Impacts of solar multiple on the performanceof direct steam generation solar power tower plant with integratedthermal storage

Abstract

Solar multiple (SM) and thermal storage capacity are two keydesign parameters for revealing the performance of direct steam generation(DSG) solar power tower plant. In the case of settled land area, SMand thermal storage capacity can be optimized to obtain the minimumlevelized cost of electricity (LCOE) by adjusting the power generationoutput. Taking the dual-receiver DSG solar power tower plant witha given size of solar field equivalent electricity of 100 MW_e in Sevilla as a reference case, the minimum LCOE is21.77 ￠/kWh_e with an SM of 1.7 and a thermalstorage capacity of 3 h. Besides Sevilla, two other sites are alsointroduced to discuss the influence of annual DNI. When compared withthe case of Sevilla, the minimum LCOE and optimal SM of the San Josesite change just slightly, while the minimum LCOE of the Bishop sitedecreases by 32.8% and the optimal SM is reduced to 1.3. The influenceof the size of solar field equivalent electricity is studied as well.The minimum LCOE decreases with the size of solar field, while theoptimal SM and thermal storage capacity still remain unchanged. Inaddition, the sensitivity of different investment in sub-system isinvestigated. In terms of optimal SM and thermal storage capacity,they can decrease with the cost of thermal storage system but increasewith the cost of power generation unit.

Keywords

direct steam generation / solarpower tower / solar multiple / thermalenergy storage capacity / levelized cost of electricity(LCOE)

Introduction

Concentrated solar power (CSP) isan electricity generation technology that uses the heat provided bythe solar irradiation concentrated on a small area and that can beenhanced by the incorporation of thermal energy storage [1,2]. Of all CSP technologies available, solar power tower is likelyto play an essential role in future development due to its potentialto provide dispatchable solar electricity at low cost and relativehigh efficiency [3].

To overcome the shortage of the unsteadyfluctuation of solar energy, a solar power tower plant commonly consistsof a solar field, a solar receiver, a thermal energy storage system,and a steam turbine power generation unit. Of different types of solarpower tower plants, two promising ones, the molten salt power towerplant and the direct steam generation (DSG) power tower plant areusually discussed. For the molten salt power tower plant, molten saltis usually utilized as both heat transfer fluid and thermal energystorage medium. The 15 MW_e Solar Tres PowerPlant is the first commercial molten salt power tower plant with alarge thermal storage size of 16 h and an annual capacity of about65% [4]. The two-tankmolten salt is usually used as the thermal energy storage system formolten salt power tower plant whose specific investment is about 30$/kWh_th [3]. The one-tank latent heat thermal energy storage system with phasechange material (PCM) can also be used for molten salt power towerplant with similar specific investment [5]. For DSG power tower plant, the heat transfer fluidis water/steam, while the thermal energy storage medium could be saturatedpressured water, rock, or molten salt. The 11 MW_e PS10 is the first commercial DSG solar power tower plant with asmall thermal storage size of 50 min [6]. Owing to the pinch point, the thermal energy storagesystem consisting of PCM for the latent part and molten salt for thesensible part is an effective option for DSG power tower plant. Suchthermal energy storage system is extensively applied in parabolictrough power plants with DSG [7–10], whose specificinvestment is about 43 $/kWh_th [11]. Although the levelized cost ofelectricity (LCOE) of molten salt power tower plant is a little lowerthan that of DSG power tower plant, molten salt power tower planteasily suffers from salt freezing in receiver tubes during startupand great corrosion of molten salt [12–14]. Therefore, DSG power tower plant is a good choice from a securityperspective. However, further reduction of the LCOE of the DSG powertower plant should be studied.

Solar multiple (SM) and thermal storagecapacity are two key design parameters for the sensitivity analysisof the annual plant performance and the economic assessment. SM isthe ratio between the equivalent electricity produced by the solarfield at design point and the rated output of the power generationunit. Increasing the SM of a CSP plant represents either increasingthe size of the solar field or decreasing the capacity of the practicalpower generated. If the land area is not settled, the size of solarfield equivalent electricity can be optimized by achieving the lowestLCOE for a fixed power generation output. However, the required landarea is usually very large. For example, the land area of the 20 MW_e Gemasolar Power Plant with a thermal storage size of16 h is up to 2.0874 km² [15]. Thus, sometimes the land areathat can be provided may be smaller than the required one. If theland area, as well as the solar field is settled, the power generationoutput should be optimized to obtain the lowest LCOE. Boudaoud etal. [16] investigateda 20 MW_e solar power tower plant with a moltensalt cavity receiver. It can be concluded that the SM increases withthe storage capacity. Meanwhile, the LCOE decreases since the storagesection has the lowest investment. Cocco et al. [17] studied the performance of a 1MW_e CSP plant using linear Fresnel collectorsand achieved the lowest LCOE with a two-tank storage system for astorage capacity of about 4 h and an SM of 1.6. Montes et al. [18] observed that the LCOE of a 50MW_e DSG parabolic trough power plant with thermalstorage and an auxiliary natural gas-fired boiler increased with SM,mainly owing to the great investment in the solar field. The aboveliteratures adjusted the SM by varying the size of solar field, whileJorgenson et al. [19]adjusted the SM by changing the size of the molten salt power towerplant. The study offered a discussion of the sensitivity of plantoperation to the SM and thermal energy storage capacity.

