Mixed-Integer Conic Formulation of Unit Commitment with Stochastic Wind Power

Due to the high randomness and volatility of renewable energy sources such as wind energy, the traditional thermal unit commitment (UC) model is no longer applicable. In this paper, in order to reduce the possible negative effects of an inaccurate wind energy forecast, the chance-constrained program...

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Published in:Mathematics (Basel) Vol. 11; no. 2; p. 346
Main Authors: Zheng, Haiyan, Huang, Liying, Quan, Ran
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.01.2023
Subjects:
Alternative energy sources
Approximation
chance-constrained programming
Constraints
Food science
Generators
Linear programming
Mathematical models
Mixed integer
mixed-integer second-order conic programming
Optimization
Quadratic programming
Random variables
Randomness
Renewable energy sources
Renewable resources
sample average approximation
Software
stochastic wind power
Unit commitment
Wind effects
Wind power
Wind power generation
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary:Due to the high randomness and volatility of renewable energy sources such as wind energy, the traditional thermal unit commitment (UC) model is no longer applicable. In this paper, in order to reduce the possible negative effects of an inaccurate wind energy forecast, the chance-constrained programming (CCP) method is used to study the UC problem with uncertainty wind power generation, and chance constraints such as power balance and spinning reserve are satisfied with a predetermined probability. In order to effectively solve the CCP problem, first, we used the sample average approximation (SAA) method to transform the chance constraints into deterministic constraints and to obtain a mixed-integer quadratic programming (MIQP) model. Then, the quadratic terms were incorporated into the constraints by introducing some auxiliary variables, and some second-order cone constraints were formed by combining them with the output characteristics of thermal unit; therefore, a tighter mixed-integer second-order cone programming (MISOCP) formulation was obtained. Finally, we applied this method to some systems including 10 to 100 thermal units and 1 to 2 wind units, and we invoked MOSEK in MATLAB to solve the MISOCP formulation. The numerical results obtained within 24 h confirm that not only is the MISOCP formulation a successful reformulation that can achieve better suboptimal solutions, but it is also a suitable method for solving the large-scale uncertain UC problem. In addition, for systems of up to 40 units within 24 h that do not consider wind power and pollution emissions, the numerical results were compared with those of previously published methods, showing that the MISOCP formulation is very promising, given its excellent performance.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math11020346