A new economic feasibility approach for solar chimney power plant design

Energy Conversion and Management 126 (2016) 1013–1027

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

A new economic feasibility approach for solar chimney power plant design Chiemeka Onyeka Okoye a, Og˘uz Solyalı b,⇑, Onur Taylan c,d a

Sustainable Environment and Energy Systems, Middle East Technical University Northern Cyprus Campus, Kalkanli, Guzelyurt, Mersin 10, Turkey Business Administration Program, Middle East Technical University Northern Cyprus Campus, Kalkanli, Guzelyurt, Mersin 10, Turkey c Mechanical Engineering Program, Middle East Technical University Northern Cyprus Campus, Kalkanli, Guzelyurt, Mersin 10, Turkey d Center for Solar Energy Research and Applications (GÜNAM), Middle East Technical University, Ankara 06800, Turkey b

a r t i c l e

i n f o

Article history: Received 19 June 2016 Received in revised form 23 August 2016 Accepted 26 August 2016

Keywords: Solar chimney power plant Electricity generation Optimal dimensions Nonlinear optimization Economic feasibility

a b s t r a c t Solar chimney power plants have been accepted as one of the promising technologies for solar energy utilization. The objective of this study is to propose an effective approach to simultaneously determine the optimal dimensions of the solar chimney power plant and the economic feasibility of the proposed plant. For this purpose, a two-stage economic feasibility approach is proposed based on a new nonlinear programming model. In the first stage, the proposed optimization model which determines the optimal plant dimensions that not only minimize the discounted total cost of the system, but also satisfy the energy demand within a specified reliability taking into account the stochasticity of solar radiation and ambient temperature is solved using a commercial optimization solver that guarantees finding the global optimum. In the second stage, the net present value of building the plant is computed by deducting the discounted total cost found in the first stage from the present value of revenues obtained due to selling the electricity generated by the plant. The proposed approach is novel because it determines the optimal dimensions of the plant together with its economic feasibility by taking into account the energy demand and uncertainty in solar radiation and ambient temperature. The proposed approach is applied on a study in Potiskum, Nigeria, which reveals that building a plant with a collector diameter of 1128 m and chimney height of 715 m to Potiskum would be profitable for investors at an annual rate of return of 3% and would provide electrification to about 7500 people with a high level of reliability. The proposed approach is benchmarked with an intuitive approach and an approach that does not consider uncertainty in solar radiation and ambient temperature. The results clearly revealed the value of the proposed approach. Managerial insights on the impact of the efficiency of the collector, the efficiency of the turbine, electricity price, electricity demand, meteorological conditions, and discount rate on the size of the plant and the net present value are obtained through detailed sensitivity analyses. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction The increasing demand for electricity has motivated considerable research interest in a wide range of engineering applications aimed at providing a sustainable solution for the energy security problem. The wider utilization of renewable energy sources of solar, wind, biomass and geothermal is currently being propelled not only by the environmental concern of conventional thermal fossil fuels which contribute approximately 80% of the global energy [1], but also by the continuous upsurge in their price trend resulting from the increasing population induced demand. The ⇑ Corresponding author. E-mail addresses: [email protected] (C.O. Okoye), [email protected] (O. Solyalı), [email protected] (O. Taylan). http://dx.doi.org/10.1016/j.enconman.2016.08.080 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

solar energy among other choices seems to be promising and ultimately has been accepted as one of the future alternatives for electricity generation [2]. An increase in the use of solar energy and other renewable technologies could decrease the environmental pollution and the dependence on the finite fossil fuel resources. The problems of huge capital cost, enormous land area requirement, and reliability associated with solar energy systems have widely been addressed through robust design, optimization and formulation of new concepts using cheap and hybrid materials [1,3]. Moreover, there have been these kinds of studies assessing the techno-economic feasibility and lifecycle of renewable energy technologies [4–6]. Solar chimney power plant (SCPP) offers a unique opportunity to generate electricity by combining relatively simple and reliable old technologies of the solar thermal collector, chimney and turbine as shown in Fig. 1.

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Nomenclature

gch gcoll g coll gtur

Acronyms NPV net present value (€) SCPP solar chimney power plant TC discounted total cost (€) TMY typical meteorological year Indices j m

nhour  hour n h1r

days of the year months of the service life of plant

q

Parameters area of the solar collector (m2) Acoll C black;tube unit cost of black tube for water storage (€/m3) C ch capital cost of chimney (€) C coll capital cost of collector (€) C electricity unit price of electricity (€/kWh) C tur capital cost of turbine (€) C water unit cost of water (€/m3) unit capital cost of chimney due to material and conCC sc struction costs (€/m3) Cp specific heat capacity (J/kg
K) C O&M cost of system operation and maintenance (€) diameter of the chimney (m) Dch  E average daily energy demand (kWh) Ej energy demand in day j (kWh) EPj amount of energy produced in day j (kWh) g gravitational constant, 9.81 (m/s2) Gh solar radiation (W/m2) h1; h2 heat transfer coefficients (W/m2
K) height of the collector (m) Hcoll Hsl height of the water storage layer (m) i monthly discount rate Jm set containing all days of month m lower bound for chimney height (m) Lch Lcoll lower bound for collector diameter (m)

r r real Ta Tc Tf Tp U ch U coll Pele Ptcoll CC sc PtHcoll PtO&M Pttg Rev m S X

efficiency of chimney efficiency of the solar collector average daily efficiency of the solar collector efficiency of the turbine number of sunshine hours average daily sunshine hours value at which the probability of X being less than or   coll gtur n  hour Þ is equal to 1  r equal to ðC p EÞ=ðA coll g H ch g air density (kg/m3) desired system reliability realized system reliability ambient temperature of the location (K) temperature of the glass collector (K) air flow temperature (K) temperature of the absorber (K) upper bound for chimney height (m) upper bound for collector diameter (m) power output from the SCPP (kW) product of capital cost of the collector per square meter and the specific capital cost of chimney percent age capital cost for every one meter height of the collector inlet percentage capital cost of the system percentage capital cost of collector and chimney revenue obtained from the energy produced in month m (€) number of months in the service life of SCPP continuous random variable denoting the ratio of solar radiation to ambient temperature (W/m2
K)

Variables diameter of the solar collector (m) Dcoll Hch height of chimney (m) Z objective function value (€)

Chimney diameter Chimney height

Collector diameter Fig. 1. Schematic of a solar chimney power plant, adapted from [7].

SCPP has numerous advantages over other solar energy utilization alternatives, such as; (i) the ability to utilize global solar radiation, (ii) the high reliability due to low rotating part, (iii) not using scarce water resources for heat rejection during operation, (iv) the ability to work during nights by using the natural ground as a stor-

age medium, (v) the use of the greenhouse effect for drying of agricultural produce, (vi) the low operation and maintenance cost of the system, and (vii) high durability and long lifecycle time [8– 10]. Therefore, SCPP has attracted much attention for electricity generation. As a result, experimental studies involving SCPP are

