1. Introduction
Concentrating solar power (CSP) is a technology that uses mirrors or lenses to reflect sun rays into a focal point (or line), allowing thermal energy to accumulate in a material with good heat storage capability. This concentrated thermal energy can be used to drive various thermal applications. Among those applications of CSP are electricity generation, district heating systems, industrial process heating, water desalination, etc. [
1,
2]. The primary significance of CPS is that it is a clean energy source with a meager contribution to greenhouse gas emissions throughout the life cycle of the CSP plant, especially when compared to conventional fossil fuel energy sources [
3]. Moreover, fossil fuels reserves are depleting, and their supply can be disrupted due to various geopolitical phenomena, necessitating the search for more sustainable energy solutions to power humanity. CSP plants are classified into four types: parabolic trough (PT), solar power tower (SPT), parabolic dish (PD), and linear Fresnel (LF) [
4]. The performance parameters such as concentration, operational temperature range, efficiency, capacity, costs, and land use vary depending on these configurations [
5]. The PT configuration is the most commonly used CSP configuration, followed by the SPT configuration, due to their superior performance under the aforementioned factors [
6]. Since solar energy is inherently intermittent due to its dependence on the diurnal cycle and climate conditions, all CSP plants, regardless of configuration, require a thermal energy storage (TES) system to maintain the balance of demand and supply [
7].
TES, where excess energy is stored in a thermal reservoir using a storage medium, is most suited to this type of application due to its cost-effective and efficient operation compared to other energy storage types available. Consequently, the main purpose of a TES system can be identified as storing heat energy when the sun is available and utilizing the stored energy to operate a thermal cycle when the sun is unavailable. As a result, TES ensures that the CSP plant continues to operate at a lower cost while also providing other benefits such as increased plant reliability, efficiency, energy savings, and annual capacity factor [
8,
9,
10,
11]. Sensible heat thermal energy storage (SHTES), latent heat thermal energy storage (LHTES), and thermochemical storage are the three main types of TES available [
12]. SHTESs are designed to store heat energy as sensible heat of the working material, LHTES is designed for the latent heat of the physical phase transition of storage material, while some sensible heat is also efficiently stored, and thermochemical storage is designed to store thermal energy through a chemical reaction of storage materials [
13]. Despite the fact that LHTES and thermochemical storage have higher energy density than SHTES, SHTES is the most commonly installed TES type, particularly in CSP power plants, due to its economic benefits and simplicity [
14,
15]. LHTES is less expensive than thermochemical storage and thus can be identified as the next potential candidate for CSP plants [
16]. Furthermore, the performance of TES can be improved by upgrading the configuration, geometry and materials used. Improvement of the storage medium by encapsulation, modification of the chemical composition, and addition of micro-/nano-particles of foreign material are some of the more popular methods. The enhancement of thermo-physical properties of storage materials through the addition of nanoparticles has numerous success stories, as evidenced by previous literature [
17,
18,
19].
Any of these TES systems can be integrated with a CSP plant in such a way that the TES system is always charged prior to delivering thermal energy to the application (active TES), and the TES system can be charged with excess thermal energy that is not required by the application (passive TES). In general, active TES consists of direct integration with the same storage medium as heat transfer fluid (HTF), whereas indirect integration uses two different materials as the storage medium and HTF [
20]. Therefore, the optimal design of a CSP plant integrated with TES must be tailored to the situation while also taking into account the other system requirements. The levelized cost of energy (LCOE) is one such important design consideration in CSP plant design to predict economic competitiveness. With the recent drive towards decarbonization, CSP technologies have received increased attention, with numerous R&D contributions leading to a reduction of more than 50% of the LCOE of CSP plants [
21]. As a result, CSP plant construction is accelerating, with the installed capacity of CSP expected to reach 22.4 GW by 2030 to utilize a larger portion of the total global CSP potential of 2,945,926 TWh/y [
22]. The current global weighted average cost of CSP in electricity generation is approximately 0.108 USD/kWh, according to data from the International Renewable Energy Agency (IRENA) [
23]. However, the LCOE is entirely dependent on the geographical location of the CSP plant and the regional macroeconomic conditions. As a result, it is worthwhile creating a systematic model that any project developer anywhere around the world can use in making CSP plant design and development decisions.
