Frequency Coupling Matrix of a Voltage Source

Summary form only given. 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 inter-harmonic 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 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.