rus
Issue #7/2023
E. A. Ionova
Energy Yield of Multijunction Solar Cells With Allowance for the Latitude Variability of the Spectral Composition Radiation
Energy Yield of Multijunction Solar Cells With Allowance for the Latitude Variability of the Spectral Composition Radiation
DOI: 10.22184/1993-7296.FRos.2023.17.7.516.524
Ioffe Physical-Technical Institute of the Russian Academy of Sciences, Saint-Petersburg, Russia
An energy yield assessment of the multijunction solar cells is proposed with allowance for the total spectral composition of direct solar radiation during the annual period. It is shown that the energy yield ratio of a four-junction solar cell near the equator is 45% in the case of an atmosphere with a low aerosol composition and 44% in the case of an atmosphere with an aerosol filling typical for the urban areas. At a latitude of +30°, the annual energy yield of this solar cell can be 1001 kWh/m2. To calculate the energy yield of installations and photovoltaic modules with such solar cells, this value adjustment is required due to the energy losses caused by the power plant design.
Ioffe Physical-Technical Institute of the Russian Academy of Sciences, Saint-Petersburg, Russia
An energy yield assessment of the multijunction solar cells is proposed with allowance for the total spectral composition of direct solar radiation during the annual period. It is shown that the energy yield ratio of a four-junction solar cell near the equator is 45% in the case of an atmosphere with a low aerosol composition and 44% in the case of an atmosphere with an aerosol filling typical for the urban areas. At a latitude of +30°, the annual energy yield of this solar cell can be 1001 kWh/m2. To calculate the energy yield of installations and photovoltaic modules with such solar cells, this value adjustment is required due to the energy losses caused by the power plant design.
Теги: multijunction solar cell; energy yield; efficiency; air mass; so photovoltaics атмосферная масса кпд многопереходный солнечный элемент солнечная электростанция энерговыработка
Energy Yield of Multijunction Solar Cells With Allowance for the Latitude Variability of the Spectral Composition Radiation
E. A. Ionova
Ioffe Physical-Technical Institute of the Russian Academy of Sciences, Saint-Petersburg, Russia
An energy yield assessment of the multijunction solar cells is proposed with allowance for the total spectral composition of direct solar radiation during the annual period. It is shown that the energy yield ratio of a four-junction solar cell near the equator is 45% in the case of an atmosphere with a low aerosol composition and 44% in the case of an atmosphere with an aerosol filling typical for the urban areas. At a latitude of +30°, the annual energy yield of this solar cell can be 1001 kWh/m2. To calculate the energy yield of installations and photovoltaic modules with such solar cells, this value adjustment is required due to the energy losses caused by the power plant design.
Keywords: multijunction solar cell; energy yield; efficiency; air mass; solar power plant, photovoltaics
Article received: 19.09.2023
Article accepted: 11.10.2023
Introduction
At present, the highest efficiency of solar radiation photoelectric conversion is provided by the solar cells (SCs) based on the A3B5 semiconductor compounds with several active p-n junctions generated for individual parts of the solar spectrum [1]. The evaluation of prospective ground-based application of a solar energy system requires an assessment of its energy yield. The energy yield of multijunction solar cells under consideration is not fully determined by the integral photometric irradiance. Their photocurrent is determined by the smallest photocurrent of individual p-n junctions, so an important role is played by the photon ratio in sections of the solar radiation spectrum belonging to various p-n junctions. However, the spectral composition of ground-level solar radiation is constantly in a state of flux. During the annual period, any spectrum change is associated, first of all, with the axial and orbital Earth’s rotation, leading to the dependence of annual spectral composition of solar radiation on a geographic latitude.
At the current economic and technological point of development, the terrestrial use of multijunction solar cells is justified only when converting solar radiation concentrated with a high multiplicity. In this case, the solar cell is located at the concentrator’s optical focus and the expensive solar cell aperture is replaced by the aperture of a cheap concentrator. An optical system with radiation focusing requires assembly into the concentrating photovoltaic modules that are technologically somewhat more complicated than the solar panels based on the silicon solar cells, and also requires application of the Sun tracking systems. When converting the concentrated solar radiation, the multijunction solar cell efficiency remains at the highest level.
