# A Regional Day-Ahead Rooftop Photovoltaic Generation Forecasting Model Considering Unauthorized Photovoltaic Installation

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Background and Motivation

#### 1.2. Literature Review

#### 1.3. Contributions

#### 1.4. Structure of This Study

## 2. Problem Formulation of Unauthorized Photovoltaic (PV) Installation and Regional Rooftop PV Forecasting

#### 2.1. Problem Statement

_{PV}(d, t)

_{PV}(d, t) = 0 ∀ d ∈ D, ∀ t ∈ T. For rooftop PV, the PV output power is BTM except at representative solar sites, implying that most rooftop PV power is not measured and collected. The home classification according to rooftop PV installation, rooftop PV authorization, and sub meter of PV power installation is shown in Figure 1 and Table 2.

#### 2.2. Framework of the Proposed Approach

## 3. Proposed Methodology of Regional Rooftop PV Generation Forecasting

#### 3.1. Unauthorized PV Detection Model

#### 3.1.1. Four Weather Groups Clustering

#### 3.1.2. Generation Real and Virtual Typical Net Load Pattern and Minimum Net Load Pattern

Algorithm 1. Generation virtual TNLP |

Input: ${TNLP}_{Sam}^{A}\left(t\right)$, ${TNLP}_{Sam}^{D}\left(t\right)$, ${TPP}_{Sam}^{A}\left(t\right),{TPP}_{Sam}^{D}\left(t\right),N,\omega PV,Sam\in \left[1,{N}_{H1}\right]$Output: if $\omega PV==1$then${TNLP}_{n}^{A}$(t), ${TNLP}_{n}^{D}$(t) else${TLP}_{n}^{A}$(t), ${TLP}_{n}^{D}$(t) Endfor$n=1:N$do${TLP}_{Sam}\left(t\right)={TNLP}_{Sam}\left(t\right)+{TPP}_{Sam}\left(t\right);$ ${TLP}_{Norm,Sam}\left(t\right)=\frac{{TLP}_{Sam}\left(t\right)}{\mathrm{max}\left({TLP}_{Sam}\left(t\right)\right)}$; for t = 0:23 dorandomly select r $\in \left[1,{N}_{H1}\right]$ ${TLP}_{n,Norm}^{A}$(t) = ${TLP}_{r,Norm}^{A}$(t); ${TLP}_{n,Norm}^{D}$(t) = ${TLP}_{r,Norm}^{D}$(t); End${TLP}_{n}^{A}\left(t\right)={TLP}_{n,Norm}^{A}\left(t\right)\times \mathrm{max}\left({TLP}_{Sam}\left(t\right)\right);$ ${TLP}_{n}^{D}\left(t\right)={TLP}_{n,Norm}^{D}\left(t\right)\times \mathrm{max}\left({TLP}_{Sam}\left(t\right)\right);$ if $\omega PV==1$ then |

${TPP}_{Norm,Sam}^{A}\left(t\right)=\frac{{TPP}_{Norm,Sam}^{A}\left(t\right)}{{C}_{Sam}};$ ${TPP}_{Norm,Sam}^{D}\left(t\right)=\frac{{TPP}_{Norm,Sam}^{D}\left(t\right)}{{C}_{Sam}};$ randomly select PV capacity ${C}_{rand}\in \left[1,10\right]$ ${TPP}_{Vir}^{A}\left(t\right)={TPP}_{Norm,Sam}^{A}\left(t\right)\times {C}_{rand};$ ${TPP}_{Vir}^{D}\left(t\right)={TPP}_{Norm,Sam}^{D}\left(t\right)\times {C}_{rand};$ ${TNLP}_{n}^{A}\left(t\right)={TLP}_{n}^{A}\left(t\right)-{TPP}_{Vir}^{A}\left(t\right);$ ${TNLP}_{n}^{D}\left(t\right)={TLP}_{n}^{D}\left(t\right)-{TPP}_{Vir}^{D}\left(t\right);$ Elsebreak; EndEnd |

