Energy and Exergy Analysis of a Hybrid Photovoltaic–Thermoelectric System with Passive Thermal Management

Abstract

Hybrid photovoltaic (PV) and thermoelectric generator (TEG) systems combine heat and light energy harvesting in a single module by utilizing the entire solar spectrum. This work analyzed the feasibility and performance of a hybrid photovoltaic–thermoelectric generator system with efficient thermal management by integrating heat pipe (HP), radiative cooling (RC), and heat sink (HS) systems. The proposed system effectively reduces the PV operation temperature by evacuating the residual heat used in the TEG system to generate an additional amount of electricity. The remaining heat is evacuated from the TEG’s cold side to the atmosphere using RC and HS systems. This study also analyzed the inclusion of two TEG arrays on both sides of the HP condenser section. This numerical analysis was performed using COMSOL Multiphysics 5.5 software and was validated by previous analysis. The performance was evaluated through an energy and exergy analysis of the TEG and PV systems. Enhancing the thermal management of the hybrid PV-TEG system can increase energy production by 2.4% compared to a PV system operating under the same ambient and solar radiation conditions. Furthermore, if the proposed system includes a second array of TEG modules, the energy production increases by 5.8% compared to the PV system. The exergy analysis shows that the enhancement in the thermal management of the PV operating temperature decreases the thermal exergy efficiency of the proposed system but increases the electricity exergy efficiency. Including TEG modules on both sides of the condenser section of the HP shows the system’s best thermal and electrical performance. These results may be helpful for the optimal design of realistic solar-driven hybrid systems for globally deserted locations.

1. Introduction

Advocacy for environmental protection and the rapid depletion of fossil fuels encouraged the scientific community to develop clean and green energy sources, with solar energy being the most abundant. Solar energy conversion systems are widely used worldwide as an option for providing electricity for commercial, residential, and industrial requirements. Solar photovoltaic (PV) technology is the most relevant solar energy conversion technology, with a global installed capacity of around 709 GW in 2020 [1] and a global generation of 1002.9 TWh in 2022 [2]. However, the widespread use of PV technology has the limitation of efficiently converting solar radiation to electricity. A photovoltaic cell is a semiconductor device that converts a small fraction of solar radiation, approximately 20%, into electricity. The rest of the incoming solar energy is transformed into heat, progressively reducing the PV cell’s conversion efficiency. Several possible solutions have been explored to solve the problem of PV cell temperature increase during its operation. PV cooling solutions can be organized into cooling systems that do not require moving parts (passive) and require moving parts (active). Passive cooling systems usually use natural convection and radiative heat transfer mechanisms.

On the other hand, active cooling systems use forced convection heat transfer mechanisms and need additional energy to move the fluid and mobile parts of the system. The several PV cooling options explored in the literature are passive heat sinks [3], heat pipe (HP) cooling [4,5], natural airflow cooling, water cooling [6,7], phase change materials (PCMs) [8,9], nanofluid cooling [10,11], microchannel [12], liquid immersion or submerging, water impingement [13,14], forced air cooling [15,16], thermoelectric cooling [17,18], and radiative cooling [19].

Apart from the PV cell, there are other devices for harvesting solar energy and converting it into electricity and heat [20,21]. Like a PV cell, a thermoelectric generator (TEG) is a solid-state semiconductor device that converts heat into electricity directly using the Seebeck effect [22]. Very recently, the use of photovoltaic and thermoelectric generators simultaneously has emerged as a promising technology among solar energy conversion technologies. TEGs can recover the waste heat from PV systems by generating electricity, thus increasing the overall conversion efficiency. The unique features of TEG technology are compact, modular, durable, containing no moving parts, noise-free, emission-free, and highly stable. These features make thermoelectric devices more attractive and competitive than other innovative technologies combined with PV systems [23]. Hence, it is a promising route for enhancing the overall performance of the combined photovoltaic–thermoelectric generator (PV-TEG) hybrid system. PV technology can only harvest the ultraviolet and visible portions of the solar spectrum, while thermoelectric technology can extract the heat from the infrared part. Thus, the combined PV-TEG system can harvest a broader range of solar spectrum [24]. However, special care must be taken while designing a PV-TEG hybrid system because of the operating temperature of both units. A PV cell operates efficiently at a lower operating temperature, while a TEG needs a large temperature gradient across its hot and cold junctions for efficient operation.

Several studies have also demonstrated the feasibility of photovoltaic–heat pipe systems for residual heat transfer mechanisms [25,26]. A heat pipe, being an efficient heat transfer device, can evacuate a large quantity of heat with negligible temperature fluctuations. It has the advantage of functioning as a diode, i.e., the heat flow in the heat pipe is unidirectional from the evaporator to the condenser. Heat pipes can effectively transmit the waste heat of a PV cell to the atmosphere. Radiative cooling in the heat pipe condensing process has also been studied. Furthermore, a heat pipe can be integrated with a PV system, allowing the residual heat from the PV to be utilized for further electricity generation by coupling it with a thermoelectric generator system.

