# Evaluation Method for Hosting Capacity of Rooftop Photovoltaic Considering Photovoltaic Potential in Distribution System

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- We propose an evaluation method for the hosting capacity of rooftop PV considering photovoltaic potential in the distribution system. Simulation experiments demonstrate that the proposed method can more accurately reflect the operation of the distribution system and the rooftop PV hosting capacity than the traditional evaluation method that assigns the same installed PV capacity to each distribution substation supply area.
- Because the existing methods make it difficult to carry out large-scale PV hosting capacity evaluation in the actual distribution system, we constructed a multi-level evaluation system for PV hosting capacity by combining multi-source data such as geographic information system data, metering system data, and satellite image data of the power grid corporation.
- An improved PSPNet is adopted to efficiently extract roof contours from satellite map images with high accuracy and implement the estimation of rooftop photovoltaic potential for each distribution substation supply area, which can meet the requirements of a large-scale evaluation of the PV hosting capacity in the distribution system.

## 2. Methodology

#### 2.1. Estimation of Rooftop Photovoltaic Potential Based on Improved PSPNet

_{1}is the mapping of G(x,y) to S(x,y); and f

_{2}is the mapping of S(x,y) to P(x,y).

#### 2.1.1. Improved PSPNet

#### 2.1.2. Building Roof Extraction Based on the Improved PSPNet

- (1)
- Collection of the dataset: select some representative building images from the satellite map image of the planning area for labeling and appropriately add the WHU building dataset to prepare data for subsequent model training;
- (2)
- Construction of the segmentation model: build the model based on the improved PSPNet described above;
- (3)
- Training the PSPNet model: set reasonable initial training hyperparameters and continuously optimize and iterate its parameters during the training process to save the model parameters with the best performance;
- (4)
- Extraction of building roofs: based on the satellite map images of the planning area, segment and extract the building roofs associated with each distribution substation using the trained PSPNet model and analyze the experimental results.

#### 2.1.3. Estimation of Rooftop Photovoltaic Potential

#### 2.2. Multi-Level PV Hosting Capacity Evaluation System for the Distribution System

#### 2.2.1. Data Preparation

- (1)
- Grid equipment data. These include the CIM/XML file of the distribution system to be evaluated and the Scalable Vector Graphics (SVGs) of the primary wiring diagram based on it, the conductor models, lengths, and unit equivalent impedances of each branch of the distribution system, and the distribution transformer models;
- (2)
- Photovoltaic installation data. The available area for PV panel installation, rooftop photovoltaic potential, and power factor adjustment range of photovoltaic inverters;
- (3)
- Typical operation scenario data. These include typical time-series data of rooftop photovoltaic power and load in each distribution substation supply area;
- (4)
- Security constraint data. These include bus voltage deviation limits, conductor current limits, and rated capacity of distribution transformers.

#### 2.2.2. Construction of a Multi-Level PV Hosting Capacity Evaluation System

#### 2.2.3. Indicator Calculation Model

- (1)
- The average voltage excursion index (AVEI) reflects the degree of deviation of the node voltage value from the rated value in the distribution system after accessing rooftop PV in a certain operation cycle, and the smaller its value, the better:$$VEI={\displaystyle \sum _{i\in N}\frac{{\left({U}_{i,t}-{U}_{i,rated}\right)}^{2}}{{U}_{i,rated}^{2}}}\times 100\%$$$$AVEI=\frac{1}{96}{\displaystyle \sum _{t=1}^{96}{\displaystyle \sum _{i\in N}\frac{{\left({U}_{i,t}-{U}_{i,rated}\right)}^{2}}{{U}_{i,rated}^{2}}}\times 100\%}$$
- (2)
- The average voltage qualification rate (AVQR) reflects the ratio of the number of qualified voltage nodes to the total number of nodes in the distribution system after accessing rooftop PV in a certain operation cycle, and the larger the value, the better.$$VQR=\frac{{N}_{V,t}}{N}\times 100\%$$$$AVQR=\frac{1}{96}{\displaystyle \sum _{t=1}^{96}\frac{{N}_{V,t}}{N}}\times 100\%$$
- (3)
- The average line loss rate (ALLR) reflects the overall network losses in the distribution system after accessing rooftop PV in a certain operation cycle, and the smaller its value, the better:$$LLR=\frac{{P}_{loss,t}}{{P}_{c,t}}\times 100\%$$$$ALLR=\frac{1}{96}{\displaystyle \sum _{t=1}^{96}\frac{{P}_{loss,t}}{{P}_{c,t}}\times 100\%}$$
- (4)
- The average net Load fluctuation rate (ALFR) reflects the intensity of net load fluctuation per unit of time in the distribution system after accessing rooftop PV in a certain operation cycle, and the smaller its value, the better:$$LFR=\frac{\left|{P}_{t}-{P}_{t-1}\right|}{{P}_{t}}\times 100\%$$$$ALFR=\frac{1}{96}{\displaystyle \sum _{t=1}^{96}\frac{\left|{P}_{t}-{P}_{t-1}\right|}{\left|{P}_{t}\right|}\times 100\%}$$
- (5)
- The average photovoltaic penetration rate (APPR) reflects the ratio of PV power to total load in the distribution system after accessing rooftop PV during a certain operation cycle, and the larger its value, the better:$$PPR=\frac{{\displaystyle \sum _{i\in D}{P}_{i,t}^{DG}}}{{P}_{t}}\times 100$$$$APPR=\frac{1}{96}{\displaystyle \sum _{t=1}^{96}\frac{{\displaystyle \sum _{i\in D}{P}_{i,t}^{DG}}}{{P}_{t}}\times 100\%}$$

