Abstract
This paper proposes a distance-based distributionally robust energy and reserve (DB-DRER) dispatch model via Kullback–Leibler (KL) divergence, considering the volatile of renewable energy generation. Firstly, a two-stage optimization model is formulated to minimize the expected total cost of energy and reserve (ER) dispatch. Then, KL divergence is adopted to establish the ambiguity set. Distinguished from conventional robust optimization methodology, the volatile output of renewable power generation is assumed to follow the unknown probability distribution that is restricted in the ambiguity set. DB-DRER aims at minimizing the expected total cost in the worst-case probability distributions of renewables. Combining with the designed empirical distribution function, the proposed DB-DRER model can be reformulated into a mixed integer nonlinear programming (MINLP) problem. Furthermore, using the generalized Benders decomposition, a decomposition method is proposed and sample average approximation (SAA) method is applied to solve this problem. Finally, simulation result of the proposed method is compared with those of stochastic optimization and conventional robust optimization methods on the 6-bus system and IEEE 118-bus system, which demonstrates the effectiveness and advantages of the method proposed.
Highlights
During the past decades, the issues of fossil fuel depletion and climate change are becoming more and more grievous
Proposed a data-driven distributionally robust framework for unit commitment based on Wasserstein metric considering the wind power generation forecasting errors, and results showed that the proposed method could immunize the solutions against the worst-case distribution in the ambiguity set
The most basic approach to construct an ambiguity set is to define a confidence interval for uncertainty variable, (e.g., 95% can be set as the confidence level value), but it is too simple to describe the correlation between variables and has strong conservation
Summary
The issues of fossil fuel depletion and climate change are becoming more and more grievous. Reference [19] studied the economic dispatch problem of power systems under the distribution information of random variable as ambiguous, the ambiguity set was constructed as an ellipsoidal by using the mean and the covariance matrix, and conditional value-at-risk management is used to reformulate the proposed DRO model into a solvable convex optimization. By using an adjustable uncertainty set, [26] studied the energy and reserve scheduling problem by considering the wind power uncertainty, and a two-stage data-driven DRO model was proposed, the ambiguity was defined as Wasserstein balls which contains all the possible probability distributions. Proposed a data-driven distributionally robust framework for unit commitment based on Wasserstein metric considering the wind power generation forecasting errors, and results showed that the proposed method could immunize the solutions against the worst-case distribution in the ambiguity set.
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