# Relationships between the Number and Power of Hungarian Household-Sized Photovoltaic Power Plants and Selected Indicators of the Settlements: A Case Study

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## Abstract

**:**

## 1. Introduction

#### 1.1. Changes in the Spread of Photovoltaic Technology

#### 1.2. The Hungarian System of Feed-in-Tariffs—Overview

#### 1.3. Introduction to the Methodology of Regional Development Indicators in Hungary

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- Every particular settlement indicator is suitable for identifying relationships concerning the number and power of photovoltaic HMKEs.
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- The ranking of the settlements based on the complex indicators derived from the settlement indicators shows a correlation with the ranking of the settlements according to the number and power of photovoltaic HMKEs/1000 people in Hungary.
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- A regression model that can be used to determine the quantity of photovoltaic HMKEs in the settlements can be created.

## 2. Materials and Methods

#### 2.1. Methods

_{1}, X

_{2},…, X

_{p}variables can be accounted for by the X

_{j}explanatory variable [38].

_{i j}: normalized basic indicator, min(fa

_{i j}): the lowest value of the basic indicator, max(fa

_{i j}): the highest value of the basic indicator.

_{1}to x

_{n}: independent variables, Y: dependent variable, β

_{1}: the regression coefficient of variable x

_{1}, β

_{n}: the regression coefficient of variable x

_{n}.

#### 2.2. Material

- ELMŰ-ÉMÁSZ, EON (2417 settlements):
- Total HMKE power per 1000 population (kW);
- Residential HMKE power per 1000 population (kW);
- Business HMKE power per 1000 population (kW);
- Total HMKEs per 1000 population (pcs);
- Residential HMKEs per 1000 population (pcs); and
- Business HMKEs per 1000 population (pcs).

- ELMŰ-ÉMÁSZ, EON, NKM (2631 settlements):
- Total HMKEs per 1000 population (pcs).

- EON (1763 settlements):
- Total HMKE power per 1000 population (kW);
- Residential HMKE power per 1000 population (kW);
- Public HMKE power per 1000 population (kW);
- Business HMKE power per 1000 population (kW);
- Total HMKEs per 1000 population (pcs);
- Residential HMKEs per 1000 population (pcs);
- Public HMKEs per 1000 population (pcs); and
- Business HMKEs per 1000 population (pcs).

## 3. Results and Discussions of the Correlation Analysis between the Number and Power of HMKEs and the Settlements’ Level of Development

_{5}: the number of electricity consumers per 1000 population, pcs; x

_{1}: the number of registered economic organizations per 1000 population; x

_{3}: the total budgetary expenditure of municipalities per 1000 population. It was established that both the regression model and the parameters were significant (p = 0.000); furthermore, based on the value of are R (0.554), there was a moderately strong correlation between the explanatory variables of the model and the number of HMKEs per 1000 population, and the five indicators explained the differentiation of the quantity of HMKEs at the settlements’ level to an extent of 30.7%.

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- There are certain settlement indicators each of which individually shows a correlation with the quantity and power of photovoltaic HMKEs. These relationships could be identified irrespective of the service regions of the specific electricity suppliers. There was a moderately strong correlation between the number of registered economic organizations per 1000 population, the number of operating commercial accommodation units per 1000 population, the number of businesses in the hospitality industry per 1000 population, and the quantity of total photovoltaic HMKEs per 1000 population. Furthermore, there was also a moderately strong correlation between the total budgetary expenditure of the municipalities per 1000 population, the number of businesses in the hospitality industry per 1000 population, the number of residential electricity consumers per 1000 population, the number of electricity consumers per 1000 population, the length of the low-voltage electricity distribution network per 1000 population, and the power of total photovoltaic HMKEs per 1000 population.
- -
- The ranking of the settlements based on the complex indicator created from the settlement indicators showed a correlation with the ranking of the settlements according to the number and power of the photovoltaic HMKEs per 1000 population. The relationship between the rankings was moderately strong, with the exception of the residential, public, and business photovoltaic HMKE users in the service region of EON, where the correlation was only weak.
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- A regression model was created from the settlements’ database containing data from all three electricity supplier regions. In this model, the quantity of photovoltaic HMKEs per 1000 population is explained by the number of electricity consumers per 1000 population, the number of economic organizations per 1000 population, and the total budgetary expenditure of the municipalities per 1000 population.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ELMŰ-ÉMÁSZ | ELMŰ-ÉMÁSZ Energiaszolgáltató ZRT./ELMŰ-ÉMÁSZ Energy Service Privately Held Company/ |

EON | E.ON Hungária Zrt./E.ON Hungária Privately Held Company/ |

fa_{i j} | normalized basic indicator |

HMKE | household-sized power plants |

CDI | complex development index |

KSH | Központi Statisztikai Hivatal/Hungarian Central Statistical Office/ |

min(fa_{i j}) | the lowest value of the basic indicator |

max(fa_{i j}) | the highest value of the basic indicator |

NKM | NKM Energia Zrt./NKM Energia Privately Held Company/ |

pSi | Polycrystalline |

PV | Photovoltaic |

TEIR | Országos Teületfejlesztési és Területrendezési Információs Rendszer/National Regional Development and Spatial Planning Information System/ |

x_{1} to x_{n} | Represent independent variables |

β_{1} | The regression coefficient of variable x_{1} |

β_{n} | The regression coefficient of variable x_{n}. |

## Appendix A. Correlations between the Quantity and Power of the Residential, Business, and Public HMKEs and the Development Indicators

**Table A1.**The strengths of the relationships between the quantity of the residential HMKEs per 1000 population and the settlement indicators

^{1}(

^{1}Pearson correlation coefficient/p-value; if p < 0.05, then there is a significant verified relationship between the two variables) (In the case of the Pearson correlation coefficients in the table grey background indicates weak correlations, yellow means weak moderate, and purple moderately close ones. In the case of the partial correlation the blue background signals partial explanation (the controlled variable explains the relationship between variables i and j only partially), while the black one shows irrelevant comparison.).

