Various plant configurations

The main parameters of the plant configurations discussed in this paper are listed in Table 1. Pretorius [2] found that plants with larger chimney diameters provide lower COE. The effect of varying the chimney diameter is investigated using two base configurations with a 1000 m and a 1500 m high chimney.

The question of how big a first large-scale solar chimney power plant should be has been asked many times. To reduce the risk for a first prototype, building a smaller plant could be an option.

The implications on the design of the PCU of building such a smaller plant are discussed in this paper. The most promising options to improve the plant performance, which are double glazing the collector and applying anti-reflective coating [2], are also investigated.

Table 1: List of main parameters of the considered plant geometries

Configuration

1

2

3 4 5 6

7 8 9 10 11

Chimney height, m

500

1000

1500

Chimney diameter, m

100

120

150 180 210 240

160 190 220 250 280

Collector diameter, m

2000

5000

7000

Coll. inlet roof height, m

4

5

6

3. Results

The multiple horizontal axis turbine configuration using a single rotor layout with IGVs provides the lowest cost of electricity for all plant geometries investigated here. The optimum number of turbines is 10 for the smallest plant and 42 for the biggest plant. The optimal turbine diameter is 31 m for the smallest plant and 41 m for the biggest plant. The lowest COE was found with Configuration 8 (Tab. 1) at 0.105 €/kWh. The COE for the smallest plant is 2.5 times higher due to a much lower annual power output.

Reducing the number of turbines below the optimum increases the COE mainly because of a decrease in efficiency and an increased generator cost. Increasing the number of turbines beyond

image104

the optimum increases the COE mainly because the reduction in generator cost is outweighed by the cost for transportation, for the ducts and for assembly and installation (see Figure 2). The counter rotating turbine layouts show similar trends as the single-rotor layout with IGVs. They provide a COE which is only about 1 % higher than the one of the single-rotor layout with IGVs (Figure 3).

Solar chimney cost models found in the literature either assume a constant specific initial cost (€/kW) for the PCU, or they assume the cost of the PCU to be a constant percentage of the sum of

the collector and chimney cost. The specific initial cost of the PCU resulting from the model presented here ranges from 437 to 1644 €/kW for the various plant geometries. The PCU cost as a percentage of the sum of the collector and chimney cost ranges from 17 to 30 %.

On the example of Configuration 5 it is shown that the implementation of double glazing and anti­reflective coating holds a potential to significantly reduce the COE of the solar chimney power plant. With the models chosen in this study the cost of electricity is reduced by 17.8 %. The annual power output increases by 51.7 % while the initial investment cost only increases by 26.0 %.

As can be seen from Figure 4 and Tables 2 and 3, the notion to use larger chimney diameters, as brought forward by Pretorius [2], can indeed be supported; for the plant with a 1000m high chimney the optimum chimney diameter is between 150 and 180m. For the plant with a 1500m high chimney, the optimum chimney diameter is 190m. These values are higher than the ones cited in earlier publications. But they are also significantly lower than the ones suggested by Pretorius

[2]

image105 image106

(210 m for the 1000 m high chimney and 280 m for the 1500 m high chimney). This is because the plant cost model and the cost model for the PCU used here are more sensitive to a change in chimney diameter than the ones of Pretorius (2006) as the collector cost is less dominant.

Fig. 4. Plant cost and COE vs. chimney diameter for the reference plant with (a) a 1000m and (b) a 1500m

high chimney.

Tab. 2. Results for various chimney diameters for the plant with a 1000m high chimney.

Chimney height, [in]

1000

Chimney diameter, [m]

120

130

180

210

240

Number of turbines, [ -]

19

23

26

27

29

Turbine diameter, [m]

30.0

34.1

36.6

38.7

41.0

Turbine speed, |rpm]

28

23

23

21

20

Turbine tip speed, [m/s]

43.9

44.0

43.3

42.6

42.0

Turbine through flow velocity, [m/s]

14.3

12.6

12.3

12.4

11.6

Diffuser area ratio, [-]

1.0

1.0

1.1

1.3

1.4

Efficiency of PCU (tt), [%]

79.8

79.9

79.1

78.0

77.8

Annual power output, [GWh]

240.7

284.7

311.3

328.0

341.8

Cost of collector, [M€]

193.4

193.4

193.4

193.4

193.4

Cost of chimney, [M€]

93.1

117.1

138.3

139.1

179.1

Cost of PCU, [M€]

48.2

68.4

84.8

96.1

111.0

Cost of PCU, [as % of Cc + Cm;[

16.7

22.0

23.3

27.3

29.8

Cost of electricity, [€/kWh]

0.1449

0.1368

0.1368

0.1392

0.1433

Tab. 3. Results for various chimney diameters for the plant with a 1500m high chimney.

