Optimal Design of Integrated Solar Power Plants Accounting for the

Article pubs.acs.org/IECR

Optimal Design of Integrated Solar Power Plants Accounting for the Thermal Storage System and CO2 Mitigation through an Algae System José Francisco Hernández-Martinez,† Eusiel Rubio-Castro,‡ Medardo Serna-González,† Mahmoud M. El-Halwagi,§,∥ and José María Ponce-Ortega*,† †

Chemical Chemical § Chemical ∥ Chemical ‡

Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán 58060, México and Biological Sciences Department, Universidad Autonoma de Sinaloa, Culiacan, Sinaloa 80000, México Engineering Department, Texas A&M University, College Station, Texas 77843, United States and Materials Engineering Department, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

ABSTRACT: Electricity generation through the burning of fossil fuels is one of the main contributors to the climate change problem. The use of renewable energy sources is a promising strategy to help mitigate this problem. This paper considers two forms of renewable energy: solar and biomass (algae) for power generation. The paper also accounts for the thermal storage of solar energy. A multiobjective optimization formulation is developed to reduce greenhouse gas emissions and cost in the electricity generation process. The model is based on a new superstructure that incorporates various design configurations and screens different thermal storage systems. A case study is presented to show the applicability of the proposed approach and how the economic and environmental objectives can be reconciled.

and produces less than 20 MWe.10 The steam accumulator represents an attractive option for facilitating the operation of solar thermal power plants by offering short time energy storage.12 The most used material for the SHS system is the melting salts in one (thermocline) or two-tanks. The quality of the outflow for molten salts depends on the system configuration.13 The molten salts thermocline uses only a single tank as storage container and can reduce significantly the cost with respect to two-tank TES.14 Another SHS system consists of using two tanks, one cold and other hot, using a combination of molten salts. Sometimes the heat transfer fluid (HTF) is used as storage material (direct method) using molten salts or another material, these materials are stored in a cold tank in a temperature range of 200−300 °C, the stored salt in the tank is passed through the pipes of the solar collector to be heated, and then it is sent to the hot tank for its storage. To generate steam for the Rankine cycle, the hot salts transfer energy to the water to become steam using a heat exchanger, finally sending the exhaust salts to the cold tank to complete the storage cycle. When a different HTF is used as storage material (indirect method), the storage cycle is similar to the direct method, the difference is that the salt stored in the cold

1. INTRODUCTION Fossil fuels have been the main resource to generate electricity. The use of these fuels contributes significantly to greenhouse gas emissions (GHGE), which adversely affect the environment and human health. Renewable energy represents an attractive option to replace the use of fossil fuels for producing electric energy and for decreasing the environmental impact.1 Several studies have been proposed to enhance the performance of electricity generation through hybrid power plants and cogeneration systems that combine fossil fuels along with renewable energy (e.g., Rankine cycle and concentrating solar power “CSP”).2,3 Different types of solar collectors have been integrated to improve the performance of these power plants.4−6 Under this context, Tora and El-Halwagi proposed a systematic approach for designing integrated solar systems to yield a stable power outlet,7 then Tora and El-Halwagi incorporated absorption refrigerators8 and trigeneration systems.9 Kuravi et al.10 proposed a thermal energy storage (TES) system coupled with a solar collector to satisfy the energy demands in periods when the solar radiation is not available. There are several TES systems, which include sensible heat storage (SHS), latent heat storage (LHS), and thermochemical storage (TCS). Tian and Zhao11 presented a review for the use of solar collectors and TES. One of the main SHS systems is the steam accumulator, which is charged with hot vapor at high pressure and dispatches at low pressure and high temperature © XXXX American Chemical Society

Received: July 3, 2016 Revised: September 20, 2016 Accepted: September 27, 2016

A

DOI: 10.1021/acs.iecr.6b02539 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

Figure 1. Problem statement.

