Techno-economic optimization for the design of solar chimney power plants

Energy Conversion and Management 138 (2017) 461–473

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Techno-economic optimization for the design of solar chimney power plants Babkir Ali Donadeo Innovation Centre for Engineering, Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T6G 1H9, Canada

a r t i c l e

i n f o

Article history: Received 1 November 2016 Received in revised form 7 February 2017 Accepted 9 February 2017

Keywords: Solar thermal Solar chimney power plants Optimization Floating chimney Power generation

a b s t r a c t This paper aims to propose a methodology for optimization of solar chimney power plants taking into account the techno-economic parameters. The indicator used for optimization is the comparison between the actual achieved simple payback period for the design and the minimum possible (optimum) simple payback period as a reference. An optimization model was executed for different twelve designs in the range 5–200 MW to cover reinforced concrete chimney, sloped collector, and floating chimney. The height of the chimney was optimized and the associated collector area was calculated accordingly. Relationships between payback periods, electricity price, and the peak power capacity of each power plant were developed. The resulted payback periods for the floating chimney power plants were the shortest compared to the other studied designs. For a solar chimney power plant with 100 MW at electricity price 0.10 USD/kWh, the simple payback period for the reference case was 4.29 years for floating chimney design compared to 23.47 and 16.88 years for reinforced concrete chimney and sloped collector design, respectively. After design optimization for 100 MW power plant of each of reinforced concrete, sloped collector, and floating chimney, a save of 19.63, 2.22, and 2.24 million USD, respectively from the initial cost of the reference case is achieved. Sensitivity analysis was conducted in this study to evaluate the impacts of varied running cost, solar radiation, and electricity price on the payback periods of solar chimney power plant. Floating chimney design is still performing after applying the highest ratio of annual running cost to the annual revenue. The sensitivity analysis showed that at the same solar radiation and electricity price, the simple payback period for 200 MW with sloped collector design would almost have the double simple payback period for 5 MW with floating chimney design. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction The energy demand in the world is in continuous increase [1] due to the population growth and higher rate of consumption per capita to face the improvement of the living standards. Utilization of sustainable and non-depleted sources of energy can face part of this increased demand for energy. The solar energy as a clean and renewable source of energy can play a major role in addressing these challenges. Intensive research efforts to improve the reliability and feasibility of the renewable energy systems can support the dissemination of these technologies. To some extent, the fundamental, theoretical, and technical issues of solar energy were covered, but still, there are constraints in the practical application of the renewable energy systems. Pretorius and Kroger [2] evaluated technically the effect of design parameters and materials quality on the performance of solar chimney power plant (SCPP) and Tingzhen et al. [3] conducted heat E-mail address: [email protected] http://dx.doi.org/10.1016/j.enconman.2017.02.023 0196-8904/Ó 2017 Elsevier Ltd. All rights reserved.

transfer analysis of SCPP after divided the complete system into three regions of the collector, chimney, and turbine. Intermittency of solar and wind energy and high capital cost of renewable energy technologies are some of the challenges facing the dissemination of these clean technologies [4]. Solar photovoltaic (PV) technologies are obstacle by high cost, low financial ability, and limited application of the product [5]. Latent heat energy storage systems were proposed to face the intermittency in solar radiation. Aydin et al. [6] evaluated the impact of latent heat storage systems on the solar energy used for space heating in Istanbul, Turkey. Phase change materials used for latent heat storage systems are found suitable for domestic solar water heaters due to the high storage capacity and stable heat transfer temperature [7]. Heat generated by thermal conversion of solar energy is proposed to be injected into the ground to save energy [8]. Solar chimney used in natural ventilation of buildings by makes use of the difference in air density due to the temperatures difference, which is known as stack effect or buoyancy. Stackeffect increases the air flow rate to cool the building in warm humid

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B. Ali / Energy Conversion and Management 138 (2017) 461–473

Nomenclature AC CFD COCH CP CPUAR CR D design-C design-F design-S ELP G g GTC GYREV H HOPT INCH INCL INCST INTG PK PV

solar collector area computational fluid dynamics chimney unit price of (H ⁄ D) specific heat of air equal to 1005 J/kg K cost per unit area of the collector including the land cost the ratio of annual running cost to the annual revenue chimney diameter solar power plant with reinforced concrete chimney solar power plant with floating chimney solar power plant with sloped collector electricity price in USD/kWh global solar radiation gravitational acceleration equal to 9.81 m2/sec gas turbine cycle uniform annual revenue of the solar chimney power plant chimney height optimum chimney height chimney initial cost collector initial cost the initial cost of the solar chimney power plant turbine and generator initial cost maximum power plant capacity at solar radiation 1000 W/m2 solar photovoltaic

