Inaccuracies due to the frequency warping in simulation of electrical systems using combined state-space nodal analysis

The simulation of electromagnetic transients may suffer from inaccuracies due to a phenomenon known as frequency warping (FW). This paper presents an analysis of the effects of FW on the accuracy of digital simulations, demonstrating that the use of the trapezoidal integration rule (TR), commonly employed in many electromagnetic transients simulators, is the root cause of such inaccuracies. Although FW is considered a major problem in digital signal processing, it is often overlooked when simulating electrical transients. The analysis is carried out in a fourth-order RLC circuit, from which the analytic solution is derived. The circuit is solved using the combined state-space nodal method, considering the TR or recursive convolutions as solution methods for the state-space representation. It was observed that the FW caused a change in the natural oscillation frequency of the system, causing a pulsating behavior of absolute error. The accumulation of errors over time can result in deteriorated solutions when either the time steps are not sufficiently small or the simulation runs for a long enough duration. This paper emphasizes the significance of accounting for the FW phenomenon in digital simulations that rely on integration methods, such as the TR.