Moving Least Square Approximation in the Fitting of Characteristics Curves of Reversible Pump Turbine

摘要

The complete characteristic curves of reversible pump turbine, which plays a key role in the transient simulation in pumped storage plant because the serious safety problem in the plants are usually induced by the overpressure in water conveyance system after a full-load rejection during abnormal conditions, has been approximated by variety of approaches such as linear interpolation and least square surface fitting. However, the least square surface fitting is mesh-dependence which requires regular distribution of the data that the scattered testing data of complete characteristic curves can not meet. Therefore, the mesh free method, moving least square (MLS) approximation, is introduced in this paper to approximate the curves transferred from the new transformation method for the first time. Then, the effects of different basis functions and weight functions, weight function parameters and scaling parameters on the error norms of MLS approximation of the characteristic curves are discussed one by one while the total number of nodes within the domain of influence of the fixed node is initially fixed and the radius of support domain are adjusted all the time to satisfy the requirement. Finally, based on the comparison of the fitting accuracy of the characteristic curves, quadratic basis function and Gaussian weight function surpass other functions and are chosen for MLS approximation of the curves. Gaussian weight function parameter, which determines the shape of the weight function, and scaling parameter, which determines the influence domain of the weight function, are recommended to be within the range of 3.25 to 4.25 and the range of 1.0 to 1.5 respectively, because the overall error norm are achieved their minimum value within those ranges.