Some studies have analyzed integrated photovoltaic–thermoelectric generator–heat pipe (PV-TEG-HP) systems. A numerical model of a hybrid PV-TEG system with and without a flat plate heat pipe was investigated by Shittu et al. [25]. The results depicted that the efficiency of the proposed system was 61.01% and 1.47% higher than the conventional PV-only and PV-TEG systems, respectively, at a solar concentration ratio of 6. A PV-TEG system based on a flat plate microchannel heat pipe was proposed by Li et al. [27]. They developed a mathematical model of the system and evaluated its performance under different ambient conditions. The proposed PV-TEG showed a higher electrical output and economic performance than the conventional PV system. A theoretical investigation of a hybrid PV-TEG-HP system was evaluated by Makki et al. [28]. They developed a mathematical model based on the energy balance within the system to evaluate the performance of the hybrid system and the thermal management of PV cells. The analysis was developed under different ambient conditions, including varying ambient temperature, air velocity, and solar irradiation. The authors suggest this system can be applied in desert climates with important electricity requirements.

Most recently, radiative cooling has been investigated as a potential solution to control the temperature rise in a PV cell. Some studies have verified the capability of radiative cooling technology to reduce the PV temperature during the solar radiation period. Along this line, some system configurations have been verified. The first analyzed approach was modifying the PV surface, replacing the glass surface, or coating the glass surface with an enhanced emissivity material like polydimethylsiloxane (PDMS) [29].

Instead of the various approaches to analyzing the technical feasibility of the integration between PVs and RCs, integrating a heat pipe with a PV module for efficient evacuation of PV residual heat and eventually transferring it to the atmosphere resulted in a maximum reduction in PV temperature.

The present study continues a previously analyzed photovoltaic–heat pipe–thermoelectric generator–radiative cooling system (PHTR) [30], which investigates the performance of this hybrid system under desert climatic conditions. Following the previously published hybrid PHTR system, this study explores two ways to enhance electricity production using the residual heat of the PV system. The first approach includes enhancing the PHTR thermal management by including a heat sink system on the TEG cold side and a radiative cooling system. The second approach includes a second array on the lower condenser section of the heat pipe to enhance the use of the PV remanent heat. A computational model of the proposed PV + HP + TEG + RC + HS (PHTRH system) has been developed and analyzed using COMSOL Multiphysics software. The numerical results of the proposed model have also been validated with previously published results. Furthermore, in this study, we developed an energy and exergy analysis to compare the performance of the different hybrid conversion systems.

2. Materials and Methods

The proposed PHTRH system builds upon the base model published previously [30]. It includes a PV system, a heat pipe, a TEG system, and a radiative cooling layer on top of the TEG system. The PV cell consists of glass on its top, then ethyl vinyl acetate (EVA), silicon cell, and polyester Tedlar layers. The heat pipe consists of copper walls, a porous wick (copper–water), and the vapor core (water). The TEG system is an array of p-type and n-type thermocouples made of Bi₂Te₃, which are electrically connected in a series. The radiative cooling system consists of a silver film and a high-emissivity infrared-emitting material layer applied to the cold side of the TEG system. The heat pipe efficiently transfers excess heat from the PV system to the TEG, where a portion is converted into electricity. The residual heat is then dissipated into the atmosphere through radiative and convective cooling processes. In this configuration, the rear side of the PV module is linked to the evaporator section of the heat pipe, while the hot side of the TEG is connected to its condenser section. The rest of the surfaces of the heat pipe are considered adiabatic.

The PV system captures solar radiation and is modeled using the Radiosity Method for Diffuse-Gray Surfaces (RMDGS). This includes the incoming heat flux, represented by hourly solar radiation, and radiative cooling, which considers the optical properties of the PV surface. The TEG system consists of 625 (1 array) or 1250 (2 arrays) Bi₂Te₃ thermoelectric generator (TEG) modules. The hot side of the TEG is positioned on the condenser zone of the heat pipe, while the cold side is exposed to the environment. The incoming and outgoing heat fluxes at the cold side of the TEG surface are also modeled by applying the Radiosity Method for Diffuse-Gray Surfaces (RMDGS). The modeling of the TEG system is simplified using layers of Bi₂Te₃ and alumina that exhibit the same thermal resistance as that of a standard TEG module composed of various layers, including alumina, Bi₂Te₃, air, and copper. The heat pipe system consists of a flat plate design made of copper and filled with water. The heat pipe is divided into three parts: the evaporation section, the adiabatic section, and the condenser section. Waste heat produced in the photovoltaic silicon layer, the result of the disparity between the solar power absorbed and the electrical power generated, is directed to the evaporation section of the heat pipe.

The wall, wick, and vapor core represent the heat pipe system. The radiative cooler (RC) is positioned above the cold side of the thermoelectric generator (TEG). It is made from an infrared-emitting material, such as a glass–polymer hybrid metamaterial and a silver layer. The RC system employs the Radiosity Method for Diffuse-Gray Surfaces (RMDGS) to model the surface-to-surface radiation. The emissivity values for the photovoltaic (PV) and TEG surfaces and the atmospheric emissivity are detailed in

Table 1. Emissivity values that were used in this study.

Spectral Band (μm)	PV	TEG	Atmospheric
0–2.5	0.90	0.01	0.9
2.5–8	0.85	1.00	0.9
8–13	0.85	1.00	0.2
13–∞	0.85	1.00	1.0

. Additionally, the upper surface of the TEG features enhancements for radiative cooling. This table also presents the atmospheric emissivity for various subsystems used in this study [26].

