# Predicting the Output of Solar Photovoltaic Panels in the Absence of Weather Data Using Only the Power Output of the Neighbouring Sites

## Abstract

**:**

## 1. Introduction

#### 1.1. Time Series Forecasting

#### 1.2. Forecasting of Solar PV Power

- A study of the feasibility of forecasting solar PV outputs in the absence of meteorological data.
- Utilizing popular deep learning models for the forecast of the solar PV output for optimization of the performance and minimization of the maintenance costs of PV sites.
- Identifying an appropriate method for the forecast of solar PV output at various forecasting lengths.
- Suggesting a suitable workflow for the forecasting of solar PV outputs in scenarios where meteorological data are unavailable and under three different settings: the multivariate, univariate and multi-in uni-out settings.

## 2. Methods

#### 2.1. Data Description

#### 2.2. Used Forecasting Models

#### 2.2.1. Recurrent Neural Network (RNN) [38]

#### 2.2.2. Gated Recurrent Unit (GRU) [39]

#### 2.2.3. Long Short-Term Memory (LSTM) [37]

#### 2.2.4. Transformer [24]

#### 2.3. Forecast Settings

## 3. Experiment and Results

#### 3.1. Implementation Details

#### 3.2. Details of Hyper-Parameters Used

^{−5}as the models seemed to overfit even in very few epochs when set to a value higher than this. Additionally, due to the same reason, each configuration of the models used were also very simple. The number of RNN, GRU and LSTM layers used was 2 and the number of encoders and decoders in Transformer was set to 3. The weight decay was set to 1 × 10

^{−6}, and the batch size was set to a fixed value of 64 for each of the settings. The number of epochs for Transformer used was 50 as compared with 100 for the rest of the models because Transformer was overfitting very early.

#### 3.3. Evaluation Metrics

#### 3.3.1. Mean Square Error (MSE)

#### 3.3.2. Mean Absolute Error (MAE)

#### 3.4. Results

#### 3.4.1. Results of Multi-In Multi-Out Setting

#### 3.4.2. Results of Multi-In Uni-Out Setting

#### 3.4.3. Results of Uni-In Uni-Out Setting

#### 3.4.4. Comparative Analysis of Results Obtained

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

TSF | Time Series Forecasting |

PV | Photo Voltaic |

RNN | Recurrent Neural Network |

GRU | Gated Recurrent Unit |

LSTM | Long Short-Term Memory |

LB | Lookback |

FH | Forecast Horizon |

TCN | Temporal Convolution Networks |

GNN | Graph Neural Networks |

SVM | Support Vector Machines |

GHI | Global Horizontal Irradiance |

DNI | Direct Normal Irradiance |

GA | Genetic Algorithm |

ARIMA | Autoregressive Integrated Moving Average |

KNN | K- Nearest Neighbours |

RF | Random Forest |

GAM | Generative Additive Model |

GRBT | Gradient Boosted Regression Trees |

BPTT | Back Propagation Through Time |

MSE | Mean Square Error |

MAE | Mean Absolute Error |

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**Figure 6.**The architecture of Transformer [24].

**Figure 8.**Visualization of the forecasts of PV output from RNN, GRU, LSTM and Transformer in the univariate setting for varying lookback lengths and forecast horizons. Lookback length has been written as ’LB’, and forecast horizon has been written as ’H’. (

**a**) LB:48 H:4; (

**b**) LB:48 H:8; (

**c**) LB:48 H:12; (

**d**) LB:48 H:24; (

**e**) LB:96 H:4; (

**f**) LB:96 H:8; (

**g**) LB:96 H:12; (

**h**) LB:96 H:24; (

**i**) LB:144 H:4; (

**j**) LB:144 H:8; (

**k**) LB:144 H:12; (

**l**) LB:144 H:24.

Time | Site 1 | Site 2 | Site 3 | Site 4 | Site 5 | ....... | Site 47 | Site 48 | Site 49 | Site 50 |
---|---|---|---|---|---|---|---|---|---|---|

2020-01-01 06:45 | 0 | 0 | 0 | 0 | 0 | ....... | 0 | 0 | 0 | 0 |

2020-01-01 07:00 | 0 | 0 | 0 | 0 | 0 | ....... | 0 | 0 | 0 | 0 |

2020-01-01 07:15 | 0 | 0 | 0 | 0 | 0 | ....... | 0 | 0 | 0 | 0 |

2020-01-01 07:30 | 0 | 207 | 216 | 0 | 225 | ....... | 0 | 186 | 217 | 215 |

2020-01-01 07:45 | 212 | 205 | 217 | 217 | 218 | ....... | 212 | 192 | 265 | 215 |

2020-01-01 08:00 | 211 | 250 | 212 | 271 | 211 | ....... | 212 | 494 | 465 | 215 |

