Convex Relaxation of Non-Isothermal Optimal Power and Gas Flow

Conventional convex relaxation of the OPGF model relies heavily on the isothermal assumption, which greatly sacrifices the solution accuracy. This paper develops a novel convex non-isothermal optimal power-gas flow (NI-OPGF) model which avoids the assumption of constant gas temperature to effectively improve the model optimality and computational efficiency. A simplified pipeline thermal (SPT) model with only bilinear constraints is established to describe the heat transfer of gas, which significantly decreases the mathematical complexity of the problem. The implicit difference method is adopted to transform the original gas flow constraints in the form of partial differential into algebraic equations. To address the nonconvexity of the original NI-OPGF problem, cubic and bilinear constraints appearing in the non-isothermal gas flow model are relaxed into a group of linear constraints by convex envelopes. The effectiveness of the proposed method is verified by systematical numerical experiments on a test system.