With the rapid development of plug-in electric vehicles (PEVs), the charging of a number of PEVs has already brought huge impact and burden to the power grid, particularly at the medium and low voltage distribution networks. This presents a big challenge for further mass roll-out of electric vehicles. To assess the impact of charging of substantial number of electric vehicles on the grid, a model of 30000 PEVs integrated with unit commitment (UCEV) was investigated in this study. The unit commitment was a large-scale, mixed-integer, nonlinear, NP-Hard (non-deterministic polynomial) optimization problem, while the integration of PEVs further increased the complexity of the model. In this paper, a global best inspired negatively correlated search (GBNCS) method which extends the evolutionary logic of negatively correlated search is proposed to tackle the UCEV problem. In the proposed algorithm, a rounding transfer function in GBNCS, is deployed to convert real-valued variables into binary ones; further, the global best information is combined in the population to improve the efficiency of the algorithm. Numerical results confirmed that the proposed GBNCS can achieve good performance in both a basic IEEE 10 unit commitment problem and the UCEV problem. It was also shown that, among four charging modes, the off-peak charging mode and EPRI (Electric Power Research Institute) charging mode are more economical in PEV charging.
FPTAS for mixed-integer polynomial optimization with a fixed number of variables
