Equivalent Circuit Analysis of Photovoltaic-Thermoelectric Hybrid Device with Different TE Module Structure

Combining two different types of solar cells with different absorption bands into a hybrid cell is a very useful method to improve the utilization efficiency of solar energy.The experimental data of dye-sensitized solar cells (DSSCs) and thermoelectric generators (TEG) was simulated by equivalent circuit method, and some parameters of DSSCs were obtained. Then, the equivalent circuit model with the obtained parameters was used to optimize the structure design of photovoltaic(PV-) thermoelectric (TE) hybrid devices. The output power (Pout) first increases to a maximum and then decreases by increasing the TE prism size, and a smaller spacing between p-type prism and n-type prism of a TE p-n junction causes a higher output power of TEG and hybrid device. When the spacing between TE prisms is 15μm and the optimal base side length of TE prism is 40μm, the maximum theoretical efficiency reaches 24.6% according to the equivalent circuit analysis.This workwould give some enlightenment for the development of high-performance PV-TE hybrid devices.


Introduction
Dye-sensitized solar cells (DSSCs) have been widely studied since reported by O'Regan and Grätzel in 1991 [1].They were considered as an alternative to conventional solar cells due to their low cost and high theoretical conversion efficiency [2,3].In a DSSC, a mesoporous semiconductor film is sensitized with organic dye molecules which can absorb sunlight and generate excited electrons.However, typical DSSCs only absorb part of visible and near-infrared light [4] and unabsorbed sunlight wastes as heat, which is one of the main causes of the low experimental conversion efficiency of DSSCs.
In order to improve the conversion efficiency, it may be an effective method to combine two different DSSCs with different range of light absorption into a hybrid cell.Nattestad et al. proposed a novel p-DSSC/n-DSSC hybrid cell, which realized a 2.42% conversion efficiency [5].Yanagida et al. prepared DSSC (N719 dye)/DSSC (black dye) hybrid cells with a power conversion efficiency of 10.6% [6].However, the research that two DSSCs were integrated did not achieve a satisfying high conversion efficiency.Even if for the integrated DSSCs, a considerable part of the sunlight was unabsorbed and converted into heat, so the waste heat utilization of the solar cells should be the key to improve the solar energy utilization efficiency.Actually, our previous work [7] reported a novel method to improve the solar energy conversion efficiency, which is to combine a transparent DSSC, a solar selective absorber (SSA), and a thermoelectric generator (TEG) into a hybrid device, and the novel photovoltaic-thermoelectric (PV-TE) hybrid device achieved a high conversion efficiency of 13.8% [7].However, the problem of matching between the output current or voltage of DSSC and TEG was not taken into account, so the conversion efficiency of PV-TE hybrid device did not reach the best.In this work, the photovoltaicthermoelectric hybrid device is analyzed with an equivalent circuit method.The equivalent circuit method has often been used to analyze solar cells [8] as well as to evaluate DSSCs 2 Advances in Condensed Matter Physics [9][10][11].The relation between the conversion efficiency of the hybrid device and the internal structure of TE module is calculated based on equivalent circuit models.

Modeling of Equivalent Circuit for
DSSCs and TE Modules 2.1.Modeling of Equivalent Circuit for DSSCs.This work analyzed the DSSCs by using an equivalent circuit of a onediode model shown in Figure 1(a) as described in previous reports [11,12], and the equation of the equivalent circuit is written as follows [12]: where  ph is the photocurrent,  0 is the initial current,   is the series resistance,  sh is the parallel resistance,  is the diode factor,  is the elementary electric charge,  is the Boltzmann constant, and  is the temperature.The existing experimental data [7] (AM 1.5G, 100 mW cm −2 ) as the scattered small circles in Figure 2(a) are fitted by using formula (1) and least square method, to calculate some parameters of DSSC, and the fitting curve is shown as the solid line in Figure 2(a).Through the simulation, the values of  0 ,  ph ,   ,  sh , and  for the DSSC are obtained as 20.16 pA, 1.296 mA, 32.08 Ω, 7500 Ω, and 1.427, respectively, which will be necessary for the subsequent analysis of hybrid devices.

Modeling of Equivalent Circuit for TE Modules.
A thermoelectric generator (TEG) with simple structure can be regarded as a steady voltage source in series with internal resistance [13,14].The equivalent circuit of the TEG was shown in Figure 1(b).The output current () and the resistance of the TE generator ( TE ) could be calculated using the following [13]: where  is the Seebeck coefficient,  ℎ is the hot-side temperature,   is the cold-side temperature,  TE is the thermoelectric material resistance,   ,   ,   , and   , respectively, represent the length and the area of n-type thermoelectric material and the p-type thermoelectric material,   and   are the conductivity of n-type thermoelectric material and p-type thermoelectric material, respectively, and  is the number of p-n junctions in TEG.All the TE p-n junctions are square prisms in the same size as shown in Figure 3; that is,   =   =  and   =   =  =  2 , where  is the base side length of p-type prism or n-type prism in a p-n junction.Then, (3) can be simplified into (4).Consider Here, the n-type and the p-type thermoelectric material stay the same; namely,   and   remain unchanged, so (4) can be further simplified to be as follows: where   is defined as effective conductivity according to the following: Equations ( 2) and ( 4) are used to fit the existing experimental data by least square method to calculate some parameters of TEG as follows:   = 5.25 * 10 4 Sm −1 and  = 0.222 mV K −1 , which will be necessary for the subsequent analysis of hybrid devices.The - curves of both experimental and fitting data are shown in Figure 2(b).The fitting curve is slightly higher than the experimental curve for the reason that the fitting calculation reckons without contact resistance of the TE modules.