Indicator | Pearson Correlation Coefficient | Partial Correlation Coefficient | |||||
---|---|---|---|---|---|---|---|

Residential HMKEs per 1000 Population (pcs) | Number of Residential Electricity Consumers per 1000 Population (pcs) | Number of Electricity Consumers per 1000 Population (pcs) | Length of the Low-Voltage Electricity Distribution Network per 1000 Population (km) | Number of Registered Businesses per 1000 Population (pcs) | Number of Units of Operating Commercial Accommodation Units per 1000 Population (pcs) | NUMBER of Businesses in the Hospitality Industry per 1000 Population (pcs) | |

Number of registered businesses per 1000 population (pcs) | 0.272/0.000 | 0.449/0.000 | 0.455/0.000 | 0.395/0.000 | 0.184/0.000 | 0.243/0.000 | |

Total budgetary revenue of the municipalities per 1000 population (HUF 1000) | 0.099/0.000 | 0.482/0.000 | 0.494/0.000 | 0.439/0.000 | 0.259/0.000 | 0.199/0.000 | 0.262/0.000 |

Total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | 0.140/0.000 | 0.476/0.000 | 0.487/0.000 | 0.432/0.000 | 0.249/0.000 | 0.192/0.000 | 0.256/0.000 |

Number of residential electricity consumers per 1000 population (pcs) | 0.490/0.000 | 0.129/0.000 | 0.150/0.000 | 0.166/0.000 | 0.053/0.000 | 0.049/0.000 | |

Number of electricity consumers per 1000 population (pcs) | 0.502/0.000 | 0.024/0.000 | 0.132/0.000 | 0.136/0.000 | 0.050/0.000 | 0.054/0.000 | |

Length of the low-voltage electricity distribution network per 1000 population (km) | 0.448/0.000 | 0.264/0.000 | 0.283/0.000 | 0.148/0.000 | 0.114/0.000 | 0.170/0.000 | |

Number of units of operating commercial accommodation units per 1000 population (pcs) | 0.213/0.000 | 0.454/0.000 | 0.467/0.000 | 0.417/0.000 | 0.251/0.000 | 0.189/0.000 | |

Number of businesses in the hospitality industry per 1000 population (pcs) | 0.276/0.000 | 0.423/0.000 | 0.439/0.000 | 0.400/0.000 | 0.239/0.000 | 0.061/0.000 |

**Table A2.**The strengths of the relationships between the power of the residential HMKEs per 1000 population and the settlement indicators

^{1}(

^{1}Pearson correlation coefficient/p-value; if p < 0.05, then there is a significant verified relationship between the two variables) (In the case of the Pearson correlation coefficients in the table grey background indicates weak correlations, yellow means weak moderate, and purple moderately close ones. In the case of the partial correlation the blue background signals partial explanation (the controlled variable explains the relationship between variables i and j only partially), while the black one shows irrelevant comparison.).

Indicator | Pearson Correlation Coefficient | Partial Correlation Coefficient | ||||
---|---|---|---|---|---|---|

Residential HMKE Power per 1000 Population (kW) | Number of Residential Electricity Consumers per 1000 Population (pcs) | Number of Electricity Consumers per 1000 Population (pcs) | Length of the Low-Voltage Electricity Distribution Network per 1000 Population (km) | Number of Registered Businesses per 1000 Population (pcs) | Number of Businesses in the Hospitality Industry per 1000 Population (pcs) | |

Number of registered businesses per 1000 population (pcs) | 0.274/0.000 | 0.362/0.000 | 0.385/0.000 | 0.347/0.000 | 0.183/0.000 | |

Total budgetary revenue of the municipalities per 1000 population (HUF 1000) | 0.078/0.000 | 0.403/0.000 | 0.433/0.000 | 0.399/0.000 | 0.265/0.000 | 0.207/0.000 |

Total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | 0.115/0.000 | 0.397/0.000 | 0.426/0.000 | 0.392/0.000 | 0.256/0.000 | 0.201/0.000 |

Number of residential electricity consumers per 1000 population (pcs) | 0.409/0.000 | 0.183/0.000 | 0.169/0.000 | 0.185/0.000 | 0.024/0.000 | |

Number of electricity consumers per 1000 population (pcs) | 0.439/0.000 | –0.059/0.000 | 0.133/0.000 | 0.157/0.000 | 0.017/0.000 | |

Length of the low-voltage electricity distribution network per 1000 population (km) | 0.405/0.000 | 0.180/0.000 | 0.226/0.000 | 0.163/0.000 | 0.115/0.000 | |

Number of units of operating commercial accommodation units per 1000 population (pcs) | 0.163/0.000 | 0.381/0.000 | 0.413/0.000 | 0.381/0.000 | 0.257/0.000 | 0.153/0.000 |

Number of businesses in the hospitality industry per 1000 population (pcs) | 0.219/0.000 | 0.395/0.000 | 0.390/0.000 | 0.366/0.000 | 0.247/0.000 |

**Table A3.**The strengths of the relationships between the quantity of the business HMKEs per 1000 population and the settlement indicators

^{1}(

^{1}Pearson correlation coefficient/p-value; if p < 0.05, then there is a significant verified relationship between the two variables) (In the case of the Pearson correlation coefficients in the table grey background indicates weak correlations and yellow means weak moderate ones. In the case of the partial correlation the red background indicates a partially distorted correlation, blue signals partial explanation (the controlled variable explains the relationship between variables i and j only partially), while the black one shows irrelevant comparison.).

