Optimal Design and Operation of Energy Systems under Uncertainty

This paper is concerned with integrated design and operation of energy systems that are subject to significant uncertainties. The problem is cast as a two-stage stochastic nonconvex mixed-integer nonlinear program, in which the first and second stages include design decisions and operational decisions, respectively. By exploiting the separable and decomposable structure of the problem, an efficient global optimization method, called nonconvex generalized Benders decomposition (NGBD), is developed based on convex relaxation and generalized Benders decomposition. The efficiency of NGBD can be further improved via the notion of piecewise convex relaxations. The advantages of the proposed formulation and solution method are demonstrated through case studies of two industrial energy systems, a natural gas production network and a polygeneration plant. The first example shows that the stochastic programming formulation can result in better expected economic performance than the deterministic formulation, and that the NGBD solution method is dramatically more efficient than a state-of-the-art global optimization solver, especially for large numbers of scenarios. The second example further shows that the integration of piecewise convex relaxations can improve the efficiency of NGBD by at least an order of magnitude.