Hour-Ahead Solar Irradiance Forecasting Using Multivariate Gated Recurrent Units

Abstract

Variation in solar irradiance causes power generation fluctuations in solar power plants. Power grid operators need accurate irradiance forecasts to manage this variability. Many factors affect irradiance, including the time of year, weather and time of day. Cloud cover is one of the most important variables that affects solar power generation, but is also characterized by a high degree of variability and uncertainty. Deep learning methods have the ability to learn long-term dependencies within sequential data. We investigate the application of Gated Recurrent Units (GRU) to forecast solar irradiance and present the results of applying multivariate GRU to forecast hourly solar irradiance in Phoenix, Arizona. We compare and evaluate the performance of GRU against Long Short-Term Memory (LSTM) using strictly historical solar irradiance data as well as the addition of exogenous weather variables and cloud cover data. Based on our results, we found that the addition of exogenous weather variables and cloud cover data in both GRU and LSTM significantly improved forecasting accuracy, performing better than univariate and statistical models.

Full text

energies
Article
Hour-Ahead Solar Irradiance Forecasting Using
Multivariate Gated Recurrent Units
Jessica Wojtkiewicz 1, Matin Hosseini 2, Raju Gottumukkala 1,3,* and Terrence Lynn Chambers 1
1College of Engineering, University of Louisiana at Lafayette, Lafayette, LA 70504, USA;
jessicaw1@louisiana.edu (J.W.); tlchambers@louisiana.edu (T.L.C.)
2School of Computing & Informatics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA;
matinhosseiny@gmail.com
3Informatics Research Institute, University of Louisiana at Lafayette, Lafayette, LA 70504, USA
*Correspondence: raju@louisiana.edu
Received: 8 September 2019; Accepted: 12 October 2019; Published: 24 October 2019


Abstract:
Variation in solar irradiance causes power generation fluctuations in solar power plants.
Power grid operators need accurate irradiance forecasts to manage this variability. Many factors
affect irradiance, including the time of year, weather and time of day. Cloud cover is one of the
most important variables that affects solar power generation, but is also characterized by a high
degree of variability and uncertainty. Deep learning methods have the ability to learn long-term
dependencies within sequential data. We investigate the application of Gated Recurrent Units (GRU)
to forecast solar irradiance and present the results of applying multivariate GRU to forecast hourly
solar irradiance in Phoenix, Arizona. We compare and evaluate the performance of GRU against Long
Short-Term Memory (LSTM) using strictly historical solar irradiance data as well as the addition of
exogenous weather variables and cloud cover data. Based on our results, we found that the addition
of exogenous weather variables and cloud cover data in both GRU and LSTM significantly improved
forecasting accuracy, performing better than univariate and statistical models.
Keywords:
solar irradiance; time series forecasting; gated recurrent units; deep learning; multivariate
1. Introduction
In recent years, solar electricity has grown in popularity due to the lowering costs of manufacturing
and the rising efficiency of solar panels. In order to fully integrate solar electricity into power grid
systems, information regarding the amount of solar irradiance from the sun at a given location and
future time period must be known to estimate the amount of electricity that will be generated and
dispatch accordingly [
1
]. This can be a challenge for power grid operators given the stochastic nature
of solar irradiance due to cloud cover, humidity, air temperature, and other environmental factors.
Using accurate predictions of future solar irradiance values, power grid operators would be able to
determine how much energy will be generated in the near future, dispatch power to supply electricity
as needed, and schedule power generation to meet the varying demands of electricity throughout
the year [1].
Global Horizontal Irradiance (GHI) is defined as the amount of solar irradiance hitting a surface
horizontal to the Earth’s surface [
2
]. GHI is an important measurement for photovoltaic (PV) power
plants, because it allows plant operators to estimate the amount of power generated at a given time
and model PV performance over time. GHI can be measured using a pyranometer or calculated based
on the Direct Normal Irradiance (DNI) and Diffuse Horizontal Irradiance (DHI), where DNI is the
beam irradiance from the sun directly hitting the surface at a perpendicular angle and DHI is the
surrounding irradiance that has been scattered by the Earth’s atmosphere coming from equal angles
Energies 2019,12, 4055; doi:10.3390/en12214055 www.mdpi.com/journal/energies