In this study, we analyzed two modified configurations of the base model to boost the overall performance of the base model system. In these modified configurations, the temperature gradient across the TEG system can be increased by enhancing the heat transfer mechanism from the TEG cold side using a heat sink. The overall energy output can also be improved by using a second array of TEG modules in the condenser zone of the heat pipe (lower side). These configurations are shown in Figure 1a,b. Figure 1a shows the inclusion of a passive heat transfer mechanism at the TEG cold side using an aluminum fin heat sink, i.e., model-1. A radiative cooling surface enhancement is considered in the flat face of each fin. Figure 1b shows the addition of a secondary TEG modules array with an aluminum heat sink in the lower side of the heat pipe condenser section, i.e., model-2, thus using two TEG modules arrays at both faces of the heat pipe condenser section, and aluminum heat sinks are attached to the cold sides of the TEGs. The RC enhancement is only considered in the upper heat sink. In this way, the radiative cooling surface covers the same area related to the base PHTR base model, considering that this surface must be kept parallel to the Earth’s surface. Consequently, the heat sink enhances the cooling due to the more significant surface area added by its vertical walls. Additionally, the high sidewalls of the fins can reduce the absorption of solar radiation in the bottom horizontal surfaces of the heat sink, since those will turn into shadow areas in the hours far apart from noon, consequently enhancing the action of radiative cooling.

Table 2. Aluminum heat sink geometry and thermal conductivity.

Dimensions of the Aluminum Heat Sink (m)	Thermal Conductivity of Aluminum Heat Sink (W/m K)
1 × 1 × 0.05 (length × width × height)	238
100 rectangular fins, each with dimensions of 0.005 × 1 × 0.045

provides the rectangular aluminum fin heat sink (HS) geometry and thermal conductivity.

The individual subsystems of the proposed PHTRH system are modeled and coupled using multiphysics modeling. Some assumptions have been considered:

• Directionally independent emissivity is considered.
• Radiation heat transfer with the sky and convection heat transfer with the atmosphere are assumed at the top surfaces of the PV and HS systems.
• The cross-sectional area for all the PV layers is the same, and all the layers are in direct contact.
• The heat pipe surfaces not in contact with the PV and TEG modules are considered adiabatic.

We used the same boundary conditions and equations previously published in [30] to analyze the PV, TEG, HP, and RC systems. As illustrated in Figure 1a,b, a radiative cooling surface is incorporated on the flat face of each rectangular fin of the heat sink to maintain the radiative cooling principle of the PHTR base system. The heat sink is designed according to the specifications outlined in Table 2. The primary function of the heat sink is to improve heat dissipation on the TEG cold side through convective heat transfer.

The lateral surface area of the heat sink’s vertical walls plays a vital role in enhancing the convection heat transfer, enabling a more efficient transfer of heat through the cold side of the TEG. This research, carried out with a thorough methodology, seeks to assess the impact of integrating a heat sink into the energy and exergy efficiencies of the PHTRH system. Based on the correlations described by Churchill and Chu [31], as shown in Equations (1) and (2), the convective heat transfer coefficient can be estimated for natural convection near a vertical surface and a horizontal surface for both laminar and turbulent flow, respectively, as follows:

$$h=\left\{\begin{array}{c}{\displaystyle \frac{k}{l}}\left(0.68+{\displaystyle \frac{0.67{Ra}_L^{\frac{1}{4}}}{{\left(1+{\left(\frac{0.492k}{\mu C_p}\right)}^{\frac{9}{16}}\right)}^{\frac{4}{9}}}}\right),if{Ra}_L\le {10}^9\\ or\\ {\displaystyle \frac{k}{l}}\left(0.83+{\displaystyle \frac{0.39{Ra}_L^{\frac{1}{6}}}{{\left(1+{\left(\frac{0.492k}{\mu C_p}\right)}^{\frac{9}{16}}\right)}^{\frac{8}{27}}}}\right),if{Ra}_L>{10}^9\end{array}\right\}$$

(1)

$$h=\left\{\begin{array}{c}{\displaystyle \frac{2k}{l}}\left({\displaystyle \frac{0.339{Pr}^{1/3}{Re}_L^{\frac{1}{2}}}{{\left(1+{\left(\frac{0.047}{Pr}\right)}^{\frac{2}{3}}\right)}^{\frac{1}{4}}}}\right),if{Re}_L\le {5\ast 10}^5\\ or\\ {\displaystyle \frac{2k}{l}}{Pr}^{1/3}\left(0.037{Re}_L^{4/5}-871\right),if{Re}_L>{5\ast 10}^5\end{array}\right\}$$

(2)

To further enhance the use of the waste heat of the PV system, a second array of 625 Bi₂Te₃ TEG modules is located on the lower side of the heat pipe condenser section, as shown in Figure 1b. This second TEG modules array has the characteristics shown in

Table 3. Materials, thermal conductivities, and thicknesses of the TEG system [32].

Material	Thermal Conductivity (W/m K)	Thickness (mm)
Alumina	27	1.60
Bi2Te3	1.7 (average)	8.52

and includes a heat sink on its cold side with the characteristics mentioned in Table 2. This heat sink does not consider radiative cooling enhancement, since it does not face the Sun.

The PHTRH models, presented as model-1 and model-2, were compared with the PHTR base model. The comparison included energy and exergy analyses of the three models of the PHTRH system.

