Abstract: The resource allocation problem in smart grids has gained attention in practical applications, with the goal of minimizing total system generation costs while meeting various constraints. To address capacity safety constraints and initial input limitations and to ensure supply-demand balance in distributed microgrid resource allocation, this study investigates a resource allocation problem with coupled equality and local inequality constraints. A distributed optimization algorithm independent of the initial system conditions is proposed to achieve optimal resource allocation across multiple microgrid nodes. The algorithm is based on penalty functions and the differential inclusion theory. It constructs suitable penalty parameters to ensure that the state variables of all agents enter and remain within the feasible region defined by the inequality constraints in finite time, thus effectively addressing capacity constraints and initial input limitations. In addition, under the condition of an undirected connected network, the algorithm introduces an innovative consensus mechanism to ensure that all agents satisfy the coupled equality constraints. This enables effective resource coordination among agent nodes, achieving a balance between the power supply from generators and demand from users. An analysis using Lyapunov stability theory shows that the algorithm guarantees the convergence of agents to the optimal solution of the resource allocation problem. Compared with existing distributed algorithms, the proposed algorithm features a simple structure, low computational cost, flexible initial point selection, and improved privacy protection. In addition, it does not require the computation of an exact penalty parameter in advance. Finally, two simulation case studies of power systems are conducted, which validate the effectiveness of the algorithm for solving distributed microgrid resource allocation problems.

Key words: multi-agent systems, coupled equality constraints, resource allocation problem, distributed optimization algorithm, smart grid

摘要： 智能电网中的资源分配问题在实际应用中备受关注,其目标是在满足多种约束条件的前提下,实现系统总发电成本的最小化。针对分布式微电网资源分配中存在的容量安全约束、初始输入限制和供需平衡等问题,研究了一类带耦合等式约束和局部不等式约束的资源分配问题,并提出了一种不依赖系统初始条件的分布式优化算法,以实现多微电网节点的最优资源分配。该算法基于罚函数和微分包含理论,通过构造合适的惩罚参数,确保所有智能体的状态变量在有限时间内进入不等式约束的可行域并永驻其中,进而解决容量约束与初始输入受限问题。此外,在无向连通网络的条件下,该算法设计了一种新颖的共识机制,确保所有智能体都满足耦合等式约束,进而实现智能体节点间资源的有效协同分配,以平衡电厂供给与用户需求。基于李雅普诺夫稳定性理论的分析表明该算法能够确保智能体收敛至资源分配问题的最优解。与现有分布式算法相比,所提算法具有结构简单、计算量低、无需事先计算精确的惩罚参数、初始点选取灵活且利于隐私保护的特点。最后,通过两个电力系统的仿真案例验证了该算法在解决分布式微电网资源分配问题上的有效性。

关键词: 多智能体系统, 耦合等式约束, 资源分配问题, 分布式优化算法, 智能电网

CLC Number: 

• TP31