Gas Network Optimization: A comparison of Piecewise Linear Models

Gas network optimization manages the gas transport by minimizing operating costs and fulfilling contracts between consumers and suppliers. This is an NPhard problem governed by non-convex and nonlinear gas transport functions that can be modeled by mixed integer linear programming (MILP) techniques. Under these methods, piecewise linear functions describe nonlinearities and binary variables avoid local optima due to non-convexities. This paper compares theoretically and computationally basic and advanced MILP formulations for the gas network optimization in dynamic or in steady-state conditions. Case studies are carried out to compare the performance of each MILP formulation for different network configurations, sizes and levels of complexity. In addition, since the accuracy of linear approximations significantly depends on the number and location of linear segments, this paper also proposes a goal programming method to construct a-priori the piecewise linear functions. This method is based on the minimization of the mean squared error of each approximation subject to predefined error goals.