A Prediction of the Transient Phenomena by the Load Rejection for a 50MW Francis Hydropower Plant

2.1 Field test and model calibration

The hydropower is overhauled at regular intervals to check and maintain the stability of the equipment. At this point, the load rejection, force for guide vane opening and closing, and output test are performed, to evaluate the hydro turbine and generator. Among these tests, the load rejection ensures that the hydro turbine generator safely switches to a no-load or shutdown state when a power system or mechanical accident occurs during normal operation.

The accuracy of the simulation was verified by comparing the results of the field test and simulation analysis for the load rejection of the 50-MW Francis turbine. Table 1 presents the conditions and specifications of the modeled operating hydropower system and Francis turbine, respectively.

Table 1

Dam operating conditions and specification

In the load rejection test, the stability of the turbine generator is verified by measuring the inlet pressure head, rotation speed, and voltage of the generator.

Table 2 presents the measurement items and equipment, while the installation location is illustrated in Fig. 1.

Table 2

Load rejection test measurement equipments

Fig. 1

Installation location(Generator voltage, Inlet pressure, Wicket gate opening)

The generator circuit breaker system was opened manually for the test; accordingly, the measured data before and after the load rejection are presented in Table 3.

Table 3

Load rejection test conditions and results

To verify the reliability of the simulation, modelling was performed under conditions identical to those adopted in the field test. Among the major components of the dam, the waterway has a total length of 2634.61 m from the reservoir to the surge tank, and the penstock is 218.61 m from the surge tank to the Francis turbine. The model comprises two Francis turbines branching at 132.11 m at the penstock.

The field test conditions are as follows. The rejection load, rotational speed, inlet pressure head, and guide vane servomotor stroke were 50.2 MW, 257 rpm, 101.7 mAq, and 225.7 mm, respectively. At this point, the reservoir and tailrace levels were 159.25 m and 56.2 m, respectively. To determine the initial condition of a hydraulic system with the Francis turbine, stabilization is conducted using these parameters. The specified rotational speed (N_c) and turbine torque (T_c) are known, while the corresponding guide vane opening (y_c) is determined. Consequently, the specified operating points were determined to be N_c = 257 rpm, T_c =1.903106, and y_c=0.8102. Table 4 presents the simulation conditions including boundary conditions such as the reservoir level. Fig. 2 presents the simulation modeling diagram.

Table 4

Modelling parameters and values

Fig. 2

Modelling diagram

Fig. 3 presents a comparison of the simulation results with the field tests under identical conditions. In the field test, the inlet pressure head of the surge tank increased from 101.7 mAq at the beginning of the test to a maximum value 173.6 mAq after load rejection. In the simulation, the inlet pressure increased from 100.71 mAq at the beginning of the simulation to a maximum value of 169.09 mAq after load rejection. The difference in the maximum inlet pressure between the simulation and the field tests was 2.6 %. The rotational speed of the turbine increased to 321.4 rpm in the field test, while that of the simulation increased to 315.06 rpm, resulting in a 1.97 % difference between the simulations and field tests. The simulated results under conditions identical to those in the field test results for a load rejection exhibit a certain degree of similarity.

Fig. 3

Comparison of simulation results with field tests under identical conditions

2.2 Numerical methods

Hydropower plants consist of several components that must be included when modelling their dynamic behaviors. The Francis turbine has fixed runner blades; hence, the discharge through the turbine is controlled by the guide vane. Fig. 4 presents a simplified cross-sectional view of a vertical Francis turbine as a plant to be analyzed. From the right, the water passing through the penstock passes through the spiral case, rotates the runner, and is discharged through the diffuser⁽¹¹⁾.

Fig. 4

Cross-sectional diagram of the Francis turbine

Under an unsteady flow, the conditions at a point change with time and the velocity varies along the pipe. The terms “water hammer” and “transient flow” are used synonymously to describe the unsteady flow of a fluid in a pipeline⁽¹²⁾. The momentum and continuity equation are basic differential equations for transient flow.

The momentum equation expresses the balance of the forces acting on the fluid volume, the momentum flux through the surfaces, and the rate of change of the momentum in the volume itself. The integral form of the momentum equation applied to a volume of fluid is expressed in Equation (1), while the mass balance in a control volume is expressed in Equation (2).

where, ρ, $$ \overrightarrow{C}$$, $$ \overrightarrow{n}$$, $$ \overrightarrow{u}$$, and dA denote the density of water [kg/m³], flow velocity [m/s], norminal vector, moving velocity of the control volume [m/s], and cross-sectional area [m²], respectively.

From these equations, we can calculate an unsteady flow via several methods, such as characteristics, algebraic, and implicit method. In this study, we employ the 1-D hydraulic analysis software (SIMSEN)⁽¹³⁾ developed by the EPFL Laboratory for transient phenomena in hydraulic systems.

