Improvement of Francis turbine internal characteristic model and its expanding application on outer characteristic

Abstract: The combined characteristic curve of Francis turbine shows the performance of turbine working in the high efficiency area. But it isn't sufficient for simulating the system transmit process in a large area, such as turbine working in the low efficiency area and negative area in the rejection transient process. Therefore, expanding the combined characteristic curve of turbine to low efficiency and negative efficiency areas is necessary before the simulation. In general, the combined characteristic curve expanding methods, such as frequently used methods of back propagation of artificial neural network method and radial basis function neural network method, are based on the trend of each parameter in the high efficiency area. But the inherent laws in the turbine are not considered in those methods, and the expanding results are relying largely on personal experience. In this paper, the energy loss formulas on each component of turbine, such as guide vane inlet, blade inlet, blade outlet and so on, were obtained by velocity triangle analysis. According to the turbine flow regulation equation combined with the energy balance equation, the Francis turbine internal characteristic model was obtained. For the complex style and more parameters features of the model, a parameter identification method which combined the genetic algorithm and the least square algorithm was designed to avoid the remaining local optimum only by genetic algorithm or can't be solved only by the least square algorithm. It was proved that the algorithm was effective through contrast of the measurements and the simulation of turbine HLN574 in the case. The Francis turbine internal characteristic model agreed well with measurements in most area, except the area of large unit speed area. The cause of error in the large unit speed area was analyzed for complex flow state in the large unit speed area and the assumed conditions can’t be satisfied. For obtaining the effect of model error on transient process simulation result, a rejection transient was simulated each time by Francis turbine internal characteristic model and measurement curve and the simulated result showed that this effect was small. Therefore, we concluded: 1) Energy loss as conditions charge should be considered in the Francis internal characteristic model and the energy balance equation and flow regulation equation should be also considered; 2) The designed parameter identification method was effective in the internal characteristic model parameters ensure; 3) The model error would increase in large unit speed area but it can be ignored in the simulation of transient process. The application of this model in the combined characteristic curve expanding could reduce the randomness of traditional methods. The model has important value in the calculation of transient process.