A digital computer method is presented for the accurated evaluation of temporary overvoltage transients on a series-compensated transmission line. The synchronous generator is represented by a five-coil dynamic model, and the effect of the excitation control system associated with the generator is included in the analysis. The transmission network is represented by differential equations involving the network state variables. This kind of study is essential in choosing economical voltage ratings for surge arresters protecting high-voltage station equipment, in view of the modern practice of allowing surge diverters to reseal after temporary overvoltages exceeding their voltage ratings for a limited duration of time. These studies, when conducted for the case of series-compensated transmission lines, can reveal the limit of compensation level beyond which the danger of self-excited oscillation can occur in a particular system.