# A Review on Deep Learning Models for Forecasting Time Series Data of Solar Irradiance and Photovoltaic Power

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Solar Irradiance Variability

## 3. Deep Learning Models

#### 3.1. Neural Network

_{n}is the output, n is the number of input, w

_{j}is the weight, I

_{j}is the input, and b is the bias.

#### 3.2. RNN

_{t}) can be formulated as

_{t}is the input at time t, h

_{t}is the hidden neuron at time t, U is the weight of the hidden layer, and W is the transition weights of the hidden layer. The input and previous hidden states are combined to produce information as the current and previous input go through the tanh function. Then, the output is the new hidden state, performing as the neural network memory because it holds information from the previous network.

#### 3.3. LSTM

- X
_{t}is the input vector to the memory cell at time t. - W
_{i}, W_{f}, W_{c}, W_{o}, U_{i}, U_{f}, U_{c}, U_{o}, and V_{o}are weight matrices. - b
_{i}, b_{f}, b_{c}, and b_{o}are bias vectors. - h
_{t}is the value of the memory cell at time t. - S
_{t}and C_{t}are the values of the candidate state of the memory cell and the state of the memory cell at time t, respectively. - σ and tanh are the activation functions.
- i
_{t}, f_{t}, and o_{t}are values of the input gate, the forget gate, and the output gate at time t.

_{t}), input gate (i

_{t}), and output gate (o

_{t}) in Equations (3), (4) and (7) have values from 0 to 1 through the sigmoid function (σ). A value of one means that all input information passes through the gate, but a value of 0 shows that no input information passes [23]. The values of the candidate state of the memory cells in Equation (6) calculate the new information at time t, and its output through the tanh function has a value between −1 and 1. The state of the memory at the cell, controlled by the forget and input gates, is calculated as variable C

_{t}of time t (Equation (7)). The selected values are converted into output by multiplying them by o

_{t}and output becomes h

_{t}(Equation (8)).

#### 3.4. GRU

_{t}is the reset gate, Z

_{t}is the update gate, A

_{t}is the memory content, σ and tanh are the activation functions, and h

_{t}is the final memory at the current time step. The reset (r

_{t}) and update gate (Z

_{t}) have values from 0 to 1 through the sigmoid function (σ) in Equations (9) and (10). Meanwhile, the memory content (A

_{t}), using the rest gate to store the relevant information from the past, has a value between −1 and 1 through tanh.

#### 3.5. The Hybrid Model (CNN–LSTM)

## 4. Evaluation Metrics

_{pred}, P

_{meas}, and n represent the forecasted values at each time, the measured values at each time, and the number of sample data for the period, respectively.

## 5. Analysis of Past Studies

^{2}, called the solar constant. This value is attenuated to the earth’s surface through a complex series of reflections, absorptions, and remissions. Solar irradiance fluctuates because it is affected by several factors such as atmosphere condition, geographic location, season, and time of day. Although the amount of power generated by PV at a particular location depends on how much of the solar irradiance reaches it, the PV power output also relies on the solar panel’s size and efficiency. Therefore, it is essential to describe the specification of the solar panel for getting accurate PV output information.

#### 5.1. Accuracy

^{2}. For LSTM and GRU, the best performance was the prediction of solar irradiance for 10 min ahead at 5 min intervals. However, RNN tends to result in lower accuracy than other models for day-ahead hourly forecasting.

^{2}. Meanwhile, Niu et al. [37] have the largest error in forecasting solar irradiance using the RNN model where the RMSE value is 195 W/m

^{2}; however, the sky conditions are not mentioned in the present study. Hence, further study regarding deep learning models to predict solar irradiance is required to create a concrete solution.

^{2}, respectively.

#### 5.2. Types of Input Data

#### 5.3. Forecast Horizon

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

#### 5.4. Type of Season and Weather

#### 5.5. Training Time

#### 5.6. Comparison with Other Models

^{2}, whereas FFNN and SVR obtained 0.160 and 0.110 W/m

^{2}, respectively.

