Application of matrix methods to the solution of travelling-wave phenomena in polyphase systems

The interest in travelling waves and surge phenomena in power systems has grown considerably because of the relevance to power-line carrier communication and protection, fault location, switching of unloaded lines and the recovery voltages on circuit-breakers under short-line fault conditions. The paper summarizes the solution to the single-conductor wave equation, develops the solution for the 2-conductor case by classical methods, and then indicates the rapidly growing complexity of the problem with increasing numbers of conductors when solving by classical methods. The 2-conductor case is then solved by using the method of matrix algebra. These results are shown to be valid for any number of conductors, and the concept of surge impedance and propagation coefficient for polyphase systems is introduced. The single-phase equation is shown to be a particular case of the general equation and the similarity between the results of the two cases is indicated. Examples of the matrix method are given, including a proof that symmetrical components are a particular case of the general result. The paper concludes by indicating that the method is particularly suitable for calculations carried out with a digital computer.