This paper presents a current injection power flow analysis and optimal generation dispatch method for bipolar DC microgrids. In bipolar DC systems, despite a certain local voltage being balanced by the converter control, voltage unbalance can occur at buses that are electrically far from the balanced voltage. In addition, from the aspect of system operation, the optimization of operation cost and voltage unbalance has not been fully investigated yet. Herein, for steady-state analysis, the current injection Newton-Raphson power flow for a bipolar DC microgrid is developed using static models of the network, voltage balancer, sources, and loads. Afterwards, the optimization problem is formulated based on voltage sensitivity, which can be obtained from the Jacobian matrix, to reduce the operation cost while resolving the voltage unbalance. The problem of quadratic programming can be solved sequentially to find the final optimal solution. The case study validates that the power flow method is sufficiently accurate compared to the simulation in PSCAD/EMTDC and that optimal generation can be achieved while reducing the operation cost and mitigating voltage unbalance.

This paper presents a new droop control method to reduce battery degradation costs in islanded direct current (DC) microgrids for multiple battery energy storage systems (BESSs). BESSs may have varying installation costs and battery cycle life characteristics depending on battery type, energy capacity, and maximum output power. These differences cause different battery degradation costs among BESSs despite exchanging the same amount of energy. To autonomously reduce the total battery degradation cost, an incremental cost (IC) of a BESS is used as a criterion for determining the state-of-charge level of BESSs and is calculated based on the battery cycle life curve containing the battery degradation information. By adopting an IC–voltage droop control, the BESSs can maintain an operating point of equal IC, an optimal point for cost minimization. Subsequently, small-signal stability analysis is performed using the state-space model of the proposed method. The case study validates that the proposed method can reduce the total battery degradation cost with a small-signal stable operation in islanded DC microgrids.

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.