A mathematical programming framework for energy planning in services’ sector buildings under uncertainty in load demand: The case of a hospital in Athens

The aim of this paper is to provide an integrated modeling and optimization framework for energy planning in large consumers of the services’ sector based on mathematical programming. The power demand is vaguely known and the underlying uncertainty is modeled using elements from fuzzy set theory. The defined fuzzy programming model is subsequently transformed to an equivalent multi-objective problem, where the minimization of cost and the maximization of demand satisfaction are the objective functions. The Pareto optimal solutions of this problem are obtained using a novel version of the ε-constraint method and represent the possibly optimal solutions of the original problem under uncertainty. In the present case, in order to select the most preferred Pareto optimal solution, the minimax regret criterion is properly used to indicate the preferred configuration of the system (i.e. the size of the installed units) given the load uncertainty. Furthermore, the paper proposes a model reduction technique that can be used in similar cases and further examines its effect in the final results. The above methodology is applied to the energy rehabilitation of a hospital in the Athens area. The technologies under consideration include a combined heat and power unit for providing power and heat, an absorption unit and/or a compression unit for providing cooling load. The obtained results demonstrate that, increasing the degree of demand satisfaction, the total annual cost increases almost linearly. Although data compression allows obtaining realistic results, the size of the proposed units might be slightly changed.