The outdoor field test and energy yield model of the four-terminal on Si tandem PV module

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: The outdoor field test of the 4-terminal on Si tandem photovoltaic module (specifically, InGaP/GaAs on Si) was investigated and performance model, considering spectrum change affected by fluctuation of atmospheric parameters, was developed and validated. The 4-terminal on Si tandem photovoltaic module had about 40 % advantage in seasonal performance loss compared with standard InGaP/GaAs/InGaAs 2-terminal tandem photovoltaic module. This advantage is expanded in (subarctic zone) < (temperate zone) < (subtropical zone). The developed and validated model used all-climate spectrum model and considered fluctuation of atmospheric parameters, and can be applied every type of on-Si tandem solar cells.


Introduction
High-efficiency is the typical research target of photovoltaic technology. However, it is also known through field experience and theoretical analysis considering spectrum fluctuation that the photovoltaic system that wins the race of efficiency does not always gain the best yield in the real installation [1][2][3][4].
Currently, Si solar cell has commonly prevailed in the market. The best efficiency of the Si that was confirmed testing laboratories is 26.7% [5], and the theoretical limit is 29.43% [6]. For further improvement of efficiency, multi-junction or tandem configuration is preferred. The idea of multijunction cells was suggested [7] and investigated [8] in the early days of photovoltaic technology. The significant progress was triggered by AlGaAs/GaAs tandem cells with tunnel junctions [9] and metal interconnections [10][11][12]. At that moment, it was predicted that the power-conversion efficiency of multi-junction solar cells would reach close to 30% [13], but this was not fulfilled by difficulties in stable tunnel junctions [14] and defects in the AlGaAs [15]. The break-through was a highperformance, stable tunnel junctions with a double-heterostructure [16]. InGaP was introduced for the top cell [17], and as a result, it was finally achieved to almost 30 % efficiency by a GaInP/GaAs cell [18]. Higher efficiencies have been made with InGaP/GaAs/InGaAs triple-junction cells [19] and with a 5-junction cell [20].
On-Si tandem solar cells use the widely-used Si solar cell as the bottom junction of the tandem solar cell. Because the technology of Si solar cells is well-established, the production cost of the solar cell is expected to reduce, at least, the one to the substrate or the bottom junction [21]. The III-V/Si (III-V on Si) 3-junction and 2-junction tandem solar cells right now exhibit excellent efficiency with 35.9% [22] and 32.8% [22]. The perovskite on Si 2-junction tandem solar cells reached to 28.0% [23]. That of CdZnTe on Si tandem solar cell was 16.8% [24], and GaAs nano-wire on Si tandem solar cell consideration of atmospheric parameters, it is next to impossible to predict the annual energy yield, in other words, it is next to impossible to design the optimal tandem solar cells in yearly energy yield.
Recently, tandem solar cells have been considered for use in non-concentrating applications, out of CPV, including vehicle-integrated photovoltaic (VIPV) and car-roof photovoltaics (PV) [72][73][74][75][76][77][78][79][80][81][82][83][84]. It was thought that most electric vehicles (EV) might be able to run by solar energy using tandem cells on the car roof [1]. The area of the car roof and other car-bodies are limited. Moreover, solar cells cannot be laminated to an undevelopable curved surface of the car body. It is difficult to cover the restricted area of the car-roof surface entirely. Therefore, extremely high performance that can be brought by tandem solar cells is highly required.
The analysis of the spectrum sensitivity on CPV was done in our previous research [85][86]. The calculation and analysis for CPV were more straightforward because we did not have to consider angular effects combined with the mixture of the direct and diffused components of the sunlight. Different from CPV applications that the cell is always perpendiculary illuminated by the sun using a solar tracker, and only utilizes the direct sunlight, the typical application needs to use a diffused component of the sunlight from the sky, ground reflection, and skewed solar rays, with a combination of direct and diffused elements as a function of the sun orientation relative to the solar panel orientation. For an extension to non-concentrating applications, we need to solve the complicated coupling of spectrum and angles ( Table 1). The key parameters are atmospheric parameters that are dependent on each other. For example, different incident angle modifier and different orientation lead to a diverse mixture of direct and diffused sunlight. Table 1. The difference in performance modeling between CPV and standard installation [1]. The outdoor performance of CPV was intensively studied in more than 20 years considering spectrum mismatching problem of the tandem solar cells.

