# Spectral Factor of Colored Solar Cells: A Case Study on the Main Urban Areas in Romania

Authors: Sergiu-Mihai Hategan; Marius Paulescu
Journal: International Journal of Photoenergy
 (2022)

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## Abstract

PV modules for Building-Integrated Photovoltaic (BIPV) applications are made of different colors aimed at raising the visual aesthetic of the building. But a colored coating applied to the surface of a basic PV module is inherently associated to a decrease in conversion efficiency. From a different perspective, the efficiency of a PV module is evaluated under the industry standard test conditions (STC). Due to spectral mismatch, the efficiency of a PV module operating in outdoor conditions may substantially differ from the standard value evaluated at STC. In this study, the influence of spectral solar irradiance distribution on the colored PV module efficiency is evaluated in terms of spectral factor (SF). SF quantifies the relative power gain or loss caused by the spectral difference from STC. The theory is illustrated with a case study on the main four urban areas in Romania. The actual solar radiation spectrum is estimated with the simple Leckner spectral solar irradiance model, based on atmospheric parameters retrieved from the Aerosol Robotic Network (AERONET). The results emphasize that the aesthetic of BIPV comes at a high energy cost: depending on the color, a coating applied on the surface of a crystalline silicon PV module may reduce its conversion efficiency even by half.


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## Body

## 1. Introduction

Building-Integrated Photovoltaics (BIPV) generically define the class of photovoltaic (PV) modules and systems that can replace conventional building components (e.g., roofs, facades, and windows). BIPV appears as a powerful and versatile tool for accomplishing the increasing demand for zero-energy buildings [1]. BIPV must comply with both electrical and construction conditions for performance and safety. Currently, the PV modules for BIPV applications are made of different shapes, colors, and textures aimed at raising the visual look of the building (see, e.g., [2]). PV modules used to replace windows present different degrees of transparency. Such features inherently reduce the PV conversion efficiency. Instead, these features offer the possibility to increase the visual acceptance and architectural flexibility of BIPV systems. Current reviews emphasize the progress of BIPV technologies aimed at meeting the architectural needs [3].There are two options for the integration of PV modules in buildings. (1) Preserving the PV module appearance and using them as a design element: this option is associated with the early history of BIPV. (2) Hiding PV modules in the building envelope: this is the predominant option nowadays. In this case, the solar cells are native uniformly colored [4] or covered by a colored layer [5]. However, altering the surface of a standard PV module may lead to a decrease in its electrical efficiency. The cause is the absorption of solar radiation by the color layer in the spectral range in which the solar cells operate. For example, Ref. [6] presents a comparison of the two approaches in the case of perovskite solar cells. These approaches used to modulate the perovskite solar cell color appearance are as follows: the first one is based on the adjustment of the cell’s internal layers (i.e., absorber and electrodes), while the second is based on the addition of external colored or nanostructured layers to the standard perovskite solar cell. For more inside colored PV modules and options for BIPV design, we point the reader to [2].Like any PV module, colored PV modules have to deal with spectral mismatch in real operating conditions. The efficiency of commercial photovoltaic (PV) modules is evaluated under the industry standard test conditions (STC) (in plane solar irradiance of 1000 W/m2 with a spectral distribution AM1.5G and a cell temperature of 25°C [7]). Since the PV modules operate normally in outdoor conditions, where the spectrum of the incident solar radiation very rarely matches the AM1.5G spectral distribution, the efficiency of PV modules may be different from the specification at STC [8]. In order to describe the relative performance of a PV module operating under an arbitrary solar spectrum (outdoor conditions) with respect to AM1.5G spectrum, the International Electrotechnical Commission (IEC) recommends the spectral factor (SF) [9]. Basically, SF estimates the gain or loss in efficiency for a specific PV module, due to the difference between the actual solar radiation spectrum and the STC spectrum. SF is defined in the next section. Only a few of the current studies on the changes in solar radiation spectrum are conducted on the basis of measured spectra. Such observational data are rarely available [10], mainly because the spectral measurements are complicated and expensive. As an effective alternative, computer simulations of solar spectra in the real atmosphere are used instead of measurements (e.g., [10]).In this paper, the influence of spectral solar irradiance distribution on the efficiency of the colored PV modules efficiency is evaluated in terms of spectral factor. The theory is illustrated with a case study on the main four urban areas in Romania: Bucharest (44°21′N, 26°17′E, 89 masl), Cluj (46°46′N, 23°33′E, 405 masl), Iasi (47°45′N, 27°33′E, 175 masl), and Timisoara (45°46′N, 21°25′E, 85 masl). Four hypothetical PV generators of different colors (red, green, blue, and white) based on the technology proposed in [5] have been considered. In order to conduct the study, the actual solar radiation spectrum was estimated with Leckner’s spectral solar irradiance model [11], appling at its input atmospheric parameters measured in situ and retrieved from the Aerosol Robotic Network (AERONET) [12]. SF was computed and analyzed for nine years (2012–2020). The quantitative assessment of losses due to the spectral mismatch in real operating conditions of colored PV modules represents a novelty per se. The results stress the price that must be paid from the energy when aesthetic is prioritized upon integrating PV systems in buildings.


