# Investigating the Power of LSTM-Based Models in Solar Energy Forecasting

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

- Analyze and compare the relevant papers that have been proposed and discussed LSTM models on solar irradiance prediction.
- Identify better models among standalone and hybrid models of LSTM to predict solar irradiation and PV power by comparing the features of prediction parameters.
- Discuss in depth regarding the characteristics and mechanism of LSTM and how it is able to integrate with other methods to improve the performance of solar prediction accuracy.

## 2. Related Works

## 3. LSTM

## 4. Hybrid Models

## 5. Evaluation Metrics

_{pred}, X

_{meas}, and n denote the projected values at each time point, the measured values at each time point, and the sample size of a period, respectively.

## 6. Analysis of Past Studies

#### 6.1. Accuracy

#### 6.2. Types of Input Data

#### 6.3. Forecast Horizon

- Very short-term forecast (ahead by 1 min to several minutes);
- Short-term forecast (ahead by 1 h or several hours to 1 day or 1 week);
- Medium-term forecast (ahead by 1 month to 1 year); and
- Long-term forecast (ahead by 1–10 years).

^{2}. The values of the error metrics increased with the progression of step time. Thus, the hybrid model is better than the standalone models.

#### 6.4. Type of Season and Weather

^{2}, 17.23%, and 20.50 W/m

^{2}, respectively. The forecasting performance of the proposed model was better under different climatic conditions compared with those of the other models (Table 7).

#### 6.5. Training Time

## 7. Future Directions

- In terms of comparing and analyzing the available source code, not all the reviewed papers provided the data source codes; it is recommended for future works to find the data sources to describe the data and analyze their differences.
- Regarding performance evaluation, it is difficult to compare accuracy efficiently between the prediction models due to several main factors such as different evaluation metrics used, weather conditions of selected regions, forecasting horizons, size of input parameters, and so on. Thus, it is suggested to find specific research papers that discuss or review similar factors as mentioned, to compare the performance effectively.
- This paper has mostly reviewed very short-term and short-term forecast horizons for solar irradiance and solar power forecasting (Table 3 and Table 4). For future work, it is recommended to expand the review on medium-term and long-term forecast horizons by applying various combinations of DL and ML models to enhance the existing hybrid models.

## 8. Conclusions

- In terms of predicting solar irradiance, hybrid models outperform standalone models. In particular, the evaluation measures of hybrid models are significantly lower than those of standalone models. Among the hybrid models, CNN–LSTM requires complex input data, such as images, because it includes a CNN layer.
- When evaluating model performance, training time must be considered. Because hybrid models must extract two types of feature (i.e., spatial and temporal features), they take a longer time to process data compared to standalone models.
- The prediction accuracy for models that run a large batch size of data is lower when compared to other prediction models that use small data batch sizes. This is because more data are required to be extracted, and there is a more complicated process to produce the most accurate prediction.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**FFNN model [22].

**Figure 2.**RNN vs. FNN [19]. x: input, y: output, w: h: hidden layer, w: loop.

**Figure 3.**Structure of an RNN with unfolded architecture [19].

**Figure 4.**Structure of internal LSTM cell [25].

**Figure 5.**Basic structure of a CNN [26].

Ref. | Criteria | |||
---|---|---|---|---|

LSTM | Hybrid Model | Evaluation Metrics | Analysis of Past Studies | |

[8] | X | − | √ | X |

[9] | − | √ | √ | X |

[10] | √ | − | √ | √ |

[11] | − | − | √ | √ |

[12] | X | − | √ | √ |

[13] | − | √ | √ | √ |

[14] | − | − | − | √ |

Evaluation Metric | Equation |
---|---|

Error | $Error={X}_{pred}-{X}_{meas}$ |

MAE | $\frac{1}{n}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}\left|{X}_{pred}-{X}_{meas}\right|$ |

MAPE | $\frac{1}{n}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}\left|\frac{{X}_{pred}-{X}_{meas}}{{X}_{meas}}\right|\times 100$ |

MBE | $\frac{1}{n}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}\left({X}_{pred}-{X}_{meas}\right)$ |

rMBE | $\frac{{{\displaystyle \sum}}_{i=1}^{n}\left({X}_{pred}-{X}_{meas}\right)}{{{\displaystyle \sum}}_{i=1}^{n}{X}_{meas}}\times 100$ |

rRMSE | $\frac{\sqrt{\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}{\left({X}_{pred}-{X}_{meas}\right)}^{2}}}{\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}{X}_{meas}}\times 100$ |

RMSE | $\sqrt{\frac{1}{n}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}{\left({X}_{pred}-{X}_{meas}\right)}^{2}}$ |

