Optimization of Setting Angle Distribution to Suppress Hump Characteristic in Pump Turbine

Pump turbines play a quite important role of peak-valley shifting in the grid, and the hump margin is a critical criterion related to the safety and stability of operation in pump mode. Aiming at investigating the influence of runner outlet setting angle distribution on hump performance of a pump turbine, three runners with different linear distributions of setting angle at outlet were proposed, and the corresponding hump performance comparison was analyzed numerically through the SST k - ω turbulent model. The numerical result shows that, compared to the experiment, the relative errors of all simulated performances (energy characteristic, torque characteristic, and efficiency) were within 3%. Moreover, it was found that setting angle distribution modes could lead to a remarkably different performance in the hump region and, for the runner whose setting angle at shroud was 10° larger than that at hub, the hump safety margin could be increased from 4% to 4.5%. Thereafter, the corresponding mechanisms including energy input and hydraulic loss were investigated through the Euler head theory and the entropy method, respectively. It was found that hydraulic loss distribution played a more important role than the input energy on controlling hump performance. Moreover, for the runner with the largest hump margin, the hydraulic loss was distributed more evenly in the decreasing discharge direction, contributing to the elimination of hump performance. In addition, hydraulic loss distribution was calculated through local entropy production rate (LEPR) method. For all proposed runners, when the pump turbine entered the hump region from a normal operation point, the hydraulic loss was mainly concentrated in vaneless areas and guide/stay vane channels, while the runner with a large setting angle at shroud could better control the hydraulic loss distribution in both the spatial location and the discharge varying direction, increasing the hump margin. The design method presented in our paper is more likely to be applied in engineering applications.