Adaptive Nonlinear Optimization of District Heating Networks Based on Model and Discretization Catalogs

TL;DR

This paper introduces an adaptive optimization algorithm for district heating networks that intelligently switches between models and discretizations to achieve accurate solutions efficiently.

Contribution

It presents a novel adaptive algorithm that dynamically selects models and discretizations for efficient, accurate optimization of district heating networks.

Findings

Achieves low computational costs with prescribed accuracy.

Solves previously unsolvable problem instances.

Proves finite termination of the adaptive algorithm.

Abstract

We propose an adaptive optimization algorithm for operating district heating networks in a stationary regime. The behavior of hot water flow in the pipe network is modeled using the incompressible Euler equations and a suitably chosen energy equation. By applying different simplifications to these equations, we derive a catalog of models. Our algorithm is based on this catalog and adaptively controls where in the network which model is used. Moreover, the granularity of the applied discretization is controlled in a similar adaptive manner. By doing so, we are able to obtain optimal solutions at low computational costs that satisfy a prescribed tolerance w.r.t. the most accurate modeling level. To adaptively control the switching between different levels and the adaptation of the discretization grids, we derive error measure formulas and a posteriori error measure estimators. Under reasonable assumptions we prove that the adaptive algorithm terminates after finitely many iterations. Our numerical results show that the algorithm is able to produce solutions for problem instances that have not been solvable before.