A General Analytical Method for Calculating Inverter DC-Link Current Harmonics

Accurate identification of a DC-link ripple current is an important part of switched power-converter design, since the spectral content of this current impacts on DC bus-capacitor lifetime, the stability of the converter control, and the electromagnetic-interference (EMI) performance of the system. Conventionally, the RMS magnitude of the ripple current is used to evaluate this impact, but this approach does not readily differentiate between pulsewidth-modulation (PWM) strategies, and can be challenging to evaluate for more complex converter topologies. This paper presents a new generalized approach that analytically determines the harmonic spectrum of the DC-link and DC-bus capacitor currents for any voltage-source switched converter topology. The principle of the strategy is that the product of a phase-leg-switching function and its load current in the time domain, which defines the switched current flowing through the phase leg, can be evaluated in the frequency domain by convolving the spectra of these two time-varying functions. Since PWM has a discrete line-frequency spectrum, this convolution evaluates as an infinite summation in the frequency domain, which reduces to a simple frequency shift of the PWM spectrum when the load current is assumed to be a fundamental single-frequency sinusoid. Hence, the switched currents flowing through the phase legs of an inverter can be evaluated as a summation of harmonics for any PWM strategy or inverter topology and can then be readily combined using superposition to determine the DC-link and DC bus-capacitor currents. The analytical approach has been verified against experimental results for an extensive range of two-level and multilevel converter topologies and PWM strategies.