The development feasibility of solar power plants with the multijunction solar cells is determined by their energy yield. The efficiency of solar cells and relevant photovoltaic modules is determined as the ratio of absorbed and generated energy, where the absorbed energy has a standardized spectral distribution (for example, IEC 60904–3). This is a direct solar radiation incident to an area perpendicular to its propagation direction, with an air mass (AM) parameter of 1.5. The paper [2] shows that, in order to assess the operating efficiency of multijunction solar cells and to optimize the solar cell development process with a larger number of p-n junctions, it is important to consider the total ground-based spectral composition of solar radiation. This activity can also be attributed to the study of the existing multijunction solar cells.
The purpose of this work is to develop an energy yield assessment method for the highly efficient multijunction solar cells at various geographical latitudes during the annual period.
1. Influence of the spectral composition of direct solar radiation on the solar cell photocurrent
The article discusses the up-to-date high-performance solar cells with 2, 3, 4, 5 and 6 active p-n junctions and a high-performance silicon solar cell with an HJT structure given in a periodic review with the record-breaking efficiency values for their SC type [1]. Comparison of the indicated solar cells by the energy yield during an annual period is possible provided for the identical Sun tracking. The study of both multijunction solar cells and single-junction solar cells has been performed with the photoconversion analysis of direct solar radiation. To calculate the short-circuit currents, we have used the external quantum efficiency spectra published in [1, 3–6] for SCs with 2, 3, 4, 5, 6 p-n junctions and SCs with HJT-structure, respectively. To calculate energy yield, we have used the values of open-circuit voltage (Uoc) and fill factors of the current-voltage curve (FF) at the concentration ratios at which the declared current record-breaking efficiency values have been established (see table).
During an annual period, the power and spectrum of direct solar radiation (DSR) are primarily determined by the total path through the atmosphere that is based on the variety of the Sun zenith angle values specific for different geographical latitudes. The radiation path in the atmosphere is determined by the air mass (AM) parameter that depends on the zenith angle. In this work this angle is calculated by the formula (Kasten, 1989) [8]. A change in AM from 1 to 6 with a step of 0.01 has been considered. The upper AM limit is due to the fact that when AM > 6 the Sun is located at a height above the horizon of less than 10°. As a rule, this fact is associated with the solar battery shading by the ground-based facilities.
Secondly, the DSR is determined by the aerosol atmospheric content being the main factor in the DSR dispersion in the atmosphere. The aerosol atmospheric composition has both a constant and changing nature, and the first one prevails during the annual period. Two types of atmospheric composition have been considered, namely an atmosphere with the low aerosol turbidity complying with IEC60904-3 (β(500 nm) = 0.084, α1 / α2 = 0.94 / 1.42) [9], and an atmosphere with aerosol turbidity typical for the urban areas, with the aerosol specifications of (β(500 nm) = 0.20 [10], α1 / α2=0.84/1.19 [11]).
The DSR spectra have been determined by the SMARTS2.9.5 program with the adjustment of scattering and absorption calculation function ratios [9]. The spectra have been presented as the number of photons in a wavelength interval with the width of 1 nm crossing an area of 1 × 1 m2 in 1 second (Fig. 1). In the shaded area between the spectra with AM1 and AM6, the arrows show the changes in the photon flux spectral distribution that occur twice a day. The straight arrows indicate a decrease in the maximum point of the AM1 and AM6 spectra during the transition from the first type of atmosphere to the second one. Thus, it has been demonstrated that any changes in the radiation path in the atmosphere have a predominant effect on the DSR spectral composition during the annual period compared to the aerosol filling.
The short circuit currents (Isc) under irradiation with an AM parameter from 1 to 6 have been first calculated separately for each SC p-n junction by multiplying the spectral specification of p-n junction by the solar radiation spectra, after which Isc of the entire solar cell has been isolated based on the minimum Isc value of all active p-n junctions (Fig. 2). In contrast to the single-junction solar cells, the dependences of Isc on the AM of multijunction solar cells may have inflection points on the AM scale, where the minimum Isc value is transferred from one p-n junction to another, when the Sun position is changed. As shown in Fig. 2, for the SCs with 3 or 5 p-n junctions to the left of the inflection point, Isc is determined by the 2nd or 3rd p-n junction, and to the right – by the 1st p-n junction. The numerical values of the Isc (AM) dependence, together with the set of Sun positions above the horizon at a given geographic point, determine the current component of the system’s energy output.