## 2. Spectral Factor

Spectral factor (SF) quantifies the spectral gain or loss that a solar cell may experience under the actual solar radiation spectrum compared to the standard AM1.5G. According to IEC 60904-7:2008 [9], SF is defined as
(1)SF=∫λminλmaxGλSRλdλ∫λminλmaxGλdλ⋅∫λminλmaxGSTCλdλ∫λminλmaxGSTCλSRλdλ,where SRλ represents the relative spectral response of a solar cell at wavelength λ. The subscript STC indicates the standard test conditions of PV devices. The absolute spectral response SRaλ is defined as the ratio of the short-circuit current ISCλ generated by a solar cell to the sunlight power incident on its surface.
(2)SRaλ=ISCλAGλ,A/W.In Equation (2) Gλ denotes the solar irradiance and A represents the solar cell surface area. Relative spectral response SRλ is just SRaλ normalized to the maximum value of SRaλ:
(3)SRλ=SRaλSRa,max.The short-circuit current of a solar cellISC is obviously proportional to ∫λminλmaxGλSRλdλ. Therefore, Equation (1) can be rewritten as
(4)SF=ISCG0G0,STCISC,STC=ISC/G0ISC,STC/G0,STC,where G0 denotes the solar irradiance in the spectral band λmin,λmax. Equation (4) clearly underlines the SF meaning. SF greater than 1 indicates a spectral gain (i.e., the PV module efficiency is greater than that at STC) while SF smaller than 1 indicates a spectral loss (i.e., the PV module efficiency is smaller than that at STC).


## 3. Data and Methodology

We can imagine a scenario in which PV systems of different colors (red, green, blue, and white) operate in the four major urban areas in Romania. The color of PV modules is obtained using the technology proposed by the outstanding paper [5]. The aim of this study is to evaluate the spectral gain/loss of the considered colored solar cells operating in real atmospheric conditions, i.e., under the incidence of solar radiation with real spectral distribution. Thus, in order to compute the spectral factor (Equation (1)), the spectral solar irradiance was estimated using the Leckner model [11]. This is a simple parametric spectral solar irradiance model which has proven over years its accuracy in many applications (e.g., [13, 14]). The real atmospheric conditions have been ensured by applying at model inputs in situ measured atmospheric parameters: ozone column content, water vapor column content, and the Ångström parameters. The colored solar cells selected for this study and the input parameters of the Leckner model are briefly discussed next.


