idealisation has been made as the capacity of the generator is small compared to that of the power grid. The classical model based on ParkGorev transformation has been used to represent the machines. The current state space model has been used. The small signal stability has been assessed by examining the eigenvalues of the state matrix. Reduced order model has also been developed for the same machine including exciter parameters and the stability has been examined by applying Routh’s array on the characteristic equation. Index Term-Small signal stability, Current state space, Linearized model, Reduced order model, Exciter control Symbols used (All quantities are in p.u. and time-constants in sec. unless otherwise mentioned),   Angular speed of the generator (r/s), power angle(r) , a a R X Armature resistance, leakage reactance , d ds X X D-axis unsaturated/saturated synchronous reactance , q qs X X Q-axisunsaturated/ saturated synchronous reactance ' ' , d ds X X D-axis unsaturated/ saturated transient reactance " " , d ds X X D-axis/Q-axis sub-transient reactance , , e e e R X Z External resistance,leakage reactance, impedance to infinite bus, ' ' , d do T T D-axis S.C./O.C. transient time constant. " " , d do T T D-axis S.C./ O.C. subtransient time constant " " , q qo T T Q-axis S.C./ O.C. subtransient time constant , d q I I D-axis &Q-axis components of armature current , d q V V D-axis & Q-axis components of armature voltage , FD E E Generator Induced e.m.f, exciter output , t b V V Voltage at generator terminal, infinite bus 1 6 K K  Constants of D’Mello& Concordia , D H Damping/ Inertia constant , , , A A F F K T K T Constants of exciter model IEEE, type 1s ' ' , q E E Voltage behind transient reactance/ its q-axis component