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now well-established for different locations, as various research sought to assess the performance of SCPP under given environmental conditions. Examples of these studies include Pasumarthi and Sherif [11] and Raney et al. [12] for the USA; Zhou et al. [13] and Guo et al. [14] for China; Kasaeian et al. [15] and Ghalamchi et al. [16] for Iran; Kalash et al. [17] for Syria; Mehla et al. [18] for India; and Bug˘utekin [19] for Turkey. Moreover, the first pilot SCPP in Manzanares, Spain, which was connected to the grid, produced power continuously throughout the seven years of operation [20]. The constructional features, operational principles, technical feasibility, and energy production of the pilot SCPP were presented by Haaf et al. [21] and Haaf [22], where brief discussions of the energy balance and cost analysis were presented. The authors mentioned that SCPP systems would be economically feasible for large-scale power plants. For this reason, extrapolation of the pilot plant experimental results to the large scale power plant was presented by Schlaich et al. [8]. The reported plant capacity and levelized electricity cost ranged from 5–200 MW and 0.21–0.74 €/kWh, respectively. In another study, Nizetic et al. [23] assessed the feasibility of SCPP under Mediterranean climate conditions and concluded that the unit cost of the energy generated from the system was higher than the cost of other energy generation technologies. Feasibility studies on SCPP are categorized into technical [9,24– 29] and economic [7,8,23,30–32] using location-specific meteorological data. The technical feasibility studies assess the energetic performance of SCPP for a given location and are often a function of the meteorological variables (i.e., solar radiation and ambient temperature). These studies merely discuss the amount of energy that would be produced using either a new energy generation model or an already existing model. On the other hand, the economic feasibility studies assess whether the proposed system is economically viable in addition to evaluating the energetic performance. In other words, for a particular plant size with known meteorological conditions, economic feasibility studies determine the amount of energy that could be produced with the resulting cost of energy per kWh or other economic viability metric indicators (i.e., net present value (NPV), internal rate of return (IRR), simple payback period (SPP) and save to investment ratio (SIR)). Okoye and Atikol [7] adopted NPV, IRR, SIR and SPP as economic viability metric indicators to assess the feasibility of replacing 28.8 MW fossil fuel power plant with an equivalently sized SCPP in North Cyprus. Schlaich et al. [8] assessed the economic feasibility of different SCPP capacities located in Spain and found that the resulting levelized cost of electricity decreases as the plant capacity increases. Nizetic et al. [23] reported that the 0.24–0.70 €/kWh levelized cost of electricity obtained from SCPP in Croatia is higher than the cost of energy from other power sources in the region. Similarly, Li et al. [30] utilized capital asset pricing model and risk-adjusted discount rate to study the economic feasibility of SCPP by calculating the total NPV in phases. Based on the analysis results, the authors concluded the advantages of SCPP over a coalfired power plant in China. Okoye and Taylan [31] assessed the performance of SCPP for rural applications in Nigeria. They found from the calculated cost of energy that the proposed plants can sustainably substitute the widely adopted diesel power generating set in the region. Shariatzadeh et al. [32] determined the design parameters of a solar chimney cogeneration power plant combined with solid oxide electrolysis/fuel cell by considering the annual equivalent cost minimization of the total capital cost of the system. They concluded that the proposed system could be economically affordable in the long term. Note that it is possible for a system to be technically feasible but economically infeasible due to the influence of notable location specific variables (e.g., price of materials for construction, interest rate, the price of electricity, and demand). A summary of these feasibility studies is given in a table by Cao

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et al. [29] and Okoye and Taylan [31]. The recent comprehensive review of Zhou et al. [20] not only lists these studies but also calculates the resulting unit cost of energy when they are not provided. The performances of solar collector, chimney and turbine are very important in estimating the resulting power output from a SCPP system. For this reason, the available literature on SCPP extensively employs both analytical and numerical models for better understanding and improvement. A comprehensive heat transfer model, temperature distribution along the collector, and various operational strategies of SCPP were addressed by Bernardes et al. [33–35]. Guo et al. [36] presented a numerical model for the SCPP collector and compared the collector performances with and without radiation model. They claimed that studies which did not incorporate radiation models tend to overestimate the temperature rise in the collector; thus, the efficiency of the collector. Ming et al. [37] studied the power output smoothing methods for solar chimney power generation system. They found that hybrid energy storage of water and sandstone could effectively decrease the fluctuations in solar chimney power output for smooth operation during the period when there is no solar radiation. For the operation of SCPP during nights, Ming et al. [38] presented conjugate simulations of energy storage layer, the collector and the chimney in the power output estimation of the system. Pretorius and Kröger [39] compared the performance of different ground storage layers such as sandstone, granite, and limestone on the power output. The study showed an insignificant annual power output decrease of about 0.3% for granite relative to sandstone and limestone. Furthermore, Bernardes [40] investigated the effects of thermal diffusivity and some ground materials on fluctuations of power production. He found that ground materials with lower thermal diffusivity and effusivity substantially reduced power output peaks for periods with greater heat gain. Guo et al. [41] carried out thermodynamic analysis of SCPP with soil heat storage using unsteady state theoretical model. They found that soil heat storage with high specific heat capacity and thermal conductivity leads to less fluctuation in the daily power output. Furthermore, Cao et al. [2] compared conventional and sloped SCPP using detailed heat transfer model for Lanzhou, China. They found that larger solar collector angle results in improved performance during the winter relative to the summer, and subsequently concluded that the sloped SCPP is more suitable for areas of high latitude. Ming et al. [42] presented a modified SCPP that has the capability of extracting freshwater from air in addition to producing electrical energy. Hu et al. [43] analyzed the effect of guide wall on the performance of SCPP. In the small-scale experimental prototype, they found that there is a reduction in mass flow rate with the introduction of guide wall. Amirkhani et al. [44] utilized artificial neural network and adaptive neuro fuzzy inference system models to predict the performance of SCPP. They concluded that these models can reduce computational cost relative to the numerical methods widely utilized for the SCPP assessment. Koonsrisuk and Chitsomboon [45] compared some of the available simple theoretical models for the SCPP power output performance using computational fluid dynamics. They rated the performance of the analytical models in terms of their ability to reproduce the experimental results and found that the best analytical model was the one proposed by Schlaich et al. [8]. Gannon and von Backström [46] presented an experimental investigation involving the performance of solar chimney turbine. They reported that the efficiency of turbine was between 77% and 90%. Guo et al. [47] investigated the power regulating strategy option for solar chimney turbine by varying the turbine performance with rotational speed. They found through comparison that the fan model is a convenient approach in the understanding of the turbine pressure drop and updraft velocity. Recently, Al-Kayiem and Chikere [48] presented

