基于伯恩斯坦-伽辽金优化的含连续时间热动力学的热电联合系统调度
Integrated Heat and Power System Scheduling with Continuous-Time Thermal Dynamics via Bernstein-Galerkin Optimization
AI总结：
本文针对现有热电联合调度模型无法准确表征热动力学的问题，提出纳入连续时间热动力学的调度框架，通过伯恩斯坦-伽辽金变换实现高效优化，提升了调度的准确性与经济性。
AI中文摘要：
区域供热网络（DHN）与电力系统的协同调度可通过利用热惯性提升运行灵活性并降低成本。现有多数模型采用简化的离散时间DHN模型，无法充分表征连续时空热动力学，易导致灵活性估计偏差与调度方案次优。本文提出一种明确纳入DHN连续时间热动力学的热电联合系统调度框架，开发伯恩斯坦-伽辽金变换方法将偏微分热动力学约束转化为有限代数约束，在保持动态保真度的同时实现可处理的优化，将原无限维变分问题转化为可通过优化求解器求解的有限维系数优化问题。与传统离散化方法相比，该方法对热动力学的表征更准确，所得调度方案的经济性能与可靠性均有所提升。
英文摘要：
Coordinated scheduling of district heating networks (DHNs) and electric power systems can improve operational flexibility and reduce costs by exploiting thermal inertia. Most existing formulations rely on simplified discrete-time DHN models, which may inadequately represent continuous spatiotemporal thermal dynamics and can lead to biased flexibility estimation and suboptimal schedules. In this paper, an integrated heat and power system scheduling framework that explicitly incorporates the continuous-time thermal dynamics of DHNs is proposed. A Bernstein-Galerkin transform method is developed to convert the underlying partial-differential thermal-dynamics constraints into a finite set of algebraic constraints, enabling tractable optimization while retaining dynamic fidelity. The resulting model transforms the original infinite-dimensional variational problem into a finite-dimensional coefficient optimization that can be solved using optimization solvers. Compared with conventional discretization approaches, the proposed method provides a more accurate representation of thermal dynamics and yields schedules with improved economic performance and reliability.