As discussed above, the land areais settled in some cases and the settled land area may be smallerthan the required one. Under this condition, the power generationoutput can be optimized to obtain the lowest LCOE. However, literaturereview revealed that there were few investigations concerning theinfluences of SM and thermal storage capacity on the LCOE of solarpower tower with DSG when the land area was settled. In the previousstudy, a dual-receiver solar power tower plant with DSG was proposedand its thermal performances were investigated [20]. The new design combined an externaland a cavity receiver, corresponding to the boiling and superheatingsections respectively, and provided a simple yet controllable heatflux distribution on both sections [20]. For this dual-receiver DSG solar power tower plantwith thermal energy storage in Sevilla, the influence of SM and thermalstorage capacity on the annual discarded thermal energy, electricityproduction, capacity factor, and the LCOE are given by adjusting thepower generation output from 33 MW_e to 100MW_e and varying the thermal storage capacityfrom 0 h to 12 h, while the land area is fixed at 4.8 km² and the electrical equivalent inflow from the solarfield remains the same, i.e., 100 MW_e. Then,taking this case as a reference, the effects of site, the size ofsolar field equivalent electricity, and sub-system investment in theminimum LCOE and optimal SM and thermal storage capacity are discussed.

Solar power tower plant

Meteorological data

The reference case concerens a typicalmeteorological year database obtained from the System Advisor Model(SAM) software [21] forthe site of Sevilla (37.4°N, 5.9°W), Spain. The hourly meteorologicaldatabase includes direct normal irradiation (DNI), ambient temperature,and wind velocity. Table 1 summarizes the annual meteorological dataand the design conditions.

Solar field and dual-receiver

Figure 1 shows the dual-receiverwith the schematic surrounding solar field proposed in Ref. [20]. As the land area is fixed at 4.8km² for the reference case, the correspondingsolar field could provide an equivalent electricity of 100 MW_e at design point. The resulted solar field layout isillustrated in Fig. 2. The blue sector, which has a view angle of90° and 1268 heliostats, focuses the sunlight to the bottom superheater.The red sector with 3332 heliostats is dedicated to the top boilersection. The width and height of the heliostat are respectively 12.84m and 9.45 m. The heliostat has a reflectivity of 0.88 and an opticalerror of 2.9 mrad.

For the dual-receiver, the top externalreceiver is located at a height of 190 m from the ground, which isdetermined by [22]

(1)H=\lambda Q_{\mathrm{inc}}^{0\mathrm{.288}},

where Q_inc is the totalincident solar energy collected by the dual-receiver and l is the coefficient that isequal to 37.6 m/MW_th^0.288. The external receiver is cylindrical in shape with a height of20 m and a diameter of 17 m. The bottom cavity receiver center islocated 27 m blow the external receiver center, which has a half octagonshape with a height of 19 m and a radius of 13 m. All tubes are coatedby Pyromark with an emissivity of 0.95. The cavity ceiling, floor,and lip passive insulation walls are made of ceramic fibers, whoseemissivity is 0.2. At the design point, the dual-receiver collectsan incident solar radiation of about 304MW_th and obtains a thermal efficiency of 87%.

Power generation unit and thermal storage system

A schematic diagram of the DSG solarpower tower plant is shown in Fig. 3. It consists of a solar field,a solar receiver, a thermal storage system, and a power generationunit.

For the reference case, the SM isadjusted from 1.0 to 3.0 and the energy inflow from the settled solarfield remains 100 MW_e, so the power generationscale varies from 100 MW_e to 33 MW_e. The steam parameters usually remain the same for thethermal power plant capacity below 150 MW_e [23]. Therefore, for different powergeneration scales, the inlet feed water temperature is set to be 205°C,while the outlet parameters of the superheat steam are respectively10.7 MPa and 515°C with a condensing pressure of exhaust steamof 0.007 MPa from the turbine. The isentropic efficiencies of theturbine and pump machinery are both assumed to be 0.9 at the ratedcondition, resulting in a Rankine cycle efficiency of 0.4058 throughthe heat balance calculation. As a reference, Flueckiger et al. [24] applied a similar power generationunit and obtained a Rankine cycle efficiency of 0.4116 for a 100 MW_e power tower plant with the main steam parameter of538°C and 12.5 MPa.

