Title: Adaptive Pricing for Optimal Coordination in Networked Energy Systems with Nonsmooth Cost Functions Show Chinese title

Title: 具有非光滑成本函数的网络化能源系统中的自适应定价以实现最优协调

Abstract: Incentive-based coordination mechanisms for distributed energy consumption have shown promise in aligning individual user objectives with social welfare, especially under privacy constraints. Our prior work proposed a two-timescale adaptive pricing framework, where users respond to prices by minimizing their local cost, and the system operator iteratively updates the prices based on aggregate user responses. A key assumption was that the system cost need to smoothly depend on the aggregate of the user demands. In this paper, we relax this assumption by considering the more realistic model of where the cost are determined by solving a DCOPF problem with constraints. We present a generalization of the pricing update rule that leverages the generalized gradients of the system cost function, which may be nonsmooth due to the structure of DCOPF. We prove that the resulting dynamic system converges to a unique equilibrium, which solves the social welfare optimization problem. Our theoretical results provide guarantees on convergence and stability using tools from nonsmooth analysis and Lyapunov theory. Numerical simulations on networked energy systems illustrate the effectiveness and robustness of the proposed scheme. Show Chinese abstract

Abstract: 基于激励的分布式能源消费协调机制在特别是在隐私约束下，在使单个用户目标与社会福利对齐方面显示出前景。 我们的先前工作提出了一种双时间尺度自适应定价框架，其中用户通过最小化本地成本来响应价格，系统运营商根据用户的整体响应迭代更新价格。 一个关键假设是系统成本需要平滑地依赖于用户需求的总和。 在本文中，我们通过考虑更现实的成本由解决具有约束的DCOPF问题确定的模型来放松这一假设。 我们提出了定价更新规则的一个广义形式，该规则利用了系统成本函数的广义梯度，由于DCOPF的结构，该函数可能是非光滑的。 我们证明了由此产生的动态系统收敛到一个唯一的平衡点，该平衡点解决了社会福利优化问题。 我们的理论结果使用非光滑分析和Lyapunov理论工具提供了关于收敛性和稳定性的保证。 在网络化能源系统上的数值模拟展示了所提出的方案的有效性和鲁棒性。