#### 2.2.4. CRITIC Method

- (1)
- Indicator Normalization

- (2)
- Calculation of Information Carrying Capacity

- (3)
- Calculation of Indicator Weights

## 3. Results and Discussion

#### 3.1. Estimation Results of Roof Photovoltaic Potential

#### 3.1.1. Dataset

#### 3.1.2. Parameter Settings

#### 3.1.3. Evaluation Metrics

#### 3.1.4. Rooftop Photovoltaic Potential Estimation of Each Distribution Substation Supply Area and Precision Analysis

^{2}. Since the planning area in this paper is mainly rural, the vast majority of roofs are flat roofs and the house density is low, which are less used for other purposes, so the orientation coefficient ${f}_{1}$ and shading coefficient ${f}_{2}$ are taken as 0.9 and 0.8, respectively. According to the extraction results of the improved PSPNet model and Formula (2), the rooftop PV potential of each distribution substation supply area is shown in Table 4. It can be seen that the estimation of rooftop PV potential derived from the model in this paper is close to the actual value.

#### 3.2. Result Analysis of Roof Photovoltaic Hosting Capacity Evaluation

^{2}and a current limit of 445 A), which will cost approximately USD 3315(USD 1800 per kilometer). The distribution transformer of substation 2 can be replaced with S11-630 (which has a rated capacity of 630 kVA), which will cost approximately USD 8130.

## 4. Conclusions

- (1)
- Based on the improved PSPNet model, the rooftop contour in the satellite map image is extracted, and then the rooftop photovoltaic potential of each distribution substation supply area is estimated. The experimental results show that the DAPPM can effectively solve the problem of roof holes in the original PSPNet model. Compared with other models, improved PSPNet can ensure segmentation accuracy while maintaining a small number of parameters and reasoning time, which can effectively achieve the rooftop photovoltaic potential estimation of distribution substation supply area and meet the requirements of large-scale evaluation of the PV hosting capacity in the distribution system.
- (2)
- The proposed method considering photovoltaic potential can more accurately reflect the operation of the distribution system and the rooftop PV hosting capacity than the traditional evaluation method that assigns the same installed PV capacity to each distribution substation supply area.
- (3)
- Based on the rooftop photovoltaic potential estimation of the distribution substation supply area, combined with the multi-source data of the grid digitization system, and considering the safety, economy, and flexibility of the distribution system operation, a multi-level evaluation system of the PV hosting capacity is constructed. The experimental results show that the actual distribution system in the case has the lowest comprehensive score of hosting capacity in typical Scenario 3. In this scenario, the distribution system cannot fully accommodate the new rooftop photovoltaic, the voltage of nodes 6, 7, 17, 18, 19, and 20 will continuously exceed the limit, branch ② will have continuous current overload, and the distribution transformer in substation 2 will have continuous reverse overload. It is necessary to consider adding flexible resource control equipment, such as energy storage and SVC, or transforming the distribution network to make the PV hosting capacity of the distribution system reach 8548 kw so as to fully consume the new rooftop photovoltaic in the future.

