Dynamic Ramping for Demand Response of Processes and Energy Systems based on Exact Linearization

Abstract

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.

Figures (9)

• Figure 1: Simultaneous scheduling of a flexible production process and its local multi-energy system reacts to variable electricity prices using the demand response potential of the process by modulating the production rate $\rho$ and thus process energy consumption.
• Figure 2: Constraints for ramping degree of freedom $\nu$ as function of production rate $\rho$. True nonlinear limits in comparison to static ramping limits, linear limits, and piece-wise affine (PWA) limits for an illustrative case with first-order dynamics. For first-order dynamics, the transformed state vector $\boldsymbol{\varphi}$ is of dimension one and equal to the production rate $\rho$. Consequently, the limits on the ramping degree of freedom $\nu$ only depend on $\rho$.
• Figure 3: Case Study: Simultaneous scheduling of two continuous stirred tank reactors (CSTRs) with variable production rates $\rho_1$ and $\rho_2$, a boiler, and a combined heat and power plant (CHP). The waste heat of the two CSTRs, $Q_{wh1}$ and $Q_{wh2}$, is used to partly satisfy a non-flexible heat demand. Additionally, a non-flexible electricity demand has to be fulfilled.
• Figure 4: True nonlinear limits and linear dynamic ramping constraints for the non-jacketed CSTR 1. Static ramping constraints are indicated for comparison.
• Figure 5: True nonlinear limits (TNL) and corresponding linear dynamic ramping constraints (DRC) for the jacketed CSTR 2. The limits are functions of the production rate $\rho$ and its first derivative $\dot{\rho}$. In this figure, the limits are given depending on $\dot{\rho}$ for 3 different values of $\rho$.