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# Photovoltaic-thermal (PVT) collectors: Calculation and validation

nPro helps to generate hourly resolved power profiles for photovoltaic-thermal collectors. On this page you learn how these are calculated and how they have been validated.

## How are PVT profiles calculated in nPro?

The calculation of heat and electricity profiles are based on the nPro solar thermal and photovoltaic calculation models. For the heat generation profiles nPro uses the Standard ISO 9806. Hereby, nPro supports different calculation approaches based on ISO 9806: ISO 9806:2017 as well as three calculation methods based on ISO 9806:2013: quasi-dynamic, steady-state and unglazed. In the following, the formulas are provided.

### Formulas for heat generation based on ISO 9806

• ISO 9806:2017: Newest calculation standard: \begin{gathered} q=\eta_{0, b} K_b\left(\theta_L, \theta_T\right) G_b+\eta_{0 . b} K_d G_d-a_1\left(T_m-T_a\right)-a_2\left(T_m-T_a\right)^2\\ -a_3 u^{\prime}\left(T_m-T_a\right)+a_4\left(E_L-\sigma T_a^4\right)-a_6 u^{\prime} G-a_7 u^{\prime}\left(E_L-\sigma T_a^4\right)\\ -a_8\left(\vartheta_m-T_a\right)^4 \end{gathered}
• ISO 9806:2013: Quasi-Dynamic Approach: This method involves dynamic simulations that provide insights into the system's behavior over time, accounting for fluctuations in solar radiation and other variables. It's particularly useful for capturing real-world dynamics. \begin{gathered} q=\eta_{0, b} \cdot K_{\theta, b}\left(\theta_L, \theta_T\right) \cdot G_b+\eta_{0, b} \cdot K_{\theta, d} \cdot G_d-c_6 \cdot u \cdot G \\ -c_1 \cdot\left(T_m-T_a\right)-c_2 \cdot\left(T_m-T_a\right)^2-c_3 \cdot u \cdot\left(T_m-T_a\right)+c_4 \\ \cdot\left(E_L-\sigma \cdot T_a^4\right) \end{gathered}
• ISO 9806:2013: Steady-State Approach: In contrast to dynamic simulations, the steady-state method simplifies the analysis by assuming constant conditions. This is valuable for quick estimations and comparisons under stable scenarios. \begin{gathered} q=G \cdot \eta_0-a_1 \cdot\left(T_m-T_a\right)-a_2 \cdot\left(T_m-T_a\right)^2 \end{gathered}
• ISO 9806:2013: Unglazed Approach: This method pertains to scenarios where the solar collector lacks a protective cover. It's particularly relevant when studying systems with direct exposure to environmental conditions. \begin{gathered} q=G^{\prime \prime} \cdot \eta_0 \cdot\left(1-b_u \cdot u\right)-\left(b_1+b_2 \cdot u\right) \cdot\left(\vartheta_m-\vartheta_a\right)\\ G^{\prime \prime}=G+\frac{\varepsilon}{\alpha} \cdot\left(E_L-\sigma \cdot T_a^4\right) \end{gathered}

### Pre-defined collector models in nPro

In nPro a couple of pre-defined collector models are available. The model parameters of these models are listed in the following and are taken form the research study Jonas et al.: "Implementation and Experimental Validation of a Photovoltaic-Thermal (PVT)", EuroSun 2018 Conference Proceedings, DOI: 10.18086/eurosun2018.02.16 which compaired experimental data with detailed collector model simulations in TRNSYS:

• WISC, in nPro referred to as uncovered uninsulated:
• covered - without backside thermal insulation,in nPro defined as covered uninsulated
• covered - with backside thermal insulation, in nPro referred to as covered insulated
Table 1: Pre-defined PVT collector models in nPro
Parameter Unit Uncovered, uninsulated (WISC) Covered, uninsulated Covered, insulated
$$\eta_{0,\text{b}}$$ --- 0.436 0.596 0.573
$$K_{\mathrm{d}}$$ --- 0.91 0.93 0.94
$$b_{0,\text{ th }}$$ --- 0.114 0.122 0.120
$$c_1$$ $$W/(m^2 K)$$ 7.750 6.583 5.008
$$c_2$$ $$W/(m^2 K^2)$$ 0.026 0.024 0.059
$$c_3$$ $$(J)/(m^3 K)$$ 1.640 0.000 0.011
$$c_4$$ --- 0.000 0.066 0.039
$$c_5$$ $$J/(m^2K)$$ 35800 16075 16631
$$c_6$$ $$s/m$$ 0.008 0.009 0.003

### User-defined collector models

In addition to pre-defined PVT collectors, nPro supports four calculation methods to define your own PVT collector model. These calculation methods are:

• ISO 9806:2017
• ISO 9806:2013, quasi-dynamic
• ISO 9806:2013, unglazed
With the nPro tool you can generate and download heat and electricity generation profiles in hourly resolution for a user-defined PVT collector model.

## How were the heat generation profiles validated?

The profiles generated with nPro have been compared with generation profiles created with the ScenoCalc tool from the SP Technical Research Institute of Sweden for a variety of different locations and orientations. The ScenoCalc tool is an open Excel sheet that is recognized by all institutions for energy yield prediction when certifying collectors according to the Solar Keymark procedure. The tool is limited to the consideration of a single collector. However, it is ideally suited as a basis for almost any type of solar thermal collector. An excerpt of the validation is shown in the tables below.