### 3.1. Colored Solar Cells

Reference [5] reported a nanophotonic color coating method for standard solar cells named Selectively Modulated Aesthetic Reflector Technology (SMART). SMART coating selectively reflects specific wavelengths from visible light spectrum aimed at providing the human eye with the perception of a predefined color. The rest of the spectrum is almost fully transferred to the solar cell for PV conversion. Figure 1 illustrates schematically this concept.Figure 1
Schematic of a colored solar cell.The methods of fabrication for the SMART coating are detailed in [5]. The coatings are based on two layers of silicon nitride (SiN) and silicon oxynitride (SiON). These layers are deposited using radio frequency plasma-enhanced chemical vapor deposition at a low temperature of 200°C. The thickness of the photonic crystals depends on the color and reflectivity required for the cell. In this study, we have used the characteristics of colored solar cells provided in [5], as a starting point for evaluating the spectral effects on colored solar cells.The physical quantity of interest for computing SF (see Equation (1)) is the spectral response SRλ of the whole colored solar cell. It was evaluated taking into account that SRaλ and the external quantum efficiency EQE are similar physical quantities, directly related:
(5)SRaλ=qλhcEQEλ,where h is the Planck constant, c is the speed of light, and q is the electron charge. Figure 5 from Ref. [5] provides EQE for four colored solar cells. These cells are basically monocrystalline silicon solar cells covered with different SMART coatings: red, green, blue, and white. For each color, firstly the EQEλ curve was digitized, then SRaλ was evaluated using Equation (5), and finally SRλ was computed by normalization with the maximum value reached by SRaλ. Figure 2 displays the resulted curves SRλ.Figure 2
Illustration of the relative spectral responseSRλ evaluated for four colored solar cells from [5]. The curve color corresponds to the cell color except the white cell for which SRλ is displayed in gray.Figure 3
Distribution of the Ångström exponentα, Ångström turbidity coefficient β, and water vapor column content w (g/cm2) measured at the AERONET stations: Bucharest, Cluj, Iasi, and Timisoara during January 2012 to December 2020. For each physical quantity, the total number of recordings is 162722 broken down on stations as follows: 64248 at Bucharest, 34689 at Cluj, 39340 at Iasi, and 24445 at Timisoara.We checked the accuracy of the curves from Figure2 by computing SRλ with a second approach. On this approach, SRλ is regarded as a result of the superposition of the filter (coating layer) effect on the incident solar radiation flux and the standard silicon solar cell spectral response. Thus, firstly we digitized the transmittance of the coating layer τSMARTλ from [5] and SRa‐Siλ from [15]. For obtaining SRλ, the absolute spectral response of the colored solar cell SRaλ was calculated as τSMARTλ⋅SRa‐Siλ and normalized to its maximum value. The curves computed with the second method overlap the corresponding curves from Figure 2. Minor differences occur only at the edges of the spectral domain. For computing SF, we used SRλ retrieved from EQE, since it is based on the direct measurements performed on the colored solar cells.


### 3.2. Input Parameters

The following atmospheric parameters are required at input of Leckner’s spectral solar irradiance model: ozone column content, water vapor column content, and Ångström parameters. All these parameters have been collected from four AERONET stations located in Romania: Bucharest, Cluj, Iasi, and Timisoara. Data were taken from the AERONET database 2.0 level (quality assured) in the longest possible period between January 1st 2012 and December 31st 2020 [12]. The retrieved datasets are not continuous, several gaps existing in each dataset. Thus, the time series of SF are also accompanied by gaps.Figure3 displays the histograms of the Ångström exponent α, Ångström turbidity coefficient β, and the water vapor column content w measured at each station. At all stations, the distribution of α is unimodal, with a peak around 1.5 indicating the prevalence of the urban-industrial aerosol (see, e.g., [16] for an aerosol classification). The distribution of β is also unimodal and skewed to the right. The atmospheric turbidity is relatively low (β<0.2), but all the stations recorded severe episodes of pollution with aerosols too (β>0.5, even more than 1). The distribution of w is different from station to station from a rather uniform distribution at Bucharest to a bimodal distribution in Timisoara.Figure 4
Spectral solar irradianceGλ estimated with Leckner’s model [12] emerging from the coating layer. The curve color corresponds to the cell color except the white cell for which SRλ is displayed in gray. The curve in black corresponds to AM1.5G solar spectrum. The characteristic signature of each spectrum measured by the average photon energy (APE) (Equation (6) is presented.