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 only by direct solar irradiance using a 2-axis solar tracker.
Four-terminal (4T) tandem cells were designed so that the output of the Si cell and other top junctions were taken independently, thus robust to the spectrum change. In the case of III-V/Si threejunction solar cells that are frequently considered as an excellent candidate for the high-efficiency solar cells, the output terminal from the top cell comes from two-junction III-V solar cells, and the top two-junction cell is still susceptible to spectrum change. Therefore, a long-term field test of the module using III-V/Si 4T solar cells is essential to the validation of the use of this configuration. Currently, the best efficiency confirmed by the third-party is 33.3% [87].
Other groups of the 4T type tandem cells are partial concentrator cells and 3T tandem cells. The partial concentrator solar cell was first proposed in 2017, using wide-acceptance concentrator optics that selectively concentrate onto the top III-V cells stacked on the larger size Si bottom cell. This type of the tandem solar cell was considered to the application to VIPV [89] and various design method and modeling were invented [90][91][92]. Several prototypes were made [79] and as high as 27.4 % of annual average efficiency was anticipated [78]. 3T type tandem cells are basically connecting one of the terminals of the pairs of two-terminal. This method has an advantage of simplifying the interconnection of the solar cells among the PV module. Several types of the tandem cells, including Ge-based III-V cell [93], polymer type [94], III-V monolithic [95], and III-V on Si [96]. It was also studied advantage of the better spectrum matching operation using this 3T configuration [97].
The background of this study and our motivation are summarized as follows: 1. Tandem solar cells are high-efficiency, and various types of the device structure were studied. On-Si tandem is one of them and it has a distinct advantage of the cost using well-established Si solar cell technology.
2. Regardless of the type of the materials, the annual performance of the tandem solar cells does not perform well by the spectrum mismatching loss. 3. 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 essential role. 4. 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 are demanded. The knowledge in precise spectrum-mismatching modeling in CPV is expanded to the non-concentration standard installation. 5. 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 kind of climate considering atmospheric fluctuation.

Methods
The purpose of our work is to develop an accurate way of predicting the performance of photovoltaic modules using tandem 4T solar cells, considering spectrum variation. The base model of the spectrum is Bird's model [98]. Bird's model only covers the clear sky days, and we expanded it to cover all-climate roughly [99]. This new spectrum model and the response of the tandem module was validated by the long-term (multiple years) measurement of the performance of the module [99].

Device configuration
The fundamental difference of 2T and 4T configuration is that the former one connects entire sub-cells all in series, and the latter divides the circuit into two pieces using two-pairs of output lead, namely, four-terminal ( Figure 1). Each pair of leads can be connected to two independent loads so that each 2T output can be controlled by independent MPPT (maximum power point tracking). There are two advantages. One is less loss in spectrum mismatching because the shorter-wavelength zone and longer-wavelength zone are connected independent loads. Another is more flexibility in the design of the solar cell. In this particular case, the 4T configuration uses Si to the bottom sub-cell and III-V two-junction cell in the top sub-cell. Both sub-cell technologies are well-established, and it is not necessary to consider various constraints of the integration into one-piece (typically monolithic growth) solar cells.

Measurement system
The field test was done at the University of Miyazaki. The details of the measurement setup can be found in our recent publication of Applied Sciences [99], as shown in Figure 2.

4-terminal output
The module with InGaP/GaAs two-junction cell on Si solar cell was provided by SHARP and tested at the University of Miyazaki simultaneously with a 2T three-junction module (InGaP/GaAs/InGaAs). An I-V curve tracer measured the performance of these two PV modules. Pyranometers were placed on 25° (EKO MS-602) and 35° (EKO MS-411) in the slope angle to measure global irradiance. Another pyranometer was installed on a two-axis sun-tracking (EKO MS-602) to measure global normal irradiance. Every 3 minutes, the irradiance of these sensors was captured and logged from 5:30 a.m. to 6:30 p.m. The solar spectrum, specifically the global spectrum on the sloped surface, was measured by the spectro-radiometers (EKO MS-711, MS-712). Their slope angles were 35°. Measurements of the global spectrum were every 10 min from 5:00 a.m. to 8:00 p.m.

