A multi-layer model of stratified thermal storage for MILP-based energy management systems

Both the planning and operation of complex, multi-energy systems increasingly rely on optimization. This optimization requires the use of mathematical models of the system components. The model most often used to describe thermal storage, and especially in the common mixed-integer linear program (MILP) formulation, is a simple integrator model with a linear loss term. This simple model has multiple inherent drawbacks since it cannot be applied to represent the temperature distribution inside of the storage unit. In this article, we present a novel approach based on multiple layers of variable size but fixed temperature. The model is still linear, but can be used to describe the most relevant physical phenomena: heat losses, axial heat transport, and, at least qualitatively, axial heat conduction. As an additional benefit, this model makes it possible to clearly distinguish between heat available at different temperatures and thus suitable for different applications, e.g., space heating or domestic hot water. This comes at the cost of additional binary decision variables used to model the resulting hybrid linear dynamics, requiring the use of state-of-the-art MILP solvers to solve the resulting optimization problems. The advantages of the more detailed model are demonstrated by validating it against a standard model based on partial differential equations and by showing more realistic results for a simple energy optimization problem.