SynopsisA method of computing switching overvoltages based on the numerical inversion of the modified Fourier transform is discussed. Several applications are made to practical studies of varying degrees of complexity. The results of a 3-phase switching problem are shown to be in agreement with those obtained by other workers using analogue simulation. The method allows more complete representation of the problem than was previously possible. Indeed, during the course of the work, the type of data necessary to permit an even closer representation became apparent, and attention is drawn to the desirability of recording this on future site tests.
List of symbolst = time T = travel time a -'smoothing' parameter on = angular frequency used as transform parameter f+(a + jco) = modified Fourier transform of/(/) Cl = integration range in the truncated inversion integral a = sigma factor / = length of line m = integer transform parameter associated with finite cosine transform p = Laplace-transform parameter v, V, v, V (or with suffixes) /, I, /, / (or with suffixes) Z, 2 (or with suffixes) L,M rs = voltages and their transforms = currents and their transforms = impedances and their transforms mutual induc-1inductance per unit length tance per unit length L s = source-side inductance R = resistance per unit length R s = source-side resistance r = switching resistor C rs , K r = capacitance per unit length a 2 = {R + (a+joj)L}(a + jw)C
A computationally efficient method is described by which sequential pole closure may be taken into account when integral transforms are used for the calculation of switching phenomena. The method is used to illustrate the effects of switching-in resistors and trapped charges on the overvoltages resulting in a particular case of long-line energisation.
IntroductionSome recent papers 1 >2>3 on the calculation of switching transients have employed integral-transform techniques as the basic tool to permit the representation of the frequency dependence of the line parameters. The object of the present note is to extend their scope by describing a computationally efficient method which is applicable when the. individual poles of the breakers close sequentially. The method is general, in that it can be used for any linear system with multiple inputs or for a system containing nonlinear elements capable of a piecewise linear approximation.The method is illustrated for the energisation of a long, open-circuited transmission line through a breaker complete with switching-in resistors, as shown in Fig. 1. The effect of initial charges trapped on the lines is also considered.
2Outline of the method Consider the closure of a switch S ]k at time r lk {\ < k < 3) in the network of Fig. 1, with E k the corresponding R11 line E 2
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