climates [9]. Experimental investigations showed that airflow across a small chimney increases with the increase in each of solar radiation and the gap between absorber and glass cover [10]. A chimney is used for lifting air through the solar dryer to dry agricultural products [11]. Maia et al. [12] conducted an experimental study for the airflow inside a solar chimney used for drying of agricultural products and recommended to include the amount of water evaporated from the product into the performance evaluation of the dryer. A similar design consists of black tubes as a collector surrounding the chimney is proposed for nine cities in China with a different application to generate freshwater from the air [13]. Solar chimney power plant (SCPP) is proposed to be used for electricity generation and consists mainly of the solar collector, chimney, and turbine. Zou and He [14] evaluated a hybrid system integrating a solar chimney with a dry cooling tower and found that the output power can be increased up to 20 times compared to the conventional SCPP. An SCPP model of 2.5 m chimney height and 2 m collector diameter was constructed and tested with the application of corona wind to improve the airflow speed to 72% and the output power to about 5 times [15]. An SCPP was designed theoretically based on Jordanian weather conditions with 210 m chimney height and 40 m collector diameter to result in a maximum output power of 85 kW [16]. Electricity generation based on solar chimney technology is being proposed for Australia to generate 200 MW from a power plant with 1000 m chimney height and 5000 m collector diameter [17]. Optimization of the design parameters and geometry of the SCPP would contribute significantly into the feasibility of electricity generation based on this clean technology. The rotational speed of the turbine corresponding to the maximum turbine efficiency has to be slightly increased in order to achieve the maximum output power from an SCPP [18]. The solar collector as well known in other solar thermal applications is made in flat surface from transparent material either of glass panels or plastic film to harness the solar radiation through

Q RCST RYCST SCPP SPback SPmin T Ta TCST USD

DP DT

a b

x gC gCH gG gT gTOT

air volume flow rate across the turbine running cost of the solar chimney power plant the uniform annual running cost of the solar chimney power plant solar chimney power plant simple payback period simple minimum (optimum) payback period the torque of the turbine shaft collector inlet temperature the total cost of the solar chimney power plant United States Dollar adjusted for the value of the year 2014 the total pressure drop across the turbine the temperature difference between air inflow and outflow from the collector effective absorption coefficient the factor of the convective energy loss (W/m2 K) the rotational speed of the turbine shaft collector efficiency chimney efficiency electric generator efficiency turbine efficiency the total efficiency of the solar chimney power plant

greenhouse effect and heat the air flowing through the chimney. The heated air flows through the solar chimney due to its density difference between inlet and outlet of the chimney. This heated air is forced the turbine to rotate and to generate electricity [19]. Compared to the electricity generation from conventional sources of energy, SCPPs are still constrained by huge initial cost and need long construction period [20], require large area of land for the collector, and the total system efficiency is very low [21]. The chimney associated with the SCPP is very tall compared to the conventional buildings which add a significant uncertainty with the construction and materials to be used. One of the challenges facing SCCP is the continuity of power generation during the night-time [22]. As SCPP is one of the renewable energy technologies, has the advantage of low environmental impact on air and water [23], unlike the conventional power plants based on fossil fuels. The solar energy source is freely available and storage systems can be added to the SCPPs to recover for the input energy when the solar radiation is unavailable. Black tubes filled with water located under the collector is one of the systems used for thermal energy storage and the amount of filled water depends mainly on the SCPP output power [24]. Al-Kayiem and Aja [25] concluded that SCPP performance can be improved considerably by adding another thermal energy source or by retrofitting a proper storage system. Flat mirrors to intensify the solar radiation on the solar chimney zone are also proposed to improve the SCPP performance [26]. The 50 kW SCPP prototype built and operated in Manzanares, Spain for seven years since 1982 [27] proved the reliability and assured the potential of the technology. The main objectives of Manzanares prototype were to verify the theoretical calculations of the design and to test the SCPP output power and the system efficiency under different weather conditions. The prototype was designed with 194.6 m chimney height, 10 m chimney diameter, and 122 m mean collector radius [28]. Manzanares prototype was operated for a total period of 8611 h at an average of 8.9 h

