Modeling and control of heat networks with storage: The single-producer multiple-consumer case

In heat networks, energy storage is a viable approach to balance demand and supply. In such a network, a heat carrier is used in the form of water, where heat is injected and extracted through heat exchangers. The network can transport and store heated water in stratification tanks to shift loads in time. A setup is considered, which includes a single producer with a storage tank and multiple consumers. For this topology, a model is derived consisting of differential equations that describe temperature and volume dynamics. We design a controller such that both the volume and the temperature converge to specified setpoints. The extracted heat that is demanded is unknown, while the flow rates passing through the heat exchanger of the consumers are set to a measurable constant. We regard both the flow rates and the heat injection of the producer as the control input. The controller uses techniques from output regulation, such that the prescribed setpoints are reached while satisfying the demand. We prove that under the proposed controller all solutions are bounded and convergence to the desired setpoints. Finally a case study is discussed and numerical simulations are provided.