A 0-1 linear relaxation and stochastic approximation method for real-time pricing in a smart grid with non-convex constraints

In this article, real-time pricing (RTP) for a smart grid with complicated non-convex and/or non-smooth constraints is explored. First, piecewise linear functions are adopted to approximate any kinds of utility function and RTP is formulated into bilevel non-convex programming. Then, a 0-1 relaxatio...

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Bibliographic Details
Published in:Engineering optimization 2024-12, Vol.56 (12), p.2131-2147
Main Authors: Tao, Li, Wang, Zongyao, Su, Xia
Format: Article
Language:English
Subjects:
0-1 relaxation method
Approximation
Constraints
Convexity
distributed simultaneous perturbation stochastic approximation
Integer programming
Linear functions
Linear programming
Mixed integer
mixed integer linear programming
Real time
real-time pricing
Relaxation method (mathematics)
Smart grid
Time of use electricity pricing
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Summary:In this article, real-time pricing (RTP) for a smart grid with complicated non-convex and/or non-smooth constraints is explored. First, piecewise linear functions are adopted to approximate any kinds of utility function and RTP is formulated into bilevel non-convex programming. Then, a 0-1 relaxation method is used to linearize sparse constraints and piecewise linear utility functions, to obtain mixed integer linear programming. Finally, a distributed simultaneous perturbation stochastic approximation (DSPSA) method is designed to solve the bilevel non-convex programming. The RTP strategy is generalizable because sparse constraints and non-differentiable and/or non-concave utility functions are widespread in practice, and the piecewise linear functions approximation method is applicable to all kinds of utility function, not just to non-smooth and/or non-concave utility functions. In addition, the 0-1 linear relaxation and stochastic approximation method make the bilevel non-convex programming easily solvable by DSPSA, which converges rapidly while maintaining the high accuracy of solutions.
ISSN:0305-215X
1029-0273
DOI:10.1080/0305215X.2024.2302892