1. Introduction
Fossil fuel reserves in the world are rapidly decreasing, and so it is important to tap the abundant solar energy source to both meet future energy demands and reduce greenhouse gas (GHG) emissions. Concentrating Solar Power (CSP) alternatives are among the most promising alternatives to fossil fuels because they rely on conventional technology and are relatively easy to scale up [
1]. Of all CSP technologies available today, the solar power tower (PT) is expected to both significantly reduce its cost and improve its efficiency over time [
2,
3]. This technology has several potential advantages over other CSP technologies (parabolic trough, linear Fresnel, and solar dish), including higher operating temperatures, which allow for greater efficiency of the thermodynamic cycle, low water consumption, and high-energy-density storage [
3]. The design of these power plants poses considerable challenges given the complexity of the mathematical models required in both optical and thermal analyses of their main components. To speed up the growth in the installed capacity of PT plants and the associated cost reductions, practical design procedures and reliable data on investment costs are required.
A typical PT plant consists of a solar field (SF), known as a heliostat field, a solar receiver (SR), a thermal energy storage (TES) unit, and a power block (PB). To simplify the analysis of the PT plants, Jebamalai [
4] proposed a methodology to design SRs, including external and cavity receivers. Srilakshmi et al. [
5,
6] presented a procedure to determine the preliminary tower height and the reflective area of the SF. Khosravi et al. [
7] proposed a design and optimization approach by combining adaptive neuro-fuzzy inference with a genetic algorithm and teaching–learning-based optimization algorithm. Yan Luo et al. proposed optimization techniques to find the optimum design of PT plants based on successive response surface methodology [
8] and the “Sobol’-Simulated Annealing” algorithm [
9]. Albarbar and Arar [
10] proposed optimal designs for a medium-scale PT plant. The authors investigated the effects of the receiver’s geometric parameters on the performance of medium-scale PT plants.
Indeed, the most complex part in the design of PT plants is the heliostat field. Thus, several methods have been proposed to layout and estimate its optical performance. Siala and Elayeb [
11] proposed a graphical method by dividing the field into certain groups of heliostats. Sanchez and Romero [
12] proposed a method to layout the field based on the yearly direct solar radiation. Wei et al. [
13] coupled Monte Carlo ray tracing with the parametric search algorithm to optimize the heliostat field layout. Noone et al. [
14] proposed a discretization approach to layout the heliostat field. Pitz-Paal et al. [
15] coupled a genetic algorithm with the Nelder–Mead algorithm to design the heliostat field. M. Besarati and Goswami [
16] developed a quick method to design the SF based on minimum shadowing and blocking. Belhomme et al. [
17] developed an approach to design the SF by processing highly resolved heliostat geometry data containing the local normal vectors of the mirror surface of a heliostat. Collado et al. [
18] proposed the division of the SF into several regions to get an accurate heliostat field design.
To facilitate the design of the heliostat field, numerous codes have been developed. DELSOL3 [
19], SOLTRACE [
20], MUEEN [
19], SENSOL [
19], CAMPO [
21], Solstice [
22], SolarPILOT [
23], HFLD, and CRS4-2 are widely used, among others. Some of these codes are useful to investigate the optical performance of the solar field, but they require the geometric design parameters of the receiver and the tower as input data. For instance, SolarPILOT requires the nominal thermal power of the SR, its geometric dimensions, and the tower height to design the heliostat field. In case the input data are just estimates, such as in [
24], the design parameters of a PT plant may be highly uncertain, thus jeopardizing the viability of a given project. This is also true for the case of Campo and many other codes.
This paper aims to fill a gap in the design and cost estimation of PT plants because there is a lack of cost data accounting for the scale effect. In addition, to the best of the authors’ knowledge, there is no published method to calculate the design data required by some software, such as SolarPilot and Campo. The rapid growth in the installed capacity of PT technology and the associated cost reductions require practical tools to calculate design parameters, investment costs, and economic indices that take into account the influence of technical and financial parameters.
We propose a practical methodology to design and to estimate the costs of PT plants. The methodology is useful to estimate the input design data required by the codes cited above. The design approach used allows for calculation of the geometric parameters of the main parts of the PT plants from a minimum set of input data (nominal power production, geographical parameters of the site, and solar radiation data). The cost estimation approach takes into account the technical and financial parameters to estimate the investment costs and economic indices. The next section describes the proposed methodology. The validation of the methodology is described in
Section 3.
Section 4 presents a case study on the use of the methodology to design and to determine the economic indices of PT plants.
Section 5 presents a sensitivity analysis to show the influence of the technical and financial parameters on the design and economic indices of PT plants. The last section summarizes the most important results.
3. Validation of the Design Approach
Two operational PT plants of different sizes were selected to validate the proposed design methodology: Gemasolar (19.9 MW
e) and Crescent Dunes (110 MW
e). The former is located in Almeria, Spain while the latter is located in Nevada, USA. The two plants use SENER’s heliostat HE35 of 120 m
2, 88% reflectivity [
25], and a total error on the reflected ray of 2.9 mrad [
34]. The geometry of the SR and the tower were calculated using the expressions given in
Section 2. Then, they were introduced in SolarPILOT to estimate the optical efficiency of the SF. The estimated SF optical efficiencies of Gemasolar and Crescent Dunes are 55.1% and 42.1%, respectively.
Table 2 illustrates the input data used in the validation of the proposed methodology.