Figure 2. Proposed superstructure.

tank does not pass through the solar collector and it uses an additional heat exchanger to receive the energy from the HTF. A model was developed by NREL15 to estimate the cost of any direct or indirect two-tank SHS systems. Herrmann et al.16

presented some comparisons in terms of cost and security for both methods (direct and indirect), and they concluded that direct methods are cheaper and safer than indirect methods if the storage system is big enough, but this method can cause B


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solar collector to the Rankine cycle or to the storage systems, from the storage systems to the Rankine cycle, and from the Rankine cycle to the biofuel processing. In the model formulation, the subscripts s and t are used for storage tanks and time periods, respectively, and the model is presented in the next subsections. 2.1. Energy Balance for the Solar Collector. The heat absorbed in the solar collector (Qsolar ) is proportional to the t selected area (ASC) and the available solar radiation in the location at any time period t (ASRt), which is modeled as follows:

incrustations in the pipes of the solar collector. There are several geometries for LHS.17,18 To enhance the performance of LHS as a phase change material (PCM), it was proposed to encapsulate it or add different materials to increase its conductivity. Nithyanandam and Pitchumani19 presented an analysis for CSP systems. From the energy point of view, the PCM storage system has the advantage to operate with small temperature differences between charging and discharging; also it allows storing energy in relatively small volumes.20 Recently, thermochemical storage systems have attracted attention, obtaining temperatures of 1000 °C.21 Pardo at al.22 presented a review of different thermochemical systems. However, in several places around the world power plants that use CSP coupled with TES systems still use fossil fuels as a backup with the corresponding emissions, which should be reduced.23 There are several pathways to produce biofuels from biomass to achieve the reduction of GHGE produced by fossil fuels and to extend the useful life of their reserves.24−26 One of these pathways is by CO2 sequestration through an algae system to produce different biofuels such as biodiesel, methane, and hydrogen.27,28 In this context, Slade and Bauen29 examined the main aspects of microalgae production related to the sustainability (energy and carbon balance, environmental impacts, and production cost). Gutiérrez-Arriaga et al.30 presented a multiobjective optimization approach for the sustainable generation of electricity, whereas Bamufleh et al.31 incorporated social objectives. Gutiérrez-Arriaga et al.32 presented an integrated approach for biodiesel production from algae in a power plant using a multiobjective genetic algorithm. Lira-Barragán et al.33 presented a sequential approach for recovering flue gases from steam power plants through an algae system. Gutiérrez-Arriaga et al.34 incorporated the waste heat recovery from power plants through a cogeneration system. Abdelhady et al.35 reported a systematic approach for integrating a thermal solar collector with process cogeneration. Hernández-Calderón et al.36 developed a model for the optimal design of an algae recovery system using CO2 from multiple industrial plants. Furthermore, Yan et al.37 reported several alternatives to reduce the CO2 emissions for power generation, whereas Maroufmashat et al.38 analyzed the effect of multiple hubs. The conceptual problem addressed in this paper is illustrated in Figure 1. It should be noted that the design of CSP coupled with TES and power plants depends strongly on the available area of the solar collector, solar radiation, and weather conditions. Furthermore, previously reported approaches have not considered the simultaneous design of these systems and their integration, mainly the energy storage system is not considered during the first design stage. Therefore, this paper proposes a new optimization formulation for designing integrated solar power plants involving thermal storage and microalgae systems. The proposed model is based on a new superstructure that incorporates the interactions between the involved units, and the objective is to simultaneously minimize the total annual cost and the generated emissions. The proposed model is general and can be used to analyze the design and operation for different cases.

Q tsolar = ASR t ASC ,

∀t

(1) solar‑CAP

The selected capacity for the solar collector (Q ) is limited by the maximum available solar energy (Qsolar‑MAX), and the binary variable YSC is used to determine the existence of the solar collector as follows: Q solar‐CAP ≤ Q solar‐MAXY SC

(2)

The collected solar energy can be delivered to the Rankine cycle (Qsolar‑RC ) or to some of the storage units (Qsolar‑SS ): t s,t Q tsolar = Q tsolar‐RC +