B. Ali / Energy Conversion and Management 138 (2017) 461–473

per day and required supervision from one person [29]. Manzanares power plant was uneconomical due to the small size of the operated prototype and the limited power capacity [30]. The turbine for Manzanares prototype was designed to rotate around a single vertical axis, with a single rotor, and without inlet guide vanes [31]. Estimation of SCPP output power based on the input solar radiation was developed by Fathi et al. [32] and the numerical results were compared to the Manzanares prototype as an actual reference case. Different designs for SCPP were proposed to improve the performance and feasibility of the system. Schlaich [33] recommended the reinforced concrete chimney from the viewpoint of lifespan and cost. Bilgen and Rheault [34] proposed a 5 MW SCPP with sloped collector design for high latitudes in Canada. The sloped collector is designed to be built in a suitable mountain hills to shorten the chimney height. Cao et al. [35] conducted a simulation for a design of sloped SCPP to be located in Lanzhou, Northwest China and found valuable although of the low total efficiency of the system. The sloped design was found more cost-effective compared to the reinforced concrete design [36]. Floating solar chimney is a structure with balloons inflated by a gas lighter than air and found to be 5–6 times lesser in cost than the corresponding reinforced concrete SCPP with a power capacity 40 MW [37]. Zhou et al. [31] reviewed SCPP technologies and expected that with further research in materials, this technology can play a major role in the field of power generation. The improvement in the design and the selected materials for SCPP would be more sustainable if accompanied with techno-economic analysis of the system. The earlier techno-economic studies for SCPP were carried out focusing on the cost and cash flow with uncertain assumptions for the future values such as interest rate, inflation rate, carbon credits, electricity price, depreciation period, and the lifespan [38]. Fluri et al. [39] developed a new model for SCPP cost and found some underestimations on the previous models regarding the initial cost and the calculated levelized electricity cost. Certain values of the expected interest rates (6% and 8%) were considered to analyze the SCPP feasibility and the calculated levelized electricity costs were found higher compared to the other electricity generation sources [40]. Akhtar and Rao [41] investigated the feasibility of 200 MW SCPP in Rajasthan, India and studied the effects of variation in the interest rate, inflation rate, and operation period on the levelized electricity cost. A cost-benefit analysis [42] showed that the most sensitive factors for the net present value of SCPP are the electricity price and inflation rate while carbon credits, income tax rate, and interest rate are the least sensitive. Some earlier studies targeted optimization of SCPP design from the technical point of views without integration with the economic analysis. Patel et al. [43] optimized the SCPP geometry through computational fluid dynamics (CFD) without consideration of the economic parameters. An optimization methodology for the design parameters of the SCPP was introduced by Gholamalizadeh and Kim [44] based on a triple objective function covering expenditure, total efficiency, and output power. The minimum dimensions of an SCPP sufficient to supply electricity to about fifty rural households were determined by Onyango and Ochieng [45] without taking into account components cost and the associated financial parameters. A comprehensive review of SCPP studies was conducted by Kasaeian et al. [46] and recommended to determine optimized dimensions for chimney and collector, constructing large scale SCPP, and establishing decision-making support procedures for new SCPP. A feasibility study for SCPP is introduced by Okoye et al. [47] to integrate the optimum power plant dimensions and economic aspects for a certain design of reinforced concrete, with a specific location in Nigeria (Potiskum), and with an annual rate of return to calculate the discounted net present value. Guo et al. [48] highlighted the importance of collector and chimney

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dimensions on the output power of SCPP and optimized specific design with a 100 MW power capacity for Hami region in China. The novelty of the current study is the integration of design and economical parameters to optimize the performance and feasibility of SCPP. Optimization is indicated through simple payback period to avoid uncertain future economic parameters and investigated different SCPP designs with a wide range of power capacity to represent a generic analysis not specific to a certain geographical location. The main objective of this paper is to propose a methodology to optimize the SCPP design from technical and economical viewpoints. The key objectives of this paper are:
To determine the optimum configuration of the SCPP including the chimney height and the collector area.
To develop the minimum (optimum) simple payback period for each SCPP as a reference for optimization.
To take the difference between actual and minimum payback period as the indicator for the optimization potential.
To conduct a comparative techno-economic assessment for different designs of SCPP.
To develop the relationship between payback periods (actual and minimum), electricity price, and SCPP power capacity for each of power plant with reinforced concrete chimney (design-C), sloped collector (design-S), and floating chimney (design-F).
To study the impact of the running cost on the payback period for SCPP.
To study the effect of solar radiation and electricity price on the payback period for SCPP. 2. Methods Three design configurations of SCPP were studied in this paper as shown in Fig. 1 to cover reinforced concrete chimney (design-C), sloped collector (design-S), and floating chimney (design-F). The working principle in the three studied systems is the same and air as the working fluid is heated in the collector after utilizing the incoming solar radiation. The kinetic energy of the working fluid is used to rotate an air turbine located at the bottom of the chimney. This kinetic energy is a result of the density difference between the hot air at the bottom and cold air at the top of the chimney. The rotating turbine is coupled to an electric generator to produce power. In design-C, the chimney is made of reinforced concrete, design-S with inclined solar collector following a mountain slope, and design-F has the same configuration of design-C, except the chimney is made of lighter material than reinforced concrete. To cover small and large scales of power capacity, a range of 5–200 MW was selected in this study. The simple payback period was estimated for each design after gathered, harmonized, and developed the associated initial and operation costs derived from real data in the literature. Initial costs and conversion efficiencies were assumed based on literature to include the main SCPP components of the collector, chimney, and turbine and generator set. The developed designs are assumed to be generic to represent reference case for this study and not specific to a location. Payback period and chimney height relationship for each reference case design was developed to identify the minimum payback period point (optimum) and the associated optimum chimney height. Optimized configurations were compared to the reference case and the resulted save in total initial cost and gain in the payback period were estimated. A generic correlation for any SCPP was developed to relate the optimized chimney height with the design and cost parameters. A general trend of payback periods (actual and minimum) based on the associated peak power and electricity price were developed for optimized and unoptimized (reference) cases.

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Fig. 1. Schematic of the studied solar chimney power plants.