Energies 2019,12, 4055 2 of 13
of the surface [
2
,
3
]. In non-concentrating PV power plants, forecasting future PV power production
primarily utilizes GHI forecasts, while concentrated solar power forecasting can only benefit from
forecasts of DNI [
3
]. The amount of GHI and DNI hitting the Earth’s surface is dependent on the
amount of cloud cover over a particular site [
3
–
5
] as well as weather patterns in the area, such as
air temperature, relative humidity, wind speed and direction, and dew point [
2
,
6
,
7
]. Forecasting
GHI and PV power output are similar in that both depend on surrounding weather and cloud
activity [
8
]. Using GHI forecasts and the characteristics of a particular PV panel, power production can
be predicted for some time in the future to measure PV power plant performance and efficiency for
PV installations [
9
,
10
]. In this paper, we forecast GHI rather than PV power production in order to
compare our results to existing literature in forecasting solar irradiance.
Given the high degree of variability, forecasting solar irradiance has been largely studied in the
literature in order to obtain higher prediction accuracy and more efficient modeling. Research efforts
in forecasting solar irradiance include the use of physics, statistics, and machine learning models using
cloud imagery, historical solar irradiance, and exogenous weather data to predict solar irradiance over
short and long time horizons [
1
]. Physics-based models, including Numerical Weather Prediction
(NWP) models, use satellite and ground-based sky image data to evaluate cloud formations and predict
solar irradiance [
11
,
12
].While physics-based models explain causality through closed-form equations
or numerical simulations, the solutions are in some cases limited with respect to their computational
tractability [
1
]. On the other hand, statistics-based models, including Regression [
13
], Exponential
Smoothing Models [
14
], and variants of the Autoregressive Integrated Moving Average (ARIMA)
model [
4
,
13
,
15
], have been implemented for solar irradiance forecasting over shorter horizons. These
models use statistical analysis in order to map inputs to the forecast variable; however, considering
the non-stationary nature of solar irradiance data, statistical models fail to accurately predict sudden
changes in solar irradiance [
13
]. Various operational decisions are often dependent on short- and
long-term forecasts, where short-term forecasting refers to forecasts over one to six hours and long-term
forecasting refers to predicting solar irradiance over six hours to a couple of days [
1
]. In practice,
statistical models and forecasting models using satellite cloud imagery perform well for short-term
forecasts [
1
,
16
]; these forecasts provide insight on how much solar power may be generated in the
near future and influence intraday power scheduling decisions [
14
]. Conversely, physics-based
models perform better for long-term forecasts which are used to develop plans for integrating solar
power systems [
16
]. Multivariate time series models capture the influence of multiple variable on
the target variable to improve forecasting performance. Many previous studies [
4
] have shown
empirical relationship between various variables such as solar zenith angle, ambient temperature,
cloud cover, humidity, and air temperature and irradiance. We chose to experiment with multivariate
GRU to evaluate if the model is able to capture the dynamic dependencies of these variables on
future irradiance.
Machine learning models including Artificial Neural Networks have the ability to train the
model using historical solar irradiance data, exogenous meteorological data, or both to capture
the stochasticity of solar irradiance data. Melzi et al. [
15
] compared the performance of several
machine learning techniques to statistical models using previous hours of solar irradiance and previous
days containing the same number of daylight hours in order to forecast hourly solar irradiance.
They found that combining exogenous variables to solar irradiance data improved model performance.
Li et al. [
6
] evaluated the use of Hidden Markov Models (HMM) and Support Vector Regression (SVR)
to forecast short-term solar irradiance under different weather conditions. They used exogenous
weather variables, such as relative humidity, air temperature, and wind speed, as observation states
within their HMM and found that these variables had a large impact on future solar irradiance.
Aguiar et al. [
17
] designed Artificial Neural Networks that used ground solar irradiance data along with
solar radiation and Total Cloud Cover forecasts as inputs to the model. The best results of their study
were obtained by combining exogenous satellite data and Total Cloud Cover data. Yang et al. [
4
] tested
the application of three different forecasting methods using GHI, DNI, DHI and cloud cover. Moreover,

