The interconnected electrical power grids are operated by multilevel control centers with hierarchical architecture. Since large-scale renewables are integrated in different voltage levels, the traditional isolated op...
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The interconnected electrical power grids are operated by multilevel control centers with hierarchical architecture. Since large-scale renewables are integrated in different voltage levels, the traditional isolated operation of interconnected power grids is uneconomical and meets operational risk due to lack of coordination. Therefore, the coordination between control centers in different levels and areas are indispensable. However, existing distributed approaches may either encounter numerical problems or converge slowly when the nonlinear AC optimal power flow (ACOPF) models are applied. Moreover, the total iteration number presents an exponential increase with the levels of hierarchical grids. In order to improve computational efficiency, this paper proposes a nested decomposition method for the coordinated operation of multilevel ACOPF problem, which has superlinear convergence and can achieve the optimal solution (KKT point). During each iteration, a projection function, which embodies the optimal objective value of a lower level power grid projected onto its boundary variable space, is computed with second-order exactness. Thus, the proposed method can be applied to nonlinear continuous optimizations with high efficiency. The paper also provides a rigorous proof for its convergence under the condition that the lower level optimization problems are convex with continuously differentiable objectives and constraints. Numerical tests are conducted with three trilevel power grid of different scales, which verify that the computational efficiency and scalability of the proposed algorithm are superior to those of existing methods.
This paper proposes a three-stage unit commitment model for the market operation of transmission and distribution coordination under the uncertainties of renewable generation and demand variations. The first stage is ...
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This paper proposes a three-stage unit commitment model for the market operation of transmission and distribution coordination under the uncertainties of renewable generation and demand variations. The first stage is for the independent system operator (ISO) that determines the commitment decisions of the transmission-level generators and the distribution-level system reconfiguration;the second stage optimizes the transmission economic dispatch;then distribution system operators (DSOs) in the third stage perform their economic dispatch and exchange information with the ISO at the boundary nodes. Between the transmission and distribution networks, not only conventional thermal generators but renewables and variable demands are considered, which are tackled via a multi-stage stochastic programming approach. The model adopts a convexified AC branch flow formulation in the distribution system. We devise a generalized nested L-shaped algorithm to solve the proposed framework in an efficient manner. Numerical experiments on multi-scale test systems corroborate the efficacy of this strategy.
In this paper, we introduce the multistage stochastic program with fuzzy probability distribution. We focus on the case where fuzzy probability distribution is defined by (triangular) fuzzy numbers. We extend Ben Abde...
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In this paper, we introduce the multistage stochastic program with fuzzy probability distribution. We focus on the case where fuzzy probability distribution is defined by (triangular) fuzzy numbers. We extend Ben Abdelaziz and Masri [Stochastic programming with fuzzy linear partial information on probability distribution, European Journal Operational Research 162 (2005) 619-629] solution strategy, for the two-stage stochastic program with fuzzy probability distribution, to solve the multistage model. The proposed solution strategy is based on two transformation steps. In the first step, the fuzzy transformation step, we propose to use the X-cut defuzzification technique. The level cc relates to the DM credibility degree on information sources. This step ends with a certainty equivalent program. In the second step, the stochastic transformation step, we decompose the certainty equivalent program based on a minimax approach. The obtained problem is then solved using a modified version of the nested decomposition method. The modification on the nested decomposition method concerns the way in which we generate optimal constraints. The modified nesteddecomposition algorithm may be used to solve the multistage problem with interval probability distribution. (C) 2008 Elsevier B.V. All rights reserved.
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