The thermal energy storage capacityis varied from 0 to 12 h in the reference case. The thermal energystorage system is made up of a sensible part of three molten salttanks and a latent part of PCM. As a higher salt volume in the coldtank than that in the hot tank, which is due to the much lower availabletemperature difference, a buffer tank is needed [7]. NaNO₃ isused as PCM with a melting temperature of 306°C. Assuming a drivingtemperature difference of 10 K between steam cycle and storage system,the steam has to condense at 316°C and 10.7 MPa while the charginghas to evaporate at 296°C and 8.1 MPa during discharge. The globalthermal efficiency of the thermal energy storage system h_tes remains to be 0.95 by considering both charging and dischargingutilization factors [18]. The energy balance for the thermal storage system is expressedas

(2)m_{\mathrm{c}}\cdot (h_{\mathrm{c}\mathrm{1}}-h_{\mathrm{c2}})\cdot {\eta }_{\mathrm{tes}}=m_{\mathrm{d}}\cdot (h_{\mathrm{d}\mathrm{2}}-h_{\mathrm{d}\mathrm{1}}),

where m_c is the mass flow rate of steam during the storage charge process, m_d is the mass flowrate of steam during the storage discharge process, h_c1 and h_c2 are respectivelythe inlet and outlet water/steam enthalpy during the storage chargeprocess, and h_d1 and h_d2 are respectively the inlet and outlet water/steam enthalpy duringthe storage discharge process.

Figure 4 demonstrates the operatingmodes of the solar power tower plant. The x-axis represents the ratio between the equivalent electricityproduced by the dual-receiver outlet power and the rated output ofthe power generation unit. The y-axis represents the dual-receiver outlet pressure. The dual-receiveroutlet pressure is the same as the turbine inlet pressure as longas the turbine is operated. The operating modes of the solar powertower plant are as follows:

Mode 1 If the dual-receiver outlet equivalent electricity is larger thanthe rated output of the power generation unit, the turbine is operatedat rated condition and the excess power of the dual-receiver outletis stored. But if the accumulated stored thermal energy is largerthan the thermal storage capacity, the exceeding thermal energy isdiscarded.

Mode 2 If the dual-receiver outlet equivalent electricity is larger than70% of the rated output of the power generation unit, the turbineinlet is operated in sliding pressure mode between 8.1 MPa and 10.7MPa without storage discharge or charge. When the turbine inlet pressureis reduced to 8.1 MPa, both the allowable mass flow rate of the turbineinlet steam and the Rankine cycle efficiency are reduced, so the powergeneration unit output is reduced to 70% of the rated output.

Mode 3 If the dual-receiver outlet equivalent electricity is lower than70% of the rated output of the power generation unit, the turbineinlet is operated in a fixed pressure mode at 8.1 MPa with optionalstorage discharge. But if the sum of the dual-receiver outlet equivalentelectricity and the storage discharge equivalent electricity is blow30% of the rated output, Mode 3 is replaced by Mode 4.

Mode 4 If the output of the power generation unit is below 30% of the ratedoutput, the turbine is not operated and the whole dual-receiver outletpower is stored.

For sliding pressure operation, thepressure drop over a turbine stage exhibits the following relationshipwith a variable mass flow rate, which is the so-called Flugel formula

(3){\displaystyle \frac{P_{\mathrm{1}}^{\mathrm{2}}-P_{\mathrm{2}}^{\mathrm{2}}}{P_{\mathrm{1},\mathrm{0}}^{\mathrm{2}}-P_{\mathrm{2},\mathrm{0}}^{\mathrm{2}}}}={\left({\displaystyle \frac{m}{m_{\mathrm{0}}}}\right)}^{\mathrm{2}}.

For derated power output cycle operation,the pressure drop over a turbine stage is limited to 30% of the ratedoutput. The isentropic efficiency of the turbine is influenced byderated performance. The percent reduction in turbine efficiency isconsidered as [25]

(4)\mathrm{Percent reduction}=\mathrm{0.191}-\mathrm{0.409}\left({\displaystyle \frac{m}{m_{\mathrm{0}}}}\right)+\mathrm{0.218}{\left({\displaystyle \frac{m}{m_{\mathrm{0}}}}\right)}^{\mathrm{2}},

(5){\displaystyle \frac{{\eta }_t}{{\eta }_{t,\mathrm{0}}}}=\mathrm{1}-\mathrm{Percent reduction}.

