# The Outdoor Field Test and Energy Yield Model of the Four-Terminal on Si Tandem PV Module

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## Abstract

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## Featured Application

**This technology is expected to be applied to high-performance photovoltaic applications like zero-emission buildings, light-weight aerospace, and possibly, vehicle-integrated photovoltaic.**

## Abstract

## 1. Introduction

- Tandem solar cells are highly efficient, and various types of the device structure were studied. On-Si tandem is one of them, and it has a distinct advantage of cost, using well-established Si solar cell technology.
- Regardless of the type of material, the annual performance of the tandem solar cells does not perform well due to spectrum mismatching loss.
- The modeling of the spectrum mismatching loss was studied relying on the airmass variation. The intensive study on CPV performance in more than 20 years revealed that the fluctuation of atmospheric parameters played an essential role.
- Due to the development of the new application of the high-efficiency solar cell, including vehicle-integrated solar cells, the precise annual energy yield modeling of the tandem solar cells is required. The knowledge on precise spectrum-mismatching modeling in CPV is expanded to the non-concentration standard installation.
- 4T on Si tandem solar cell is a good candidate for the robustness to the spectrum variation. Its outdoor operation and energy yield modeling was intensively studied in this article. The model did not rely only on airmass but considered real fluctuation of the spectrum in all kinds of climate, considering atmospheric fluctuation.

## 2. Methods

#### 2.1. Device Configuration

#### 2.2. Measurement System

#### 2.3. Spectrum Model

^{2}nm. $f$ is the weather correction factor defined by Equation (2), ${I}_{1\lambda}$ is the global spectral irradiance calculated using Bird’s spectrum model [96] at a wavelength. The unit of $f$ is W/m

^{2}nm. ${I}_{2\lambda}$ is the global spectral irradiance calculated by a spectrum model assuming full cloud covering the sky at a wavelength. The unit of ${I}_{2\lambda}$ is W/m

^{2}nm. $DNI$ is the direct normal irradiance, and ${I}_{d\lambda}$ is the direct normal solar spectral at a wavelength. The unit of ${I}_{d\lambda}$ is W/m

^{2}nm. The spectrum calculated by this model, in contrast to Bird’s model, is shown in Figure 3 [97]. Note that the Bird’s spectrum model was improved by considering atmospheric parameter variability. The Y-axis corresponds to the normalized global spectrum irradiance by integrated spectral irradiance. The black trend line is the measured and normalized global solar spectral irradiance. The gray trend line is the reference spectrum in AM 1.5G. The red trend line and the blue trend line are the calculated global solar spectral irradiance by the MS2E method. Note that Bird’s model only considers air mass, namely, the atmospheric parameters are constant. In the wintertime, atmospheric parameters are close to those under the standard conditions, so that the estimated solar spectrum approaches to the reference AM1.5G spectrum. In the summertime, the aerosol density often drops lower than that of the standard value, and the precipitable water grows larger. The short-wavelength region of the solar spectrum becomes thick, and the long-wavelength part becomes thin. During cloudy days, the influence of cloud appears in the short-wavelength part of the solar spectrum so that the long-wavelength region drops.

#### 2.4. Performance Model

## 3. Results

## 4. Discussion

#### 4.1. Comparison Between 4T and 2T Configuration

_{pp}, which are defined by Equations (3) and (4).

_{pp}value given by Equation (4) corresponds to the degree of suppression of the seasonal variation of performance of 4T configuration relative to standard 2T configuration. Both PR and R

_{pp}values were integrated throughout the day, and their daily trend was plotted in time series. The result with contrast to 2T configuration is shown in Figure 6 and Table 3. Note that the peak-to-peak value of the PR variation of 4T configuration was 0.084, and that of 2T was 0.139. The degree of improvement of seasonal variation R

_{pp}was 39.8% (Figure 7a). As a result, the annual energy yield per nominal power of 4T configuration increased to 1500 kWh/kW, and that of 2T was 1442 kWh/kW (Table 3). The improvement was mainly seen in the summer. It corresponded to the variation of water precipitation (Figure 7b). The bandgap of the bottom cell of Si is 1.11 eV, and the absorption edge is 1100 nm so that the performance of the Si bottom cell would not be affected by the water absorption typically seen in around 1200 nm.

#### 4.2. Regional Difference in the Behavior of 4T and 2T Performance

_{pp}value) increased accordingly.

