In this paper, based on differential inclusions and the saddle point dynamics, a novel second-order continuous-time algorithm is proposed to solve the optimal resource allocation problem in power systems. The considered cost function is the sum of all local cost functions with a set of affine equality demand constraints and an inequality constraint on generating capacity of the generator. In virtue of nonsmooth analysis, geometric graph theory, and Lyapunov stability theory, all generators achieve consensus on the Lagrange multipliers associated with a set of affine equality constraints while the proposed algorithm converges exponentially to the optimal solution of the resource allocation problem starting from any initial states over an undirected and connected graph. Moreover, the obtained results can be further extended to the optimal resource allocation problem in case of switching communication topologies. Finally, two numerical examples involving a smart grid system composed of five generators and the IEEE 30-bus system demonstrate the effectiveness and the performance of the theoretical results.

中文翻译：

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电力系统资源优化配置的二阶连续时间算法


本文基于微分包含和鞍点动力学，提出了一种新的二阶连续时间算法来解决电力系统中的最优资源分配问题。所考虑的成本函数是具有一组仿射等式需求约束和发电机发电能力不等式约束的所有局部成本函数的总和。凭借非光滑分析、几何图论和李亚普诺夫稳定性理论，所有生成器在与一组仿射等式约束相关的拉格朗日乘子上达成共识，同时所提出的算法从任何初始值开始指数收敛到资源分配问题的最优解无向连通图上的状态。此外，所获得的结果可以进一步扩展到切换通信拓扑情况下的最优资源分配问题。最后，涉及由五台发电机组成的智能电网系统和IEEE 30总线系统的两个数值例子证明了理论结果的有效性和性能。