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historic and recent progress in SCPP enhancing technologies. They concluded that the SCPP performance could be significantly enhanced with the integration of other sources of thermal energy or other thermal energy storage. In addition to the performances of solar collector, chimney and turbine, the main factors affecting the system performance of a SCPP are the solar radiation and ambient temperature. Some other studies have established the importance of environmental conditions on the resulting power output from the system; thus, emphasizing that case studies involving SCPP are very valuable [2,49]. The importance of using TMY data set in the long-term solar system performance assessment was mentioned in the study of Ohunakin et al. [50], where they provided a detailed method for converting historical measurements of solar radiation into TMY format. Ninic [51] mentioned that the SCPP is presently competitive for areas in which global radiation is greater than 1950 kWh/m2. These areas include but not limited to the larger part of Africa, North and South America, the greater part of Australia, the Near East, and the western part of Asia [51]. From the reviewed literature, it is apparent that there is no single plant configuration available. As a result, different dimensions of chimney height, chimney diameter, and collector diameter have been chosen in these studies [7–9,23–32]. Schlaich et al. [8] mentioned that there is no optimum SCPP plant configuration since the resulting power output increases with an increase in the dimensions. They emphasized that a SCPP can only be optimized considering local environmental conditions including the price of electricity and the costs of labor, land and concrete. With known local conditions, an optimization model can be used to simultaneously increase the resulting power output and decrease the capital cost of SCPP. An attempt was made by Pretorius and Kroger [52] by means of thermo-economic analysis in which an approximated cost model was developed and presented. Considering the total capital cost of the system, Shariatzadeh et al. [32] determined the design parameters of a solar chimney cogeneration power plant combined with solid oxide electrolysis/fuel cell using genetic algorithms (GAs). Dehghani and Mohammadi [53] and Gholamalizadeh and Kim [54] also developed GAs to provide near-optimal solutions for the sizing of SCPP. In [53,54], the Pareto front which represents the set of non-dominated solutions based on the specified objective functions was presented. The multi-objective optimization model presented by Dehghani and Mohammadi [53] simultaneously considers power output maximization and capital cost minimization of SCPP, whereas the optimization model of Gholamalizadeh and Kim [54] attempts to maximize both the total efficiency and power output and at the same time minimize the capital cost. To our knowledge, all optimization algorithms proposed so far for the sizing of SCPP are based on heuristic procedures using GAs (see [53,54]). However, as Pérez et al. [55] stated, GAs try to find the global optimum solution, but they do not guarantee either local or global optimum. The authors then explained that the solutions obtained from GAs do not mostly even satisfy the Karush-Kuhn-Tucker (KKT) optimality conditions (for KKT conditions, see e.g. pp. 691–700 of Winston [56]). In other words, while [32,53,54] are able to offer some solutions to their respective applications, they do not guarantee either local or global optimal dimensions for the SCPP. Moreover, no existing economic feasibility study takes energy demand and stochasticity of solar radiation and ambient temperature into account. In addition, except for [32], all of the existing economic feasibility studies consider a given plant size. Note that the economic feasibility of building the SCPP is not assessed in [53,54]. The objective of this study is to propose an effective approach to simultaneously determine the optimal dimensions of the SCPP and the economic feasibility of the proposed plant. For this purpose, a two-stage economic feasibility approach is proposed based on a

new nonlinear programming model. In the first stage, the proposed nonlinear programming model determines the optimal SCPP dimensions that not only minimize the capital cost of building the plant and the present value of the periodic operation and maintenance costs, but also satisfy the energy demand within a specified reliability taking into account the stochasticity of solar radiation and ambient temperature. The proposed model is solved using a commercial optimization solver that guarantees finding the global optimum. In the proposed optimization model, one of the best and previously validated theoretical energy generation models available in the literature [45] for estimating the power output performance of SCPP is utilized and a water storage layer is also considered to ensure a smoother energy generation. In the second stage, the NPV of building the SCPP is computed by deducting the discounted total cost (TC) found in the first stage from the present value of revenues obtained due to selling the electricity generated by the SCPP. The novelty of this present study is that it is the first one that determines the optimal dimensions of SCPP together with its economic feasibility by considering energy demand and stochasticity of solar radiation and ambient temperature. Also, note that the proposed approach guarantees finding the optimal dimensions of SCPP unlike [32,53,54]. The proposed approach is evaluated on locations in Nigeria where there are available land resources with a chronic energy shortage. In addition, the proposed approach is benchmarked with an intuitive approach and an approach that does not consider uncertainty in solar radiation and ambient temperature. The results clearly revealed the value of the proposed approach. Managerial insights on the impact of varying collector efficiency, turbine efficiency, electricity price, discount rate, energy demand, meteorological conditions, and desired system reliability on the optimal dimensions of the SCPP and the economic feasibility of building the SCPP are obtained through detailed sensitivity analyses. The rest of the study is organized as follows. In Sections 2 and 3, a brief problem statement and the two-stage economic feasibility approach are presented, respectively. The application of the approach, benchmarking with similar approaches, and the results are presented in Section 4. In Section 5, sensitivity analyses involving the effect of various parameters on the proposed plant dimensions, discounted total cost of the system, and NPV are performed. Finally, the study is concluded in Section 6.

2. Problem formulation In this section, a detailed description of the problem addressed is presented. Building a SCPP as a renewable energy source is considered in order to satisfy the electricity demand of an urban or rural area with the specified meteorological data such as solar radiation and temperature. To satisfy a given energy demand within a specified reliability, the aim is to determine the optimal size of SCPP that minimizes the present value of total service life costs of building and operating the SCPP, and then to assess the economic feasibility of the obtained size of SCPP given the price of electricity, discount rate and the service life of the plant. As stated in Section 1, the best analytical model for the SCPP power output performance which is the one proposed by Schlaich et al. [8] is used. Following Schlaich et al. [8], the electrical power output Pele from the SCPP is directly proportional to the collector area and chimney height and calculated as:

Pele ¼ Gh Acoll gch gcoll gtur

ð1Þ

where Gh is the available solar radiation, Acoll is the area of the solar collector, and gch , gcoll , and gtur are the chimney, collector, and tur-

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bine efficiencies, respectively. Note that Acoll ¼ pD2coll =4 where Dcoll is the diameter of the collector. The formula for estimating gch is given in Eq. (2) [8,23,25] as:

gch ¼

g Hch CpT a

ð2Þ

where g is the gravitational constant, Hch is the height of chimney, C p is the specific heat capacity of air, and T a is the ambient temperature. Several formulations are available in the literature for the estimation of the collector efficiency [7,9,23,25]. These formulations define the collector efficiency as a function of the available solar radiation and the temperature difference between the surroundings and the inlet of the chimney. In reality, the associated heat losses via convection and radiation affect the air temperature and; thus, the efficiency of the collector. A recent study by Guo et al. [36] revealed that the efficiency of the solar chimney collectors is overestimated when radiation model is not taken into consideration. This overestimation can introduce errors in the economic feasibility of SCPP and ultimately lead to the wrong conclusion. For this reason, the collector efficiency is calculated using the formulation expressed in Eq. (3) which takes into consideration not only the solar radiation and temperature difference between the collector outlet and the surroundings but also the convective and radiation heat transfer losses.

gcoll ¼

h1 ðT c  T f Þ þ h2 ðT p  T f Þ Gh

ð3Þ

where h1 is the heat transfer coefficient between the glass collector and the air flowing inside the collector, h2 is the heat transfer coefficient between the absorber and the air flowing inside the collector, T c is the temperature of the glass collector, T f is the air flow temperature at the collector outlet and T p is the temperature of the absorber. A detailed method for estimating h1 ; h2 , T c ; T f , and T p were presented by Pasumarthi and Sherif [57], Bernardes et al. [33] and Okoye and Taylan [31]. Moreover, Bernardes [34] presented a comprehensive analysis of the available heat transfer coefficients applicable to SCPP. From the recent review work of Zhou and Xu [20], the selected values for turbine efficiency widely adopted in SCPP studies range between 50% and 90%. The turbine converts the resulting heat energy of the airflow emanating from the collector into electricity. For this reason, the efficiency being less than 100% accounts for the conversion losses in turning the shaft. Nizetic et al. [23] showed that for different SCPP capacities, the efficiency of the turbine remains approximately the same at 80%. Koonsrisuk and Chitsomboon [45] reported that the theoretical model by Schlaich et al. [8] for power output performance is the best even though the resulting system efficiency and power output from the model are independent of the chimney diameter. On the other hand, the simulation results of computational fluid dynamics in [45] for validation suggested that the efficiency and power output increases with the chimney diameter. Similarly, Hamdan [24] explained that this increase occurs only when the chimney diameter is below a critical value which depends on the Reynolds number and boundary layer thickness. The author reported that for a SCPP with a chimney diameter above the critical value, the effect of increasing the chimney diameter on the power output is very insignificant (i.e., the power variation of about 0.14% is found when the chimney diameter is increased from 60 m to 80 m). The urban or rural area with a given population has an energy demand Ej in day j, which has to be met by the SCPP with a certain level of reliability. Reliability r is defined here as the percentage of days in a year that the amount of energy generated by the SCPP is sufficient to satisfy the demand. The amount of energy generated

by the SCPP during a time period is found by multiplying the power output in Eq. (1) with the duration of sunshine in that time period. Based on the amount of energy demand satisfied and the unit price of electricity C electricity , revenue is obtained every month throughout the service life S (i.e., contract period) of the SCPP. The unit price of electricity is the amount determined either by the public utility for electricity or by the agreement with the government and the private sector that builds the SCPP in a buildoperate-transfer (BOT) system. Building a SCPP incurs some capital cost as well as periodic operation and maintenance costs. The approximate cost model proposed by Pretorius and Kröger [52] and subsequently utilized in Dehghani and Mohammadi [53] and Gholamalizadeh and Kim [54] is adopted for the capital cost of building the SCPP in this study. Accordingly, the capital cost of chimney C ch , collector C coll , and turbine C tur are given, respectively, as:

