Benders Decomposition-based Global Optimization for Natural Gas and Power Flow Systems
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Mixed-integer nonlinear programming (MINLP) framework has been attracting more and more attention since late last century. It can be applied to address various process systems engineering problems, such as process design and operation, large-scale system scheduling, and supply chain management [19,42]. As a class of the many such problems, integrated design and operation of large-scale energy system is to determine both the network design decisions and the flows in operation to achieve the best expected profit, while meeting the customer demands and product specifications. It is well known that these integrated design and operation problems are nonconvex MINLPs, and therefore inherently difficult for which classical gradient-based optimization methods cannot guarantee an optimal solution. Decomposition-based methods have been used to achieve global optimal solutions for nonconvex MINLPs. One of the popular decomposition-based optimization methods is Benders decomposition. Its extensions, generalized Benders decomposition (GBD)  and nonconvex generalized Benders decomposition (NGBD) , can guarantee the convergence to a global optimum with mild assumptions. In this thesis, our primary goal is to incorporate domain reduction into Benders decomposition-based global optimization methods for a class of large-scale energy systems that are MINLP problems with separable structure, which not only ensures a global optimum but also converges faster than the standard Benders decomposition-based methods and commercial global optimization solvers. The research objective is twofold. One is how to reduce the search domain and feasible region with a minimum amount of computation; to achieve this, the domain reduction methods based on convex nonlinear programming (NLP) relaxations  are extended to Benders decomposition-based methods. The other is customization of decomposition-based methods for large-scale energy systems; to demonstrate this, an integrated design and operation of natural gas production network problem that addresses gas flows, pressures and uncertainties is proposed with multi-loop NGBD, a customized Benders decomposition-based method that is faster than the regular method by at least an order of magnitude.