## 3.1. Colored Solar Cells

Reference [5] reported a nanophotonic color coating method for standard solar cells named Selectively Modulated Aesthetic Reflector Technology (SMART). SMART coating selectively reflects specific wavelengths from visible light spectrum aimed at providing the human eye with the perception of a predefined color. The rest of the spectrum is almost fully transferred to the solar cell for PV conversion. Figure 1 illustrates schematically this concept.Figure 1
Schematic of a colored solar cell.The methods of fabrication for the SMART coating are detailed in [5]. The coatings are based on two layers of silicon nitride (SiN) and silicon oxynitride (SiON). These layers are deposited using radio frequency plasma-enhanced chemical vapor deposition at a low temperature of 200°C. The thickness of the photonic crystals depends on the color and reflectivity required for the cell. In this study, we have used the characteristics of colored solar cells provided in [5], as a starting point for evaluating the spectral effects on colored solar cells.The physical quantity of interest for computing SF (see Equation (1)) is the spectral response SRλ of the whole colored solar cell. It was evaluated taking into account that SRaλ and the external quantum efficiency EQE are similar physical quantities, directly related:
(5)SRaλ=qλhcEQEλ,where h is the Planck constant, c is the speed of light, and q is the electron charge. Figure 5 from Ref. [5] provides EQE for four colored solar cells. These cells are basically monocrystalline silicon solar cells covered with different SMART coatings: red, green, blue, and white. For each color, firstly the EQEλ curve was digitized, then SRaλ was evaluated using Equation (5), and finally SRλ was computed by normalization with the maximum value reached by SRaλ. Figure 2 displays the resulted curves SRλ.Figure 2
Illustration of the relative spectral responseSRλ evaluated for four colored solar cells from [5]. The curve color corresponds to the cell color except the white cell for which SRλ is displayed in gray.Figure 3
Distribution of the Ångström exponentα, Ångström turbidity coefficient β, and water vapor column content w (g/cm2) measured at the AERONET stations: Bucharest, Cluj, Iasi, and Timisoara during January 2012 to December 2020. For each physical quantity, the total number of recordings is 162722 broken down on stations as follows: 64248 at Bucharest, 34689 at Cluj, 39340 at Iasi, and 24445 at Timisoara.We checked the accuracy of the curves from Figure2 by computing SRλ with a second approach. On this approach, SRλ is regarded as a result of the superposition of the filter (coating layer) effect on the incident solar radiation flux and the standard silicon solar cell spectral response. Thus, firstly we digitized the transmittance of the coating layer τSMARTλ from [5] and SRa‐Siλ from [15]. For obtaining SRλ, the absolute spectral response of the colored solar cell SRaλ was calculated as τSMARTλ⋅SRa‐Siλ and normalized to its maximum value. The curves computed with the second method overlap the corresponding curves from Figure 2. Minor differences occur only at the edges of the spectral domain. For computing SF, we used SRλ retrieved from EQE, since it is based on the direct measurements performed on the colored solar cells.