Indicator | Pearson Correlation Coefficient | Partial Correlation Coefficient | ||||
---|---|---|---|---|---|---|

Business HMKEs per 1000 Population (pcs) | Number of Registered Businesses per 1000 Population (pcs) | Total Budgetary Revenue of the Municipalities per 1000 Population (HUF 1000) | Total Budgetary Expenditure of the Municipalities per 1000 Population (HUF 1000) | Number of Electricity Consumers per 1000 Population (pcs) | Length of the Low-Voltage Electricity Distribution Network per 1000 Population (km) | |

Number of registered businesses per 1000 population (pcs) | 0.305/0.000 | 0.250/0.000 | 0.303/0.000 | 0.145/0.000 | 0.113/0.000 | |

Total budgetary revenue of the municipalities per 1000 population (HUF 1000) | 0.291/0.000 | 0.266/0.000 | 0.205/0.000 | 0.181/0.000 | 0.151/0.000 | |

Total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | 0.351/0.000 | 0.246/0.000 | 0.011/0.000 | 0.151/0.000 | 0.131/0.000 | |

Number of residential electricity consumers per 1000 population (pcs) | 0.178/0.000 | 0.271/0.000 | 0.269/0.000 | 0.327/0.000 | 0.188/0.000 | 0.106/0.000 |

Number of electricity consumers per 1000 population (pcs) | 0.229/0.000 | 0.251/0.000 | 0.256/0.000 | 0.310/0.000 | 0.050/0.000 | |

Length of the low-voltage electricity distribution network per 1000 population (km) | 0.202/0.000 | 0.258/0.000 | 0.260/0.000 | 0.319/0.000 | 0.121/0.000 | |

Number of units of operating commercial accommodation units per 1000 population (pcs) | 0.144/0.000 | 0.291/0.000 | 0.271/0.000 | 0.333/0.000 | 0.193/0.000 | 0.172/0.000 |

Number of businesses in the hospitality industry per 1000 population (pcs) | 0.047/0.020 | 0.302/0.000 | 0.288/0.000 | 0.349/0.000 | 0.234/0.000 | 0.197/0.000 |

**Table A4.**The strengths of the relationships between the power of the business HMKEs per 1000 population and the settlement indicators

^{1}(

^{1}Pearson correlation coefficient/p-value; if p < 0.05, then there is a significant verified relationship between the two variables) (In the case of the Pearson correlation coefficients in the table grey background indicates weak correlations and yellow means weak moderate ones. In the case of the partial correlation the blue background signals partial explanation (the controlled variable explains the relationship between variables i and j only partially), while the black one shows irrelevant comparison.).

Indicator | Pearson Correlation Coefficient | Partial Correlation Coefficient | ||
---|---|---|---|---|

Business HMKE Power per 1000 Population (kW) | Number of Registered Businesses per 1000 Population (pcs) | Total Budgetary Revenue of the Municipalities per 1000 Population (HUF 1000) | Total Budgetary Expenditure of the Municipalities per 1000 Population (HUF 1000) | |

Number of registered businesses per 1000 population (pcs) | 0.241/0.000 | 0.177/0.000 | 0.210/0.000 | |

Total budgetary revenue of the municipalities per 1000 population (HUF 1000) | 0.214/0.000 | 0.209/0.000 | 0.140/0.000 | |

Total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | 0.254/0.000 | 0.194/0.000 | 0.014/0.000 | |

Number of residential electricity consumers per 1000 population (pcs) | 0.138/0.000 | 0.213/0.000 | 0.195/0.000 | 0.233/0.000 |

Number of electricity consumers per 1000 population (pcs) | 0.156/0.000 | 0.204/0.000 | 0.188/0.000 | 0.223/0.000 |

Length of the low-voltage electricity distribution network per 1000 population (km) | 0.151/0.000 | 0.205/0.000 | 0.189/0.000 | 0.227/0.000 |

Number of units of operating commercial accommodation units per 1000 population (pcs) | 0.107/0.000 | 0.230/0.000 | 0.198/0.000 | 0.239/0.000 |

Number of businesses in the hospitality industry per 1000 population (pcs) | 0.098/0.000 | 0.229/0.000 | 0.198/0.000 | 0.241/0.000 |

**Table A5.**The strengths of the relationships between the quantity of the residential HMKEs per 1000 population and the settlement indicators

^{1}(

^{1}Pearson correlation coefficient/p-value; if p < 0.05, then there is a significant verified relationship between the two variables) (In the case of the Pearson correlation coefficients in the table grey background indicates weak correlations, yellow means weak moderate, and purple moderately close ones. In the case of the partial correlation the blue background signals partial explanation (the controlled variable explains the relationship between variables i and j only partially), while the black one shows irrelevant comparison.).