Energies 2019,12, 4055 3 of 13
the addition of cloud cover information was shown to significantly improve the accuracy of forecasting
models. Additionally, hybrid models have been developed by combining machine learning techniques
with physics- or statistics-based models to improve overall forecasting performance compared to using
a single type of model [
18
,
19
]. Reikard [
13
] evaluated the performance of regression combined with
neural networks and found that the hybrid model performed better than regression or neural networks
alone. Ogliari et al. [
20
] proposed a mixed method containing a physical-neural network model and a
five parameters model for forecasting future PV power production, where the combination of these
two forecasting methods resulted in competitive forecasting 24 h in advance.
More recently, deep learning techniques have been utilized in solar irradiance and solar power
production forecasting. Gated Recurrent Neural Networks (RNN) are a special type of deep learning
model that have shown promising results in forecasting sequential data due to their ability to pass
long-term information from previous computations as inputs [
21
]. Long Short-Term Memory (LSTM)
and Gated Recurrent Units (GRU) are two gated RNNs that have been shown to perform well for many
different problems in predictive analytics, including speech recognition and traffic prediction [
22
,
23
].
LSTM and GRU differ from one another by the number of gates within their architecture and the
transfer of information. Some empirical research has been done to measure the performance of GRU
compared to LSTM given their differences; however, more research is needed to determine which
network is superior and the preference for one gated RNN over another is often dependent on the
data set [
24
]. Alzahrani et al. [
25
] used deep neural networks, namely LSTM, to predict short-term
solar irradiance using data collected every millisecond over a four day period. They found that LSTM
outperformed other traditional machine learning methods including SVR and Feedforward Neural
Networks (FFNN). Abdel-Nasser and Mahmoud [
26
] tested various LSTM architectures in order to
forecast PV power production using historical data and concluded that LSTM is able to accurately
learn complex patterns in PV power time series. Qing and Niu [
7
] propose the use of LSTM for hourly
day-ahead solar irradiance prediction using weather forecasts of the same day as input. The weather
variables include temperature, dew point, humidity, visibility, wind speed, and weather type. They
found that the LSTM learning algorithm is more accurate than linear least squares regression and neural
networks using the back propagation algorithm due to better generalization. Husein and Chung [
27
]
proposed the use of LSTM for day-ahead solar irradiance forecasting using only exogenous features
and compared their proposed model to FFNN. LSTM outperformed traditional FFNN in all tested
locations chosen based on average climate, leading to an increase in energy savings. Kumar et al. [
28
]
used LSTM and GRU in spark clusters for hyperparameter tuning to forecast short-term electric load
in power grids. Sorkun et al. [
29
] investigated the use of univariate RNNs, namely LSTM and GRU, for
one hour ahead solar irradiance time series forecasting. They found that LSTM and GRU outperformed
traditional RNNs indicating that gated RNNs are competitive in solar irradiance forecasting, but using
only historical solar irradiance with LSTM or GRU was not superior to one another. Wang et al. [
8
]
implemented multivariate GRU networks on groups of training sets containing similar features in order
to accurately forecast short-term PV power output. Their multivariate GRU network outperformed
existing forecasting models due to the addition of highly-correlated features and splitting the training
sets into groups using K-means methods. Through their analysis, they also found that GRU has
an advantage over LSTM due to less training time over large data sets. Although literature for the
application of LSTM and GRU exists for predicting PV power production, an experimental study
comparing LSTM and GRU with and without exogenous weather and cloud cover data has not
been conducted.
In this paper, we evaluate the application of multivariate GRU for solar irradiance forecasting and
compared the proposed model with univariate and multivariate LSTM. To the best of our knowledge,
GRU in combination with hourly exogenous weather and cloud cover data has not been applied to
short-term solar irradiance forecasting. The key contributions of this paper are the following:
•
Propose the application of multivariate GRU to forecast hourly solar irradiance in Phoenix, Arizona
one to ten time steps ahead using historical solar irradiance and exogenous weather variables

