Abstract: Intersection, aggregation, intertangling and the extremely unstable S-shape area on both ends of the characteristic curve of pump turbine pose great difficulty for the accurate simulation of pump turbine’s transition process. In view of this, scholars both in China and abroad conducted in-depth researches on the mathematic transform and the fitting method for characteristic curve. In this paper we summarize the research achievements. According to the expression method we divide the research results into two-dimensional mathematical transformation and three-dimensional curved surface fitting. We also point out the breakthrough and insufficiency of the research results, and finally propose the direction and several suggestions for further research.

Key words: pump turbine, characteristic curve, mathematical transformation, curved surface fitting