# Towards Scalable Economic Photovoltaic Potential Analysis Using Aerial Images and Deep Learning

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Existing PV Potential Analysis with Respect to Potential Type

#### 1.2. Existing PV Potential Analysis with Respect to Method

#### 1.3. Contributions of the Paper

- A methodology for scalable, bottom-up, economic PV potential analysis using aerial images and deep learning as well as publicly available data;
- The application of CNNs for semantic segmentation of roof segments and roof superstructure. Initial results are discussed to point out the advantages and disadvantages of the methodology;
- A comprehensive summary of research challenges and opportunities for this novel approach.

## 2. Materials and Methods

#### 2.1. Physical Potential

#### 2.2. Geographic Potential

#### 2.2.1. Datasets for Semantic Segmentation

#### 2.2.2. Performance Evaluation of Semantic Segmentation

#### 2.2.3. Semantic Segmentation for Roof Segments

^{−4}and is divided in half after 40 epochs. The second training phase incorporates all existing weights lasting for 100 epochs. It starts at a learning rate of 4 × 10

^{−5}which is divided in half after 60 and 80 epochs, respectively. During the training process, random augmentations are applied to the images to artificially increase the dataset and make the network less prone to overfitting [81]. The augmentations can be split into three different categories, which can be applied at the same time. Initially, the image is mirrored on the horizontal or vertical center axis. Afterward, the image can be randomly cropped to 80% of its size. Lastly, the image is changed on a pixel level by varying its brightness, contrast, gamma, or saturation. On the test set, we achieve an IoU of 0.89 averaged over all classes and 0.84 only focusing on roof classes.

#### 2.2.4. Semantic Segmentation for Roof Superstructures

#### 2.3. Technical Potential

#### 2.4. Economic Potential

#### 2.5. Case Study and Parameterization

## 3. Results and Discussion

#### 3.1. Results Convolutional Neural Networks

#### 3.2. Results Economic Potential

#### 3.3. Comparison of Aerial Image and LiDAR Based Approach

## 4. Research Opportunities

#### 4.1. Deep Learning for Extraction of Roof Information

#### 4.2. Improving Economic PV Potential Estimation Based on Aerial Images

#### 4.3. Using Economic PV Potential for Energy System Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Calculations

Calculation of the Technical Potential | |

Physical Potential | ${E}_{phy}={I}_{hor,glob}={I}_{hor,dir}+{I}_{hor,diff}$ |

Geographic Potential | ${E}_{geo}={I}_{tilt,eff}{A}_{usable}N{F}_{S}$ |

Global Irradiation on Tilted Surface | ${I}_{tilt,glob}={I}_{tilt,dir}+{I}_{tilt,diff}+{I}_{tilt,Ground}$ |

Effective Irradiation on Tilted Surface | ${I}_{gen,eff}={I}_{gen,glob}{U}_{irr}$ |

Module Area on a Tilted Surface | ${A}_{mod,proj}={w}_{Module}{l}_{Module}\mathrm{cos}{\theta}_{T}$ ${A}_{usable}=n{A}_{mod,proj}$ |

Technical Potential | ${\mathrm{E}}_{\mathrm{tech}}={E}_{geo}{\eta}_{Module}PR$ |

Calculation of the Economic Potential | |

Investment Costs | ${C}_{Invest}=\left({P}_{PV,max}{c}_{pv}\right)\left(1+VAT\right)$ |

Maintenance Costs | ${C}_{Maint}={\displaystyle {\displaystyle \sum}_{t=1}^{T}}\left({C}_{Maint,fix}+{P}_{PV,max}\text{}{c}_{Maint,var}\right){\left(1+{i}_{inf}\right)}^{t}{\left(1+i\right)}^{-t}$ |

Weighted Average Cost of Capital | $WACC=\frac{Equity}{Equity+Debt}{i}_{Equity}+\frac{Debt}{Equity+Debt}{i}_{Debt}$ |

Self-Consumption Ratio | $sc\left(t\right)=\frac{{E}_{sc}\left(t\right)}{{E}_{tech}\left(t\right)}$ |

Fed-In Electricity Within One Year | ${E}_{Feed-in}={\displaystyle {\displaystyle \sum}_{t=1}^{{N}_{Year}}}\left(1-sc\left(t\right)\right){E}_{tech}\left(t\right)$ |

Self-Consumed Electricity Within One Year | ${E}_{sc}={\displaystyle {\displaystyle \sum}_{t=1}^{{N}_{Year}}}sc\left(t\right){E}_{tech}\left(t\right)$ |

Net Present Value | $NPV={R}_{Feed-in}+{R}_{sc}-{C}_{Invest}-{C}_{Maint}-{C}_{EEG}$ |