#### 3.1.3. Feature Extraction Based on TNLP and MNLP

#### 3.1.4. Training and Test of Unauthorized PV Detection Model

#### 3.2. Unauthorized PV Capacity Estimation Model

#### 3.2.1. Generation Virtual Net Load

Algorithm 2. Generation virtual NL |

Input: ${\mathrm{C}}_{\mathrm{Au}}$ = [${\mathrm{C}}_{1},{\mathrm{C}}_{2},{\mathrm{C}}_{3},\dots ,{C}_{{N}_{Au}}$], ${NL}_{Sam}^{WG}\left(d,t\right)$, ${P}_{PV,Sam}^{WG}\left(d,t\right),Au\in \left[1,{N}_{Au}\right],Sam\in \left[1,{N}_{Sam}\right]$Output: $N{L}^{WG}\left(d,t\right)$Initialize ${\mathrm{Dis}}_{\mathrm{cap}}=0;cap\in \left[1,10\times int\left(Max\left({C}_{Au}\right)\right)\right]$ ${\mathrm{GL}}_{\mathrm{Sam}}^{\mathrm{WG}}\left(d,t\right)={\mathrm{NL}}_{\mathrm{Sam}}^{\mathrm{WG}}\left(d,t\right)+{\mathrm{P}}_{\mathrm{PV},\mathrm{Sam}}^{\mathrm{WG}}\left(d,t\right);$ for $n=1:{N}_{Au}$ dofor i = 1:$int\left(Max\left({C}_{Au}\right)\right)$ dofor j = 1:10 doif $i+0.1\left(j-1\right)\le {C}_{n}<i+0.1j$ then${Dis}_{int\left(Max\left({C}_{Au}\right)\right)+i+j}+=1$ elseContinue; endendend${Count}_{cap}=Max\left({Dis}_{cap}\right)-{Dis}_{cap};$ for $WG=A:D$ do${P}_{PV,mean}^{WG}\left(t\right)=\frac{1}{{N}_{d}^{WG}}{\displaystyle {\displaystyle \sum}_{d=1}^{N\_d^WG}}{P}_{PV,Sam}^{WG}\left(d,t\right);$ ${P}_{PV,Norm}^{WG}\left(t\right)=\frac{1}{{C}_{PV,Sam}}{P}_{PV,mean}^{\mathrm{WG}}\left(t\right);$ endfor $l=1:10\times int\left(Max\left({C}_{Au}\right)\right)$ dofor $c=1:{Count}_{l}$ doSelect randomly PV capacity ${C}_{rand}\in $ [1+(l−1)/10,1+l/10] Select randomly $\mathrm{r}\in \left[1,{\mathrm{N}}_{\mathrm{Sam}}\right]$ for WG = A:D do${NL}_{r}^{WG}\left(d,t\right)={GL}_{r}^{WG\left(d,t\right)}-{P}_{PV,Norm}^{WG}\left(t\right)\times {C}_{rand}$ endendend |

#### 3.2.2. Extracting Minimum Net Load Pattern (MNLP) for Four Weather Classes

_{A}(t) and MNLP

_{D}(t) each denote MNLP in A and D of WG. They are shown in Equations (11) and (12). D

_{A}and D

_{D}in Equations (11) and (12) denote the set of days when the WG is A and the set of days when the WG is D, where d is the day index.

#### 3.2.3. Extracting Features from MNLP

^{A}(t). It varies by PV output and GL values. If PV output is maximum or GL is minimum, it has negative values of significantly larger magnitude. It is available to estimate PV capacity using ${\mathrm{F}}_{1}^{\mathrm{E}}.$ The second feature ${\mathrm{F}}_{2}^{\mathrm{E}}$ denotes difference of MNLP

^{A}(t) and MNLP

^{D}(t) during a day. So, ${\mathrm{F}}_{3}^{\mathrm{E}}$ is originally the sum of the difference of MNLP

^{A}(t) and MNLP

^{D}(t) for intermediate start time and end time of PV generation. However, it is difficult to recognize PV capacity when the PV capacity is small. Therefore, the sum of difference between MNLP

^{A}(t) and MNLP

^{D}(t) for intermediate start time and end time of PV generation is chosen as the third feature. In the testing process, the MNLP of a test home is used to extract three features and unauthorized PV capacity is estimated through three features.

