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Optimal annual operation of the dry cooling system of a concentrated solar energy plant in the south of Spain
Energy xxx (2015) 1e9
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Optimal annual operation of the dry cooling system of a concentrated solar energy plant in the south of Spain Mariano Martín* Departamento de Ingeniería Química, Universidad de Salamanca, Pza. Caídos 1-5, 37008 Salamanca, Spain
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 September 2014 Received in revised form 10 February 2015 Accepted 15 March 2015 Available online xxx
This work presents the optimization of the operation of a concentrated solar power plant with dry cooling over a year, evaluating the molten salts storage, the power block and the air cooling system as a function of the climate and atmospheric conditions. We locate the plant in the south of Europe, Almería (Spain), due to the high solar irradiation and for comparison purposes with a wet cooling based facility. The optimization of the system is formulated as a multiperiod MINLP (mixed integer non-linear programming problem) that is solved for the optimal production of electricity over a year defining the main operating variables of the thermal cycles and the cooling system. The power produced ranges from 9.5 MW in winter to 25 MW in summer, where 5% of this power is consumed by the air cooling system. The annual production cost of electricity is 0.16 V/kWh and the investment required is 265 MV, both slightly higher than when wet cooling is used, but with negligible water consumption. For the selected location, the wet based technology generates slightly less CO2 than the air cooled facility. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Energy Concentrated solar power Rankine cycle Dry cooling Mathematical optimization
1. Introduction Energy and water consumption are major concerns nowadays. While pursuing energy efficiency has become a natural trend, water savings have not received the same attention until very recently. Lately some reports claim that two thirds of the planet will suffer water stress in the next decade [1]. The link between energy production and water consumption is well established when using fossil fuels. However, social pressure towards cleaner energy production and lower environmental impact are leading to develop alternative technologies and use renewable energy sources whose water consumption is still under evaluation. Considering solar energy, it is important to note that the solar energy that reaches the surface of the Earth is more than enough to cover the mankind needs [2]. However, the solar energy received at the surface is only a few kWh/m2/day. To achieve higher intensities and high operating temperatures CSP (concentrated solar power) technologies are used. They are based on the concentration of solar radiation to heat up a fluid that is used to generate steam and ultimately power. CSP plants consist of three parts: solar field, steam turbine and cooling unit. Over the last years, demonstration solar plants are
* Corresponding author. Tel.: þ34 923 294479. E-mail address: [email protected].
being built across the globe [3e5]. For the continuous operation of these plants during the night and in overcast days, thermal energy from the heat tank and/or an additional source of energy are typically used [3]. The thermodynamic cycle selected is a Rankine one with regeneration since they provide efficiency advantages [6]. Finally, like any other power plant, the cooling system is a challenge because energy production has associated a certain water consumption. Mainly we can use wet cooling or dry cooling. However, the low price for water results in less attention paid to its consumption and availability. Therefore, wet cooling is widely used in the power industry but it has as a drawback, the consumption of water. Water is lost by evaporation in the cooling towers [7]. In case of a solar based power plant, it is important to highlight that typically regions where the solar incidence is high correspond with those where the availability of water is low. Thus, indirect and direct dry cooling can be implemented. Indirect dry coolers use water to condensate the steam from the low pressure turbine. An air cooler cools down the water in a closed cycle. Direct dry cooling typically uses either an A-frame configuration so that air is used directly as cooling agent to condensate the steam or by means of natural convection, where a design similar to wet cooling towers is provided so that the air moves driven by density gradient. A-frame are the most common air cooled condensers. Over the last years, a number of simulation based studies have compared the use of wet and dry cooling technologies in power
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plants, conventional or CSP. Kelly and Price [8] published a report comparing wet, forced or mechanical draft, and dry heat rejection for a Rankine Cycle using the GateCycle Program. They presented that the efficiency of the cycle increases for higher inlet pressure and temperature at the turbine and decreasing temperature and pressure at the outlet. The exhaust pressure and temperature have an important effect on the cooling. The low prices of freshwater revealed that the levelized cost of energy was lower in the case of the wet system while the capital investment cost was 5% lower too. The penalty in the energy production cost was at least 8% for dry cooling facilities. Finally, they found that the production cost of the wet cooling plant reached that of the dry cooling based one when the cooling water reached the value of $14.8 per 1000 gal. Turchi et al. [9] presented a report that evaluated the efficiency and impact of dry and wet cooling technologies in parabolic trough CSP plants. They used the SAM (solar advisor model) from the NREL. The switch from wet to dry cooling increases from 3 to 8% the cost of electricity, reducing the water consumption by more than 90%. The water consumed is due to steam cycle maintenance and mirror washing. The investment of the dry cooled facilities was 2% higher. Zhai and Rubin [10] compared the performance of wet induced draft cooling tower and dry A-framed cooling technologies for coal power plants. The models were implemented in the IECM package [11]. The results showed that the dry cooling system was more than twice as expensive per kW of cooling, resulting in an investment cost 8.5% higher when using the dry cooling system, and the efficiency of the plant got reduced 2%. The advantage was the null water consumption versus the 2.46 t of water per MWh produced required by the wet cooling system. Blanco-Marigorta et al. [12] and Habl et al. [13] compared a forced draft wet cooling tower with an A-frame air cooler for the operation of the Andasol 1 power plant following a process simulation approach. This plant uses a Rankine cycle and concentrated solar technology as source of energy. Apart from comparing the effect of the exhaust pressure on the energy output, the dry cooling technology plant showed a reduced energy output in the summer months due to the enhanced need for cooling as a result of the higher ambient temperature. No results on actual water consumption are reported. The electricity production cost in the zone around the Andalucian Granada are 15.27 ct/kWh when using wet cooling and 16.08 ct/kWh in case of dry cooling. Barigozzi et al. [14] performed a sensitivity based optimization study to compare a forced wet cooling condensation system and an A-frame air cooler condenser for cogeneration plants. They modeled the plant using the Thermoflex software to evaluate the effect of the exhaust pressure of the turbine and the air humidity on the power output. The air cooled condenser resulted the best way to reject heat if the ambient temperature is lower than 15 C. However, no consideration on water consumption was presented. Another interesting comparison was presented in the use of concentrated solar power for water desalinization. Liqreina [15] presented the operation of dry cooled based plants, in particular Andasol in Spain and Ma'an in Jordan, and compared the use of dry cooling with wet cooling over a year long using also a simulation based approach, Greenius software. The dry cooled facility presented regularly 4e8% lower energy production. The LCOE tuned out to be 0.1284 V/kWhe with an investment of 248 MV, while the dry cooled based plant showed a cost of 0.1491 V/kWh with an investment of 289 MV for a production facility of 50 MW. The water consumption of the wet cooled was 1.6 L/kWh, while the dry cooled was 0.095 L/kWh, computed using SAM software. Palenzuela et al. [16] used a simulation based approach using EES (engineering equation solver) software assuming a steady state operation. The efficiency of the dry cooling based plant was 2% lower than the evaporative water cooling system, while the
levelized energy cost of the dry cooling was 0.249 V/kWh vs. the 0.241 V/kWh of the wet system. The problem with the use of modular commercial simulation software is that it is not that easy to see how cost estimations are implemented nor the detailed design of the cooling systems, which are the key issues for the energy and water consumption associated. Furthermore, only sensitivity based studies were carried out to evaluate and optimize the effect of some operating parameters. On the other hand, the advantage is that rigorous thermodynamics are solved. Lately, Martín & Martín [17] optimized a concentrated solar plant operating over a year using a mathematical programming approach and later it was coupled with a biomass polygeneration system to provide for the energy when solar is not enough [18]. The process consisted of a regenerative Rankine cycle using wet cooling technology. Apart from determining the optimal pressures and temperatures using an equation based optimization approach, the authors showed that an average of 2.1 L of water per kWh produced was consumed over a year of operation. In this paper we use mathematical programming techniques for the conceptual optimal design and operation of a concentrated solar power plant using an A-frame air cooling system over a year. Our aim is to evaluate the cooling system that, while reducing water consumption compared to the wet cooling based facility [17], requires energy for the operation of the A-frame. The facility is located in Almería (Spain), a region with one of the highest solar radiations in Europe, the same region selected for the previous work [17]. The paper is organized as follows. Section 2 describes the modeling features and the atmospheric conditions of the selected location. In Section 3 we present the optimization procedure. Next, in Section 4 the main results are discussed such as the major operating conditions, the power consumed by the cooling system and the units of the A-frame needed, followed by an economic evaluation and a comparison between dry and wet cooling facilities based on CO2 savings. Finally, in Section 5 we draw some conclusions. 2. Modeling 2.1. Modeling assumptions The plant consists of three parts, the heliostat field including the collector and the molten salts storage tanks, the steam turbine and the air cooler steam condenser. Fig. 1 presents the flowsheet for the process where the heliostat field has not been included. For the detailed information on the modeling features of the heliostat field and the steam turbine, we refer to the supplementary material and to previous work [17,18]. Our process is based on the use of a tower to collect the solar energy and a regenerative Rankine cycle. The steam is generated in a system of three heat exchangers where water is heated up to saturation and then evaporated using the total flow of molten salts. However, only a fraction of the flow of salts is used to superheat the steam before it is fed to the first body of the turbine. The rest is used to reheat up the steam before it is fed to the second body. In the second body of the turbine, part of the steam is extracted at a medium pressure and it is used to heat up the condensate. The rest of the steam is finally expanded to an exhaust pressure, condensed and recycled. In the model, we consider conservative average efficiencies for the heliostat field and the turbine efficiency based on rules of thumb for the conceptual design of the facility over a year, using a time period of a month, for comparison purposes with previous work [17]. Refs. [19e21] can be used to include the operation of the solar field into this formulation accounting for the decrease in the efficiency of the turbine as function of the load and the efficiency of the solar field as a function of the direct normal irradiation. In Refs. [19,20] we see that the efficiency
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Fig. 1. Flowsheet of the concentrated power plant facility.