Aseri et al. [
24] conducted a study on the techno-economic appraisal of 50 MW nominal capacity parabolic trough solar collector and solar power tower-based CSP plants with a provision of 6.0 h of TES at two potential locations in India for different condenser cooling options. Musi et al. [
25] conducted a study to evaluate the LCOE of CSP plants, and the findings show a country- and technology-level learning effect for CSP plant LCOE. Furthermore, the construction of large CSP plants does not currently result in LCOE reductions, and LCOE reductions are generally positively correlated with greater thermal energy storage, a higher capacity factor, and, to a lesser extent, power output. Mahlangu et al. [
26] conducted research to evaluate the external costs associated with a solar CSP plant using life cycle analysis. Some of the relevant studies in the open literature include Hussain et al. [
27], who conducted a study that presented a cost analysis of a 20 MW concentrated solar power plant with a thermal energy storage system in Bangladesh. However, none of these studies provide a comprehensive outlook on the energy generation costs associated with CSP plants.
As a consequence, this comprehensive study is dedicated to identifying the parameters that affect the LCOE of CSP plants and developing an aggregated mathematical model that can be used in estimating the LCOE of future TES-integrated CSP plant designs prior to construction. Given the maturity of CSP and TES technologies, the work presented in this paper has chosen PT and SPT CSP configurations, shown in
Figure 1, as well as SHTES and LHTES configurations, to be integrated into CSP plants as active indirect storage systems. Both SHTES and LHTES storage types are considered in a single-tank thermocline arrangement. All TES configurations are taken into account for both regular working materials and nano-enhanced storage materials. Furthermore, due to the high-temperature attainment of the SPT arrangement, in which the use of SHTES has less economic competitiveness, the SPT solar plant arrangement will be integrated only with the LHTES storage type. The use of phase transitions to increase storage energy density can drastically reduce storage material requirements and thus storage size and cost. The consideration of nanotechnology in CSP plants was evaluated depending on a hypothesis. Thermal energy is being used to generate electricity in three different power generation cycles: the Rankine cycle, the Brayton cycle, and the combined power cycle. Therefore, the research presented in this paper will contribute to the development of a mathematical model that is applicable for both PT and SPT configurations, as well as the identification and verification of LHTES in improving CSP plant performance over other available TES types. There was no previous study that considered all three power generation cycles considered in this study at the same time, and no attention was previously given to the evaluation of LCOE with the integration of nanoparticles into the TES medium.
4. Mathematical Modelling
Following the LCOE equation, this section develops a model to calculate the LCOE of the energy generated by the CSP plant. As shown in Equation (7), the energy generated by the CSP plant (E
t) is dependent on the DNI at the plant’s location (latitude and longitude), unit area of solar collector (A
1), number of solar collectors (N), the efficiency of solar collectors (η
collector), the efficiency of the solar receiver (η
receiver), HTF efficiency (η
HTF), heat exchanger (HE) efficiency (η
HE), number of heat exchangers (N
HE), efficiency of TES system (η
TES), thermal cycle efficiency (η
thermal), turbine efficiency (η
T) and electricity generator efficiency (η
G). All other system component losses are assumed to be insignificant. In the current study, the efficiency of the receiver, heat exchangers, HTF, and generator was assumed to be constant for each of the selected configurations using industry-standard values. As a result, Equation (7) can be reduced to Equation (8). In the event that the plant is assumed to have only two mandatory heat exchangers (N
HE = 2) required for the TES system to mount with the CSP plant in an active indirect manner. The unit area of a solar collector is accounted for using a standard solar collector available on the market, resulting in a constant for a chosen CSP configuration. The spacing between collectors varies depending on the solar collector, and therefore, the collector efficiency varies as well. Other factors influencing collector and receiver efficiency mainly include construction geometry and materials. Once the solar collector is chosen for the specific CSP plant, the number of solar collectors required is determined by the available DNI level and the end-use application energy demand. The land requirement for a solar field varies depending on the number of solar collectors, causing plant costs to vary proportionally.