Equivalent Circuit Analysis of PV-TE Hybrid Devices.
In the hybrid device, the DSSC and TEG are connected in series.The equivalent circuit of the hybrid device is shown in Figure 1(c).According to the nature of the series, the current and the voltage in the hybrid device comply with the following formula: where  DSSC and  TE are the output current through the DSSC and TEG, respectively, and  DSSC and  TEG are the output voltage of the DSSC and TEG, respectively.The - relationship of the hybrid device can be expressed as (8), which can be obtained by simultaneous equations (1), ( 2), ( 4), (5), and (6).Consider where Δ =  ℎ −   and  =   +  TE .Figure 2(c) shows the - curves of the experimental and the fitting results of the PV-TE hybrid device, where fitting calculation ignores the wire resistance and contact resistance, and thus the fitting short-circuit current is slightly larger than the experimental result.

Improvement of PV-TE Hybrid Device with Different TE Module Structure
As for the PV-TE hybrid devices, it is difficult to improve the efficiency of DSSC and the performance of the TE materials.Relatively, changing the structure of TE modules is easy to implement.The effect of the size of the TE modules on the efficiency of the hybrid device is analyzed on the basis of the above calculated results, to determine the best size of the TE modules.The results of calculation can greatly facilitate the experimental procedure.The above calculation is to fit the experimental data, which verified the feasibility of the calculation method and determined some parameters required in the optimization process.The following optimization calculation assumes that the temperature difference (Δ) between the two sides of TEG is fixed at 6 K with the same effective gross lighting area.The optimization calculation is to change the output properties of TEG by changing the size of TE modules and to better match the outputs of DSSC. Figure 3 shows the top view of the TE p-n junctions array.The number of p-n junctions changes with the TE p-n junction's sectional area and spacing between p-type prism and n-type prism in a TE p-n junction prism, which can be expressed as follows: where  is the effective area of TEG (here, it is 6.25 mm 2 ),  is the base side length of TE prism, and  is the spacing between p-type prism and n-type prism of a TE p-n junction, as shown in Figure 3.When  or  of TE p-n junction decreased and the total effective area of TEG remains unchanged, the number of p-n junctions increases.As a result, the output power of TEG increases, but it is also accompanied with the internal resistance of TEG increasing, which would decrease the TEG's short-circuit current.The structure for the best performance of each component may not be consistent with that for the optimal efficiency of the whole hybrid device, which means that it is infeasible to get an optimal hybrid cell by simply combining an optimal DSSC and an optimal TEG.Comprehensive evaluation of these two factors is necessary to find an optimal solution of the area and space of TE p-n junctions and, consequently, to obtain the optimal properties of the PV-TE hybrid devices.It is possible to further improve the efficiency of the PV-TE hybrid devices in our previous work as reported in [7] by optimizing the design of internal structure parameters in the TE modules to make a good match between the outputs of PV cells and TEG.
A series model of the PV-TE hybrid devices is designed as shown in Figure 1(c), in accordance with our previous experimental structure of hybrid devices [7]. Figure 4 shows the effects of internal structure parameters in the TE modules on the output power ( out ) of hybrid cell with a limited total effective area.The output power ( out ) first increases to a maximum and then decreases by increasing the TE prism size . Figure 5 shows the - curves of TEG, DSSC, and hybrid cell under simulated AM 1.5 solar spectrum irradiation at 100 mW cm −2 .When  is 30 m, the optimal TE prism size  is 42 m and the maximum output power is 1.185 mW with Advances in Condensed Matter Physics  a corresponding photoelectric conversion efficiency of the PV-TE hybrid device 18.96% as shown in Figure 5(a).This result is better than our previous experimental result [7].If  is reduced to 15 m, the optimum  is 40 m and the optimum output power reaches 1.389 mW with the corresponding efficiency 24.6% as shown in Figure 5(b), which is higher than that of the hybrid device with  = 30 m.When  decreases from 30 m to 15 m, the TEG can accommodate more TE pn junctions, which converts more thermal energy into electric energy resulting in a higher efficiency.It can be expected that a smaller  would cause a higher output power of TEG, but it would increase the difficulty of processing.

Conclusions
In summary, the photovoltaic-thermoelectric hybrid device is analyzed by the equivalent circuit method, and the internal structure size effect of TE modules on the properties of hybrid devices is investigated.Our preliminary simulational results demonstrate that the PV-TE hybrid device is anticipated for a much higher solar energy utilization efficiency than our previously reported experimental results by optimizing internal structure sizes of TE modules.When the spacing between TE prisms is 15 m and the optimal base side length of TE prism is 40 m, the maximum theoretical efficiency reaches 24.6% according to the equivalent circuit analysis.This work gives some good enlightenment for the development of high-performance PV-TE hybrid devices.Meanwhile, this work fixes the temperature difference between the two sides of TEG and reckons without contact resistance of the TE modules in order to simplify the calculation, so there is still considerable room for further improvement of the hybrid devices and more efforts should be made to the simulational and experimental research on the high-performance PV-TE hybrid system.

Figure 2 :
Figure 2: The experimental and fitting - curves of (a) single DSSC, (b) single TE, (c) series DSSC, and TE hybrid device.

Figure 3 :Figure 4 :Figure 5 :
Figure 3: The top view of the TE p-n junctions array schematic diagram.