An analysis of power system transient angle stability using finite element technique

In a case of numerical analysis of slow electromechanical oscillations in a large power system, Electromagnetic Transients Program (EMTP) is not an appropriate tool since it requires too small simulation step size causing computational inefficiency. Consequently, in order to avoid computational inefficiency, such studies are always done with the so-called Transient Stability Programs (TSP). In TSP, some assumptions are made in order to represent a synchronous generator mathematically by a classical model that leads to less accurate results. The combined simulation of the electromagnetic and electromechanical transients has always been a challenging task. In this paper, advanced computing approach for numerical analysis of power system transient stability has been developed. The proposed numerical algorithm is based on a finite element technique (FET) procedure. According to FET terminology, each large power system element (generator, transformer, power line, etc.) is defined as a single finite element (FE) with corresponding local system of algebraic equations that are obtained in frequency domain. Variables of each FE are defined as dynamic phasors during entire time-domain simulation. The time-domain model of turbine governor as well as excitation system has been also developed and incorporated into synchronous generator FE model. The proposed numerical algorithm, based on the FET representation of the power system elements, allows us to avoid assumption of TSP since variables of each FE are defined as dynamic phasors during entire time-domain simulation. Due to above mentioned improvements, simulation of the electromechanical transients is accurate as well as EMTP, and it allows us the use of larger step sizes and to study very large power systems. The accuracy of the computer program, based on the presented model, has been tested with solutions obtained by well-known and established EMTP simulation tool.