On the Optimality of Voltage Unbalance Attenuation by Inverters

In this paper, we investigate the control of inverter-based resources (IBRs) for optimal voltage unbalance attenuation (OVUA). This problem is formulated as an optimization program under a tailored dq-frame, which minimizes the negative-sequence voltage at the point of common coupling (PCC) subject to the current, active power, synchronization stability, and feasibility constraints. The program is inherently nonconvex and intractable. So, to guarantee the optimality, a rigorous optimality analysis is performed by leveraging analytical optimization. The analysis is divided into two cases: full mitigation of VU and partial attenuation of VU. For the former case, we analytically solve the original program since the resultant VU is immediately deducible. For the latter one, directly solving the problem becomes very hard. Thus, we reformulate the program into an equivalent but more tractable form under certain conditions, by which the analytical optimum can be finally derived. It is found that the optimum trajectory has three stages (O1-O3), depending on two critical boundary conditions (C1 and C2). Finally, we implement the optimum with a photovoltaic (PV)-storage system by developing an OVUA controller. The proposed approach is demonstrated by dynamic simulations under different VU conditions and is compared with several existing practices.