Physics-informed Neural Network Modelling and Predictive Control of District Heating Systems

TL;DR

This paper introduces a physics-informed RNN approach for modeling and controlling district heating systems, combining physical knowledge with data-driven methods to improve accuracy and computational efficiency for optimal operation.

Contribution

It proposes the PI-RNN methodology that embeds physical network topology into RNNs, enabling faster training and higher accuracy for DHS modeling and control.

Findings

PI-RNN achieves higher modeling accuracy than standard RNNs.

The approach enables real-time NMPC for DHS with limited computational resources.

Simulation results show effective cost reduction and system efficiency improvements.

Abstract

This paper addresses the data-based modelling and optimal control of District Heating Systems (DHSs). Physical models of such large-scale networked systems are governed by complex nonlinear equations that require a large amount of parameters, leading to potential computational issues in optimizing their operation. A novel methodology is hence proposed, exploiting operational data and available physical knowledge to attain accurate and computationally efficient DHSs dynamic models. The proposed idea consists in leveraging multiple Recurrent Neural Networks (RNNs) and in embedding the physical topology of the DHS network in their interconnections. With respect to standard RNN approaches, the resulting modelling methodology, denoted as Physics-Informed RNN (PI-RNN), enables to achieve faster training procedures and higher modelling accuracy, even when reduced-dimension models are exploited. The developed PI-RNN modelling technique paves the way for the design of a Nonlinear Model Predictive Control (NMPC) regulation strategy, enabling, with limited computational time, to minimize production costs, to increase system efficiency and to respect operative constraints over the whole DHS network. The proposed methods are tested in simulation on a DHS benchmark referenced in the literature, showing promising results from the modelling and control perspective.