Indicator | Pearson Correlation Coefficient | Partial Correlation Coefficient | |||||
---|---|---|---|---|---|---|---|

Residential HMKEs per 1000 Population (pcs) | Number of Residential Electricity Consumers per 1000 Population (pcs) | Number of Electricity Consumers per 1000 Population (pcs) | Number of Registered Businesses per 1000 Population (pcs) | Length of the Low-Voltage Electricity Distribution Network per 1000 Population (km) | Number of Units of Operating Commercial Accommodation Units per 1000 Population (pcs) | Number of Businesses in the Hospitality Industry per 1000 Population (pcs) | |

Number of registered businesses per 1000 population (pcs) | 0.212/0.000 | 0.479/0.000 | 0.481/0.000 | 0.346/0.000 | 0.174/0.000 | 0.273/0.000 | |

Total budgetary revenue of the municipalities per 1000 population (HUF 1000) | 0.060/0.012 | 0.503/0.000 | 0.507/0.000 | 0.205/0.000 | 0.383/0.000 | 0.196/0.000 | 0.293/0.000 |

Total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | 0.064/0.007 | 0.502/0.000 | 0.506/0.000 | 0.204/0.000 | 0.382/0.000 | 0.195/0.000 | 0.292/0.000 |

Number of residential electricity consumers per 1000 population (pcs) | 0.505/0.000 | 0.074/0.000 | 0.111/0.000 | 0.029/0.000 | 0.016/0.000 | 0.051/0.000 | |

Number of electricity consumers per 1000 population (pcs) | 0.508/0.000 | –0.028/0.000 | 0.098/0.000 | 0.014/0.000 | 0.006/0.000 | 0.044/0.000 | |

Length of the low-voltage electricity distribution network per 1000 population (km) | 0.387/0.000 | 0.353/0.000 | 0.358/0.000 | 0.106/0.000 | 0.121/0.000 | 0.207/0.000 | |

Number of units of operating commercial accommodation units per 1000 population (pcs) | 0.204/0.000 | 0.472/0.000 | 0.476/0.000 | 0.184/0.000 | 0.355/0.000 | 0.225/0.000 |

**Table A6.**The strengths of the relationships between the power of the residential HMKEs per 1000 population and the settlement indicators

^{1}(

^{1}Pearson correlation coefficient/p-value; if p < 0.05, then there is a significant verified relationship between the two variables) (In the case of the Pearson correlation coefficients in the table grey background indicates weak correlations, yellow means weak moderate, and purple moderately close ones. In the case of the partial correlation the blue background signals partial explanation (the controlled variable explains the relationship between variables i and j only partially), while the black one shows irrelevant comparison.).

Indicator | Pearson Correlation Coefficient | Partial Correlation Coefficient | ||||
---|---|---|---|---|---|---|

Residential HMKE Power per 1000 Population (kW) | Number of Residential Electricity Consumers per 1000 Population (pcs) | Number of Electricity Consumers per 1000 Population (pcs) | Number of Registered Businesses per 1000 Population (pcs) | Length of the Low-Voltage Electricity Distribution Network per 1000 Population (km) | Number of Businesses in the Hospitality Industry per 1000 Population (pcs) | |

Number of registered businesses per 1000 population (pcs) | 0.210/0.000 | 0.381/0.000 | 0.384/0.000 | 0.315/0.000 | 0.205/0.000 | |

Total budgetary revenue of the municipalities per 1000 population (HUF 1000) | 0.054/0.024 | 0.409/0.000 | 0.415/0.000 | 0.204/0.000 | 0.354/0.000 | 0.227/0.000 |

Total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | 0.059/0.014 | 0.408/0.000 | 0.414/0.000 | 0.203/0.000 | 0.354/0.000 | 0.226/0.000 |

Number of residential electricity consumers per 1000 population (pcs) | 0.411/0.000 | 0.099/0.000 | 0.127/0.000 | 0.091/0.000 | 0.027/0.000 | |

Number of electricity consumers per 1000 population (pcs) | 0.417/0.000 | –0.064/0.008 | 0.117/0.000 | 0.077/0.000 | 0.019/0.000 | |

Length of the low-voltage electricity distribution network per 1000 population (km) | 0.358/0.000 | 0.235/0.000 | 0.242/0.000 | 0.112/0.000 | 0.141/0.000 | |

Number of units of operating commercial accommodation units per 1000 population (pcs) | 0.155/0.000 | 0.386/0.000 | 0.392/0.000 | 0.188/0.000 | 0.334/0.000 | 0.177/0.000 |

Number of businesses in the hospitality industry per 1000 population (pcs) | 0.233/0.000 | 0.349/0.000 | 0.356/0.000 | 0.178/0.000 | 0.310/0.000 |

**Table A7.**The strengths of the relationships between the quantity of the public HMKEs per 1000 population and the settlement indicators

^{1}(

^{1}Pearson correlation coefficient/p-value; if p < 0.05, then there is a significant verified relationship between the two variables) (In the case of the Pearson correlation coefficients in the table white background indicates non–significant relationships, grey weak and yellow means weak moderate ones. In the case of the partial correlation the red background indicates a partially distorted correlation and blue signals partial explanation (the controlled variable explains the relationship between variables i and j only partially), while black shows irrelevant comparison.).

Indicator | Pearson Correlation Coefficient | Partial Correlation Coefficient | |
---|---|---|---|

Public HMKEs per 1000 Population (pcs) | Total Budgetary Revenue of the Municipalities per 1000 Population (HUF 1000) | Total Budgetary Expenditure of the Municipalities per 1000 Population (HUF 1000) | |

Number of registered businesses per 1000 population (pcs) | 0.055/0.020 | 0.215/0.000 | 0.256/0.000 |

Total budgetary revenue of the municipalities per 1000 population (HUF 1000) | 0.221/0.000 | 0.145/0.000 | |

Total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | 0.262/0.000 | 0.016/0.000 | |

Number of residential electricity consumers per 1000 population (pcs) | –0.001/0.981 | 0.224/0.000 | 0.265/0.000 |

Number of electricity consumers per 1000 population (pcs) | 0.010/0.661 | 0.223/0.000 | 0.264/0.000 |

