# Spatiotemporal Modeling of the Electricity Production from Variable Renewable Energies in Germany

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data

#### 2.1. Power Plant Datasets

#### 2.2. Applied Weather Product

^{2}[27].

#### 2.3. Calibration and Validation Data

^{3}. Such power curves can be looked up in the datasheets of the turbine manufacturer or on the internet, e.g., at the wind energy platform (www.thewindpower.net (accessed on 25 June 2020)) [28].

- Power reduction because of mutual shading of adjacent turbines (wake effect).
- Loss of power due to ice or dirt on the rotor blades of the wind turbines.
- Feed-in interruptions because of energy surpluses in the power grids.
- Switch-offs due to turbine overhauls or bat and bird protection.

## 3. Models

#### 3.1. Wind Power Model

#### 3.2. Photovoltaic Model

## 4. Results

#### 4.1. Wind Power Generation

- Deviations caused by the wind speed extrapolation from 10 m to the hub height.
- The uncertainties of the weather data and the fact of hourly averaged values.
- Weather-related variations in air pressure are not considered in the model.
- The assignment of turbines to power classes with typical power curves.

#### 4.2. Photovoltaic Power Generation

- The use of average values due to the lack of specific data for photovoltaic systems.
- The uncertainties of the weather data and the fact of hourly averaged values.
- Decrease of the power generation because of snow on the modules.
- Feed-in reductions due to energy surpluses or maintenance work.

#### 4.3. Common Power Generation

_{XY}is the correlation coefficient (denoted as R-value in Table 3), X

_{i}and Y

_{i}stand for the first differences of the simulated and measured time series of length n, and X

_{m}and Y

_{m}are the corresponding mean values. This Pearson correlation shows a strong positive linear relationship with a correlation coefficient of 0.96, indicating that the trends of both time series vary in the same magnitude and direction. Table 3 gives an overview of the most important values and statistical measures for the individual and joint simulation results.

#### 4.4. Energy Transition Atlas

_{st}of variable renewables can be calculated by Equation (2):

_{vr}is the sum of the onshore turbine and photovoltaic system capacity installed in the considered area, and E

_{vr}stands for the produced electricity from these renewable energies in this period and area. The following figure (Figure 10) shows the monthly capacity factors at NUTS-3 level in Germany for the year 2016.

_{st}describes the spatiotemporal coverage rate, E

_{vr}has the same meaning as for Equation (2), and U

_{tot}is the total electricity consumption in the considered period and area. In this context, a coverage rate of 100% means that the power generation from variable renewables fully offsets the electricity consumption. The total consumption is defined by the sum of electricity consumptions from the following four main sectors, household U

_{hh}, trade and commerce U

_{tc}, industry U

_{in}, and transport U

_{tr}, as given in Equation (4):

## 5. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Conflicts of Interest

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**Figure 1.**Installed capacity of (

**a**) onshore turbines and (

**b**) photovoltaic systems shown as spatial sums at NUTS-3 level in Germany for the year 2016. In the grey areas of Figure 1a no wind turbines are installed.

**Figure 2.**(

**a**) Plotted power curve (blue line) of an Enercon E-40 with 500 kW rated power as an example for a typical onshore turbine. (

**b**) Flowchart of the development process with all involved data from calibration to validation of the simulation models.

**Figure 5.**Simulated (black line) and measured (blue line) feed-in patterns of all onshore turbines in Germany for 2016.

**Figure 6.**Simulated (black line) and measured (orange line) feed-in patterns of all photovoltaic systems in Germany for 2016.

**Figure 7.**Simulated (black line) and measured (green line) feed-in patterns of variable renewables, i.e., onshore turbines and photovoltaic systems, in Germany for 2016.

**Figure 8.**Intra-annual increase of installed (

**a**) onshore turbine and (

**b**) photovoltaic system capacity at NUTS-3 level in Germany for 2016. In the grey areas of Figure 8a no wind turbines have been added during this year.

**Figure 9.**Monthly electricity production from variable renewables at NUTS-3 level in Germany for 2016.

**Figure 11.**Spatially resolved values of the (

**a**) total electricity consumption, (

**b**) annual electricity production from variable renewable energies, and (

**c**) coverage rate reached with variable renewables at NUTS-3 level in Germany for 2016.

Parameter | Wind Power Model | Photovoltaic Model |
---|---|---|

Latitude | required | optional |

Longitude | required | optional |

LAU-Id ^{1} | optional | required |

Commission date | required | required |

Decommission date | optional | optional |

Rated power | required | required |

Hub height | required | not applicable |

Rotor diameter | not applicable | not applicable |

Turbine type | optional | not applicable |

^{1}The LAU-Id is an eight-digit identifier for the unique determination of a local administrative unit (LAU).

Power Class (kW) | Turbine Type | Power Range (kW) |
---|---|---|

100 | Fuhrländer FL100 | P_{R} ≤ 150 |

200 | Enercon E-30 | 150 < P_{R} ≤ 250 |

500 | Enercon E-40 | 250 < P_{R} ≤ 750 |

1000 | Vestas V52 | 750 < P_{R} ≤ 1500 |

2000 | Enercon E-82 | 1500 < P_{R} ≤ 2500 |

3000 | Vestas V112 | 2500 < P_{R} ≤ 3500 |

5000 | Enercon E-126 | P_{R} > 3500 |

Data | Onshore Turbines | Photovoltaics | Common Values |
---|---|---|---|

Installed capacity | 45.3 GW | 40.7 GW | 86.0 GW |

Feed-in | 64.0 TWh | 33.9 TWh | 97.9 TWh |

RMSE | 45.6 GWh | 13.9 GWh | 46.5 GWh |

RMSE/Feed-in | 0.07% | 0.04% | 0.05% |

R-value | 0.97 | 0.97 | 0.96 |

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**MDPI and ACS Style**

Lehneis, R.; Manske, D.; Schinkel, B.; Thrän, D.
Spatiotemporal Modeling of the Electricity Production from Variable Renewable Energies in Germany. *ISPRS Int. J. Geo-Inf.* **2022**, *11*, 90.
https://doi.org/10.3390/ijgi11020090

**AMA Style**

Lehneis R, Manske D, Schinkel B, Thrän D.
Spatiotemporal Modeling of the Electricity Production from Variable Renewable Energies in Germany. *ISPRS International Journal of Geo-Information*. 2022; 11(2):90.
https://doi.org/10.3390/ijgi11020090

**Chicago/Turabian Style**

Lehneis, Reinhold, David Manske, Björn Schinkel, and Daniela Thrän.
2022. "Spatiotemporal Modeling of the Electricity Production from Variable Renewable Energies in Germany" *ISPRS International Journal of Geo-Information* 11, no. 2: 90.
https://doi.org/10.3390/ijgi11020090