The efficiency of the PV and TEG energy conversion systems was analyzed. The PV system included the previous analysis by Skoplaki, E. and Palyvos, J. A. [33] through the following equations:

$$P_{PV}=P_{sun}\ast {\eta }_{PV}$$

(3)

$${\eta }_{PV}={\eta }_{ref}\ast [1-{\beta }_{ref}\left(T_{PV}-T_{ref}\right)]$$

(4)

where η_ref is the PV cell efficiency at 20 °C, β_ref is the slope of η_ref versus the temperature curve, considering a value of 0.0045 °C⁻¹ (β_ref) and 0.2 (η_ref) for the crystalline silicon solar cell. TPV is the PV cell operating temperature, and Tref is the reference PV cell temperature. The PV operating temperature was obtained in the computational model as the average temperature of the Si layer. The TEG system was analyzed using Equations (5)–(8). The TEG conversion efficiency is evaluated using the equations previously analyzed by Montero et al. [22]:

$${\eta }_{TEG}={\displaystyle \frac{P_{TEG}}{Q_{TEG}}}\ast 100$$

(5)

$$P_{TEG}=I_{ml}\ast V_{ml}$$

(6)

$$V_{ml}=-0.00000003{\mathsf{\Delta }T}^3-0.00003241{\mathsf{\Delta }T}^2+0.02732069\mathsf{\Delta }T-0.01757096$$

(7)

$$I_{ml}=-0.00000011{\mathsf{\Delta }T}^3+0.0000036{\mathsf{\Delta }T}^2+0.00564739\mathsf{\Delta }T-0.00270758$$

(8)

where P_TEG and Q_TEG are the TEG power and the heat inlet to the TEG system, respectively. $I_{ml}$ and $V_{ml}$ are the match load electrical intensity and voltage of the TEG system, respectively, and ΔT is the temperature difference between the TEG hot and cold sides, considering a maximum T_hot of 300 °C, a minimum T_cold of 30 °C, and a maximum temperature difference of 270 °C. Q_TEG is obtained in the computational model, and $I_{ml}$ and $V_{ml}$ are evaluated using the polynomial equations obtained using the TEG module datasheet [32].

The exergy analysis included thermal exergy efficiency and electrical exergy efficiency. The exergy efficiency followed the analysis presented by Petela R. [34], Chow T. et al. [35], and Ghasempour et al. [36]. The input exergy was calculated using the following equation:

$${Ex}_{in}=G_{sun}\ast A\ast (1-{\displaystyle \frac{4}{3}}\ast {\displaystyle \frac{T_{amb}}{T_{sun}}}+{\displaystyle \frac{1}{3}}\ast {\left({\displaystyle \frac{T_{amb}}{T_{sun}}}\right)}^4)$$

(9)

where G_sun is the incident solar irradiation, A is the PV area, T_amb is the ambient temperature, and T_sun is the sun temperature (5772 K).

The thermal and electrical exergy were calculated using the following equations:

$${Ex}_{th}=Q_{res}\ast \left(1-{\displaystyle \frac{T_{amb}}{T_{PV}}}\right)$$

(10)

$${Ex}_{el}=P_{PV}+P_{teg}$$

(11)

where Q_res is the heat transfer through the heat pipe, TPV is the PV cell temperature, P_PV is the PV cell power, and P_teg is the thermoelectric generator power.

The thermal and electrical exergy efficiency are calculated through those equations:

$${\xi }_{th}={\displaystyle \frac{{Ex}_{th}}{{Ex}_{in}}}$$

(12)

$${\xi }_{el}={\displaystyle \frac{{Ex}_{el}}{{Ex}_{in}}}$$

(13)

The proposed model is developed and solved using COMSOL Multiphysics 5.6 software with a multiphysics coupling feature. This study consists of heat transfer with radiation of the PV and TEG surfaces and a non-isothermal flow simulation of the heat pipe wick and vapor chamber. In this study, we used the previously validated-based model [30].

The results of the proposed model are validated and compared with published results. The validating process considers three steps.

In the first step, the results of the computational model consisting of the coupled photovoltaic–heat pipe–radiative cooling (PHR) system are validated against those obtained by Ahmed et al. [26]. The root mean squared error (RMSE) between our PHR model and the one developed by Ahmed et al. [26] is 0.12, and the normalized root mean squared error (NRMSE) is 0.8%.

The second step involves validating the PV-only system model (consisting of only a PV module) and comparing our results with the PV system modeled by Ahmed et al. [29]. The proposed PV-only model yields an RMSE value of 0.39 compared to the model developed by Ahmed et al. [29], and the NRMSE is 2%.

In the third step, the TEG model, which was computationally modeled and experimentally validated by the authors in a previous study [22], is considered. The TEG system model is a thermal resistance network of alumina, copper connections, air between the thermoelectric (TE) legs, and n- and p-type Bi₂Te₃ TE legs in the computational model. The thermal resistance is modeled using Bi₂Te₃ and alumina layers, accounting for the resistance of all materials.

3. Results and Discussion

The numerical model of the PHTRH system is modeled in COMSOL Multiphysics. The local climate, including ambient temperature, global horizontal irradiation (GHI), and wind velocity of the Atacama Desert, Chile, has been selected (68.9 W, 22.48 S, 2291 m.a.s. l) [37]. The ambient conditions were selected for January and June, representing the summer and winter seasons. The proposed study considered the daily hours of solar radiation for January and June, as shown in Figure 2a,b, respectively.

