复杂能源网络的时延分布式均衡动力学

Distributed Equilibrium Dynamics with Delayed Information in Complex Energy Networks

摘要: 针对复杂能源网络中局部决策、物理邻接作用与信息时延并存的问题，建立以节点可控有功功率为策略的分布式能源博弈模型，并采用直流潮流校核均衡对应的节点相角和线路潮流。物理图与通信图分开建模，以有界端到端信息年龄描述多跳传播造成的状态陈旧，在此基础上构造分布式近端最佳响应算法。在紧凸性与连续性的条件下均衡存在，强单调性保证其唯一性，块响应矩阵给出有界时延下的充分收缩条件。仿真结果表明，算法可在所设条件下收敛到同一均衡；信息年龄增大会减慢收敛，当增强供需失配惩罚时，可减小稳态失配，会压缩理论收缩裕度。结果说明，信息新鲜度和供需调节强度共同影响均衡的形成过程。

Abstract: This paper studies distributed equilibrium formation in complex energy networks with decentralized decisions, physical adjacency, and delayed information. Each node chooses its controllable active-power injection in a noncooperative game whose local cost includes operating cost, a soft system-wide supply-demand mismatch penalty, and a penalty on power differences between physically adjacent nodes. The equilibrium is checked separately with a lossless DC power-flow model. The physical graph and the directed communication graph are modeled independently, while a bounded end-to-end information age represents state staleness caused by multihop communication. Based on this information model, each node performs a proximal best response using delayed source states. Existence follows from continuity on the compact convex strategy set, and strong monotonicity guarantees uniqueness; a complete response-sensitivity matrix provides a sufficient contraction condition under bounded information age. Numerical tests on a six-node network show that the node strategies converge to the same equilibrium under the stated conditions. Larger information age slows convergence. Increasing the supply-demand mismatch penalty reduces the steady mismatch over the tested range, but also narrows the theoretical contraction margin. These results show that information freshness and supply-demand regulation jointly shape the convergence of the distributed equilibrium process in the considered model.