Gauss-legendre quadrature estimates of discharge for the performance testing of low-head hydroelectric turbines

Abstract

The performance testing of low-head hydroelectric turbines is necessary for the efficient and economic operation of a generating station. Of the information required for performance testing, discharge is the most difficult to measure accurately. The velocity-area method is typically used to measure discharge through a low-head plant. Herein the combination of acoustic technology and Gauss-Legendre quadrature (GLq) integration is investigated as an alternative method of measuring discharge. Physical hydraulic modeling was performed to examine the accuracy of discharge estimates associated with different GLq sampling strategies. Data obtained from laboratory testing indicate that the accuracy of estimating discharge increases with the number of GLq levels used. Discharge errors of less than 1% were observed (for undisturbed flow conditions) when 8 or more GLq levels were used.Key words: turbine, performance testing, acoustic discharge measurement, Gauss-Legendre quadrature integration.