Chimney height, [in]

1500

Chimney diameter, [m]

І60

190

220

250

280

Number of turbines, [ -]

32

36

39

41

42

Turbine diameter, [m]

30.9

34.6

37.8

39.4

41.3

Turbine speed, [rpm]

33

30

27

25

24

Turbine tip speed, [m/s]

53.6

53.5

53.4

52.4

52.0

Turbine through flow velocity, [m/s]

16.8

15.3

14.2

14.3

14.1

Diffuser area ratio, [-]

1.0

1.0

1.0

1.2

1.3

Efficiency of PCU (tt), |%|

80.1

80.1

80.0

79.2

78.7

Annual power output, [GWh]

725.9

820.8

888.6

930.2

960.3

Cost of collector, [MG]

379.1

379.1

379.1

379.1

379.1

Cost of chimney, [MG]

273.7

321.8

368.8

414.8

459.7

Cost of PCU, [M€]

110.1

144.0

176.2

198.1

217.9

Cost of PCU, [as % of Q + Ccoi]

16.9

20.5

23.6

24.9

26.0

Cost of electricity, [€/kWh]

0.1073

0.1045

0.1052

0.1075

0.1106

Подпись: Fig. 5. Plot of plant cost and COE vs. number of turbines for configuration 1.

For a smaller plant (configuration 1) a PCU with 10 horizontal axis turbines provides the lowest cost of electricity (Fig. 5). Even though the overall plant cost for this small plant is only a fraction of the cost of a large plant (e. g. a tenth of the cost of configuration 7) the optimal cost of electricity is 2.5 times higher due to a much lower annual power output. In comparison to configuration 7, for the smaller plant discussed here, the generators, the electrical interface/connection, the power electronics and the ducts contribute a much smaller portion to the PCU cost. In contrast, the inlet guide vanes, the turbine rotors, transportation as well as assembly and installation contribute a much bigger portion. The cost of the chimney for this plant is 21.82M€, the cost of the collector 30.77M€. The initial capital cost of the PCU is between 17.30 and 20.31M€, which is equal to 32.9 to 38.6% of the sum of the cost of the collector and the chimney. This is a much bigger portion than for the larger plants. As a consequence the optimal diffuser area ratio is higher for the smaller plant and the efficiency of the PCU is reduced.

4. Conclusion

For all plants discussed here PCUs with multiple horizontal axis turbine configuration using a single rotor layout with IGVs provides the lowest cost of electricity. For the counter rotating turbine layouts the cost of electricity is only 1.1% higher than with a single rotor layout with IGVs.

While the size and performance of the different plants vary a lot, the optimal PCUs all look very similar. The optimal number of turbines varies, but their individual size, the number of blades and even the efficiency of the PCU remain close to constant. The cost of the PCU, however, varies significantly; the specific initial cost of the PCU varies between 437 and 1644€/kW.

A large plant with e. g. a 1500 m tall chimney provides a low cost of electricity and a high annual power output. But the financial (and technological) risk is also high. Moving towards smaller plants the risk is reduced. But the annual power output is also reduced, and the cost of electricity increases. Measures like double glazing and anti-reflective coating could counteract this trend.

Acknowledgements

The authors would like to express their gratitude to the VolkswagenStiftung, Germany, and to the National Research Foundation of South Africa for financial support. They would also like to thank Dr. J. P. Pretorius for providing the plant simulation results.

References

[1] Schlaich, J., Schiel, W., Friedrich, K., Schwarz, G.,Wehowsky, P., Meinecke, W. and Kiera, M. (1995). The solar chimney — Transferability of results from the Manzanares solar chimney plant to larger scale — plants. Tech. Rep., Schlaich Bergermann und Partner, Civil Engineers, Stuttgart, Germany.

[2] Pretorius, J. P. (2006). Optimization and Control of a Large-scale Solar Chimney Power Plant. Ph. D. thesis, University of Stellenbosch.

[3] Pretorius, J. P. and Kroger, D. G., Critical evaluation of solar chimney power plant performance. Solar Energy, 80 (2006) 535-544.

[4] Bernardes, M. A.D. S. (2004). Technische, okonomische und okologische Analyse von Aufwindkraft — werken (Technical, Economical and Ecological Analysis of Solar Chimney Power Plants). Ph. D. thesis, Universitat Stuttgart. (in German).

[5] Denantes, F. and Bilgen, E., Counter-rotating turbines for solar chimney power plants. Renewable Energy, 31 (2006) 1873-1891.

[6] Fluri, T. P. (2008) Turbine Layout for and Optimization of Solar Chimney Power Conversion Units. Ph. D. thesis, University of Stellenbosch.

[7] Fluri, T. P. and Von Backstrom, T. W. Performance analysis of the power conversion unit of a solar chimney power plant, Solar Energy Journal, (2008) accepted for publication.

[8] Riggs, J. L., Bedworth, D. D. and Randhawa, S. U. (1996). Engineering Economics. 4th edn. McGraw-Hill.

[9] Schlaich, J. (1995). The Solar Chimney — Electricity from the Sun. Edition AxelMenges.