## ABSTRACT

The purpose of this chapter is to provide a method to estimate the magnitude and shape, i.e., the front steepness and the tail time constant, of the surge that arrives at the entrance to the station, which is denoted as the incoming surge. The magnitude and waveshape of this surge is a function of the distance between the station and the stroke-terminating point, the magnitude of the stroke current, and the initiating event—shielding failure or backflash. In turn, the number of surges that arrive at the station is a function of this distance and the BFR or SFR. Since the stroke current and the BFR or SFR are statistical quantities, it is apparent that the magnitude and shape of the surge is a random event and must be considered in probabilistic terms. Thus the incoming surge is statistical, which leads to the concept that the magnitude and shape of the incoming surge may be based on a design rate of the number of surges per year that equal or exceed a specific steepness and magnitude. The reciprocal of the number of surges is the return period or mean time between surges or MTBS in units of years per surge. That is, a surge may be selected so that the probability that its severity is equaled or exceeded is, for example, once in 100 years. If this 100 year surge produces voltages within the station that just equal the insulation strength, the mean time between failure of the equipment, the MTBF, is 100 years. However, this last statement applies only for a single-line station where the MTBS is equal to the MTBF.