Real-Time Optimal Scheduling of a Water Diversion System Using an Improved Wolf-Pack Algorithm and Scheme Library

A water diversion system (WDS) with cascade pumping stations (CPSs) plays an important role in the application of water resources. However, high energy consumption is reported due to unreasonable scheduling schemes and long decision times. Herein, this paper presents a new method to achieve optimal scheduling schemes effectively, including the head allocation of CPSs, the number of running pumps, and pump blade angles. A double-layer mathematical model for a WDS was established with the goal of achieving minimal energy consumption, considering the constraints of flow rate, water level, and the characteristics of pump units. The inner-layer model was used to obtain scheduling schemes of single-stage pumping stations, as well as the water levels and flow rates of water channels, while the outer-layer model was used to optimize inter-stage head allocation. An improved wolf-pack algorithm (IWPA) was proposed to solve the model, using a Halton sequence to obtain the uniform initial population distribution and introducing simulated annealing (SA) to improve the global searchability. Moreover, an idea for a pre-established scheme library was suggested for inner-layer models to obtain the solutions in real time with less calculation workload. Taking an actual project as a case, in contrast with the actual schemes, the optimal scheduling method could result in energy savings of 14.37-20.39%, a CO2 emission reduction of 13-32 tons per day, and water savings of 0.14-18.34%. Moreover, the time complexity decreased to square order, and the CPU time of the optimal method was about 1% that of the traditional method. This study provides an efficient method for the high-value utilization of energy and water resources for a WDS.