Optimal distributed balancing control for three-phase four-wire low voltage grids

In this work a distributed control method is proposed to mitigate the unbalance in a low voltage grid based on an approximated three-phase power flow. As the power flow is both explicit and linear with respect to the apparent power, it can be substituted into the objective function of the controllers leading to a separable optimization problem. The resulting subproblems are coupled in the costs which are related to the negative-sequence voltage formulated as a linear function of the apparent power. By exchanging nodal measurements via a communication bus, the controllers adjust their set-points in order to mitigate the unbalance with a Jacobi-like coordination algorithm. The effectiveness of the approach is demonstrated in a simulation study with an unbalanced low voltage grid.