Solar collectors will not capture total incident DNI on the solar field, since collector efficiency is not 100%. To determine the actual energy collected by SPT collectors (P
T), Equation (9), derived from Equations (10) and (11), can be used [
32,
47]. Equation (12) is used for PT plant collectors as other components that affect efficiency are considered under receiver efficiency. Here, DNI is related to the location selected which the current study considers 1000 kWh/m
2/year of the bottom line. A
i is the solar collector area of the i
th collector, θ
i is the angle between the incident solar rays and normal to i
th mirror element, f
sp,i is the spillage factor, f
at,i is the attenuation factor, f
b is the blocking factor, f
sh is the shadowing factor, α
c is the reflectivity, and f
optical is the factor for optical efficiency.
Accordingly, the efficiency of collector in SPT plant can be derived as;
Furthermore, in addition to the cosine factor, f
at,i is critical in SPT plants because as the plant grows larger, the loss increases, and it can be found as follows using Equation (13) or (14) depending on the size of the solar plant, where D is the distance between the solar collector and the focal point of the receiver. The shadowing factor and spillage factor in this study was taken as constant values where more realistic values for these factors can be calculated as per Talebizadeh et al. [
51]. Hussaini et al. conducted a study that considered 0.88 of nominal reflectivity and 0.98 cleanliness over the entire life span, resulting in α
c = 0.84 [
52], considered in collector efficiency estimation in this study.
SPT receiver efficiency (η
receiver) can be calculated as per Equation (15) [
53], while the PT receiving efficiency is directly considered the same as the HTF efficiency. The current study has no consideration of conductive heat transfer loss. Here, q
in,HTF is the solar power transferred to HTF, q
solar incident is the incident solar power on the receiver, and q
loss,receiver is the heat loss in the receiver.
Receiver heat loss mainly consists of two losses, as shown in equation 16: the radiation heat loss (q
rad) and the convection heat loss (q
conv).
Radiation heat loss of the receiver can be calculated as per Equation (17), considering the radiation shape factor of the receiver (SF), which the presented study considered to be SF = 1, the radiative area of the receiver (A
R), the emissivity of the receiver (ε), the Stefan Boltzmann constant (σ = 5.67037442 × 10
−8 kg s
−3 K
−4), the receiver temperature (T
R), and the ambient temperature (T
ambient).
Convection heat loss of the receiver can be found by Equation (18), where h
conv is the convective heat transfer coefficient, which can be calculated by Equation (19), and H
R is the total height of the receiver.
The effectiveness of the receiver determines heat transfer from the receiver to the HTF. Essentially, the efficiency at the receiver is primarily determined by the receiver’s reflectivity and the conduction and convection heat transfer coefficients, which are used to calculate thermal energy loss to the environment. The efficiency of the receiver is also subject to natural degradation over time, and cleanliness is another major parameter that influences these efficiencies. Assuming that this decay is negligible for the lifespan of the CSP plant receiver, it will be treated as a constant value for each configuration, as shown in
Table 5.
The efficiency of the HTF (η
HTF) is primarily determined by environmental factors such as ambient temperature (T
ambient), humidity, and airflow velocity at the geographical location. Despite this, the HTF chosen for the study is solar salt with a chemical composition of 40 wt.% KNO
3+ 60 wt.% NaNO
3 for the PT plant and KCl/MgCl
2/NaCl for the SPT plant is considered under a constant efficiency value, as shown in
Table 5. The TES system is critical in CSP plants for improving overall energy system performance while lowering energy costs. The storage material, container material, insulation, environmental conditions, and geometric configuration of a TES all impact its efficiency. In this study, Equation (20) is used to estimate the efficiency of TES (η
TES) [
54], where E
TES is the energy stored in the TES, q
out,
HTF is thermal energy output from the HTF to TES, and E
loss,TES is the thermal energy loss from TES.
Therefore, the thermal energy loss from the TES can be found by Equation (21), considering the overall heat transfer coefficient (U
TES), heat transfer area of the TES (A
ht), and TES outlet temperature (T
TES).
The heat transfer area of the TES can be then calculated using Equation (22), considering D
TES as the diameter of the TES and H as the height of the TES.
