Domain partitioned transformation of pump-turbine characteristic curves in 3-D space

Pump-turbine characteristic curves are the most important boundary condition in the hydraulic transient simulation of a pumped-storage hydropower station. Conventional representation of them, however, has serious defects, For instance, the "S" and "hump" shapes, composed of multiple values and steep twists, lead to the difficulty in interpolation between known guide-vane opening curves, which is necessary in hydraulic transient simulations. Here, a new transformation method was figured out to settle this problem thoroughly and to improve the accuracy of interpolation between the constant opening curves. Prior to the transformation, the characteristic curves are partitioned into eight domains. Curves of each domain were transformed through different formulae that fit the curves well. Eight characteristic surfaces in the 3-D space can be obtained by adding the guide vane opening as the coordinate axis. The theoretical method has been validated by the excellent agreements achieved by comparing the curves interpolated on the characteristic surfaces with the measured data.