Simulation of electric circuits containing high-speed switches

This paper describes a method of handling the real-time simulation of electric power circuits by utilizing multi-rate sampling of the external input control signals for solid-state switches. With pulse-width modulation frequencies of 10 kilohertz and higher, sample frequencies of at least 1 megahertz are often required to realize sufficient accuracy in a real-time simulation of the overall circuit. The paper describes how the average value of the multi-rate input samples over each time-step h used in the numerical simulation of the circuit state equations can be employed in a way that permits the overall circuit simulation to be run on currently available general-purpose microprocessors. Real-time simulation of a simple boost-converter circuit is utilized to illustrate the proposed methodology. It is shown that the number of mathematical operations required for each integration step can be greatly reduced by pre-computing the coefficients in the numerical integration difference equations for each of the N possible multi-rate average switch-input values that can occur, where N is the multi-rate frame ratio. The paper also describes a method for compensating for the one-frame delay associated with the use of multi-rate input averaging.