(737a) Optimal Scheduling of an Energy System for District Heating

The raising share of renewable electricity generation leading to more volatile power markets is a major challenge for combined heat and power (CHP) plants. Traditional CHP plant operation is heat driven and hence CHP plants must provide heat when it is needed without considering if the produced electricity can be sold profitably. If thermal storage is available, a more flexible operation is possible. Besides heat storage tanks at supply (CHP plants) and demand points (city districts), the pipeline system used for carrying the hot water in the heating grid can also be used for storage. However, finding an optimal operating schedule for CHP plants considering pipeline dynamics is not trivial, as the controllable variables are highly interconnected.

The dynamics of temperature variation associated with the flow of hot water cause time delays that range from a few minutes to several hours, which are comparable with the schedules in power systems operation. A large portion of past publications relies on the node method (Benonysson et al., 1995), where time delays in the grid are calculated as transport delays influenced by mass flow or velocity. Li et al. (2016a) defined these time delays as integer variables in a combined heat and power dispatch model that generates large-scale mixed-integer nonlinear programming (MINLP) problems.

Also working with a system in Northeastern China, Zheng et al. (2018) consider a constant circulation flow in all pipes, with the CHP supply temperature changing with the thermal demand. This allows to replace the nonlinear programming (NLP) formulation that accounts for the thermal inertia of the network with a linear programming (LP) formulation. However, this simplification is not feasible for most district heating systems, where mass flow is controlled by consumers according to current demand and supply temperature. The outputs of the model are optimized supply and return temperatures from/to the heat source over a 24-h scheduling horizon.

While the modelling of time delays in pipes has been identified as a major challenge in the context of the optimal operation of district heating systems (Li et al., 2016b), one can benefit from important developments that have occurred in the area of pipeline scheduling of refined petroleum products (liquids).

In order to determine the time taken for a product, injected at an input node, to reach an output node, researchers started considering a discrete volume representation of the pipeline coupled with a discrete-time representation of the scheduling horizon (Rejowski and Pinto, 2004). The current state-of-the-art features continuous representations in both time and volume that can handle arbitrary network layouts and reversible mass flows (Castro, 2017), following the seminal work of Cafaro and Cerdá (2004). The most relevant aspect for district heating systems, is that variable processing rates can be handled efficiently by mixed-integer linear programming (MILP) formulations without defining the rates as explicit model variables.

In this paper we consider a simple topology, with one CHP plant and one District connected by a pipeline. The main novelty concerns the definition of a discrete set of supply temperatures for the CHP plant, with the optimization selecting the most convenient for a particular time interval. Batches of hot water at different temperatures will move through the pipeline one after the other (plug flow) at a rate also to be decided by the optimization, until reaching the District. The discrete set of temperatures, together with location variables, replaces the traditional approach of modelling temperatures as continuous variables, at different spatial grid points in the network. The other novelty is related to the use of a hybrid discrete-continuous time representation. It combines the advantages of the discrete-time formulation for handling hourly-changing electricity prices and heat demands, and of the continuous-time formulation for handling continuous processing rates.

The performance of the formulation is illustrated with a motivating example inspired by a district heating system in Germany. The results show that solutions with an optimality gap of 0.03% can be obtained in under 10 minutes of computational time, which is quite reasonable for a day-ahead decision-making tool. Compared to a closely-related LP formulation that neglects pipeline dynamics, we obtained a benefit of 0.5 % in revenue from electricity sales. This value rises to 2.1 % if the pipeline volume is increased by a factor of 2.6. We also performed a sensitivity analysis to evaluate the impact of the initial temperature on solution quality, helping us to understand why low initial temperatures may lead to an infeasible problem.

Acknowledgments: Financial support from Fundação para a Ciência e Tecnologia (FCT) through projects IF/00781/2013 andUID/MAT/04561/2019 as well as by the German Federal Ministry of Education and Research (BMBF) within the Kopernikus Project ENSURE ‘New ENergy grid StructURes for the German Energiewende’ and ABB Corporate Research.

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