Approximation of Weymouth Equation Using Mathematical Programs with Complementarity Constraints for Natural Gas Transportation

Abstract

Environmental demands around the world have led to an increasing interest in natural gas due to its advantages over other hydrocarbons used in power generation, which has led to the search for the best way to solve the transportation problem associated with this resource. In this paper, we propose a methodology that allows us to address the non-convexity related to the Weymouth equation that makes the optimization problem so difficult. The mentioned equation, in charge of relating the flows through the pipelines and the pressures at the nodes, is characterized by having a discontinuity in the form of a sign function. The proposal of this work is based on the use of Mathematical Programs with Complementarity Constraints (MPCC) to achieve a good approximation since it allows make certain continuous variables to behave as discrete variables in such a way that it is possible to avoid having to pose a mixed integer programming problem and this one. This approach showed a smaller approximation error (or at least equal) with other approximations used in the state of the art when tested in three different networks: one of 8 nodes, one of 48 nodes tested in other related works, and one of 63 nodes representing the Colombian natural gas transportation system.

Keywords

• natural gas
• Weymouth equation
• discontinuous functions
• MPCC