A comparison between the predicted and the actual technical design parameters of Gemasolar and Crescent Dunes is shown in
Table 3a,b, respectively. The mean bias error (MBE) is used to measure the accuracy of the proposed methodology. It is defined as:
where
m and
p are the actual value and the predicted value, respectively.
The average relative absolute MBE in the estimation of the design parameters of Gemasolar and Crescent Dunes is 8.2% and 9.3%, respectively. The proposed methodology has shown good agreement with SolarPILOT in the prediction of the power incident on the receiver.
Overall, the uncertainty of the proposed methodology in the estimation of the design parameters of the SR and the tower height is less than its uncertainty in the estimation of the design parameters of the storage and the solar field. The relative MBE in the estimation of the geometric design parameters (height and diameter) of Gemasolar’s receiver is 2.9%. The height of its tower is also estimated with good accuracy (relative MBE = 3.9%). For the case of Crescent Dunes, the relative MBE in the estimation of the geometric design parameters of the receiver is 6.5%. Due to the complexity of the optical modeling of the heliostat field, the methodology showed less accuracy in the estimation of its total reflective area. The relative MBE in the estimation of the reflective area of the solar field for the case of Gemasolar and Crescent Dunes is 15.9% and 12.4%, respectively.
5. Sensitivity Analysis
A sensitivity analysis was carried out to investigate the influence of the technical and financial parameters on the performance of the PT plants.
Figure 5 shows the variation of the dimensions of the SR as a function of the nominal power of the PT plant. As can be seen, there is a logarithmic relation between the dimensions of the SR and the nominal power of the PT plant.
Figure 6 (left) shows the variation of the absorptive surface of the SR with the allowable heat flux. A 50-MW
e plant is taken as an illustrative example (even for the results illustrated in
Figure 7,
Figure 8 and
Figure 9). The allowable heat flux depends on the thermal and mechanical properties of the materials used to build the SR. The higher the allowable heat flux, the lower the SR’s absorptive surface and the higher its surface temperature. The SR’s absorptive surface could be decreased from 603.5 m
2 to about 200 m
2 by increasing the allowable heat flux of the current commercial PT plants to 1600 kW/m
2. This could result in a significant cost reduction, but it requires the use of new materials that perform well under high heat flux.
The influence of the operation period and the depreciation period on the LCOE is shown in
Figure 7. If the operation period is increased from 25 to 30 years, the LCOE decreases from 140 to about 132 USD/MWh, which represents a cut of 5.7%. The depreciation period influences the LCOE. As
Figure 7 (right) illustrates, the longer the depreciation period, the higher the LCOE. When the depreciation period is as long as the operation period, the LCOE increases to 151 USD/MWh. This value is 8% higher than the one obtained when the depreciation period is five years (140 USD/MWh).
Figure 8 illustrates the influence of the degradation rate and the discount rate on the LCOE. The results show that the degradation rate has a critical influence on the LCOE. The considered average degradation rate in
Section 4 is 0.75%, which corresponds to a LCOE of 140 USD/MWh. If this value is doubled (1.5%), the LCOE increases to reach more than 150 USD/MWh. High degradation rates could raise the LCOE and jeopardize the viability of the solar power project. Indeed, if the average degradation rate reaches 5%, the LCOE jumps to 208.3, which represents an increase of 49% compared with the reference case (degradation rate of 0.75%).
The real discount rate has also a strong influence on the LCOE. As
Figure 8 (right) illustrates, if the real discount rate is 10%, the LCOE reaches 253.6 USD/MWh.
Figure 9 shows the influence of the price of electricity on the SPB and the IRR. The SPB decreases sharply with the increases of the electricity price. To reduce the SPB to eight years, it is necessary to raise the electricity price to 200 USD/MWh. In addition, an SPB shorter than five years requires electricity prices higher than 300 USD/MWh. This is mainly related to the high specific investment costs of the PT technology. The IRR increases with the increase in the electricity price. It is about 2% for electricity prices around 100 USD/MWh. To reach an IRR of 10%, the electricity prices should be around 200 USD/MWh.
6. Conclusions
A practical methodology has been proposed for the design and cost estimation of commercial PT plants. The design approach was validated through a comparison of the predicted design parameters with the actual technical data of two operational PT plants of medium- and large-scale sizes. The average absolute mean bias error in the prediction of the complete design of the PT plants is 8.75%.
The investment costs were estimated taking into account the scale effect. The results showed that the plant size has a strong influence on investment costs. The specific investment costs of 5, 10, 50, and 100 MWe are 7393.9, 6804.5, 6161.6, and 5786 USD/MWe, respectively.
The proposed methodology was applied to design and estimate the costs of six PT plants in the range of 10–100 MWe for integration into the mining industry. The economic assessment indicates that the TLCC of the PT plant represents 125% of the investment costs, which results in a long SPB. The SPB of the PT plants ranges from 16 years for a 100-MWe plant to 19 years for a 10-MWe plant. The LCOE decreases as the size of the PT increases, from 112.89 USD/MWh for a 10-MWe plant to 95.28 USD/MWh for a 100-MWe plant.
The sensitivity analysis showed that the allowable heat flux has a strong influence on the size of the solar receiver. In addition, the degradation rate and the real discount rate have a crucial impact on the viability of solar power projects.
The proposed methodology is universal, since it has the potential to provide the key information for prospective analysis of the implementation of any PT plants with cylindrical receivers.