An Instantaneous Power Theory Extension for the Interphase Power Imbalance Problem

In grid-connected power converters, active and reactive power references are typically provided for calculating current and/or voltage references. This is generally achieved by using the standard instantaneous power theory (IPT). However, when a converter is required to operate with different per-phase power levels, the IPT cannot be applied to fully describe this interphase power interaction. To address this limitation, this work presents an interpretation of the interphase power imbalance problem, which enables the representation of the system as a combined electrical interaction between the unequal per-phase active powers on the inverter side and balanced power on the grid side. To achieve this, a Clarke transformation based on sequence order rotation is proposed. Thus, per-phase quadrature $\alpha \beta$-components can be obtained, allowing the instantaneous per-phase unbalanced power on the inverter side to be analytically derived. Based on this representation, an analytical expression of the instantaneous zero-sequence voltage (ZSV) is obtained. This ZSV allows one to extract unbalanced per-phase power on the inverter side while injecting balanced power on the grid side. A case study showing experimental results from a 10 kVA cascaded H-bridge converter applied to a scaled-down medium-voltage photovoltaic system are presented.