#### 3.2.4. Training and Test PV Capacity Estimation Model

#### 3.3. Regional PV Forecasting Model

#### 3.3.1. Clustering and Sampling of Rooftop PV

Algorithm 3. Clustering of rooftop PV |

Input: $\mathrm{a}\mathrm{given}\mathrm{data}\mathrm{X}=\left\{\left({lat}_{1},{lon}_{1}\right),\left({lat}_{2},{lon}_{2}\right),\dots .,\left({lat}_{n},{lon}_{n}\right)\right\}$The number of cluster k Maximum number of iteration I Output:$\mathrm{clustering}\mathrm{result}$${o}_{nk}$ for all n PV k center of cluster CRandomly initialize C = $\left\{\left({lat}_{1}^{C},{lon}_{1}^{C}\right),\left({lat}_{2}^{C},{lon}_{2}^{C}\right),\dots .,\left({lat}_{k}^{C},{lon}_{k}^{C}\right)\right\}$ for $i=1:I$ do// Assignment step for n = 1:N do${o}_{nk}=\left\{\begin{array}{l}1,\mathrm{if}\mathrm{k}={\mathrm{argmin}}_{\mathrm{i}}{\left|\left({\mathrm{lat}}_{\mathrm{n}}-{\mathrm{lat}}_{\mathrm{k}}^{\mathrm{C}}\right)\right|}^{2}+{\left|\left({\mathrm{lon}}_{\mathrm{n}}-{\mathrm{lon}}_{\mathrm{k}}^{\mathrm{C}}\right)\right|}^{2}\\ 0,\mathrm{otherwise}\end{array}\right.$ end// Update step for $k=1:K$ do${lat}_{k}^{C}=\frac{1}{{{\displaystyle \sum}}_{n=1}^{N}{o}_{nk}}{\displaystyle {\displaystyle \sum}_{n=1}^{N}}{o}_{nk}{lat}_{n};$ ${lon}_{k}^{C}=\frac{1}{{{\displaystyle \sum}}_{n=1}^{N}{o}_{nk}}{\displaystyle {\displaystyle \sum}_{n=1}^{N}}{o}_{nk}{lon}_{n};$ endend |

#### 3.3.2. Individual Rooftop PV Generation Forecasting

_{actual}, F

_{Max}, F

_{Min}and F

_{Norm}denote original feature, maximum of feature, minimum of feature, and normalized feature. Next, the individual rooftop PV generation model is constructed in Equation (17).

_{PVi}

_{nd}(t) is the predicted PV generation at time t; time resolution is one hour as described in Section 2.1. ${\mathrm{F}}_{1}^{\mathrm{Norm}},{\mathrm{F}}_{2}^{\mathrm{Norm}},{\mathrm{F}}_{3}^{\mathrm{Norm}},{\mathrm{F}}_{4}^{\mathrm{Norm}},{\mathrm{F}}_{5}^{\mathrm{Norm}}$ denote normalized one day ahead PV generation, normalized solar irradiance, normalized cloud cover, normalized precipitation, and normalized temperature. Finally, the test of individual PV generation forecasting is performed through the trained PV generation forecasting model.

#### 3.3.3. Upscaling Sample Rooftop PV Generation by Cluster

_{c,ind}(t) denotes predicted individual generation ind th for the representative solar site at time t in cluster c. N

_{rep}denotes the number of representative solar sites. uf

_{c}denotes upscaling factor of cluster c that corresponds to the scaled up coefficient of individual power generation. The PV generation of a cluster (or sub region) is made by multiplying each individual PV generation by the upscaling factor and aggregating them. Equation (19) shows how the upscaling factor is calculated. It is defined as the ratio of total rooftop PV capacity in the cluster to the sum of representative solar sites capacity.

#### 3.3.4. Aggregating PV Generation of a Cluster

## 4. Case Study

#### 4.1. Experimental Data Description

_{PV}, the number of given home with rooftop PV was 300, all home in the region were 1500. ${\mathrm{r}}_{\mathrm{Au}}$ is 0.5 (i.e., 50%), which means the ratio of home installed unauthorized rooftop PV of all rooftop PV. In other words, 150 homes are authorized and the other 150 homes are unauthorized in the case study. Finally, an important assumption in our work is that the number of systems is constant over 2 years. Because it is difficult to find this by complete enumeration, there are few papers on this. According to [29], identified unauthorized rooftop PV installation rate is about 50% in Cape Town, South Africa. Therefore, unauthorized rooftop PV installation rate is assumed 0.5 (i.e., 50%) based on [29]. ${\mathrm{r}}_{\mathrm{Sam}}$, the ratio of the number of home PV generation data is measured and among the home installed authorized PV, is assumed 0.08 (8%). ts and te are assumed to be 9 and 16. This is because the period that PV generation mainly occurs is from 9 to 16.