The amount of heat energy that can be stored in SHTES and LHTES is given by the following equations, Equations (23) and (24), respectively, assuming the negligible heat storage in the components inside of TES [
55,
56]. Here, E
SHTES is the amount of heat energy that can be stored in SHTES, m
SHTES is the storage material mass of SHTES, E
LHTES is the amount of heat energy can be stored in LHTES, m
LHTES is the storage material mass of LHTES, C
P is the specific heat capacity of the storage medium of SHTES (Solid or Liquid), C
PS is the specific heat capacity of the storage medium of LHTES in the solid state, C
PL is the specific heat capacity of the storage medium of LHTES in the liquid state, T
melt is the melting temperature of storage medium, H
m is the melting enthalpy of storage medium, a
m is the melting fraction, T
initial is the initial temperature of storage medium, and T
final is the final temperature of storage medium.
In this study, we assumed congruent melting (a
m = 1) of LHTES Phase Change Material (PCM). However, for greater precision, the melting fraction can be calculated using Equation (25) [
57], where V/V
0 is the melted volume fraction, Fo is the Fourier number, Ste is the Stephan number and Ra is the Rayleigh number.
Once the amount of energy required for 6 h of full load operation of the end-use thermal cycle has been determined, the capacity of the TES required to operate the thermal application can be calculated using Equation (26). As a result, the installed CSP plant capacity can be calculated using Equation (27), where CA
TES is the TES capacity, CA
CSP is the CSP plant capacity, and h
OP is the operational hours without the heat source.
The storage material’s energy density determines the size of the TES required to store thermal energy. The energy density of a storage material is the amount of energy that can be stored per unit mass or volume. The storage material’s energy density (ED) can be denoted by Equations (28) and (29) for sensible storage medium and latent storage medium, respectively. Hence, ED
SHM is the energy density of sensible heat storage material, and ED
LHM is the energy density of latent heat storage material.
Accordingly, the TES capacity Equation (26), can be modified to Equation (30).
Accordingly, it is obvious that as the energy density of the storage material increases, the quantity of storage material required to store energy to operate the thermal cycle decreases, resulting in a reduction in the volume of the TES. Reduced TES size lowers TES costs while also providing other advantages such as less space consumption, less pump work, and lower heat losses. However, as the properties of a storage material become more desirable, the material price rises. To select a storage material candidate for TES, careful consideration of material unit price increment and material quantity and container material requirement reduction is required. Once the quantity of storage material (storage medium) is known, the volume of the TES (V
TES) can be calculated using Equation (31). V
storage medium is the storage medium volume. Furthermore, the 36/14 of D
TES/H ratio proposed by Vilella et al. [
56] for cylindrical TES tanks is used in this study as well.
Thus, the volume of the storage medium can be found by Equation (32). Here, ρ
SHTES is the density of the sensible heat storage medium, and ρ
LHTES is the density of the latent heat storage medium, the calculation of which uses density values reported in
Table 6.
The dimensions of the storage tank can thus be determined using Equation (33), with the aforementioned notations.
The discharge time of the TES (D
discharge), specifically, the storage duration (operational hours without the heat source), can be calculated using Equation (34). Here, Q
HTF is the heat transfer rate of HTF.
Q
HTF then can be calculated as per Equation (35), where ṁ
HTF is the HTF mass flow rate, C
P,HTF is the specific heat capacity of the HTF, and T
thermal is the temperature required for thermal cycle operation.
Then, ṁ
HTF can be calculated by Equation (36), where ρ
HTF is the HTF density, A
pipe is the cross-section of the HTF pipe, and ν is the HTF flow velocity.
Incorporating compatible nanoparticles into the storage medium can improve the thermal and physical properties of the storage material. One such property that can be improved to reduce the TES size is energy density. Reducing the size of the TES can lower the overall OPEX and CAPEX of the CSP system. The composite energy density, ED
SHTES, and ED
LHTES for sensible storage material and PCM in LHTES can be calculated using Equations (37) and (38). In this case, C
P,composite is the specific heat capacity of the nanocomposite.