Ref. | Forecast Horizon | Time Interval | Model | Input Parameter | Historical Data Description | Error Metrics |
---|---|---|---|---|---|---|

[1] | Ahead by 1 h | Hourly | LSTM–CNN | - Temperature
- Wind speed
- Wind direction
- Relative humidity
- Precipitation
- Solar zenith angle
- Dew point
- Pressure
- Cloud type
- Clear-sky global horizontal irradiance (GHI)
- GHI
| 1 January 2015 to 31 December 2019 (5 years) | Average RMSE:Los Angeles: 57.983 W/m ^{2}San Diego: 47.826 W/m ^{2}San Francisco: 66.023 W/m ^{2} |

[29] | - Ahead by 15 min
- Ahead by 30 min
- Ahead by 45 min
- Ahead by 60 min
- Ahead by 75 min
- Ahead by 90 min
| Hourly | MSCA–CLSTM | GHI | 2018 (1 year) | Average RMSE:Columbus: 0.0177 W/m ^{2}San Antonio: 0.0183 W/m ^{2}Detroit: 0.0183 W/m ^{2} |

[30] | - Ahead by 15 min
- Ahead by 30 min
- Ahead by 45 min
- Ahead by 60 min
- Ahead by 75 min
- Ahead by 90 min
| 15 min | CNN–LSTM | - Average solar irradiance
- Average ambient temperature
- Average relative humidity
| 1 January 2016 to 1 January 2017 | RMSE (6 steps):5.79–34.89 W/m ^{2} |

[31] | Multiple forecast horizon (1 day to 8 months) | 30 min | CLSTM | GSR | 1 January 2006 to 31 August 2018 | RMSE (W/m^{2}):1 day: 8.189 1 week: 16.011 2 weeks: 14.295 1 month: 32.872 |

[26] | Ahead by 1 h | Hourly | CNN–LSTM | - GHI
- Dew point temperature
- Solar zenith angle
- Wind speed
- Wind direction
- Precipitable water
- Relative humidity
- Temperature
| 1 January 2006 to 31 December 2012 | Average MAE:Dallas: 41.88 W/m ^{2}San Jacinto: 52.00 W/m ^{2}Zapata: 43.66 W/m ^{2}Moore: 37.26 W/m ^{2}Lamb: 37.20 W/m ^{2} |

[32] | Ahead by 1 h | Hourly | CEEMDAN-CNN–LSTM | Solar irradiance | 6 year data | Average RMSE: 38.49 W/m^{2} |

[33] | Ahead hourly every day | Hourly | LSTM | - Temperature
- Dew point
- Humidity
- Visibility
- Wind speed
- Weather type
| - March 2011 to August 2012
- January 2013 to December 2013 (30 months)
| RMSE: 76.245 W/m^{2} |

[34] | Ahead by 1 h | Hourly | LSTM | - Wind speed
- Wind direction
- GHI
| 2000 to 2014 | Average 24-h RMSE:80.0 W/m ^{2} |

Ref. | Forecast Horizon | Interval Data | Model | Input Variables | Historical Data Description | Size PV Power (kW) | Error Metrics |
---|---|---|---|---|---|---|---|

[35] | - Ahead by 7.5 min
- Ahead by 15 min
- Ahead by 30 min
| 7.5 min | CNN-ALSTM | - PV power
- PV module temperature
- Current
- Voltage
| October 2014 to September 2018 | N/A | Overall RMSE:7.5 min: 1.30 15 min: 1.40 30 min: 2.04 |

[36] | - Ahead by 10 min
- Ahead by 30 min
- Ahead by 60 min
- Ahead by 90 min
- Ahead by 120 min
- Ahead by 150 min
- Ahead by 180 min
| 10 min | 5D CNN–LSTM | - Active power generated
- Average phase current
- AC voltage generated
- Direct radiationGlobal radiation
- Diffuse radiation
- Temperature
- Humidity
- Wind speed
- Barometric pressure
| 1 year data (2019–2020) | 1.70 | RMSE:10 min: 0.0830 30 min: 0.2257 60 min: 0.4593 90 min: 0.7289 120 min: 1.0588 150 min: 1.4438 180 min: 2.0570 |

[37] | 1 day | 15 min | BCLSTM + IFFS | Numerical weather prediction (NWP) data | 1 January 2017 to 31 December 2018 (2 years) | N/A | RMSE: 0.1075 kW |