## 3.2. Input Parameters

The following atmospheric parameters are required at input of Leckner’s spectral solar irradiance model: ozone column content, water vapor column content, and Ångström parameters. All these parameters have been collected from four AERONET stations located in Romania: Bucharest, Cluj, Iasi, and Timisoara. Data were taken from the AERONET database 2.0 level (quality assured) in the longest possible period between January 1st 2012 and December 31st 2020 [12]. The retrieved datasets are not continuous, several gaps existing in each dataset. Thus, the time series of SF are also accompanied by gaps.Figure3 displays the histograms of the Ångström exponent α, Ångström turbidity coefficient β, and the water vapor column content w measured at each station. At all stations, the distribution of α is unimodal, with a peak around 1.5 indicating the prevalence of the urban-industrial aerosol (see, e.g., [16] for an aerosol classification). The distribution of β is also unimodal and skewed to the right. The atmospheric turbidity is relatively low (β<0.2), but all the stations recorded severe episodes of pollution with aerosols too (β>0.5, even more than 1). The distribution of w is different from station to station from a rather uniform distribution at Bucharest to a bimodal distribution in Timisoara.Figure 4
Spectral solar irradianceGλ estimated with Leckner’s model [12] emerging from the coating layer. The curve color corresponds to the cell color except the white cell for which SRλ is displayed in gray. The curve in black corresponds to AM1.5G solar spectrum. The characteristic signature of each spectrum measured by the average photon energy (APE) (Equation (6) is presented.


## 4. Results and Discussion

### 4.1. Filtered Solar Radiation in Actual Operating Conditions

As Figure1 shows, the colored solar cell investigated here consists of a crystalline silicon solar cell covered by the SMART coating, which acts as spectral filter for the incoming solar radiation flux. The first step in this study was to assess how the coating layer modifies the spectrum and power of the solar radiation flux incident on the solar cell surface. For this, an incoming solar radiation flux with standard AM1.5G spectral distribution was considered (black curve in Figure 4). The spectrum transmitted by each of the four SMART layers (red, green, blue, and white) was computed on the basis of Leckner’s spectral solar irradiance model and the spectral transmittance of the SMART layer. Figure 4 displays the results. Visual inspection reveals a substantial attenuation of the incoming flux AM1.5G, irrespective of the coating color. In the spectral absorption range 0.3μm,1.2μm, broadband irradiance at the filter output is 820.3 W/m2 for AM1.5G spectrum, 580.4 W/m2 for red coating, 619.4 W/m2 for green, 637.3 W/m2 for blue, and 465 W/m2 for white. This means that the passing of red, green, blue, and white coatings results in decreasing the density of incoming solar energy flux to 70.7%, 75.5%, 77.7%, and 56.7% from AM1.5G, respectively. Thus, the aesthetic of BIPV comes at a high energy cost.Figure 5
Spectral factor (SF) estimated at the station Bucharest for the four colored solar cells. The curve colors correspond to the cell colors except the white cell for which SF is displayed in gray. The curve in black corresponds to the silicon solar cell.In order to capture the characteristic signature of the solar radiation spectrum at the filter output, we evaluate the average photon energy (APE) index [17]:
(6)APEeV=hcq∫λminλmaxGλdλ∫λminλmaxλGλdλ,where Gλ is the spectral solar irradiance. q, c, and h denote the elementary charge, the speed of light, and Planck’s constant, respectively. Over AM1.5G spectrum and a standard wavelength range 0.35μm,1.05μm, APE computed on the basis of Leckner’s model is equal to 1.892 eV. A higher value of APE indicates a blue-shift in spectrum while a smaller value of APE indicates a red-shift in spectrum. The values of APE listed in Figure 4 indicate a red-shift of the transmitted spectra. The largest shift is experienced by the spectrum passing through the white coating layer. The red-shift could be explained by the large absorption and reflection in the visible range that gives the PV cell its specified color. The transmittance of the SMART coating is larger in the near-infrared region, thus producing a red-shift in terms of APE.