The transition to an atmospheric condition with a large aerosol filling leads to a decrease in Isc and, that is typical only for multijunction solar cells, to a change in the Isc (AM) shape due to the shift of inflection point to the left and a possible change in the p-n junction providing the minimum Isc value. The influence of aerosol turbidity in the spread typical for the difference between an urban area and remoted regions, is shown by the solar cells with 3 and 5 p-n junctions (Fig. 2). The solar cell with 5 p-n junctions demonstrates a smaller decrease in Isc compared to the transparent atmosphere, primarily due to the lower absolute Iscvalues.
2. Positions of the Sun above the horizon during the annual period
The minute-based Sun positions have been determined on the basis of the AM parameter using a publicly available computing unit [12] consisting of the materials (Meeus, 1991) [13]. The selection of a minute as an AM calculation step provides sufficient accuracy in reflecting the nature of AM changes in all regions of the planet. Figure 3 graphically shows that the number of minutes per year with the AM values in an interval with the width of 0.01 differs significantly at various latitudes both in the amount and in the shape of statistical distribution N(AM). For example, for φ = 10, 40, 60°, the average annual AM values in the range of 1–6 are 1.85, 2.21, 2.66, and the total number of radiance minutes with AM 1–6 is 235 · 103, 226 · 103, 191 · 103, respectively. To calculate energy yield at a known latitude, it is convenient to represent the set of Sun positions during an annual period as a set of AM values from 1 to 6 with a step of 0.01 and the number of minutes in which the Sun position is determined by this AM (Fig. 3).
3. Energy yield dependence of the multi junction solar cells on latitude
The feature of the daily and annual Earth’s rotation leads to the statistical distributions of the Sun positions at various latitudes that are constant over the annual period. The annual energy input calculated on the basis of these statistical distributions is a constant value equal to the conditionally maximum irradiance for a given latitude interval, if the atmosphere considered has a composition that ensures a low scattering and absorption level. The first considered atmospheric type complies with this condition, since the atmosphere has an even lower aerosol composition in a small number of geographical locations.
The maximum annual energy yield of SCs in a known latitude interval has been calculated according to the relevant statistical distribution of N(AM) and Isc(AM) for the first type of atmosphere (Fig. 2). The values of Uoc and FF of the current-voltage curve given in the table have been used.
The energy yield ratio (Kw) of SCs was calculated similar to the efficiency as the ratio of the maximum annual energy yield and the maximum annual irradiance. The curvature of the latitude dependence Kw and the reduced Kw value compared to the solar cell efficiency (shown by the dotted line) indicates the influence of the DSR spectral composition during the annual period on the energy yield of multijunction solar cells (Fig. 4). The type of the Kw latitude dependence is determined by the SC structure in terms of its solar spectrum division into the absorption areas by individual p-n junctions. For the considered SCs, the Kw value varies within the latitudinal range within 3 percentage points.
The shape of the latitudinal dependences of the maximum annual SC energy yield actually follows the shape of the latitudinal dependence of the annual energy input with an accuracy of Kw(ϕ) (Fig. 5). The highest values of the maximum annual energy yield at low latitudes are associated with a large contribution to the annual spectral composition of powerful solar radiation with AM from 1 to 1.5. The minima at the latitudes of approximately 70° are related to an increased contribution of unaccounted DSR with an AM greater than 6, and a subsequent increase in the maximum annual energy yield is associated with an increase in the time periods when the Sun does not set below the horizon.
