Optimal Power and Gas Flow With a Limited Number of Control Actions

Current research regarding integrated optimal power and gas flow (OPGF) requires the adoption of a relatively large number of control actions, which is undesirable in practice owing to time and communication constraints. The present study therefore proposes OPGF with a limited number of control actions (denoted as OPGF-LNC). Imposing a bound on the number of control actions inevitably introduces binary variables, and the resulting OPGF-LNC with nonlinear power/gas flow models is a mixed integer nonlinear programming (MINLP) problem. To avoid the poor numerical performance of MINLP, dc power flow model and a two-stage piecewise linear gas flow model are employed. Consequently, the OPGF-LNC problem is simplified to a mixed-integer linear programming (MILP) problem. Furthermore, the tradeoff between control costs and the allowed number of control actions is analyzed, and soft constraint relaxation is deployed when satisfactory results are unattainable using all possible control actions. Simulation results using an IEEE 39-node system and a 48-node gas network verify that the MILP approach always produces reliable optimal solutions while MINLP is divergent in some cases. In addition, substantial benefits are demonstrated with the implementation of reasonable soft constraint relaxation.