‐SS , ∑ Q ssolar ,t

∀t (3)

s

2.2. Energy Balance and Selection for the Storage Systems. The stored energy for each unit (Qs,t) is calculated multiplying the corresponding efficiency (ηs) times the stored energy in the previous time period (Qs,t−1) plus the delivered energy in the time period (Qsolar‑SS ) minus the energy that is s,t sent to the Rankine cycle QRC s,t : ‐SS Q s , t = ηsQ s , t − 1 + Q ssolar − Q sRC ,t ,t′

Q sCAP ≤ Q smaxYs ,

∀ s, t

(4)

∀s

(5)

The storage capacity for each unit is represented in eq 5 by QCAP , which has to be lower or equal than the maximum s capacity (QMAX ), and here the binary variable Ys is used to s denote the existence of the unit. The maximum capacities QMAX s can be obtained from NREL39 and IRENA.40 2.3. Heat Exchanger Energy Balance. The stored heat in the units and the energy from the solar collector are received from the heat exchanger (HX), this HX is used to promote the steam production to produce electricity in the turbine. Equation 6 represents the energy balance in the HX, where Qout‑HX is the output flux that is given by the amount of energy t sent from the solar collector (Qsolar‑SRC ) and the sum of the t energy from the storage units (QRC s,t ) both multiplying for the HX efficiency ηHX: Q tout‐HX = ηHX (Q tsolar‐SRC +

), ∑ Q sRC ,t s

∀t (6)

The existence of the HX is represented by eq 7, where the capacity (QHX‑CAP) is restricted by the maximum capacity allowed (QHX‑MAX), which is used to activate the binary variable (YHX): Q HX‐CAP ≤ Q HX‐maxY HX

2. MODEL FORMULATION The model is based on the superstructure represented in Figure 2. This scheme includes a solar collector, five storage systems, one algae system, biofuel processing, and a simple steam Rankine cycle. It takes into account the heat exchange from the

(7)

2.4. Energy Balance in the Boiler. Nowadays, in several parts of the world, the existing power plants use backup fossil fuels to complete the power generation cycle. Then, a boiler can be needed in the system, which is modeled through a C


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Industrial & Engineering Chemistry Research CAPCost = kF[ay + b(CAP)c ]

binary variable (Yboiler) and the corresponding capacity (Qboiler‑CAP), which is restricted by the maximum allowed (Qboiler‑MAX): Q boiler‐CAP ≤ Q boiler‐MAXY boiler

The operating costs depend on the hours of operation per year (HD) times the unit operating cost (UOC) and the energy (∑ t Q t ) used for each unit:

(8)

t>1

The inlet energy to the turbine (Qin‑turbine ) in the form of steam t to generate electricity is supplied by the heat exchanger (Qout‑HX ) and the boiler (Qboiler ): t t Q tin‐turbine = Q tout‐HX + Q tboiler ,

∀t

Opcost = HDUOC ∑ Q t t t>1

∀t

(Eboiler‑total ) t

Whereas, the total emissions account for the sum of the emissions during all the time periods (Eemissions ): t min Etboiler‐total =

A

=

∑

Etalgae‐adsorption ΩAA

t

(11)

3. VALIDATION OF THE MODEL The proposed model was validated comparing it with an existing system in Spain, the Andasol 1 process (see Table 1). Table 1. Andasol 1 System Specifications Plant Configuration

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Solar Field solar field aperture area (Ha) no. of solar collector assemblies solar field inlet temp (°C) solar field outlet temp (°C) solar field temp difference (°C) Power Block turbine capacity (gross MW) output type power cycle pressure (bar) turbine efficiecy Thermal Storage storage type storage capacity (h)

The algae production, in the same way that the solar collector, depends on the available area, which defines the maximum algae production (AlgaeMAX). The capacity calculated by the model (AlgaeCAP) could be lower or the same as the maximum capacity of the algae, which is determined by the binary variable (YAlgae): Algae

CAP

≤ Algae

MAX

Y

Algae

(13)

It should be noticed that the produced algae biomass is function of the available solar radiation, the area used for the pounds as well as the operating conditions and nutrients. One important limitation for this integrated system is the available area for the solar collector as well as for the algae cultivation; therefore, eq 2 is used to constrain the available area for the solar collector and eq 13 incorporates the limit for the algae cultivation system. 2.7. Biodiesel Production. The produced biodiesel depends on the recovery (RL) and transesterification of lipid factors (TRANS) from the produced algae (Aproduction): F biodiesel = RLTRANS Aproduction

(18)

The previous formulation is a multiobjective mixed-integer nonlinear programming (MINLP) problem, whose solution represents the best possible trade-offs between the economic and environmental objectives. To solve this problem, the epsilon-constraint method can be used to obtain a Pareto curve that represents a set of solutions that compensate both objectives (see the work of Fuentes-Cortes et al.41,42).

