One-machine dynamic stability analysis using the Eigenvalue Test of the A-matrix - Coronel, Antonio C. (1972)
There are instances when synchronism among generating units is lost. The loss of synchronism may have been initiated by a short circuit or by a mere switching in a of block of load. The analysis of this kind of problem of a power system network is embodied in what is called stability studies or analysis. The problem of stability has been under investigation since the 1920's and some results of such investigations are herein briefly discussed. The study of stability is conveniently classified into transient and dynamic or steady state stability. This thesis is mainly concerned with establishing detailed procedures in forming the so-called A-matrix and extracting its eigenvalues for stability analysis. One machine connected to an infinite bus is considered. The two-axes theory of synchronous machines is used in the formation of the generators equations. A modified Park's transformation transforms time varying parameters into non-time varying quantities. Matrix algebra and per unit system are used extensively for inconvenience in determining the required system equations. The eigenvalue test requires that the equations are in the linear canonical forms. In the linearized form, the coefficient matrix depends on the initial conditions. To write the generator system equations in the canonical form, matrix inversion and multiplication are applied, For convenience and to remove error in the computation, a computer program is developed. The computer program computes the intitial quantities required, other than those given. The excitation system and the turbine control system are analyzed from their schematic diagrams furnished by the manufacturer. Block diagrams are consructed as aid in the analysis. The A-matrices are formed separately and typical values substituted. To illustrate the method of forming the A-matrix and extracting its eigenvalues for analysis, Snyder I of the Meralco system is considered. The computer program, after forming the individual A-matrices, places the matrices into a null matrix to form the integrated A-matrix, after which, the coupling elements are computed and also entered into the A-matrix. The output of the program is a listing of the eigenvalues.