## 6. Conclusions

- In the case of the single model, most studies explain that LSTM and GRU show better performance than RNN in all conditions because LSTM and GRU have internal memory to overcome the vanishing gradient problems occurring in the RNN.
- The hybrid model (CNN–LSTM) outperforms the three standalone models in predicting solar irradiance. More specifically, the evaluation metrics for this hybrid model are substantially smaller than those of the standalone models. However, the CNN–LSTM model requires complex input data, such as images, because it has a CNN layer inside.
- The training time should be considered to recognize the performance of the models. This work reveals that the statistics of GRU are more efficient than that of LSTM in the case of computational time because the average time for LSTM to train the data is relatively longer than that for GRU. Therefore, considering training time and forecasting accuracy, the GRU model can generate a satisfactory result for forecasting PV power and solar irradiance.
- Comparisons between the deep learning models and other machine learning models conclude that these models were better used in predicting solar irradiance and PV power (Section 5.6). Most studies show that the accuracy of the proposed models is better than other models, such as ANN, FFNN, SVR, RFR, and MLP.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviation

ANN | Artificial neural network |

BPNN | Back propagation neural network |

CNN | Convolutional neural network |

DHI | Diffuse horizontal irradiance |

FFNN | Feedforward neural network |

GHI | Global horizontal irradiance |

GRU | Gated recurrent unit |

LSTM | Long short-term memory |

MAE | Mean absolute error |

MAPE | Mean absolute percentage error |

MLP | Multilayer perceptron |

PV | Photovoltaic |

RBF | Radial basis function |

ReLU | Rectified linear unit |

RFR | Random forest regression |

RMSE | Root-mean-square error |

RNN | Recurrent neural network |

rRMSE | Relative root-mean-square error |

SVR | Support vector regression |

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**Figure 1.**The variability of global horizontal irradiance (GHI) at Kookmin University, South Korea, as a function of time scale. The figure includes 1 day of 1 min data, 2 days of 10 min data, 4 days of 1 h data, 48 days of day data, and 12 months of monthly data.

**Figure 8.**Illustration of convolutional neural network (CNN)–long short-term memory (LSTM) architecture.

**Figure 9.**The number of publications that apply the deep learning models to predict solar irradiance and photovoltaic (PV) power from 2005 to 2020.

**Figure 10.**Distribution of studies using deep learning models to predict (

**a**) solar irradiance and (

**b**) PV power.

Activation Function | Equation | Plot |
---|---|---|

Linear | $f\left(x\right)=x$ | |

ReLU | $f\left(x\right)=\mathrm{max}\left(0,x\right)$ | |

Leaky ReLU | $f\left(x\right)=\mathrm{max}\left(0.1\cdot x,x\right)$ | |

Tanh | $f\left(x\right)=\mathrm{tanh}\left(x\right)$ | |

Sigmoid | $f\left(x\right)=\frac{1}{1+{e}^{-x}}$ |

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

Error | ${P}_{pred}-{P}_{meas}$ |

Mean absolute error (MAE) | $\frac{1}{n}{\displaystyle \sum _{i=1}^{n}\left|{P}_{pred}-{P}_{meas}\right|}$ |

Mean absolute percentage error (MAPE) | $\frac{1}{n}{\displaystyle \sum _{i=1}^{n}\left|\frac{{P}_{pred}-{P}_{meas}}{{P}_{meas}}\right|}\cdot 100$ |

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

Relative Mean bias error (rMBE) | $\frac{{\displaystyle \sum _{i=1}^{n}\left({P}_{pred}-{P}_{meas}\right)}}{{\displaystyle \sum _{i=1}^{n}{P}_{meas}}}\cdot 100$ |

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

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

Forecasting skill | $1-\frac{RMS{E}_{\mathrm{mod}el}}{RMS{E}_{persistence}}$ |

Authors and Ref. | Forecast Horizon | Time Interval | Model | Input Parameter | Historical Data Description | RMSE (W/m^{2}) |
---|---|---|---|---|---|---|

Cao et al. [38] | 1 day | hourly | RNN | -Solar irradiance | 1995–2000 (2192 days) | 44.326 |

Niu et al. [37] | 10 min ahead | every 10 min | RNN | -Global solar radiation -Dry bulb temperature -Relative humidity -Dew point -Wind speed | 22–29 May 2016 (7 days) | 118 |