Revenues from Feed-In | ${R}_{Feed-in}={\displaystyle {\displaystyle \sum}_{t=1}^{T}}{E}_{Feed-in}{e}_{tariff}{\left(1-b\right)}^{t}{\left(1+i\right)}^{-t}$ |

Revenues from Self-Consumption | ${R}_{sc}={\displaystyle {\displaystyle \sum}_{t=1}^{T}}{E}_{sc}{p}_{Electricity}{\left(1+\Delta {p}_{Electricity}\right)}^{t}{\left(1-b\right)}^{t}{\left(1+i\right)}^{-t}$ |

EEG-levy (Levy for self-consumption in Germany) | ${C}_{EEG}=\{\begin{array}{ll}0,& \text{}{P}_{PV,max}10\text{}kWp\\ {\displaystyle {\displaystyle \sum}_{t}^{T}}0.4\text{}{E}_{sc}\text{}{c}_{eeg}{\left(1+\Delta {c}_{eeg}\right)}^{t}{\left(1+i\right)}^{-t},& \text{}10\text{}kWp\le {P}_{PV,max}\le 750kWp\\ {\displaystyle {\displaystyle \sum}_{t}^{T}}{E}_{sc}{c}_{eeg}{\left(1+\Delta {c}_{eeg}\right)}^{t}{\left(1+i\right)}^{-t},& else\end{array}$ |

Variable | Unit | Description | Variable | Unit | Description |
---|---|---|---|---|---|

${A}_{mod,proj}$ | m² | Projected Horizontal Module $A=\pi {r}^{2}$ | $\mathrm{ev}$ | - | Self-Consumption Rate |

${A}_{usable}$ | m² | Area all Modules on Segment | $Debt$ | € | Debt |

$b$ | - | Degradation Rate | $h$ | - | Hurdle Rate |

${w}_{Module}$ | m | Module Width | ${I}_{tilt,Ground}$ | kWh/m² | Ground-Reflected Irradiation on a Tilted Surface |

${C}_{Maint}$ | € | Maintenance Costs | ${I}_{tilt,diff}$ | kWh/m² | Diffuse Irradiation on a Tilted Surface |

${C}_{Maint,fix}$ | € | Fix maintenance Costs | ${I}_{tilt,dir}$ | kWh/m² | Direct Irradiation on a Tilted Surface |

${c}_{Maint,var}$ | €/kWp | Variable maintenance Costs | ${I}_{tilt,eff}$ | kWh/m² | Effective Irradiation on a Tilted Surface |

${C}_{EEG}$ | € | Costs from EEG Levy | ${I}_{tilt,glob}$ | kWh/m² | Global Irradiation on a Tilted Surface |

${C}_{Invest}$ | € | Investment Costs | ${I}_{hor,diff}$ | kWh/m² | Diffuse Irradiation on a Horizontal Surface |

${c}_{eeg}$ | €/kWh | EEG Levy | ${I}_{hor,dir}$ | kWh/m² | Direct Irradiation on a Horizontal Surface |

$\Delta {c}_{eeg}$ | - | Yearly Change EEG Levy | ${I}_{hor,glob}$ | kWh/m² | Global Irradiation on a Horizontal Surface |

${c}_{pv}$ | €/kWp | Specific Investment Costs | $i$ | - | Internal Rate of Return |

${E}_{sc}$ | kWh | Self-Consumption | ${i}_{Equity}$ | Interest Rate (Equity) | |

${E}_{Feed-in}$ | kWh | Feed-In Electricity | ${i}_{Ebt}$ | Interest Rate (Debt) | |

${E}_{geo}$ | kWh | Geographic Potential | ${i}_{inf}$ | - | Inflation Rate |

${E}_{eco}$ | kWh | Economic Potential | $NPV$ | € | Net Present Value |

${E}_{phy}$ | kWh/m² | Physical Potential | ${l}_{Modul}$ | m | Length of pv Module |

${E}_{tech}$ | kWh | Technical Potential | $VAT$ | - | Value Added Tax |

${E}_{Consumption}$ | kWh | Electricity Consumption | ${U}_{irr}$ | - | Utilization Factor Irradiation |

$Equity$ | € | Equity | ${P}_{PV,max}$ | kWp | Plant Size |

${e}_{Tariff}$ | €/kWh | Feed-In Tariff |

## Appendix B. Technical and Economic Assumptions

Factor | Variable | Value |
---|---|---|

Module Placement on Flat Roofs | South-Orientation | |

Area Usage on Flat Roofs | F | 1:2 |

Module Slope on Flat Roofs | - | 36° |

Shadow Utilization Factor | $N{F}_{S}$ | 0.85 |

Performance Ratio | $PR$ | 0.80 |

Module Peak Power | ${P}_{module}$ | 300 Wp |

Efficiency | ${\eta}_{module}$ | 20.0% |

Module Length | ${l}_{module}$ | 1650 mm |

Module Width | ${b}_{module}$ | 992 mm |

Factor | Variable | Value | Source |
---|---|---|---|

Specific Investment Costs (incl. Value-added tax, VAT) | ${c}_{pv}$ | 1071 €/kWp | [3] + VAT |