The temperature of the PV module in the reference PV-only system (T_{PV, only}) and the PV system (T_PV), TEG hot side (T_H), and TEG cold side (T_C) temperatures in the PHTR base model system for January and June are shown in Figure 3a,b, respectively. The PV-only system does not consider the radiative cooling, thermoelectric generator, and heat pipe systems. For this PV-only system, the maximum PV operating temperature reaches around 50 °C and 32 °C for the summer and winter, respectively. It is a consequence of the low heat dissipation in the PV module by convection heat transfer to the environment; consequently, it depends directly on the PV module surface area and the heat convection coefficient. For the PV module’s upper surface, we consider a relation between the wind velocity v_wind and the convection heat transfer coefficient h_c, following the analysis presented by Duffie and Beckman [38]:

$$h_c=2.8+3v_{wind}$$

(14)

As observed in Figure 3a,b, the PV and TEG cold and hot side temperatures in the PHTR base system follow the climate conditions of the chosen location. The PV and TEG operation temperatures depend on the GHI, ambient temperature, and wind velocity. In Figure 3a, the observed temperatures at 10:00 show their dependence on the wind velocity, which governs the convection heat transfer to the outside environment from the PV and TEG surfaces. The maximum PV operation temperature in the PHTR base system reaches around 42 °C and 29 °C in the summer and winter, respectively. Figure 3a,b also show the dependency of PV operating temperatures on the GHI variation, observing the higher temperatures around noon. At a low GHI, the PV and TEG temperatures are lower than the ambient, which proves the radiative cooling action over the TEG and PV surfaces, thus reducing their temperatures. The efficient heat pipe operation for transmitting heat between the PV and TEG systems is also reflected in their operating temperatures. Finally, a difference in the PV operating temperatures is also observed for extreme ambient conditions (June and January for winter and summer, respectively). The last is a direct consequence of the lower ambient temperature in winter, which enhances the convective heat transfer to the environment. Higher irradiation levels and time are observed in January, positively impacting the PV and TEG systems’ electricity generation.

The PV (in the PHTR base system) and PV-only power and conversion efficiency for January and June are shown in Figure 4a,b, respectively. It is observed that the PV conversion efficiencies in both the PV-only reference system η_PV,only and the PHTR base system η_PV follow the PV operation temperature. Also, the PHTR base system boosted the conversion efficiency and power of the PV-only system. The minimum observed efficiency of the PHTR base system η_PV is around 19.1% and 18% for winter and summer, respectively. The maximum difference between the conversion efficiency of PV-only and the PHTR base system is about 0.3% and 0.8% for winter and summer, respectively. However, the PV power enhancement is not substantial for both months. The average PV power difference is around 0.8 W and 0.9 W for winter and summer, respectively. The enhancement in the PV conversion efficiency due to the inclusion of the RC system depends on the ambient conditions of the selected location. Cloud coverage, air temperature, and wind speed can affect the radiative cooling performance mechanism. As is observed in Figure 2a,b, the wind velocity reaches around 5 m/s in almost all simulated periods, which directly impacts the efficiency of the radiative cooling system. The last is evident in Figure 4a at 10:00, where the wind velocity is almost 1 m/s, causing the PV efficiency to fall to 17.2%. When the RC mechanism is included, the PV efficiency increases to 18.0%, showing the impact of the radiative cooling mechanism. Conversely, when the wind velocity rises to 1 m/s, it effectively maintains convective heat transfer between the PV and TEG surfaces and the surrounding environment, as observed during the remainder of the simulated period.

The TEG power and conversion efficiency in the hybrid system for January and June are presented in Figure 5a,b, respectively. The conversion efficiency is relatively low due to a limited temperature gradient between the TEG hot and cold sides. As the hot and cold side temperatures directly depend on the PV waste heat and the heat transfer to the ambient, enhancing the TEG cold side cooling mechanism is crucial. As illustrated in Figure 5a,b, the power output of the TEG is smaller than that of the PV system for the two analyzed months. Moreover, the maximum conversion efficiencies obtained are 0.048% and 0.021% in the summer and winter, respectively. In the summer, the TEG power output is higher due to increased waste heat transfer from the PV system at elevated solar irradiance levels.

The conversion efficiency of the TEG system can be improved using different thermoelectric materials coupling or enhancing the figure of merit of the Bi₂Te₃ thermoelectric coupling, as analyzed by Han et al. [39]. If the Bi₂Te₃ is doped with CuI/Sn, the figure of merit (ZT) can reach a value of 1.24 instead of 0.1 at 425 K for the doped and pure Bi₂Te₃, respectively. Furthermore, an average ZT value of 1.02 and 0.2 is observed for doped and pure Bi₂Te₃ for the range of 300–525 K. This doped Bi₂Te₃ thermoelectric material can be used in the TEG modules to enhance the energy generation in the TEG system.

Figure 6a,b illustrate the power output and conversion efficiency of the PV module in the PHTR base system and model-1 (Figure 1a) for the January and June months, respectively.

Both figures demonstrate that the modified model’s PV power and conversion efficiency are improved compared to the PHTR base system. The average and maximum increments in PV power of model-1 compared to the PHTR base system are around 3.2 W and 8 W for summer and winter, respectively. Compared to the base model, the average and maximum increments in PV conversion efficiency in the modified model of Figure 1a are around 0.6% and 1.25% for summer and winter, respectively.