To cover a wide range of geographical locations, the impact on payback periods due to the change in uncertain parameters of running cost, solar radiation, and electricity price were studied through conducting sensitivity analysis.

flow rate, specific heat, and the temperature difference between ambient and outlet from the collector. The collector efficiency of SCPP depends mainly on the absorptivity, convective energy losses, temperature difference between inflow and outflow from the collector, and the global solar radiation [40]:

3. Model description Payback period is the period of time to get back the investment and it has two forms of simple and very rarely used discounted [49]. The discounted payback period considers the time value of money and hence it is longer than simple payback period. In this paper, the minimum (optimum) simple payback period is considered as a reference to measure to what extent the actual design is far from the optimum conditions. Using simple or discounted payback period would not affect significantly the difference between actual and optimum payback period because the time value of money would have the same effect on both payback periods and consequent slight effect on the difference. The key factor for the SCPP performance is the total conversion efficiency of the system. The total efficiency is disaggregated into collector efficiency, chimney efficiency, turbine efficiency, and electric generator efficiency. Hence, the total efficiency of the SCPP can be given by [47,50]:

gTOT ¼ gC  gCH  gT  gG

ð1Þ

where gTOT is the total efficiency; gC is the collector efficiency; gCH is the chimney efficiency; gT is the turbine efficiency; gG is the electric generator efficiency. The solar collector is one of the essential parts in the solar thermal applications. The function of the collector is to transform the received solar radiation into thermal energy through greenhouse effect to heat the air. The collector efficiency depends mainly on physical properties of the materials used and the design arrangement such as double or single glazing. Since the efficiency is the ratio between output energy to the input. The input energy to the collector is the total solar radiation received within the defined area of the collector and the output energy is the heat transferred to the air. The heat transferred to the air is a function of the mass

gC ¼ a  b 


 DT G

ð2Þ

where a is the absorptivity; b is the convective energy losses; DT is the temperature difference throughout the collector; G is the global solar radiation. The chimney efficiency analyzed by Gannon and Backstrom [28] after considered the similarity between the solar chimney cycle and gas turbine cycle (GTC). The similarity is assumed due to the same working fluid (air) used in both cycles, the compressor in GTC is replaced by atmospheric lapse rate, the solar collector is used instead of the combustor in GTC, and the chimney is added to the turbine in SCPP. The chimney efficiency, in this case, is proportional directly to the chimney height and inversely to the collector inlet temperature. The constant of proportionality is the gravitational acceleration divided by the specific heat of air [25,28,50]:

gCH ¼

gH CP  T a

ð3Þ

where g is the gravitational acceleration; H is the chimney height; CP is the specific heat of air; Ta is the collector inlet temperature. The turbine efficiency can be calculated by dividing the output mechanical power over the input power. The output power from the turbine is the product of the shaft torque and the rotational speed and the input power is obtained by the product of air volume flow rate and total pressure drop across the turbine [18,51]:

gT ¼

POUT Tx ¼ PIN Q  DP

ð4Þ

where POUT is the output mechanical power; PIN is the input power; T is the shaft torque; x is the rotational speed; Q is the air volume flow rate; DP is, the total pressure drop across the turbine.

B. Ali / Energy Conversion and Management 138 (2017) 461–473

The output power from the turbine represents the input power to the electrical generator. The output from the generator is the net electrical power for the solar chimney power plant. Due to the construction constraints, the collector area in SCPP is more flexible to be changed than the chimney height and diameter. The change in collector area affects both the performance and the economic aspects of the SCPP. The performance is affected by the quantity of power to be collected from solar radiation, which is directly proportional to the collector area. The power collected increases the revenue of the SCPP while increasing the collector area would have a negative effect on the total initial cost. The total cost of the SCPP is the sum of total initial cost and running cost [49]:

TCST ¼ INCST þ RSCT

ð5Þ

where TCST is the total cost; INCST is the total initial cost; RCST is the running cost. The simple payback period is selected in this paper to judge about the feasibility of the project and as a key factor in identifying the power plant that returning the original investment in shorter time. As per the definition of the payback period, the accumulation of the uniform annual revenue of the power plant should cover the total cost during the payback period. After rearranging Eq. (5) and introducing the uniform annual running cost, the initial cost can be rewritten as [49]:

INCST ¼ SPback  ðGYREV  RYCST Þ

ð6Þ

where SPback is the simple payback period; GYREV is the accumulation of the uniform annual revenue; RYCST is the uniform annual running cost. Assume that constant ratio of the annual revenue is assigned to the annual running cost. The annual revenue is the product of the net electrical power generated per year and the market value (price) of the electricity. The net electrical power generated per year depends mainly on the total efficiency, collector area, and the global solar radiation [38]:

PG ¼ gTOT  AC  G

ð7Þ

where PG is, the annual net electricity generated; AC is the collector area; G is the annual global solar radiation. The total initial cost includes the initial cost for the collector, chimney, and turbine and generator. The collector initial cost can be given by [37]:

INCL ¼ AC  CPUAR

ð8Þ

where INCL is the collector initial cost; CPUAR is the cost per unit area of the collector including the land cost. The total initial cost for the chimney is expressed in terms of its height, diameter, and per unit price as [37]:

INCH ¼ COCH  H  D

ð9Þ

where INCH is the chimney initial cost; COCH is the chimney cost per unit height times diameter; D is the chimney diameter. Rearranging Eq. (6), the simple payback period is given by:

SPback ¼

AC  CPUAR þ COCH  H  D þ INTG ð1  CRÞ  ðgTOT  AC  G  ELP Þ

ð10Þ

where INTG is the turbine and generator set initial cost; CR is a constant ratio of the annual revenue assigned for the annual running cost; ELP is the electricity price. The collector area appears in the numerator and denominator at the right-hand side of Eq. (10) as a key factor for both the cost and the output power of the SCPP. The collector area can be given from Eq. (10) as:

AC ¼

COCH  H  D þ INTG ð1  CRÞ  ðSPback  gTOT  G  ELP Þ  CPUAR

465

ð11Þ

From Eq. (11), the minimum simple payback period (SPmin) is obtained with the infinite collector area. The infinite collector area occurs when the denominator of Eq. (11) tends to zero and hence:

SPmin ¼

CPUAR ð1  CRÞ  ðgTOT  G  ELP Þ

ð12Þ

4. Input data and assumptions for the reference case An excel based model is prepared to evaluate the actual (SPback) and minimum (SPmin) payback periods with a range of electricity price (ELp) 0.01–2.0 USD/kWh and a representative value of 0.10 USD/kWh was selected based on literature [52–54] for comparative assessment. The global solar radiation (G) is taken constantly for all designs at 2300 kWh/m2/year [22–24]. The collector inlet temperature is taken constantly at 302 K (29 °C) throughout the execution of the model as a design value [23,30,47,55]. Collector area (AC) is adjusted according to the total efficiency (gTOT) and maximum power capacity (PK) at solar radiation 1000 W/m2. The collector efficiency (gC), turbine efficiency (gT), and electric generator efficiency (gG) are assumed constant at 42%, 85%, and 80%, respectively [23,30,39,40]. The chimney efficiency (gCH) is calculated from Eq. (3). Chimney dimensions (H and D), running cost ratio (CR), and all the associated systems cost were based on literature [24,36,37]. All the associated costs are updated and brought to 2014 United States Dollar (USD) [56,57]. Table 1 shows the input data for the reference case of twelve SCPPs with different power capacity range 5–200 MW. CR, G, and ELP are variated later in the sensitivity analysis to study their effect on the simple payback periods. 5. Reference case results Figs. 2–5 show the simple payback periods (SPmin and SPback) based on the electricity price (ELp) for the reference case with power capacity 5, 30, 100, and 200 MW, respectively. Design-F is always at the bottom of the graph (see Figs. 2–5) showing shorter payback periods compared to design-S and design-C. These shorter payback periods are mainly due to the lower initial costs for all power capacities of design-F compared to the other designs (see Table 1). For example, the initial costs of 100C and 100S are respectively more than 5 times and 3 times the initial cost of 100F. Taller chimneys of design-F were set with the encourage from the lowcost materials. These taller chimneys provided higher conversion efficiencies associated with reduced collector area. The average total efficiency of 100F is more than double the average efficiency of 100C and more than one and half the average efficiency of 100S (see Table 1). Reduced collector area and low material cost for the chimneys led to the lower total initial cost of design-F. Total initial cost profiles for the reference case are interpolated by regression analysis from Table 1 data based on the peak power (PK) of the SCPP as shown in Fig. 6. Compared to design-C with the same power capacity, the design-S chimney is shorter with lesser cost but its sloped collector has a higher cost. The resultant total initial cost for design-C is higher than the corresponding initial cost for design-S based on the same power capacity (see Fig. 6). The corresponding SPback for 100F at 0.10 USD/kWh is 4.29 years compared to 23.47 and 16.88 years for 100C and 100S, respectively. The difference between the simple actual payback period and the minimum payback period (SPback  SPmin) for all studied reference case models is drawn at the electricity price (ELp) 0.10 USD/

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Table 1 Input data for the reference case. Design-Ca

Design-Sb

Design-Fc

5C

30C

100C

200C

5S

30S

100S

200S

5F

30F

100F

200F

PK in MW at solar radiation = 1000 W/m2 Ta (K) H (m) AC (km2) D (m) G (kWh/m2/year) Average gTOT (%) CR INCLd (million USD) INCHe (million USD) INTGf (million USD) Miscellaneous initial costf (million USD)

5 302 550 0.98 45 2300 0.510 0.005 12.26 29.15 12.27 7.67

30 302 750 4.31 70 2300 0.696 0.004 48.08 75.17 49.09 24.54

100 302 1000 10.78 110 2300 0.927 0.004 121.87 239.30 115.05 61.36

200 302 1000 21.56 120 2300 0.927 0.005 224.34 260.78 204.02 64.43

5 302 633 0.85 28 2300 0.587 0.31 22.22 10.93 3.48 0.00

30 302 1155 2.80 52 2300 1.071 0.205 72.52 33.89 23.96 0.00

100 302 1614 6.68 78 2300 1.496 0.175 172.20 76.72 71.44 0.00

200 302 1614 13.36 110 2300 1.496 0.175 344.38 108.20 142.89 0.00

5 302 1000 0.54 18 2300 0.927 0.023 5.51 2.38 1.29 0.00

30 302 1700 1.90 45 2300 1.577 0.023 19.44 10.12 7.75 0.00

100 302 2500 4.31 80 2300 2.319 0.023 44.07 26.44 25.84 0.00

200 302 3000 7.19 112 2300 2.782 0.023 73.44 44.42 51.69 0.00

INCST (million USD)