Energies 2019,12, 4055 4 of 13
•
Assess the impact of adding exogenous weather variables, such as solar zenith angle, relative
humidity, air temperature, and cloud cover, to LSTM and GRU networks
•
Performance comparison of prediction accuracy and computation time between GRU and LSTM
using various configurations (i.e., univariate, multivariate without cloud cover, and multivariate
with cloud cover)
The rest of the paper is organized as follows: Section 2gives a brief description of the proposed
model and describes our experimental plan to evaluate univariate and multivariate GRU against
univariate and multivariate LSTM. Section 3provides a performance comparison of GRU to LSTM
and discusses the experimental results. Section 4concludes our research paper and provides a plan for
future work in this research area.
2. Materials and Methodology
We designed a Gated Recurrent Unit (GRU) to forecast hourly solar irradiance using real-world
solar irradiance data, exogenous meteorological variables, and cloud cover time series data. We provide
an experimental plan for evaluating the proposed model against LSTM and existing literature in terms
of accuracy and computation time.
2.1. Multivariate GRU
GRU was first proposed by Cho et al. [
30
] as a simpler RNN architecture compared to LSTM,
resulting in easier computation and implementation. The GRU network consists of designing
multiple cells that adaptively remember and forget information as new information is received [
30
].
The feedback loops of the GRU network are unrolled in time such that the output of a previous cell
is used as input to the next cell in addition to the current input example. This key feature allows
gated RNNs to accurately understand and predict sequential data over time. GRU cells are similarly
configured to LSTM cells; however, since GRU cells contain only two gates compared to three gates
in LSTM, GRU requires fewer computations overall [
29
]. GRU cells contain a reset (
r
) and update (
u
)
gate, as shown in Figure 1. The update gate decides how much information will be remembered, while
the reset gate determines whether new information will be added to the previous state [
29
]. GRU cells
are maintained using the following equations:
ri=σWr
ixi+Zr
iht−1
i(1)
ui=σWu
ixi+Zu
iht−1
i(2)
ˆ
ht
i=σWixi+Ui(ht−1
i∗ri)(3)
ht
i=uiht−1
i+ (1−ui)ˆ
ht
i(4)
where irepresents the i-th hidden unit, W,Z, and Uare the trained weight matrices, xrepresents the
time series input vector,
σ
denotes the chosen activation function,
t
represents time, and
ht−1
represents
the previous output. These formulas are similar to LSTM in nature and more explanation is given
in [30].
Due to its ability to manage long-term dependencies in sequential data, GRU performs well for
time series forecasting problems. The GRU cells within a network are trained by minimizing a specific
cost function using Backpropagation Through Time. In our experiments, specific cost functions perform
better for univariate and multivariate cases: minimizing the mean squared error for the univariate
experiments and the mean absolute error for the multivariate cases resulted in better performance.
To forecast the amount of solar irradiance at time
t
, the observations from
T
previous time steps are
considered. In our case, we utilize the last
T=
48 time steps or hours in order to obtain the best results.
In the univariate experiments, the GRU and LSTM networks contain one deep layer with 10 units;
meanwhile, multivariate experiments contain three layers with 60, 30, and 10 units, respectively.
We train the univariate models using 100 epochs, and multivariate models using 50 epochs. Both

Energies 2019,12, 4055 5 of 13
univariate and multivariate models use a batch size of 35 and Adam optimizer with a learning rate of
0.0001. The total number of trainable parameters in the GRU is 29,051 compared to 38,731 parameters
for LSTM.
Figure 1. Structure of a Gated Recurrent Units (GRU) cell [24].
2.2. Data Description
Real-world data sets containing solar irradiance, weather, and cloud cover data are collected. Data
sets range from 1 January 2004 to 31 December 2014, yielding 96,360 total observations. Hourly solar
irradiance and weather data are obtained from the National Renewable Energy Laboratory’s National
Solar Radiation Database for Phoenix International Airport in Phoenix, Arizona. GHI and weather
variables, including solar zenith angle, relative humidity, and air temperature, from 2004 to 2014 are
chosen for our experiments. These particular variables were chosen based on Pearson correlation
coefficients between GHI and each of the variables, which indicates a strong linear relationship between
the two variables. The Pearson correlation coefficients are
−
0.87,
−
0.51, and 0.57 for the solar zenith
angle, relative humidity, and air temperature, respectively. Figure 2shows examples of hourly input
data using the first day of each month in 2004. The time at which solar irradiance occurs at sunrise and
sunset as well as the amount of solar irradiance around noon varies throughout the year. Additionally,
on days where cloud cover is present, the GHI curve features sudden drops in solar irradiance
through the day. For the cloud cover data set, the National Oceanic and Atmospheric Administration
(NOAA) hosts the International Satellite Cloud Climatology Project (ISCCP) that provides global cloud
information at high resolutions. We utilize the ISCCP HXG files which contain data in three-hour
intervals at 0.1 equal angles of latitude and longitude. Within these files, cloud cover data is represented
in binary with 0 and 1 indicating no cloud and cloud cover, respectively. We calculate a ratio of pixels
containing cloud cover to total pixels in order to determine the surrounding cloud activity of a given
location. For our experiments, we used an area of three pixels squared with the location of interest in
the middle. The solar irradiance, weather, and cloud cover data are then aggregated by repeating the
cloud cover ratios three times per interval to match the hourly data set. Before training the networks,
the data set containing solar irradiance, weather, and cloud cover data is normalized using Min-Max
normalization, reducing the range of data between zero and one.

