# 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.

### 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:

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.).

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 % |

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 % |

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.

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

- 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
- ScenoCalc tool from Solar Keymark (version 6.1)
- PVWatts of the National Renewable Energy Laboratory (USA)

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