Optimization of Closure Law of Guide Vanes of Francis Turbine : A Case Study of a Typical Operational Hydropower Project of Nepal

Abstract

This thesis addresses the optimization of closure law of guide vanes of Francis turbine in an operational hydropower plant. Sanima Mai Hydropower Project (22 MW), located at Ilam district of Nepal has been taken as primary reference. A mathematical model has been developed using the Bentley hammer software to model the hydraulic transient parameters during the full load rejection. The mathematical model is validated by comparing the results of the model with the data of the load rejection test which were carried out during commissioning phase of the project. The value of rise of maximum pressure and maximum speed as obtained from the model is compared with data of load rejection test for various closure time. The comparison of these result shows that the maximum discrepancy between numerical and experimental data is 3.2 %, hence concluding the reliability of the developed mathematical model. Various combinations of single-phase linear and three-phase close-delay-close (CDC) closure patterns have been applied to the validated model to study the effect of the closure pattern. The value of maximum hydrodynamic pressure and the maximum rotational speed of turbine are calculated for all the cases of guide vane closure. To quantify the effectiveness of a closure pattern to harmonize the rise of hydrodynamic pressure and the rotational speed of turbine, a non-linear objective function has been proposed and based on the extent of the minimization of the defined objective function, different closure laws are compared. For a single-phase closure law, the maximum pressure decreases and the maximum speed increases on increasing the closure time and vice-versa. The optimum closure law for single phase linear closure pattern is obtained at closure time of seven seconds which keeps the maximum pressure and maximum speed at 1542 KPA and 755 RPM respectively .The corresponding value of objective function is 6.4. For a three-phase CDC pattern, maximum speed increases on increasing any of the four parameters; t1, t2, t3 and s, provided that the remaining three variables remains unchanged. However, there are no any clear trends observed for the maximum pressure. Nevertheless, it has been concluded that the value of objective function is better controlled when the speed of first closure is faster than the speed of second closure. The optimum closure law for a three phase CDC pattern is obtained at t1= 4 second, t2= 5 second, t3 = 9 second and s= 0.35 which keeps the maximum pressure and maximum speed at 1507 KPA and 754 RPM respectively. The corresponding objective function is 5.6.

The optimum closure law obtained in both the pattern ensures the target hydraulic transient parameters within the defined range. Moreover, the comparison of the value of objective function for single phase and three phase CDC linear closure pattern concludes that the three-phase CDC pattern ensures better regulation than the single phase closure pattern.