- (1)
- The influence of the rooftop type of the building, the minimum installation area of photovoltaic panels, the rooftop association mode, and the environmental factors on the rooftop photovoltaic potential estimation of distribution substation supply area;
- (2)
- How to efficiently obtain the data required for hosting capacity evaluation from the digitization system of the distribution network;
- (3)
- The estimation of rooftop PV potential in this paper is mainly applied to a rural area in Shantou, China, and we aim to extend the methodology to urban areas with higher housing densities and more complex distribution systems in the future.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Branch | From | To | Unit Resistance (Ω/km) | Unit Reactance (Ω/km) | Basic Load (kW) | Power Factor | Conductor Cross-Sectional Area (mm ^{2}) | Length (km) | Current Limit (A) | Distribution Transformer Capacity at To_Node (kVA) |
---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 2 | 0.21 | 0.36 | 190 | 0.967 | 150 | 0.493 | 445 | 250 |

2 | 2 | 3 | 0.45 | 0.38 | 400 | 0.961 | 70 | 0.984 | 275 | 800 |

3 | 3 | 4 | 0.45 | 0.38 | 440 | 0.959 | 70 | 0.858 | 275 | 500 |

4 | 4 | 5 | 0.45 | 0.38 | 390 | 0.956 | 70 | 0.822 | 275 | 500 |

5 | 5 | 6 | 0.85 | 0.40 | 350 | 0.958 | 35 | 0.964 | 170 | 500 |

6 | 6 | 7 | 0.21 | 0.36 | 200 | 0.958 | 150 | 0.877 | 445 | 250 |

7 | 2 | 8 | 0.85 | 0.40 | 150 | 0.949 | 35 | 0.888 | 170 | 250 |

8 | 8 | 9 | 1.01 | 0.42 | 470 | 0.958 | 25 | 1.217 | 130 | 630 |

9 | 9 | 10 | 0.85 | 0.40 | 480 | 0.954 | 35 | 1.045 | 170 | 630 |

10 | 10 | 11 | 0.45 | 0.38 | 330 | 0.957 | 70 | 0.726 | 275 | 500 |

11 | 10 | 12 | 0.45 | 0.38 | 145 | 0.945 | 70 | 0.833 | 275 | 250 |

12 | 12 | 13 | 1.01 | 0.42 | 260 | 0.956 | 25 | 1.453 | 130 | 315 |

13 | 4 | 14 | 0.45 | 0.38 | 240 | 0.949 | 70 | 1.204 | 275 | 315 |

14 | 14 | 15 | 0.85 | 0.40 | 250 | 0.963 | 35 | 0.865 | 170 | 315 |

15 | 15 | 16 | 0.85 | 0.40 | 190 | 0.997 | 35 | 0.921 | 170 | 250 |

16 | 16 | 17 | 1.01 | 0.42 | 600 | 0.946 | 25 | 1.401 | 130 | 800 |

17 | 17 | 18 | 0.85 | 0.40 | 120 | 0.960 | 35 | 0.908 | 170 | 200 |

18 | 6 | 19 | 0.21 | 0.36 | 120 | 0.947 | 150 | 0.781 | 445 | 200 |

19 | 19 | 20 | 1.01 | 0.42 | 720 | 0.956 | 25 | 1.554 | 130 | 1250 |

**Figure A1.**Evaluation indicator variation curves for different scenarios of the tested distribution system.

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**Figure 1.**Flowchart for evaluating the PV hosting capacity of the distribution system considering the estimation of rooftop photovoltaic potential.

**Figure 3.**Structural schematic diagram of the original PSPNet. (

**a**) Input image. (

**b**) Feature map. (

**c**) Pyramid Pooling Module. (

**d**) Segmentation.

**Figure 9.**Variation curves for loss function, MIOU, and accuracy. (

**a**) Curve of loss value. (

**b**) Curve of MIOU value. (

**c**) Curve of accuracy value.

**Figure 10.**Contrast chart of the extraction for each model. (

**a**) Original image. (

**b**) Label. (

**c**) DeeplabV3+. (

**d**) PSPNet. (

**e**) Improved PSPNet.

Stage | Hyperparameter Type | Parameter Value | |
---|---|---|---|

Downsample factor | 8 | ||

Freezing stage | Batch_size | 8 | |

Init learning rate | 1 × 10^{−2} | ||

Unfreezing stage | Batch_size | 4 | |

Init learning rate | 1 × 10^{−2} | ||

Learning rate decay type | CosineAnnealing | ||

Momentum | 0.9 | ||

Weight_decay | 1 × 10^{−4} | ||

Minimum image size | 256 × 256 |

Metrics | Calculation Formula | Explanation |
---|---|---|

MIOU | $MIOU=\frac{1}{k+1}{\displaystyle \sum _{i=0}^{k}\frac{TP}{FN+FP+TP}}$ | The mean of the intersection over union values |