Figure 7a,b provide the power output and conversion efficiency of the TEG module in the PHTR base model and model-1 (Figure 1a) for the January and June months, respectively. Model-1 shows that TEG’s power output and conversion efficiency are improved. The average and maximum increments in TEG power of the modified model compared to the base model are around 0.07 W and 0.25 W, respectively, for both analyzed months. The average and maximum increments in TEG conversion efficiency of the modified model compared to the base model are around 0.019% and 0.032%, respectively, for both analyzed months.

Adding a heat sink (HS) in the TEG cold side impacts the conversion efficiency of both PV and TEG systems. For the PV system, the HS located on the TEG cold side mitigates the impact of reduced air velocity over the PV surface. This results in improved thermal regulation and reduces the dip in the efficiency curve by enhancing the residual heat dissipation. In the TEG system, the HS improves the heat transfer from the TEG cold side to the environment by convective air cooling due to the enhancement in the heat transfer area. Consequently, the TEG efficiency curve aligns with the increase in solar radiation throughout the simulation period.

Figure 8a,b display the total power output of the combined PV + TEG in the PHTR base model and model-1 (Figure 1a) for the January and June months, respectively. The average and maximum increments in total power for both analyzed months are around 2 W and 5.9 W, respectively. It is also observed that the power enhancement is higher in summer than in winter due to more solar irradiation. Furthermore, the increment is more significant during noon, following the increment in solar irradiation.

Figure 9a,b show the PV power and conversion efficiency for both modified models of Figure 1a,b. Including the second array of the TEG modules in the lower side of the condensing section of the heat pipe negatively impacts the PV operating temperature and decreases its conversion efficiency. The increment in the PV operation temperature results from the increment in global thermal resistance caused by the inclusion of the second array of the TEG modules. The average and maximum decreases in PV power output in the modified model of Figure 1b compared to the modified model of Figure 1a are around 5.3 W and 11.8 W, respectively. Similarly, the average and maximum decreases in PV conversion efficiency in the modified model of Figure 1b compared to the modified model of Figure 1a are around 0.9% and 1.7%, respectively.

Figure 10a,b present the TEG power and conversion efficiency for both modified models of Figure 1a,b. The average and maximum increments in the TEG power of the modified model of Figure 1b compared to the modified model of Figure 1a are around 8.4 W and 19.3 W, respectively. The average and maximum increments in the TEG conversion efficiency of the modified model of Figure 1b compared to the modified model of Figure 1a are around 0.49% and 0.82%, respectively. The increase in TEG power is attributed to the higher number of TEG modules. It is essential to clarify that the heat sink cooling system only manages the convection heat transfer between the TEG cold side and the environment.

Figure 11a,b show the total power output of the combined PV + TEG in model-1 (Figure 1a) and model-2 (Figure 1b) with an added secondary TEG module for the January and June months. In the modified model of Figure 1b, the TEG power output is improved due to the inclusion of a second TEG array that contributes to boosting the combined PV + TEG power output. Including the second array of TEG modules increases the thermal resistance in the condensing section of the heat pipe. It has two consequences: On the one hand, this increases the PV operation temperature and TEG hot side temperature; on the other hand, increasing the heat dissipation area allows for decreasing the TEG cold side temperature. The last allows us to observe a significant increase in the temperature difference between the TEG hot and cold sides and, consequently, the TEG system efficiency and power. The added TEG modules increase energy production and compensate for the reduced PV energy production due to the increased operating temperature. As observed in Figure 11a,b, the difference in total power output of both modified models increased in the summer compared to the winter because of higher solar radiation.

Figure 12a,b show the energy produced by each system under the climatic conditions of the Atacama Desert for summer and winter, respectively. The following figures also show the increment in each system’s energy production compared to the reference PV-only system. The increment in energy generation of the three proposed systems, including the PHTR base model, model-1, and model-2, with an additional TEG modules array (Double TEG), as compared to the PV-only reference system, are 0.9%, 3.7%, and 7.7%, respectively, for summer and 1%, 2.4%, and 5.8% for winter. As observed, the PV system’s remanent heat can help generate additional electricity using the secondary TEG modules array.

Furthermore, radiative cooling enhances the heat transfer from the TEG system to the ambient. Finally, the results showed that the inclusion of a second TEG system needs an additional cooling system to enhance its conversion efficiency. Including a passive heat transfer system (heat sink) on the TEG cold side further increases electricity generation and controls the temperature of the PV system. Moreover, it has been verified that, under the Atacama Desert climatic conditions of high solar irradiation, ambient temperatures nearly close to the PV-only reference temperature, and air velocities of around 5 m/s, the heat sink, used as an enhanced cooling mechanism in the TEG cold side, helps to improve the energy conversion efficiency of both the PV and TEG systems. The RC system helps maintain the temperature difference between the TEG hot and cold sides during low wind velocity periods, during which the HS cooling system reduces the convection heat transfer to the ambient.

The proposed PV + HP + TEG + RC + HS system can also operate under other worldwide climates. As observed in the simulations under the Atacama Desert climate conditions, January and June correspond to summer and winter, respectively. Summer conditions present a maximum solar irradiation of around 1100 W/m², the ambient temperature reaches an average of 22 °C, and the average wind velocity is 6 m/s. On the other hand, winter conditions show a maximum solar irradiation of 700 W/m², an average ambient temperature of around 18 °C, and an average wind velocity of around 7 m/s. The average solar irradiance that the Earth receives is roughly 1000 W/m², measured under standard conditions. The global average ambient temperature and wind velocity vary significantly worldwide [40]. However, in general terms, it is possible to consider an average ambient temperature of 15 °C [41] and wind velocity of 6.7 m/s [42]. The average cloud cover worldwide is also an environmental condition with high variability. However, it is possible to consider a maximum of 68% [43]. Considering the previous data, the proposed PV + HP + TEG + RC + HS system can operate in other worldwide locations, presenting a good performance in terms of energy generation (associated with solar irradiation) and effective control of the PV operation temperature (associated with the ambient temperature and wind velocity). Nevertheless, lower cloud coverage is a key factor for radiative cooling (RC), and it is necessary to select locations with the lowest average cloud coverage to secure a good performance of the RC system.