61.35

196.88

537.58

753.57

36.63

130.37

320.36

595.47

9.18

37.31

96.35

169.55

a

Based on the design framework from Schlaich et al. [24]. Based on the design framework from Cao et al. [36]. c Based on the design framework from Papageorgiou [37]. d CPUAR of 12.50, 11.15, 11.30, and 10.40 USD/m2 were used for 5C, 30C, 100C, and 200C, respectively [24]. CPUAR of 26.09, 25.88, 25.78, and 25.78 USD/m2 were used for 5S, 30S, 100S, and 200S, respectively [36], and CPUAR of 10.22 USD/m2 was used for all models of design-F [37]. e COCH of 1178, 1432, 2175, and 2173 USD/m2 were used for 5C, 30C, 100C, and 200C, respectively [24]. COCH of 1546, 1502, 1696, and 1696 USD/m2 were used for 5S, 30S, 100S, and 200S, respectively [36], and COCH of 132.22 USD/m2 was used for all models of design-F [37]. f Taken from Schlaich et al. [24] for design-C, from Cao et al. [36] for design-S, and at a rate 258430 USD/MW for design-F [37]. b

Fig. 2. Simple payback periods for the reference case of 5 MW power plants.

kWh as shown in Fig. 7. This difference is an indicator for the potential optimization of the techno-economic parameters of the SCPP. The more potential to optimize these parameters is indicated by the higher the difference and the lower difference indicates that the design is closer to the optimum payback period. All SCPP with design-C are located at the top of the graph with a higher difference, followed by design-S, and SCPPs with design-F are at the bottom with a lesser difference. Design-F presents the lowest difference because it is the best among the reference case models and therefore there would be less space for improvement. Reference case results showed that total initial cost, collector area, and chimney dimensions (height and diameter) are the essential parameters for the design optimization of the SCPP. 6. Design optimization The relationship between simple payback period (SPback) and the chimney height (H) was developed for each model in the reference case of this study. The minimum payback period (SPmin) for

each relationship was specified and the corresponding chimney height was identified to represent the optimum (HOPT). The corresponding optimum collector area is estimated after using the obtained HOPT and maintaining the power capacity fixed at the same value of the reference case. Design optimization of each SCPP is mainly indicated by the decrease in two economical parameters of initial cost and simple payback period compared to the reference case. The peak power capacity of SCPP is the maximum input solar radiation fallen on collector area and converted to electric power as follows [30]:

PK ¼ 103  gTOT  AC

ð13Þ

where PK is the peak power capacity of the SCPP in MW at the total solar radiation 1000 W/m2. From Eqs. (1), (3), (13), and (10):

SPback ¼

ð103 PK CP Ta CPUAR Þ H

þ COCH  H  D þ INTG

g  gC  gT  gG  ð1  CRÞ  ð103  PK  G  ELP Þ

ð14Þ

B. Ali / Energy Conversion and Management 138 (2017) 461–473

467

Fig. 3. Simple payback periods for the reference case of 30 MW power plants.

Fig. 4. Simple payback periods for the reference case of 100 MW power plants.

The relationship in Eq. (14) between SPback and H is shown for brevity in Fig. 8 for design-C at electricity price 0.10 USD/kWh. From Fig. 8, the optimum chimney height (HOPT) occurs at [58]:

dSPback ¼ 0; dH from which

HOPT

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 103  PK  CP  Ta  CPUAR ¼ COCH  D  g  gC  gT  gG

ð15Þ

The key point to reconfigure the reference case design of SCPP is the adjustment of chimney height and collector area in such a way that the output power is kept the same in the new optimized design. After optimization, the conversion efficiency of SCPP would be increased in the case of increasing chimney height (see Eq. (3)) and this performance improvement would lead to reducing the sufficient collector area. The other case is the optimization by decreasing the chimney height of the reference case to affect negatively the conversion efficiency which would be compensated by increasing the collector area. In this two optimization cases, either

conversion efficiency of SCPP is increased to compensate for the smaller collector area or the decrease in the conversion efficiency would be compensated by increasing the solar input energy through larger collector area. The controlling factors in both optimization cases are the shortest payback period, lowest initial cost, and constant output power. The profiles of the optimum height with the peak power (PK) of the SCPP are given in Fig. 9 as well as the profile for the chimney height of the reference case. The chimney heights at the reference case of design-F are increased in the optimum zone. The low material cost for design-F allowed for taller chimney heights to improve the conversion efficiency and reduce the collector area. Optimized height for design-S kept slightly below the height at the reference case and then increased after 160 MW. Decreasing the chimney height and increasing the collector area of design-S is limited by the higher cost per unit area of the sloped collector (CPUAR). The optimum chimney height for design-C is decreased from the reference case heights. Reinforced concrete chimneys (design-C) have high cost and decreasing the height would contribute significantly to reduce the total initial cost even after adding sufficient collector area to balance the required output power.