of the turbine may decrease up to 3% when it operates at half load, while the effect of the direct irradiation can decrease the efficiency of the field by 5%. Although important concepts, the expected error in the equation based models for the turbine is expected to be on that range, while we use a low efficiency for the solar field to be on the save side. For the condensation of the steam we propose the use of a direct air cooled system. Based on Heyns [22], we consider a system given by a number of streets, up to three. Each one has 10 units. Each of the units of the A-frame has two bundles with two lines of rows of 60 tubes each. The geometrical characteristics of the finned tubes can be seen in Appendix A. The energy balance given by eqs. (1)e(5) provides the air flow needed. We assume that the maximum approach temperature is 10 C.
mair $Cp;air $ Tout;month Tamb;month ¼ Q ðHX5Þ;
(1)
Tout;month Tturb3 10;
(2)
rair $Rgases $Tamb;month ¼ Patm $MW;air
(3)
fair $rair ¼ mair ;
(4)
2 nfans $0:25$p$ Dfan ¼ 0:25$tube L$Width$nbundles ;
(7)
In order to compute the area that the heat exchanger provides, the design parameters as presented in Manassaldi et al. [23] are used, eqs. 8e10
1 Aof ¼ 2 p$finN $ tube2Df tube2D þ p$tubeDf $fintf $finN ; 4
(8)
Aot ¼ Aof þ p$tubeD $ 1 fintf $finN ;
(9)
Aheat;exchanger ¼ tubesNrow $tubesN $tube L$Aot $streets$units $bundles (10) Based on literature [22], the main resistance to the heat transfer is the film coefficient of the air side. We approximate the global heat transfer coefficient Uglobal by h air using the correlation presented by Pieve & Salvadori [24], eq. (11):
fair;fan $nfans ¼ fair ;
(5)
The power consumed by the fan in the A-frame type condenser is computed using the results in Ref. [22], eqs. (6)e(7). We assume an efficiency, h, of 90% based on the same study:
Powerfan
2 ¼ 0:001$nfans ðrair =1:2Þ$ 0:4762$ fair;fan 1 ; 59:414$fair;fan þ 186644 h
kair $0:134$ðReair Þ0:681 $ðPrair Þ0:33 tubeD 10:11 10:2 0 0 finpf fintf finpf fintf A A $@ $@ ; 0:5$ tubeDf tubeD fintf
Uglobal z
(11) where
(6)
Reair ¼
fair $tubeDeq ; mair $Amin
(12)
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0 @ðtube
Df tube D2 Þ ð2$finpf Þ 2
tubeDeq ¼
þ
tubeDf $fintf finpf
0 @1 þ
1 . þ tubeD $ 1 fintf finpf A
1 ðtubeDf tubeD ÞA
;
finpf
Amin ¼ bundles$streets$units$tubesN $tubeL $ finpt tubeD 2$fintf $0:5$ tubeDf tubeD $finN $Sinq (14) Prair
(13)
Cp;air $mair ¼ ; kair
(15)
3. Optimization procedure The equation based model is formulated as a multiperiod MINLP problem written in GAMS [30]. We maximize the energy produced, z, given by Eq. (18), over the 12 time periods:
z¼
X
WðTurbine1;tpÞ þ WðTurbine2;tpÞ þ WðTurbine3;tpÞ WFan
tp
The physical properties of the air are calculated using the correlations presented in Ref. [22], see eqs. (A-1,A-3) in the Appendix. Finally, we use Cheng approximation to compute the LMTD (logarithm mean temperature difference), [25]. Thus, the cooling area is computed as in eq. (16):
Q ðHX5Þ ¼ U_global LMTD Area_Cooling;
(16)
The area provided by the heat exchanger must be at least 10% larger.
Area_HX 1:1Area_Cooling ;
(17)
The physical design of the heat exchanger is based on the bundle of tubes for an A-frame heat exchanger. The size of the fan and the number of tubes per row are adjusted for the performance of the heat exchanger to be within the real operation of an air cooled condenser and typical configurations of the tubes [26].
2.2. Operating conditions In Table 1 we present the monthly atmospheric conditions of the region where we allocate the facility including the radiation received in Almería, the sun hours, the ambient temperature of the air and its humidity [27e29]. It is important to notice that the same formulation can be used for any other region by using the appropriate data to compare the performance of the plant under different conditions.