### 4.2. Spectral Factor under Actual Operating Conditions

For each colored solar cell and the basic silicon solar cell, the spectral factor was estimated based on the definition (Equation (1)). The integral was computed over the spectral domain 0.3μm,1.2μm. For silicon solar cells, the absorption edge can be considered at an approximate wavelength of 1.2 μm. Figure 5 shows the results for Bucharest. Similar results, with minor differences, were obtained for the other three cities. For the basic silicon PV technology, SF varies roughly between 0.995 and 1.01. Remember that a SF value greater than one means a spectral gain. Irrespective of the solar cell color, as in the case of the basic silicon solar cell, the same fluctuations of SF over time are observed. These fluctuations are induced by the random changes of the atmospheric parameters, of which distributions are synthetically gathered in Figure 3. However, the differences of SF fluctuations between the basic silicon solar cell and the colored solar cells are considerable. While for the silicon solar cell SF fluctuate around its value at STC, SF=1, the colored solar cells experience substantial lower average values of spectral factor. The mean values of SF in Bucharest are SF¯=0.853 for blue cell, SF¯=0.809 for green cell, SF¯=0.715 for red cell, and SF¯=0.605 for white cell. For all locations, mean values of SF are displayed in Table 1, indicating a massive loss in output power. The average values of SF are quite similar in all locations, with the highest values for the blue cell, followed closely by the green cell, with lower values for the red cell and significantly lower for the white cell. The SF values for blue and green cells have a small overlap between the maximum and minimum values for green and blue, respectively.Table 1
Minimum, maximum, and mean values of spectral factor (Equation (1)) evaluated over 2012-2020 for the four colored solar cells considered in this study. The computation was done assuming the cells operating in the main four urban areas in Romania.
Cell colorRedGreenBlueWhiteLocationMinMaxMeanMinMaxMeanMinMaxMeanMinMaxMeanBucharest0.6950.7280.7150.7730.8350.8090.8130.8730.8530.5670.6330.605Cluj0.6950.7280.7160.7760.8340.8110.8170.8730.8550.5730.6340.607Iasi0.6950.7290.7150.7750.8350.8090.8160.8740.8530.5700.6340.605Timisoara0.7000.7270.7150.7830.8330.8100.8220.8720.8530.5790.6300.606Irrespective of the cell color, SF experiences a moderate seasonality: SF reaches its highest levels in the winter months and its lowest levels in the summer months, which is a native characteristic of the monocrystalline silicon solar cells [18]. Therefore, from the spectral gain/loss perspective, the efficiency of a monocrystalline silicon-based colored PV module is greater in the winter than in the summer. Taking into account that a PV system provides most of the energy in the summer months, such behavior represents a disadvantage. A possible solution is the using of the polycrystalline silicon solar cell as the basis for the colored PV modules. From the same perspective of spectral gain/loss, the polycrystalline silicon solar cells have an opposite seasonal behavior: SF reaches its lowest levels in the winter months and its highest levels in the summer months [18].Visual inspection of Figure5 emphasizes differences in the amplitude of SF variation for different colors of the cells. While for the red cell the dispersion of SF is comparable to that of the basic silicon solar cell, for the green, blue, and white cells a substantial increase in SF dispersion is observed. Figure 6 shows the SF histograms for all considered cells operating in all locations, substantiating the relatively large fluctuations of SF as a result of the atmospheric parameter fluctuations. Each row shows the simulated behavior of the colored cells in an urban area: Bucharest, Cluj, Iasi, and Timisoara. In both locations Cluj and Timisoara, for all colors, the distributions of SF appear bimodal. At the same time, for the Bucharest and Iasi, unimodal distributions, similar for all four colors, are observed. These differences and similarities can be attributed to local atmospheric differences between the chosen locations, with Timisoara and Cluj being in the western part of Romania and the other two cities in the eastern part.Figure 6
Distribution of spectral factor (broken down in 30 classes) evaluated over 2012-2020 for the four colored solar cells considered in this study. The computation was done assuming the cells operating in the main four urban areas in Romania. The distribution color corresponds to the cell color except the white cell for whichSRλ is displayed in gray.


