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<p>This paper investigates the demand-side management of smart grid, with a focus on modeling a class of weighted network congestion games with resource failures (WCGRF). Firstly, a model for the WCGRF is established with a new cost function, providing a mathematical framework for analysis. What’s more, a sufficient condition is identified for the WCGRF to be classified as a potential game, and by the semi-tensor product method, the potential equation is constructed. Secondly, building upon the algebraic formulation of the WCGRF, we consider the <i>k</i>-degree stability for the game dynamics, and a criterion for detecting whether the stable strategy combination is <i>k</i>-degree stable is presented. In addition, an event-triggered controller (ETC) is proposed to guarantee that the stable profile achieves <i>k</i>-degree stability. Finally, the theoretical validity of the findings is verified through an illustrative example.</p>

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Potential characteristics and stable degree analysis of smart grid based on weighted network congestion games with resource failure

  • 期刊论文

  • 发表日期：

    2026年4月3日

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  • Yuli Han,
  • Peilian Guo,
  • Haitao Li,
  • Juhan Li

摘要

This paper investigates the demand-side management of smart grid, with a focus on modeling a class of weighted network congestion games with resource failures (WCGRF). Firstly, a model for the WCGRF is established with a new cost function, providing a mathematical framework for analysis. What’s more, a sufficient condition is identified for the WCGRF to be classified as a potential game, and by the semi-tensor product method, the potential equation is constructed. Secondly, building upon the algebraic formulation of the WCGRF, we consider the k-degree stability for the game dynamics, and a criterion for detecting whether the stable strategy combination is k-degree stable is presented. In addition, an event-triggered controller (ETC) is proposed to guarantee that the stable profile achieves k-degree stability. Finally, the theoretical validity of the findings is verified through an illustrative example.