A Novel Electro-Magnetic Transient Analysis Method for Distributed Parameter Transmission Lines

The Electro-magnetic transient analysis for power system, which is the basis of the transient protection, fault analysis, transient computation, etc, plays an important role in the area of protective relaying. Modern Electro-magnetic transient analysis techniques are all based on the characteristic method, in which the analysis firstly proceeded in frequency domain by Laplace transformation and the time domain solution is obtained by taking inverse Laplace transform. The mathematics involved in this process is tedious and the complexity increases in non-linear circuits due to the convolution in each time interval, which needs a large amount of historic datum. Recently, several methods have been proposed to deal with this drawback and to avoid time domain convolution. The Finite Element Method requires the line to be subdivided into a finite number of regions. This allows the telegraph equations to be converted into a one-dimensional differential vector equation related to variable t and the recursive formulas of each element can be obtained. Waveform relaxation techniques avoid time domain convolution by solving the transmission line equations in the frequency domain and using the faster Fourier transform (FFT) to transform the results back and forth between time and frequency domain at each iteration. However this requires many data points in order to avoid aliasing effects when very fast signals have to be studied. Recently, growing attention has been devoted to wavelets in applied electromagnetic, mainly for the solution of Galerkin-like problems and as shape functions in the moment method to obtain sparse matrices. This paper presents a novel technique of transient analysis for power system, which based on a new principle, the orthogonal projection method. According to the approximation principle, signals can be approximated by the linear combination of a set of orthogonal basis, in which the set of coefficients of the linear combination are also called projection to the basis. Certainly the voltage and the current at each point on the line can be approximated to be the linear combination of a certain set of orthogonal basis, for example, the Daubiechies basis. The differential functions of the current and voltage are also approximated by the linear combination of a set of projection values with the orthogonal basis. After projection onto orthogonal bases, which map to a function space relates to time variable t over a given resolution, the differential equations related to the voltage and current of transmission line transform to algebraic vector equations, based on which the projected equivalent models of each unit can be obtained. Then, the transients of the transmission system can be computed in the projection domain accordingly. EMTP simulation tests are presented which validate the method described.