In addition, the pumps operate ata maximum efficiency at a rated condition. The change in pump efficiencyis a function of the mass flow ratio [25]

(6){\displaystyle \frac{{{\displaystyle \eta }}_{\mathrm{p}}}{{{\displaystyle \eta }}_{\mathrm{p},\mathrm{0}}}}=\mathrm{2}\left({\displaystyle \frac{m}{{{\displaystyle m}}_{\mathrm{0}}}}\right)-{{\displaystyle \left({\displaystyle \frac{m}{{{\displaystyle m}}_{\mathrm{0}}}}\right)}}^{\mathrm{2}}.

The power generator efficiency isa function of the ratio between the derated and rated output powerfrom the turbine and expressed as [25]

(7){\eta }_g=\mathrm{0.908}+\mathrm{0.258}\left({\displaystyle \frac{W}{W_{\mathrm{0}}}}\right)-\mathrm{0.3}{\left({\displaystyle \frac{W}{W_{\mathrm{0}}}}\right)}^{\mathrm{2}}+\mathrm{0.12}{\left({\displaystyle \frac{W}{W_{\mathrm{0}}}}\right)}^{\mathrm{3}}.

Annual performance calculation

Based on the above models, the annualperformance can be calculated by using the Matlab software as follows:

(1) For a given day and hour, thesolar field efficiency is calculated by the altitude and azimuth ofthe sun and the dual-receiver efficiency is calculated by the DNI,the ambient temperature and the wind speed of this time. The rankinecycle efficiency is 0.4058 at rated condition. As a result, the equivalentelectricity of the dual-receiver outlet power can be achieved.

(2) According to the relationshipbetween the dual-receiver outlet equivalent electricity and the ratedoutput of the power generation unit, the operating mode of the solarpower tower plant can be decided. Then, the electricity productionand thermal energy discard is obtained for a given day and hour.

(3) The annual electricity productionand the annual thermal energy discard are respectively gained by thesum of the hourly electricity production and thermal energy discardthroughout the year. The annual thermal energy discard factor is obtainedby the ratio of the annual thermal energy discard to the annual dual-receiveroutlet power. The annual capacity factor is obtained by the ratioof the annual electricity production to the annual theoretical maximumcorresponding to the constant electricity output at rated condition.

Economic calculation

Based on the annual electricity production,the LCOE is determined by Eq. (8).

(8)

where k_d is the real debtinterest (8%), k_insurance is the annual insurance rate (1%), n is the plant lifespan of 30 years, C_invest is the total investment in the plant, C_O&M is the cost of annual operation and maintenance,and E is the annual electricityproduction [18].

Cost models used for the economicanalysis of the DSG solar power tower are listed in Table 2, whichhave been set according to Refs. [11,18,21,26,27].

Results and discussion

Efficiency of the reference case

The reference case is the DSG solarpower tower plant in Sevilla with a settled land area of 4.8 km² and a settled size of solar field in the equivalentelectricity of 100 MW_e. The values in the solarfield efficiency matrix can be calculated by using the Monte-Carlomethod and expressed through the altitude and azimuth of the sun.The altitude of the sun is the angle between the sun ray and the ground,while the azimuth of the sun is the angle between the south directionand the projection of the sun ray on the ground. The minimum DNI valuefor the start-up of the solar field is 300 W/m² to ensure the solar energy collected by the dual-receiver is highenough to produce steam [18].

The solar field efficiency is thecombination of cosine efficiency, shadowing and blocking efficiency,spillage efficiency, atmosphere attenuation efficiency, and reflectivity.Only cosine efficiency, shadowing and blocking efficiency, and spillageefficiency are functions of time, which usually increase with solaraltitude. Therefore, as depicted in Fig. 5, the solar field efficiencyincreases with solar altitude in most cases. However, the cosine efficiencydecreases with the solar altitude in the case of low solar azimuthand high solar altitude, which results in the decrease of solar fieldefficiency with solar altitude. For the annual performance calculation,the solar field efficiency matrix is used to interpolate the solarfield efficiency defined by the hourly varying altitude and azimuthof the sun.

The dual-receiver efficiency matrixof the reference case which can be expressed through the levelizedDNI, the ambient temperature and the wind speed, is illustrated inFig. 6. The levelized DNI of 1.0 corresponds to the DNI at designpoint. The lowest ratio is 0.4 and corresponds to a DNI in the morninghours, whereas the highest ratio is 1.2 for hours with a higher DNIthan that at design point. Figure 6 also indicates that DNI has thelargest impact on the dual-receiver efficiency, while the influenceof the ambient temperature is the least. The dual-receiver efficiencymatrix is used within the annual performance assessment to interpolatethe dual-receiver efficiency defined by the hourly based practicalmeasurements of the DNI, the ambient temperature, and the wind speed.

