Power System Simulation by Phase Coordinate Method

Abstract

This paper presents a new method of simulation for unsymmetrical faults in power system. The new method is based on the phase coordinate method. The symmetrical component method has been used traditionally for unbalanced faults in power system. This is mainly because the synchronous generators can be easily treated by the method. However, when analyzing a system that has elements with unsymmetrical impedance, the symmetrical component method can not be used. In such cases, the simulations can be easily executed by using the phase coordinate method. However, there are few papers that present detailed procedures of simulation based on the phase coordinate method. This paper, at first, presents phase coordinate models of the elements in power system; i.e., synchronous generator, transmission line, transformer and load. Next it presents a method of power flow calculation of a power system including elements with unsymmetrical impedances. Finally it presents detailed procedures of simulations based on the phase coordinate models derived.

Unbalanced power flow calculation of a power system containing a variable-speed generator

“…(15) must be symmetrical for power flow calculations. The impedance matrix of the generator, [Z abc AG ], is not constant and will change depending on saturation (Z GN g changes depending on the changes of X N ) [9].…”

“…Representing the number of the three-phase node in a power system by N, the admittance matrix, [Y abc SY S1 BBBB], for the external circuits of generators can be determined by arranging the driving point (3 u 3) admittance matrix of each three-phase node and the transfer admittance (3 u 3) matrix between the three-phase nodes, and the node equation may then be expressed as follows [9]. The superscripts added to some matrices or vectors denote the numbers of rows and column. ]…”

“…denotes a vector of the injection currents which can be expressed using the specified P and Q values (equals zero for floating nodes). A basic equation for power flow calculation of a power system including only synchronous generators can be expressed as follows [9], where [Z In the case of a power flow calculation of a power system including variable-speed generators, however, Eq. (27) cannot be used and some modifications are needed, because input powers to the converter circuit P C1 , Q C1 must be considered.…”

“…Although all synchronous generators are assumed to be P/Q specified in Ref. 9, the above method can also be applied to the case, in which there exist P/V specified synchronous generators. Figure 3 shows the algorithm of the method explained above.…”

“…The phase coordinate method has some excellent features [4], the primary one being that it can easily be used to analyze a power system which has elements of unsymmetrical impedance. The authors, considering the positive points, have presented the phase coordinate model of conventional synchronous machines [8], and power flow calculation and power system transient stability simulation methods, based on the phase coordinate method [9].…”