(18) Subject to the process model described in section 2. The main decision variables are the operating inlet and discharge pressures at the three bodies of the turbine, the split fraction for the molten salts to be used at HX1 and at HX4, the fraction of steam extracted from the second body of the turbine, the air flow rate, the number of units and fans in operation for the cooling system and the air outlet temperature. The problem consists of 3200 equations and 3500 variables. The complexities due to the integration of the design of the cooling system together with the Rankine cycle result in the need for proper initialization by using several starting points based on data from the literature and bounds for the variables such as flowrates. Furthermore, we decompose the problem into the 12 months. Next, we relax each MINLP (multiperiod mixed integer non-linear programming problem) problem so that the number of units, fans and streets for the air coolers are treated as continuous variables solving 12 NLP. After the optimization, we round the values obtained and re-optimized the operation of the plant. Note that the relaxed solution can be interpreted as a fan not operating at full load while the integer solution implies fully used of each of the units. For design and costing purposes, an integer solution is needed. CONOPT 3.0 [31] is used to solve the problem. This formulation can also be used to evaluate daily or weekly operation of the plant by changing the time periods from a monthly basis to an hourly or daily basis monitoring the atmospheric conditions which can be useful for the integration of the solar energy into the grid. This will allow for
Table 1 Atmospheric conditions [27e29]. Month
kWh/m2$day
Day
Sun (H)
Sun (h/day)
T Amb ( C)
% Humidity
J F M A May June July Aug Sep Oct Nov Dec Average
4.377 5.125 5.319 6.387 6.697 8.587 8.668 7.342 6.057 4.126 3.513 3.326 5.794
31 28 31 30 31 30 31 31 30 31 30 31 30.4
191 191 228 250 299 322 338 312 257 221 187 176 248
6.161 6.821 7.355 8.333 9.645 10.733 10.903 10.065 8.567 7.129 6.233 5.677 8.13
12.5 13.2 14.7 16.4 19.1 22.7 25.7 26.4 24.0 20.0 16.2 13.7 18.7
69 68 66 64 66 64 63 65 66 68 70 70 66.6
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process control on the operation of the fans, the effect of clouds and accounding for the temperature interval during the day. In this case, more detailed evaluation of the efficiency of the solar field must be included. Actually the effect of the variation of the temperature from month to another is similar to that on a daily basis, the fans usage varies accordingly. However, in this work we focus on the conceptual design of the facility and average monthly operation. 4. Results We divide this section in three parts presenting the optimal operating conditions, an economic evaluation and a comparison between wet and dry cooled facilities based on CO2 savings. 4.1. Plant operation
Fig. 3. Total energy produced in the CSP plant and consumption by the dry cooling system.
The optimization of the flowsheet reveals that 30% of the salts from storage tank 1 are used in HX1 to heat up the saturated steam while the rest are sent to HX4 for the reheating stage. For all the periods it turns out that the superheated steam enters the first body of the turbine at 125 bar and 555 C exiting it at 11 bar. This stream is reheated up in HX4 to 500 C and fed to the second body of the turbine. The outlet pressure of the second body of the turbine varies from one month to the other, see Fig. 2. This is the main difference when compared to the wet cooling facility in Ref. [17]. 15% of the stream that leaves the second body of the turbine is extracted and sent to HX6 while the rest is expanded in the third body of the turbine to an exhaust pressure of 0.19 bar. This stream is condensed in HX5, the A-frame system. In Fig. 2 we present the continuum solution and the integer solution as discussed in the solution procedure. Both are quite similar. The exhaust pressure we obtained, 0.19 bar as saturated steam, is similar to Palenzuela's work cases 1,3&4 [32], 0.18 bar, higher than the values presented by Nezammahalleh et al. [33], Xu's et al. [34] or Ghobeity et al. [35], and lower than Salcedo et al. [36] or Palenzuela's case 2 [32]. Halb et al. [13] presented a sensitivity study evaluating the effect of the exhaust pressure on plant efficiency considering a range of values from 0.06 to 0.2 bar. They found a decrease in power efficiency with the exhaust pressure pointing out that a value of 0.073 bar is the most convenient. The value corresponds also to Andasol solar power plant, that uses trough technology, instead of the Tower based design we considered based on GEMASOLAR plant. Furthermore, we fix the exhaust to be saturated vapor to avoid any mechanical problems in the turbine. Fig. 3 shows the year-round production of electricity. During summer we obtain a maximum of 25 MW for two consecutive
months, June and July, while the lowest production capacities are found in November and December, just below 10 MW. From these values, similar in every case to the facility that uses wet cooling [17], we use a fraction in order to provide for the fans of the A-frame system. In Fig. 3 we also see a blue (in web version) section of the column representing this consumption, around 5%. The configuration of the air cooler condenser and the air flow needed to condense the steam are the ones that determine this consumption of energy. In Fig. 4 we present the fan consumption power along the year. We show two solutions, the integer one and the relaxed non linear solution. Again, both are similar. We see that the hottest month requires a large consumption since the LMTD is smaller and a higher air flow needs to be provided. However, as presented in Fig. 5, we see a constant increase of 14 C in the air temperature across the A-frame. For this figure we consider only the integer solution. The use of fans and units over the yearis shown in Fig. 6. They correspond to monthly average use since we use average monthly data for the atmospheric conditions, see Table 1. This figure allows introducing controllability issues in the operation of the plant. We see that our formulation is capable of computing the number of units that must be in operation at a time and the fans devoted. The integer solution assumes that fans are operating at full capacity. However, the continuous solution can be interpreted as the fraction of the total power of the fan needed. For design purposes we need the integer solution to determine the units to be installed. Furthermore, typically each unit will have a fan, see also sizing of the units in Appendix A. The results in Fig. 6 show that the fans will not be operating at full capacity in such a case but almost at one half of it.
Fig. 2. Exhaust pressure at the outlet of the second body of the turbine.
Fig. 4. Fan power consumption over a year.
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Cð$MÞ ¼ ð0:0652$ðkg=s of steamÞ þ 1:8377Þ
Fig. 5. Air inlet and outlet temperatures.
Fig. 6. Usage of the units and fans. Planning of the plant operation.
In spite of the use of local solvers, due to the size and mathematical complexity of the problem, the consistency in the results for the different months suggest that good results are obtained, although no global solution can be claimed.
(19)
Alternatively, we can estimate the cost of the dry cooling system compared to the wet cooling one. In the literature [39] it is reported that the cost of a dry cooling system is from 1.2 to 1.85 times that of a wet cooling tower capable of removing the same amount of energy. To be on the save side we consider 1.85 times the cost of a cooling tower, since it its 20% higher than the value provided by Ref. [40]. The total cost for the equipment accounts for 75 MV2013. Fig. 8 presents the share of the different sections to the equipment cost. More than 50% of the equipment cost is due to the solar field and the collector while the turbine and the heat transfer system contribute with around 20% each. Finally the dry cooling equipment represents 6.2% of the total amount. For the evaluation of the investment cost [37], the installed equipment represents 1.5 times the equipment cost. Piping, isolation, instrumentation and utilities represent 20%, 15%, 20% and 10% of the equipment cost respectively for comparison purposes with the wet based CSP plant [17]. Land and buildings cost is estimated to be 8 MV, and the cost of the molten salts is considered to be 0.665 V/kg [17]. These items add up to the fix cost (195 MV). The fees represent 3% of the fix cost, other administrative expenses and overheads and the plant layout represent 10% of the direct costs (fees plus fix capital) and 5% of the fix cost respectively. The plant start up cost represents 15% of the investment. The investment adds up to 265 MV. See Table A1 in the appendix for the details. We results of the previous paper revealed an investment cost of 260 MV. Thus, the different cooling system has a small effect on the investment of the plant. Fig. 7 presents the contribution of the different section of the plant towards the final cost. If we compare this figure with an equivalent one for the wet based CSP plant, we see that the contribution of the cooling system almost doubled. The ultimate comparison is to the real plant of GEMASOLAR, located in Seville, which was projected at 230 MV for 20 MW gross [3]. Furthermore, we estimate the production cost of the electricity [37]. For the average annual cost, we consider the labor costs (0.5% of investment), equipment maintenance (2.5% of fix costs), amortization (linear with time in 20 years), taxes (1% investment), overheads (1% investment) and administration (5% of labour, equipment maintenance, amortization, taxes and overheads). The
4.2. Economic evaluation The investment includes equipment cost and installation, piping and instrumentation, land, chemicals and administration. The factorial method [37] relies on the equipment cost from MATCHE [38]. We consider the units described in the flowsheet given by Fig. 3, the heliostats and the A-frame cooler. The design point for equipment sizing corresponds to a radiation of 900 W/m2 and we assume the atmospheric conditions of July. We obtain 2870 heliostats and a maximum power at the turbine of 62 MW. Furthermore, we need 3 streets of 10 units each and 15 fans so that we can cope with the peak in solar availability. However, as presented in Fig. 6, most of the units will be idle in winter time. We validate the results of the air cooling system with GEA [26]. For the values obtained in this scenario, we price the equipment. The cost estimation of the cooling system is difficult. There is a range of values in the literature. Some studies are based on old plants' data. EPRI [39] presented a correlation as function of the equivalent flow of cooling water is provided. Based on this study for our case 13 MV is obtained. However, more recent studies reveal that the cost is correlated with the flow of steam to be condensed as EPRI [40], as given in eq. (19)
Fig. 7. Equipment section contribution to investment cost.
