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172 H. Safaei et al. / Applied Energy 103 (2013) 165–179 simulation. Then the associated capital and fuel costs are used to calculate the average cost of electricity (COE) in $/MWh of electric- ity for the simulation period. The capital and fuel cost of the boiler would be lower in the DCAES system compared to the CAES config- uration (due to waste heat recovery). The difference between these values in the DCAES and CAES configurations would be considered as a negative cost (savings) in calculation of COE of the DCAES sys- tem. In addition, the carbon intensity of natural gas (66.0 kg CO2e/ GJ was used to calculate the average carbon intensity of electricity generation (kg CO2e/MWh electricity) in the two systems. Prior to detailed presentation of results at various emission taxes and pipeline lengths, it is beneficial to better understand how the objective function and constraints of the optimization im- pact the simulation. As a case in point, Fig. 3 illustrates the distri- bution of electricity supply, distribution of available wind energy, distribution of energy supplied to compressor for storage, distribu- tion of heat supply, and the energy level of the cavern over a 7 day period at an emission tax of $60/tCO2e in the DCAES scenario. The time frame is arbitrary chosen as the 48th week of the year (Satur- day, November 26 to Friday, December 2, 2011) and as expected, electric load is lower over the weekend. Most of the available wind energy is directly used by the electric load and expander of DCAES is mainly dispatched during hours with low availability of wind. Not surprisingly, less efficient SCGT is poorly competitive with other three types of generators at such a high emission tax and only dispatched for very few hours. Furthermore, waste heat of compression supplies a high portion of the heat load during hours with high availability of wind energy (charging period of cavern). Wind energy is only curtailed when it exceeds the electric load and the storage of this energy is limited by the capacity of the com- pressor. Finally, the cavern is depleted at the end of week to simu- late a weekly cycle of energy storage. 3.1. Optimal size of components An important aspect in determining the average COE is the size of various system components of the CAES and DCAES configura- tions. Fig. 4 illustrates the optimal size of the single and combined cycle gas turbines, expander, compressor and wind farm as well as the maximum hourly electric load (for comparison) at various val- ues of emission tax in the CAES configuration. As shown, the gen- eration fleet is only composed of gas turbines in the absence of any emission tax (effective fuel price of $5.0/GJ). The optimal size of wind farm increases as emission tax is introduced while the opti- mal size of the CAES facility remains zero until a tax of $40/tCO2e. This observation implies that better environmental performance and fuel economy of CAES are not strong enough to justify invest- ing in this capital intensive technology at low levels of emission penalties. As the tax (and thus effective fuel price) increases from zero, the size of SCGT (with higher fuel costs but a lower specific capital cost) decreases while the size of the more efficient but more expensive CCGT increases at a mild rate. However, as CAES enters the picture at $40/tCO2e, the optimal size of gas turbines declines at a sharp rate while the optimal size of wind farm increases rap- idly. Therefore, relatively high emission taxes would be required for economic competitiveness of the more expensive but less pol- luting wind farms and CAES facilities with conventional gas tur- bines. Another interesting observation is the relatively large size of the combined cycle gas turbines even at high emission tax levels. As a case in point, the size of CCGT is 409 MW while the size of the wind farm and expander reach 1160 and 397 MW at a high emis- sion tax of $80/tCO2e. This behavior can be explained by the good thermal efficiency of CCGT technology and low GHG intensity of natural gas as its fuel. Not surprisingly, the size of the energy storage facility remains zero at tax levels below $40/tCO2e in the DCAES scenario as well (Fig. 5). Utilizing less efficient gas turbines would result in lower levelized cost of electricity (objective of optimization) at low tax levels compared to building more efficient but capital intensive DCAES plants. The overall trend is similar to the CAES configura- tion: rapid increase in the size of the wind farm and expander of DCAES and decline in the size of the gas turbines at emission tax of $40/tCO2 and higher. Nevertheless, comparing Figs. 4 and 5 leads to an interesting observation: the size of the wind farm, expander, compressor, and simple cycle gas turbines are larger in the DCAES system compared to the CAES configuration at the same levels of CCR fðSizeCCGT CapExCCGTÞ þ ðSizeSCGT CapExSCGTÞ þðSizeExp CapExExpÞ þ ðSizeComp CapExCompÞ þðSizeWind CapExWindÞ þ ðSizeCav CapExCavÞ þðD CapEx Þ CapExMarginal ðHL Size Þ þðSize CapEx HRU HRU 36524 n Þg þ X PriceEff Elh HR Pipe HOB Max HOB h1⁄41 3:6 þ ElhSCGT HRSCGT þ ElhExp HRExp HeathHRU g ð3Þ HOB The major constraints in this optimization are the following: Hourly electricity generated by the wind farm, simple and com- bined cycle gas turbines and the expander of the storage facility should be equal to the hourly electric load. Heat provided by the HOB and HRU at each hour should be equal to the hourly heat load. Hourly generation of each component of the system should be less or equal to its optimal size. Hourly heat provided by the HRU should be less or equal to the compression energy at that hour multiplied by the efficiency of the HRU. Summation of the hourly wind-based electricity provided to the electric load and to the compressor of the energy storage plant should be less or equal to the optimal size of the wind farm multiplied by its capacity factor at that hour. Conservation of energy should be honored for the energy stor- age plant at each hour; change in energy level of the cavern should be equal to the difference between energy stored and generated by the plant during that hour. The minimum size of SSCGT, CCGT, compressor, expander, and wind farm is set to either 10 MW or 0 MW to simulate a close to real world scenario. This constraint is imposed to avoid the small size of this equipment (e.g. a 0.2 MW gas turbine) which would have a high specific cost ($/kW) due to economies of scale. The air storage facility would be sized for a week-long storage period and it is assumed to be depleted by midnight Friday each week. Since the electric load and thus its price would be lower on the weekend compared to weekdays, the cavern would most probably be generating electricity during the weekdays and storing energy during the weekend. 3. Results and discussion In order to compare the performance of the DCAES system with the CAES system, a base fuel price of $5.0/GJ was assumed while the emission tax was varied from 0 to 80 $/tCO2e at $10/tCO2e intervals. Each $10/tCO2e increase in the emission tax corresponds to approximately $0.66 increase in the effective fuel price. At each effective fuel price, the optimal size and dispatch strategy of vari- ous components were determined by the mixed integer linear opti- mization code developed in MATLAB. The following is a description of the results. NG CCGT CCGTPDF Image | 20 kW ORC Turbine Off-Design Performance Analysis
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