Novel algorithm for on-line calculating traveling waves based on orthogonal projection theorem

A novel electro-magnetic transient analysis technique by means of the orthogonal projection method for lossy transmission line is proposed. By employing the proposed method, the traveling waves propagating from one terminal to another can be quickly obtained with less amount of computation under any larger sampling steps. First of all, the differential function to variable time can be approximated to be the convolution with a fixed vector relates to a certain set of orthogonal basis, e.g. Daubieches basis. The partial differential telegraph equations relates to both variable time t and distance x are then transformed to be that only relates to x. The solution of such equation can be obtained accordingly. The discrete coefficients of propagation function for lossy line are obtained as well, by which the propagating traveling waves can be calculated precisely in any larger sampling periods with less computation quantities. Compared with the results given by EMTP, the new method is efficiency and accurate.