Mode-Constrained Two-Stage Current Injection Optimization for Voltage Unbalance Mitigation in IBR-Rich Distribution Network

Under unbalanced grid conditions, inverter-based resources (IBRs) are required to remain connected to the grid and provide reactive current injection to mitigate voltage unbalance (VU) at the point of common coupling (PCC). Most existing research focuses primarily on steady-state reference current generation under such conditions, whereas current overshoot and oscillations induced by reference-switching have been largely overlooked. Driven by this gap, this article proposes a mode-constrained two-stage current injection optimization framework. In the first stage, the dominant oscillatory modes of a grid-connected IBR are identified through closed-loop transfer function modeling and eigenvalue analysis. In the second stage, a reference-switching trajectory optimization problem is formulated in the frequency domain, in which the trajectory is constructed through a virtual-acceleration sequence. By maximizing the virtual energy contained in the sequence under spectral energy constraints, the fastest and optimal trajectory is indirectly obtained, and the excitation of dominant oscillatory modes during reference switching is thereby prevented. Since this framework is implemented at the reference level, it is fully compatible with existing controllers and adaptable to varying operating conditions. Simulation and experimental results confirm the effectiveness of the proposed optimization framework.