Circuit modeling and statistical analysis of differential-to-common-mode noise conversion due to filter unbalancing in three-phase motor drive systems

This work deals with circuit modeling of noise mode conversion due to system asymmetry in a three-phase motor drive system. In fact, it is well-known that in case of system asymmetry (e.g., slightly asymmetrical LC filter parameters), differential-mode noise can convert into common-mode noise, resulting in increased level of conducted electromagnetic interference. This phenomenon has been observed with measurements and reported in previous works, but a clear and rigorous analytical description is still a challenging point. The main novelty proposed in the paper is a rigorous analytical description of differential-to-common-mode noise conversion based on the Clarke transformation and the eigenvalue analysis. In particular, the magnitude and the frequency location of the differential-mode resonances injected into the common-mode circuit are derived in closed form. Moreover, since system asymmetry is usually uncontrolled (e.g., component tolerance and parasitic elements), a statistical analysis is also presented by treating the parameters of the LC filter as random variables. Thus, a second contribution proposed in the paper is the analytical derivation in closed form of the probability density function, the mean value, and the standard deviation of the random frequency location of the resonance peaks injected into the common-mode circuit. The importance of the analytical results derived in the paper is two-fold. First, a deep theoretical understanding of the phenomenon in terms of circuit theory concepts is achieved. Second, the impact of differential-to-common-mode noise conversion is described in quantitative terms. Thus, the obtained analytical results can be used to predict or explain the noise conversion impact on the frequency-domain measurements of common-mode currents. Theoretical derivations are validated through a time-domain Simulink implementation of a three-phase motor drive system, and a frequency-domain analysis through the discrete Fourier transform