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been optimized along a natural year using mathematical programming techniques. The average production of energy is 17.2 MW but it ranges from 9.5 MW during winter to 25 MW during summer as a result of the solar radiation received. However 5% of the energy is consumed by the cooling system. The advantage is the reduced water consumption. The investment of the plant is 265 MV and the production cost 0.16 V/kWh, a little high compared to fossil fuel based electricity. However, economies of scale are expected to reduce the production cost and the investment per kW generated when the production capacities reaches those of current thermal power facilities similarly to the wet production facility. The formulation does not only allow planning the operation of the plant in the short and medium term, which is interesting for controllability issues, but also, for a given allocation, it is capable of selecting the cooling technology with lower CO2 emissions. Fig. 8. Production costs breakdown.
total production costs adds up to 17.9 MV/yr for an annual production of 111 GWh, See Table A2 in the appendix for the details. Fig. 8 presents the breakdown of the production cost. The average production cost results 0.16 V/kWh. Halb et al. [13] reported a price, for dry cooling, of 0.16 V/kWh while the values reported in the literature are in the range from $0.13 to $0.17/kWh [41] depending on the technology and location [42]. The levelized cost of electricity, i ¼ 0.05 (NREL, 2012) results in 0.32 V/kWh, in the upper bound of the range of the ones reported for different concentrated solar plants [43]. 4.3. Enviromental impact of dry vs. wet cooling facilities Each kWhe of grid electricity participates in 0.632 kg of CO2 emissions [44]. Thus, the electricity produced by CSP plants contribute to reduce the emissions of CO2 by that amount. Furthermore, 0.30 kg CO2 are produced per m3 of water consumed [45,46]. Thus the environmental potential savings for the wet facility [17], and the ones by the dry cooling system can be seen Table 2. The wet facility actually presents larger savings, 5%, than the dry cooling. However, the availability of water would be the actual parameter to determine the feasibility of the facility. Assuming that the dry technologies produce 94.8% of the energy of a wet cooled plant, based on the results of both plants, dry and wet based CSP facilities, we can develop the following equation to determine when it is preferable to use dry compared to wet as function of the power production and water consumption, eq. (22).
0:032 Energy ProducedðkWhÞ þ 0:30 Water Consumed m3 < 0
(22)
5. Conclusions The operation of a concentrated solar plant based on a regenerative Rankine cycle and that uses dry cooling technologies has
Table 2 CO2 savings.
Power (GWh) Water (evaporated) (m3) Savings CO2 (t/yr)
Wet
Dry
117 245703.971 73871.4839
111 0 70129.8688
Acknowledgment The author would like to acknowledge Salamanca Research for optimization software licenses. Nomenclature Aof outside finned area per unit length, m2 Aot total outside surface area per unit length, m2 Bundles number of bundles per unit (2) Cp,air heat capacity (kJ/kg K) Dfan diameter of the fan (m) fair flow of air (m3/s) fair,fan maximum flow of air per fan (m3/s) finN fins per unit length, 1/m (389) fintf mean fin thickness, m (0.000375) finpf fin pitch, m (0.00257) finpt longitudinal pitch, m (0.0762) kair thermal conductivity, W/mK mair mass flow of air (kg/s) MW,air air molecular weight (kg/kmol) nfans number of fans nbundles number of bundles. Patm atmospheric pressure (Pa) Powerfans power consumed by the fans (kW) Q(unit) heat flow of unit (kJ/s) Rgases ideal gases constant (J/kmol K) Streets streets of units tube_L length of the tubes (m) (10) tubeD finned tube root diameter m (0.0381) tubeDf fin outside diameter, m (0.06985) tubesNrow number of rows of tubes/2 tubesN number of tubes per bundle Tout,month air output temperature (K) Tamb,month air atmospheric temperature (K) Tturb3 exhaust temperature (K) Units unit per street Width width of the bundle (m) rair air density (kg/m3) h efficiency (0.9) Sin q Sin of the angle Angle of the unit (0.5) Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.energy.2015.03.041.
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Appendix A. Air cooler geometry Table A2 Operating costs of the CSP facility. Operating costs Labor Maintenance Equipment Taxes Other Administration
(V2014) 1,325,562 4,762,165 5,628,237 2,651,125 2,651,125 850,911
References
Fig. A1. Street dimensions. fin_tf Fin width (m) /0.000375/, tube_D Tube bare diameter (m) /0.0381/, tube_Df Outside diamter (m) /0.06985/, fin_pf Pitch between fins (m) /0.00257/, tube_L Tube length (m) /10/, fin_pt Pitch between tubes (m) /0.0762/, tubes_Nrow Number of rows of tubes /2/, fin_N Number of fins per m /389/, Width With of each unit of tubes (m) /8/, D_fan Fan diameter 24 ft (m) /7.3/ (24 ft), bundles Number of bundles /2/, tubes_N Bumber of tubes per side of the A-frame /60/, Sin q ¼ 0.5.
Appendix B. Air properties
mair ¼2:287973$106 þ 6:259793$108 $ 0:5$ Tamb;month þ Tout;month 2 3:131956$1011 $ 0:5$ Tamb;month þ Tout;month 3 þ 8:15038$1015 $ 0:5$ Tamb;month þ Tout;month ; kair ¼ 4:937787$104 þ 1:018087$104 $ 0:5 Tamb;month (A-1) þ Tout;month 2 4:627937$108 $ 0:5 Tamb;month þ Tout;month 3 þ 1:250603$1011 0:5 Tamb;month þ Tout;month ; Cp;air ¼ 1:045356$103 3:161783$101 $ 0:5 Tamb;month (A-2) þ Tout;month 2 þ 7:083814$104 $ 0:5 Tamb;month þ Tout;month 3 þ 8:15038$1015 $ 0:5 Tamb;month þ Tout;month ; (A-3) Appendix C. Economic evaluation
Table A1 Detailed investment cost Item Equipment cost Installed equipment Piping Isolations n Instrumentacio Electric installation Ground Utilities Chemicals Fixed capital Honoraries Direct capital Fees Other expenses Start up Total investment
V2014 75,043,161 112,564,742 15,008,632 11,256,474 7504316 7,504,316 8,000,000 7,504,316 21,143,808 190,486,605 5,714,598 196,201,204 9,524,330 19,620,120 39,766,880 265,112,534
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M. Martín / Energy xxx (2015) 1e9 [24] Pieve M, Salvadori G. Performance of an air-cooled steam condenser for a waste-to-energy plant over its whole operating range. Energ Convers Manag 2011;52:1908e13. [25] Biegler LT, Grossmann IE, Westerberg AW. Systematic methods of chemical process design. New Jersey: Prentice Hall; 1997. [26] GEA. GEA heat exchangers. 2014. http://www.gearainey.com/opencms/ opencms/grc/en/Air_Cooled_Heat_Exchangers/calculators/ACC_Calculator. html [last accessed Feb 2014]. nez Alonso C, Sa nchez de Cos Escuin MC, [27] Sancho Avila JM, Riesco Martín J, Jime pez Bartolome M. Atlas de radiacio n solar AEMET (Spain) Montero Cadalso J, Lo Madrid. 2013. Spain, www.aemet.es/documentos/es/serviciosclimaticos/ datosclimatologicos/atlas_radiacion_solar/atlas_de_radiacion_24042012.pdf [last accessed January 2013]. gicos normales. Almería Aeropuerto. 2012., www. [28] AEMET. Valores climatolo aemet.es/es/serviciosclimaticos/datosclimatologicos/valoresclimatologicos? [last accessed January 2013]. [29] Junta de Andalucía. www.agenciaandaluzadelaenergia.es/Radiacion/ radiacion1.php; 2012 [last accessed January 2013]. [30] Brooke A, Kendrick D, Meeraus A. GAMS a users guide. release 23.5. South San Francisco: The Scientific Press. USA; 2010. [31] Drud AS. CONOPTda large-scale GRG code. INFORMS J Comput 1994;6(2): 207e16. n-Padilla DC, Guille n E, Ibarra M, Blanco J. [32] Palenzuela P, Zaragoza G, Alarco Assessment of different configurations for combined parabolic-trough (PT) solar power and desalination plants in arid regions. Energy 2011;36: 4950e8. [33] Nezammahalleh H, Farhadi F, Tanhaemami M. Conceptual design and technoeconomic assessment of integrated solar combined cycle system with DSG technology. Sol Energy 2010;84:1696e705.
