A variation of trapezoidal integration (called trapezoidal integration with damping) for the solution of dynamic equations is described and tested. This method has several advantages over ordinary trapezoidal integration for the simulation of transients in power systems. The method is compared to ordinary trapezoidal integration, backward Euler and Gear 2nd order. The comparison is based upon local truncation error and upon performance of each method as a differentiator. The method is tested using a transmission line model response to a voltage step function, and the response of a HYDC converter with its controllers. Trapezoidal integration with damping is free from numerical problems, even when used as a differentiator; it provides a ready means for obtaining the "average behavior" of a simulator; it is fully compatible with trapezoidal; and it is very accurate.
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Alvarado et al. (1983) studied this question.
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