Maintenance Costs Variable | ${c}_{Maint,var}$ | 22.50 €/kWp | [3,100] |

Maintenance Cost Fix | ${C}_{Maint}$ | 100.00 € | [3,100] |

Electricity Price | ${p}_{Electricity}$ | 30 ct/kWh | Assumption |

Yearly Change of Electricity Price | $\Delta {p}_{Electricity}$ | 2.0% | Assumption |

Feed-In Tariff up to 10 kWp | ${e}_{feed-in}$ | 7.81 ct/kWh | [101] |

Feed-In Tariff up to 40 kWp | ${e}_{feed-in}$ | 7.59 ct/kWh | [101] |

Feed-In Tariff up to 100 kWp | ${e}_{feed-in}$ | 5.95 ct/kWh | [101] |

EEG-Levy | ${c}_{eeg}$ | 6.50 ct/kWh | [102] |

Interest Rate Equity | ${i}_{Equity}$ | 6.0% | [103] (p 159) |

Interest Rate Debt | ${i}_{Debt}$ | 2.0% | [104] |

Debt Ratio | $l$ | 80.0% | [3] |

Inflation Rate | ${i}_{inf}$ | 1.5% | Assumption |

Degradation | $b$ | 0.25% | [105,106] |

Time Horizon | $T$ | 20a | [3,107,108] |

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**Figure 3.**Relative deviation of roof area depending on roof tilt angle (

**a**) and relative yearly energy generation (

**b**) in comparison to a 37° tilted, south-facing roof surface located in Munich, Germany.

**Figure 5.**Example results of the roof segmentation, (

**a**,

**b**) show correct segmentation, (

**c**) shows mediocre segmentation, and (

**d**) show incorrect segmentation results. Labels: ENE: east-north-east, SSE: south-south-east, WSW: west-south-west, NNW: north-north-west, NNE: north-north-east, NE: north-east, SSW: south-south-west, SW: south-west.

**Figure 6.**Example results of the superstructure segmentation, (

**a**) led to a correct segmentation, (

**b**) shows mediocre segmentation, and (

**c**) led to incorrect segmentation.

**Figure 7.**Image (

**a**) detected superstructures and module placement and (

**b**) resulting economic potential calculated as IRR for each segment.

**Figure 8.**Image (

**a**) google maps aerial image, (

**b**) solar potential map screenshot, (

**c**) merged building outlines from solar potential map, (

**d**) merged radiation visualization from solar potential map.

**Figure 9.**Examples of urban, suburban, and rural aerial images from Google Maps Static API in the greater Munich area.

**Figure 10.**Relative Frequency of OSM building labels in Bavaria based on 5 Mio. Labels, excluding building type “yes”.

Value | This Paper | LiDAR | Difference | Diff. in% |
---|---|---|---|---|

Total Area in m^{2} | 9188.97 | 10,185.4 | −996.43 | −10.84 |

Total Modules | 3211 | 5637 | −2426 | −75.55 |

Mean Modules | 45.22 | 79.39 | −34.17 | −75.55 |

Total Potential in MWh/Year | 625.18 | 1364.57 | −739.39 | −118.27 |

Mean Potential in kWh/Year | 8805.35 | 19,219.27 | −10,413.92 | −118.27 |

Mean Slope in Deg | 30.94 | 21.51 | 9.43 | 30.49 |

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**MDPI and ACS Style**

Krapf, S.; Kemmerzell, N.; Khawaja Haseeb Uddin, S.; Hack Vázquez, M.; Netzler, F.; Lienkamp, M. Towards Scalable Economic Photovoltaic Potential Analysis Using Aerial Images and Deep Learning. *Energies* **2021**, *14*, 3800.
https://doi.org/10.3390/en14133800

**AMA Style**

Krapf S, Kemmerzell N, Khawaja Haseeb Uddin S, Hack Vázquez M, Netzler F, Lienkamp M. Towards Scalable Economic Photovoltaic Potential Analysis Using Aerial Images and Deep Learning. *Energies*. 2021; 14(13):3800.
https://doi.org/10.3390/en14133800

**Chicago/Turabian Style**

Krapf, Sebastian, Nils Kemmerzell, Syed Khawaja Haseeb Uddin, Manuel Hack Vázquez, Fabian Netzler, and Markus Lienkamp. 2021. "Towards Scalable Economic Photovoltaic Potential Analysis Using Aerial Images and Deep Learning" *Energies* 14, no. 13: 3800.
https://doi.org/10.3390/en14133800