Additionally, this study includes an exergy analysis of the hybrid systems that were previously analyzed. Figure 13 shows the thermal and electrical exergy efficiency for all the PHTR hybrid systems analyzed in this study.

The thermal exergy depends on the rate between the ambient and PV cell temperatures, as described in Equation (10). The objective of the PHTRH system is to reduce the PV operation temperature, and, in this case, the thermal exergy efficiency decreases with the enhancement of thermal management and the inclusion of the radiative cooling and heat sink. On the other hand, including a second TEG array increases the PV operation temperature and consequently increases the thermal exergy efficiency of the PHTRH system.

The electrical exergy of the PHTRH system corresponds to its total electricity generation, which is the combined output of the PV and TEG components. As thermal management improves, the PV power output increases, leading to a rise in electrical exergy. However, adding a second array of the TEG modules raises the PV operating temperature, which, in turn, reduces the PV power output. Despite this, the additional TEG modules help compensate for the PV power loss, ultimately enhancing the overall electricity generation of the system.

The thermal and electrical exergy efficiencies are determined by comparing the respective exergy values to the input exergy, which is calculated using Equation (9) and is directly influenced by the ambient temperature. The thermal exergy efficiency is closely tied to the PV operating temperature, decreasing as the temperature rises, as illustrated in Figure 13. The highest thermal efficiency is achieved when the system incorporates the second TEG array, which increases the PV operating temperature. The maximum thermal exergy efficiency daily average reached 3.6%.

The electrical exergy efficiency depends on the electricity generated by the PHTRH system, and as is observed in Figure 13, it increases as the PV and TEG systems increase their power. The daily average electrical exergy efficiency reaches a maximum of 18.7% and a minimum of 17.6% for the PHTRH system with two TEG arrays and the base PHTR system, respectively.

The proposed PHTRH system highlights a critical trade-off between electrical exergy efficiency and thermal exergy efficiency, which is inherent in hybrid photovoltaic–thermoelectric generator (PV-TEG) systems. Electrical exergy efficiency, which measures the useful electrical energy output relative to the total exergy input, is highly sensitive to the operating temperature of the PV module. As demonstrated by Chow et al. [35], reducing the PV operating temperature through enhanced thermal management improves the electrical exergy efficiency, as lower temperatures mitigate the degradation of the PV conversion efficiency. In the proposed system, the integration of heat pipes, radiative cooling, and heat sinks reduces the PV operating temperature by up to 10 °C, leading to an increase in electrical exergy efficiency to a maximum of 18.7%. However, this reduction in PV temperature negatively impacts the thermal exergy efficiency, which is inversely proportional to the PV operating temperature, as described by Petela [34]. Thermal exergy efficiency, which quantifies the useful thermal energy output relative to the total exergy input, decreases as the PV temperature drops, reaching a minimum of 3.6% in the proposed system. This trade-off is further exacerbated by the inclusion of a second TEG array, which increases the PV operating temperature due to the higher thermal resistance but enhances the overall energy production by better utilizing waste heat. While this results in a slight decrease in electrical exergy efficiency, the additional electricity generated by the second TEG array compensates for this loss, demonstrating the system’s ability to balance the trade-offs effectively. The proposed PHTRH system addresses these challenges by optimizing the thermal management strategy, ensuring that the gains in electrical exergy efficiency outweigh the losses in thermal exergy efficiency. This innovative approach not only improves the overall performance of the hybrid system but also provides a sustainable solution for maximizing energy conversion in high-temperature environments such as the Atacama Desert. Furthermore, as highlighted by Ghasempour et al. [36], the integration of advanced thermal management techniques, such as radiative cooling and heat sinks, plays a crucial role in enhancing the exergy performance of hybrid PV-TEG systems, making the proposed PHTRH system a significant advancement in the field.

The use of a PV system, heat pipe, TEG system, and radiative cooling system proposed in the PHTR hybrid system was economically evaluated by Kumar et al. [30], reaching an LCOE between 0.065 USD/kWh and 0.089 USD/kWh, which is smaller than that of a PV without a cooling system. The LCOE is evaluated by dividing the total cost of the construction and operation of the conversion system by the total energy generated; an increment in the energy generation can reduce the LCOE. Considering a TEG cost of 150 USD/kW [23], it will add 469 USD to the global cost of the PV + HP + TEG + RC + HS system, which reaches around 1000 USD, considering the actual LCOE for PV projects is 0.057 USD/kWh [44]. On the other hand, the energy generated by the system will reach around 10,640 kWh for 25 years, considering the project’s useful life. With these considerations, the LCOE for the PV + HP + TEG + RC + HS system reaches around 0.094 USD/kWh, which is close to the upper LCOE limit for a PV + HP + TEG + RC, as reported by Kumar et al. The last demonstrates that the enhancement in the power and energy conversion efficiency compensates for the increment in the hybrid system cost.