C ch ¼

ph 4

C coll ¼

i ðDch þ 0:001Hch Þ2  D2ch Hch CC sc

p D2coll 4

ðPtcoll CC sc Þ þ

p D2coll 4

ðPtcoll CC sc ÞPt Hcoll Hcoll

C tur ¼ Pttg ðC ch þ C coll Þ

ð4Þ

ð5Þ ð6Þ

where Dch is the chimney diameter, CC sc is the specific capital cost of chimney due to material and construction costs and Pttg is the specific percentage of the capital cost of collector and chimney. While the term in Eq. (4) assumes that the average chimney thickness increases by one millimeter per one cubic meter increase in chimney height, the expression in Eq. (5) presumes that the base cost of the collector per m2 will be Pt coll percent of CC sc plus an additional Pt Hcoll percent for every one meter height of the collector inlet. The operation and maintenance cost, C O&M , that is incurred monthly is a percentage Pt O&M of the total capital costs of the chimney, collector and turbine, and can be expressed as:

C O&M ¼ PtO&M ðC ch þ C coll þ C tur Þ

ð7Þ

In addition, several studies mentioned that the use of water storage layer does not contribute significantly to the power output but helps to smooth the power output over time for continuous operation after the sunset and before the sunrise [8,37,40]. Thus, the water storage layer provides continuous availability of energy, which is an important advantage of SCPPs. However, this advantage comes with the capital cost of storage layer C storage , which can be estimated as:

C storage ¼ Acoll Hsl ðC water þ C black;tube Þ

ð8Þ

where Hsl is the thickness of water filled black tube, and C water and C black;tube are the unit costs of water and black tube per volume, respectively. The costs of land, transmission lines and connection to the network are not included. After the service life, the ownership of the SCPP is transferred to the government. Thus, the salvage value of the plant at the end of the contract period is assumed to be zero for the investors. In addition, all revenues and operation and maintenance costs are discounted to their present values using a monthly discount rate i. The size of the SCPP to be constructed is limited. The minimum Lcoll ðLch Þ and maximum U coll ðU ch Þ sizes of the collector diameter (chimney height) of the plant are defined due to the limited available area and construction specific restrictions. For instance, such minimum and maximum sizes are provided in Dehghani and Mohammadi [53].

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3. The two-stage economic feasibility approach In this section, the proposed two-stage economic feasibility approach is presented. In the first stage, a nonlinear programming model is proposed to determine the optimal dimensions of the SCPP taking into account the present value of the total service life cost of the system. Given the optimal dimensions of the SCPP and its total cost, the present value of the revenues throughout the service life of the SCPP is computed using a daily analysis and the feasibility of the system is determined in the second stage. The nonlinear programming model to be used in the first stage is presented first. The decision variables used in the model are as follows:

Rev m ¼

 Dcoll : diameter of the solar collector.  Hch : height of the chimney.

S X

m

ðC O&M =ð1 þ iÞ Þ

ð9Þ

The collector diameter and the chimney height of the SCPP have to be within the predetermined minimum and maximum sizes. These are ensured by the following constraints:

Lcoll 6 Dcoll 6 U coll

ð10Þ

Lch 6 Hch 6 U ch

ð11Þ

In order to ensure that the amount of energy generated by the SCPP is sufficient to satisfy the energy demand with a given level of reliability, constraint (12), in which average daily values of  collector efficiency g  coll , and number of sunshine energy demand E,  hour are used, and X ¼ Gh =T a is defined as a continuous ranhours n dom variable to incorporate the uncertainty in daily solar radiation and daily ambient temperature, is developed. The aim in using  g  hour instead of their values for each  coll , and n average daily values E, day is to simplify the analysis. Thus, the probability of meeting average daily energy demand by the SCPP with a given level of reliability, r, can mathematically be expressed as:

ð12Þ

Note that Eq. (12) is regarded as a chance-constraint ensuring the probability that energy generated by the plant being not less than the average daily energy demand is at least r. Using the daily values of Gh and T a from the typical meteorological year (TMY 2) data, the best fitting probability distribution for X can be found by statistical goodness of fit tests. Defining h1r as the value at which the probability of X being less than or equal to  p Þ=ðAcoll g Hch g  hour Þ is equal to 1  r, Eq. (12) can be trans coll gtur n ðEC formed into the following deterministic constraint:

h1r Acoll

g Hch g coll gtur n hour P E Cp

16m6S

ð14Þ

where Jm is the set containing all days of month m, EPj denotes the amount of energy produced in day j (i.e., EPj ¼ Gh pðDcoll =2Þ ððg Hch Þ=ðC p T a ÞÞgcoll gtur nhour with Gh , T a , gcoll , and nhour being the corresponding values in day j). Note that the revenues are calculated monthly because the consumers pay their electricity bills monthly. Thus, the NPV of the system can be found as follows: 2

m¼1

  g Hch P XAcoll g coll gtur nhour P E P r Cp

X minðEP j ; Ej ÞC electricity j2Jm

The objective function in the optimization model is to minimize Z which is defined as the sum of capital costs of building the SCPP and the discounted operation and maintenance costs over the service life of the SCPP as:

Z ¼ C ch þ C coll þ C tur þ C storage þ

optimality using the Excel add-in optimization solver, What’sBest! 13.0 (see www.lindo.com). What’sBest! 13.0 is selected as the nonlinear programming solver in this study as it guarantees finding the global optimum solution unlike the majority of nonlinear programming solvers. In addition, note that this approach guarantees finding the global optimum solution of the proposed optimization model unlike [53,54]. In the second stage, the economic feasibility of the system is determined by calculating the NPV of the system given the optimal values of the collector diameter Dcoll , chimney height Hch and present value of total cost Z  . In order to find the NPV of the system, the revenue Rev m obtained from the energy produced in each month m is calculated as follows:

ð13Þ

Thus, the following optimization model is solved in the first stage: min Z subject to constraints (10), (11) and (13). The proposed optimization model is a nonlinear programming model due to the nonlinearities in Eqs. (9) and (13). This optimization model can be solved to near-optimality using heuristics like GAs or to optimality using nonlinear programming solvers. As the number of decision variables and nonlinear terms in the model is small, this optimization model is decided to be solved to global

NPV ¼

S X m ðRev m =ð1 þ iÞ Þ  Z 

ð15Þ

m¼1

Because of the uncertainty in daily solar radiation and ambient temperature, the realized reliability of the system rreal can be different from the desired system reliability r. The realized system reliability is obtained by considering the daily energy balance as follows:

rreal ¼

365 X

ESj =365

ð16Þ

j¼1

where ESj ¼ 1 if EPj P Ej , and ESj ¼ 0 otherwise. Similarly, considering the daily energy balance, the loss of load probability (LLP) of the system, which is a widely used performance measure for the renewable energy systems [58], can be derived. The LLP of the system as a probability of insufficient power supply to the load demand can be expressed as:

LLP ¼

365 365 X X EDj = Ej j¼1

ð17Þ

j¼1

where the energy deficit EDj in day j is equal to maxðEj  EPj ; 0Þ. The flowchart of the proposed approach is depicted in Fig. 2. 4. Results and discussion The proposed approach is implemented on locations in Nigeria. Nigeria is selected because of the widely reported high solar radiation and continuous chronic energy shortage. The advantages of SCPP such as low maintenance requirement, high durability, and high reliability are urgently needed to tackle the issue of unavailability of installed capacity in the country. The reported daily average solar radiation and sunshine duration in Nigeria are 5.25 kWh and 6.25 h, respectively [59]. Solar resources are highly variable from one location to another. The north of the country has more resources relative to the other parts of the country; hence, is favorably disposed to solar resource development and deployment. In this study, the rural area of Potiskum in Yobe State is studied due to; (i) favorable meteorological conditions, (ii) the lack of grid connectivity, (iii) abundant land resources, and (iv) being predominantly occupied by farmers. The lack of access to grid implies the

C.O. Okoye et al. / Energy Conversion and Management 126 (2016) 1013–1027

1019

Fig. 2. Flowchart of the proposed SCPP feasibility design approach.

need for electrification. Currently, households generate electricity using their own diesel generators. The available land resource is important for large scale SCPP development in Potiskum, which is located in the arid zone of the northeastern part of Nigeria between the latitude 11°430 N to 11°710 N and longitude 11°040 E to 11°070 E with a population of 205,876. The typical meteorological year (TMY 2) data of the location are used in this study. TMY 2 data are obtained from Meteonorm software (see www.meteonorm.com) and contain the daily data of solar radiation and ambient temperature. The daily average solar radiation, ambient temperature, and sunshine hours of Potiskum are 5.94 kWh/m2, 28.88 °C and 9.5 h, respectively. Fig. 3 shows the variations in the solar radiation and ambient temperature for a typical day, and the average solar radiation and ambient temperature for each month of a typical year in Potiskum. The annual discount rate of 3% (i.e., i ¼ 0:25% per month) is adopted as in Okoye et al. [60]. The efficiency of the turbine is taken as 80% based on the experimental study by Gannon and von Backström [46]. Even though the unit electricity price of diesel generators in Nigeria is 0.563 €/kWh [61], 0.25 €/kWh is assumed to be the price negotiated with the government for the sale of electricity produced by the SCPP which is built as a BOT project. Although von Backström et al. [62] mentioned that the intended design service life of a commercial SCPP ranges from 80 to 120 years, the service life of SCPP is taken as 40 years (i.e.,

S = 480 months) following the study of Nizetic et al. [23]. PtHcoll , Ptcoll , and Pttg are assumed to be 8%, 8%, and 10%, respectively, following Dehghani and Mohammadi [53]. The annual operation and maintenance cost, Pt O&M , is assumed as 0.5% of the total capital cost as in Schlaich et al. [8]. The lower and upper bounds for the collector diameter and chimney height are 100 6 Dcoll 6 1500 m, and 60 6 Hch 6 800 m, respectively, based on [53]. The chimney diameter is taken as 60 m to be above the critical value discussed in Section 2. Water storage height of 20 cm is assumed based on the study by Schlaich et al. [8], and the cost of water and black tube are obtained from the utility and manufacturers as 0.142 €/m3 and 2 €/m3, respectively. The estimated cost of reinforced cement concrete (1:1:2) per cubic meter is 250 €/m3 which includes the costs of materials (cement, aggregate, sand, and steel reinforcement), labor with mechanical mixers and vibrator, water, transportation and miscellaneous. The total daily electrical energy demand of 1500 households in Potiskum is calculated as 22,500 kWh assuming a 15 kWh daily consumption for a household of five residents (i.e., 3 kWh daily consumption per capita is assumed according to Ibitoye and Adenikinju [63]). Table 1 summarizes all the input parameters used in the proposed SCPP system analysis. To find the best fitting probability distribution for X (i.e., the ratio of daily solar radiation to daily ambient temperature), the available data are fitted to several probability distributions which

C.O. Okoye et al. / Energy Conversion and Management 126 (2016) 1013–1027 40

800

36

700

Solar radiation Ambient temperature

34

600

32 500 30 400 28 300

26

200

24

100

32 28 24

400

20 300

16 12

200

8 100

4

22

24

Hours

Dec.

22

Oct.

20

Nov.

18

Sep.

16

Jul.

14

Aug.

12

Jun.

10

Apr.

8

May

6

Mar.

4

Jan.

2

0

0

20

0

36

500

Feb.

Solar Radiation (W/m 2)

600

38

Ambient Temperature ( oC)

Solar radiation Ambient temperature

Solar Radiation (W/m 2)

900

Ambient Temperature ( oC)

1020

Months

Fig. 3. The solar radiation and the temperature profile of Potiskum.

Table 1 Summary of the SCPP system design parameters. Parameter

Unit

Value

Chimney height Collector diameter Chimney diameter Annual discount rate Cost of water Service life Cost of operation and maintenance Cost of black tube Cost of reinforced concrete Water storage height Price of electricity Pt Hcoll Pt coll Pt tg Number of households Number of residents in a household Daily energy consumption per capita Desired system reliability

m m m % €/m3 year € €/m3 €/m3 m €/kWh % % % – – kWh %

60 6 Hch 6 800 100 6 Dcoll 6 1500 60 3 0.142 40 0.5% of total capital cost 2 250 0.2 0.25 8 8 10 1500 5 3 95

include but not limited to beta, burr, burr (4P), normal, chi-squared, Dagum, Dagum (4P), Cauchy, gamma, gamma (3P), gumbel max, gumbel min, Kumaraswamy and log-logistic (3P) distributions. The goodness-of-fit is measured using the KolmogorovSmirnov (K-S), the Anderson-Darling (A-D) and the Chi-squared tests. These goodness-of-fit tests were performed by means of the Easyfit software (see www.mathwave.com/easyfitxl-distribution-fitting-excel.html.), and in all tests Dagum (4P) achieved the best rank for the current study. Thus, Dagum (4P) with the following fitting parameters: shape k ¼ 0:15689, shape a ¼ 1502:6, scale b ¼ 71:729 and location c ¼ 69:758 is utilized in this analysis. The probability density function and probability-probability (P-P) plots are presented in Fig. 4 to show how well the distribution fits the observed meteorological data. As mentioned in Section 3, the proposed nonlinear programming model is solved to global optimality using the Excel add-in optimization solver, What’sBest! 13.0. Note that the solution time of the model is just a second. The second stage of the proposed approach to find the NPV of the proposed SCPP is implemented in Excel. The results show that the proposed SCPP is feasible with a positive NPV of approximately 2.37 million € which indicates a marginal economic return on the invested capital. In other words, the present value of the revenue from the proposed SCPP is more than the present value of the cost of building and operating the plant over the considered service life. Note that a negative NPV