#### 4.2. Performance Metric

#### 4.2.1. Unauthorized PV Detection Performance Metric

#### 4.2.2. Unauthorized PV Capacity Estimation Performance Metric

#### 4.2.3. Regional PV Generation Forecasting Performance Metric

#### 4.3. Simulation Results

#### 4.3.1. Unauthorized Rooftop PV Detection Results

#### 4.3.2. Unauthorized Rooftop PV Capacity Estimation Results

#### 4.3.3. Regional Rooftop PV Generation Forecasting Results

## 5. Discussion

#### 5.1. Upscaling Factor Analysis

#### 5.2. Feature Correlation Analysis

## 6. Conclusions

- Investigating the impact of NL home-owned energy storage and electric vehicles on unauthorized PV detection performance.
- Exploring rooftop PV capacity uncertainty in addition to unauthorized PV installation. For example, there are rooftop PV faults and real-time rooftop PV penetration.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Home classification according to photovoltaic (PV) installation, authorization, and sub meter.

**Figure 5.**PV capacity distribution histogram in [41].

**Figure 10.**Regional PV output forecasting distributions; (

**a1**) nRMSE of Case 1 (

**a2**) nMAE of Case1 (

**b1**) nRMSE of Case 2 (

**b2**) nMAE of Case2 (

**c1**) nRMSE of Case 3 (

**c2**) nMAE of Case 3.

Literature Group | Research Subject | Reference |
---|---|---|

1 | Regional utility scale photovoltaic (PV) forecasting | [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] |

2 | Regional behind the meter (BTM) PV forecasting | [28,34,35,36,37] |

3 | Unauthorized PV detection and PV capacity estimation | [27,38,39,40] |

Question | H1 | H2 | H3 | H4 |
---|---|---|---|---|

Is there a rooftop PV sub meter at home? | Yes | No | No | No |

Is a rooftop PV at home authorized? | Yes | Yes | No | No |

Is a rooftop PV installed at home? | Yes | Yes | Yes | No |

Parameters | Value | Parameters | Value |
---|---|---|---|

N_{home} | 1500 | r_{S}_{a}_{m} | 0.08 |

N_{PV} | 300 | t_{s} | 9 |

r_{Au} | 0.5 | t_{e}, t_{f} | 16, 19 |

**Table 4.**Unauthorized PV detection result by method in [39].

Metric | Best | Average | Worst |
---|---|---|---|

PA | 96.00 | 90.69 | 77.33 |

NPA | 99.67 | 96.58 | 89.67 |

OA | 98.00 | 95.93 | 90.15 |

Metric | Best | Average | Worst |
---|---|---|---|

PA | 100 | 99.81 | 96.67 |

NPA | 98.33 | 97.02 | 95.67 |

OA | 98.52 | 97.33 | 96.07 |

Study | Best (%) | Average (%) | Worst (%) |
---|---|---|---|

[35] | 66.00 | 92.79 | 113.00 |

Proposed method | 34.00 | 44.21 | 63.00 |

Error Metric (%) | Case 1 | Case 2 | Case 3 |
---|---|---|---|

Normalized Root Mean Square Error (nRMSE) | 11.29 | 6.41 | 5.41 |

Normalized Mean Absolute Error (nMAE) | 6.01 | 3.52 | 2.95 |

Feature | ${\mathbf{F}}_{1}^{\mathbf{D}}$ | ${\mathbf{F}}_{2}^{\mathbf{D}}$ | ${\mathbf{F}}_{3}^{\mathbf{D}}$ | ${\mathbf{F}}_{4}^{\mathbf{D}}$ | ${\mathbf{F}}_{5}^{\mathbf{D}}$ | ${\mathbf{F}}_{6}^{\mathbf{D}}$ |
---|---|---|---|---|---|---|

MIC value | 0.445 | 0.135 | 0.217 | 0.207 | 0.600 | 0.722 |

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## Share and Cite

**MDPI and ACS Style**

Kim, T.; Kim, J.
A Regional Day-Ahead Rooftop Photovoltaic Generation Forecasting Model Considering Unauthorized Photovoltaic Installation. *Energies* **2021**, *14*, 4256.
https://doi.org/10.3390/en14144256

**AMA Style**

Kim T, Kim J.
A Regional Day-Ahead Rooftop Photovoltaic Generation Forecasting Model Considering Unauthorized Photovoltaic Installation. *Energies*. 2021; 14(14):4256.
https://doi.org/10.3390/en14144256

**Chicago/Turabian Style**

Kim, Taeyoung, and Jinho Kim.
2021. "A Regional Day-Ahead Rooftop Photovoltaic Generation Forecasting Model Considering Unauthorized Photovoltaic Installation" *Energies* 14, no. 14: 4256.
https://doi.org/10.3390/en14144256