Distributionally Robust ChanceConstrained Energy Management for Islanded Microgrids With the development of smart grid, energy management becomes critical for reliable and efficient operation of power systems. In this work, we develop a chanceconstrained (CC) energy management model for an islanded microgrid which includes distributed generators (DGs), energy storage system (ESS), and renewable generation such as wind power. The objective function of this model consists of generation cost, emission cost and ESS degradation cost. To capture the uncertainty of renewable generation, a novel ambiguity set is introduced without knowing its probability distribution or exact moment information. Based on the ambiguity set, the chance constraint can be processed with distributionally robust optimization (DRO) method and the energy management problem is reformulated as a tractable secondorder conic programming (SOCP) problem. The proposed approach is tested with a case study and simulation results indicate that it is effective and reliable. Moreover, the comparison with the method based on known moment information and some other methods is also conducted to show the performance of the proposed method.

Stochastic Nonlinear Programming Model for Power Plant Operation via Piecewise Linearization In this paper, we consider the application of mathematical optimization models to energy problems. Using the latest information technology, we try to utilize renewable energy whose output is unstable. Such efforts are collectively called smart communities. Stochastic programming deals with optimization under uncertain conditions. Since the output of solar power generation in a smart community is uncertain, application of stochastic programming is required. Considering practical operational constraints, this model becomes a stochastic programming problem involving nonlinear recourse, which cannot be solved with typical solvers directly. The problem can be reformulated as a largescale mixed integer programming problem by piecewise linear approximation to obtain an optimal solution. In our algorithm, we add points for piecewise linear approximation iteratively and increase accuracy of the approximation. In numerical experiments, the effectiveness of the stochastic programming model is shown by comparing it with the deterministic model. Moreover, we calculate a recovery period of investment cost for photovoltaic generation and a storage battery and show usefulness of our model when evaluating a practical operation.