Statistical Estimation of Phase-to-Phase Risk of Failure

Estimation of the phase-to-phase risk of failure, Rpp, as a bivariate function of the phase-to-phase over- voltage amplitude U and the ratio ¿= V- /( V+ + V-) of the phase-to-ground components may be obtained by convolution of the bivariate overvoltage probability frequency density p( U, ¿) and the bivariate breakdown probability of the insulation Pb( U, ¿). This paper shows, however, that the ratio ax of overvoltages liable to cause breakdown varies within only a narrow range (~0.4 to 0.5) for which the phase-to-phase 50% breakdown voltage undergoes only a minor variation. This allows a simplified estimation of Rpp for a properly selected central value of a and not a variable one. It is shown that ¿¿0.40 constitutes a reasonable value for this purpose. Under this assumption, Rpp may be expressed as a function of a phase-to-phase safety factor ¿pp = UblO/ U2 where UblO is the phase-to-phase voltage causing a 10% breakdown probability and U2 the phase-to- phase overvoltage that might be exceeded with a 2% probability.