Full Title: A Probabilistic Framework for Security Constrained Reserve Scheduling of Networks with Wind Power Generation
Author(s): Maria Vrakopoulou, Kostas Margellos, John Lygeros and Go ̈ran Andersson
Publication Date: 9/2012
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This paper proposes a novel probabilistic frame- work to design an N-1 secure day-ahead dispatch, while deter- mining the minimum cost reserves for power systems with high wind penetration. To achieve this, we build on previous work, and formulate a stochastic optimization program with chance constraints, which encode the probability of satisfying the transmission capacity constraints of the lines. To incorporate then a reserve decision scheme, we take into account the steady state behavior of the secondary frequency controller, and hence consider the reserves to be a linear function of the total generation-load mismatch. The overall problem results in a chance constrained bilinear program; to achieve tractability, two alternative convex reformulations are proposed, and the so called scenario approach is employed. This approach is based on sampling the uncertain parameter (in this paper the wind power) while keeping the desired probabilistic guarantees. To illustrate the effectiveness of the proposed technique we apply it to the IEEE 30-bus network, and compare the alternative reformulations in terms of cost and performance by means of Monte Carlo simulations, corresponding to different wind power realizations generated by a Markov chain based model.