An optimal control method for valve regulation based on Pontryagin’s principle in energy interconnection systems

Traditional optimization-based scheduling for interconnected energiy systems is performed offline and produces static pre-schedules that may become suboptimal or even infeasible when real-time operating conditions and disturbances deviate from the original assumptions. To address this issue, an optimal control method based on the Pontryagin maximum principle (PMP) is proposed to compute real-time valve trajectories under a given batch schedule. Firstly, a control-oriented low-order dynamic response model of pipeline is constructed to describe the effects of real-time changes in valve opening on flow, head and pressure, taking into account the hydrodynamic properties and the physical properties. Then, based on the dynamic response model, a optimal valve control strategy is formulated to determine valve-opening trajectories that minimize demand tracking errors and pressure losses subject to delivery constraints. In addition, the strategy exhibits good robustness to small disturbances and parameter variations, preserving the desired flow targets under the given schedule. Finally, several case studies are conducted to demonstrate the effectiveness of the proposed method.