Optimal Operation of a Single Unit with an Adjustable Blade in an Interbasin Water Transfer Pumping Station Based on Successive Approximation Discretization for Blade Angle

In the mathematical model of the optimal operation of a single pump unit with a fully adjustable blade in the Chinese South-to-North Water Diversion Project, the decision variable, namely, blade angle, was uniformly dispersed in its feasible region in a fixed step size in consideration of the requirements of the pumping head and matching motor power. 1D dynamic programming was applied to solve the original model. When the obtained blade for each time period was set as the middle reference value and the discrete region of the blade was reduced to two times of the step size in the previous time, the blade angle was correspondingly reduced and dispersed in this new discrete region, thus eliminating unnecessary optimization space. Then, 1D dynamic programming was applied again to optimize the blade angle of the single pump unit further. After a series of successive approximation discretization of the blade angle and corresponding solutions of the obtained mathematical model, the optimization process was considered completed when the given control precision met the requirement. A case study showed that under typical operating conditions, the total cost saving percentage of water pumping quantity reached 0.048%–0.463%, with an average saving rate of 0.192%. The actual total water pumping quantity of the single unit decreased by 2153 m3 on the average. The proposed discretization method exerted a better optimization effect and needed a smaller computational amount compared with traditional one-time uniform discretization in the original feasible region of the blade angle.