Energies 2019,12, 4055 6 of 13
(a) GHI (b) Relative Humidity
(c) Temperature (d) Solar zenith angle
Figure 2. Hourly input data for the first day of each month in 2004.
2.3. Experimental Evaluation
In order to fully evaluate our proposed GRU network, we perform a set of three experiments.
For our first experiment, we evaluate the univariate case of GRU comprising only of historical solar
irradiance (i.e., GHI) from the Phoenix International Airport. Our model uses the past 48 time steps,
or GHI from the last 48 h, to forecast solar irradiance at the next time step. We tested the model
for 24, 48, and 72 h (one to three previous days) and found that using 48 time steps resulted in the
best performance for LSTM and GRU forecasting models. Our second experiment extends the first
by adding sequences of hourly solar zenith angle, relative humidity, and air temperature to build a
multivariate case of GRU. Lastly, our third experiment adds the corresponding ratio of cloud cover to
the multivariate model from the second experiment for a total of four exogenous variables. In both
multivariate experiments, the last 48 h of data for each variable are used in training to predict solar
irradiance and exogenous variables for the next hour. In order to measure model performance, we only
consider the predictions for GHI.
For each experiment, the data is split into 80 percent training, 10 percent validation, and 10 percent
testing in order to validate and compare model performance. The training, validation, and testing
data sets are in sequence and mutually exclusive. Both GRU and LSTM are implemented using the
TensorFlow and Keras libraries in Python. In order to evaluate model performance, we calculate
the Mean Absolute Percentage Error (MAPE) and Root Mean Squared Error (RMSE). For a series of
predicted values, the MAPE computes the average percentage error between actual and predicted
values. Meanwhile, RMSE measures the standard deviation of the forecast error between actual and
predicted values. MAPE and RMSE are calculated using the following formulas:

Energies 2019,12, 4055 7 of 13
MAPE =100
N
N
∑
i=1
|A−P|
|A|(5)
RMSE =
N
∑
i=1r(A−P)2
N(6)
where
A
and
P
indicate the actual and predicted values, respectively, and
N
is the total number of
predictions. In all experiments, the MAPE and RMSE are calculated for daylight hours only.
3. Results and Discussion
3.1. Experimental Results
Table 1summarizes the results for hour-ahead forecasting from three experiments for LSTM and
GRU: univariate models, multivariate models without cloud cover, and multivariate with cloud cover.
We observe that for both LSTM and GRU, multivariate models outperform univariate models. In the
case of multivariate LSTM, the improvement was 18.33% and in the case of Multivariate GRU the
improvement was 15.25%. We observe that Multivariate LSTM with cloud cover has slightly better
performance compared with Multivariate GRU. We further study the performance of both LSTM and
GRU with multiple step ahead forecasts from 1-step ahead to 10-steps ahead forecast. We observe in
Figure 3that both GRU and LSTM based multivariate models outperform univariate models until
7 time steps ahead with no significant different between them.
Table 1. Comparison of forecast errors at one time step across one year of hourly testing data.
Model Univariate Multivariate without
Cloud Cover
Multivariate with
Cloud Cover
MAPE RMSE MAPE RMSE MAPE RMSE
LSTM 29.13% 67.17 25.37% 66.57 23.79% 66.75
GRU 30.29% 68.27 28.99% 67.29 25.67% 67.97
Figure 3.
Mean Absolute Percentage Error (MAPE) and Root Mean Squared Error (RMSE) values for
each model predicted ten time steps into the future.
Figure 4shows the average MAPE and RMSE along with standard error bars for each month of
the testing set using multivariate GRU and LSTM with cloud cover. Across all months, the average
MAPE and RMSE values were very close between multivariate GRU and LSTM models. In six out of
12 months (i.e., January, April, May, June, October, and November), the MAPE values for multivariate
GRU and LSTM were below 20 percent. Similarly, RMSE values below 40 occurred in five out of