Length of the low-voltage electricity distribution network per 1000 population (km) | –0.005/0.845 | 0.225/0.000 | 0.266/0.000 |

Number of units of operating commercial accommodation units per 1000 population (pcs) | 0.008/0.742 | 0.223/0.000 | 0.266/0.000 |

Number of businesses in the hospitality industry per 1000 population (pcs) | 0.006/0.791 | 0.227/0.000 | 0.268/0.000 |

**Table A8.**The strengths of the relationships between the power of the public HMKEs per 1000 population and the settlement indicatorsv

^{1}(

^{1}Pearson correlation coefficient/p-value; if p < 0.05, then there is a significant verified relationship between the two variables) (In the case of the Pearson correlation coefficients in the table white background indicates non–significant relationships, grey weak and yellow means weak moderate ones. In the case of the partial correlation the green background signals cases where the background variable did not cause any difference in the strength of the relationship, while blue background indicates partial explanation (the controlled variable explains the relationship between variables i and j only partially), and black marking shows irrelevant comparison.).

Indicator | Pearson Correlation Coefficient | Partial Correlation Coefficient | |
---|---|---|---|

Public HMKE Power per 1000 Population (kW) | Total Budgetary Revenue of the Municipalities per 1000 Population (HUF 1000) | Total Budgetary Expenditure of the Municipalities per 1000 Population (HUF 1000) | |

Number of registered businesses per 1000 population (pcs) | 0.052/0.028 | 0.219/0.000 | 0.240/0.000 |

Total budgetary revenue of the municipalities per 1000 population (HUF 1000) | 0.225/0.000 | 0.110/0.000 | |

Total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | 0.245/0.000 | 0.047/0.000 | |

Number of residential electricity consumers per 1000 population (pcs) | 0.045/0.057 | 0.221/0.000 | 0.241/0.000 |

Number of electricity consumers per 1000 population (pcs) | 0.051/0.031 | 0.219/0.000 | 0.240/0.000 |

Length of the low-voltage electricity distribution network per 1000 population (km) | 0.019/0.417 | 0.225/0.000 | 0.245/0.000 |

Number of units of operating commercial accommodation units per 1000 population (pcs) | 0.053/0.025 | 0.219/0.000 | 0.239/0.000 |

Number of businesses in the hospitality industry per 1000 population (pcs) | 0.125/0.000 | 0.201/0.000 | 0.223/0.000 |

**Table A9.**The strengths of the relationships between the quantity of the business HMKEs per 1000 population and the settlement indicators

^{1}(

^{1}Pearson correlation coefficient/p-value; if p < 0.05, then there is a significant verified relationship between the two variables) (In the case of the Pearson correlation coefficients in the table grey background indicates weak correlations and yellow means weak moderate ones. In the case of the partial correlation the blue background signals partial explanation (the controlled variable explains the relationship between variables i and j only partially), while the black one shows irrelevant comparison.).

Indicator | Pearson Correlation Coefficient | Partial Correlation Coefficient | |
---|---|---|---|

Business HMKEs per 1000 Population (pcs) | Number of Registered Businesses per 1000 Population (pcs) | Number of Units of Operating Commercial Accommodation Units per 1000 Population (pcs) | |

Number of registered businesses per 1000 population (pcs) | 0.254/0.000 | 0.178/0.000 | |

Total budgetary revenue of the municipalities per 1000 population (HUF 1000) | 0.129/0.000 | 0.237/0.000 | 0.193/0.000 |

Total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | 0.185/0.000 | 0.226/0.000 | 0.180/0.000 |

Number of residential electricity consumers per 1000 population (pcs) | 0.157/0.000 | 0.226/0.000 | 0.168/0.000 |

Number of electricity consumers per 1000 population (pcs) | 0.182/0.000 | 0.218/0.000 | 0.157/0.000 |

Length of the low-voltage electricity distribution network per 1000 population (km) | 0.174/0.000 | 0.214/0.000 | 0.178/0.000 |

Number of units of operating commercial accommodation units per 1000 population (pcs) | 0.213/0.000 | 0.226/0.000 | |

Number of businesses in the hospitality industry per 1000 population (pcs) | 0.076/0.001 | 0.245/0.000 | 0.211/0.000 |

**Table A10.**The strengths of the relationships between the power of the business HMKEs per 1000 population and the settlement indicators

^{1}(

^{1}Pearson correlation coefficient/p-value; if p < 0.05, then there is a significant verified relationship between the two variables) (In the case of the Pearson correlation coefficients in the table grey background indicates weak correlations.

Indicator | Business HMKE Power per 1000 Population (kW) |
---|---|

Number of registered businesses per 1000 population (pcs) | 0.130/0.000 |

Total budgetary revenue of the municipalities per 1000 population (HUF 1000) | 0.113/0.000 |

Total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | 0.138/0.000 |

Number of residential electricity consumers per 1000 population (pcs) | 0.063/0.008 |

Number of electricity consumers per 1000 population (pcs) | 0.076/0.001 |

Length of the low-voltage electricity distribution network per 1000 population (km) | 0.068/0.004 |

Number of units of operating commercial accommodation units per 1000 population (pcs) | 0.082/0.001 |

Number of businesses in the hospitality industry per 1000 population (pcs) | 0.055/0.022 |

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**Figure 1.**Europe’s photovoltaic power potential [19].

