1. A 0–1 linear relaxation and stochastic approximation method for real-time pricing in a smart grid with non-convex constraints.
- Author
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Tao, Li, Wang, Zongyao, and Su, Xia
- Subjects
- *
NONCONVEX programming , *SIMULATED annealing , *PIECEWISE linear approximation , *STOCHASTIC approximation , *LINEAR programming , *BILEVEL programming - Abstract
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. [ABSTRACT FROM AUTHOR] more...
- Published
- 2024
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