2020-01-01 08:15 | 225 | 377 | 209 | 363 | 585 | ....... | 214 | 745 | 708 | 235 |

2020-01-01 08:30 | 240 | 424 | 865 | 648 | 798 | ....... | 239 | 953 | 934 | 250 |

2020-01-01 08:45 | 260 | 541 | 1087 | 948 | 1017 | ....... | 321 | 1138 | 1147 | 306 |

2020-01-01 09:00 | 506 | 861 | 1278 | 1147 | 1251 | ....... | 428 | 1315 | 1322 | 505 |

....... | ....... | ....... | ....... | ....... | ....... | ....... | ....... | ....... | ....... | ....... |

2020-06-22 14:15 | 794 | 1176 | 1738 | 1177 | 715 | ....... | 1447 | 1349 | 1370 | 1417 |

2020-06-22 14:30 | 839 | 885 | 970 | 866 | 972 | ....... | 792 | 892 | 897 | 780 |

2020-06-22 14:45 | 911 | 1043 | 1021 | 1093 | 458 | ....... | 1489 | 1211 | 1241 | 1419 |

2020-06-22 15:00 | 1681 | 643 | 1130 | 659 | 591 | ....... | 567 | 693 | 703 | 567 |

2020-06-22 15:15 | 1474 | 1032 | 1123 | 823 | 275 | ....... | 1086 | 1057 | 947 | 1007 |

....... | ....... | ....... | ....... | ....... | ....... | ....... | ....... | ....... | ....... | ....... |

RNN, LSTM, GRU | Transformer | ||
---|---|---|---|

Hyper-Parameter | Value | Hyper-Parameter | Value |

Number of hidden state | 64 | Number of heads | 4 |

Number of recurrent layers | 2 | Number of encoder layers | 3 |

Number of decoder layers | 3 | ||

Number of expected features in the encoder/decoder inputs | 128 | ||

Feedforward network dimension | 256 | ||

Number of epochs | 100 | Number of epochs | 50 |

Dropout | 0.3 | Dropout | 0.3 |

Weight Decay | $1\times {10}^{-6}$ | Weight Decay | $1\times {10}^{-6}$ |

Learning rate | $1\times {10}^{-4}$ | Learning rate | $1\times {10}^{-4}$ |

**Table 3.**Results in multi-in multi-out setting. Lower MSE and MAE values are better. The best results are shown in bold and underlined.

Models | RNN | GRU | LSTM | Transformer | |||||
---|---|---|---|---|---|---|---|---|---|

LBL | FHL | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE |

48 | 4 | 0.1337 | 0.2111 | 0.1280 | 0.2049 | 0.1334 | 0.2084 | 0.1070 | 0.1786 |

8 | 0.2351 | 0.3103 | 0.1643 | 0.2479 | 0.1927 | 0.252 | 0.1429 | 0.2245 | |

12 | 0.2059 | 0.2796 | 0.2414 | 0.3027 | 0.2197 | 0.2739 | 0.1856 | 0.2618 | |

24 | 0.2514 | 0.3168 | 0.237 | 0.2946 | 0.2998 | 0.3199 | 0.2352 | 0.2768 | |

96 | 4 | 0.1356 | 0.2109 | 0.1345 | 0.2081 | 0.1377 | 0.2052 | 0.0971 | 0.1722 |

8 | 0.1657 | 0.2409 | 0.1574 | 0.2387 | 0.1612 | 0.2286 | 0.1137 | 0.2113 | |

12 | 0.2386 | 0.2927 | 0.2165 | 0.2828 | 0.2646 | 0.2881 | 0.1603 | 0.2404 | |

24 | 0.276 | 0.3416 | 0.2709 | 0.3113 | 0.4467 | 0.4007 | 0.2069 | 0.2451 | |

144 | 4 | 0.1472 | 0.2203 | 0.1427 | 0.2174 | 0.1385 | 0.2088 | 0.115 | 0.1823 |

8 | 0.2331 | 0.2985 | 0.158 | 0.2336 | 0.2523 | 0.1887 | 0.1246 | 0.2345 | |

12 | 0.3148 | 0.3478 | 0.2233 | 0.2851 | 0.2465 | 0.1773 | 0.1687 | 0.2312 | |

24 | 0.3475 | 0.3800 | 0.4703 | 0.3966 | 0.2359 | 0.2997 | 0.184 | 0.2211 |

**Table 4.**Results in multiple-in uni-out setting. Lower MSE and MAE values are better. The best results are shown in bold and underlined.

