Comparative analysis of thermoelectric elements optimum geometry between photovoltaic-thermoelectric and solar thermoelectric
Introduction
The demand for electrical power is growing speedily therefore, there is an increased pressure on the existing grids to deliver this power in addition to providing a stable and sustainable supply of electricity [1,2]. In addition, the electrical energy consumption reflects the degree of economic development in a country thus, there is a relationship between economic growth and electric power consumption [3,4]. Fuel consumption and environmental pollution are two important research areas being paid more attention recently due to their direct effect on the living condition of humans [5,6]. Therefore, research on attractive green technologies for use in waste heat recovery, reducing fuel consumption in automobiles and reducing environmental pollution is urgently needed [7]. Thermoelectric generator (TEG) can convert waste heat into electricity directly without noise, pollution and moving parts based on the Seebeck effect [[8], [9], [10]]. It can be used in waste heat recovery in automobiles and for generating electrical power. However, the application of the thermoelectric generator is still limited due to its low conversion efficiency [11]. Nevertheless, with the thermoelectric (TE) material development, the TE demonstrates a broad potential application prospect. This is because the TE efficiency is directly related to its material by a property known as thermoelectric figure of merit. Asides material optimization, geometry optimization is another way to improve the performance of TE devices and thus increase their potential application. Therefore, the geometry design and optimization of TE, and the TE device integration application have been paid more attention to by researchers. A TE device is a solid-state device which is capable of converting waste heat into electrical energy via the Seebeck effect and it is also called a thermoelectric generator (TEG). Therefore, a solar thermoelectric generator (STEG) is simply a thermoelectric generator whose heat source is the solar irradiations from the sunlight. In reality, the STEG can be used to generate electricity thus, they are an attractive green energy solution for standalone power conversion or in hybrid solar systems. In addition, STEG have been used in power generation for health monitoring system, wireless sensors, space applications and several other low power applications. A PV-TE on the other hand is a hybrid device which combines the advantages of the Photovoltaic and thermoelectric generator. Similar to the STEG, the PV-TE can also be used to generate electricity. The overall electrical energy generation of a PV-TE is a combination of the generation from the PV and the TEG individually. In addition, the PV-TE can also be used for powering wireless sensor networks, autonomous medical devices and for terrestrial and space applications.
Sahin et al. [12] theoretically analysed the thermoelectric legs with different geometric configuration, and the results obtained indicated that the variation of the shape parameter has a favourable influence on the device efficiency. Similarly, Al-Merbati et al. [13] presented the effect of pin geometry on TE power generation and found that thermoelectric legs with trapezoidal shape enhance performance. Freunek et al. [14] built a physical model for TEG and geometric optimization was performed which resulted in the finding that Peltier heat influenced the output power of TEG by about 40%. Rezania et al. [15] optimized the TE footprint ratio, and demonstrated that the maximum output and cost-performance are achieved at An/Ap < 1.
Presently, the research on the Photovoltaic-thermoelectric (PV-TE) hybrid device is a growing significantly and has been paid more attention by several researchers because it can produce more electricity due to its wide solar spectrum [[16], [17], [18]]. Van Sark et al. [19] found that the development of new TE materials can lead to efficiency increase of about 50%. Yin et al. [20] used a theoretical analysis method to study a PV-TE system and observed an efficiency increase of about 4.6%. Shittu et al. [21] performed a parametric optimization of TE legs in PV-TE and found that the PV cell influences the PV-TE optimum geometry. Singh et al. [22] studied an irreversible concentrated PV-TE and found that Thomson effect has a negative effect on the performance of hybrid PV-TE and irreversibility increases with increase in concentration ratio. Motiei et al. [23] performed a two dimensional numerical modelling of a hybrid PV-TE device without considering Thomson effect or temperature dependent material properties. The authors observed a PV efficiency and output power enhancement of 0.59% and 5.06% respectively. Yin et al. [24] presented an optimal design method for concentrating photovoltaic-thermoelectric hybrid systems. They calculated the thermoelectric thermal resistance and presented the optimal structure of the thermoelectric generator and the effects of reference efficiency; PV temperature coefficient and thermoelectric figure of merit were studied. The authors found that the overall efficiency of the hybrid PV-TE device could be optimized by calculating the optimal temperature distribution. Babu et al. [25] presented a theoretical analysis of a novel non-concentrated flat plate hybrid PV-TE device using MATLAB/SIMULINK environment. They found that the novel system resulted in the production of 5% additional energy with an increase in the overall efficiency of 6% at standard conditions. Similarly, Lamba et al. [26] also presented a theoretical model for a hybrid PV-TE device based on first and second laws of thermodynamics and MATLAB was used to perform the numerical simulations. They found that the maximum output power and efficiency of the hybrid device increased by 5% compared to the concentrated PV only system. Li et al. analysed the primary constraint conditions for an efficient PV-TE hybrid device and found that PV-TE efficiency increases as thermoelectric leg length reduces [27,28]. Hashim et al. performed the model optimization for TE geometry in a hybrid PV- device and argued that the thermoelectric element dimension in the PV-TE has a significant influence on the overall hybrid device power output [29].