[38] | - Ahead by 7.5 min
- Ahead by 15 min
- Ahead by 30 min
- Ahead by 60 min
| 7.5 min | ALSTM | - PV power
- PV module temperature
| October 2014 to September 2018 | 20.0 | Overall RMSE:7.5 min: 1.39 15 min: 1.60 30 min: 1.81 60 min: 2.09 |

[10] | Ahead by 1 h | 5 min | WPD–LSTM | - PV power output
- GHR
- Diffuse horizontal radiation
- Ambient temperature
- Wind speed
- Relative humidity
| 1 June 2014 to 12 June 2016 | 26.5 | Average RMSE: 0.2357 |

[39] | N/A | 5 min | LSTM–CNN | - Current phase average
- Active power
- Wind speed
- Weather temperature, Celsius
- Weather humidity
- Global horizontal radiation
- Diffuse horizontal radiation
- Wind direction
| Half-year data (53,280 samples) | N/A | RMSE: 0.621 |

[40] | Ahead by 1 h | Hourly | PCA–LSTM | The dataset has 49 features- Temperature
- Humidity
- Sun exposure angle
- Light amplitude
- Time
- Season and other characteristics
| The first 24 historical data points | N/A | NRMSE: 0.0472% |

[41] | - Ahead by 15 min
- Ahead by 30 min
- Ahead hourly
- Ahead daily
- Ahead weekly
- Ahead monthly
| 15 min | Auto-LSTM | - PV power
- Weather data
| 2014–2015 (2 years) | 1.30 | Daily forecasting RMSE:Smart meter 1: 4.4414 Smart meter 2: 7.1925 |

[42] | Ahead hourly | 15 min | LSTM | PV power | 13 January 2010 to 29 January 2010 | 20,000 | RMSE (ahead by 1 h): 0.841 |

[43] | Ahead by 1 h | Hourly | DRNN–LSTM | - PV power
- Temperature
- Humidity
- Wind speed
| 1 January 2018 to 1 February 2018 | 106.60 | RMSE: 7.536 |

[44] | Ahead by 1 day | Every 1 min or 5 min | LSTM | PV power | One month | N/A | Average RMSE: 0.512 |

[45] | Ahead by 1.5 h | 15 min | Stacked LSTM | PV power | 1 September 2016 to 31 January 2019 (84,768 observation) | N/A | RMSE:0.09394 |

[46] | Ahead by 1 h | Hourly | LSTM-FC | - Temperature
- Humidity
- Weather
- Wind direction
- Wind speed
| 1 January 2018 to 31 December 2018 | N/A | RMSE:2.5605 |

[47] | Ahead by 1 day | 5 min | EMD-SCA-LSTM | - PV power
- GHI
- Relative humidity (RH)
- Diffuse horizontal irradiance (DHI)
- Air temperature (AT)
| 1-year data (2017) | 5.83 | RMSE:0.5283 kWMAE:0.3063 kWR^{2}:0.9210 |

Step Ahead | MAE (W/m^{2}) | RMSE (W/m^{2}) | MAPE (%) | R^{2} | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

LSTM | CNN | CNN–LSTM | LSTM | CNN | CNN–LSTM | LSTM | CNN | CNN–LSTM | LSTM | CNN | CNN–LSTM | |

1 | 6.61 | 6.51 | 3.83 | 10.43 | 9.82 | 5.79 | 10.19 | 11.29 | 7.50 | 0.998 | 0.998 | 0.999 |

2 | 12.15 | 11.69 | 7.32 | 20.46 | 18.09 | 11.71 | 51.74 | 37.45 | 19.64 | 0.993 | 0.994 | 0.997 |

3 | 18.39 | 16.73 | 10.61 | 31.12 | 26.41 | 18.18 | 28.62 | 52.21 | 31.87 | 0.984 | 0.988 | 0.994 |

4 | 24.16 | 21.81 | 13.68 | 40.33 | 34.53 | 23.48 | 70.51 | 91.84 | 50.08 | 0.974 | 0.979 | 0.99 |

5 | 31.21 | 27.26 | 17.01 | 52.5 | 43.11 | 29.25 | 30.99 | 52.79 | 55.47 | 0.957 | 0.969 | 0.985 |

6 | 36.89 | 32.38 | 20.07 | 62.27 | 50.99 | 34.89 | 44.81 | 127.29 | 59.28 | 0.942 | 0.957 | 0.979 |

Season | Types of Weather | Error | WPD–LSTM | LSTM | GRU | RNN | MLP |
---|---|---|---|---|---|---|---|

Winter | Sunny (Day 1) | MBE (kW) | −0.0055 | −0.0058 | 0.1588 | −0.0085 | −0.0284 |