would imply that the system is not feasible. The obtained global optimal plant dimensions and other feasibility parameters are presented in Table 2. As seen in Table 2, the realized reliability of the designed SCPP system is 93.2% at the target reliability value of 95%, which implies that the energy demand can fully be met in 340 days of a year. Note that the realized reliability obtained from the proposed SCPP is 1.8% less than what is desired. This is mainly due to the approximation in using average daily value for the collector efficiency which actually depends on the variation in solar radiation and ambient temperature. We also observe from Table 2 that the LLP of the designed SCPP system is 0.014 at 95% desired system reliability. The observed LLP value of 0.014 implies that on an annual basis, about 8.1 GW h energy demand out of 8.21 GW h can be satisfied with the proposed SCPP system. Indeed, satisfying 98.6% of energy demand without battery storage is very satisfactory. The daily LLP and monthly revenue generated by the proposed SCPP are presented in Figs. 5 and 6, respectively. Fig. 5 reveals that the days of high LLP coincides with the rainy season period in Nigeria which generally starts from April to September depicting that the effect of seasonality may be pronounced in the region. As expected, undesirable weather conditions, such as cloudy weathers, can be experienced in some days during this period. Fig. 6 presents the monthly generated revenue considering the fact that the consumers pay their utility bills monthly. 4.1. Benchmarking with intuitive approach and the approach without uncertainty In this section, the proposed approach is benchmarked with an intuitive approach and the approach that does not consider uncertainty in solar radiation and ambient temperature. The intuitive approach parametrically simulates different pairs of chimney height and collector diameter that satisfy the daily average demand to determine the SCPP size with the lowest discounted total cost. Basically, all integer values of chimney height and collector diameter satisfying the daily average demand are enumerated and the one with the lowest discounted total cost is selected. The approach without uncertainty is the same as the proposed approach except constraint (13). Instead of constraint (13), the following constraint is considered in the approach without uncertainty:

Acoll

g Hch g coll gtur n hour P E Cp

ð18Þ

All approaches are implemented on Potiskum. The results are presented in Fig. 7 and Table 3.

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C.O. Okoye et al. / Energy Conversion and Management 126 (2016) 1013–1027

Probability Density Function

P-P Plot 1

0.36

0.9

0.32

0.8

0.28

0.7

P (Model)

0.4

f(x)

0.24 0.2 0.16

0.6 0.5 0.4

0.12

0.3

0.08

0.2

0.04

0.1 0

0 0.5

1

1.5

0

2

0.2

0.4

x Histogram

0.6

0.8

1

P (Empirical) Dagum (4P)

Dagum (4P)

Fig. 4. Probability density function and probability-probability (P-P) plot of the Dagum (4P) distribution.

Table 2 Summary of the proposed SCPP in Potiskum.

180

Unit

Value

Collector diameter Chimney height Net present value Discounted total cost Realized system reliability Loss of load probability Annual revenue generated Simple payback period

m m million € million € % – million € Year

1127.5 715.1 2.37 44.74 93.2 0.014 1.997 22.4

160 140

Monthly Revenue (€)

Parameter

x103

120 100 80 60

1.0 40 20 0.8 Dec

Nov.

Oct.

Sep.

Aug.

Jul.

Jun.

May

Apr.

Mar.

Feb.

0.6

Months Fig. 6. Monthly revenue from the proposed SCPP in Potiskum. 0.4

0.2

1250

39.0 Collector Diameter (m) Discounted total cost (million €)

1200

38.5 38.0

0.0 40

80

120

160

200

240

280

320

37.5

360

Days Fig. 5. Daily LLP of the SCPP design in Potiskum.

In Fig. 7, different SCPP sizes together with the associated discounted total costs are depicted. It is seen from Fig. 7 that 980 m collector diameter and 601 m chimney height has the lowest discounted total cost (33.06 million €); thus, is selected. Note that the realized system reliability, loss of load probability, and the annual revenue generated are calculated in the second stage of the proposed approach using the obtained collector diameter and chimney height. The intuitive approach managed to find a discounted total cost value close to the one found by the approach without uncertainty. Nevertheless, the approach without uncertainty found a slightly smaller discounted total cost and a better

Collector Diameter (m)

0

1150 37.0 36.5

1100

36.0 1050

35.5 35.0

1000

34.5 34.0

950 33.5

Discounted total cost (million €)

Daily LLP

Jan.

0

33.0

900

32.5 850 400

450

500

550

600

650

700

750

32.0 800

Chimney Height (m) Fig. 7. Different combinations of SCPP size and the associated cost using intuitive approach.

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Table 3 Results obtained by the intuitive approach and the approaches with and without uncertainty. Parameter

Unit

Intuitive approach

Collector diameter Chimney height Net present value Discounted total cost Realized system reliability Loss of load probability Annual revenue generated Simple payback period

m m million € million € % – million € Year

980 601 11.37 33.06 66.6 0.070 1.882 17.6

NPV than the intuitive approach. As previously mentioned in Okoye et al. [60], concern about system reliability has been identified as one of the main barriers to the solar application in Nigeria. The reliability barrier is not only peculiar to Nigeria but also to other locations in Africa and Asia with little or no access to grid connectivity. Table 3 shows a smaller plant size (collector diameter and chimney height) and lower discounted total cost with improved NPV and simple payback period for design without uncertainty relative to the base design (i.e., the design considering uncertainty in solar radiation and ambient temperature) as expected. However, this improvement comes at an expense of lower realized system reliability and higher LLP. The implication is that on an annual basis, 66.6% of the energy demand in Potiskum would be satisfied relative to the 93.2% obtained in the base design. Note that an ideal system would be the one with 100% realized system reliability and zero LLP. Moreover, for areas such as Potiskum without grid connectivity, energy generation with higher reliability is needed to enhance socio-economic development. In other words, there is a trade-off in decreasing the collector diameter and chimney height by about 14% each at an expense of decreasing the realized system reliability by about 27%. Overall, the intuitive method and the approach without uncertainty are not able to capture the high reliability offered by the base design. 5. Sensitivity analyses In order to examine the impact of various parameters affecting the performance of the proposed SCPP, different scenarios are identified and marked as A, B, C, D and E. In each of these scenarios, the effect of varying a parameter is evaluated on the optimal SCPP dimensions, the discounted total cost (TC) and the NPV, while the other parameters are kept constant as previously defined in Section 4. The ranges in this study are selected based on results of different SCPP studies found in the literature for collector [28,36] and turbine [20] efficiencies, and discount rate [60]. 5.1. Scenario A: Effects of the collector and turbine efficiencies In Scenario A, the collector and turbine efficiencies are varied between 20–60% and 50–90%, respectively, each with increments of 5%. The results are presented in Figs. 8 and 9, respectively. In Fig. 8, it is found that increasing the collector efficiency leads to a corresponding decrease in TC and increase in NPV. The implication is that as collector efficiency increases, the marginal economic return on the SCPP investment over its service life enhances. In addition, the optimal SCPP collector diameter and chimney height decrease as more energy is produced with more efficient collectors considering that the energy demand to be satisfied is constant. This result emphasizes the importance of the collector in the economic feasibility of SCPP and as such, adequate care should be taken in the collector design to avoid either overestimation or underestimation of the efficiency which obviously

Proposed approach Without uncertainty

With uncertainty

968.8 614.8 11.39 33.03 66.6 0.071 1.882 17.6

1127.5 715.1 2.37 44.74 93.2 0.014 1.997 22.4

affects investment decision. Ideally, the associated heat losses via convection and radiation should be considered in the collector design as recommended by Guo et al. [36]. Note that for a collector efficiency greater than 35%, the proposed SCPP system design is feasible as positive NPV values are obtained at the electricity price of 0.25 €/kWh. The optimal chimney height is equal to its upper limit for 25% collector efficiency, whereas when the collector efficiency is 20%, the model does not give any feasible solution as the optimal SCPP is beyond the defined limits (i.e., 100 6 Dcoll 6 1500 m and 60 6 Hch 6 800 m). As seen in Fig. 9, a similar trend with respect to the collector efficiency is observed when turbine efficiency increases. With increasing turbine efficiency, TC and the optimal dimensions of the proposed SCPP decrease whereas NPV increases accordingly. For turbine efficiency greater than or equal to 75%, the proposed SCPP is considered to be economically feasible due to the positive NPV values. Note that the chimney height is the same for turbine efficiency of 50% and 55% due to the upper bound on the chimney height. Thus, to satisfy the desired demand within the specified reliability, the optimal collector diameter increases as the turbine efficiency decreases from 55% to 50%. As observed in Figs. 8 and 9, TC decreases and NPV increases at a rate less than the linear rate when the collector or turbine efficiency increases. As negative NPVs are obtained when the collector efficiency is less than or equal to 35% and the turbine efficiency is less than 75%, the investors can either ask for a higher unit price of electricity from the government or a longer BOT contract period to have a return on the investment.

