A comprehensive approach to fixed-step simulation of switched circuits

Because of its reduced calculation effort and deterministic execution time, fixed-step simulation is a prerequisite for real-time performance. However, when simulating switched circuits, it introduces errors in the form of switching delays and inconsistent initial conditions. In order to eliminate these errors, the present paper describes a physically sound method for accurate and efficient fixed-step/real-time simulation of switched circuits. Assuming that switching is instantaneous and respecting the conservation of energy principle, the simulation method provides simple and straightforward procedures for eliminating switching delays and for calculating consistent initial conditions, even though the switching time may not coincide with a calculation time-step and the circuit may pass through a series of simultaneous switchings. Furthermore, the simulation method proposes a simple decoupling technique to isolate parts of the circuit where the switching occurs, in order to reduce the effort required for the calculation of initial conditions. Implementation of the proposed simulation method in the nodal approach and in the state space approach is shown. A 12 pulse thyristor rectifier and a PWM inverter are used to highlight simulation accuracy. Simulation results, with and without the simulation method, are compared to variable-step simulation and to other documented methods. Finally, the simulation of a full HVDC system serves to demonstrate real-time simulation performance.