30 min ahead | 121 | |||||

1 h ahead | 195 | |||||

Qing et al. [39] | 1 day ahead | hourly | LSTM | -Temperature -Dew Point -Humidity -Visibility -Wind Speed | March 2011–August 2012 January 2013–December 2013 (30 months) | 76.245 |

Wang et al. [25] | 1 day ahead | every 15 min | CNN–LSTM | -Solar irradiance | 2008–2012 2014–2017 (3013 days) | 32.411 |

LSTM | 33.294 | |||||

Aslam et al. [40] | 1 h ahead | hourly | LSTM | -Solar irradiance | 2007–2017 (10 years) | 108.888 |

GRU | 99.722 | |||||

RNN | 105.277 | |||||

1 day ahead | LSTM | 55.277 | ||||

GRU | 55.821 | |||||

RNN | 63.125 | |||||

Ghimire et al. [36] | 1 day ahead | every 30 min | CNN–LSTM | -Solar irradiance | January 2006–August 2018 | 8.189 |

Husein et al. [3] | 1 day ahead | hourly | LSTM | -Temperature -Humidity -Wind speed -Wind direction -Precipitation -Cloud cover | January 2003–December 2017 | 60.310 |

Hui et al. [41] | 1 day ahead | hourly | LSTM | -Temperature -Relative humidity -Cloud cover -Wind speed -Pressure | 2006–2015 (10 years) | 62.540 |

Byung-ki et al. [42] | 1 day head | hourly | LSTM | -Temperature -Humidity -Wind speed -Sky cover -Precipitation -Irradiance | (1825 days) | 30.210 |

Wojtkiewicz et al. [43] | 1 h ahead | hourly | GRU | -GHI -Solar zenith angle -Relative humidity -Air Temperature | January 2004–December 2014 | 67.290 |

LSTM | 66.570 | |||||

Yu et al. [44] | 1 h ahead | hourly | LSTM | -GHI -Cloud type -Dew point -Temperature -Precipitation -Relative humidity -Solar Zenith Angle -Wind speed -Wind direction | 2013–2017 | 41.370 |

Yan et al. [45] | 5 min ahead | every 1 min | LSTM | -Solar irradiance | 2014 | 18.850 |

GRU | 20.750 | |||||

10 min ahead | LSTM | 14.200 | ||||

GRU | 15.200 | |||||

20 min ahead | LSTM | 33.860 | ||||

GRU | 29.580 | |||||

30 min ahead | LSTM | 58.000 | ||||

GRU | 55.290 |

Authors and Ref. | Forecast Horizon | Interval Data | Model | Input Variable | Historical Data Description | RMSE (kW) | PV Size |
---|---|---|---|---|---|---|---|

Vishnu et al. [49] | 1 h ahead | hourly | CNN–LSTM | -Irradiation -Wind speed -Temperature | March 2012–December 2018 | 0.053 | N/A |

1 day ahead | 0.051 | ||||||

1 w ahead | 0.045 | ||||||

Gensler et al. [50] | 1 day ahead | hourly | LSTM | -PV power | (990 days) | 0.044 | N/A |

Wang et al. [51] | 1 h ahead | hourly | GRU | -Total column liquid water -Total column ice water -Surface pressure -Relative humidity -Total cloud cover -Wind speed -Temperature -Total precipitation -Total net solar radiation -Surface solar radiation -Surface thermal radiation | April 2012–May 2014 | 68.300 | N/A |

Zhang et al. [34] | 1 min ahead | every 1 min | LSTM | -Sky images -PV Power | 2006 | 0.139 | 10 × 6 m^{2} |

Abdel-Nassar et al. [52] | 1 h ahead | hourly | LSTM | -PV power | (12 months) | 82.150 | N/A |

Lee et al. [53] | 1 h ahead | hourly | LSTM | -PV power | June 2013–August 2016 (39 months) | 0.563 | N/A |

Lee et al. [54] | 1 h ahead | hourly | RNN | -Temperature -Relative humidity -Wind speed -Wind direction -Sky index -Precipitation -Solar altitude | June 2017–August 2018 | 0.160 | N/A |