4. Energy yield ratio of solar cells in the second type atmosphere.
In the case of the second type atmosphere typical for the urban area, the energy yield ratio Kw of the solar cells has also been calculated. The Kw ratio is calculated for ϕ from 0° to 90° N, but at the high latitudes the results for the two types of atmospheres are speculative due to the actually particularly transparent atmosphere. Figure 6 shows in the form of a shaded area that when transferring from the first type atmospheric composition to the second one, there is a decrease in Kw that increases with the distance from the equator. At the latitudes around the equator, Kw of multijunction solar cells is less by about 1.5 percentage points, and at a latitude of 30°, Kw of solar cells with 1, 2, …6 p-n junctions is reduced by 0.5, 1.9, 1.3, 2.0, 2.0, 2.5 percentage points, respectively.
The basic reason for the decrease in Kw is that the decrease in incoming energy upon increasing the aerosol turbidity predominantly occurs in the DSR spectral region related to the absorption region of the p-n junction that limits the solar cell photocurrent. However, since the incoming radiation is calculated in a wide range of 280–4 000 nm significantly exceeding the absorption region of this p-n junction, the irradiance is decreased less than the energy yield. In the case of multijunction SCs, an additional reason for the decrease in Kw is the break shift of the p-n junction that limits the SC current, to the left on the AM scale, leading to a decrease in the SC current (Fig. 2).
5. Assessment issue of actual energy generation
The actual electricity generation during the annual period is lower than the limit value described in paragraph 3, due to the fact that either the absorbing and scattering atmospheric properties are enhanced or the direct radiation is completely absent due to shading by the clouds. To assess the actual power generation in the selected area, it is necessary to consider the actual annual energy input. In this case, it is possible to use the available data on the annual energy input of direct solar radiation [14] and use the calculated energy yield ratios. In the regions with high atmospheric seasonality (for example, rainy seasons), the clarification may be required, for which it is necessary to repeat the calculation procedure described in the article with a breakdown by season. The energy yield ratio value can be selected based on the atmospheric aerosol content in the region. Moreover, it is necessary to consider a decrease in the energy yield depending on the type of power plant, due to the optical losses when concentrating the DSR and electrical losses for the solar cell switching.
For example, at a latitude of 30° (in the case of a second type atmosphere throughout the year), a solar cell with 4 p-n junctions has Kwϕ = 42.59% (Fig. 6), and the annual irradiation in relation to the materials [14] is 2 350 kWh / m2. Thus, the annual energy yield of a given solar cell can be estimated as 1 001 kWh / m2 with an accuracy up to the difference between the real atmospheric composition and atmosphere of the second type. The energy yield of the photovoltaic module and the entire power plant with this solar cell will be reduced by the value of about 10–20%, determined by the design parameters of a particular system.
Conclusion
This paper proposes the annual energy yield assessment method for the multijunction photoconverters by the example of solar cells with 1–6 p-n junctions and record-breaking efficiency. It is shown that the annual generation can be estimated on the basis of energy yield ratio that turns out to be lower than the value determined for the AM1.5 spectrum. The energy yield ratio varies depending on the atmosphere aerosol filling.
AUTHOR
Evgenia A. Ionova, research fellow at the Ioffe Physical-Technical Institute of the Russian Academy of Sciences, Saint-Petersburg, Russia, lab. photoelectric converters. Area of interest: concentrator photovoltaics
ORCID ID 0000-0003-2886-6706
E. A. Ionova
Ioffe Physical-Technical Institute of the Russian Academy of Sciences, Saint-Petersburg, Russia
An energy yield assessment of the multijunction solar cells is proposed with allowance for the total spectral composition of direct solar radiation during the annual period. It is shown that the energy yield ratio of a four-junction solar cell near the equator is 45% in the case of an atmosphere with a low aerosol composition and 44% in the case of an atmosphere with an aerosol filling typical for the urban areas. At a latitude of +30°, the annual energy yield of this solar cell can be 1001 kWh/m2. To calculate the energy yield of installations and photovoltaic modules with such solar cells, this value adjustment is required due to the energy losses caused by the power plant design.