MAPE (%) | 1.7526 | 1.7744 | 2.1019 | 2.633 | 5.5833 | ||

RMSE (kW) | 0.2466 | 1.2541 | 1.2399 | 1.2468 | 1.1944 | ||

Cloudy (Day 2) | MBE (kW) | 0.1127 | −0.0497 | 0.0184 | −0.0901 | 0.2429 | |

MAPE (%) | 1.7365 | 0.1276 | 1.9913 | 2.7622 | 6.1295 | ||

RMSE (kW) | 0.1773 | 1.1279 | 0.2206 | 0.2868 | 0.6075 | ||

Rainy (Day 3) | MBE (kW) | −0.0214 | −0.1913 | 0.1651 | −0.3158 | −0.0495 | |

MAPE (%) | 6.7328 | 8.4150 | 10.8690 | 9.3110 | 10.7191 | ||

RMSE (kW) | 0.4374 | 2.2336 | 2.0876 | 2.1223 | 1.9916 | ||

Spring | Sunny (Day 4) | MBE (kW) | 0.1425 | −0.0239 | 0.0377 | −0.0240 | 0.3277 |

MAPE (%) | 2.0973 | 1.3243 | 2.0199 | 3.1087 | 6.8559 | ||

RMSE (kW) | 0.2250 | 0.1643 | 0.2456 | 0.3431 | 0.7173 | ||

Cloudy (Day 5) | MBE (kW) | −0.0675 | 0.1165 | 0.5523 | 0.0711 | −0.2168 | |

MAPE (%) | 8.1383 | 15.3881 | 14.9651 | 13.0762 | 15.4708 | ||

RMSE (kW) | 0.1453 | 0.2759 | 0.6452 | 0.4222 | 0.3312 | ||

Rainy (Day 6) | MBE (kW) | 0.0566 | 0.2304 | 0.5502 | 0.0674 | 0.1121 | |

MAPE (%) | 3.8080 | 9.9553 | 14.8235 | 11.3013 | 8.3763 | ||

RMSE (kW) | 0.2807 | 0.8107 | 1.0036 | 0.8604 | 0.7572 | ||

Summer | Sunny (Day 7) | MBE (kW) | 0.0481 | 0.1115 | 0.2936 | −0.1382 | 0.3617 |

MAPE (%) | 2.6031 | 8.4936 | 10.8292 | 8.8545 | 10.8997 | ||

RMSE (kW) | 0.2664 | 0.9701 | 1.0748 | 0.8514 | 1.0822 | ||

Cloudy (Day 8) | MBE (kW) | 0.0183 | 0.2012 | 0.5218 | −0.0583 | 0.1048 | |

MAPE (%) | 3.4360 | 13.0028 | 11.8370 | 14.8472 | 11.5344 | ||

RMSE (kW) | 0.2382 | 0.8398 | 0.9323 | 0.8812 | 0.7810 | ||

Rainy (Day 9) | MBE (kW) | −0.0127 | 0.0924 | 0.4668 | −0.2068 | −0.3127 | |

MAPE (%) | 3.8936 | 9.8571 | 12.5799 | 16.0052 | 14.7068 | ||

RMSE (kW) | 0.1253 | 0.3009 | 0.5805 | 0.4993 | 0.4479 | ||

Autumn | Sunny (Day 10) | MBE (kW) | −0.0799 | −0.2050 | 0.0959 | −0.1813 | 0.2752 |

MAPE (%) | 2.0367 | 7.4015 | 8.3304 | 7.8951 | 8.3189 | ||

RMSE (kW) | 0.1929 | 0.7395 | 0.8029 | 0.7778 | 0.7495 | ||

Cloudy (Day 11) | MBE (kW) | 0.0049 | 0.1174 | 0.5692 | −0.1111 | 0.1729 | |

MAPE (%) | 3.7923 | 5.0279 | 9.9234 | 7.0087 | 14.4850 | ||

RMSE (kW) | 0.2576 | 1.0540 | 1.2110 | 1.1365 | 1.0643 | ||

Rainy (Day 12) | MBE (kW) | 0.0029 | −0.0799 | 0.1202 | −0.3103 | 0.3244 | |

MAPE (%) | 4.3427 | 8.3508 | 9.3104 | 7.3294 | 14.8202 | ||

RMSE (kW) | 0.3903 | 2.4216 | 2.3687 | 2.4275 | 2.4343 |

Season | Indicator | Methods | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

