The increasing share of volatile renewable electricity production motivates demand response. Substantial potential for demand response is offered by flexible processes and their local multi-energy supply systems. Simultaneous optimization of their schedules can exploit the demand response potential, but leads to numerically challenging problems for nonlinear dynamic processes. In this paper, we propose to capture process dynamics using dynamic ramping constraints. In contrast to traditional static ramping constraints, dynamic ramping constraints are a function of the process state and can capture high-order dynamics. We derive dynamic ramping constraints rigorously for the case of single-input single-output processes that are exactly input-state linearizable. The resulting scheduling problem can be efficiently solved as a mixed-integer linear program. In a case study, we study two flexible reactors and a multi-energy system. The proper representation of process dynamics by dynamic ramping allows for faster transitions compared to static ramping constraints and thus higher economic benefits of demand response. The proposed dynamic ramping approach is sufficiently fast for application in online optimization.

不稳定的可再生电力生产份额的增加推动了需求响应。灵活的流程及其本地多能源供应系统提供了巨大的需求响应潜力。同时优化他们的时间表可以利用需求响应潜力，但会导致非线性动态过程的数值具有挑战性的问题。在本文中，我们建议使用动态斜坡约束来捕获过程动态。与传统的静态斜坡约束相比，动态斜坡约束是过程状态的函数，可以捕获高阶动态。对于完全可线性化输入状态的单输入单输出过程，我们严格推导出动态斜坡约束。由此产生的调度问题可以作为混合整数线性规划有效地解决。在一个案例研究中，我们研究了两个柔性反应堆和一个多能源系统。与静态斜坡约束相比，动态斜坡对过程动态的正确表示允许更快的转换，因此需求响应的经济效益更高。所提出的动态斜坡方法对于在线优化中的应用来说足够快。