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Analysing Grid-Level Effects of Photovoltaic Self-Consumption Using a Stochastic Bottom-up Model of Prosumer Systems^{ †}

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^{2}

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^{†}

## Abstract

**:**

## 1. Introduction

_{p}in 2022 to 215 GW

_{p}in 2030 and to 400 GW

_{p}in 2040 in Germany [9], large amounts of self-consumed energy in absolute numbers are anticipated. Hence, errors in the estimation of self-consumption have the potential for disruptive effects on the grid.

_{p}[6].

## 2. Methodology

#### 2.1. Data Sets

**PV system master data:**All renewable energy systems in remuneration under the German Renewable Energy Sources Act (“Erneuerbare-Energien-Gesetz” EEG) are listed in the EEG master data record. It comprises basic system characteristics such as the nominal power, the date of commissioning, the address and whether time-resolved feed-in measurements are taken. In order to cover the state of the PV portfolio in 2018, the record used here is the version of 18 December 2018. From 31 January 2019 on, the EEG master data was integrated into the Marktstammdatenregister (MaStR) [17], including additional information, e.g., on building usage, which has been used to set-up the prosumer model here.**Annual meter readings:**Regular power meter readings provide annual energy totals for each PV system. The total energy generation is additionally broken down into feed-in under the EEG FIT, self-consumption and direct marketing.**Transfer time series EUZ:**Feed-in time series are recorded on a distribution grid level for the data transfer between the distribution system operator (DSO) and the TSO (in German “Einspeiseüberführungszeitreihen” EUZ). They contain the time course of the PV feed-in under the EEG FIT in a 15 min resolution. For each distribution grid, two time series subsume the “SOL systems” which are measured on the one hand and the “SOT systems” which are derived from estimated feed-in profiles on the other hand. As the latter are not based on measurements, they were not be used in this study.

#### 2.2. Model System

#### 2.2.1. System Locations and Building Classification

#### 2.2.2. Generation Model

#### Solar Irradiance and Temperature

#### PV System Classification and Simulation Parameters

_{p}and two age categories by date of commissioning before and after 1 January 2010. For the resulting 10 classes of systems, assumptions on the system environment and technologies are made based on long-standing experience with yield assessments and monitoring of PV systems. An overview of the different PV simulation parameters is given in Table 1.

#### PV Module Orientations

_{p}only very few reference systems are available. As the contribution of those systems to the total PV power generation is particularly large, the orientation was determined manually on the basis of satellite images when possible. Tilt and azimuth angles that could not be determined in this way are then drawn independently from known distributions [26]. Figure 1 shows the marginal distributions of both angles for all power categories.

#### Postprocessing to Account for Additional Losses

#### 2.2.3. Consumption Model

#### Residential Sector

#### Nonresidential Sector

#### Modelling Consumption

#### 2.2.4. Self-Consumption Model

## 3. Model Validation

_{p}, this is not necessarily an error in the data. Therefore, the set of prosumers in the model portfolio was selected differently for the two validation steps according to the best information available.

#### 3.1. Comparison with Annual Meter Readings

#### 3.2. Comparison with Transfer Time Series

- The difference between the annual feed-in energy integrated over the EUZ and the meter reading sum over all systems is less than 5%.
- The share of systems (in number and nominal power) for which meter readings are available is at least 90%.
- The EUZ contains data for the whole year, and no irregularities like jumps or data gaps are observed.
- There are at least 10 systems of the distribution grid in the model portfolio.
- The model portfolio contains at least 50% of the SOL systems in the distribution grid.

_{p}nominal power out of which the prosumer model covers 1761 systems with 225.1 MW

_{p}nominal power. Table 4 summarizes the composition of this portfolio.

## 4. Model Results and Discussion

#### 4.1. Variations of Self-Consumption over the Year

#### 4.2. Variation of Self-Consumption with Different Parameters

#### Post-FIT Scenario

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Distributions of azimuth (

**left**) and tilt angles (

**right**) of the PV systems to be simulated (in blue) and reference systems (in orange) by nominal power classes. In the legend, both the numbers N of the sampled PV systems to be simulated and the reference systems for each class are given. The tilt angles for smaller systems often take high values (steeper roof inclinations of smaller residential buildings), low values for medium-sized systems (flatter roof inclination of large commercial buildings and rack mounting on flat roofs) and intermediate values for large systems (optimised for maximum energy yield). The azimuth angles are increasingly concentrated to the south as the nominal power increases (transition from available roof orientations to yield-optimised south orientations).

**Figure 2.**Mean electric load on workdays, Saturdays and Sundays for residential buildings, nonresidential buildings and the whole consumption model.

**Figure 3.**Scatter plot of the aggregated specific feed-in as modelled time series vs. measured transfer time series EUZ for the “PV-scaled” reference model and the prosumer model.

**Figure 4.**(

**Top**) Type week of specific feed-in in the “PV-scaled” reference model and the prosumer model in comparison with the transfer time series EUZ and the specific load. (

**Bottom**) Specific feed-in difference between the two models and the EUZ in the type weeks above.

**Figure 5.**Course of self-consumption over the year. (

**Top**) Monthly average of daily specific PV generation split into feed-in (dark colours) and self-consumption (light colours) for the SOL (green)/complete model (orange) portfolios. (

**Bottom**) Corresponding self-consumption rates per month.

**Figure 6.**Dependency of self-consumption on PV generation and time of day for the SOL (

**left**) and the complete model (

**right**) portfolios. The scatter symbols show the specific self-consumption ${\widehat{P}}_{\mathrm{SC}}$ and PV generation ${\widehat{P}}_{\mathrm{PV}}$ for each time step separated into workdays (blue circles), Saturdays (orange squares) and Sundays (green diamonds). The colours are shaded by the time of the day from morning (light) to evening (dark). The black lines indicate the relation between self-consumption and PV generation as predicted by the linear “PV-scaled” reference model based on the modelled overall self-consumption rates.