Kossyvakis et al. [30] suggested that thermoelectric devices with shorter legs should be used to obtain increased efficiency from the hybrid PV-TE device when operated under sufficient illumination. Consequently, they argued that this would allow the consumption of less material and in turn reduce the overall system cost. Kraemer et al. [31] also resonated this suggestion thus, shorter thermoelectric materials are beneficial for enhancing the performance of thermoelectric devices. In addition, Chen et al. [32] and Liu et al. [33] also performed an extensive study on the geometry optimization of thermoelectric devices however, there is limited research on the geometry optimization of thermoelectric elements in a hybrid PV-TE device. As a result of the complex relationship between the Photovoltaic and the thermoelectric device, it is imperative to find the optimum geometry for the thermoelectric device in a hybrid PV-TE.
It can be seen from the above review that the PV-TE optimization is different from the TE alone optimization. For example, for TE alone, the aim is to maximize the TE efficiency, but for PV-TE, its total efficiency of PV and TE is a key factor for the optimization. Thus, for PV-TE device, the optimization of TE alone will not be sufficient as the PV cell performance will also influence its overall performance. That means the TE operating at its maximum conversion efficiency will not definitely lead to the maximum electrical efficiency of the PV-TE. In other words, the optimized geometry of TEG may not be suitable for PV-TE optimization.
The geometry optimization includes many aspects, such as TE length, cross-section area, and different shapes etc. At present, TE alone optimization with trapezoidal leg on the efficiency and power output can also be seen in the literatures [12,13], and this is an effective approach to increase the performance of TE alone, and may be a reference for PV-TE optimization. However, because of the different PV cells characteristics, there will be a limitation on the TEG maximum performance. Therefore, the geometry optimization results of STEG cannot be used directly in the PV-TE device as PV-TE needs to balance the PV characteristic and the TEG characteristic. Thus, for the PV-TE optimization, the trapezoidal thermoelectric leg may not be suitable for every type of PV cell it is integrated with. There are a very few researches on the best application of trapezoidal thermoelectric legs in a PV-TE for optimum performance and more so, there are only a handful of research on the comparison of PV-TE and STEG employing trapezoid leg or rectangular leg.
To make up for the above deficiency, this paper introduces two typical trapezoidal shapes for PV-TE. A finite element method is used to study the performance of the hybrid PV-TE device numerically with the aid of COMSOL Multiphysics software. The developed model is verified using published data from literature. Furthermore, the PV-TE with trapezoidal leg and rectangular leg based on two different PV cells are compared, and the PV-TE with the optimum leg geometry integrated with different PV cells is identified. In addition, the optimum thermoelectric geometry for PV-TE and STEG are also compared and the effect of solar irradiation on the optimum geometry is demonstrated. This work will present the optimum geometry for the PV-TE considering the influence of the PV cells and the thermoelectric element. Also, the optimum geometry for STEG will be presented and a comparison between the PV-TE and STEG will be made. This study will provide a valuable basis for the optimization of PV-TE considering the thermoelectric geometry for optimum performance. In addition, the results from this study will be useful to researchers interested in optimizing PV-TE and STEG.
