An Analytical Model for DC-Link Capacitor Ripple Current in Multi-Phase H-Bridge Inverters

Ripple currents on the direct current (DC) bus in variable frequency drive (VFD) systems originate from motor load current fluctuations and the high-frequency switching of power devices. The resulting Joule heating within the DC-link capacitors is a primary driver of lifespan degradation. To address the lack of systematic models for predicting these currents in multi-phase H-bridge inverters and to mitigate the over-design inherent in empirical approaches, this paper introduces a novel analytical method for precise ripple current quantification and capacitor optimization. First, a dynamic DC-link capacitor model is established based on a single-phase H-bridge inverter, leading to the derivation of expressions for the instantaneous, average, and root mean square (RMS) input currents. Furthermore, by incorporating the 2 k π/ N phase difference (where k is an integer from 0 to N -1) among N parallel H-bridge units, a universal analytical expression for the RMS input current and its harmonic spectrum in a multi-phase system is derived. The analysis reveals that the ripple current harmonics are concentrated at 2 m times the switching frequency (with m being an integer within a specified range) and their associated sidebands. The derived expression quantitatively characterizes the influence of the modulation index and power factor angle on the ripple amplitude. A 160 kW twelve-phase H-bridge inverter serves as a case study. MATLAB simulations and hardware experiments demonstrate close agreement between the theoretical calculations and the corresponding simulated and measured results, with errors in the input current harmonic amplitudes all below 5%. Compared to traditional empirical design, the proposed method reduces capacitor volume and cost by approximately 15%-20% while ensuring system reliability. This method is directly extensible to other multi-phase inverter topologies, providing a theoretical foundation for the accurate selection of DC-link capacitors.