2.6. Algae Production. The biomass produced by the algae system (A production ) depends on the amount of CO 2 (∑tEalgae‑adsorption ), which is multiplied by the available area t (AA) and a conversion factor, Ω (see the work of Slade and Bauen for values of Ω29): production

∑ Etemissions t

(10)

∀t

(17)

min TAC = TCOST − TSALES

The emissions that are generated in the boiler are sent to the algae production (Ealgae‑adsorption ) or discharged to the ambient t (GHGEt): Etemissions = GHGEt + Etalgae‐adsorption ,

(16)

2.9. Objective Functions. The model incorporates two objective functions, the first one is the minimization of the total annual cost (TAC) and the second one is the minimization of the total emissions (Etboiler‑total). The total annual cost incorporates the total cost (TCOST) and the total sales (TSALES):

(9)

It should be noticed that the proposed model is general and it can be adjusted to different situations and conditions. In the case that the use of fossil fuels as backup is not allowed (i.e., Yboiler is fixed as zero), the effect is that larger units are needed for capturing and storage the solar energy, which as consequence increases the capital costs. However, it has a significant reduction in the overall greenhouse gas emissions. 2.5. CO2 Emissions. The CO2 emitted by the boiler ) depends on the type of used fuel, the needed energy (Qboiler t and the boiler efficiency (ηemissions) (see the work of GutiérrezArriaga at al.32): Etemissions = ηemissionsQ tboilerμ ,

(15)

51 624 293 393 100 50 steam Rankine 100 38.1 two-tank molten salts 7.5

The model follows the specification of Andasol 1, including the total aperture area of 510 120 m2, the inlet and outlet temperatures, the cycle pressure, and the total power generated, 50 MW. To validate the proposed model, the algae system was not considered because it does not exist in the case of Andasol 1. The solar radiation of Granada Spain was considered (see Figure 3). For this case, the model consists of 996 constraints, 933 continuous variables, and 10 discrete variables, and this was coded in the software GAMS using the solvers DICOPT, CONOPT, and CPLEX43 and solved in a CPU time of 0.0125 s in computers with an Intel i7 processor and 16 GB given the results shown in Table 2. The solution is presented in Figure 4.

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2.8. System Cost. The capital costs for the used units (CAPCost) depend on the unit constants (a, b, c) as well as the capacity (CAP) and the corresponding binary variables, and it accounts for the annualization factor (kF): D


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4. RESULTS AND DISCUSSION As case study was considered the Andasol 1 process to incorporate the optimal design of a new energy storage and algae system in order to minimize the total annual cost and the involved emissions. In this case, the efficiency for transferring energy to the Rankine cycle was considered as 50%, the considered time period is 24 h a day, the model accounts for the seasonal variability for the solar radiation through the year for the considered location, and the results of the case study represent a year of operation with the hourly radiation. Figure 5

Figure 3. Behavior of solar radiation in Granada, Spain.