The proposed PHTRH system demonstrates significant advancements over conventional photovoltaic–thermoelectric generator (PV-TEG) systems by integrating advanced thermal management techniques. Existing PV-TEG systems, such as those studied by Shittu et al. [25], typically achieve electrical efficiencies of around 15–20% but suffer from high PV operating temperatures, which degrade both the PV and TEG performance. These systems often rely on passive cooling methods, such as natural convection or simple heat sinks, which are insufficient for maintaining optimal temperature gradients across the TEG. For instance, conventional systems using heat pipes (HPs) have shown improved thermal management by efficiently transferring waste heat from PV modules to TEGs, as demonstrated by Li et al. [27]. However, these systems often lack effective cooling mechanisms for the TEG cold side, limiting their overall efficiency. Similarly, systems incorporating radiative cooling (RC), such as those explored by Ahmed et al. [26], have demonstrated the potential to reduce PV temperatures by dissipating heat into the atmosphere. However, without complementary cooling mechanisms like heat sinks, the temperature gradient across the TEG remains suboptimal, restricting electricity generation. Additionally, while heat sinks (HSs) have been used to enhance convective cooling in some PV-TEG systems, their standalone application often fails to achieve significant temperature reductions under high solar irradiance conditions, as noted by Krstic et al. [3]. Furthermore, the concept of a double TEG array has been proposed to utilize waste heat better, but its implementation in conventional systems has been limited by inadequate thermal management, resulting in only marginal improvements in energy production.

In contrast, the proposed PHTRH system addresses these limitations by integrating heat pipes, radiative cooling, and heat sinks into a unified framework. This combination effectively reduces PV operating temperatures by up to 10 °C compared to conventional systems, as demonstrated in similar studies by Ahmed et al. [26]. The inclusion of a second TEG array in the proposed model allows for better utilization of waste heat, increasing the overall energy production by 5.8% compared to standalone PV systems, a significant improvement over the 1–2% gains typically observed in traditional PV-TEG configurations [27]. The use of radiative cooling, as explored by Xuan et al. [19], enhances the system’s ability to dissipate heat passively, reducing the need for energy-intensive active cooling methods. Moreover, integrating a heat sink into the TEG array ensures efficient heat dissipation, maintaining a high temperature gradient across the TEG modules. These innovations collectively result in a more efficient and sustainable hybrid system capable of operating effectively even in high-temperature environments such as the Atacama Desert. The proposed PHTRH system not only overcomes the limitations of conventional PV-TEG systems but also sets a new benchmark for hybrid solar energy conversion technologies.

4. Conclusions

The present study analyzes a hybrid photovoltaic–thermoelectric generator (PV + TEG) system in which different passive cooling technologies thermally control the operating temperature of the PV system. The PV + HP + TEG + RC system (PHTR) is coupled with an additional passive cooling system (heat sink) to enhance the temperature difference between the TEG hot and cold sides and with the inclusion of an additional TEG array in the condenser section of the HP, resulting in a new hybrid system concept: PV + HP + TEG + RC + HS (PHTRH). The following conclusions are drawn from the analysis of the two models of the proposed PHTRH system:

• The heat pipe and radiative cooling system can efficiently remove the waste heat from the PV system, generating additional electricity in a coupled TEG system.
• The radiative cooling allows for a minor temperature difference between the TEG hot and cold sides. In other words, radiative cooling can help remove the PV waste heat but does not significantly improve the conversion efficiency in the TEG system.
• Including heat sink cooling enhances the TEG system’s performance by efficiently removing the waste heat.
• The predominance of each cooling system is associated with the environmental conditions. The radiative cooling system will increase its predominance in clear skies and low wind conditions. On the other hand, a heat sink cooling system can operate better under low environment temperatures and high wind velocity. The heat pipe system can operate under all ambient conditions and efficiently couples the PV and TEG energy conversion systems.
• The PHTR and PHTRH model-1 systems generate around 1% and 3% more electricity than the PV-only system under the studied location’s ambient conditions.
• It is possible to include a second array of the TEG to use a large quantity of PV waste heat. In this case, the PHTRH model-2 system can generate around 7% more electricity than the PV-only system under the ambient conditions of the studied location.
• Under the Atacama Desert ambient conditions of high solar irradiation, an average wind velocity of 5 m/s, and ambient temperature close to the reference PV-only temperature, it is found that all the proposed hybrid systems can control the PV temperature below the reference PV-only system temperature.
• The electrical and thermal exergy efficiencies show an inverse relationship between them. It is a consequence of the PV operation temperature, as the electrical exergy efficiency increases when the PV operation temperature decreases, and the thermal energy efficiency decreases when the PV operation temperature decreases.
• The PV and TEG powers increase with an enhancement in the thermal management of the PHTHR system, meaning a reduction in the PV operating temperature and an increase in the PV waste heat used by the TEG system.
• The heat pipe, radiative cooling, and heat sink are complementary passive heat transfer systems. The heat pipe efficiently removes the PV waste heat, and the heat sink and radiative cooling systems help to increase the energy production in the TEG system.

Extending the present analysis to other locations with less solar irradiation and different ambient conditions is necessary. Additionally, this PHTRH system can be simulated using different PV cells, HP types, TEG modules, and HS geometries and materials to gain a broad understanding of each subsystem’s impact on the overall performance.