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 tool 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.

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 type	Module efficiency $\eta_{0,\text{el}}$	Temperature coefficient $\gamma$
Monocrystalline	21 %	0.36 %/°C
Polycrystalline	16 %	0.42 %/°C
Thin-film	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 East	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 %