A mixed integer approach for time-dependent gas network optimization

A gas network consists of pipes to transport the gas from the suppliers to the consumers. Due to friction with the pipe walls, gas pressure gets lost. Compressors compensate this pressure loss at the cost of consuming fuel gas. The aim of gas network optimization is to minimize the fuel gas consumption of the compressors in such a way that the contracts with consumers and suppliers are fulfilled. This problem leads to a very complex mixed integer nonlinear optimization problem. We present a linear approach which concentrates on time-dependent and discrete aspects. The nonlinearities are approximated by piece-wise linear functions using the concept of SOS (special ordered sets) constraints. We develop a branch-and-cut algorithm which has the potential to guarantee global optimality of the linearized problem where the nonlinearities are approximated within a given accuracy. We include an adequate handling of the SOS conditions and a separation algorithm for switching processes of compressors. A simulated annealing algorithm is included yielding feasible solutions. Our computational results show the success of our approach in this challenging field of gas network optimization.