Robust Optimization Method for Voltage Balancer Planning in Bipolar DC Distribution Systems

This article proposes a new method for determining the optimal placement and sizing of voltage balancers (VBs) in bipolar DC distribution systems. In bipolar DC systems, asymmetric structures, such as distributed generation, loads, and line parameters, can cause voltage imbalances with respect to the poles. Such imbalances can be mitigated by using VBs that balance local positive and negative voltages in a decentralized manner, similar to voltage compensators in conventional AC systems. In this study, a deterministic optimization model is formulated to minimize the installation cost of VBs while maintaining the voltage imbalance within the allowable range. The model is proposed with mixed-integer linear programming using the big-M method and current-injection power flow equations. Subsequently, the uncertainty boundaries of renewable energy sources and loads are incorporated to formulate a robust optimization model as a tri-level optimization problem, which is solved using a column and constraint generation framework. The case study validates the effectiveness of the proposed method for mitigating voltage imbalances with minimum investment cost in bipolar DC distribution systems.