C-C-L | C-L | C-S | C-B | C-A | LSTM | SVM | BP | ARIMA | Per. | ||

Spring | RMSE (W/m^{2}) | 42.87 | 56.76 | 64.97 | 64.46 | 79.88 | 79.63 | 84.62 | 82.20 | 112.46 | 126.76 |

nRMSE (%) | 17.88 | 25.46 | 29.15 | 28.92 | 35.84 | 35.72 | 37.96 | 36.87 | 50.45 | 56.87 | |

MAE (W/m^{2}) | 22.80 | 37.74 | 36.09 | 35.98 | 41.84 | 42.21 | 51.09 | 41.87 | 63.77 | 76.89 | |

Summer | RMSE (W/m^{2}) | 47.60 | 55.15 | 58.73 | 65.07 | 82.44 | 70.62 | 73.09 | 70.94 | 110.09 | 125.63 |

nRMSE (%) | 17.34 | 21.68 | 23.09 | 25.58 | 32.41 | 27.76 | 28.72 | 27.89 | 43.28 | 49.39 | |

MAE (W/m^{2}) | 26.80 | 36.76 | 37.60 | 39.44 | 43.09 | 39.12 | 41.14 | 35.66 | 65.76 | 80.06 | |

Autumn | RMSE (W/m^{2}) | 37.59 | 47.19 | 47.76 | 50.86 | 69.79 | 54.86 | 59.71 | 55.49 | 103.07 | 122.39 |

nRMSE (%) | 17.65 | 19.59 | 19.83 | 21.11 | 28.98 | 22.78 | 24.79 | 23.04 | 42.79 | 50.81 | |

MAE (W/m^{2}) | 19.66 | 29.59 | 27.79 | 29.01 | 36.14 | 27.28 | 38.96 | 28.38 | 60.32 | 75.99 | |

Winter | RMSE (W/m^{2}) | 25.97 | 38.19 | 46.82 | 45.31 | 50.23 | 47.26 | 54.24 | 48.27 | 81.98 | 107.96 |

nRMSE (%) | 15.73 | 19.60 | 24.04 | 23.26 | 25.79 | 24.26 | 27.85 | 24.78 | 42.09 | 55.42 | |

MAE (W/m^{2}) | 13.25 | 22.14 | 28.33 | 23.69 | 25.65 | 20.18 | 32.44 | 21.86 | 41.92 | 64.54 | |

Annual | RMSE (W/m^{2}) | 38.49 | 49.87 | 55.10 | 57.07 | 71.72 | 64.37 | 68.93 | 65.57 | 102.61 | 121.75 |

nRMSE (%) | 17.23 | 21.85 | 24.14 | 25.00 | 31.42 | 28.20 | 30.20 | 28.73 | 44.96 | 53.34 | |

MAE (W/m^{2}) | 20.50 | 31.56 | 32.45 | 32.03 | 36.68 | 32.20 | 40.90 | 31.95 | 57.94 | 74.64 |

LSTM | CNN | CNN–LSTM | LSTM–CNN | |
---|---|---|---|---|

Training time (s) | 70.490 | 787.494 | 983.701 | 871.606 |

Running time (s) | 5.439 | 5.425 | 8.692 | 7.196 |

Model | Time (s) |
---|---|

5D LSTM | 9.1394 |

2D CNN–LSTM | 8.0362 |

5D CNN–LSTM | 69.1148 |

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## Share and Cite

**MDPI and ACS Style**

Jailani, N.L.M.; Dhanasegaran, J.K.; Alkawsi, G.; Alkahtani, A.A.; Phing, C.C.; Baashar, Y.; Capretz, L.F.; Al-Shetwi, A.Q.; Tiong, S.K.
Investigating the Power of LSTM-Based Models in Solar Energy Forecasting. *Processes* **2023**, *11*, 1382.
https://doi.org/10.3390/pr11051382

**AMA Style**

Jailani NLM, Dhanasegaran JK, Alkawsi G, Alkahtani AA, Phing CC, Baashar Y, Capretz LF, Al-Shetwi AQ, Tiong SK.
Investigating the Power of LSTM-Based Models in Solar Energy Forecasting. *Processes*. 2023; 11(5):1382.
https://doi.org/10.3390/pr11051382

**Chicago/Turabian Style**

Jailani, Nur Liyana Mohd, Jeeva Kumaran Dhanasegaran, Gamal Alkawsi, Ammar Ahmed Alkahtani, Chen Chai Phing, Yahia Baashar, Luiz Fernando Capretz, Ali Q. Al-Shetwi, and Sieh Kiong Tiong.
2023. "Investigating the Power of LSTM-Based Models in Solar Energy Forecasting" *Processes* 11, no. 5: 1382.
https://doi.org/10.3390/pr11051382