Worked Example 12.4
In a pumped-storage hydropower project, water is delivered from the upper
impounding reservoir through a low-pressure tunnel and four high-pressure
penstocks to the four pump–turbine units. The elevation of the impounding
reservoir water level is 500 m AOD, and the elevation of the downstream
reservoir water level is 200 m AOD. The maximum reservoir storage which
can be utilized continuously for a period of 48 h is 15 106 m^3.
The low-pressure tunnel is constructed as follows: length4 km; dia-
meter8 m; friction factor, 0.028.
The high-pressure penstocks (4 nos.) are constructed as follows:
length of each penstock500 m; diameter2 m, friction factor, 0.016;
turbine efficiency when generating90%; generator efficiency (16 poles,
50 Hz)90%, turbine efficiency when pumping80%; barometric pres-
sure10.3 m of water; Thoma’s cavitation coefficient, 0.043(Ns/100)^2.
- Determine the maximum power output from the installation.
- Estimate the specific speed and specify the type of turbine.
- Determine the safe turbine setting relative to the downstream reser-
voir water level. - If a simple surge chamber 6 m in diameter is provided at the end of
the low-pressure tunnel, estimate
(a) the maximum upsurge and downsurge in the surge chamber for
a sudden rejection of one unit and
(b) the maximum downsurge for a sudden demand of one unit.Solution
The discharge available 15 106 /(48 60 60)86.8 m^3 s^1. The power
output is calculated as follows:
velocity in tunnel86.8/((π/4)88)1.73 m s^1.Therefore
head loss in tunnelLV^2 /2gD2.13 m,discharge per penstock86.8/421.7 m^3 s^1 ,velocity in penstock21.7/((π/4)22)6.91 m s^1.Therefore
head loss in penstockLV^2 /2gD9.73 m,gross head at turbine 500 200 300 m,