The above results are based on adual-receiver outlet pressure of 10.7 MPa. When the power generationunit is operated in sliding pressure mode, the dual-receiver outletpressure is reduced and the corresponding saturation steam temperatureis lower, which results in a lower dual-receiver surface temperatureand a higher dual-receiver thermal efficiency. However, the heat transfercalculation results show that the variation in the dual-receiver thermalefficiency is less than 0.5% when the dual-receiver outlet pressurevaries from 10.7 MPa to 8.1 MPa for a given time. The influence ofdual-receiver outlet pressure is so small that the same dual-receiverefficiency matrix is applied for different outlet pressures.

Daily performance analysis

The daily performance analysis isperformed for the size of solar field in the equivalent electricityof 100 MW_e in Sevilla with an SM of 1.7 anda thermal storage capacity of 3 h. In this case, the rated electricityoutput is about 60 MW_e and the correspondingturbine inlet heat should be 155 MW_th.

Figure 7 illustrates the generatedelectricity power, dual-receiver outlet power, and thermal energystored in the tank for 5 days centered on the summer solstice, fromJune 19 to 23. When the dual-receiver outlet power exceeds 155 MW_th, the excess power is sent to the thermal storage system.It can also be seen in Fig. 7 that the generated electricity poweris at most 70% of the rated output once the thermal storage systemis discharged, because the turbine inlet steam pressure is reducedto 8.1 MPa during discharge.

Annual performance and economic analysis

The annual performance and economicassessment of the DSG solar power tower are performed using the hourlymeteorological data for the size of solar field in the equivalentelectricity of 100 MW_e in Sevilla with adjustingSM from 1.0 to 3.0 and the thermal storage capacity from 0 to12 h.Figures 8 to 10 show the annual thermal energy discard factor, theannual electricity production, and the annual capacity factor in functionof SM and thermal storage capacity, respectively.

As displayed in Fig. 9, the highestannual electricity production can be achieved at SM= 1.3, the storagecapacity of 3h with a value of 171.40 GWh_e.When the thermal storage capacity is 3 h, the annual electricity productionincreases with SM at the initial stage, because higher SM correspondsto a smaller size of power generation unit, which means that the turbineoperates for a longer time at the rated condition and results in ahigher annual Rankine cycle efficiency. Figure 8 shows that no thermalenergy is discarded when SM is less than 1.3 and the thermal storagecapacity is 3 h. However, a continuous increase in SM under the samethermal storage capacity results in the discard of more thermal energy,which leads to the reduction of annual electricity production. Inaddition, as the thermal storage capacity increases, the discard ofthermal energy decreases and the generation of annual electricityincreases. But when the thermal storage capacity is large enough,further increase of the storage capacity will have no effect on increasingthe annual electricity production.

Figure 10 shows that the annual capacityfactor increases with SM or the thermal storage capacity. As mentionedabove, the annual electricity production first increases, then decreaseswith the increase of SM. The electricity output at rated condition,namely the size of power generation unit, decreases with SM. Therefore,the decreasing rate of the annual electricity production should belower than that of the size of the power generation unit. Accordingto the present analysis, the annual capacity factor is 0.253 whenSM is 1.3 and the storage capacity is 3 h.

The variation of the LCOE with SMand thermal storage capacity is shown in Fig. 11. It can be observedthat the DSG solar power tower plant has a minimum LCOE of 21.77 ￠/kWh_e and the optimal values of SM and the thermal storagecapacity are respectively 1.7 and 3 h.

The investment in land, solar field,dual-receiver and tower remain the same for different SMs becauseof the same solar field. The investment in the power generation unitand the thermal storage system decreases with SM due to the reductionof the size of power generation unit. Therefore, the overall economiccost decreases with SM.

As mentioned above, the annual electricitygeneration increases first, and then decreases with SM. As a result,it can be concluded that the LCOE decreases initially with SM. However,the further trend is decided by the decreasing rate of the overalleconomic cost and the annual electricity generation. The overall economiccost increases with thermal storage capacity due to the higher thermalstorage investment. The annual electricity generation also increaseswith the thermal storage capacity. Consequently, the relationshipbetween the thermal storage capacity and the LCOE is decided by thevariation rate of the overall economic cost and the annual electricitygeneration with the thermal storage capacity.