5.2. Scenario B: Effects of the electricity price and discount rate In this scenario, the electricity price changes from 0.15 to 0.35 €/kWh in increments of 0.025 €/kWh and the annual discount rate is varied from 2% to 6% in increments of 0.5%. These parameters are varied both at the same time, in addition to varying them once at a time as previously stated, and the results are depicted in Figs. 10 and 11. In Fig. 10, it is clear that the increase in the unit price of electricity favors the economic feasibility of the plant as the NPV of the proposed plant linearly increases. On the other hand, increasing the discount rate decreases the NPV at a rate less than the linear rate. From Fig. 10, it is possible to estimate the critical electricity price and discount rate value that makes the NPV be equal to zero. This information is precious to investors as it at a glance offers the margin to start negotiation for the proposed project. For instance, it is found that for varying discount rate from 2% to 6% at the electricity price of 0.25 €/kWh, the critical discount rate (i.e., the maximum rate of return) for the NPV to be zero is 3.37%. Similarly, for the electricity price range from 0.15 to 0.35 €/kWh at a discount rate of 3%, the critical electricity price of 0.237 €/kWh makes the NPV zero. In other words, positive NPVs indicating feasible systems

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Collector Diameter Chimney Height

10

60

5 55 0 50 -5 45 -10 40

-15

35

-20

30

-25 20

25

30

35

40

45

50

55

Optimal Collector Diameter (m)

15

Net Present Value (million €)

Total Cost (million € )

65

825

1500

20 TC NPV

800

1400 775 750

1300

725 1200 700 675

1100

650 1000

Optimal Chimney Height (m)

70

625 900

60

600 20

25

Collector Efficiency (%)

30

35

40

45

50

55

60

Collector Efficiency (%)

Fig. 8. Effect of collector efficiency on the proposed SCPP design in Potiskum.

10

Collector Diameter Chimney Height

5

57.5 55.0

0 52.5 50.0 -5 47.5 45.0

-10

42.5

Optimal Collector Diameter (m)

1350

Net Present Value (million €)

Total Cost (million € )

60.0

825

1375

TC NPV

800

1325 1300

775

1275 1250

750

1225 725

1200 1175

700

1150 1125

Optimal Chimney Height (m)

62.5

675

1100 -15

40.0 50

55

60

65

70

75

80

85

90

1075

650 50

Turbine Efficiency (%)

55

60

65

70

75

80

85

90

Turbine Efficiency (%)

Fig. 9. Effect of turbine efficiency on the proposed SCPP design in Potiskum.

40

Electricity Cost of 0.15 €/kWh Electricity Cost of 0.2 €/kWh Electricity Cost of 0.25 €/kWh Electricity Cost of 0.3 €/kWh Electricity Cost of 0.35 €/kWh

Net Present Value (million €)

30

20

10

0

-10

-20

-30 2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

Discount Rate (%)

to buy the electrical energy produced from the SCPP at a higher price in order to attract the BOT investments. In addition, note that the cost of electricity from the widely utilized diesel power generators in Nigeria is 0.563 €/kWh [61], which is much greater than the electricity price values considered in this study. Furthermore, the diesel power generators result in environmental costs, unlike the SCPPs. For changing electricity price, the optimal SCPP size ðDcoll ¼ 1128 m; Hch ¼ 715 mÞ and the TC (44.74 million €) remain constant since the objective function of the proposed model is independent of the electricity price. Fig. 11 shows the effect of the annual discount rate on the TC and optimal SCPP dimensions. For instance, increasing the discount rate from 2% to 6%, the TC decreases by 5.4%. The figure also shows that the optimal collector diameter and the optimal chimney height are almost insensitive to annual discount rate. This is because only operation and maintenance cost constituting a small fraction of the total cost is affected by the discount rate in the optimization model.

Fig. 10. Effects of electricity price and discount rate on the NPV of the proposed SCPP design in Potiskum.

5.3. Scenario C: Effects of the energy demand per capita

are obtained for higher electricity prices and lower discount rates than their corresponding critical values. As a commitment to rural electrification program which, in turn, enhances the socioeconomic development of the region, the government can offer

The proposed plant is designed based on a 3 kWh daily consumption per capita as discussed in Section 4. The consumption pattern changes with location, awareness and the attitude of individuals to energy conservation, the income of the individuals and the characteristic of the house. For this reason, the effect of energy

C.O. Okoye et al. / Energy Conversion and Management 126 (2016) 1013–1027 1220

46.0

Optimal Collector Diameter (m)

45.5

Total Cost (million €)

720 Collector Diameter Chimney Height

1200

45.0 44.5 44.0 43.5 43.0

719

1180 718 1160 717

1140 1120

716

1100

715

1080 714 1060

42.5

713

1040 42.0 2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

712

1020

6.0

Optimal Chimney Height (m)

1024

2.0

2.5

3.0

Discount Rate (%)

3.5

4.0

4.5

5.0

5.5

6.0

Discount Rate (%)

Fig. 11. Effect of discount rate on the proposed SCPP design in Potiskum.

demand on the performance of the SCPP design is studied by varying the energy demand from 1 to 5 kWh per capita with steps of 0.5 kWh in this scenario. Note that the proposed plant is designed for 1500 households assuming an average of five residents in a house. The results presented in Fig. 12 indicate that increasing the energy demand increases not only the optimal plant dimensions but also the TC and NPV. This trend is in agreement with the observations in previous studies [7,8] that the economic feasibility of SCPP improves with increasing plant dimensions. As seen in Fig. 12, the proposed system at the electricity price of 0.25 €/kWh is feasible for more than 2.57 kWh per capita energy consumption. In addition, for energy demand higher than 4 kWh per capita, the chimney height reached its upper bound (i.e., 800 m) and the collector diameter increased further to meet the target reliability. 5.4. Scenario D: Effects of the local meteorological conditions This scenario considers the effect of meteorological conditions on the optimal plant dimensions, TC, NPV and LLP. Several studies have demonstrated that solar radiation and ambient temperature are very important in the SCPP design. Herein solar radiation and ambient temperature data from four locations different from Potiskum are identified and utilized as an input to the proposed optimization model. The locations are selected in such a way not only to represent the two notable solar zones in Nigeria as reported

This scenario examines the reliability of the proposed SCPP at varying desired system reliability values. Although 95% desired system reliability used in the original design seems reasonable for a solar system, changing this value highlights the possible tradeoff between the plant optimal dimensions, TC, NPV, LLP and

1400

20.0 TC NPV

850 Collector Diameter Chimney Height

15.0 55 12.5 50

10.0

45

7.5

40

5.0 2.5

35

0.0 30 -2.5

Optimal Collector Diameter (m)

17.5

Net Present Value (million €)

60

Total Cost (million € )

5.5. Scenario E: Effects of the desired system reliability

800

1300

750

1200

700 1100 650 1000 600 900

550

800

25

500

-5.0 -7.5

20 1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Energy Demand Per Capita (kWh)

5.0

700

450 1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Energy Demand Per Capita (kWh)

Fig. 12. Effect of energy demand per capita on the proposed SCPP design in Potiskum.