Keywords: multijunction solar cell; energy yield; efficiency; air mass; solar power plant, photovoltaics
Article received: 19.09.2023
Article accepted: 11.10.2023
Introduction
At present, the highest efficiency of solar radiation photoelectric conversion is provided by the solar cells (SCs) based on the A3B5 semiconductor compounds with several active p-n junctions generated for individual parts of the solar spectrum [1]. The evaluation of prospective ground-based application of a solar energy system requires an assessment of its energy yield. The energy yield of multijunction solar cells under consideration is not fully determined by the integral photometric irradiance. Their photocurrent is determined by the smallest photocurrent of individual p-n junctions, so an important role is played by the photon ratio in sections of the solar radiation spectrum belonging to various p-n junctions. However, the spectral composition of ground-level solar radiation is constantly in a state of flux. During the annual period, any spectrum change is associated, first of all, with the axial and orbital Earth’s rotation, leading to the dependence of annual spectral composition of solar radiation on a geographic latitude.
At the current economic and technological point of development, the terrestrial use of multijunction solar cells is justified only when converting solar radiation concentrated with a high multiplicity. In this case, the solar cell is located at the concentrator’s optical focus and the expensive solar cell aperture is replaced by the aperture of a cheap concentrator. An optical system with radiation focusing requires assembly into the concentrating photovoltaic modules that are technologically somewhat more complicated than the solar panels based on the silicon solar cells, and also requires application of the Sun tracking systems. When converting the concentrated solar radiation, the multijunction solar cell efficiency remains at the highest level.
The development feasibility of solar power plants with the multijunction solar cells is determined by their energy yield. The efficiency of solar cells and relevant photovoltaic modules is determined as the ratio of absorbed and generated energy, where the absorbed energy has a standardized spectral distribution (for example, IEC 60904–3). This is a direct solar radiation incident to an area perpendicular to its propagation direction, with an air mass (AM) parameter of 1.5. The paper [2] shows that, in order to assess the operating efficiency of multijunction solar cells and to optimize the solar cell development process with a larger number of p-n junctions, it is important to consider the total ground-based spectral composition of solar radiation. This activity can also be attributed to the study of the existing multijunction solar cells.
The purpose of this work is to develop an energy yield assessment method for the highly efficient multijunction solar cells at various geographical latitudes during the annual period.
1. Influence of the spectral composition of direct solar radiation on the solar cell photocurrent
The article discusses the up-to-date high-performance solar cells with 2, 3, 4, 5 and 6 active p-n junctions and a high-performance silicon solar cell with an HJT structure given in a periodic review with the record-breaking efficiency values for their SC type [1]. Comparison of the indicated solar cells by the energy yield during an annual period is possible provided for the identical Sun tracking. The study of both multijunction solar cells and single-junction solar cells has been performed with the photoconversion analysis of direct solar radiation. To calculate the short-circuit currents, we have used the external quantum efficiency spectra published in [1, 3–6] for SCs with 2, 3, 4, 5, 6 p-n junctions and SCs with HJT-structure, respectively. To calculate energy yield, we have used the values of open-circuit voltage (Uoc) and fill factors of the current-voltage curve (FF) at the concentration ratios at which the declared current record-breaking efficiency values have been established (see table).
During an annual period, the power and spectrum of direct solar radiation (DSR) are primarily determined by the total path through the atmosphere that is based on the variety of the Sun zenith angle values specific for different geographical latitudes. The radiation path in the atmosphere is determined by the air mass (AM) parameter that depends on the zenith angle. In this work this angle is calculated by the formula (Kasten, 1989) [8]. A change in AM from 1 to 6 with a step of 0.01 has been considered. The upper AM limit is due to the fact that when AM > 6 the Sun is located at a height above the horizon of less than 10°. As a rule, this fact is associated with the solar battery shading by the ground-based facilities.
Secondly, the DSR is determined by the aerosol atmospheric content being the main factor in the DSR dispersion in the atmosphere. The aerosol atmospheric composition has both a constant and changing nature, and the first one prevails during the annual period. Two types of atmospheric composition have been considered, namely an atmosphere with the low aerosol turbidity complying with IEC60904-3 (β(500 nm) = 0.084, α1 / α2 = 0.94 / 1.42) [9], and an atmosphere with aerosol turbidity typical for the urban areas, with the aerosol specifications of (β(500 nm) = 0.20 [10], α1 / α2=0.84/1.19 [11]).