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Energy journal homepage: www.elsevier.com/locate/energy
Optimal annual operation of the dry cooling system of a concentrated solar energy plant in the south of Spain Mariano Martín* Departamento de Ingeniería Química, Universidad de Salamanca, Pza. Caídos 1-5, 37008 Salamanca, Spain
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 September 2014 Received in revised form 10 February 2015 Accepted 15 March 2015 Available online xxx
This work presents the optimization of the operation of a concentrated solar power plant with dry cooling over a year, evaluating the molten salts storage, the power block and the air cooling system as a function of the climate and atmospheric conditions. We locate the plant in the south of Europe, Almería (Spain), due to the high solar irradiation and for comparison purposes with a wet cooling based facility. The optimization of the system is formulated as a multiperiod MINLP (mixed integer non-linear programming problem) that is solved for the optimal production of electricity over a year defining the main operating variables of the thermal cycles and the cooling system. The power produced ranges from 9.5 MW in winter to 25 MW in summer, where 5% of this power is consumed by the air cooling system. The annual production cost of electricity is 0.16 V/kWh and the investment required is 265 MV, both slightly higher than when wet cooling is used, but with negligible water consumption. For the selected location, the wet based technology generates slightly less CO2 than the air cooled facility. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Energy Concentrated solar power Rankine cycle Dry cooling Mathematical optimization
1. Introduction Energy and water consumption are major concerns nowadays. While pursuing energy efficiency has become a natural trend, water savings have not received the same attention until very recently. Lately some reports claim that two thirds of the planet will suffer water stress in the next decade [1]. The link between energy production and water consumption is well established when using fossil fuels. However, social pressure towards cleaner energy production and lower environmental impact are leading to develop alternative technologies and use renewable energy sources whose water consumption is still under evaluation. Considering solar energy, it is important to note that the solar energy that reaches the surface of the Earth is more than enough to cover the mankind needs [2]. However, the solar energy received at the surface is only a few kWh/m2/day. To achieve higher intensities and high operating temperatures CSP (concentrated solar power) technologies are used. They are based on the concentration of solar radiation to heat up a fluid that is used to generate steam and ultimately power. CSP plants consist of three parts: solar field, steam turbine and cooling unit. Over the last years, demonstration solar plants are
* Corresponding author. Tel.: þ34 923 294479. E-mail address: [email protected].
being built across the globe [3e5]. For the continuous operation of these plants during the night and in overcast days, thermal energy from the heat tank and/or an additional source of energy are typically used [3]. The thermodynamic cycle selected is a Rankine one with regeneration since they provide efficiency advantages [6]. Finally, like any other power plant, the cooling system is a challenge because energy production has associated a certain water consumption. Mainly we can use wet cooling or dry cooling. However, the low price for water results in less attention paid to its consumption and availability. Therefore, wet cooling is widely used in the power industry but it has as a drawback, the consumption of water. Water is lost by evaporation in the cooling towers [7]. In case of a solar based power plant, it is important to highlight that typically regions where the solar incidence is high correspond with those where the availability of water is low. Thus, indirect and direct dry cooling can be implemented. Indirect dry coolers use water to condensate the steam from the low pressure turbine. An air cooler cools down the water in a closed cycle. Direct dry cooling typically uses either an A-frame configuration so that air is used directly as cooling agent to condensate the steam or by means of natural convection, where a design similar to wet cooling towers is provided so that the air moves driven by density gradient. A-frame are the most common air cooled condensers. Over the last years, a number of simulation based studies have compared the use of wet and dry cooling technologies in power
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M. Martín / Energy xxx (2015) 1e9
plants, conventional or CSP. Kelly and Price [8] published a report comparing wet, forced or mechanical draft, and dry heat rejection for a Rankine Cycle using the GateCycle Program. They presented that the efficiency of the cycle increases for higher inlet pressure and temperature at the turbine and decreasing temperature and pressure at the outlet. The exhaust pressure and temperature have an important effect on the cooling. The low prices of freshwater revealed that the levelized cost of energy was lower in the case of the wet system while the capital investment cost was 5% lower too. The penalty in the energy production cost was at least 8% for dry cooling facilities. Finally, they found that the production cost of the wet cooling plant reached that of the dry cooling based one when the cooling water reached the value of $14.8 per 1000 gal. Turchi et al. [9] presented a report that evaluated the efficiency and impact of dry and wet cooling technologies in parabolic trough CSP plants. They used the SAM (solar advisor model) from the NREL. The switch from wet to dry cooling increases from 3 to 8% the cost of electricity, reducing the water consumption by more than 90%. The water consumed is due to steam cycle maintenance and mirror washing. The investment of the dry cooled facilities was 2% higher. Zhai and Rubin [10] compared the performance of wet induced draft cooling tower and dry A-framed cooling technologies for coal power plants. The models were implemented in the IECM package [11]. The results showed that the dry cooling system was more than twice as expensive per kW of cooling, resulting in an investment cost 8.5% higher when using the dry cooling system, and the efficiency of the plant got reduced 2%. The advantage was the null water consumption versus the 2.46 t of water per MWh produced required by the wet cooling system. Blanco-Marigorta et al. [12] and Habl et al. [13] compared a forced draft wet cooling tower with an A-frame air cooler for the operation of the Andasol 1 power plant following a process simulation approach. This plant uses a Rankine cycle and concentrated solar technology as source of energy. Apart from comparing the effect of the exhaust pressure on the energy output, the dry cooling technology plant showed a reduced energy output in the summer months due to the enhanced need for cooling as a result of the higher ambient temperature. No results on actual water consumption are reported. The electricity production cost in the zone around the Andalucian Granada are 15.27 ct/kWh when using wet cooling and 16.08 ct/kWh in case of dry cooling. Barigozzi et al. [14] performed a sensitivity based optimization study to compare a forced wet cooling condensation system and an A-frame air cooler condenser for cogeneration plants. They modeled the plant using the Thermoflex software to evaluate the effect of the exhaust pressure of the turbine and the air humidity on the power output. The air cooled condenser resulted the best way to reject heat if the ambient temperature is lower than 15 C. However, no consideration on water consumption was presented. Another interesting comparison was presented in the use of concentrated solar power for water desalinization. Liqreina [15] presented the operation of dry cooled based plants, in particular Andasol in Spain and Ma'an in Jordan, and compared the use of dry cooling with wet cooling over a year long using also a simulation based approach, Greenius software. The dry cooled facility presented regularly 4e8% lower energy production. The LCOE tuned out to be 0.1284 V/kWhe with an investment of 248 MV, while the dry cooled based plant showed a cost of 0.1491 V/kWh with an investment of 289 MV for a production facility of 50 MW. The water consumption of the wet cooled was 1.6 L/kWh, while the dry cooled was 0.095 L/kWh, computed using SAM software. Palenzuela et al. [16] used a simulation based approach using EES (engineering equation solver) software assuming a steady state operation. The efficiency of the dry cooling based plant was 2% lower than the evaporative water cooling system, while the
