Mathematical model is presented for prediction of thermal losses from central receiver solar thermal power plant. Results obtained are verified with evidence from solar experiments. Code is developed for studying the effect of variation of weather conditions i.e. variation of incident solar radiation, wind speed and ambient temperature during the entire year on the thermal performance of receiver. Thermal losses have its effect on efficiency of the receiver and hence the overall cost of solar thermal to electric power. Radiation and convection losses are the major components of thermal losses. Simulation is done for weather data of Jaipur city of India
2. Sandhya Jadhav and Dr. V. Venkat Raj
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Kristler in 1986 is a performance and design optimization software developed by using FORTRAN 77.
Although receiver radiation and convection losses are also calculated, the detail is probably insufficient for
use in receiver evaluation, thus only flux density calculation capabilities are used for receiver analysis.
SOLERGY developed in 1987 used FORTRAN 77 for simulation of the plant.
Code is developed using Visual Basic for studying the thermal performance of the central receiver
solar thermal power plant for different amount of solar radiation received during the entire year. The code
developed simulates the operation and annual power output of a solar central receiver power plant using an
actual simulated weather data recorded at time intervals of 1 hour. It calculates the net electrical energy
output including parasitic power requirements over 24 hrs a day. It has subroutine for each major plant
system, receiver, thermal energy storage and turbine. Annual plant performance is found by adding the
performance at every considered time step.
For each time step, the heliostat field concentrates the incident solar radiation and directs it on to the
receiver placed on the top of the tower. On receiving the adequate amount of solar radiation from the
heliostat field, the receiver starts working. The operation of the receiver depends upon the power received
from the heliostat field and the previous receiver status. The lower receiver power limit is set by the
minimum flow rate that the receiver flow valves can handle. If the power to the receiver is greater than the
receiver thermal rating, the input is decreased to the thermal rating, by heliostat defocusing. All thermal
power from the receiver is delivered to thermal storage tank, provided that storage tank can accept it (i.e.
until storage tank is full). The turbine operates, after a specific level in thermal storage is achieved.
2. THERMAL LOSSES IN THE RECEIVER
In Solar thermal power plants, heat loss can significantly reduce the efficiency and consequently the cost
effectiveness of the system. It is therefore vital to fully understand the nature of these heat loss
mechanisms. The magnitude of the thermal losses varies and it depends on the receiver type, geometry
and size. Apart from receiver configurations weather conditions also play a significant role in thermal
losses of receiver. Therefore it becomes important to study the effect of incident solar flux, ambient
temperature and wind speed. Thermal losses in receiver are due to conduction, convection and radiation
processes. Experimental works have shown that conduction losses are very small. Therefore neglecting
thermal power loss due to conduction, the total thermal power lost by the receiver is the summation of loss
due to radiation by the receiver and loss due to convection by the receiver. These losses account for most
of the receiver thermal losses resulting from calculation. They are evaluated in the receiver simulation
model.
3. EFFECT OF VARIATION IN WEATHER CONDITIONS
Variation of incident flux, wind speed and ambient temperature affects the performance of receiver and
hence thermal losses from receiver. Therefore, effect of variation in incident flux, wind speed and ambient
temp is studied.
3.1. Variation of Incident Solar Radiation
Figure 1 Monthly average incident flux in W/m2
for Jaipur.
0
200
400
600
800
Jan March May July Sept Nov
IncidentFluxinW/m2
Month
3. Simulation of Solar Thermal Central Receiver Power Plant and Effect of Weather Conditions on
Thermal Power Generation
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The total solar incident flux obtained in year 2007 in Jaipur is shown in Fig.1. It is observed that most
of the sunny days of the year the incident flux received is 900 W/m2
as. On rainy seasons and cloudy days
it is zero. Therefore the effect of variation of incident flux is studied for the values ranging from 0 to 900
W/m2
. As most of the days in the year, wind speed is observed to be 4m/s and the ambient temperature to
be 300
C, therefore these values are considered for simulation.
Figure 2 (a) Variation in thermal losses due to radiation with increase in incident flux
Figure 2 (b) Variation in thermal losses due to convection with increase in incident flux
Figure 2 (c) Variation in thermal power with increase in incident flux
Increase in solar radiation increases the receiver temperature and hence the loss due to radiation also
increases. It can be observed from Fig.2a that the radiation loss increases considerably, almost 4 times
when incident solar radiation increases from 100 W/m2
to 900 W/m2
. Thermal loss due to convection on
the other hand increases by only a small amount i.e. only by 0.6 MWth as shown in Fig 2b. Due to the
increase in thermal losses, the total loss in the receiver increases with increase in flux intensity as shown in
Fig 2c. As the flux intensity increases, the net power absorbed by the receiver increases but as there is
increase in losses, net power generated and the overall efficiency of the receiver is almost constant and is
within a range of 78% to 82%.
0.00
4.00
8.00
12.00
16.00
20.00
0 200 400 600 800 1000
Thermalpowerlossdue
toradiationinMWth
Incident flux in W/m2
2.20
2.30
2.40
2.50
2.60
2.70
2.80
2.90
0 200 400 600 800 1000
Thermalpowerlossdueto
ConvectioninMWth
Incident flux in W/m2
0.00
100.00
200.00
0 100 200 300 400 500 600 700 800 900
ThermalPowerinMWth
Incident flux in W/m2
power absorbed net power Power loss
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3.2. Variation in Wind Speed
It is observed that the average value of wind speed is more than 1.5 m/s in all the months as shown in Fig
3. Hourly data of weather however shows that on many hours of the day, there is no wind i.e. wind velocity
is zero m/s. The maximum value of wind speed is observed to be 15.4 m/s. Therefore for simulation, wind
velocity is varied from 0 m/s to 20 m/s. As most of the days in the year, solar incident flux is observed to
be 700 W/m2
and the ambient temperature is 300
C, therefore the solar incident radiation is taken to be 700
W/m2
and ambient temperature is assumed to be 300
C for simulation.