MPA | $MPA=\frac{1}{k+1}{\displaystyle \sum _{i=0}^{k}\frac{{p}_{ii}}{{\displaystyle \sum _{j=0}^{k}{p}_{ij}}}}$ | The mean accuracy of pixel-wise classification |

Accuracy | $Accuracy=\frac{TP+TN}{TP+TN+FP+FN}$ | The proportion of correctly classified samples in a classification task |

F1 score | $F1-score=\frac{2TP}{\left(TP+FN\right)\left(TP+FP\right)}$ | The harmonic mean of precision and recall |

Times | Execution time, typically representing the time consumption of model inference | |

Parameters | Total number of parameters included in the model | |

FLOPs | The number of floating point operations performed by a model |

Method | MIOU (%) | MPA (%) | Accuracy (%) | F1 Score | Time (ms) | Param (M) | FLOPs (G) |
---|---|---|---|---|---|---|---|

DeeplabV3+ | 81.08 | 87.32 | 95.21 | 0.8892 | 50.98 | 5.813 | 13.22 |

PSPNet | 82.51 | 89.10 | 95.54 | 0.8990 | 49.96 | 46.71 | 29.69 |

Improved PSPNet | 83.77 | 89.93 | 95.89 | 0.9073 | 49.68 | 23.70 | 19.93 |

Distribution Substation No. | Extracted Rooftop Area (m^{2}) | Available Area for PV Panel Installation (m^{2}) | Estimated Rooftop PV Potential (kW) | Real Rooftop PV Potential (kW) |
---|---|---|---|---|

2 | 3009 | 2166 | 325 | 309 |

3 | 6870 | 4947 | 742 | 782 |

4 | 2657 | 1913 | 287 | 245 |

5 | 4074 | 2933 | 440 | 410 |

6 | 7981 | 5746 | 862 | 895 |

7 | 2870 | 2067 | 310 | 336 |

8 | 2491 | 1794 | 269 | 284 |

9 | 3889 | 2800 | 420 | 447 |

10 | 4028 | 2900 | 435 | 470 |

11 | 3194 | 2300 | 345 | 326 |

12 | 2574 | 1853 | 278 | 295 |

13 | 2870 | 2066 | 310 | 322 |

14 | 3056 | 2200 | 330 | 315 |

15 | 3324 | 2393 | 359 | 383 |

16 | 2407 | 1733 | 260 | 246 |

17 | 8148 | 5867 | 880 | 924 |

18 | 2083 | 1500 | 225 | 198 |

19 | 1667 | 1200 | 180 | 205 |

20 | 11,954 | 8607 | 1291 | 1255 |

Total | 79,146 | 56,985 | 8548 | 8644 |

Indicator | AVEI | AVQR | ALLR | ALFR | APPR | Comprehensive Score |
---|---|---|---|---|---|---|

Scenario 1 | 1.04 | 91.04 | 0.2790 | 6.45 | 48.65 | 64.13 |

Scenario 2 | 0.56 | 1 | 0.2745 | 6.15 | 28.13 | 52.92 |

Scenario 3 | 2.26 | 75.16 | 0.3580 | 9.43 | 107.62 | 41.76 |

Scenario 4 | 0.81 | 95.52 | 0.2741 | 4.30 | 50.02 | 76.94 |

Scenario 5 | 1.33 | 84.06 | 0.3302 | 4.36 | 66.48 | 72.55 |

Weights | 0.1285 | 0.1420 | 0.1666 | 0.1453 | 0.4176 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Xu, Y.; He, J.; Liu, Y.; Li, Z.; Cai, W.; Peng, X.
Evaluation Method for Hosting Capacity of Rooftop Photovoltaic Considering Photovoltaic Potential in Distribution System. *Energies* **2023**, *16*, 7677.
https://doi.org/10.3390/en16227677

**AMA Style**

Xu Y, He J, Liu Y, Li Z, Cai W, Peng X.
Evaluation Method for Hosting Capacity of Rooftop Photovoltaic Considering Photovoltaic Potential in Distribution System. *Energies*. 2023; 16(22):7677.
https://doi.org/10.3390/en16227677

**Chicago/Turabian Style**

Xu, Yilin, Jie He, Yang Liu, Zilu Li, Weicong Cai, and Xiangang Peng.
2023. "Evaluation Method for Hosting Capacity of Rooftop Photovoltaic Considering Photovoltaic Potential in Distribution System" *Energies* 16, no. 22: 7677.
https://doi.org/10.3390/en16227677