Effect of site

To investigate the effect of siteon the minimum LCOE and related optimal parameters of the DSG solarpower tower, two other regions, namely, San Jose (37.4°N, 121.9°W),and Bishop (37.4°N, 118.4°W), USA have been selected. Thesizes of solar field equivalent electricity of these two sites areboth fixed at 100 MW_e by adjusting SM from1.0 to 3.0 and thermal storage capacity from 0 to 12 h. Table 3 givesthe meteorological data for these two sites. It shows that there isan increase of 10.1% and 55% in the annual DNI in the San Jose siteand Bishop site respectively when compared with the Sevilla site,while the design conditions of these three sites are similar.

Table 4 tabulates the minimum LCOEand related optimal parameters for different sites. It can be seenthat the LCOE decreases with DNI and Bishop site has the lowest LCOEof 14.62 ￠/kWh_e in the three sites. When comparedwith the Sevilla site, the annual DNI and the annual electricity productionof the Bishop site respectively increase by 55.0% and 62.4%, whilethe minimum LCOE of the Bishop site decreases by 32.8%. This is causedby the fact that the annual electricity production increases withDNI and the overall economic cost is almost the same for the samesize of solar field equivalent electricity.

As the DNI of the Sevilla site isnot much different from that of the San Jose site, the optimal SMof these two sites are the same. However, the optimal SM of the Bishopsite is 1.3, which is lower than those of the other two sites, becausethe overall economic cost is almost the same for different sites andthe thermal energy discard factor increases with higher DNI and higherSM. Therefore, the optimal SM of the Bishop site should be lower toobtain a lower thermal energy discard factor and a higher annual electricityproduction. The optimal thermal storage capacity of the three sitesare the same, because the relatively low optimal SM of the three sitesleads to the low thermal energy discard factor and thermal storagecapacity.

Effect of size of solar field equivalent electricity

The effect of the size of solar fieldequivalent electricity on the minimum LCOE and related optimal parametersof the DSG solar power tower plant is also investigated by varyingthe size of solar field equivalent electricity from 50 to 150 MW_e. The site is fixed at Sevilla and the variation ofSM and thermal storage capacity are respectivly fixed at 1.0–3.0and 0–12 h. Table 5 shows the minimum LCOE and related optimalparameters for different sizes of solar field equivalent electricity.

The annual electricity productionper unit area of heliostats is proportional to the annual solar-to-electricityefficiency, because the annual solar energy available per unit areaof heliostats (1773 kWh/m² for the siteof Sevilla considered here) is fixed. The annual solar-to-electricityefficiency decreases with the size of solar field equivalent electricitymainly due to decreasing solar field efficiency. Therefore, as presentedin Table 5, the annual electricity production per unit area of heliostatsdecreases with the size of solar field equivalent electricity. However,the decreasing rate of the overall economic cost per unit area ofheliostats with the size of solar field equivalent electricity shouldbe larger than that of the annual electricity production per unitarea of heliostats. Consequently, Table 5 shows that the minimum LCOEreduces from 24.53 ￠/kWh_e to 20.92 ￠/kWh_e when increasing the size of solar field equivalentelectricity from 50 MW_e to 150 MW_e. Furthermore, the decreasing rate of the minimum LCOEdrops with the size of solar field equivalent electricity.

Table 5 also demonstrates that theminimum LCOE of different sizes of solar field equivalent electricityoccur when the SM and the thermal storage capacity are respectively1.7 and 3 h. On the one hand, the DNI are the same for different sizesof solar field equivalent electricity, so the trends of the thermalenergy discard factor and the annual electricity production with SMand thermal storage capacity are similar for different sizes of solarfield equivalent electricity. On the other hand, the overall economiccosts decrease with SM and increase with the thermal storage capacityfor different sizes of solar field equivalent electricity. As a result,the minimum LCOE are achieved with the same optimal SM and thermalstorage capacity for different sizes of solar field equivalent electricityfrom 50 to 150 MW_e when the annual electricityproductions are relatively high and the overall economic costs arerelatively low.

Effect of investment

The effect of sub-system investment(investment in land, solar field, dual-receiver, tower, thermal storagesystem, and power generation unit) on the minimum LCOE and relatedoptimal parameters of the DSG solar power tower has also been studiedby just varying the investment in the reference case. Figure 12 showsthe sensitivity analysis of investment. The investment ratio is theratio of current to reference investment. The minimum LCOE ratio isthe ratio of current to reference minimum LCOE. The reference investmentand the reference minimum LCOE are calculated in the reference case.The results show that the investment in solar field has the highestinfluence on the minimum LCOE, followed by the cost of dual-receiverand the cost of power generation unit. Regarding the solar field,the minimum LCOE can be reduced by about 10% by decreasing the costof solar field by 25%. Besides, the reduction rate of the minimumLCOE is 6% when the cost of dual-receiver is decreased by 25%.

