Extension of Random Walk Modelling of CM Current Harmonics in Multi-converter Setups

This paper presents an extension of a Pearson's Random Walk (PRW) discussed in our previous papers as a modelling tool for predicting the common mode (CM) current in multi-converter setups, based on the CM current of a single converter. Our earlier work was limited by the assumption that CM current could only be modeled as a sinusoidal damped oscillation. Here, we introduce a more general approach where the PRW modelling can be applied to any periodic signal with an existing Fourier Transform. Beyond theoretical discussion, we validate our extended methodology through multiple test cases using signals commonly found in power electronic (PE), electromagnetic compatibility (EMC), and other electrical circuit applications - including damped sinusoids, exponential decays, chirps, Lorentzian pulses, half-sine pulses, Gaussian pulses, and sawtooth waves. Our test results confirm our theoretical derivations, demonstrating that the PRW can be effectively extended to model diverse classes of periodic signals. We also address limitations associated with test signal post-processing.