Analytic method using laplace transform for a modified TRV of a circuit breaker

When circuit parameters are known, it is easy to calculate the modified transient recovery voltage (TRV) with resister breaking or MOSA operating by numerical simulations. But, when the TRV is only known, it is very difficult to calculate the modified TRV by numerical simulations. This paper shows the theoretical analytic method of the modified TRV at such a circuit impedance modification as breaking with parallel resister or MOSA operating. A TRV can be calculated by injecting a current from circuit breaker terminals to back impedance. TRV and injected current wave shapes can be expressed with a group of ramp waveforms in Laplace domain. By using our analytic method, the back impedance can be easily derived in the Laplace domain from the TRV and injected current waveforms. As a result, it is shown that the modified TRV at circuit impedance modification can be calculated. Moreover, the same method can be used to calculate the TRV that is reduced by asymmetrical current breaking.