## 4.1. Filtered Solar Radiation in Actual Operating Conditions

As Figure1 shows, the colored solar cell investigated here consists of a crystalline silicon solar cell covered by the SMART coating, which acts as spectral filter for the incoming solar radiation flux. The first step in this study was to assess how the coating layer modifies the spectrum and power of the solar radiation flux incident on the solar cell surface. For this, an incoming solar radiation flux with standard AM1.5G spectral distribution was considered (black curve in Figure 4). The spectrum transmitted by each of the four SMART layers (red, green, blue, and white) was computed on the basis of Leckner’s spectral solar irradiance model and the spectral transmittance of the SMART layer. Figure 4 displays the results. Visual inspection reveals a substantial attenuation of the incoming flux AM1.5G, irrespective of the coating color. In the spectral absorption range 0.3μm,1.2μm, broadband irradiance at the filter output is 820.3 W/m2 for AM1.5G spectrum, 580.4 W/m2 for red coating, 619.4 W/m2 for green, 637.3 W/m2 for blue, and 465 W/m2 for white. This means that the passing of red, green, blue, and white coatings results in decreasing the density of incoming solar energy flux to 70.7%, 75.5%, 77.7%, and 56.7% from AM1.5G, respectively. Thus, the aesthetic of BIPV comes at a high energy cost.Figure 5
Spectral factor (SF) estimated at the station Bucharest for the four colored solar cells. The curve colors correspond to the cell colors except the white cell for which SF is displayed in gray. The curve in black corresponds to the silicon solar cell.In order to capture the characteristic signature of the solar radiation spectrum at the filter output, we evaluate the average photon energy (APE) index [17]:
(6)APEeV=hcq∫λminλmaxGλdλ∫λminλmaxλGλdλ,where Gλ is the spectral solar irradiance. q, c, and h denote the elementary charge, the speed of light, and Planck’s constant, respectively. Over AM1.5G spectrum and a standard wavelength range 0.35μm,1.05μm, APE computed on the basis of Leckner’s model is equal to 1.892 eV. A higher value of APE indicates a blue-shift in spectrum while a smaller value of APE indicates a red-shift in spectrum. The values of APE listed in Figure 4 indicate a red-shift of the transmitted spectra. The largest shift is experienced by the spectrum passing through the white coating layer. The red-shift could be explained by the large absorption and reflection in the visible range that gives the PV cell its specified color. The transmittance of the SMART coating is larger in the near-infrared region, thus producing a red-shift in terms of APE.


