Biomedical Engineering Reference
In-Depth Information
Republic of the Congo, Paraguay, and Brazil with over 85% of their electricity. The United
States currently has over 2000 hydroelectric power plants which supply 49% of its renewable
electricity.
Hydroelectricity generation is a process to convert potential energy (height difference
along the path of the waterway) as shown in
Fig. 15.6
. The total potential energy difference
for water flowing from the upstream (reservoir) to the downstream (river) of the facility is
D
G ¼ rgh
(15.2)
r
where
is the density of water,
h is height difference between the two water surfaces, and g is acceleration due to gravity
(9.8 m/s
2
). Not all the potential energy can be converted to electric energy. A simple formula
for approximating electric power production at a hydroelectric plant is thus given by
D
G is the potential energy difference per unit mass (of water),
P ¼ h
P
rghQ
(15.3)
where P is the electric power generated, Q is the flow rate of water, and
h
P
is a coefficient of
efficiency ranging from 0 to 1. Efficiency is often higher (that is, closer to 1) with larger and
more modern turbines. If water level or height difference h is maintained constant through
the reservoir operations, the electric power generation is then directly proportional to the
available flow rate as depicted by
Eqn (15.3)
.
The flow rate through the penstock is also a function of the gate opening and the height
difference. Based on fluid mechanics, the flow rate can be estimated by
Q ¼ c
s
A
G
ðghÞ
1=2
(15.4)
where A
G
is the open cross-sectional area of intake gate and c
s
is a constant that depends on
the penstock pipe construction, intake gate, the turbine, and also weakly on the flow rate.
Therefore, the power generation can be related to the height or the flow rate via
P ¼ h
P
c
s
A
G
rðghÞ
3=2
(15.5)
or
h
P
c
s
A
2
G
rQ
3
P ¼
(15.6)
The electric energy production is proportional to the water height difference to the power of
one and half, or proportional to the cube of the flow rate, if the gate opening remains the same.
The power and flow rate relationship can be different if the water level can be controlled inde-
pendently. This is particularly true for large dam/reservoirs as constant water level is desirable
for maximum electric power output as given by
Eqn (15.3)
.
Fig. 15.7
shows the typical seasonal
flow rate variation for the Three Gorges Dam, China. One can observe that the water flow rate
is highest during the summer months and lowest during the winter months.
Example 15-3. A hydroelectricity facility was built below a mountainous area. Owing to the
weather changes from summer to winter, the available water flow changes significantly. In 1
year, the water flow rate in a low day was just one-tenth of that in a high flow summer day.
Determine the available electricity generation variation.
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