Penalized sample average approximation methods for stochastic programs in economic and secure dispatch of a power system |
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Authors: | X. J. Tong H. Xu F. F. Wu Z. Zhao |
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Affiliation: | 1.Department of Mathematics,Hunan First Normal University,Changsha,China;2.School of Mathematics,University of Southampton,Southampton,UK;3.Department of Electrical and Electronic Engineering,The University of Hong Kong,Pok Fu Lam,Hong Kong;4.Hunan Province Key Laboratory of Smart Grids Operation,Changsha,China |
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Abstract: | In this paper, we develop a stochastic programming model for economic dispatch of a power system with operational reliability and risk control constraints. By defining a severity-index function, we propose to use conditional value-at-risk (CVaR) for measuring the reliability and risk control of the system. The economic dispatch is subsequently formulated as a stochastic program with CVaR constraint. To solve the stochastic optimization model, we propose a penalized sample average approximation (SAA) scheme which incorporates specific features of smoothing technique and level function method. Under some moderate conditions, we demonstrate that with probability approaching to 1 at an exponential rate with the increase of sample size, the optimal solution of the smoothing SAA problem converges to its true counterpart. Numerical tests have been carried out for a standard IEEE-30 DC power system. |
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