Efficient Unbalanced Three-Phase Network Modelling for Optimal PV Inverter Control

High penetration levels of renewable energy generation in the distribution network require voltage regulation to avoid excessive voltage at generating nodes. To effectively control the network and optimize network hosting capacity, the distribution system operator must have an efficient model for power flow analysis. This paper presents the formulas and steps to express the power flow analysis equations of an unbalanced 3-phase network in matrix form suited to programmed solutions. A benchmark MATLAB/Simulink network with unbalanced distribution lines, photovoltaic inverters, and loads is built to verify the matrix model. To demonstrate the application of the model, the control of reverse energy flow from the photovoltaic inverters to keep the voltage in the network below the regulated level is simulated. Two decentralized control algorithms are applied in the network, including an on/off and a multi-objective constrained optimization controller. The detailed construction of the optimization problem for the 3-phase network in matrix form, which is consistent with the power flow calculation, is described. Simulation with the control methods over a day shows that the total active power of the on/off and optimized controllers deliver 41.92% and 99.39% of the available solar power, respectively, while maintaining the network node voltages within limits.