Abstract :
This method determines inherent transient recovery voltages on power systems using the state space approach. The impedance parameter, viewed from a pair of electrodes or terminals of the circuit breaker, is given as a ratio of two determinants in complex frequencies by means of the Laplace transformation of the system of differential equations with respect to loop currents of the network. The fundamental differential equations are derived from the impedance, resistance, and elastance matrices by the topological method with a transformation tensor, generated by a computer using connection data. Characteristic polynomials of the denominator and the numerator of the impedance parameter are easily factored using eigenvalues. Transient responses of the transient recovery voltages are obtained by applying the inverse transformation of the product of the impedance parameter and a fault-current function in complex frequencies, or by using the convolution integral of the indicial or impulse response and an arbitrary fault current in the time domain. The frequencies and the damping constants of the transient recovery voltages are obtained from the eigenvalues of the characteristic polynomials of the impedance parameter. Other characteristic values of the transient recovery voltages, such as the rate of rise of restriking voltage (rrrv), etc., can be derived from the oscillogram or waveshape of the transient responses. This method is simple, accurate, and effective when used with a large-scale, high-speed digital computer.