### Comparison of nPro and ScenoCalc

Table 1: Solar yield for different locations and a mean collector temperature of 25 °C. PVT collector license number: 011-7S2894 P.
Location Elevation Azimuth nPro ScenoCalc Deviation
Athens 25° South 557.93 kWh/m² 557.93 kWh/m² 0 %
Davos 30° South 7.77 kWh/m² 7.77 kWh/m² 0 %
Stockholm 45° South 20.07 kWh/m² 20.07 kWh/m² 0 %
Andrews 25° South 347.12 kWh/m² 347.12 kWh/m² 0 %
Table 2: Solar yield calculated with nPro and ScenoCalc (version 6.1) for a PVT collector (license number 011-7S2894 P) for the location Athens (Greece) for different orientations and a mean collector temperature of 25 °C.
Orientation nPro ScenoCalc Deviation
Horizontal 539.24 kWh/m2 539.23 kWh/m2 < 0.1 %
30° / South 557.27 kWh/m2 557.27 kWh/m2 0 %
90° / East 442.62 kWh/m2 442.62 kWh/m2 0 %
90° / West 425.71 kWh/m2 425.70 kWh/m2 < 0.1 %
30° / North 482.58 kWh/m2 482.58 kWh/m2 0 %
Table 3: Solar yield calculated with nPro and ScenoCalc (version 4.04) for a PVT collector (Copa Solar PVT00201) for different locations with an orientation facing South.
Location Elevation Collector temperature nPro ScenoCalc Deviation
Athens 25° 25 °C 791.17 kWh/m² 791.21 kWh/m² < 0.1 %
Athens 25° 50 °C 21.08 kWh/m² 21.09 kWh/m² < 0.1 %
Davos 30° 25 °C 177.02 kWh/m² 177.03 kWh/m² < 0.1 %
Stockholm 45° 25 °C 165.96 kWh/m² 165.98 kWh/m² < 0.1 %
Andrews 25° 25 °C 555.99 kWh/m² 556.04 kWh/m² < 0.1 %
Andrews 25° 50 °C 6.17 kWh/m² 6.17 kWh/m² 0 %

More validation data for the thermal calculation model is provided on the documentation page for solar thermal collectors.

## Which PVT collector types can be calculated in nPro?

With nPro all kind of PVT collector types can be calculated since the ISO 9806 is implemented in full detail. The following collector types are common and can be simulated in nPro:

• Insulated Back, Glass Cover: In this type, the back of the collector is insulated to reduce heat losses, while the front is covered with a glass panel to protect the photovoltaic cells and allow sunlight to pass through. The insulation helps retain the heat generated by the collector, while the glass cover allows the photovoltaic cells to generate electricity from the sunlight.
• Insulated Back, Transparent Insulation Cover: This type also has insulation on the back of the collector to minimize heat losses. However, instead of a glass cover, a transparent insulation material is used on the front. This material allows sunlight to pass through, while also providing some insulation properties to reduce heat losses. Examples of transparent insulation materials include polycarbonate or polymethyl methacrylate (PMMA).
• Non-Insulated Back, Glass Cover: In this type, there is no insulation on the back of the collector. The front of the collector is covered with a glass panel, similar to traditional photovoltaic panels. The lack of insulation on the back allows the collector to dissipate heat more easily, but it can also lead to higher heat losses. This type is typically used in applications where heat extraction is not a primary concern, and electricity generation takes precedence.

## How are electricity generation profiles for PVT collectors calculated?

In PVT collectors, the PV cell is cooled by the heat absober on the back of the cell. Due to this reduction of the cell temperature the electricity generation increases compard to a PV only module. The formulas for the electricity generation are based on research studies for PVT collectors, e.g. the one-capacitance model described by Lämmle et al.: "PVT collector technologies in solar thermal systems: A systematic assessment of electrical and thermal yields with the novel characteristic temperature approach", Solar Energy, 155, pp. 867-879, 2017, DOI: 10.1016/j.solener.2017.07.015. Thus, the cell temperature in nPro is calculated as follows: $$T_{\text {cell,PVT }}=T_m+\frac{q_{th}}{U_{\text {cell-fluid }}}$$ Here, $$U_{\text {cell-fluid }}$$ refers to the U-value (heat transmittance) between PV cell and fluid of the solar heat absorber. For a detailed description of the PV model, we refer to the description of the PV model. In the following table, the additional electric output of the PVT module is exemplarily depicted for different locations and a polycrystalline PV cell.

Table 9: Additional electric output of the PVT module is for different locations and a polycrystalline PV cell.
Locations PV only PVT collector Additional electricity output
Athens 293.60 kWh/m² 307.02 kWh/m² 4.57 %
Davos 282.08 kWh/m² 291.74 kWh/m² 3.42 %
Stockholm 184.74 kWh/m² 187.56 kWh/m² 1.53 %
Andrews 275.23 kWh/m² 282.96 kWh/m² 2.81 %

## Sources

1. Jonas et al.: "Implementation and Experimental Validation of a Photovoltaic-Thermal (PVT)", EuroSun 2018 Conference Proceedings. DOI: 10.18086/eurosun2018.02.16., Online available: https://jonas-ing.de/wp-content/uploads/2021/02/2018_Eurosun_conf_paper.pdf
2. Lämmle et al.: "PVT collector technologies in solar thermal systems: A systematic assessment of electrical and thermal yields with the novel characteristic temperature approach", Solar Energy, 155, pp. 867-879, 2017, DOI: 10.1016/j.solener.2017.07.015

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