The DSR spectra have been determined by the SMARTS2.9.5 program with the adjustment of scattering and absorption calculation function ratios [9]. The spectra have been presented as the number of photons in a wavelength interval with the width of 1 nm crossing an area of 1 × 1 m2 in 1 second (Fig. 1). In the shaded area between the spectra with AM1 and AM6, the arrows show the changes in the photon flux spectral distribution that occur twice a day. The straight arrows indicate a decrease in the maximum point of the AM1 and AM6 spectra during the transition from the first type of atmosphere to the second one. Thus, it has been demonstrated that any changes in the radiation path in the atmosphere have a predominant effect on the DSR spectral composition during the annual period compared to the aerosol filling.
The short circuit currents (Isc) under irradiation with an AM parameter from 1 to 6 have been first calculated separately for each SC p-n junction by multiplying the spectral specification of p-n junction by the solar radiation spectra, after which Isc of the entire solar cell has been isolated based on the minimum Isc value of all active p-n junctions (Fig. 2). In contrast to the single-junction solar cells, the dependences of Isc on the AM of multijunction solar cells may have inflection points on the AM scale, where the minimum Isc value is transferred from one p-n junction to another, when the Sun position is changed. As shown in Fig. 2, for the SCs with 3 or 5 p-n junctions to the left of the inflection point, Isc is determined by the 2nd or 3rd p-n junction, and to the right – by the 1st p-n junction. The numerical values of the Isc (AM) dependence, together with the set of Sun positions above the horizon at a given geographic point, determine the current component of the system’s energy output.
The transition to an atmospheric condition with a large aerosol filling leads to a decrease in Isc and, that is typical only for multijunction solar cells, to a change in the Isc (AM) shape due to the shift of inflection point to the left and a possible change in the p-n junction providing the minimum Isc value. The influence of aerosol turbidity in the spread typical for the difference between an urban area and remoted regions, is shown by the solar cells with 3 and 5 p-n junctions (Fig. 2). The solar cell with 5 p-n junctions demonstrates a smaller decrease in Isc compared to the transparent atmosphere, primarily due to the lower absolute Iscvalues.
2. Positions of the Sun above the horizon during the annual period
The minute-based Sun positions have been determined on the basis of the AM parameter using a publicly available computing unit [12] consisting of the materials (Meeus, 1991) [13]. The selection of a minute as an AM calculation step provides sufficient accuracy in reflecting the nature of AM changes in all regions of the planet. Figure 3 graphically shows that the number of minutes per year with the AM values in an interval with the width of 0.01 differs significantly at various latitudes both in the amount and in the shape of statistical distribution N(AM). For example, for φ = 10, 40, 60°, the average annual AM values in the range of 1–6 are 1.85, 2.21, 2.66, and the total number of radiance minutes with AM 1–6 is 235 · 103, 226 · 103, 191 · 103, respectively. To calculate energy yield at a known latitude, it is convenient to represent the set of Sun positions during an annual period as a set of AM values from 1 to 6 with a step of 0.01 and the number of minutes in which the Sun position is determined by this AM (Fig. 3).
3. Energy yield dependence of the multi junction solar cells on latitude
The feature of the daily and annual Earth’s rotation leads to the statistical distributions of the Sun positions at various latitudes that are constant over the annual period. The annual energy input calculated on the basis of these statistical distributions is a constant value equal to the conditionally maximum irradiance for a given latitude interval, if the atmosphere considered has a composition that ensures a low scattering and absorption level. The first considered atmospheric type complies with this condition, since the atmosphere has an even lower aerosol composition in a small number of geographical locations.
The maximum annual energy yield of SCs in a known latitude interval has been calculated according to the relevant statistical distribution of N(AM) and Isc(AM) for the first type of atmosphere (Fig. 2). The values of Uoc and FF of the current-voltage curve given in the table have been used.
The energy yield ratio (Kw) of SCs was calculated similar to the efficiency as the ratio of the maximum annual energy yield and the maximum annual irradiance. The curvature of the latitude dependence Kw and the reduced Kw value compared to the solar cell efficiency (shown by the dotted line) indicates the influence of the DSR spectral composition during the annual period on the energy yield of multijunction solar cells (Fig. 4). The type of the Kw latitude dependence is determined by the SC structure in terms of its solar spectrum division into the absorption areas by individual p-n junctions. For the considered SCs, the Kw value varies within the latitudinal range within 3 percentage points.