**Figure 2.**The nominal power of the PV HMKE systems in Hungary [27].

**Figure 3.**The regions of the Hungarian electric companies based on [41].

Indicators | Symbol as Explanatory Variable in the Model |
---|---|

number of registered enterprises per 1000 population | x_{1} |

total revenue of the municipalities per 1000 population (HUF 1000) | x_{2} |

total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | x_{3} |

residential electricity consumers per 1000 population | x_{4} |

electricity consumers per 1000 population | x_{5} |

length of the low-voltage electricity distribution network per 1000 population (km) | x_{6} |

number of operating commercial accommodation units per 1000 population | x_{7} |

number of businesses in the hospitality industry per 1000 population | x_{8} |

**Table 2.**The strength of the relationship between the quantity of the total HMKEs per 1000 population and the settlement indicators

^{1}(

^{1}Pearson correlation coefficient/p-value; if p < 0.05, then there is a significant verified relationship between the two variables) (In the case of the Pearson correlation coefficients in the table grey background indicates weak correlations, yellow means weak moderate, and purple moderately close ones. In the case of the partial correlation the blue background signals partial explanation (the controlled variable explains the relationship between variables i and j only partially), while the black one shows irrelevant comparison.

Indicator | Pearson Correlation Coefficient | Partial Correlation Coefficient | |||||
---|---|---|---|---|---|---|---|

HMKEs per 1000 Population (pcs) ELMŰ-ÉMÁSZ, EON, NKM | Number of Residential Electricity Consumers per 1000 Population (pcs) | Number of Electricity Consumers per 1000 Population (pcs) | Number of Registered Businesses per 1000 Population (pcs) | Total Budgetary Expenditure of the Municipalities per 1000 Population (HUF 1000) | Number of Units of Operating Commercial Accommodation Units per 1000 Population (pcs) | Number of Businesses in the Hospitality Industry per 1000 Population (pcs) | |

Number of registered businesses per 1000 population (pcs) | 0.305/0.000 | 0.438/0.000 | 0.468/0.000 | 0.228/0.000 | 0.221/0.000 | 0.210/0.000 | |

Total budgetary revenue of the municipalities per 1000 population (HUF 1000) | 0.123/0.000 | 0.461/0.000 | 0.494/0.000 | 0.280/0.000 | 0.180/0.000 | 0.214/0.000 | 0.207/0.000 |

Total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | 0.275/0.000 | 0.451/0.000 | 0.478/0.000 | 0.263/0.000 | 0.205/0.000 | 0.202/0.000 | |

Number of residential electricity consumers per 1000 population (pcs) | 0.480/0.000 | 0.227/0.000 | 0.217/0.000 | 0.208/0.000 | 0.096/0.000 | 0.013/0.511 | |

Number of electricity consumers per 1000 population (pcs) | 0.515/0.000 | –0.077/0.000 | 0.188/0.000 | 0.172/0.000 | 0.085/0.000 | 0.004/0.828 | |

Length of the low-voltage electricity distribution network per 1000 population (km) | 0.035/0.000 | 0.356/0.000 | 0.405/0.000 | 0.213/0.000 | 0.225/0.000 | 0.188/0.000 | 0.174/0.000 |

Number of units of operating commercial accommodation units per 1000 population (pcs) | 0.246/0.000 | 0.434/0.000 | 0.473/0.000 | 0.286/0.000 | 0.241/0.000 | 0.123/0.000 | |

Number of businesses in the hospitality industry per 1000 population (pcs) | 0.243/0.000 | 0.427/0.000 | 0.469/0.000 | 0.280/0.000 | 0.241/0.000 | 0.129/0.000 |

**Table 3.**The strength of the relationship between the quantity of the total HMKE per 1000 population and the settlement indicators

^{1}(

^{1}Pearson correlation coefficient/p-value; if p < 0.05, then there is a significant verified relationship between the two variables) (In the case of the Pearson correlation coefficients in the table yellow background means weak moderate and purple moderately close correlations.) In the case of the partial correlation the green background signals cases where the background variable did not cause any difference in the strength of the relationship, while blue background indicates partial explanation (the controlled variable explains the relationship between variables i and j only partially), and black marking shows irrelevant comparison.

Indicator | Pearson Correlation Coefficient | Partial Correlation Coefficient | |||||||
---|---|---|---|---|---|---|---|---|---|

Total HMKEs per 1000 Population (pcs) | Number of Registered Businesses per 1000 Population (pcs) | Total Budgetary Revenue of the Municipalities per 1000 Population (HUF 1000) | Total Budgetary Expenditure of the Municipalities per 1000 Population (HUF 1000) | Number of Residential Electricity Consumers per 1000 Population (pcs) | Number of Electricity Consumers per 1000 Population (pcs) | Length of the Low-Voltage Electricity Distribution Network per 1000 Population (km) | Number of Units of Operating Commercial Accommodation Units per 1000 Population (pcs) | Number of Businesses in the Hospitality Industry per 1000 Population (pcs) | |

Number of registered businesses per 1000 population (pcs) | 0.365/0.000 | 0.160/0.000 | 0.212/0.000 | 0.436/0.000 | 0.460/0.000 | 0.393/0.000 | 0.209/0.000 | 0.208/0.000 | |

Total budgetary revenue of the municipalities per 1000 population (HUF 1000) | 0.215/0.000 | 0.339/0.000 | 0.179/0.000 | 0.470/0.000 | 0.501/0.000 | 0.441/0.000 | 0.211/0.000 | 0.215/0.000 | |

Total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | 0.276/0.000 | 0.323/0.000 | –0.017/0.000 | 0.460/0.000 | 0.485/0.000 | 0.429/0.000 | 0.220/0.000 | 0.210/0.000 | |

Number of residential electricity consumers per 1000 population (pcs) | 0.489/0.000 | 0.277/0.000 | 0.152/0.000 | 0.207/0.000 | 0.220/0.000 | 0.179/0.000 | 0.243/0.000 | 0.017/0.000 | |

