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Convex Relaxation of Dynamic Optimal Power and Gas Flow

The dynamic model of natural gas network includes a large number of time-dependent variables, which intensifies the non convexity and nonlinearity of dynamic optimal power and gas flow problem. This paper develops a novel mixed-integer linear programming (MILP) model based on the convex relaxation to improve the computational efficiency and solution quality of dynamic optimal power and gas flow (OPGF) problem. The original partial differential equations that govern the dynamic gas flow are discretized by the fully implicit finite difference method in both time and space. Nonconvex quadratic constraints are transformed into bilinear constraints, which are further converted to a set of linear constraints based on convex relaxation techniques. By introducing disaggregated variables and binary variables, a bound tightening algorithm is proposed to decrease the relaxation errors of convex model. Coupling the established simplified dynamic gas flow (SDGF) model and DC power flow model, the OPGF problem can be cast into a MILP model which can be solved efficiently. Numerical experiments based on a test system verify the effectiveness of the proposed dynamic OPGF model.