  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.
