Compressive Sensing Based Stochastic Economic Dispatch With High Penetration Renewables

This paper develops a stochastic economic dispatch algorithm to optimize performance objectives while coping with high-dimensional uncertainty in the distribution system. To build a new convex deterministic optimization model of economic dispatch with random parameters, the conic relaxation of power flow and the multivariate polynomial chaos expansions of random variables are employed. As the expansion of the multivariate random variables in terms of polynomial bases are approximately sparse, the weighted $l_1$ minimization approach is utilized to reconstruct the polynomials from compressed samples. Based on the alternating direction method of multipliers, distributed strategy is developed to solve the economic dispatch and corresponding uncertainty quantification iteratively. Compared with Monte Carlo sampling method, the proposed approach not only can reduce the computational cost for solving stochastic economic dispatch, but also provide more accurate statistical information.

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