In general, the results are very similar to the Andasol 1 process, with the same solar collectors. Table 2. Comparison of Andasol 1 and the Results of the Proposed Model Plant Configuration Andasol

model Winter

model Summer

51

51

51

624

624

624

Solar Field solar field aperture area (Ha) no. of solar collector assemblies storage type storage capacity (kWh) total annual cost (M$ USD) emissions prevented (ton CO2/y)

Thermal Storage two-tank two-tank molten salts molten salts 1010000 749340 Cost 338.5 324.3 Green House Emissions 30483.2 17600

Figure 5. Pareto curves for low and high radiation.

presents the Pareto front for the results obtained applying the epsilon-constrain method, where the average CPU time for each scenario was 2.7 s. Several interesting solutions can be identified from this Pareto front, which are described in Table 3. It should be noted that solutions A, B, C, and D represent a low radiation case, whereas the solutions E, F, G, and H represent the high radiation cases. For low radiation, scenario A (Figure 6) represents the minimum TAC, here the solar collector is not selected because it represents a high cost. The algae system exists because its

two-tank molten salts 1010000 337.1

32419.2

Figure 4. Scheme for validating the model. E


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Industrial & Engineering Chemistry Research Table 3. Results of Scenarios for the Model Minimizing GHE and TAC Results for the Scenarios at Low and High Radiation low radiation

high radiation

scenarios

A

B

C

D

E

F

G

H

total solar field aperture (Ha) no. of solar collector assemblies (SCA) solar and storage energy (MWh/y) energy used in the boiler (MWh/y) emissions sent to the environment (ton CO2/y) emissions sent to algae culture (ton CO2/y) boiler emissions (ton CO2/y) biodiesel produced (ton/y) total annual cost (M$ USD)

0 0 0 528000 29266 15086 44352 6420.4 55.2

6 73 89395 438605 21758.2 15085.6 36843.8 6420.4 118.9

19.7 243 178787 349213 15365 13969 29334 5945 227.9

77.3 949 264642 263358 9408 12417 21825 5280 593

0 0 0 528000 29266 15086 44352 6420.4 55.7

3.6 44 112436 415564 19822 15085 34907 6420.4 107.5

10.8 133 224866 303134 11717 13746 25463 5850 186.1

51 626 337297 190703 3613.3 12406 16019 5280 477

Figure 7. Scheme for the scenarios B and F.

scenario D that was reached using more than one storage system, which increases the TAC and produces the lowest biodiesel at low radiation. The reduction in the biodiesel production is due to the reduction in the use of fossil fuels to account for the reduction in the GHGE. Even using a steam accumulator, two-tank molten salt, and thermochemical storage, the GHGE cannot be reduced to zero. For the case of high radiation, similar to scenario A, scenario E (Figure 6) has the minimum total annual cost. The increment of the solar radiation in the scenario E does not affect its solution because it produces the same amount of biodiesel that scenario A. Also, these scenarios have the same structure because the minimum TAC does not include any storage system. Comparing the scenarios B and F (Figure 7), the total annual cost and the solar collector area for scenario F are both lower than the ones of scenario B. The high radiation permits a significant reduction in the number of assemblies of scenario F compared with scenario B in the same way that GHGE. Figure 5 shows that the scenarios B, C, and F are compensated solutions for the GHGE and TAC at low and high radiation, respectively. For the reduction in the GHGE in scenario G (Figure 8), a similar scheme to scenario C is needed both using a two-tank storage system. The capacity of the storage system

Figure 6. Scheme for the scenarios A and E.

production generates a profit. This scenario generates 6420.48 ton/y of biodiesel and it has the greatest CO2 emissions. The use of solar collector and storage systems promote the reduction of CO2 emissions. The scenarios B (Figure 7) and C (Figure 8) are compensated solutions between the minimum cost and the minimum emissions. Whereas, the scenario D (Figure 9) corresponds to the one with minimum emissions. To conserve 7509 ton/y of CO2 emissions, scenario B utilizes a solar collector with 73 assemblies without any storage system; this doubles the TAC compared with scenario A, both producing the same quantity of biodiesel. The solution for scenario C selects a two-tank storage system, besides the 243 assemblies in the solar collector also reach 7509 ton CO2/y less than scenario B. The use of storage systems replaces part of the heat usually delivered by the boiler to generate steam, decreasing the use of fossil fuels that also affects the biodiesel production, because the CO2 is an important factor for the algae culture. The minimum for the GHGE is found in the F


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assemblies in the solar collector and presented the lowest GHGE of all scenarios and the greatest supply of solar energy to the cycle. Also, the total collector area for scenario H is similar to that of Andasol 1, but the storage capacity is greater to reduce the TAC and emissions.

