Abstract
We develop a complementarity-constrained nonlinear optimization model for the time-dependent control of district heating networks. The main physical aspects of water and heat flow in these networks are governed by nonlinear and hyperbolic 1d partial differential equations. In addition, a pooling-type mixing model is required at the nodes of the network to treat the mixing of different water temperatures. This mixing model can be recast using suitable complementarity constraints. The resulting problem is a mathematical program with complementarity constraints subject to nonlinear partial differential equations describing the physics. In order to obtain a tractable problem, we apply suitable discretizations in space and time, resulting in a finite-dimensional optimization problem with complementarity constraints for which we develop a suitable reformulation with improved constraint regularity. Moreover, we propose an instantaneous control approach for the discretized problem, discuss practically relevant penalty formulations, and present preprocessing techniques that are used to simplify the mixing model at the nodes of the network. Finally, we use all these techniques to solve realistic instances. Our numerical results show the applicability of our techniques in practice.
Highlights
Many countries in the world are striving to make a transition towards an energy system that is mainly based on using energy from renewable sources like wind and solar power, complemented by classical energy sources like gas, oil, coal, or waste incineration
The only exception is Ipopt applied to the nonlinear optimization model (NLP)-based mixing model and the implicit Euler discretization, where some convergence issues occur within the instantaneous control approach
The running times required to compute the stationary solution that we use as the initial physical state are in the same orders of magnitude as a single instantaneous control approach iteration but slightly longer, since no good initial point can be used by the NLP solvers
Summary
Many countries in the world are striving to make a transition towards an energy system that is mainly based on using energy from renewable sources like wind and solar power, complemented by classical energy sources like gas, oil, coal, or waste incineration. A key to the success of this energy transition is the efficient and intelligent coupling of the energy resources and the optimal operation of the energy networks and energy storage In this direction, district heating networks play an important role, since they can be used as energy storage, e.g., to balance fluctuations at the electricity exchange. We develop a continuous optimization model for the short-term optimal operation of a district heating network. In contrast to the mid- to long-term planning problems addressed in these papers, in Sandou et al (2005), the authors consider a model predictive control (MPC) approach for computing a good operational control of a network for a given design. 5, we present problem-specific optimization techniques that enable us to solve instances on realistic networks with reasonable space and time discretizations.
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