Environmental Engineering Reference
In-Depth Information
8
Hydroelectric Power Generation
8.1
Principles
Hydropower plants harness the potential energy within falling water and use clas-
sical mechanics to convert that energy into electricity. The theoretical water
power
P
Wa,th
between two specific points on a river can be calculated according to
Equation (8.1) (see Chapter 2.4.1).
P
=
ρ
g
q
&
(
h
−
h
)
(8.1)
Wa
,
th
Wa
Wa
HW
TW
ρ
Wa
is the water density,
g
the gravitational constant, and
q
.
Wa
the volumetric
flow rate through the hydroelectric power station.
h
HW
und
h
TW
describe the geo-
detic level of head and tailwater.
Due to the physically unavoidable transfer losses within a hydroelectric power
station, only part of the power according to Equation (8.1) can be utilised. In or-
der to show this, the Bernoulli equation (see Chapter 2.4.1) can be converted ac-
cordingly. Thus all terms adopt the unit of a geometrical length and can be repre-
sented graphically (Fig. 8.1).
If the energy balance between two reference points - up- and downstream of a
hydroelectric power station - is set forth, the Bernoulli equation can be written
according to Equation (8.2).
2
2
2
v
v
v
p
p
Wa
,
Wa
,
2
Wa
,
2
1
+
h
+
=
2
+
h
+
+
ξ
=
const
.
(8.2)
1
2
ρ
g
2
g
ρ
g
2
g
2
g
Wa
,
Wa
,
2
In the following, the different terms of Equation (8.2) are defined as pressure
energy
p
/(
ρ
Wa
g
), potential energy
h
, kinetic energy
v
Wa,
2
/(2
g
) and as lost energy
ξ v
Wa,
2
/(2
g
).
ξ
is the loss coefficient, and
p
i
and
v
Wa,i
represent the pressure and
the flow velocity at the corresponding reference points respectively. The lost en-
ergy is thus the part of rated power that is converted into ambient heat by friction
and therefore cannot be used technically.
System setup.
A hydroelectric power station, depending on scale, normally con-
sists of a dam or weir, and the system components intake works, penstock, in
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