The economical benefit index can be presented as the net annual benefit function B. The net annual benefit function is obtained by subtracting the total cost function (5) from the revenues. The latter are given by the product of the discharging price and the discharging duration. Therefore
[$/kW-yr] (8)
where the discharging price P/hd) is a function of the discharging duration, hd (which is equivalent to the plant service factor).
8. Optimal Techno-Economical Results
Since the objective function to be maximised, Eq.(8), is nonlinear and subject to inequality constraints, a mathematical programming algorithm is to be applied for the optimization. The BCONF subroutine of the IMSL Library [20] was used for this purpose, [1]. An example of using the proposed procedure is presented for demonstration purposes. Typical cost data were taken from Vadasz and Weiner [10]. The heat price P,if
was varied between 0.01 and 0.1 $/kWh of heat from combustion and the optimization procedure was repeated for each incremental value of ~if' The resulting optimal values of the isentropic temperature ratio and of the recuperator effectiveness are presented in Fig. 3 together with the corresponding maximum values of the net annual benefit. The results show that the optimal recuperator effectiveness increases with increasing the heat price reaching a value of 0.51 for the maximum heat price considered. The optimal isentropic temperature ratio also increases with increasing the heat price as long as the heat price is not excessively high (i.e. less than 0.078 $/kWh). Over and above a critical heat price value ( ~if.CC =0.078 $/kWh ) the optimal isentropic temperature ratio reaches its maximum value (R' = 3.5)on its upper boundary and it remains unchanged as the heat price increases. The net annual benefit decreases smoothly when passing through this critical heat price point. It should be emphasised that at a critical value of ~if.a
Vadasz and Weiner [10] identified a transition to the adiabatic CAES option from their simple model (i.e. excluding recuperator, reheaters and intercoolers). It is observed here (Fig.3)that incorporating a recuperator introduces an additional degree of freedom in the optimal design and the results suggest utilising this option as a more economical alternative to an adiabatic system. The qualitative consequential environmental implications are obvious.
-- ~ 700
... 600
--"'>
"- 500
~~ 400
~~" 300
~ 200
....."8-i1 100
r----.----~---r--______, 4 "b
~.~ + + -~;.",.,.,==-=-:I3.5 ~I
... ~ ~'S
...~,,~:....- : __ R* i!~
__ h "'h_h~_~:"";'h__'h~__ h_' -E;c 2.5 Ii
,:ã:;~tããã:ãF,ã.: .. :,U
o '--_ _...i ==_:::...- __--..1...:_--====__---'-~____':5 ~8-
om 0.0325 0.055 0.0775 0.1
Figure3. Optimal results from an example demonstrating the procedure[l].
9. Conclusions
The impact of energy technologies on the environment was introduced and followed by an analysis, which places the discussion in the context of thermodynamic and techno- economical optimizations. Applying an optimal design procedure by using techno- economical analytical tools was demonstrated for a Compressed Air Energy Storage system. The parameters affecting the cost-benefit balance of the CAES plant were identified and possible optimization criteria were suggested. The results of the presented example show the advantage of using this procedure to analyse different design options
and for sensitivity analysis of the project benefit to future unpredictable variations in fuel price. In order to assess the quantitative environmental impact of energy technologies, multiple criteria optimization methods need to be used.
10. References
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2. Beckman, P., "Global Cooling" ,Access10Energy,19, No.7, 1992.
3. NASA wwwebsite, ''http://science.msfc.nasa.gov/newhome/essd/atmos_temps'', May 1998.
4. Beckman, P., "Ozone Layer Revisited" ,Access to Energy,20, No.7, 1993.
5. Beckman, P., "The Saga of Vanishing Trees" ,Access10Energy,21, No.[, 1993.
6. Olek, S., "Potential Impact of Pumped Energy Storage on the Lower Reservoir Aquatic Ecology", Proceedings of the USA-RSA bi-national Workshop on Energy and Environment, Durban-Westville, 8- 12 June 1998.
7. Vadasz, P., Pugatsch, Y. and Weiner D.,: "A Performance Analysis of a Compressed Air Energy Storage System in Aquifer",Israel Journal of Technology,25, pp. 13-21, 1989.
8. Vadiisz, P., Weiner, D.,: "Compressed Air Storage Becomes More Attractive", Modern Power Systems, 3, No. 12, pp. 45-49, December 1988.
9. Vadasz, P., Pugatsch, Y. and Weiner D.,: "Compressed Air Energy Storage: Engineering Considerations Using An Optimal Conceptual Design", Presented at the 8th Miami International Conference on Alternative Energy Sources, Miami Beach, FI, December 14-16, 1987.
10. Vadasz, P., Weiner, D.,: "Analysis and Optimization of a Compressed Air Energy Storage System in Aquifer",Presented at the 31st ASME Gas Turbine Conference, ASME Paper 86-GT-73, Dusseldorf, June 8-[2, [986.
11. Weiner, D. and Schnaid, I.: "Second-Law Analysis of a Compressed Air Energy Storage (CAES) System", Presented at the 37th ASME International Gas Turbine and Aeroengine Congress and Exposition,ASME Paper 92-GT-115, Cologne, Germany, June 1-4, 1992.
12. Schnaid, I., Weiner, D., Brokman, S., "Novel Compressed Air Energy Storage (CAES) Systems Applying Air Expanders", Presented at the International Gas Turbine and Aeroengine Congress and Exposition,ASME Paper 95-GT-282, Houston, Texas, June 5-8, 1995.
13. Touchton, G., "Gas Turbines: Leading Technology for Competitive Markets", Global Gas Turbine News,36, No.1, 1996.
14. de Biasi, V., "CHAT rivals 52% comb cycle plant efficiency at 20% less capital cost",Gas Turbine World,25, No.3, 1995.
15. Vadasz, P., Pugatsch, Y. and Weiner, D.,: "On the Optimal Location and Number of [ntercoolers in a Real Compression Process",The 33rd ASME International Gas Turbine and Aeroengine Congress and Exposition,ASME Paper 88-GT-44, Amsterdam, 1988.
16. Vad'5sz, P., Weiner, D.,: "The Optimal [ntercooling of Compressors by a Finite Number of Intercoolers", Trans. ASME. Journal of Energy Resources Technology, 114, No.3, pp. 255-260, September 1992.
17. Nakhamkin, M., Swensen, E.C., Abitante, P.A., Whims, M., Weiner, D., Vadasz, P., Brokman, S.,
"Conceptual Engineering of a 300 MW CAES Plant, Part I: Cost Effectiveness Analysis",Presented at the 36th ASME International Gas Turbine and Aeroengine Congress and Exposition,ASME Paper 91- GT-61, Orlando, FI., June 3-6, 1991.
18. Vadasz, P., Weiner, D.,: "Correlating Compressor and Turbine Costs to Thermodynamic Properties for CAES Plants",Cost Engineering,29, No. II, pp. 10-15, November 1987.
19. Vadiisz, P.,: "A Second-Order Marginal Costs Approximation for Energy Storage Charging and Discharging Price Functions",ASME Journal of Energy Resources Technology,111, pp.154-159, 1989.
20. [MSL [nc., "FORTRAN Subroutines for Mathematical Applications", User's Manual, Houston, Texas, 1991.
ON THE LOWER RESERVOIR AQUATIC ECOLOGY