#### 4.3. Further Performance Improvement

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Measured 4-terminal (4T) III-V/Si module and its solar cell structure: (

**a**) Description of 2-terminal (2T) III-V 3-junction module; (

**b**) Description of measured 4T III-V/Si module, 2 + 1 junctions. Note that the number of junctions is the same.

**Figure 2.**Measured 4T III-V/Si module and its solar cell structure: (

**a**) Description of measured 4T III-V/Si module, 2 + 1 junctions (right) with comparison to the 2-terminal III-V 3-junction module. Note that the number of junctions is the same; (

**b**) Spectro-radiometers [97].

**Figure 3.**Comparison with measured and estimated values (Bird’s model and Miyazaki Spectrum-to-Energy (MS2E) model) of global irradiances tilted at 35° [97]: (

**a**) Solar spectrum in the sunny day in winter; (

**b**) Solar spectrum in the sunny day in summer; (

**c**) Solar spectrum in the cloudy day in winter; (

**d**) Solar spectrum in the cloudy day in summer.

**Figure 4.**Seasonal trend of atmospheric parameters in Miyazaki [97]: (

**a**) Seasonal trend of aerosol optical depth; (

**b**) Seasonal trend of precipitable water.

**Figure 5.**The performance model of the tandem solar cells, considering the spectrum and angle interaction [1].

**Figure 6.**Validation of the performance model (MS2E model) to 4T tandem module, decomposing performance in each output terminal (InGaP/GaAs top cell and Si bottom cell).

**Figure 7.**Comparison of the annual output between 4T configuration and 2T configuration affected by the variation of the atmospheric parameter: (

**a**) Predicted seasonal fluctuation of the normalized energy yield of 4T (red and solid line) and 2T (black and dashed line) configuration; (

**b**) Seasonal variation of precipitable water (optical depth) in our measurement that is likely to be responsible for the difference of behavior between 2T and 4T configuration. Note that this chart is identical to Figure 4b [99].

**Figure 8.**Comparison of the annual output between 4T configuration and 2T configuration affected by the variation of the atmospheric parameter. The red solid trend line in the bottom charts corresponds to the normalized energy yield of 4T, and the black dashed trend line corresponds to that of 2T configuration.

**Table 1.**The difference in performance modeling between concentrator photovoltaic (CPV) and standard installation [1]. The outdoor performance of CPV was intensively studied in more than 20 years considering the spectrum mismatching problem of the tandem solar cells.

CPV ^{1} | Normal Installation | |
---|---|---|

Solar spectrum | Only direct | A mixture of direct, diffused from the sky, and reflection |

Angle | Always normal | Varies by time and seasons |

Spectrum by angle | Constant (only normal) | Needs consider coupling to angle |

^{1}It only generates power by direct solar irradiance using a 2-axis solar tracker.

**Table 2.**Comparison between measured and estimated (predicted by MS2E model) energy yield in a day (3 January 2019).

Measured | Estimated | Error | |
---|---|---|---|

InGaP/GaAs on Si ^{1} | 39.6 Wh | 40.4 Wh | 1.9% |

InGaP/GaAs | 28.0 Wh | 28.9 Wh | 3.4% |

Si | 11.6 Wh | 11.4 Wh | 1.9% |

^{1}4T configuration independently takes the output from the top and bottom cells; the production of the InGaP/GaAs on Si module is a simple sum from the InGaP/GaAs top layer and Si bottom layer.

**Table 3.**Summary of the outdoor performance of 4T on-Si tandem solar cell and normal 2T three-junction tandem solar cell.

PR Peak-to-Peak Value | Annual Energy Yields (kWh/kW) | |
---|---|---|

InGaP/GaAs on Si ^{1}(4-terminal configuration) | 0.084 | 1500 |

InGaP/GaAs/InGaAs (2-terminal configuration) | 0.139 | 1442 |

^{1}4T configuration independently takes the output from the top and bottom cells; the production of the InGaP/GaAs on Si module is a simple sum from the InGaP/GaAs top layer and Si bottom layer.

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**MDPI and ACS Style**

Araki, K.; Tawa, H.; Saiki, H.; Ota, Y.; Nishioka, K.; Yamaguchi, M.
The Outdoor Field Test and Energy Yield Model of the Four-Terminal on Si Tandem PV Module. *Appl. Sci.* **2020**, *10*, 2529.
https://doi.org/10.3390/app10072529

**AMA Style**

Araki K, Tawa H, Saiki H, Ota Y, Nishioka K, Yamaguchi M.
The Outdoor Field Test and Energy Yield Model of the Four-Terminal on Si Tandem PV Module. *Applied Sciences*. 2020; 10(7):2529.
https://doi.org/10.3390/app10072529

**Chicago/Turabian Style**

Araki, Kenji, Hiroki Tawa, Hiromu Saiki, Yasuyuki Ota, Kensuke Nishioka, and Masafumi Yamaguchi.
2020. "The Outdoor Field Test and Energy Yield Model of the Four-Terminal on Si Tandem PV Module" *Applied Sciences* 10, no. 7: 2529.
https://doi.org/10.3390/app10072529