Physics-based hydraulic turbine model for system dynamic studies

A one-dimensional numerical model of a Francis turbine hydropower plant for dynamic response studies is presented with an alternate representation of the turbine unit component. The conventional, simplified representation of the hydraulic turbine is replaced by a consideration of the conservation of angular momentum using inlet and outlet velocity vectors calculated based on effective turbine geometry. Specific energy loss components associated with off-design conditions such as runner blade inlet incidence loss and draft tube residual swirl flow loss are determined. Estimates for mechanical frictional losses and churning losses are calculated to ensure accurate simulation across the entire turbine operating range. The resulting model therefore takes into consideration real sources of major loss, eliminating the use of ambiguous correction factors, while remaining equally simple to implement into current power system models. The new turbine formulation is validated against transient test data from a 119 MW Francis turbine unit, while simulations based on two existing conventional models are included for comparison.