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Mathematical Problems in Engineering
Volume 2015, Article ID 135673, 8 pages
Research Article

Stochastic Optimal Dispatch of Virtual Power Plant considering Correlation of Distributed Generations

1School of Electrical Engineering, Southeast University, Nanjing 210096, China
2Department of Mathematics and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China
3Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 22 October 2014; Revised 3 March 2015; Accepted 5 March 2015

Academic Editor: Hector Puebla

Copyright © 2015 Jie Yu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Virtual power plant (VPP) is an aggregation of multiple distributed generations, energy storage, and controllable loads. Affected by natural conditions, the uncontrollable distributed generations within VPP, such as wind and photovoltaic generations, are extremely random and relative. Considering the randomness and its correlation of uncontrollable distributed generations, this paper constructs the chance constraints stochastic optimal dispatch of VPP including stochastic variables and its random correlation. The probability distributions of independent wind and photovoltaic generations are described by empirical distribution functions, and their joint probability density model is established by Frank-copula function. And then, sample average approximation (SAA) is applied to convert the chance constrained stochastic optimization model into a deterministic optimization model. Simulation cases are calculated based on the AIMMS. Simulation results of this paper mathematic model are compared with the results of deterministic optimization model without stochastic variables and stochastic optimization considering stochastic variables but not random correlation. Furthermore, this paper analyzes how SAA sampling frequency and the confidence level influence the results of stochastic optimization. The numerical example results show the effectiveness of the stochastic optimal dispatch of VPP considering the randomness and its correlations of distributed generations.