For a given size of the solar field,the investment in land, solar field, dual-receiver and tower remainthe same for different SMs and thermal storage capacities. Consequently,the optimal SM and thermal storage capacity remain to be 1.7 and 3h respectively when varying the investment in the above factors. However,the cost of power generation unit and the cost of thermal storagesystem decrease with SM due to the reduction in the size of powergeneration unit. In addition, the cost of thermal storage system increaseswith thermal storage capacity. Therefore, the optimal SM and thermalstorage capacity should vary with the investment in thermal storagesystem and power generation unit. As shown in Table 6, the optimalSM and thermal storage capacity reduce with the cost of thermal storagesystem, while increase with the cost of power generation unit. Thereason for this is that it is economic to apply a higher thermal storagecapacity for a lower cost of thermal storage system and to adopt alarger size of power generation unit for a lower cost of power generationunit. When compared with the reference case, the optimal SM and thermalstorage capacity are respectively increased to 2.7 and 9 h by reducingthe cost of thermal storage system by 50%, while respectively decreasedto 1.3 and 0 h when the investment in power generation unit is decreasedby 50%.

Conclusions

Taking a DSG dual-receiver solarpower tower plant in Sevilla with a given size of solar field in theequivalent electricity of 100 MW_e as the referencecase, the analysis of the annual performance and the economic assessmentare conducted by adjusting SM from 1.0 to 3.0 and varying the thermalenergy storage capacity from 0 h to 12 h. Based on the above, theeffects of site, size of solar field equivalent electricity, and investmentin the minimum LCOE and optimal SM and thermal storage capacity areinvestigated. The following conclusions can be obtained:

(1) For the reference case, the minimumLCOE is 21.77 ￠/kWh_e with an optimal SM of1.7 and an optimal thermal storage capacity of 3 h, while the highestannual electricity production of the DSG solar power tower plant is171.40 GWh_e with an optimal SM of 1.3 and astorage capacity of 3 h.

(2) Besides Sevilla, two other sitesof San Jose and Bishop are also studied by fixing the size of solarfield equivalent electricity. When compared with the case of Sevilla,the minimum LCOE of the San Jose site change just slightly while theminimum LCOE of the Bishop site decreases by 32.8% because of thehigher DNI. In addition, as the thermal energy discard factor increaseswith a higher DNI and a higher SM, the optimal SM of Bishop can reduceto 1.3.

(3) The influence of the size ofsolar field equivalent electricity is investigated by fixing the locationsite. The minimum LCOE reduces from 24.53 ￠/kWh_e to 20.92 ￠/kWh_e when the size of solar fieldequivalent electricity varies from 50 MW_e to150 MW_e. During this process, the optimal SMand thermal storage capacity can still stay constant. The reason forthis is that in different sizes of solar field equivalent electricity,the trends of the annual electricity production and the overall economiccost with SM and thermal storage capacity are very similar.

(4) After adjusting the sub-systeminvestment in the reference case, it is obsrved that the investmentin solar field has the largest influence on the minimum LCOE, followedby the cost of dual-receiver and the cost of power generation unit.In addition, the optimal SM and thermal storage capacity can decreasewith the cost of thermal storage system but increase with the costof power generation unit due to the economic aspects.

References

[1] Zhang H L, Baeyens  J, Degrève J,  Cacères G. Concentrated solar power plants: reviewand design methodology. Renewable &Sustainable Energy Reviews, 2013, 22: 466–481 

[2] Ma X, Xu  C, Yu Z,  Ju X. A review of salt hydrate-based sorption technologies for long-term thermal energystorage. Science Bulletin, 2015, 60(36): 3569–3579

[3] Kolb G J, Ho  C K, Mancini  T R, Gary  J A. Power tower technology roadmap and cost reduction plan. Report No. SAND2011–2419, Sandia NationalLaboratories, Albuquerque, NM, 2011

[4] Romero M, Buck  R, Pacheco J E. An update on solar central receiver systems,projects, and technologies. Journal ofSolar Energy Engineering, 2002, 124(2): 98–108

[5] Tehrani S S M,  Taylor R A,  Saberi P,  Diarce G. Design and feasibility of high temperature shell and tube latentheat thermal energy storage system for solar thermal power plants. Renewable Energy, 2016, 96: 120–136 

[6] Osuna R, Fernandez  V, Romero S,  Romero M,  Sanchez M. PS10: a 11.0-MW solar tower power plant with saturated steam receiver. In: Proceedings of the 12th Solar PACES InternationalSymposium on Concentrated Solar Power and Chemical Energy Technologies 2014, Oaxaca, México

