Calculation of nonlinear circuits for surge-voltage protection

The paper gives some general solutions of 2-element circuits involving nonlinear resistances combined with ohmic resistance, transmission lines, inductance or capacitance. Solutions are given so that many practical problems of using surge arresters for the protection of transmission lines can be readily solved for realistic surge-voltage waveforms. The inductive- and capacitative-circuit solutions are designed for the easy practical solution of overvoltage-protection problems, particularly those arising in the protection against lightning of semiconductor-rectifier installations feeding d.c. electric-railway systems. A novel way of handling the equations is developed which leads to the development of key dimensionless groups of constants, epitomising the whole nature of the circuit under investigation, and also gives the correct meaning to the nonlinear equivalents of time constants and damping factors.