Proceedings of the Institution of Electrical Engineers · 1963 · 411 citations · 0 references
EngineeringElectrical EngineeringMathematicsCircuit TheoryDifferential EquationsPropagationElectric CircuitsPower Grid AnalysisTransmission LinesElectrical Power SystemsFault LocationImpedance MatrixSurgeSurge PhenomenaSymmetrical ComponentsTransmission Line Theory
Interest in travelling waves and surge phenomena in power systems has grown due to their importance for power‑line carrier communication, protection, fault location, line switching, and circuit‑breaker recovery voltages. The paper aims to summarize the solution of the single‑conductor wave equation, extend it to the two‑conductor case using classical methods, and highlight the increasing complexity when more conductors are involved. The authors solve the two‑conductor problem by applying matrix algebra and demonstrate that this approach generalizes to any number of conductors, with symmetrical components emerging as a special case. The matrix‑based solution is valid for any number of conductors, introduces surge impedance and propagation coefficient concepts for polyphase systems, shows the single‑phase equation as a particular case, and is especially suitable for digital‑computer calculations.
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.