## 4.2. Spectral Factor under Actual Operating Conditions

For each colored solar cell and the basic silicon solar cell, the spectral factor was estimated based on the definition (Equation (1)). The integral was computed over the spectral domain 0.3μm,1.2μm. For silicon solar cells, the absorption edge can be considered at an approximate wavelength of 1.2 μm. Figure 5 shows the results for Bucharest. Similar results, with minor differences, were obtained for the other three cities. For the basic silicon PV technology, SF varies roughly between 0.995 and 1.01. Remember that a SF value greater than one means a spectral gain. Irrespective of the solar cell color, as in the case of the basic silicon solar cell, the same fluctuations of SF over time are observed. These fluctuations are induced by the random changes of the atmospheric parameters, of which distributions are synthetically gathered in Figure 3. However, the differences of SF fluctuations between the basic silicon solar cell and the colored solar cells are considerable. While for the silicon solar cell SF fluctuate around its value at STC, SF=1, the colored solar cells experience substantial lower average values of spectral factor. The mean values of SF in Bucharest are SF¯=0.853 for blue cell, SF¯=0.809 for green cell, SF¯=0.715 for red cell, and SF¯=0.605 for white cell. For all locations, mean values of SF are displayed in Table 1, indicating a massive loss in output power. The average values of SF are quite similar in all locations, with the highest values for the blue cell, followed closely by the green cell, with lower values for the red cell and significantly lower for the white cell. The SF values for blue and green cells have a small overlap between the maximum and minimum values for green and blue, respectively.Table 1
Minimum, maximum, and mean values of spectral factor (Equation (1)) evaluated over 2012-2020 for the four colored solar cells considered in this study. The computation was done assuming the cells operating in the main four urban areas in Romania.
Cell colorRedGreenBlueWhiteLocationMinMaxMeanMinMaxMeanMinMaxMeanMinMaxMeanBucharest0.6950.7280.7150.7730.8350.8090.8130.8730.8530.5670.6330.605Cluj0.6950.7280.7160.7760.8340.8110.8170.8730.8550.5730.6340.607Iasi0.6950.7290.7150.7750.8350.8090.8160.8740.8530.5700.6340.605Timisoara0.7000.7270.7150.7830.8330.8100.8220.8720.8530.5790.6300.606Irrespective of the cell color, SF experiences a moderate seasonality: SF reaches its highest levels in the winter months and its lowest levels in the summer months, which is a native characteristic of the monocrystalline silicon solar cells [18]. Therefore, from the spectral gain/loss perspective, the efficiency of a monocrystalline silicon-based colored PV module is greater in the winter than in the summer. Taking into account that a PV system provides most of the energy in the summer months, such behavior represents a disadvantage. A possible solution is the using of the polycrystalline silicon solar cell as the basis for the colored PV modules. From the same perspective of spectral gain/loss, the polycrystalline silicon solar cells have an opposite seasonal behavior: SF reaches its lowest levels in the winter months and its highest levels in the summer months [18].Visual inspection of Figure5 emphasizes differences in the amplitude of SF variation for different colors of the cells. While for the red cell the dispersion of SF is comparable to that of the basic silicon solar cell, for the green, blue, and white cells a substantial increase in SF dispersion is observed. Figure 6 shows the SF histograms for all considered cells operating in all locations, substantiating the relatively large fluctuations of SF as a result of the atmospheric parameter fluctuations. Each row shows the simulated behavior of the colored cells in an urban area: Bucharest, Cluj, Iasi, and Timisoara. In both locations Cluj and Timisoara, for all colors, the distributions of SF appear bimodal. At the same time, for the Bucharest and Iasi, unimodal distributions, similar for all four colors, are observed. These differences and similarities can be attributed to local atmospheric differences between the chosen locations, with Timisoara and Cluj being in the western part of Romania and the other two cities in the eastern part.Figure 6
Distribution of spectral factor (broken down in 30 classes) evaluated over 2012-2020 for the four colored solar cells considered in this study. The computation was done assuming the cells operating in the main four urban areas in Romania. The distribution color corresponds to the cell color except the white cell for whichSRλ is displayed in gray.


## 5. Conclusions

The study was aimed at providing an analysis on the effects of the solar radiation spectral distribution on colored solar cells, considering atmospheric data collected in the main urban areas of Romania, namely, Bucharest, Cluj, Iasi, and Timisoara. One particular technology was studied, the SMART nanophotonic color coating, in terms of spectral mismatch. The standard monocrystalline silicon solar cell was chosen as reference. Based on data collected from the AERONET during the period 2012-2020, Leckner’s model was applied to calculate the spectral factor in the selected locations. When considering standard test conditions, SMART coatings in different colors have shown a significant decrease in the density of incoming solar energy flux, with the transmitted percentage taking the values 70.7%, 75.5%, 77.7%, and 56.7% for red, green, blue, and white coating, compared to the AM1.5G spectrum. This is an inherent price that must be paid when aesthetic is prioritized upon integrating PV systems in buildings. The colored solar cells have also shown significant red-shift, with the average photon energy values lower than the value of STC. The mean values of the spectral factor and its dispersion are highly dependent on the cell color. Depending on location, the spectral factor had different distributions, showing its dependence on the local atmospheric conditions. The four urban areas considered in this study are located in a temperate climate (group C in Koppen-Geiger classification [19]). Thus, the results can be regarded as a rough indicator of the influence of spectral solar irradiance distribution on the colored PV module efficiency operating in a temperate climate. Future research could take into account other technologies of colored solar cells, such as dye-sensitized solar cells, and urban areas located in other climate groups.



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