Optimal Operation of Power Systems with Energy Storage under Uncertainty: A Scenario-based Method with Strategic Sampling

The multi-period dynamics of energy storage (ES), intermittent renewable generation and uncontrollable power loads, make the optimization of power system operation (PSO) challenging. A multi-period optimal PSO under uncertainty is formulated using the chance-constrained optimization (CCO) modeling paradigm, where the constraints include the nonlinear energy storage and AC power flow models. Based on the emerging scenario optimization method which does not rely on pre-known probability distribution functions, this paper develops a novel solution method for this challenging CCO problem. The proposed meth-od is computationally effective for mainly two reasons. First, the original AC power flow constraints are approximated by a set of learning-assisted quadratic convex inequalities based on a generalized least absolute shrinkage and selection operator. Second, considering the physical patterns of data and motived by learning-based sampling, the strategic sampling method is developed to significantly reduce the required number of scenarios through different sampling strategies. The simulation results on IEEE standard systems indicate that 1) the proposed strategic sampling significantly improves the computational efficiency of the scenario-based approach for solving the chance-constrained optimal PSO problem, 2) the data-driven convex approximation of power flow can be promising alternatives of nonlinear and nonconvex AC power flow.