Formulae for the intersecting curves of pump-turbine characteristic curves with coordinate planes in three-dimensional parameter space

Pump-turbine characteristics are important boundary conditions for simulating hydraulic transients in pumped-storage hydroelectric power stations. However, the changing laws of the characteristics of different pump turbines are not well understood. Here, two-dimensional characteristic curves are converted into three-dimensional forms, and the intersecting curves, defined by the intersection of the characteristic curves with the coordinate planes in a parameter space defined by the unit rotational speed, unit discharge, and unit torque, are determined to clarify these changing laws. Basic pump-turbine theory of the flow characteristics and idealizations of the "hump" and "S" regions of the characteristic curves are considered to determine formulae for each intersecting curve. Each formula consists of two unknown coefficients that are obtained from fits to measured data. The dependence of the coefficients on specific speed values is clarified to obtain general formulae governed by specific speed. The nonlinear changing laws of the characteristic curves and their relationship with the flow and operating conditions are analyzed and clarified. This work provides a theoretical basis for predicting the characteristic curves of any pump turbine without model-measured characteristics.