Water level optimization of water transferring channel in multi-stage pumping stations based on head-water level successive approximation optimization method

Abstract: Water level optimization of water transferring channel has a great significance on reducing operational energy consumption and increasing economic benefit for multi-stage pumping stations system. According to the mathematical model of optimal operation of multi-stage pumping stations with original pumping head and targeted water pumping quantity for each stage of parallel pumping stations, we developed water level optimization in water transferring channel between two stages pumping stations by use of successive approximation optimization method. This method was based on a combination of two stages decomposition- dynamic programming aggregation method and numerical simulation of unsteady flow with the consideration of the water transferring channel characteristics. Firstly, two stages decomposition-dynamic programming aggregation method was applied to solve the mathematical model of daily optimal operation of each stage of parallel pumping stations under a given original pumping head and targeted water quantity. Secondly, the optimal flow process of each pump unit obtained from the model solution were input to the mathematical model of one-dimension unsteady flow as boundary conditions to develop numerical simulation with the consideration of water consumption process of different water users along the water transferring channel. After that, the obtained water level for each stage of pumping stations was compared with the original water level. Meanwhile, the water level of each section in the channel also needed to be determined if it met the requirements of flood control and waterlogged elimination, navigation, and ecology. If all requirements were met, the obtained optimal operation scheme of pumping stations was considered as the optimization scheme. Otherwise, the process would be repeated again. By this successive approximation method, the final optimal operation scheme of multi-stage pumping stations was obtained. With this method above, optimal operation cost of each stage of parallel pumping stations under a given pumping head and targeted water quantity cab was obtained. In this simulation, water level variation of water transferring channel had less impact on pumping head of each pumping station in the system. The results provided a starting point for simulation under more complicated boundary conditions for optimal operation of multi-stage pumping stations. We took No.1, 2, 4 Huai'an parallel pumping stations to No.1, 3 Huaiyin parallel pumping stations as a case study for the above simulation approach. These stations are two-stage pumping stations in Jiangsu Province in Eastern Route of South-to-North Water Transfer Project. Under a typical original head of 4.13 m and 100% load for Huai'an stations, and under a typical original head of 2.7 m and 100% load for Huaiyin stations, there was a minimal average water level difference of 6.51 cm upper (or lower) from numerical simulation between No.4 and No.2 pumping stations, which meant the best matching degree could be obtained by the No.3 optimization of parallel pumping station. The corresponding optimal operation schemes of each pump unit in each time period were obtained with 7.56% optimization benefit compared with operation with fixed blade and constant speed. Besides, there was a minimal average water level difference of 14.9 cm in the whole river network from simulated results. The maximal and minimal water level and their appearing time interval could meet the navigation and ecological water level requirements.