Exact Time-Varying Turnpikes for Dynamic Operation of District Heating Networks

TL;DR

This paper investigates the role of time-varying turnpikes in optimizing district heating networks, deriving conditions for their existence and demonstrating their implications for control design.

Contribution

It introduces a novel analysis of time-varying turnpikes in DHNs, providing conditions for their existence and linking them to strict dissipativity.

Findings

Derived conditions for unique time-varying singular arcs.

Provided closed-form expressions for the time-varying turnpike.

Showed that exact time-varying turnpikes imply strict dissipativity.

Abstract

District heating networks (DHNs) are crucial for decarbonizing the heating sector. Yet, their efficient and reliable operation requires the coordination of multiple heat producers and the consideration of future demands. Predictive and optimization-based control is commonly used to address this task, but existing results for DHNs do not account for time-varying problem aspects. Since the turnpike phenomenon can serve as a basis for model predictive control design and analysis, this paper examines its role in DHN optimization by analyzing the underlying optimal control problem with time-varying prices and demands. That is, we derive conditions for the existence of a unique time-varying singular arc, which constitutes the time varying turnpike, and we provide its closed-form expression. Additionally, we present converse turnpike results showing a exact time-varying case implies strict dissipativity of the optimal control problem. A numerical example illustrates our findings.