Abstract
Due to the increasing uncertainty brought about by renewable energy, conventional deterministic dispatch approaches have not been very applicative. This paper investigates a nested sparse grid-based stochastic collocation method (NS-SCM) as a possible solution for stochastic economic dispatch (SED) problems. The SCM was used to simplify the scenario-based optimization model; specifically, a finite-order expansion using the generalized polynomial chaos (gPC) theory was applied to approximate random variables as a more facile approach compared to using complicated optimization models. Furthermore, a nested sparse grid-based approach was adopted to reduce the number of collocation points while still satisfying the nested property, thereby alleviating and effectively eliminating the need for computation. The proposed approach can be directly applied to the SED optimization problem. Lastly, simulations on the modified IEEE 39-bus system and a practical 1009-bus power system were provided to verify the accuracy, effectiveness, and practicality of the proposed algorithm.
Highlights
The application of renewable energy sources (RES), especially wind farm and photovoltaic (PV) power generation stations, have increased in last five years [1]
The stochastic economic dispatch (SED) model based on the stochastic problems is expressed as follows: u −→ξ = g x, −→ξ where x defines the vector of the deterministic variables, −→ξ is the deviation of the random parameter, and u −→ξ defines the vector of the output random variables, which can be approximated by applying the optimal generalized polynomial chaos (gPC) through finite-order expansion
Fully considering the uncertainty of RES, in this paper, we proposed the nested sparse grid-based stochastic collocation method (NS-Stochastic Collocation methods (SCM)) to simplify the scenario-based SED model, which improved the computational efficiency with minimal loss of accuracy
Summary
The application of renewable energy sources (RES), especially wind farm and photovoltaic (PV) power generation stations, have increased in last five years [1]. The Stochastic Galerkin (SGM) and Stochastic Collocation methods (SCM) were recently proposed and utilized for the resolution of stochastic problems [28], [29] Both SGM and SCM generate uncertainty analysis results based on the application of the generalized polynomial chaos (gPC) expansion theory on a polynomial of random variables. Bai et al proposed a dimension-reduced sparse grid strategy to improve the computational efficiency of the SCM [31] Both Tang et al and Bai et al presented SCM-derived algorithms that were designed to solve this type of problem without an optimization objective, their proposed methods cannot be directly applied to optimization problems such as the SED [26], [31].
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