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.

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The high penetration of photovoltaic (PV) systems and fast communications networks increase the potential for PV inverters to support the stability and performance of microgrids. PV inverters in the distribution network can work cooperatively and follow centralized and decentralized control commands to optimize energy production while meeting grid code requirements. However, there are older autonomous inverters that have already been installed and will operate in the same network as smart controllable ones. This paper proposes a decentralized optimal control (DOC) that performs multi-objective optimization for a group of PV inverters in a network of existing residential loads and autonomous inverters. The interaction of independent DOC groups in the same network is considered. The limit of PV inverter power factor is included in the control. The DOC is done by the power flow calculation and an autoregression prediction model for estimating maximum power point and loads. Overvoltage caused by prediction errors resulting in non-optimal commands from the DOC is avoided by switching to autonomous droop control (ADC). The DOC and ADC operate at different time scales to take account of communication delays between PV inverters and decentralized controller. The simulation of different scenarios of network control has proved the effectiveness of the control strategies.

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