Li et al. [55] | 15 min ahead | N/A | RNN | -PV power | January 2015–January 2016 | 6970 | N/A |

LSTM | 8700 | ||||||

30 min ahead | RNN | 15,290 | |||||

LSTM | 15,570 | ||||||

Li et al. [48] | 1 h ahead | every 5 min | LSTM | -PV power | June 2014–June 2016 (743 days) | 0.885 | 199.16 m^{2} |

GRU | 0.847 | ||||||

RNN | 0.888 | ||||||

Wang et al. [56] | 5 min ahead | every 5 min | LSTM | -Current phase average -Wind speed -Temperature -Relative humidity -GHI -DHI -Wind direction | 2014–2017 (4 years) | 0.398 | 4 × 38.37 m^{2} |

CNN–LSTM | 0.343 | ||||||

Wen et al. [57] | 1 h ahead | hourly | LSTM | -Temperature -Humidity -Wind speed -GHI -DHI | 1 January–1 February 2018 | 7.536 | N/A |

Sharadga et al. [58] | 1 h ahead | hourly | LSTM | -PV power | January–October 2010 | 841 | N/A |

2 h ahead | 1102 | ||||||

3 h ahead | 1824 |

**Table 5.**Root-mean-square error evaluation metric (RMSE) of LSTM vs. CNN–LSTM based on the input sequence.

Input Sequence (Years) | LSTM | CNN–LSTM (kW) | ||
---|---|---|---|---|

RMSE (kW) | MAE (kW) | RMSE (kW) | MAE (kW) | |

0.5 | 1.244 | 0.654 | 1.161 | 0.559 |

1 | 1.393 | 0.616 | 1.434 | 0.628 |

1.5 | 1.533 | 0.599 | 1.248 | 0.529 |

2 | 1.320 | 0.457 | 0.941 | 0.397 |

2.5 | 0.945 | 0.389 | 0.426 | 0.198 |

3 | 0.398 | 0.181 | 0.343 | 0.126 |

3.5 | 1.150 | 0.455 | 0.991 | 0.384 |

4 | 1.465 | 0.565 | 0.886 | 0.405 |

Forecast Horizon (min) | Model | Spring | Summer | Autumn | Winter | ||||
---|---|---|---|---|---|---|---|---|---|

RMSE | MAE | RMSE | MAE | RMSE | MAE | RMSE | MAE | ||

(W/m^{2}) | (W/m^{2}) | (W/m^{2}) | (W/m^{2}) | ||||||

5 | LSTM | 36.67 | 26.95 | 89.91 | 59.20 | 18.85 | 13.13 | 44.24 | 21.58 |

GRU | 36.82 | 27.18 | 89.77 | 59.70 | 20.75 | 16.03 | 43.66 | 23.60 | |

10 | LSTM | 41.02 | 29.65 | 42.23 | 32.96 | 53.01 | 33.62 | 14.20 | 11.09 |

GRU | 44.71 | 34.42 | 41.08 | 30.92 | 55.00 | 38.35 | 15.20 | 12.83 | |

20 | LSTM | 56.22 | 49.09 | 46.31 | 40.58 | 33.86 | 28.11 | 43.54 | 39.10 |

GRU | 45.23 | 36.78 | 53.97 | 47.44 | 29.58 | 24.55 | 41.03 | 37.09 | |

30 | LSTM | 58.77 | 47.54 | 58.00 | 47.82 | 81.75 | 59.08 | 61.68 | 52.29 |

GRU | 60.42 | 49.65 | 55.29 | 50.52 | 82.12 | 60.71 | 62.33 | 54.13 |

Model | RMSE (W/m^{2}) | MAE (W/m^{2}) | ||||||
---|---|---|---|---|---|---|---|---|

