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This paper addresses the data-based modelling and optimal control of DistrictHeating Systems (DHSs). Physical models of such large-scale networked systemsare governed by complex nonlinear equations that require a large amount ofparameters, leading to potential computational issues in optimizing theiroperation. A novel methodology is hence proposed, exploiting operational dataand available physical knowledge to attain accurate and computationallyefficient DHSs dynamic models. The proposed idea consists in leveragingmultiple Recurrent Neural Networks (RNNs) and in embedding the physicaltopology of the DHS network in their interconnections. With respect to standardRNN approaches, the resulting modelling methodology, denoted asPhysics-Informed RNN (PI-RNN), enables to achieve faster training proceduresand higher modelling accuracy, even when reduced-dimension models areexploited. The developed PI-RNN modelling technique paves the way for thedesign of a Nonlinear Model Predictive Control (NMPC) regulation strategy,enabling, with limited computational time, to minimize production costs, toincrease system efficiency and to respect operative constraints over the wholeDHS network. The proposed methods are tested in simulation on a DHS benchmarkreferenced in the literature, showing promising results from the modelling andcontrol perspective.

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