Simulation of transient flow in pipeline systems due to load rejection and load acceptance by hydroelectric power plants

In this paper, the implicit method of characteristics (IMOC) is extended to simulate the transient flow caused by load variation of hydroelectric power plants. The IMOC was proposed recently by the authors to remove the limitations of the commonly used conventional method of characteristics (MOC) and subsequently used for the simulation of transient flow caused by valve closure and pump failure. In the IMOC, an element-wise definition is used for all devices that may be used in a pipeline system and the corresponding equations are then assembled to form a system of equations that is solved for the unknown nodal heads and flows at each time step. In this paper, the IMOC is extended for the simulation of transient flow in the pipeline system upstream of a hydroelectric power plant. For this, an element-wise definition of the hydroelectric power plants and simple surge tank is proposed and their governing equations are derived in a matrix form required by the IMOC. Then these equations are assembled along with those of other devices of the pipeline system to construct a system of equations that is solved for the unknown head and flow. To further improve the convergence characteristics of the method, an improved formulation of the turbine is also proposed. In the proposed formulation, one of the turbine characteristic parameters, namely turbine net head, is used in addition to turbine head and discharges, to formulate the behavior of the turbine element. The method is applied to a problem of transient flow caused by load rejection and acceptance and the results are presented and compared with those of the explicit MOC. The results show the ability of the proposed method to accurately predict the variations of head and flow in the cases considered. It is also shown that the improved formulation of the turbine is computationally more efficient than the original formulation while producing the same results.