IMPROVING ACCURACY AND SPEED IN REAL-TIME SIMULATION OF ELECTRIC CIRCUITS

Abstract

This article proposes a methodology for real-time simulation of electric circuits consisting of linear circuit components combined with nonlinear elements, such as diodes and electronic switches, that exhibit discontinuous behavior. The methodology consists of sub-dividing fixed numerical integration time-steps into sub-steps over which the entire circuit behaves linearly, thus permitting the simulation over each sub-step to be performed using analytic formulas. For non-real-time simulation, this has routinely been accomplished using variable-step numerical integration. In the article, we show how real-time integration can be accomplished using a linear analytic formula over each fixed integration step, where the formula coefficients are stored functions of the sub-step parameters. For example, in a single-phase diode rectifier circuit, each fixed integration step h is divided into two sub-steps, the first of duration hen over which the diode is not conducting and the second of duration h(1 - en) over which the diode is conducting, with a simple formula used to calculate the dimensionless sub-step parameter en. The output current for the n + 1 frame is then calculated with a linear formula requiring four multiplications and four additions. Three of the five coefficients required for this calculation are rather complex functions of the parameter en. However, by restricting en to N + 1 equally spaced values between 0 and 1, the 3(N + 1) possible coefficient values can be pre-computed and stored in memory, which results in a sizeable reduction in execution time for each fixed integration step. The article includes a three-phase diode rectifier example that sub-divides each fixed integration step h into three sub-steps of duration hdn, h(en - dn) and h(1 - en).