Number of electricity consumers per 1000 population (pcs) | 0.523/0.000 | 0.245/0.000 | 0.129/0.000 | 0.169/0.000 | –0.066/0.000 | 0.137/0.000 | 0.154/0.000 | 0.010/0.000 | |

Length of the low-voltage electricity distribution network per 1000 population (km) | 0.466/0.000 | 0.254/0.000 | 0.137/0.000 | 0.194/0.000 | 0.245/0.000 | 0.299/0.000 | 0.240/0.000 | 0.138/0.000 | |

Number of units of operating commercial accommodation units per 1000 population (pcs) | 0.243/0.000 | 0.345/0.000 | 0.176/0.000 | 0.242/0.000 | 0.445/0.000 | 0.482/0.000 | 0.430/0.000 | 0.135/0.000 | |

Number of businesses in the hospitality industry per 1000 population (pcs) | 0.252/0.000 | 0.339/0.000 | 0.169/0.000 | 0.239/0.000 | 0.434/0.000 | 0.473/0.000 | 0.424/0.000 | 0.119/0.000 |

**Table 4.**The strengths of the relationships between the power of the total HMKE per 1000 population and the settlement indicators

^{1}(

^{1}Pearson correlation coefficient/p-value; if p < 0.05, then there is a significant verified relationship between the two variables) (In the case of the Pearson correlation coefficients in the table grey background indicates weak correlations and yellow means weak moderate ones.) In the case of the partial correlation the blue background signals partial explanation (the controlled variable explains the relationship between variables i and j only partially), while the black one shows irrelevant comparison.

Indicator | Pearson Correlation Coefficient | Partial Correlation Coefficient | ||||||
---|---|---|---|---|---|---|---|---|

Power of Total HMKEs per 1000 Population (kW) | Number of Registered Businesses per 1000 Population (pcs) | Total Budgetary Revenue of the Municipalities per 1000 Population (HUF 1000) | Total Budgetary Expenditure of the Municipalities per 1000 Population (HUF 1000) | Number of Residential Electricity Consumers per 1000 Population (pcs) | Number of Electricity Consumers per 1000 Population (pcs) | Length of the Low-Voltage Electricity Distribution Network per 1000 Population (km) | Number of Businesses in the Hospitality Industry per 1000 Population (pcs) | |

Number of registered businesses per 1000 population (pcs) | 0.350/0.000 | 0.149/0.000 | 0.191/0.000 | 0.301/0.000 | 0.323/0.000 | 0.291/0.000 | 0.168/0.000 | |

Total budgetary revenue of the municipalities per 1000 population (HUF 1000) | 0.203/0.000 | 0.324/0.000 | 0.159/0.000 | 0.344/0.000 | 0.372/0.000 | 0.345/0.000 | 0.176/0.000 | |

Total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | 0.255/0.000 | 0.309/0.000 | –0.008/0.688 | 0.332/0.000 | 0.355/0.000 | 0.333/0.000 | 0.172/0.000 | |

Number of residential electricity consumers per 1000 population (pcs) | 0.366/0.000 | 0.280/0.000 | 0.152/0.000 | 0.198/0.000 | 0.184/0.000 | 0.164/0.000 | 0.042/0.000 | |

Number of electricity consumers per 1000 population (pcs) | 0.398/0.000 | 0.256/0.000 | 0.135/0.000 | 0.170/0.000 | –0.075/0.000 | 0.126/0.000 | 0.033/0.000 | |

Length of the low-voltage electricity distribution network per 1000 population (km) | 0.373/0.000 | 0.260/0.000 | 0.138/0.000 | 0.185/0.000 | 0.147/0.000 | 0.196/0.000 | 0.118/0.000 | |

Number of units of operating commercial accommodation units per 1000 population (pcs) | 0.183/0.000 | 0.334/0.000 | 0.173/0.000 | 0.228/0.000 | 0.328/0.000 | 0.364/0.000 | 0.343/0.000 | 0.131/0.000 |

Number of businesses in the hospitality industry per 1000 population (pcs) | 0.213/0.000 | 0.327/0.000 | 0.164/0.000 | 0.223/0.000 | 0.308/0.000 | 0.346/0.000 | 0.333/0.000 |

**Table 5.**The strength of the relationship between the quantity of the total HMKEs per 1000 population and the settlement indicators

^{1}(

^{1}Pearson correlation coefficient/p-value; if p < 0.05, then there is a significant verified relationship between the two variables) (In the case of the Pearson correlation coefficients in the table grey background indicates weak correlations, yellow means weak moderate, and purple moderately close ones. In the case of the partial correlation the blue background signals partial explanation (the controlled variable explains the relationship between variables i and j only partially), while the black one shows irrelevant comparison.