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Fig. 5. Simple payback periods for the reference case of 200 MW power plants.

Fig. 6. Initial cost profile for the reference case as a function of the peak power.

Fig. 7. The difference between actual and minimum payback periods for the reference case at the electricity price (ELP) = 0.10 USD/kWh.

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B. Ali / Energy Conversion and Management 138 (2017) 461–473

Fig. 8. Relationship between simple payback period and chimney height for design-C at the electricity price (ELP) = 0.10 USD/kWh.

Fig. 9. Optimum and reference case chimney heights as a function of the peak power.

Table 2 shows the adjustments occurred in the values of the reference case parameters in order to optimize each model. The largest save in initial cost (INCST) results from the optimization of 100C. The reference case chimney height of 100C is reduced by 286 m after optimization (from 1000 m to 714 m) to decrease the average total efficiency (gTOT) by 28.6% (from 0.927% to 0.662%). The total amount saved which resulted from chimney height reduction of model 100C is 68.44 million USD. Out of this total saved amount, 48.81 million USD is converted to the collector to increase its reference case area by 28.6%. The net amount saved

due to optimization, in this case, would be 19.63 million USD (from 68.44 to 48.81). Each model with its known peak power capacity (PK) from the reference case and from the optimized case is run at different values of SPback, SPmin, and ELP. The correlations between these parameters were developed through regression analysis and the trend found with the following equations:

SPback ¼

J

ð16Þ

ELP  ðPK ÞL

Table 2 Adjustments to the techno-economic parameters for optimization of the SCPP design.a Design-C

Design-S

Design-F

5C

30C

100C

200C

5S

3S

100S

200S

5F

30F

100F

200F

DH (m) DAc (km2) DgTOT (%) DINCL (million USD) DINCH (million USD)

193 0.53 0.18 6.62 10.23

150 1.08 0.14 12.02 15.04

286 4.32 0.265 48.81 68.44

72 1.68 0.066 17.41 18.78

63 0.1 0.058 2.46 2.73

120 0.33 0.111 8.37 9.33

165 0.72 0.152 19.54 21.76

112 0.87 0.105 22.44 20.98

521 0.19 0.484 1.89 1.24

657 0.53 0.609 5.42 3.90

727 0.97 0.674 9.93 7.69

857 1.60 0.795 16.32 12.70

DINcst (million USD)

3.61

3.02

19.63

1.37

0.27

0.96

2.22

1.46

0.65

1.52

2.24

3.62

Adjustments (D) are differences between the optimized case and the reference case. The highlighted minus sign () indicates that the value is decreased compared to the reference case value mentioned in Table 1. a

470

SPmin ¼

B. Ali / Energy Conversion and Management 138 (2017) 461–473

M

7. Sensitivity analysis

ð17Þ

ELP  ðPK ÞN

The portion of annual revenue assigned to the annual running cost (CR), global solar radiation (G), and electricity price (ELP) are three of the most sensitive factors for SCPP payback periods (see Eq. (10)). CR would determine the level of running cost which is an essential portion in the total SCPP cost. G would determine the level of input energy to SCPP and represents the maximum limit for the output power which affects directly the revenue. ELP is the essential factor for the SCPP revenue. CR, G, and ELP are uncertain factors due to their change according to the geographical location.

where SPback and SPmin are in years, ELP is in USD/kWh, and PK is in MW. J, L, M, and N are constants resulted from the regression analysis. Table 3 shows the values of J and L used in Eq. (16) for SPback and Table 4 shows the values of M and N used in Eq. (17) for SPmin with the correlation coefficient R2 related to each design type. To assess the gain in the simple payback period (SPback) as an indicator for optimization, the difference is calculated through the model between the reference case and the optimized case. Fig. 10 shows the number of years gained from optimization at electricity price (ELp) 0.10 USD/kWh. The gain in payback period is indicated by the potential shown in Fig. 7 and limited by the target to decrease the total initial cost for the reference case.

7.1. Running cost CR taken for the reference case was specific to each design in a range 0.004–0.310 with a lower end for design-C and an upper end

Table 3 Coefficients for the relationship of simple payback period (SPback), electricity price (ELP), and peak power capacity (PK). Reference case designs

Design-C Design-S Design-F

Optimized designs

J

L

R2

J

L

R2

8.5797 7.1377 1.1195

0.303 0.301 0.203

0.9775 0.9758 0.9949

7.9647 7.0672 1.0390

0.290 0.300 0.196

0.9846 0.9746 0.9998

Table 4 Coefficients for the relationship of minimum payback period (SPmin), electricity price (ELP), and peak power capacity (PK). Reference case designs

Design-C Design-S Design-F

Optimized designs

M

N

R2

M

N

R2

1.4940 4.3690 0.7807

0.217 0.321 0.293

0.9918 0.9512 0.9973

2.5665 5.2932 0.4861

0.291 0.355 0.252

0.9701 0.9905 0.9997

Fig. 10. Payback period gained due to the optimization.