Spectrum model
The performance model we used was identical to the one we used to analyze the PV module using the 2T configuration [99]. We called it an MS2E model (Miyazaki Spectrum-to-Energy method). Let us describe a rough flow of the analysis and the model.
First, we need to define the solar spectrum. The spectrum we assumed was a linear combination of the spectrum of the clear sky condition and that of the overcasting state [99]. The spectrum of the overcasting state was assumed that the solar power was lost just by absorption, corrected by the solid angle of the sky influenced by the slope angle of the module. Then, the global solar spectrum is approximated as Equation (1) and Equation (2).
where, is the global spectral irradiance calculated by our spectrum model covering all-weather at a wavelength. The unit of is W/m 2 nm. is the weather correction factor defined by Equation (2), 1 is the global spectral irradiance calculated using Bird's spectrum model [98] at a wavelength. The unit of is W/m 2 nm. 2 is the global spectral irradiance calculated by a spectrum model assuming full cloud covering the sky at a wavelength. The unit of 2 is W/m 2 nm.
is the direct normal irradiance. And, is the direct normal solar spectral at a wavelength. The unit of is W/m 2 nm. The spectrum calculated by this model, with contrast to Bird's model is shown in Figure 3 [99]. 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 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 2-terminal InGaP/GaAs/InGaAs 4-terminal InGaP/GaAs on Si reference AM1.5G spectrum. In the summertime, the aerosol density often drops than that of the standard value, and the precipitable water grows larger. The short-wavelength region of the solar spectrum becomes fat, and the long-wavelength part becomes thin. During the cloudy days, the influence of cloud appears in the short-wavelength part of the solar spectrum so that the longwavelength region drops.  Figure 4 indicates the measured aerosol density and precipitable water by the curve fitting to the measured solar spectrum. The aerosol optical depth was much lower than the standard value used to the calculation of the reference spectrum in summer (Figure 4 (a)). This is why the measured and estimated irradiances in the summertime are high than that of global irradiances (AM 1.5G) at the wavelength range of 450-550 nm. The precipitable water was much higher than the standard value used to the calculation of the reference spectrum in summer (Figure 4 (b)). This is why the measured and estimated irradiance dips are broader than that of global irradiances (AM 1.5G) at the wavelength range of 1350-1450 nm and around 1150 nm.

Performance model
The power output of the module is the product of the short-circuit current, open-circuit voltage, and fill factor (FF). First, FF was calculated by the ratio of the spectrum mismatching. The calculation step is as follows. First, generating a correlation chart between calculated FF and the ratio of mismatching at first using random numbers. Then, the trend curve of these two parameters was fitted to the parabolic. Finally, the FF was represented as the function of the spectrum-mismatching ratio. The short-circuit current can be calculated as the integral of the product of the spectral irradiance and spectral efficiency of the module, which can be derived from the external quantum efficiency affected by spectrum mismatching. The angular characteristics in the photon absorption were measured in advance. The detailed calculation procedure was identical to our previous work [99].
We also needed to consider the coupling between spectrum and angles. The atmospheric parameters are dependent on each other. For example, a combination of the incident angle modifiers and the orientations results in a diverse mixture of the direct and the diffused sunlight. The atmospheric parameters were calculated by the spectrum, by a data-fitting calculation called the Bird's model [100][101] at the University of Miyazaki [102]. The model for this analysis is given in Figure 5 [1]. The nonlinear effect result from distributed effects often seen in III-V (especially concentrator cells) was not considered [103][104][105].

Results
First, we examined our performance model (MS2E model) that could be applied to the PV module using 4T tandem cells. We monitored the module performance in every 3 minutes from 05:30 to 18:30 on January 3, 2019. The slope angle was 35°. The location of the test site at the University of Miyazaki was N31.83°, E131.42°. The result of the measurement and the validation result is shown in Figure 6 and Table 2. The output trend in Figure 6 was decomposed to InGaP/GaAs top cell and Si bottom cell, namely, we applied independent MPPT (maximum power point tracking) search to each pair of the terminals. The predicted output of the 4T tandem module using our MS2E performance model supported by the all-climate spectrum model (Equation (1) and (2)) matched well. It was also shown that the accuracy in prediction of the daily energy yield is within plus or minus 2% of error.

Discussion
It was shown that our MS2E model is sufficiently accurate to discuss the annual and outdoor performance of 4T tandem modules. Next, let us discuss and compare with other types of tandem modules with consideration of regional variations.

Comparison between 4T and 2T configuration
The annual performance of the 4T tandem module was calculated by the validated MS2E model. For comparison robustness to the seasonal spectrum change, it is essential to introduce a normalized scale of the performance, because the area, nominal output, cell type, and power conversion efficiency are different. We used performance ratio PR and the ratio of the performance peak-to-peak Rpp that is defined by Equation (3) and Equation (4).
Note STC means the standard testing condition. PR value given by Equation (3) corresponds to how much power generation performance of the photovoltaic module drops in outdoor operation about the indoor testing result measured by the standard testing condition. Rpp 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 Rpp values were integrated throughout a 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 Rpp was 39.8 % (Figure 7 (a)). 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 7 (b)). 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.
(a) (b) 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 from the difference of behavior between 2T and 4T configuration. Note that this chart is identical to Figure  4 (b) [99]. Table 3. Summary of the outdoor performance of 4T on-Si tandem solar cell and normal 2T threejunction 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
On the other hand, InGaAs bottom cell with 1.0 eV bandgap is affected by the absorption of this band. In 2T configuration, the reduction of absorbed photons in this water band constrains the current output of series-connected entire junctions. In addition to the difference in numbers of terminals (4T or 2T), the difference of the bandgap of the bottom cell affected the degree of the seasonal variation.