Temperature dependent thermoelectric material properties would be used in this numerical study to avoid errors as the power output and efficiency of the thermoelectric device is affected by the temperature dependency of the thermoelectric material properties [34]. In addition, the resultant shapes (rectangular and trapezoidal) of the thermoelectric geometries studied are chosen and used in the simulations due to their ease of fabrication. In this study, the maximum output power is obtained at matched load condition (i.e. load resistance is equal to internal resistance) and finite element method is used to solve the heat transfer equations. Unlike the numerous researches reviewed above which used MATLAB/SIMULINK, this study uses COMSOL Multiphysics software which is based on the finite element method (FEM) to perform the three-dimensional numerical investigation of the STEG and PV-TE device. A major advantage of the FEM software is that, it allows the coupling of different physical models thus, Multiphysics simulations can be carried out and results can be easily visualized. Furthermore, FEM allows the performance of a detailed investigation which facilitates accurate design decision making due to its capability to allow the realization of optimization efforts. The main of this study is to investigate the optimum geometry of thermoelectric devices in stand-alone solar thermoelectric generators and in hybrid PV-TE devices. A comparative study between the performance of both devices (STEG and PV-TE) is presented and a detailed parametric study is performed to investigate the influence of geometric parameters (leg length, cross sectional area) and environmental parameters (solar radiation, concentration ratio) on the performance of STEG and PV-TE device.
The remaining part of this paper is organised as follows: Section 2 provides the geometry description and mathematical model, Section 3 provides the simulation details and model verification while Section 4 describes the results obtained and analysis of the results. Lastly, Section 5 provides the main conclusions drawn from this study.
Section snippets
Geometry description and mathematical model
The detailed description of the PV-TE and STEG investigated in this study will be presented in this section and the mathematical model used in performing the numerical simulation will also be presented.
Simulation details
COMSOL 5.3 Multiphysics commercial software is used to simulate the PV-TE and the STEG. In this research, two different types of PV cells are used to study the performance of the hybrid PV-TE. For Cell 1, reference efficiency of 10% is used and its temperature coefficient value is 0.001/K; while for Cell 2, reference efficiency of 15% is used and temperature coefficient value is 0.004/K Simulation parameters used for both the PV cells are shown in Table 1. Temperature dependent material
Results and discussion
In this section, the results obtained from the numerical study are presented and a detailed comparison between the PV-TE and STEG is provided under different conditions. Furthermore, the effects of solar radiation and concentration ratio on the performance of both devices (STEG and PV-TE) are discussed.
Conclusion
In this study, the utilization of different thermoelectric leg geometry for the enhancement of PV-TE and STEG performance has been investigated. Three different leg area ratios () resulting in trapezoidal, rectangular and inverted trapezoidal leg geometries respectively were used to study the performance of two PV-TE devices using two different cells and a STEG device. The effects of the PV cell characteristics on the performance of the PV-TE in relation to the different leg
Acknowledgment
This study was sponsored by the Project of EU Marie Curie International incoming Fellowships Program (745614). The authors would also like to express our appreciation for the financial supports from EPSRC (EP/R004684/1) and Innovate UK (TSB 70507–481546) for the Newton Fund - China-UK Research and Innovation Bridges Competition 2015 Project ‘A High Efficiency, Low Cost and Building Integrate-able Solar Photovoltaic/Thermal (PV/T) system for Space Heating, Hot Water and Power Supply’ and
References (47)
- et al.
Long-term electrical energy consumption formulating and forecasting via optimized gene expression programming
Energy
(2017) - et al.
Backtracking search algorithm for solving economic dispatch problems with valve-point effects and multiple fuel options
Energy
(2016) - et al.
Long-term electric energy consumption forecasting via artificial cooperative search algorithm
Energy
(2016) - et al.
Energy performance analysis of a novel solar PVT loop heat pipe employing a microchannel heat pipe evaporator and a PCM triple heat exchanger
Energy
(2019) - et al.
A review of solar photovoltaic-thermoelectric hybrid system for electricity generation
Energy
(2018) - et al.
Recent development and application of thermoelectric generator and cooler
Appl Energy
(2015) - et al.
The thermoelement as thermoelectric power generator: effect of leg geometry on the efficiency and power generation
Energy Convers Manag
(2013) - et al.
Thermodynamics and thermal stress analysis of thermoelectric power generator: influence of pin geometry on device performance
Appl Therm Eng
(2013) - et al.
Parametric optimization of thermoelectric elements footprint for maximum power generation
J Power Sources
(2014) - et al.
Numerical analysis and optimization of a spectrum splitting concentration photovoltaic-thermoelectric hybrid system
Sol Energy
(2012)