**Figure 7.**Dependency of self-consumption on PV generation and load for the SOL (

**left**) and the complete model (

**right**) portfolios. The scatter symbols show the specific self-consumption ${\widehat{P}}_{\mathrm{SC}}$ and PV generation ${\widehat{P}}_{\mathrm{PV}}$ for each time step coloured by the corresponding specific load ${\widehat{P}}_{\mathrm{Load}}$. The black lines indicate the relation between self-consumption and PV generation as predicted by the linear “PV-scaled” reference model based on the modelled overall self-consumption rates.

**Figure 8.**Dependency of the self-consumption rate on PV generation in a post-FIT scenario of 100% prosumer systems compared with the present share for the SOL (

**left**panel) and the complete model (

**right**panel) portfolios. The scatter dots show the instantaneous share of self-consumption on PV generation ${\widehat{P}}_{\mathrm{SC}}/{\widehat{P}}_{\mathrm{PV}}$ (left scale) for the present (blue) and post-FIT scenario (orange). The black lines depict the average ratio Q between future and present self-consumption shares in the indicated intervals (right scale). For a better visualisation, only data for working days are shown here.

**Table 1.**Technical and environmental parameters used for the PV power simulation with the range of values for the different classes of PV systems.

Ambient temperature increase in settlements | up to 5 K |

Irradiance-induced module temperature increase | 25–35 K at 1000 W/m^{2} |

Mean shading horizons | at 3°–7° solar elevation |

Internal shading losses | 1–2% for systems above 100 kW_{p} |

Degradation losses | 0.25% per year of operation |

String, medium, central inverters | typical models built in 2005/2015 |

Medium-voltage transformers | for systems above 100 kW_{p} |

**Table 2.**Composition of the full model portfolio with the number of PV systems (total nominal power in parentheses) by type of installation and information on self-consumption capability.

All PV Systems | Systems Designed for Self-Consumption | Systems with Reported Self-Consumption | |
---|---|---|---|

All installations | 118,650 (1755 MW_{p}) | 41,033 (566 MW_{p}) | 22,705 (405 MW_{p}) |

Residential | 98,066 (952 MW_{p}) | 35,511 (334 MW_{p}) | 18,542 (211 MW_{p}) |

Nonresidential | 20,488 (791 MW_{p}) | 5493 (231 MW_{p}) | 4148 (193 MW_{p}) |

Ground mounted | 96 (12 MW_{p}) | 29 (1 MW_{p}) | 15 (1 MW_{p}) |

**Table 3.**Comparison of the annual meter readings with the corresponding simulated energy sums. Here, feed-in integrates feed-in both under FIT and for direct marketing. The relative deviation is the difference between simulation and the reading normalized by the reading value.

Meter Readings | Simulation | Relative Deviation | |
---|---|---|---|

PV generation | 1667 GWh | 1725 GWh | +3.5% |

Feed-in | 1528 GWh | 1601 GWh | +4.8% |

Self-consumption | 139 GWh | 124 GWh | −10.7% |

Self-consumption rate | 8.3% | 7.2% | −13.3% |

**Table 4.**Composition of the SOL systems portfolio for time series validation with the number of PV systems (total nominal power in parentheses) by type of installation and information on self-consumption capability.

PV Systems | Designed for SC | |
---|---|---|

All installations | 1761 (225 MW_{p}) | 610 (69 MW_{p}) |

Residential | 360 (37 MW_{p}) | 151 (13 MW_{p}) |

Nonresidential | 1392 (184 MW_{p}) | 459 (56 MW_{p}) |

Ground mounted | 9 (4 MW_{p}) | 0 |

**Table 5.**RMSE between the aggregated modelled feed-in and the transfer time series EUZ for the reference “PV-scaled” and the simulated prosumer model (absolute and relative to the total nominal power) and relative improvement (Equation (7)).

Reference Model | Prosumer Model | Relative Improvement | |
---|---|---|---|

Absolute | 7.31 MW | 6.99 MW | 4.43% |

Relative | 1.98% | 1.89% | 4.43% |

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## Share and Cite

**MDPI and ACS Style**

Karalus, S.; Köpfer, B.; Guthke, P.; Killinger, S.; Lorenz, E. Analysing Grid-Level Effects of Photovoltaic Self-Consumption Using a Stochastic Bottom-up Model of Prosumer Systems. *Energies* **2023**, *16*, 3059.
https://doi.org/10.3390/en16073059

**AMA Style**

Karalus S, Köpfer B, Guthke P, Killinger S, Lorenz E. Analysing Grid-Level Effects of Photovoltaic Self-Consumption Using a Stochastic Bottom-up Model of Prosumer Systems. *Energies*. 2023; 16(7):3059.
https://doi.org/10.3390/en16073059

**Chicago/Turabian Style**

Karalus, Steffen, Benedikt Köpfer, Philipp Guthke, Sven Killinger, and Elke Lorenz. 2023. "Analysing Grid-Level Effects of Photovoltaic Self-Consumption Using a Stochastic Bottom-up Model of Prosumer Systems" *Energies* 16, no. 7: 3059.
https://doi.org/10.3390/en16073059