Regional difference in the behavior of 4T and 2T performance
The fact that the annual change is affected by water precipitation implies that the gain by 4T configuration may be strongly influenced by the local climate.
With the validation of the MS2E model in the estimation of PV output, we applied it more broadly. The solar database METPV-11 [106][107] has a solar irradiance measurement dataset for more than 800 sites in Japan. We examined the seasonal energy yields in various locations with different climates. For the determination of the atmospheric parameters, measurement data of the solar spectrum are needed. NEDO classified Japan into five different solar radiation climate zones to clarify regional differences in solar irradiation conditions. The global solar spectrum was monitored at five sites, including Naganuma (Subarctic zone), Tosu (Temperate zone), and Okinoerabu (Subtropical zone). We extracted aerosol density and water precipitation in each solar radiation climate zone. Correctly, the aerosol density and water precipitation were derived using a model in Equation (1) and (2) that minimizes the deviation of the global spectrum between the experimental values measured and the values. Note that the estimated global spectrum is a function of the variables aerosol density and water precipitation [99].
The result is shown in Figure 8. From left to right column, transition from the subarctic zone, temperate zone and subtropical zone, water precipitation, that were calculated by optical absorption of the spectrum using the method as mentioned above, increased. The gain of 4T configuration (Rpp value) increased accordingly.

4.3.Further performance improvement
Although the 4T configuration effectively improves the seasonal loss of multi-junction modules, there still is some annual drop. It is because the top cell has two junctions, and its spectrum mismatching drops the output of the top cell.
Further improvement of the mismatching was proposed in several articles. One is fine-tuning of the bandgap energy [108]. The second is enhancing radiative coupling that was shown in the concentrator PV application [109] and non-concentrating application [1]. Tandem solar cells are high-efficiency, and various types of the device structure were studied. On-Si tandem is one of them and it has a distinct advantage of the cost using well-established Si solar cell technology. Regardless of the type of the materials, the annual performance of the tandem solar cells does not perform well by the 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 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 are demanded. The knowledge in 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 kind of climate considering atmospheric fluctuation.

Precipitable water peak value
Many previous studies tried to calculate the spectrum conditions only by airmass and also tried to apply the model that was developed for the clear-sky conditions. The airmass based calculation was proved inaccurate in the intensive investigation to CPV modules using three-junction tandem cells. The lack of all-climate spectrum model was not the issue for the application to CPV, because it only used the direct sunlight. However, for the application to the standard installation (nonconcentration), we must count the energy generation in the partially clear-sky days and cloudy days. A new idea of approximation of the all-climate spectrum model was developed and tried to this study and successfully modeled the energy yield of the tandem cells in all climates.
The advantage of the 4T configuration of the photovoltaic module using a triple-junction solar cell, precisely, InGaP/GaAs on Si solar cell, was compared by conventional 2T triple-junction module, specifically, InGaP/GaAs/InGaAs solar cell. The behavior of seasonal variation of performance and spectrum influence was modeled and validated outdoor measurement.
The annual amplitude of the seasonal peak-to-peak performance ratio improved by about 40 %. This robust performance of the seasonal fluctuation of the solar spectrum is useful to applications to high-performance photovoltaic applications like zero-emission buildings and light-weight aerospace [110]. For the use to the vehicle-integrated photovoltaic, it is also essential to consider 3D Solar Irradiance (modeling [111] and measurement [112]), as well as the performance of the photovoltaic in the curved surface (modeling [113] and the standard [114]).
The seasonal fluctuation of the 2-terminal triple-junction solar is also responsible for seasonal variation of the water precipitation. The above-validated model was expanded to various climate zones. The advantage of 4T on Si configuration increases (subarctic zone) < (temperate zone) < (subtropical zone).
It is important to note that the model we developed and validated is not only applied 4T InGaP/GaAs on Si solar cell, but can be extended to every type of the tandem solar cells in principle, including Perovskite on Si, Perovskite on CIGS, Polymer tandem, III-V tandem regardless of monolithic, wafer-bonding and mechanical stack. It even can be applied the partial concentrator tandem cells [78] and the super-multi-junction solar cells [1].