Load restoration is an important issue for power system restoration after a blackout. A second order conic programming (SOCP) model is proposed based on the information gap decision theory (IGDT) to maximize load pickup considering the uncertainty of load increment. Because distribution functions of load increment are difficult to obtain, the optimization of load pickup is transformed to maximize the fluctuation range of load increment by the IGDT. The derived optimal fluctuation range can ensure that the reenergized system is secure, and the amount of load pickup is always better than the specified expectation. Moreover, because the optimization model of the fluctuation range is a mixed-integer nonlinear model which is challenging to solve accurately and efficiently, the nonlinear model is transformed into a SOCP model that can be efficiently solved using CPLEX. The efficiency of the IGDT-based SOCP model is validated using the New England (10-machine 39-bus) system. The simulation results show that the derived load pickup shows expected robustness with respect to the load increment uncertainty.

The re-emergence of 2-phase bipolar DC distribution network, which utilizes the neutral wire for efficient distribution, has spurred research interest in recent years. In practice, system efficiency (power loss) and voltage unbalance are major concerns for the planning and design of the 2-phase DC bipolar network. While most of the existing methodologies are power electronics solutions, there are very few works on resolving the problem from the power system perspective. This paper proposes a model based optimization method by firstly formulating the power flow model for 2-phase DC bipolar network using the single line modeling technique and nodal analysis. Secondly, a binary integer load distribution model is proposed to consider the redistribution of unipolar loads across the two unipolar distribution poles. Together with the power flow model, the system power loss and system voltage unbalance indices are formulated as a binary integer quadratic model. Thirdly, a multi-objective optimization model is formulated and solved using the weighted sum approach. The proposed method is applied to a DC LED lighting system design which considers both voltage unbalance and power loss. Using a 15 bus single source and a 33 bus multi-source network as case studies, the developed power flow model is validated with very high accuracy. Compared to existing iterative methods, the proposed model-based approach is able to significantly improve the voltage balancing across the distribution system.