Indicator | Pearson Correlation Coefficient | Partial Correlation Coefficient | |||||
---|---|---|---|---|---|---|---|

Total HMKEs per 1000 Population (pcs) | Number of Residential Electricity Consumers per 1000 Population (pcs) | Number of Electricity Consumers per 1000 Population (pcs) | Number of Registered Businesses per 1000 Population (pcs) | Length of the Low-Voltage Electricity Distribution Network per 1000 Population (km) | Number of Units of Operating Commercial Accommodation Units per 1000 Population (pcs) | Number of Businesses in the Hospitality Industry per 1000 Population (pcs) | |

Number of registered businesses per 1000 population (pcs) | 0.222/0.000 | 0.378/0.000 | 0.382/0.000 | 0.194/0.000 | 0.197/0.000 | 0.320/0.000 | |

Total budgetary revenue of the municipalities per 1000 population (HUF 1000) | 0.158/0.000 | 0.395/0.000 | 0.400/0.000 | 0.201/0.000 | 0.226/0.000 | 0.203/0.000 | 0.319/0.000 |

Total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | 0.169/0.000 | 0.394/0.000 | 0.398/0.000 | 0.196/0.000 | 0.226/0.000 | 0.198/0.000 | 0.318/0.000 |

Number of residential electricity consumers per 1000 population (pcs) | 0.411/0.000 | 0.109/0.000 | 0.142/0.000 | –0.085/0.000 | 0.086/0.000 | 0.171/0.000 | |

Number of electricity consumers per 1000 population (pcs) | 0.417/0.000 | –0.074/0.002 | 0.131/0.000 | –0.104/0.000 | 0.077/0.000 | 0.163/0.000 | |

Length of the low-voltage electricity distribution network per 1000 population (km) | 0.248/0.000 | 0.347/0.000 | 0.360/0.000 | 0.159/0.000 | 0.177/0.000 | 0.293/0.000 | |

Number of units of operating commercial accommodation units per 1000 population (pcs) | 0.227/0.000 | 0.360/0.000 | 0.366/0.000 | 0.191/0.000 | 0.203/0.000 | 0.268/0.000 | |

Number of businesses in the hospitality industry per 1000 population (pcs) | 0.345/0.000 | 0.289/0.000 | 0.296/.000 | 0.178/0.000 | 0.161/0.000 | 0.024/0.000 |

**Table 6.**The strengths of the relationships between the power of the total HMKE per 1000 population and the settlement indicators

^{1}(

^{1}Pearson correlation coefficient/p-value; if p < 0.05, then there is a significant verified relationship between the two variables) (in the case of the Pearson correlation coefficients in the table grey background indicates weak correlations and yellow means weak moderate ones.) In the case of the partial correlation the blue background signals partial explanation (the controlled variable explains the relationship between variables i and j only partially), while the black one shows irrelevant comparison.

Indicator | Pearson Correlation Coefficient | Partial Correlation Coefficient | |||||
---|---|---|---|---|---|---|---|

Power of toTal HMKEs per 1000 Population (kW) | Number of Registered Businesses per 1000 Population (pcs) | Total Budgetary Expenditure of the Municipalities per 1000 Population (HUF 1000) | Number of Residential Electricity Consumers per 1000 Population (pcs) | Number of Electricity Consumers per 1000 Population (pcs) | Length of the Low-Voltage Electricity Distribution Network per 1000 Population (km) | Number of Businesses in the Hospitality Industry per 1000 Population (pcs) | |

Number of registered businesses per 1000 population (pcs) | 0.246/0.000 | 0.173/0.000 | 0.301/0.000 | 0.313/0.000 | 0.242/0.000 | 0.208/0.000 | |

Total budgetary revenue of the municipalities per 1000 population (HUF 1000) | 0.186/0.000 | 0.221/0.000 | 0.107/0.000 | 0.321/0.000 | 0.334/0.000 | 0.275/0.000 | 0.203/0.000 |

Total budgetary expenditure of the municipalities per 1000 population (HUF 1000) | 0.212/0.000 | 0.214/0.000 | 0.318/0.000 | 0.330/0.000 | 0.273/0.000 | 0.200/0.000 | |

Number of residential electricity consumers per 1000 population (pcs) | 0.342/0.000 | 0.181/0.000 | 0.168/0.000 | 0.210/0.000 | 0.076/0.000 | 0.079/0.000 | |

Number of electricity consumers per 1000 population (pcs) | 0.356/0.000 | 0.171/0.000 | 0.159/0.000 | –0.182/0.000 | 0.053/0.000 | 0.067/0.000 | |

Length of the low-voltage electricity distribution network per 1000 population (km) | 0.299/0.000 | 0.170/0.000 | 0.172/0.000 | 0.189/0.000 | 0.210/0.000 | 0.165/0.000 | |

Number of units of operating commercial accommodation units per 1000 population (pcs) | 0.178/0.000 | 0.222/0.000 | 0.181/0.000 | 0.302/0.000 | 0.317/0.000 | 0.267/0.000 | 0.169/0.000 |

Number of businesses in the hospitality industry per 1000 population (pcs) | 0.240/0.000 | 0.215/0.000 | 0.164/0.000 | 0.262/0.000 | 0.279/0.000 | 0.245/0.000 |

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**MDPI and ACS Style**

Baranyai, N.H.; Zsiborács, H.; Vincze, A.; Rodek, N.; Makai, M.; Pintér, G. Relationships between the Number and Power of Hungarian Household-Sized Photovoltaic Power Plants and Selected Indicators of the Settlements: A Case Study. *Processes* **2021**, *9*, 4.
https://doi.org/10.3390/pr9010004

**AMA Style**

Baranyai NH, Zsiborács H, Vincze A, Rodek N, Makai M, Pintér G. Relationships between the Number and Power of Hungarian Household-Sized Photovoltaic Power Plants and Selected Indicators of the Settlements: A Case Study. *Processes*. 2021; 9(1):4.
https://doi.org/10.3390/pr9010004

**Chicago/Turabian Style**

Baranyai, Nóra Hegedűsné, Henrik Zsiborács, András Vincze, Nóra Rodek, Martina Makai, and Gábor Pintér. 2021. "Relationships between the Number and Power of Hungarian Household-Sized Photovoltaic Power Plants and Selected Indicators of the Settlements: A Case Study" *Processes* 9, no. 1: 4.
https://doi.org/10.3390/pr9010004