Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in *** averageapproximation(SAA)is the most popular method for solving JCCs in unit commitment(UC)**...
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Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in *** averageapproximation(SAA)is the most popular method for solving JCCs in unit commitment(UC)***,the typical SAA requires large Monte Carlo(MC)samples to ensure the solution accuracy,which results in large-scale mixed-integer programming(MIP)*** address this problem,this paper presents the partial sample average approximation(PSAA)to deal with JCCs in UC problems in multi-area power systems with wind *** partitions the stochastic variables and historical dataset,and the historical dataset is then partitioned into non-sampled and sampled *** approximating the expectation of stochastic variables,PSAA replaces the big-M formulation with the cumulative distribution function of the non-sampled set,thus preventing binary variables from being ***,PSAA can transform the chance constraints to deterministic constraints with only continuous variables,avoiding the large-scale MIP problem caused by *** results demonstrate that PSAA has significant advantages in solution accuracy and efficiency compared with other existing methods including traditional SAA,SAA with improved big-M,SAA with Latin hypercube sampling(LHS),and the multi-stage robust optimization methods.
Increasing penetration levels of renewables have transformed how power systems are operated. High levels of uncertainty in production make it increasingly difficulty to guarantee operational feasibility;instead, const...
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Increasing penetration levels of renewables have transformed how power systems are operated. High levels of uncertainty in production make it increasingly difficulty to guarantee operational feasibility;instead, constraints may only be satisfied with high probability. We present a chance-constrained economic dispatch model that efficiently integrates energy storage and high renewable penetration to satisfy renewable portfolio requirements. Specifically, we require that wind energy contribute at least a prespecified proportion of the total demand and that the scheduled wind energy is deliverable with high probability. We develop an approximate partial sample average approximation (PSAA) framework to enable efficient solution of large-scale chance-constrained economic dispatch problems. Computational experiments on the IEEE-24 bus system show that the proposed PSAA approach is more accurate, closer to the prescribed satisfaction tolerance, and approximately 100 times faster than standard sampleaverageapproximation. Finally, the improved efficiency of our PSAA approach enables solution of a larger WECC-240 test system in minutes.
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