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# Photovoltaics: Calculation and Validation

nPro helps to create hourly resolved generation profiles for photovoltaic systems. On this page you will learn how these are calculated and validated.

## How are the profiles generated?

The calculation of the PV generation profiles in nPro is based on a detailed calculation model, which is described in 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, S. 867-879, 2017, DOI: 10.1016/j.solener.2017.07.015. The radiation on the inclined module surface is calculated from weather profiles with the global horizontal irradiation and the direct normal irradiation and is based on the calculation method of the ScenoCalc-Tools from Solar Keymark (Version 6.1). The calculation model used in nPro assumes that the direct current of the PV system is converted into alternating current. The inverter model uses a calculation approach from the well-known and validated calculation tool PVWatts of the National Renewable Energy Laboratory (USA), which is based on analyses of performance data from inverters of the California Energy Commission. For the inverter, among other things, the partial load efficiencies in the low-light phases are modelled in detail. The calculation approach is documented in the technical description of the PVWatts tool.

With the nPro-Tool you can generate and download PV power generation profiles in hourly resolution.

### Formulas for the PV calculation

The cell temperature of PV cells is calculated as follows: $$T_{\text {Zell,PV}}=T_a+\frac{G}{U_0+U_1 u}$$ Different loss and performance ratios (PR) are taken into account: $$P R_G=a G+b \ln (G+1)+c\left[\frac{(\ln (G+e))^2}{G+1}-1\right]$$
$$P R_T=1-\gamma\left(T_{\text {Zell }}-298.15 \mathrm{~K}\right)$$
$$P R_{I A M}=1-\mathrm{b}_0\left(\frac{1}{\cos \theta}-1\right)$$ These performance indicators result in an overall performance indicator: $$P R_{\text {tot }}=PR_{IAM} \cdot PR_T \cdot PR_G$$ The specific electrical output power (direct current) is then: $$p_{e l}=\eta_{\mathrm{el}, \mathrm{STC}} \cdot PR_{\text{tot}} \cdot G$$ In addition, the system losses and the inverter losses are taken into account when calculating the AC power generation. In nPro, the model parameters are assumed as follows: $$U_0$$ = 30,02 W/m²K, $$U_1$$ = 6.28 W/m²K, $$a$$ = -0,0000109 m²/W, $$b$$ = -0,047, $$c$$ = -1,40.

### Pre-defined module-parameters

The model parameters of the predefined PV modules in nPro are listed in the following table:

Table 1: Model parameters of the predefined module types in the nPro.
Cell zype Module efficiency $$\eta_{0,\text{el}}$$ Temperature coefficient $$\gamma$$
Monocrystalline 21 % 0,36 %/°C
Polycrystalline 16 % 0,42 %/°C
Thinfilm 12 % 0,2 %/°C

## Validation of PV power generation

Below, the results of PV electricity generation by nPro are validated using the widely-used tool PVGIS as well as freely available yield tables.

In the table below, annual yields for different locations and module orientations are presented. The yield values from nPro are compared to values from the PVGIS tool. The values of the PVGIS tool represent averages for different radiation databases (Sarah2, Sarah, Era5, etc.).

Table 2: Annual yields of nPro compared with the averaged annual yields of PVGIS for different locations.
Location Orientation PVGIS nPro Deviation
Berlin 35° / South 1048 kWh/kWp 1016 kWh/kWp -3 %
35° / West or East 797 kWh/kWp 774 kWh/kWp -3 %
35° / North 517 kWh/kWp 491 kWh/kWp -5 %
Almeria 35° / South 1721 kWh/kWp 1707 kWh/kWp -1 %
35° / West or East 1371 kWh/kWp 1358 kWh/kWp -1 %
35° / North 860 kWh/kWp 899 kWh/kWp 4 %
Stockholm 35° / South 997 kWh/kWp 992 kWh/kWp 0 %
35° / West or South 755 kWh/kWp 739 kWh/kWp -1 %
35° / North 445 kWh/kWp 434 kWh/kWp -2 %
Table 3: Monthly solar yield in nPro and PVGIS for the location Berlin with an orientation of 35° / South. The PVGIS tool used Sarah2 as the radiation database. Certain deviations arise from the fact that different weather years have been used for the comparison.
Month PVGIS nPro Deviation
January 30 kWh/kWp 32 kWh/kWp 7 %
February 48 kWh/kWp 55 kWh/kWp 15 %
March 85 kWh/kWp 96 kWh/kWp 13 %
April 119 kWh/kWp 124 kWh/kWp 4 %
May 127 kWh/kWp 124 kWh/kWp -2 %
June 128 kWh/kWp 122 kWh/kWp -5 %
July 126 kWh/kWp 124 kWh/kWp -2 %
August 119 kWh/kWp 117 kWh/kWp -2 %
September 101 kWh/kWp 91 kWh/kWp -10 %
October 69 kWh/kWp 72 kWh/kWp 4 %
November 36 kWh/kWp 34 kWh/kWp -6 %
December 26 kWh/kWp 26 kWh/kWp 0 %
Table 4: Monthly solar yield in nPro and PVGIS for the location Munich with an orientation of 35° / South. The PVGIS tool used Sarah2 as the radiation database. Certain deviations arise from the fact that different weather years have been used for the comparison.
Month PVGIS nPro Deviation
January 46 kWh/kWp 48 kWh/kWp 4 %
February 60 kWh/kWp 76 kWh/kWp 27 %
March 93 kWh/kWp 105 kWh/kWp 13 %
April 117 kWh/kWp 121 kWh/kWp 3 %
May 119 kWh/kWp 119 kWh/kWp 0 %
June 119 kWh/kWp 117 kWh/kWp -2 %
July 128 kWh/kWp 125 kWh/kWp -2 %
August 122 kWh/kWp 117 kWh/kWp -2 %
September 99 kWh/kWp 100 kWh/kWp 1 %
October 80 kWh/kWp 76 kWh/kWp -5 %
November 53 kWh/kWp 53 kWh/kWp 0 %
December 47 kWh/kWp 43 kWh/kWp -9 %

In the table below, the yield relative to the maximum yield at the ideal orientation (35° / South) is presented for different module orientations. The results of nPro are compared to the average of two reference yield tables from echtsolar.de, mvv.de, and simulation results from the PVGIS tool.

Table 5: Relative electricity generation based on the electricity generation at the ideal module orientation (35° / South). The location is Berlin.
Orientation nPro Reference
Horizontal 83% 86%
30° / South 99 % 100 %
60° / South 95 % 96 %
90° / South 73 % 70 %
30° / East 78 % 81 %
60° / East 66 % 70 %
90° / East 50 % 51 %
30° / North 53 % 59 %
60° / North 28 % 35 %
90° / North 21 % 22 %

## Sources

1. 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
2. ScenoCalc tool from Solar Keymark (version 6.1)
3. PVWatts of the National Renewable Energy Laboratory (USA)

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