A convex optimization and iterative solution based method for optimal power-gas flow considering power and gas losses

Abstract

Optimal power-gas flow (OPGF) is an important problem for the coordinated operation of an integrated electricity and natural gas system (IEGS). However, it is a challenge to solve the OPGF problem due to its non-convexity. This paper proposes a new OPGF method considering both power losses and gas losses based on convex optimization to balance modeling accuracy and tractability. As for power system modeling, a DC power flow model with power losses embedded as equivalent loads is used to approximate the nonlinear AC power flow model. As for gas system modeling, (1) a second-order cone (SOC) relaxation method is proposed to address the non-convex Weymouth equations, and the tightness of the SOC relaxation is guaranteed by introducing a penalty term and an iterative tightening procedure based on the convex envelope. (2) Gas losses of compressors are also modeled as equivalent loads and two more penalty terms on compressors are introduced to improve the accuracy of gas loss modeling. The OPGF problem is finally formulated as a mixed-integer convex programming model with unknown equivalent loads, and an iterative solution approach is then developed to solve the problem. Numerical results validate the effectiveness of the proposed OPGF method.