Abstract

This paper introduces a mathematical formulation to deal with the control problem of injecting balanced grid currents when the available power from each phase of a grid-tied photovoltaic (PV) Cascaded H-Bridge (CHB) inverter is severely asymmetrical. The optimal solution, i.e., the Optimal Common-Mode Voltage (OCMV), is obtained utilizing optimal control techniques. This OCMV has an analytical expression, which uses the available power, the power factor, the grid voltage, and the maximum dc voltage. Feasible regions are analytically derived, for which the total available power at the inverter side is transferred into the grid. A parametric analysis of the OCMV implementation over these regions considering a grid-tied PV seven-level CHB inverter is presented. Even though severely unbalanced powers are considered, the proposed OCMV injection method embedded in a standard Voltage-Oriented Control (VOC) scheme shows symmetrical and low distorted grid currents.