Models | RNN | GRU | LSTM | Transformer | |||||
---|---|---|---|---|---|---|---|---|---|

LBL | FHL | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE |

48 | 4 | 0.1366 | 0.2249 | 0.1435 | 0.2264 | 0.1112 | 0.1995 | 0.1120 | 0.1762 |

8 | 0.1382 | 0.2265 | 0.1382 | 0.228 | 0.1157 | 0.2083 | 0.1184 | 0.1834 | |

12 | 0.1454 | 0.2488 | 0.1369 | 0.2264 | 0.1104 | 0.2049 | 0.1212 | 0.1893 | |

24 | 0.2217 | 0.3054 | 0.1717 | 0.2594 | 0.1517 | 0.2405 | 0.1300 | 0.2020 | |

96 | 4 | 0.1335 | 0.2249 | 0.1446 | 0.2259 | 0.1030 | 0.1947 | 0.1171 | 0.1763 |

8 | 0.1474 | 0.2331 | 0.133 | 0.2199 | 0.1154 | 0.1980 | 0.1245 | 0.1923 | |

12 | 0.1410 | 0.2417 | 0.1301 | 0.2161 | 0.1087 | 0.1975 | 0.1217 | 0.1838 | |

24 | 0.2178 | 0.2913 | 0.2174 | 0.2901 | 0.1919 | 0.2707 | 0.1747 | 0.2216 | |

144 | 4 | 0.1396 | 0.2281 | 0.1494 | 0.2304 | 0.1106 | 0.1978 | 0.0993 | 0.1624 |

8 | 0.147 | 0.2278 | 0.1399 | 0.2254 | 0.1237 | 0.2076 | 0.1153 | 0.1669 | |

12 | 0.1472 | 0.244 | 0.1347 | 0.2256 | 0.1054 | 0.1923 | 0.1192 | 0.1823 | |

24 | 0.2457 | 0.3220 | 0.2096 | 0.2812 | 0.1801 | 0.2550 | 0.1562 | 0.2112 |

**Table 5.**Results in uni-in uni-out setting. Lower MSE and MAE values are better. The best results are shown in bold and underlined.

Models | RNN | GRU | LSTM | Transformer | |||||
---|---|---|---|---|---|---|---|---|---|

LBL | FHL | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE |

48 | 4 | 0.0887 | 0.1560 | 0.0917 | 0.1624 | 0.0923 | 0.1621 | 0.094 | 0.1518 |

8 | 0.1140 | 0.2099 | 0.1066 | 0.1890 | 0.1054 | 0.1815 | 0.1128 | 0.1914 | |

12 | 0.1248 | 0.2241 | 0.1204 | 0.2033 | 0.1238 | 0.2094 | 0.1247 | 0.1924 | |

24 | 0.201 | 0.2811 | 0.1947 | 0.2671 | 0.2167 | 0.2788 | 0.1832 | 0.2531 | |

96 | 4 | 0.0892 | 0.1616 | 0.0900 | 0.1543 | 0.0879 | 0.1577 | 0.0912 | 0.1423 |

8 | 0.1057 | 0.1963 | 0.1031 | 0.1765 | 0.1004 | 0.1755 | 0.0996 | 0.1724 | |

12 | 0.1272 | 0.2197 | 0.1276 | 0.1989 | 0.1202 | 0.2056 | 0.1065 | 0.1818 | |

24 | 0.1968 | 0.2737 | 0.2324 | 0.2865 | 0.2055 | 0.2723 | 0.1624 | 0.2395 | |

144 | 4 | 0.0949 | 0.1628 | 0.0927 | 0.1577 | 0.0931 | 0.161 | 0.0832 | 0.1463 |

8 | 0.1087 | 0.1925 | 0.1096 | 0.1837 | 0.1049 | 0.1828 | 0.0999 | 0.1582 | |

12 | 0.132 | 0.2281 | 0.1266 | 0.2027 | 0.1216 | 0.2037 | 0.1123 | 0.1812 | |

24 | 0.2341 | 0.2973 | 0.2414 | 0.2927 | 0.221 | 0.2848 | 0.2120 | 0.2541 |

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## Share and Cite

**MDPI and ACS Style**

Jeong, H.
Predicting the Output of Solar Photovoltaic Panels in the Absence of Weather Data Using Only the Power Output of the Neighbouring Sites. *Sensors* **2023**, *23*, 3399.
https://doi.org/10.3390/s23073399

**AMA Style**

Jeong H.
Predicting the Output of Solar Photovoltaic Panels in the Absence of Weather Data Using Only the Power Output of the Neighbouring Sites. *Sensors*. 2023; 23(7):3399.
https://doi.org/10.3390/s23073399

**Chicago/Turabian Style**

Jeong, Heon.
2023. "Predicting the Output of Solar Photovoltaic Panels in the Absence of Weather Data Using Only the Power Output of the Neighbouring Sites" *Sensors* 23, no. 7: 3399.
https://doi.org/10.3390/s23073399