B. Ali / Energy Conversion and Management 138 (2017) 461–473

471

Fig. 11. Simple payback periods as a function of the running cost for 5 MW and 30 MW power plants at the electricity price (ELP) = 0.10 USD/kWh.

for design-S (see Table 1). The value of CR fluctuates with the geographical location of the SCPP due to the different labour cost incurred. CR is changed for all SCPP optimized designs in the same range (0.004–0.310) to study its effect on the payback periods. The resulted payback periods with variable CR are shown in Fig. 11 for 5 MW and 30 MW and in Fig. 12 for 100 MW and 200 MW power plants. Design-F is still outperforming in the payback periods even after applying the highest CR of 0.310. This outperforming is due to the low total cost derived from efficient design with taller chimney

and reduced collector area compared to the other two designs (design-S and design-C). 7.2. Solar radiation and electricity price Global solar radiation (G) was taken constantly at 2300 kWh/ m2/year for the reference case and electricity price (ELP) was considered with a representative value 0.10 USD/kWh. Since these values are different according to the geographical location, they were

Fig. 12. Simple payback periods as a function of the running cost for 100 MW and 200 MW power plants at the electricity price (ELP) = 0.10 USD/kWh.

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B. Ali / Energy Conversion and Management 138 (2017) 461–473

Table 5 Coefficients for the relationship of payback periods (SPback and SPmin), solar radiation (G), and electricity price (ELP). Pk (MW)

Design-C

5 30 100 200

Design-S

K

Z

K

Z

K

Z

11605.38 6488.03 5200.36 3779.93

3794.25 2011.30 1713.69 1214.83

10539.81 5425.91 3856.33 3600.06

7153.83 3391.80 2324.14 1951.15

1780.76 1221.37 963.30 849.16

741.32 478.38 349.41 292.34

assumed variables in Eqs. (10) and (11) to study their relationship with SPback and SPmin of SCPP, respectively, as follows:

SPback ¼

K G  ELP

SPmin ¼

Design-F

Z G  ELP

ð18Þ ð19Þ

where K and Z are constants (in USD/m2) for each SCPP as follows:

K¼

AC  CPUAR þ COCH  H  D þ INTG ð1  CRÞ  ðgTOT  AC Þ

ð20Þ

Z¼

CPUAR ð1  CRÞ  gTOT

ð21Þ

The values of K and Z for each optimized design are shown in Table 5. The lower value of K indicates the lower the simple payback period (SPback) at fixed value of G and ELp. K values help in comparison of simple payback periods for any different models at the same values of G and ELP. For example, the K value of model 200S is about the double K value of model 5F, which indicates that SPback of model 200S is double SPback of model 5F at the same solar radiation (G) and electricity price (ELP). The same proportionality can be applied for Z values with the minimum payback period (SPmin) as indicated by Eq. (19). 5C and 5S have the highest coefficients of K and Z and consequently the longest payback periods among other studied models. 5C is affected by the lower chimney height which reduced the average total efficiency and compensated by a larger area of the collector to increase the initial cost. 5S has the longest SPmin (highest Z value) and this is mainly due to the highest values of CR (0.310) and CPUAR (26.09 USD/m2) taken for this model compared to the values taken for the other models. 8. Conclusions SCPP design parameters were optimized in this study after related to the economic factors. Chimney height was firstly optimized and the associated collector area was estimated to generate the same output power of the reference case. Simple payback periods and initial cost were used as indicators for SCPP feasibility. SCPP with floating chimney (design-F) has shown shorter payback periods and lower initial costs compared to the other two studied designs (design-C and design-S). The low material cost of design-F allowed for the taller chimney to improve the conversion efficiency and to reduce the required collector area. After optimization of design-F in the reference case, the chimney height is increased to improve the conversion efficiency, have lesser collector area, and decrease the resulted economical factors including payback periods and initial cost. The chimney height in the reference case of model 100C is reduced by 28.6% after design optimization to decrease the conversion efficiency by the same percentage (28.6%) and increase the collector area by the same percentage (28.6%). The output power is kept the same for 100C and the resulted save in total initial cost due to this reconfiguration is found to be 19.63 million USD.

Sensitivity analysis in this study showed that design-F outperforms in payback periods compared to design-C and design-S even at higher running cost. Impacts of solar radiation and electricity price variations on payback periods were studied and small scale SCPP with design-C (5C) and design-S (5S) have the longest payback periods compared to the other studied models. Hybrid and storage systems are recommended to be integrated with the SCPP in order to increase the power input and to recover the fluctuation in solar radiation. The work presented in this study is recommended as a base to evaluate the effect of dividing the SCPP project into phases, to avoid high risk. To start operation of SCPP with optimum chimney height and a preliminarily reduced collector area and then adding further collector segments while acquiring more revenue. This would result in shorter payback periods, but there would be a certain limit for the maximum collector area, after which the process could be infeasible and less efficient due to the very high heat losses. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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