5.0

Optimal Chimney Height (m)

65

by Ohunakin et al. [64], but also to depict areas with less population density due to land requirement. Table 4 shows the features of the locations and the optimal SCPP design results. The results in Table 4 show that the meteorological conditions are very important in determining both the optimal SCPP dimensions and the economic feasibility of the proposed SCPP. Specifically, building a SCPP in locations at Solar Zone I is feasible unlike the locations at Solar Zone II. The location with the highest solar radiation yields the smallest plant dimensions and simple payback period, and the highest NPV. Note that the LLP of the system for 95% desired reliability depends not only on the predicted optimal plant size but also on the distribution of the meteorological conditions as observed from the probability distribution fit. Thus, locations without uniformly distributed solar radiation and temperature throughout the year (e.g., Donga) may need larger optimal plant dimensions to satisfy the energy demand within the specified reliability, which in turn decreases the NPV and LLP of the proposed SCPP.

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C.O. Okoye et al. / Energy Conversion and Management 126 (2016) 1013–1027 Table 4 Typical features and results for different selected locations. Parameter

Solar Zone I

Solar Zone II

Value Kano 12.02/08.32 456 6.08 26.3 Dagum 4P 95 94.8 1092 693 5.28 2.003 21.0 0.011 41.98

0.08

65

Loss of Load Probability

0.07

60

0.06 55 0.05 50 0.04 45 0.03 40

0.02

35 30 50

55

60

65

70

75

80

85

90

95

Donga 07.20/10.10 225 5.05 25.5 Johnson SB 95 95.3 1326 800 12.48 2.012 29.8 0.007 59.95

825 Collector Diameter Chimney Height

1450

Optimal Collector Diameter (m)

TC LLP

Magama 10.17/05.20 300 5.50 28.9 Gen. extreme value 95 94.8 1220 773 5.15 2.002 26.2 0.012 52.37

1500

0.09

70

Total Cost (million €)

Katsina 13.00/07.32 457 6.00 29.7 Dagum 4P 95 94.2 1096 695 5.00 2.002 21.1 0.012 42.24

800

Optimal Chimney Height (m)

Site Latitude (°N)/longitude (°E) Elevation (m) Daily solar radiation (kWh/m2) Ambient temperature (°C) Best fitting probability distribution for X Desired system reliability (%) Realized system reliability (%) Optimal collector diameter (m) Optimal chimney height (m) NPV (million €) Annual revenue (million €) Simple payback period (year) LLP Discounted total cost (million €)

1400 775 1350 750

1300 1250

725

1200

700

1150

675

1100 650 1050

0.01

1000

0.00 100

950

625

50

55

60

65

70

75

80

85

90

95

600 100

Desired System Reliability (%)

Desired System Reliability (%)

30

25

25

20

20

15

15 10 5 0 -5 -10

0.2 €/kWh 0.25 €/kWh 0.3 €/kWh 0.325 €/kWh 0.35 €/kWh

-15 -20 -25 -30

Net Present Value (million €)

Net Present Value (million €)

Fig. 13. Effect of desired reliability on the proposed SCPP in Potiskum.

Electricity Cost = 0.25 €/kWh

10 5 0 -5 -10 -15

2% Discount Rate 3% Discount Rate 4% Discount Rate 5% Discount Rate 6% Discount Rate

-20 -25 -30 -35

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Loss of Load Probability

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Loss of Load Probability

Fig. 14. NPV at different LLP, electricity price and discount rate values.

realized system reliability. Thus, this probability is varied from 50% to 99% (i.e., r is set to 50%, 80%, 85%, 90%, 95%, 96%, 97%, 98% and 99%), and the results are presented in Figs. 13 and 14. As depicted in Fig. 13, increasing the desired reliability increases TC and decreases LLP, both at an exponential rate. Hence, a higher desired reliability leads to higher optimal plant dimensions and TC as well as lower LLP. From Figs. 13 and 14, at the elec-

tricity price of 0.25 €/kWh, it is observed that increasing the desired system reliability from 95% to 99% increases the TC, Dcoll and Hch approximately by 50.6%, 27.8% and 11.9%, respectively, and decreases the LLP by 92.3% at the expense of decreasing the NPV by about 926.8%. Conversely, a decrease in the desired system reliability from 95% to 90% decreases the TC, Dcoll and Hch approximately by 11.2%, 5.8% and 5.8%; and increases the LLP and NPV by

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89.1% and 186.2%, respectively. Therefore, the tradeoff between improving the LLP at the expense of decreasing the NPV or vice versa should be assessed by the investors. The variations of NPV based on the obtained LLP values are depicted in Fig. 13 for changing electricity price and discount rate. Fig. 14 indicates that for the electricity prices considered, the proposed SCPP system is infeasible at the LLP of 0.001. However, at the LLP of 0.002, the proposed SCPP becomes feasible when the electricity price is 0.3 €/kWh or more. Additional information regarding the maximum rate of return and LLP that an investor can expect at different electricity price and discount rate values can be extracted from Fig. 14. For instance, at the electricity price of 0.25 €/kWh and annual discount rate of 3%, the investors cannot expect a return on the SCPP investment for an LLP less than 0.011. Similarly, when the electricity price is 0.25 €/kWh, the maximum rate of return investors can expect is 5% if an LLP value of 0.086 is acceptable.

6. Conclusions This paper presents a novel two-stage approach to jointly predict the optimal SCPP dimensions and the economic feasibility of the proposed system. This approach is important to inform potential investors on the feasibility of the environmentally friendly, highly reliable and durable SCPP technology as to foster adoption and deployment. The proposed model in the first stage determines the optimal collector diameter and chimney height by taking into account the energy demand, meteorological conditions, and the capital costs associated with the solar collector, chimney, turbine, water storage layer, and monthly operation and maintenance costs. Through the calculation of the revenues generated by the proposed SCPP, the NPV of the SCPP which determines the feasibility of the system is found in the second stage of the approach. The practicability of the proposed approach is demonstrated through the case of Potiskum in Nigeria where chronic energy shortage is prominent. The results emphasize the economic feasibility of the proposed SCPP as a sustainable alternative to diesel powered generators which are highly utilized in the region. Note that TC, NPV, generated revenues and optimal plant sizes obtained are location specific. Thus, it is important to assess the feasibility of SCPP before installation due to variable weather conditions and material costs. Benchmarking with an intuitive approach and an approach that does not take into account uncertainty in solar radiation and ambient temperature revealed that the proposed approach yields a substantially high level of reliability compared to others. In addition, this study produces precious managerial insight on the effect of some notable parameters on the optimal dimensions, TC and feasibility of the system through detailed sensitivity analyses. The obtained results reveal that for a constant energy demand at the desired system reliability; increasing the collector efficiency and turbine efficiency decreases the optimal SCPP dimensions and TC, but increases NPV. Moreover, the optimal SCPP dimensions do not depend on the electricity price and discount rate, but they increase with increasing demand and desired system reliability. Increasing electricity prices increases the NPV, but does not affect TC. Considering that the revenues and operation and maintenance cost of the proposed SCPP are discounted over the service life of SCPP, increasing discount rate decreases NPV and TC. As expected, the locations with better meteorological conditions are more likely to be economically feasible for SCPP installation since lower optimal plant dimensions can be used. Furthermore, the economic feasibility of the SCPPs is enhanced when the energy demand increases emphasizing that SCPP is truly a large-scale energy generation system. It can be deduced that increasing the system reliability results in a corresponding increase in the optimal plant size

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