Measurements and calculation on restriking-voltage transients at a substation fed by single-core cables

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For a circuitfbreaker operating at the end of a long feeder the feature determining the rate of rise of restriking voltage is the effective surge impedance of the feeder. A previous paperf dealt with the effective surge impedances and calculation of fronts of transients of restriking voltagefor substations fed through 3-core belted-type cables. The present paper deals with the surge impedance in various phase combinations of feeders consisting of three single-core paper-insulated double lead-sheathed cables laidin trefoil, and gives methods by Avhich effective surge impedances may be calculated for systems of known constants. Effective surge impedances deduced from measurements taken with the restriking-voltage indicator are compared with values deduced from calculations taking account of transient currents in the cable sheaths, and it is concluded that the agreement obtained is sufficiently good to show that all important relevant features are properlyaccounted for. As a rough guide it may be said that the effective surge impedance per phase of a system such as is described, is about 0.75√(L/C), where L is the effective power-frequency star inductance per unitlengthand C the core-to-sheath capacitance per unit length of the cable. This L and C are of course the values normally supplied by manufacturers. The inherent rate of rise of voltage for a fault current of I r.m.s. amperes in a breaker fed by such a cable is 2√(2)⨍πI × (effective surge impedanceobtained as described), i.e. for a 50-cycle system it is (0.44×10 -3 I × surge impedance) volts per microsecond. The constant 0.75 in the above is an average obtained from empirical values for different cable arrangements, but if a more accurate determination is required for anypractical cable arrangement it is shown how this can be determined from firstprinciples.