The density of a nanocomposite (ρ
composite) can be calculated using mixture theory using Equation (39) [
58,
59,
60]. Furthermore, the mixing theory holds true for the specific heat capacity of the nanocomposite (C
P,composite), resulting in Equation (40) [
61,
62,
63]. Depending on the requirements, the latent heat of fusion can be calculated numerically using the equations proposed by Pincemin et al. [
64]. In this case, ρ
r is the density of the regular storage material, ρ
n is the density of the nanomaterial, Φ is the nanoparticle concentration, C
P,r is the specific heat capacity of the regular storage medium, and C
P,np is the specific heat capacity of the nanomaterial.
The thermal efficiencies of the selected end-use single-stage thermal cycles (Rankine, Brayton, and combined cycles), η
R, η
B, and η
CC, can be expressed using Equations (41)–(43), assuming a negligible pressure drop and internal reversibility in the thermal cycle. Here, W
out is the work output from the turbine, W
in is the work input by pumps, q
in is the thermal energy from TES, ∆H
1 is the enthalpy variation of steam at condenser heat rejection, ∆H
2 is the enthalpy variation of steam at heat intake, r
p is the pressure ratio of air, and k is the specific heat ratio of air.
Assuming internal reversibility and steady flow behavior;
Therefore, the efficiency of the TES-integrated CSP plant (η
CSP) and the capacity factor (CF) were calculated using Equations (44) and (45), where E
elec, actual is the actual electricity production per year, E
solar is the solar energy received to the CSP plant for a year, and E
elec, theoretical is the theoretical maximum electricity production per year.
7. Conclusions
This paper presents a mathematical model to predict the LCOE variation of TES-integrated CSP power plants for electricity generation. Parabolic trough (PT) and solar power tower (SPT) plant configurations with SHTES and LHTES with the regular storage medium and nano-enhanced storage medium were considered. Rankine cycle, Brayton cycle, and combined power generation cycle were considered for comparison. Altogether, 18 scenarios were treated under the aforementioned combinations. Nine scenarios, scenarios 1 to 6 and 13 to 15, were dedicated to investigating the variation in electricity production costs with regular storage materials. Scenarios 7 to 12 and 16 to 18 were dedicated to evaluating the LCOE variation under nano-enhanced TES materials. Two of the 18 scenarios, i.e., scenario 1, representing parabolic trough (PT), and scenario 13, representing solar power tower (SPT) configurations, were designated as base cases using the USA-based cost details to facilitate the comparison.
Calculations of LCOE, TES contribution for LCOE, CSP plant efficiency, and TES efficiency were performed using the developed mathematical model. The results showed that the LHTES was preferred over the SHTES in terms of the energy generation cost of CSP plants. Moreover, the combined power cycle can improve the overall efficiency of the CSP plant in terms of energy utilization, and LCOE reduction appears to deliver competitive results, especially in SPT plants. Noticeably, the selection of the end-use thermal cycle is heavily influenced by the temperature level that the designated CSP plant can achieve. As a result, this will directly affect the round-trip efficiency of the CSP plant and LCOE.
Furthermore, scenario 15, which consists of SPT configuration with LHTES with regular storage medium to drive combined cycle electricity generation, returned the lowest LCOE of 7.72 ct/kWh and the highest CSP plant efficiency of 22.14% among the first nine scenarios considered. The same combination, but with the storage medium replaced with nano-enhanced material for 100 MW of installed plant capacity (scenario 18), returned a 7.63 ct/kWh minimum LCOE with a 22.70% CSP plant efficiency. Therefore, the incorporation of nano additives into storage materials could improve CSP plant performance while lowering the LCOE. Based on these results, the aforementioned scenarios 18, representing SPT plants, and 10, which shows 9.19 ct/kWh of LCOE and 14.03% CSP plant efficiency, representing PT plants, were chosen for further investigation on LCOE reduction under different DNI conditions.
Work presented in this paper is limited by the PT and SPT configurations with single tank thermocline-type SHTES and LHTES. In fact, some more options are available for CSP plants, such as the thermos-chemical energy storage, two-tank configuration, shell and tube heat exchangers, and cascade TES. More work is underway to evaluate the potential of these options and will be presented in a future communication.