[7] Birnbaum J, Eck  M, Fichtner M,  Hirsch T,  Lehmann D,  Zimmermann G. A direct steam generation solar power plant with integratedthermal storage. Journal of Solar EnergyEngineering, 2010, 132(3): 031014

[8] Feldhoff J F, Schmitz  K, Eck M,  Schnatbaum-Laumann L,  Laing D,  Ortiz-Vives F,  Schulte-Fischedick J. Comparative system analysis of directsteam generation and synthetic oil parabolic trough power plants withintegrated thermal storage. Solar Energy, 2012, 86(1): 520–530

[9] Laing D, Bahl  C, Bauer T,  Lehmann D,  Steinmann W D. Thermal energy storage fordirect steam generation. Solar Energy, 2011, 85(4): 627–633

[10] Laing D, Bauer  T, Lehmann D,  Bahl C. Development of a thermal energy storage system for parabolic troughpower plants with direct steam generation. Journal of Solar Energy Engineering, 2010, 132(2): 021011

[11] Li Y, Yang  Y. Impacts of solar multiples on the performance of integrated solar combined cyclesystems with two direct steam generation fields. Applied Energy, 2015, 160: 673–680

[12] Pacheco J E, Bradshaw  R W, Dawson  D B, Rosa  W D, Gilbert  R, Goods S,  Hale M J,  Jacobs P,  Jones S A,  Kolb G J,  Prairie M R,  Reilly H E,  Showalter S K,  Vant-Hull L L. Final test and evaluationresults from the Solar Two project. Report No. SAND2002–0120, Sandia National Laboratories, Albuquerque,NM, 2002

[13] Moore R, Vernon  M, Ho C K,  Siegel N P. Design considerations for concentrating solar power tower systemsemploying molten salt. Report No. SAND2010–6978,Sandia National Laboratories, Albuquerque, NM, 2010

[14] Rodríguez-Sánchez M R,  Soria-Verdugo A,  Almendros-Ibáñez J A, Acosta-Iborra A,  Santana D. Thermal design guidelines of solar power towers. Applied Thermal Engineering, 2014, 63(1): 428–438

[15] Collado F J, Guallar  J. A review of optimized design layouts for solar power tower plantswith campo, code. Renewable & SustainableEnergy Reviews, 2013, 20: 142–154

[16] Boudaoud S, Khellaf  A, Mohammedi K,  Behar O. Thermal performance prediction and sensitivity analysisfor future deployment of molten salt cavity receiver solar power plantsin Algeria. Energy Conversion and Management, 2015, 89: 655–664 

[17] Cocco D, Serra  F. Performance comparison of two-tank direct and thermocline thermal energy storagesystems for 1MW_e class concentrating solar power plants. Energy, 2015, 81: 526–536 

[18] Montes M J, Abánades  A, Martínez-Val J M. Performance of a direct steam generation solar thermal power plant for electricityproduction as a function of the solar multiple. Solar Energy, 2009, 83(5): 679–689

[19] Jorgenson J, Denholm  P, Mehos M,  Turchi C. Estimating the performance and economic value of multipleconcentrating solar power technologies in a production cost model. Technical Report. National Renewable Energy Laboratory,Golden, CO, 2013

[20] Luo Y, Du  X, Wen D. Novel design of central dual-receiverfor solar power tower. Applied ThermalEngineering, 2015, 91: 1071–1081 

[21] Blair N, Dobos  A P, Freeman  J, Neises T,  Wagner M,  Ferguson T,  Gilman P,  Janzou S. System advisor model, sam 2014.1.14:general description. Technical Report.National Renewable Energy Laboratory, Golden, CO, 2014

[22] Liu J. Solar Thermal Dynamic Power Generation Technology. Beijing: Chemical Industry Press, 2012 (in Chinese)

[23] Fan Q, Yan  W, Yan S. Boiler Principle. Beijing: China Electric Power Press, 2004 (in Chinese)

[24] Flueckiger S M,  Iverson B D,  Garimella S V,  Pacheco J E. System-level simulation of a solar power tower plantwith thermocline thermal energy storage. Applied Energy, 2014, 113: 86–96 

[25] Montes M J, Abánades  A, Martinez-Val J M,  Valdés M. Solar multiple optimization for a solar-only thermalpower plant, using oil as heat transfer fluid in the parabolic troughcollectors. Solar Energy, 2009, 83(12): 2165–2176

[26] Collado F J, Guallar  J. Two-stages optimised design of the collector field of solar powertower plants. Solar Energy, 2016, 135: 884–896

[27] Turchi C S, Heath  G A. Molten salt power tower cost model for the system advisor model (sam). Office of Scientific & Technical InformationTechnical Reports. University of North Texas Libraries, 2013

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag GmbHGermany