Efficient and accurate representation of asynchronous network structure changing phenomena in digital real time simulators

Abstract

Due to synchronization requirements related to the interfacing with external systems, digital real time simulators of electromagnetic transients for equipment testing employ a constant integration time step width for solving the network equations. Therefore, the network solution is only calculated at discrete and equidistantly spaced time instants while in reality the time domain is continuous. Changes in network structure that occur between the discrete solution points are generally not simulated exactly. This can lead to switching control mistakes and numerical problems. In this paper the novel Clock Synchronized Structure Changing concept, which allows the accurate and efficient simulation of structural changes at arbitrary time instants, is presented.

Position-Dependent Control of Numerical Integration in Circuit Simulation

“…2) Backward-Euler Method: a) Algorithm: When discretizing (1) with the backwardEuler method, the following relationship is obtained: (13) b) Frequency Response: Denoting the frequency response of the backward-Euler integrator through and inserting (2) and (3) leads to (14) Inserting (8) and rearranging lead to (15) Through backward-Euler integration, a real part is introduced in the frequency response. The imaginary part is the same as for the trapezoidal method.…”

A new versatile hardware platform for digital real-time simulation: Verification and evaluation

“…Moreover, the use of algorithms with multiple integrations offers significant benefit only when a large time step size compared to the switching frequency is used, as shown in [14]. A significant benefit of the approach proposed in [13] is that does not assume that the time at which the ITS occurs is known. Thanks to this characteristic, the proposed approach is more suitable for uncontrolled device like diodes.…”

“…In general, avoiding multiple integration inside the same time step is a suitable approach to keep calculation time low and deterministic in real-time applications. In this context the algorithms proposed in [13] and [14], based on interpolation and extrapolation, are much more interesting as additional overhead required by the these algorithms is typically very limited. Moreover, the use of algorithms with multiple integrations offers significant benefit only when a large time step size compared to the switching frequency is used, as shown in [14].…”

“…Various algorithms for the accounting of internal or external MITS events on controlled or uncontrolled devices are presented in [13] and [14]. The latter presents a comprehensive overview of algorithms to handle MITS events.…”

A High Performance Real-Time Simulator for Controllers Hardware-in-the-Loop Testing

“…Thus corrective measures to account for the errors due to ITS events are needed. These corrective measures utilize time stamping techniques and interpolations/extrapolations to (i) register the exact switching time instance, (ii) determine the system variables at the switching time instant, and (iii) resynchronize the simulator output with the simulation time grid [19][20][21][22][23][24]. …”