levelized energy cost of the dry cooling was 0.249 V/kWh vs. the 0.241 V/kWh of the wet system. The problem with the use of modular commercial simulation software is that it is not that easy to see how cost estimations are implemented nor the detailed design of the cooling systems, which are the key issues for the energy and water consumption associated. Furthermore, only sensitivity based studies were carried out to evaluate and optimize the effect of some operating parameters. On the other hand, the advantage is that rigorous thermodynamics are solved. Lately, Martín & Martín [17] optimized a concentrated solar plant operating over a year using a mathematical programming approach and later it was coupled with a biomass polygeneration system to provide for the energy when solar is not enough [18]. The process consisted of a regenerative Rankine cycle using wet cooling technology. Apart from determining the optimal pressures and temperatures using an equation based optimization approach, the authors showed that an average of 2.1 L of water per kWh produced was consumed over a year of operation. In this paper we use mathematical programming techniques for the conceptual optimal design and operation of a concentrated solar power plant using an A-frame air cooling system over a year. Our aim is to evaluate the cooling system that, while reducing water consumption compared to the wet cooling based facility [17], requires energy for the operation of the A-frame. The facility is located in Almería (Spain), a region with one of the highest solar radiations in Europe, the same region selected for the previous work [17]. The paper is organized as follows. Section 2 describes the modeling features and the atmospheric conditions of the selected location. In Section 3 we present the optimization procedure. Next, in Section 4 the main results are discussed such as the major operating conditions, the power consumed by the cooling system and the units of the A-frame needed, followed by an economic evaluation and a comparison between dry and wet cooling facilities based on CO2 savings. Finally, in Section 5 we draw some conclusions. 2. Modeling 2.1. Modeling assumptions The plant consists of three parts, the heliostat field including the collector and the molten salts storage tanks, the steam turbine and the air cooler steam condenser. Fig. 1 presents the flowsheet for the process where the heliostat field has not been included. For the detailed information on the modeling features of the heliostat field and the steam turbine, we refer to the supplementary material and to previous work [17,18]. Our process is based on the use of a tower to collect the solar energy and a regenerative Rankine cycle. The steam is generated in a system of three heat exchangers where water is heated up to saturation and then evaporated using the total flow of molten salts. However, only a fraction of the flow of salts is used to superheat the steam before it is fed to the first body of the turbine. The rest is used to reheat up the steam before it is fed to the second body. In the second body of the turbine, part of the steam is extracted at a medium pressure and it is used to heat up the condensate. The rest of the steam is finally expanded to an exhaust pressure, condensed and recycled. In the model, we consider conservative average efficiencies for the heliostat field and the turbine efficiency based on rules of thumb for the conceptual design of the facility over a year, using a time period of a month, for comparison purposes with previous work [17]. Refs. [19e21] can be used to include the operation of the solar field into this formulation accounting for the decrease in the efficiency of the turbine as function of the load and the efficiency of the solar field as a function of the direct normal irradiation. In Refs. [19,20] we see that the efficiency
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Fig. 1. Flowsheet of the concentrated power plant facility.
of the turbine may decrease up to 3% when it operates at half load, while the effect of the direct irradiation can decrease the efficiency of the field by 5%. Although important concepts, the expected error in the equation based models for the turbine is expected to be on that range, while we use a low efficiency for the solar field to be on the save side. For the condensation of the steam we propose the use of a direct air cooled system. Based on Heyns [22], we consider a system given by a number of streets, up to three. Each one has 10 units. Each of the units of the A-frame has two bundles with two lines of rows of 60 tubes each. The geometrical characteristics of the finned tubes can be seen in Appendix A. The energy balance given by eqs. (1)e(5) provides the air flow needed. We assume that the maximum approach temperature is 10 C.
mair $Cp;air $ Tout;month Tamb;month ¼ Q ðHX5Þ;
(1)
Tout;month Tturb3 10;
(2)
rair $Rgases $Tamb;month ¼ Patm $MW;air
(3)
fair $rair ¼ mair ;
(4)
2 nfans $0:25$p$ Dfan ¼ 0:25$tube L$Width$nbundles ;
(7)
In order to compute the area that the heat exchanger provides, the design parameters as presented in Manassaldi et al. [23] are used, eqs. 8e10
1 Aof ¼ 2 p$finN $ tube2Df tube2D þ p$tubeDf $fintf $finN ; 4
(8)
Aot ¼ Aof þ p$tubeD $ 1 fintf $finN ;
(9)
Aheat;exchanger ¼ tubesNrow $tubesN $tube L$Aot $streets$units $bundles (10) Based on literature [22], the main resistance to the heat transfer is the film coefficient of the air side. We approximate the global heat transfer coefficient Uglobal by h air using the correlation presented by Pieve & Salvadori [24], eq. (11):
fair;fan $nfans ¼ fair ;
(5)
The power consumed by the fan in the A-frame type condenser is computed using the results in Ref. [22], eqs. (6)e(7). We assume an efficiency, h, of 90% based on the same study:
Powerfan
2 ¼ 0:001$nfans ðrair =1:2Þ$ 0:4762$ fair;fan 1 ; 59:414$fair;fan þ 186644 h
kair $0:134$ðReair Þ0:681 $ðPrair Þ0:33 tubeD 10:11 10:2 0 0 finpf fintf finpf fintf A A $@ $@ ; 0:5$ tubeDf tubeD fintf
Uglobal z
(11) where
(6)
Reair ¼
fair $tubeDeq ; mair $Amin
(12)
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0 @ðtube
Df tube D2 Þ ð2$finpf Þ 2
tubeDeq ¼
þ
tubeDf $fintf finpf
0 @1 þ
1 . þ tubeD $ 1 fintf finpf A
1 ðtubeDf tubeD ÞA
;
finpf
Amin ¼ bundles$streets$units$tubesN $tubeL $ finpt tubeD 2$fintf $0:5$ tubeDf tubeD $finN $Sinq (14) Prair
(13)
Cp;air $mair ¼ ; kair
(15)
3. Optimization procedure The equation based model is formulated as a multiperiod MINLP problem written in GAMS [30]. We maximize the energy produced, z, given by Eq. (18), over the 12 time periods:
z¼
X
WðTurbine1;tpÞ þ WðTurbine2;tpÞ þ WðTurbine3;tpÞ WFan
tp
The physical properties of the air are calculated using the correlations presented in Ref. [22], see eqs. (A-1,A-3) in the Appendix. Finally, we use Cheng approximation to compute the LMTD (logarithm mean temperature difference), [25]. Thus, the cooling area is computed as in eq. (16):
Q ðHX5Þ ¼ U_global LMTD Area_Cooling;
(16)
The area provided by the heat exchanger must be at least 10% larger.
Area_HX 1:1Area_Cooling ;
(17)
The physical design of the heat exchanger is based on the bundle of tubes for an A-frame heat exchanger. The size of the fan and the number of tubes per row are adjusted for the performance of the heat exchanger to be within the real operation of an air cooled condenser and typical configurations of the tubes [26].
2.2. Operating conditions In Table 1 we present the monthly atmospheric conditions of the region where we allocate the facility including the radiation received in Almería, the sun hours, the ambient temperature of the air and its humidity [27e29]. It is important to notice that the same formulation can be used for any other region by using the appropriate data to compare the performance of the plant under different conditions.
