Steady-State Stability of a Synchronous Machine

Steady-State Stability of a Synchronous Machine By S. B. KARMAKAR (Manuscript received December 10, 1979) Mechanical oscillations of synchronous machines following the application of sudden shaft loads are important to operating engineers. This paper presents an analytical technique to determine the stability of a synchronous machine. We first decompose the nonlinear system representing the machine into an infinite number of subsystems connected in parallel. We then determine a bound on the input to the machine for which the number of subsystems will effectively be finite in number, then determine stability of the entire system by determining the stability of each subsystem. I. INTRODUCTION The problems associated with the maintenance of stability of synchronous machines and the factors affecting stability during transient disturbances have received considerable attention in recent years. If the sudden load application is such that synchronizing torque is less than the load torque, the machine will be thrown out of synchronism and instability will occur. A synchronous machine has steady-state stability if, after a small slow disturbance, it can regain and maintain synchronous speed. On the other hand, if the machine can regain and maintain synchronous speed after large sudden disturbances, it has transient stability. The maximum steady-state operating limit will depend upon the magnitude of instantaneous load changes and its ability to follow quickly any load changes. It is the purpose of this paper to determine an upper bound on the input load so that synchronism will never be lost.