1 Day | 1 Week | 2 Weeks | 1 Month | 1 Day | 1 Week | 2 Weeks | 1 Month | |

CNN–LSTM | 8.189 | 16.011 | 14.295 | 32.872 | 6.666 | 9.804 | 8.238 | 13.131 |

LSTM | 21.055 | 18.879 | 16.327 | 33.387 | 18.339 | 11.275 | 10.750 | 14.307 |

RNN | 20.177 | 18.113 | 15.494 | 41.511 | 18.206 | 11.387 | 10.492 | 26.858 |

GRU | 14.289 | 21.464 | 19.207 | 57.589 | 11.320 | 15.658 | 14.005 | 39.716 |

Season | Type of Weather | LSTM (kW) | GRU (kW) | RNN (kW) |
---|---|---|---|---|

Winter | Sunny | 1.2541 | 1.2399 | 1.2468 |

Cloudy | 1.1279 | 0.2206 | 0.2867 | |

Rainy | 2.2336 | 2.0876 | 2.1223 | |

Spring | Sunny | 0.1643 | 0.2456 | 0.3431 |

Cloudy | 0.2759 | 0.6452 | 0.4222 | |

Rainy | 0.8107 | 1.0036 | 0.8604 | |

Summer | Sunny | 0.9701 | 1.0748 | 0.8514 |

Cloudy | 0.8398 | 0.9323 | 0.8812 | |

Rainy | 0.3009 | 0.5805 | 0.4993 | |

Autumn | Sunny | 0.7395 | 0.8029 | 0.7778 |

Cloudy | 1.0540 | 1.2110 | 1.1365 | |

Rainy | 2.4216 | 2.3687 | 2.4275 |

Model | The Best Case/s | The Worst Case/s | The Average Case/s |
---|---|---|---|

LSTM | 393.01 | 400.57 | 396.27 |

GRU | 354.92 | 379.57 | 365.40 |

Region | Year | Hourly | Daily | ||
---|---|---|---|---|---|

LSTM (s) | GRU (s) | LSTM (s) | GRU (s) | ||

Seoul | 2017 | 1251.23 | 1004.15 | 88.35 | 72.56 |

2016 | 1060.82 | 832.63 | 77.98 | 64.12 | |

Busan | 2017 | 1269.21 | 1028.43 | 90.42 | 75.44 |

2016 | 1023.27 | 830.54 | 75.99 | 64.29 |

Model | LSTM (s) | CNN–LSTM (s) |
---|---|---|

Training time | 70.490 | 983.701 |

Forecast Horizon (min) | RMSE (W/m^{2}) | |
---|---|---|

ANN | RNN | |

10 | 55.7 | 41.2 |

30 | 63.3 | 53.3 |

60 | 170.9 | 58.1 |

Model | FFNN (W/m^{2}) | SVR (W/m^{2}) | LSTM (W/m^{2}) |
---|---|---|---|

RMSE | 0.160 | 0.110 | 0.086 |

Model | RMSE (kW) | |
---|---|---|

With Weather Data | Without Weather Data | |

RFR | 0.178 | 0.191 |

SVR | 0.122 | 0.126 |

CNN–LSTM | 0.098 | 0.140 |

Season | RMSE (kW) | ||||
---|---|---|---|---|---|

Winter | Spring | Summer | Autumn | Average | |

GRU | 847 | 917 | 1238 | 1074 | 1035 |

MLP | 916 | 1069 | 1263 | 1061 | 1086 |

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## Share and Cite

**MDPI and ACS Style**

Rajagukguk, R.A.; Ramadhan, R.A.A.; Lee, H.-J.
A Review on Deep Learning Models for Forecasting Time Series Data of Solar Irradiance and Photovoltaic Power. *Energies* **2020**, *13*, 6623.
https://doi.org/10.3390/en13246623

**AMA Style**

Rajagukguk RA, Ramadhan RAA, Lee H-J.
A Review on Deep Learning Models for Forecasting Time Series Data of Solar Irradiance and Photovoltaic Power. *Energies*. 2020; 13(24):6623.
https://doi.org/10.3390/en13246623

**Chicago/Turabian Style**

Rajagukguk, Rial A., Raden A. A. Ramadhan, and Hyun-Jin Lee.
2020. "A Review on Deep Learning Models for Forecasting Time Series Data of Solar Irradiance and Photovoltaic Power" *Energies* 13, no. 24: 6623.
https://doi.org/10.3390/en13246623