(18) Subject to the process model described in section 2. The main decision variables are the operating inlet and discharge pressures at the three bodies of the turbine, the split fraction for the molten salts to be used at HX1 and at HX4, the fraction of steam extracted from the second body of the turbine, the air flow rate, the number of units and fans in operation for the cooling system and the air outlet temperature. The problem consists of 3200 equations and 3500 variables. The complexities due to the integration of the design of the cooling system together with the Rankine cycle result in the need for proper initialization by using several starting points based on data from the literature and bounds for the variables such as flowrates. Furthermore, we decompose the problem into the 12 months. Next, we relax each MINLP (multiperiod mixed integer non-linear programming problem) problem so that the number of units, fans and streets for the air coolers are treated as continuous variables solving 12 NLP. After the optimization, we round the values obtained and re-optimized the operation of the plant. Note that the relaxed solution can be interpreted as a fan not operating at full load while the integer solution implies fully used of each of the units. For design and costing purposes, an integer solution is needed. CONOPT 3.0 [31] is used to solve the problem. This formulation can also be used to evaluate daily or weekly operation of the plant by changing the time periods from a monthly basis to an hourly or daily basis monitoring the atmospheric conditions which can be useful for the integration of the solar energy into the grid. This will allow for
Table 1 Atmospheric conditions [27e29]. Month
kWh/m2$day
Day
Sun (H)
Sun (h/day)
T Amb ( C)
% Humidity
J F M A May June July Aug Sep Oct Nov Dec Average
4.377 5.125 5.319 6.387 6.697 8.587 8.668 7.342 6.057 4.126 3.513 3.326 5.794
31 28 31 30 31 30 31 31 30 31 30 31 30.4
191 191 228 250 299 322 338 312 257 221 187 176 248
6.161 6.821 7.355 8.333 9.645 10.733 10.903 10.065 8.567 7.129 6.233 5.677 8.13
12.5 13.2 14.7 16.4 19.1 22.7 25.7 26.4 24.0 20.0 16.2 13.7 18.7
69 68 66 64 66 64 63 65 66 68 70 70 66.6
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process control on the operation of the fans, the effect of clouds and accounding for the temperature interval during the day. In this case, more detailed evaluation of the efficiency of the solar field must be included. Actually the effect of the variation of the temperature from month to another is similar to that on a daily basis, the fans usage varies accordingly. However, in this work we focus on the conceptual design of the facility and average monthly operation. 4. Results We divide this section in three parts presenting the optimal operating conditions, an economic evaluation and a comparison between wet and dry cooled facilities based on CO2 savings. 4.1. Plant operation
Fig. 3. Total energy produced in the CSP plant and consumption by the dry cooling system.
The optimization of the flowsheet reveals that 30% of the salts from storage tank 1 are used in HX1 to heat up the saturated steam while the rest are sent to HX4 for the reheating stage. For all the periods it turns out that the superheated steam enters the first body of the turbine at 125 bar and 555 C exiting it at 11 bar. This stream is reheated up in HX4 to 500 C and fed to the second body of the turbine. The outlet pressure of the second body of the turbine varies from one month to the other, see Fig. 2. This is the main difference when compared to the wet cooling facility in Ref. [17]. 15% of the stream that leaves the second body of the turbine is extracted and sent to HX6 while the rest is expanded in the third body of the turbine to an exhaust pressure of 0.19 bar. This stream is condensed in HX5, the A-frame system. In Fig. 2 we present the continuum solution and the integer solution as discussed in the solution procedure. Both are quite similar. The exhaust pressure we obtained, 0.19 bar as saturated steam, is similar to Palenzuela's work cases 1,3&4 [32], 0.18 bar, higher than the values presented by Nezammahalleh et al. [33], Xu's et al. [34] or Ghobeity et al. [35], and lower than Salcedo et al. [36] or Palenzuela's case 2 [32]. Halb et al. [13] presented a sensitivity study evaluating the effect of the exhaust pressure on plant efficiency considering a range of values from 0.06 to 0.2 bar. They found a decrease in power efficiency with the exhaust pressure pointing out that a value of 0.073 bar is the most convenient. The value corresponds also to Andasol solar power plant, that uses trough technology, instead of the Tower based design we considered based on GEMASOLAR plant. Furthermore, we fix the exhaust to be saturated vapor to avoid any mechanical problems in the turbine. Fig. 3 shows the year-round production of electricity. During summer we obtain a maximum of 25 MW for two consecutive
months, June and July, while the lowest production capacities are found in November and December, just below 10 MW. From these values, similar in every case to the facility that uses wet cooling [17], we use a fraction in order to provide for the fans of the A-frame system. In Fig. 3 we also see a blue (in web version) section of the column representing this consumption, around 5%. The configuration of the air cooler condenser and the air flow needed to condense the steam are the ones that determine this consumption of energy. In Fig. 4 we present the fan consumption power along the year. We show two solutions, the integer one and the relaxed non linear solution. Again, both are similar. We see that the hottest month requires a large consumption since the LMTD is smaller and a higher air flow needs to be provided. However, as presented in Fig. 5, we see a constant increase of 14 C in the air temperature across the A-frame. For this figure we consider only the integer solution. The use of fans and units over the yearis shown in Fig. 6. They correspond to monthly average use since we use average monthly data for the atmospheric conditions, see Table 1. This figure allows introducing controllability issues in the operation of the plant. We see that our formulation is capable of computing the number of units that must be in operation at a time and the fans devoted. The integer solution assumes that fans are operating at full capacity. However, the continuous solution can be interpreted as the fraction of the total power of the fan needed. For design purposes we need the integer solution to determine the units to be installed. Furthermore, typically each unit will have a fan, see also sizing of the units in Appendix A. The results in Fig. 6 show that the fans will not be operating at full capacity in such a case but almost at one half of it.
Fig. 2. Exhaust pressure at the outlet of the second body of the turbine.
Fig. 4. Fan power consumption over a year.
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Cð$MÞ ¼ ð0:0652$ðkg=s of steamÞ þ 1:8377Þ
Fig. 5. Air inlet and outlet temperatures.
Fig. 6. Usage of the units and fans. Planning of the plant operation.
In spite of the use of local solvers, due to the size and mathematical complexity of the problem, the consistency in the results for the different months suggest that good results are obtained, although no global solution can be claimed.
(19)
Alternatively, we can estimate the cost of the dry cooling system compared to the wet cooling one. In the literature [39] it is reported that the cost of a dry cooling system is from 1.2 to 1.85 times that of a wet cooling tower capable of removing the same amount of energy. To be on the save side we consider 1.85 times the cost of a cooling tower, since it its 20% higher than the value provided by Ref. [40]. The total cost for the equipment accounts for 75 MV2013. Fig. 8 presents the share of the different sections to the equipment cost. More than 50% of the equipment cost is due to the solar field and the collector while the turbine and the heat transfer system contribute with around 20% each. Finally the dry cooling equipment represents 6.2% of the total amount. For the evaluation of the investment cost [37], the installed equipment represents 1.5 times the equipment cost. Piping, isolation, instrumentation and utilities represent 20%, 15%, 20% and 10% of the equipment cost respectively for comparison purposes with the wet based CSP plant [17]. Land and buildings cost is estimated to be 8 MV, and the cost of the molten salts is considered to be 0.665 V/kg [17]. These items add up to the fix cost (195 MV). The fees represent 3% of the fix cost, other administrative expenses and overheads and the plant layout represent 10% of the direct costs (fees plus fix capital) and 5% of the fix cost respectively. The plant start up cost represents 15% of the investment. The investment adds up to 265 MV. See Table A1 in the appendix for the details. We results of the previous paper revealed an investment cost of 260 MV. Thus, the different cooling system has a small effect on the investment of the plant. Fig. 7 presents the contribution of the different section of the plant towards the final cost. If we compare this figure with an equivalent one for the wet based CSP plant, we see that the contribution of the cooling system almost doubled. The ultimate comparison is to the real plant of GEMASOLAR, located in Seville, which was projected at 230 MV for 20 MW gross [3]. Furthermore, we estimate the production cost of the electricity [37]. For the average annual cost, we consider the labor costs (0.5% of investment), equipment maintenance (2.5% of fix costs), amortization (linear with time in 20 years), taxes (1% investment), overheads (1% investment) and administration (5% of labour, equipment maintenance, amortization, taxes and overheads). The
4.2. Economic evaluation The investment includes equipment cost and installation, piping and instrumentation, land, chemicals and administration. The factorial method [37] relies on the equipment cost from MATCHE [38]. We consider the units described in the flowsheet given by Fig. 3, the heliostats and the A-frame cooler. The design point for equipment sizing corresponds to a radiation of 900 W/m2 and we assume the atmospheric conditions of July. We obtain 2870 heliostats and a maximum power at the turbine of 62 MW. Furthermore, we need 3 streets of 10 units each and 15 fans so that we can cope with the peak in solar availability. However, as presented in Fig. 6, most of the units will be idle in winter time. We validate the results of the air cooling system with GEA [26]. For the values obtained in this scenario, we price the equipment. The cost estimation of the cooling system is difficult. There is a range of values in the literature. Some studies are based on old plants' data. EPRI [39] presented a correlation as function of the equivalent flow of cooling water is provided. Based on this study for our case 13 MV is obtained. However, more recent studies reveal that the cost is correlated with the flow of steam to be condensed as EPRI [40], as given in eq. (19)
Fig. 7. Equipment section contribution to investment cost.
