Convex Optimization Method for Affine Arithmetic-based Optimal Power-Gas Flow under Wind Power Uncertainty

As wind power develops by leaps and bounds, its uncertainty has posed huge challenges for operational planning for integrated electricity-gas system (IEGS). An approach based on affine arithmetic (AA) for optimal power-gas flow (OPGF) considering uncertainty of wind power is proposed. Based on convex envelope, AA-based OPGF model is developed without non-affine operations. Uncertain wind power is treated by affine form keeping track of relationships between uncertain variables. By introducing AA theory, AA-based OPGF model can be converted into deterministic multi-objective problem. Then a tightening convex envelope algorithm is employed to enhance solution feasibility of AA-based OPGF. Numerical results demonstrate the effectiveness of the proposed AA-based method compared with Monte Carlo method. In addition, the transmission tracks of uncertain factors are also revealed.