Treatment of discontinuities in time-domain simulation of switched networks

Interpolation and reinitialization in time-domain simulation of power electronic circuits

“…If the Backward Euler method is used and if the intermediate solution in (4) is neglected, it will simply eliminate the impulse and the diode will not turn on. This problem has been demonstrated in [7] and recognized in [1]. A possible compensation for this problem is to account for the intermediate computation step [1].…”

“…It is a high frequency switching case where both current and voltage discontinuities are encountered. Circuit data is identical to the data used in [7] for both continuous and discontinuous operating modes. Fig.…”

On the Numerical Accuracy of Electromagnetic Transient Simulation With Power Electronics

“…Other Sources of Errors not Discussed in Detail 1) Control System Delays: In some tools, artificial interfacing delays are introduced in the control system model [12]- [14], [35], [39]. While the error of a one-step delayed smooth control signal is O(h), the error can be more severe if switches are controlled with non-smooth control laws.…”

“…Consequently, a sufficiently small step size is required to account for the lack of synchronization with events. To prevent this, several methods, including those of NETOMAC and PSCAD, employ linear interpolation to rollback the solution to the moment of switching before executing the corresponding switch actions [4], [14], [17], [19], [24], [25], [29]- [31], [53]- [57]. However, as the approximation error of linear interpolation is O(h 2 ), the local O(h 3 ) accuracy of the trapezoidal method is still not matched in the respective simulation steps.…”

“…The support of idealized switches requires specialized solution techniques [7], [12], [14]- [16]. Table I lists literature on techniques currently used in selected tools for (nonrealtime) electromagnetic transient simulation.…”