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been optimized along a natural year using mathematical programming techniques. The average production of energy is 17.2 MW but it ranges from 9.5 MW during winter to 25 MW during summer as a result of the solar radiation received. However 5% of the energy is consumed by the cooling system. The advantage is the reduced water consumption. The investment of the plant is 265 MV and the production cost 0.16 V/kWh, a little high compared to fossil fuel based electricity. However, economies of scale are expected to reduce the production cost and the investment per kW generated when the production capacities reaches those of current thermal power facilities similarly to the wet production facility. The formulation does not only allow planning the operation of the plant in the short and medium term, which is interesting for controllability issues, but also, for a given allocation, it is capable of selecting the cooling technology with lower CO2 emissions. Fig. 8. Production costs breakdown.
total production costs adds up to 17.9 MV/yr for an annual production of 111 GWh, See Table A2 in the appendix for the details. Fig. 8 presents the breakdown of the production cost. The average production cost results 0.16 V/kWh. Halb et al. [13] reported a price, for dry cooling, of 0.16 V/kWh while the values reported in the literature are in the range from $0.13 to $0.17/kWh [41] depending on the technology and location [42]. The levelized cost of electricity, i ¼ 0.05 (NREL, 2012) results in 0.32 V/kWh, in the upper bound of the range of the ones reported for different concentrated solar plants [43]. 4.3. Enviromental impact of dry vs. wet cooling facilities Each kWhe of grid electricity participates in 0.632 kg of CO2 emissions [44]. Thus, the electricity produced by CSP plants contribute to reduce the emissions of CO2 by that amount. Furthermore, 0.30 kg CO2 are produced per m3 of water consumed [45,46]. Thus the environmental potential savings for the wet facility [17], and the ones by the dry cooling system can be seen Table 2. The wet facility actually presents larger savings, 5%, than the dry cooling. However, the availability of water would be the actual parameter to determine the feasibility of the facility. Assuming that the dry technologies produce 94.8% of the energy of a wet cooled plant, based on the results of both plants, dry and wet based CSP facilities, we can develop the following equation to determine when it is preferable to use dry compared to wet as function of the power production and water consumption, eq. (22).
0:032 Energy ProducedðkWhÞ þ 0:30 Water Consumed m3 < 0
(22)
5. Conclusions The operation of a concentrated solar plant based on a regenerative Rankine cycle and that uses dry cooling technologies has
Table 2 CO2 savings.
Power (GWh) Water (evaporated) (m3) Savings CO2 (t/yr)
Wet
Dry
117 245703.971 73871.4839
111 0 70129.8688
Acknowledgment The author would like to acknowledge Salamanca Research for optimization software licenses. Nomenclature Aof outside finned area per unit length, m2 Aot total outside surface area per unit length, m2 Bundles number of bundles per unit (2) Cp,air heat capacity (kJ/kg K) Dfan diameter of the fan (m) fair flow of air (m3/s) fair,fan maximum flow of air per fan (m3/s) finN fins per unit length, 1/m (389) fintf mean fin thickness, m (0.000375) finpf fin pitch, m (0.00257) finpt longitudinal pitch, m (0.0762) kair thermal conductivity, W/mK mair mass flow of air (kg/s) MW,air air molecular weight (kg/kmol) nfans number of fans nbundles number of bundles. Patm atmospheric pressure (Pa) Powerfans power consumed by the fans (kW) Q(unit) heat flow of unit (kJ/s) Rgases ideal gases constant (J/kmol K) Streets streets of units tube_L length of the tubes (m) (10) tubeD finned tube root diameter m (0.0381) tubeDf fin outside diameter, m (0.06985) tubesNrow number of rows of tubes/2 tubesN number of tubes per bundle Tout,month air output temperature (K) Tamb,month air atmospheric temperature (K) Tturb3 exhaust temperature (K) Units unit per street Width width of the bundle (m) rair air density (kg/m3) h efficiency (0.9) Sin q Sin of the angle Angle of the unit (0.5) Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.energy.2015.03.041.
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Appendix A. Air cooler geometry Table A2 Operating costs of the CSP facility. Operating costs Labor Maintenance Equipment Taxes Other Administration
(V2014) 1,325,562 4,762,165 5,628,237 2,651,125 2,651,125 850,911
References
Fig. A1. Street dimensions. fin_tf Fin width (m) /0.000375/, tube_D Tube bare diameter (m) /0.0381/, tube_Df Outside diamter (m) /0.06985/, fin_pf Pitch between fins (m) /0.00257/, tube_L Tube length (m) /10/, fin_pt Pitch between tubes (m) /0.0762/, tubes_Nrow Number of rows of tubes /2/, fin_N Number of fins per m /389/, Width With of each unit of tubes (m) /8/, D_fan Fan diameter 24 ft (m) /7.3/ (24 ft), bundles Number of bundles /2/, tubes_N Bumber of tubes per side of the A-frame /60/, Sin q ¼ 0.5.
Appendix B. Air properties
mair ¼2:287973$106 þ 6:259793$108 $ 0:5$ Tamb;month þ Tout;month 2 3:131956$1011 $ 0:5$ Tamb;month þ Tout;month 3 þ 8:15038$1015 $ 0:5$ Tamb;month þ Tout;month ; kair ¼ 4:937787$104 þ 1:018087$104 $ 0:5 Tamb;month (A-1) þ Tout;month 2 4:627937$108 $ 0:5 Tamb;month þ Tout;month 3 þ 1:250603$1011 0:5 Tamb;month þ Tout;month ; Cp;air ¼ 1:045356$103 3:161783$101 $ 0:5 Tamb;month (A-2) þ Tout;month 2 þ 7:083814$104 $ 0:5 Tamb;month þ Tout;month 3 þ 8:15038$1015 $ 0:5 Tamb;month þ Tout;month ; (A-3) Appendix C. Economic evaluation
Table A1 Detailed investment cost Item Equipment cost Installed equipment Piping Isolations n Instrumentacio Electric installation Ground Utilities Chemicals Fixed capital Honoraries Direct capital Fees Other expenses Start up Total investment
V2014 75,043,161 112,564,742 15,008,632 11,256,474 7504316 7,504,316 8,000,000 7,504,316 21,143,808 190,486,605 5,714,598 196,201,204 9,524,330 19,620,120 39,766,880 265,112,534
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