A Stability and Accuracy Validation Method for Multirate Digital Simulation

摘要

This paper presents a new validation method to demonstrate the stability and accuracy of a discretized system by using multiple sampling rates. Such multirate simulations are often encountered in real-time simulation application, where large power systems are coupled with circuit containing power electronics devices. Multirate simulation should not be confused with variable-step simulation, which is a single-rate simulation type. In single-rate simulation, the discretized system is stable when its discrete poles are within the unitary circle. When using multirate solvers, state variables are discretized with different sampling rates and poles location analysis for the system's equations cannot be used. This paper introduces a formal mathematical analysis demonstrating stability of multirate real-time simulation. System state variables, regardless of their discretization time step, are found in a single matrix. Classical pole analyses are thereafter used to test stability with poles location analysis. The method is given in a generalized form, and can be applied to various multirate solvers. The proposed method was found accurate and reliable using numerical examples.