Application of augmented Lagrangian relaxation to coordinated scheduling of interdependent hydrothermal power and natural gas systems

This study proposes an optimisation model for the coordinated scheduling of interdependent electric power and natural gas transmission systems from a joint operator's viewpoint. The objective is to minimise the coordinated social cost while satisfying network and temporal constraints of the two interdependent systems. The joint operator will coordinate hourly schedules to supply natural gas to loads or generate electric power. The authors consider the application of Lagrangian relaxation (LR) or augmented LR to relax the coupling constraints of the two systems. The Lagrangian dual is decomposed into the security-constrained unit commitment subproblem with the hydro coordination and the natural gas allocation subproblem. The application of LR for solving the coordinated problem could cause oscillations in the dual solution which is due to the non-convex characteristics of the coordinated problem represented by integer variables and network constraints. Moreover, with slight changes in multiplier values, the linear cost function of the natural gas well may result in a cycling behaviour of the gas well output between its max and min limits. To avoid numerical oscillations and improve the solution quality, the augmented LR with a piecewise linear approximation of quadratic penalty terms and the block descent coordination technique are proposed. The authors consider the 6-bus with 7-node and the 118-bus with 14-node systems to verify that the applicability of the proposed method to the coordinated scheduling of electric power and natural gas transmission systems.