5. CONCLUSION This paper has presented an optimization formulation for designing integrated energy storage systems for solar power plants and incorporating an algae system to mitigate the CO2 emissions. The proposed model incorporates the optimal selection of different thermal storage systems through a mixedinteger nonlinear programming formulation. A two-objective optimization approach has been formulated to simultaneously minimize the cost and the generated emissions. An epsilonconstraint method has been implemented to show compensated solutions through Pareto curves. A case study has been presented, where two conditions for available solar radiation were analyzed. The results show attractive solutions for both scenarios. Furthermore, in both scenarios there are identified solutions that reconcile the economic and environmental objectives. In the case of compensated solutions, usually a set of thermal storage systems were identified and the algae system was incorporated. Additionally, the most compensated solutions use a set of thermal storage systems combining different technologies. It should be noticed that a regenerative Rankine cycle can be considered in a future work to improve the efficiency of the system.

Figure 8. Scheme for the scenarios C and G.

decreases in scenario G due to the high radiation compared with scenario C to yield a lower TAC. Otherwise, the scenario G has 133 assemblies, which is almost half of those in scenario C. Scenario H (Figure 9) needs compensation to satisfy energy needs even with higher radiation; in this case, three storage systems were selected as in scenario D. Scenario H includes 626

Figure 9. Scheme for the scenarios D and H. G


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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone:+52 443 3223500 ext. 1277. Fax. +52 443 3273584 (J.M.P.-O.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the financial support from the Mexican Council for Science and Technology (CONACyT) and the Research Scientific Research Council of the UMSNH.

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NOMENCLATURE

Parameters

■

a = unit fixed cost, USD AlgaeMAX = algae maximum capacity, kg/m2 ASRt = solar radiation per area, W/m2 b = unit variable cost, USD c = factor used to account for the economies of scale HD = operational hours per year, h/y kf = annualization factor, 1/y Qboiler_MAX = boiler maximum capacity, kW QMAX = storage maximum capacity, kW s QHX‑MAX = heat exchanger maximum capacity, kW Qsolar‑MAX = maximum solar energy, kW RL = recovery lipid factor TRANS = transesterification factor UOC = operational unit cost, USD/h Ys = Binary variable to determinate the existence for the storage systems, 0 or 1

QCAP = storage capacity, kW S QHX‑CAP = heat exchanger capacity, kW Qin‑turbine = energy in the turbine, kW t Qout‑HX = energy out from the heat exchanger, kW t QRC s,t = energy from the storage systems to the Rankine cycle, kW Qsolar = solar collector energy, kW t Qsolar‑CAP = solar capacity, kW t Qsolar‑RC = energy from the solar collector sent to the t Rankine cycle, kW Qsolar‑SS = energy from the solar collector sent to the Rankine s,t cycle, kW TAC = total annual cost, USD/y TCOST = total cost, USD/y TSALES = total sales, USD/y

REFERENCES

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Binary Variables

YAlgae = algae system existence, 0 or 1 Yboiler = boiler existence, 0 or 1 YHX = heat exchanger existence, 0 or 1 YSC = solar collector existence, 0 or 1 Greek Symbols

ηemissions = emission efficiency ηHX = heat exchanger efficiency ηs = storage efficiency μ = emission factor Ω = dry algae production factor

Subscripts

s = storage system t = period Variables

AA = algae area, Ha Aproduction = algae production, kg ASC = solar collector area, Ha AlgaeCAP = algae capacity, kg/m2 CAPCost = capital cost, USD/y GHGEt = greenhouse gas emissions, kg/h Ealgae‑absorption = CO2 absorbed, kg/h t Eboiler‑totales = CO2 boiler total emissions, kg t Eemissions = CO2 emission, kg/h t Fbiodiesel = biodiesel production, kg/y OpCost = operating cost, USD/y Qs,t = energy stored in every storage systems system at any time, kW Qs,t−1 = energy stored in the previous time period, kW Qboiler = boiler energy flux, kW t Qboiler‑CAP = boiler capacity, kW H


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