Figure 3 Monthly average wind speed in m/s for Jaipur.
With input values stated earlier, the performance of receiver is studied under varying values of wind
velocity from 0 m/s to 20 m/s. Power loss due to radiation (PR) remains constant as it is independent of
wind speed and is 11.46 MW and variation in heat loss due to convection is observed, thus affecting the
total power loss and net power generated from receiver along with the efficiency of the receiver.
Figure 4 (a) Variation of heat transfer coefficient Figure 4 (b) Power loss due to convection
with variation of speed with variation of wind speed
Figure 4 (c) Variation in net power generated Figure 4 (d) Variation of efficiency of receiver
with variation of wind speed with variation of wind speed
0
1
2
3
4
5
Jan March May July Sept Nov
Windspeedinm/s
Month
0
10
20
30
40
0 5 10 15 20 25
Heattransfer
CoefficientinW/m2K
Velocity of wind in m/s
0
2
4
6
8
10
0 5 10 15 20 25
PowerLossdueto
ConvectioninMWth
Velocity of Wind in m/s
74
76
78
80
82
84
0 5 10 15 20 25
Netpowergeneratedin
MW
Velocity of wind in m/s
0.72
0.74
0.76
0.78
0.80
0.82
0 5 10 15 20 25
EfficiencyofReceiver
Velocity of Wind in m/s
5. Simulation of Solar Thermal Central Receiver Power Plant and Effect of Weather Conditions on
Thermal Power Generation
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The results obtained are plotted to visualize the impact of wind speed. Fig No 4a shows that the heat
transfer coefficient increases with the increase in wind speed and the thermal power loss due to convection
also increases with wind speed as shown in Fig 4b. It can be seen that after wind speed of 5m/s, power loss
due to convection increases sharply. It is observed, at 0 m/s wind velocity, the net thermal power generated
in the receiver decreases with increase of wind speed. This shows that there is 8.9% of reduction in net
thermal power for increase of wind speed from 0m/s to 20m/s as shown in Fig No.4c. Decrease in receiver
efficiency due to increase in heat loss is also observed from 81.35% to 74.1% as shown in Fig No.4d.
3.3. Variation of Ambient Temperature
Figure 5 Monthly average ambient temperature in 0
C for Jaipur.
Fig No.5 shows the average ambient temperature for all the months of the year 2007 for Jaipur city. It
is observed that the average value of ambient temperature is more than 180
C in all the months, above 350
C
on sunny days and as low as 20
C on winter days. The highest temperature is observed as 450
C. Therefore
for simulation, ambient temperature is varied from 00
C to 450
C. The solar incident radiation is taken to be
700 W/m2
and wind speed is assumed to be 4m/s. The values of thermal losses obtained after simulation
show that with increase in ambient temperature, convection loss increases very slowly and radiation loss
decreases. Thus net power decreases as well as the efficiency also decreases by a very small amount. In
general, there is little impact of ambient temperature on the thermal performance of the receiver. Thermal
power loss due to radiation decreases by very small amount as shown in Fig No.6a. This happens due to
large difference between the receiver temperature and ambient temperature. Small increase in ambient
temperature affects the radiation loss by negligible amount. Thermal power loss due to convection
decreases sharply for the increase in ambient temperature from 00
C to 450
C as shown in Fig.No.6b. The
decrease in loss due to convection is 0.2MWth. Since there is decrease in thermal power loss due to both,
convection and radiation, the net thermal power of receiver increases as shown in Fig.No.6c. Same pattern
is observed for increase in efficiency of the receiver as shown in FigNo.6d. The efficiency of the receiver
increases as net thermal power of the receiver increases.
0
5
10
15
20
25
30
35
40
AmbientTemperaturein0C
Month
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1.70
1.75
1.80
1.85
1.90
1.95
0 5 10 15 20 25 30 35 40 45 50
Powerlossduetoconvection
inMWth
Ambient temperature in deg Celcius
11.56
11.58
11.60
11.62
11.64
11.66
11.68
0 10 20 30 40 50
Powerlossduetoradiationin
MWth
Ambient temperature in deg Celcius
74.55
74.60
74.65
74.70
74.75
74.80
74.85
0 10 20 30 40 50
Efficiencyofreceiver
Ambient temperature in deg Celcius
79.70
79.75
79.80
79.85
79.90
79.95
80.00
80.05
0 10 20 30 40 50
NetthermalpowerinMWth
Ambient temperature in deg Celcius
Figure 6 (a) Power loss due to radiation with Figure 6 (b) Power loss due to convection with
variation of ambient temperature variation of ambient temperature
Figure 6 (c) Variation in net power generated with Figure 6 (d) Variation of efficiency of receiver
variation of ambient temperature with variation of ambient temperature
4. CONCLUSION
It is observed that, the thermal losses due to radiation increases considerably with the increase in incident
flux. It is seen that due to variation in flux intensity the receiver temperature varies and hence the mean
temperature which results in variation of the working fluid properties. The net thermal power generated in
the receiver decreases with increase of wind speed. There is 8.9% of reduction in net thermal power for
increase of wind speed from 0m/s to 20m/s. The efficiency of the receiver increases as net thermal power
of the receiver increases with increase in ambient temperature. Out of these three weather parameters;
incident solar radiation is the most affecting parameter for thermal losses and hence generation of thermal
power.
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