The main hydropower turbine characteristics can be expressed by performance-characteristic curves or in a model efficiency hill chart based on the water head and flow rate coordinates or unit parameter coordinates⁽¹⁴⁾. In this study, Francis turbine-characteristics derived based on a model test using a turbine runner with a novel shape were applied as dimensionless terms n₁₁, Q₁₁, and T₁₁, which were converted to values per unit dimension and per unit head⁽¹⁵⁾. The rotational speed, discharge factor, and shaft torque factor are expressed in Equations (3), (4), and (5), respectively.

where, n, D_ref, Q, H, and T_m denote the rotational speed [rpm], turbine reference diameter [m], discharge [m³/s], turbine head [m], and model turbine shaft torque [N⋅m], respectively.

Figs. 5 and 6 show the correlation between n₁₁, Q₁₁, and T₁₁ for various guide vane openings during the Francis turbine model testing. As the rotational speed factor increases, the discharge factor has a negative value, which means the reverse flow that may occur in transient phenomena. At the same time, the shaft torque factor also has a negative value, which means operation as a pump rather than a turbine. Fig. 7 and Table 5 detail the model tests performed in accordance with IEC-60193 to derive these graphs.

Fig. 5

Discharge factor of the modeled Francis turbine

Fig. 6

Torque factor of the modeled Francis turbine

Fig. 7

Model turbine at the test rig

Table 5

Comparison of model and prototype turbines

3.1 Simulation of the surge tank level

A hydropower plant shutdown of the water flow involves closing the turbine guide vane rapidly in the event of an emergency situation. When the pressure in the penstock increases to an extreme level outside of the allowable value, accidents may occur such as the rupture of the penstock, buckling due to negative pressure, damage to turbines, and inability to open and close inlet valves⁽¹⁶⁾. To absorb pulsation, which may occur in the penstock owing to the sudden change in the flow rate, hydropower plants are equipped with protection systems, such as a surge tank. The surge tank’s height should be properly designed to ensure stability against transient phenomena occurring in hydropower plants. In this study, the surge tank level under two reservoir level conditions was analyzed, assuming an emergency shutdown situation after the loading of the hydropower plant. At this point, the changes in the surge tank level according to the reservoir level were analyzed. The total simulation time was 20 s, and each integration step was 0.005 s.

We simulated the changing of reservoir levels. Fig. 8 and 9 present the analysis results at the dam water level under two conditions. The first is an average operating water level of 160 m, based on data accumulated over the past 27 years. Second, because the water level of the dam and the pressure of the penstock and surge tank are in a proportional relationship, it was set to 179 m, which is the operational maximum water level at which the maximum pressure will emerge. The water level in tailrace was set to 57.5 m in both conditions.

Fig. 8

Simulation results (Reservoir 160 m)

Fig. 9

Simulation results (Reservoir 179 m)

Oscillation occurs at the inlet pressure as soon as the emergency shutdown starts. respectively, while the emergency shutdown occurs 10 s after loading. The surge tank level increases to 160.59 m when the reservoir level is 160 m. When the worst condition occurs, i.e., when the reservoir level is 179 m, the surge tank level increases to 180.98 m. Table 6 presents the rate of increase after the start of the emergency shutdown compared to the initial conditions.

Table 6

Simulation results according to reservoir level

The maximum level of the modelled dam’s surge tank was 198.8 m, which verified that the stability of the hydropower plant is ensured even when an emergency shutdown situation occurs while the reservoir level is maximized.

The following is a comparison of the oscillation generated by the penstock before the Francis turbine with and without a surge tank in a hydropower plant. The simulation conditions are as follows: the reservoir and tailrace levels are 179 m and 57.5 m. Fig. 10 presents the change in the pressure head at the penstock at the inlet turbine, with or without a surge tank. Without a surge tank, the pressure head increased sharply, reaching a maximum of 762.58 mAq. However, the pressure head increased to only 240.71 mAq with a surge tank.

Fig. 10

Change of pressure head at the turbine with and without a surge tank

3.2 Simulation changing the guide vane close time

We decided to change the closing time of the guide vane to observe the effects on the pressure rise triggered by a transient in a hydropower plant. This simple method can influence how the increased pressure due to a transient changes the guide vane closing time. The present guide-vane closing time was 2.74 s. We shortened this closing time to 1.37 s and extended it to 5.48 s, and then conducted the simulations under identical conditions.

Fig. 11 presents a graph of the guide vane closing times and indicates that even with changes in the guide vane closing times, the level of the surge tank does not vary significantly. However, Fig. 12 demonstrates that the pressure at the immediate inlet of the turbine varies considerably. If the current guide-vane closing time is approximately doubled, the maximum pressure can be reduced by approximately 19%, from 189.05 mAq to 152.32 mAq. In contrast, if the guide vane closing time can be shortened by one half, the maximum pressure will increase abruptly from 189.05 mAq to 262.93 mAq. Therefore, we can confirm that adjusting the closing time of the guide vanes can be a viable means of mitigating the increased pressure caused by a transient at the hydropower plant.

Fig. 11

Guide vane closing curve and surge tank level to guide vane closing time

Fig. 12

Inlet pressure to guide vane closing time