The shape of the latitudinal dependences of the maximum annual SC energy yield actually follows the shape of the latitudinal dependence of the annual energy input with an accuracy of Kw(ϕ) (Fig. 5). The highest values of the maximum annual energy yield at low latitudes are associated with a large contribution to the annual spectral composition of powerful solar radiation with AM from 1 to 1.5. The minima at the latitudes of approximately 70° are related to an increased contribution of unaccounted DSR with an AM greater than 6, and a subsequent increase in the maximum annual energy yield is associated with an increase in the time periods when the Sun does not set below the horizon.
4. Energy yield ratio of solar cells in the second type atmosphere.
In the case of the second type atmosphere typical for the urban area, the energy yield ratio Kw of the solar cells has also been calculated. The Kw ratio is calculated for ϕ from 0° to 90° N, but at the high latitudes the results for the two types of atmospheres are speculative due to the actually particularly transparent atmosphere. Figure 6 shows in the form of a shaded area that when transferring from the first type atmospheric composition to the second one, there is a decrease in Kw that increases with the distance from the equator. At the latitudes around the equator, Kw of multijunction solar cells is less by about 1.5 percentage points, and at a latitude of 30°, Kw of solar cells with 1, 2, …6 p-n junctions is reduced by 0.5, 1.9, 1.3, 2.0, 2.0, 2.5 percentage points, respectively.
The basic reason for the decrease in Kw is that the decrease in incoming energy upon increasing the aerosol turbidity predominantly occurs in the DSR spectral region related to the absorption region of the p-n junction that limits the solar cell photocurrent. However, since the incoming radiation is calculated in a wide range of 280–4 000 nm significantly exceeding the absorption region of this p-n junction, the irradiance is decreased less than the energy yield. In the case of multijunction SCs, an additional reason for the decrease in Kw is the break shift of the p-n junction that limits the SC current, to the left on the AM scale, leading to a decrease in the SC current (Fig. 2).
5. Assessment issue of actual energy generation
The actual electricity generation during the annual period is lower than the limit value described in paragraph 3, due to the fact that either the absorbing and scattering atmospheric properties are enhanced or the direct radiation is completely absent due to shading by the clouds. To assess the actual power generation in the selected area, it is necessary to consider the actual annual energy input. In this case, it is possible to use the available data on the annual energy input of direct solar radiation [14] and use the calculated energy yield ratios. In the regions with high atmospheric seasonality (for example, rainy seasons), the clarification may be required, for which it is necessary to repeat the calculation procedure described in the article with a breakdown by season. The energy yield ratio value can be selected based on the atmospheric aerosol content in the region. Moreover, it is necessary to consider a decrease in the energy yield depending on the type of power plant, due to the optical losses when concentrating the DSR and electrical losses for the solar cell switching.
For example, at a latitude of 30° (in the case of a second type atmosphere throughout the year), a solar cell with 4 p-n junctions has Kwϕ = 42.59% (Fig. 6), and the annual irradiation in relation to the materials [14] is 2 350 kWh / m2. Thus, the annual energy yield of a given solar cell can be estimated as 1 001 kWh / m2 with an accuracy up to the difference between the real atmospheric composition and atmosphere of the second type. The energy yield of the photovoltaic module and the entire power plant with this solar cell will be reduced by the value of about 10–20%, determined by the design parameters of a particular system.
Conclusion
This paper proposes the annual energy yield assessment method for the multijunction photoconverters by the example of solar cells with 1–6 p-n junctions and record-breaking efficiency. It is shown that the annual generation can be estimated on the basis of energy yield ratio that turns out to be lower than the value determined for the AM1.5 spectrum. The energy yield ratio varies depending on the atmosphere aerosol filling.
AUTHOR
Evgenia A. Ionova, research fellow at the Ioffe Physical-Technical Institute of the Russian Academy of Sciences, Saint-Petersburg, Russia, lab. photoelectric converters. Area of interest: concentrator photovoltaics
ORCID ID 0000-0003-2886-6706
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