Certificates of infeasibility via nonsmooth optimization
We consider an optimization problem of energy supply networks based on multiple-energy carriers for urban family houses by taking into account new energy supply concepts. Under the background of growing penetration of micro energy-cogeneration technologies, our goal is to design hybrid energy supply networks for providing electricity and heat, especially, we are interested in developing an optimal strategy to simultaneously determine the transmission lines of the underlying energy carriers as well as the distribution of micro energy technologies, which route the energy carrier flows. We propose a mixed-integer nonlinear programming (minlp) model to investigate the problem. However, due to its high complexity and large size of practical instances, it is challenging to compute optimal solutions. We apply piecewise linear approximation techniques and specific convexification structures to improve the solution process based on the branch-and-bound method. Numerical tests based on simulated data are presented to demonstrate the capability of our approaches.