Frequency Coupling Matrix of a Voltage-Source Converter Derived From Piecewise Linear Differential Equations

When a power-electronic converter is introduced into a linear network, voltage and current harmonics of differing orders become coupled (through the modulation effect of the converter). The interharmonic coupling introduced by the modulation effect of a converter may be mathematically represented through a frequency coupling matrix (FCM). Given that the source of the coupling is a modulation process, researchers have, in the past, focused on deriving the FCM in the frequency domain - a process that requires the truncation of the harmonic representation of signals. This paper presents an alternate approach to evaluate the FCM based on a time-domain derivation. In contrast to frequency-domain-based methods, it is shown that the time-domain approach avoids truncation. Furthermore, the time-domain approach does not require system linearization about an operating point; thus, the FCM is not limited by small-signal assumptions.