Energies 2019,12, 4055 8 of 13
12 months (i.e., January, May, June, October, and November). In both MAPE and RMSE, March,
July, August, September, and December produced the highest amounts of error throughout the year.
Additionally, the standard error bars are wider during these months, indicating high variation in
accuracy in that time period. Figure 5shows the actual solar irradiance and forecasting results for
each of the three experiments for GRU and LSTM on four different days throughout the testing
year. On these given days, cloud cover was present throughout the day and the amount of solar
irradiance during daylight hours was not consistent. In all cases, the multivariate models predicted
solar irradiance similarly to one another and closer to the actual values than the univariate models.
The highest amounts of error occurred when the model overestimated the solar irradiance or after a
sudden change in solar irradiance. On days where solar irradiance is inconsistent in the morning hours,
all models overestimated the amount of solar irradiance compared to the actual values; this may be
due to the fact that the models learned that solar irradiance increases consistently in the morning hours.
After a sudden decrease in solar irradiance, the models react to the sudden change in the following
time step, rather than accurately predicting the sudden change. Similarly, the models react to a sudden
increase in solar irradiance in the time step directly after. This often led to a high amount of error if the
actual solar irradiance increased after the decrease. Because of the reactivity of the models, overall
error is higher on days where solar irradiance is inconsistent and stochastic. It would be helpful to
seek higher resolution data for solar irradiance, weather variables, and cloud cover time series in order
to combat the problems with overestimation and reacting to sudden changes in solar irradiance [25].
Despite their architectural differences, LSTM and GRU have been shown to perform similarly to
one another, indicating that the superior model highly depends on the task [
24
]. In this case, we believe
that multivariate GRU and multivariate LSTM perform similarly in terms of model accuracy. It is
evident that the addition of exogenous weather variables increases solar irradiance forecasting accuracy
overall; however, with the addition of weather variables, there is also an increase in the training and
prediction time. Table 2describes the training and prediction times for all experiments. Multivariate
GRU and LSTM with cloud cover took approximately 4 and 6.5 times longer to train and predict than
their univariate counterparts, respectively. In all cases, however, the GRU models performed faster
than the LSTM models. The total number of trainable parameters for GRU are quite less compared
with LSTM, hence GRU has less parameters to train in comparison to the LSTM model. The biggest
difference in training time between GRU and LSTM can be seen as more variables are added to the
models. Higher amounts of training and prediction times in the multivariate models may not be
suitable for real-time solar irradiance forecasting, as it may take too long to update short-term forecasts
based on the most recent information.
Figure 4.
Average MAPE and RMSE values with corresponding standard error for each month using
multivariate GRU and Long Short-Term Memory (LSTM) with cloud cover.

Energies 2019,12, 4055 9 of 13
Figure 5.
Comparison of actual and forecast values for both LSTM and GRU models on days with
irregular solar irradiance patterns.
Table 2. Comparison of training and prediction time.
Experiment Training (h) Prediction (s)
Univariate GRU 0.65 1.55
Univariate LSTM 0.7 1.39
Multivariate GRU without cloud 2.4 8.14
Multivariate LSTM without cloud 2.66 9.23
Multivariate GRU with cloud 2.9 11.02
Multivariate LSTM with cloud 3.27 11.84
3.2. Discussion
Irradiance forecasting is a very important component for grid operators to manage the variability
and uncertainty associated with solar power. Cloud cover is the most critical variable for solar
energy power generation, but is also characterized by high degree of uncertainty and variability.
Ground-based remote sensing equipment is needed for obtaining high resolution cloud cover data.
In this paper, we studied the application of multivariate GRU for irradiance forecasting. We compared
the multivariate GRU with univariate and multivariate LSTM with and without cloud cover data.
We used cloud cover data obtained from satellite observations (which has much coarser resolution
compared to ground-based remote sensing equipment).
We observe that existing forecasting models perform well during non-cloudy days compared
to cloudy days due to a high degree of variability in cloud cover. In the proposed multivariate
GRU, we used historical solar irradiance, solar zenith angle, air temperature, relative humidity, and
cloud cover to predict hourly solar irradiance. Multivariate models with and without the addition
of cloud cover outperformed univariate GRU and LSTM. Additionally, LSTM outperformed GRU in

Energies 2019,12, 4055 10 of 13
both univariate and multivariate experiments. We compared our forecasting results to the Phoenix
results from Reikard [
13
] as shown in Table 3and observed that multivariate GRU and LSTM with
cloud cover performed similarly to their tested statistical and machine learning models. For certain
months, average model accuracy was much lower due to outliers in MAPE and RMSE. In these cases,
the monthly ranges for MAPE and RMSE were larger, leading to wider standard error bars. For
example, there were three particular days in March where the model predicted solar irradiance with
an MAPE over 100 percent. In order to improve the number of outliers, additional research is needed
to develop a model that can handle generalizing a wide variation of solar irradiance patterns on
cloudy days.
Table 3. Comparison of forecast errors from Reikard [13].
Model Error (%)
Regression 29.96
Unobserved Components Models 29.92
ARIMA 23.6
Transfer function 23.52
Neural network 29.38
Hybrid 23.67
4. Conclusions
In this paper, we propose the application of a relatively new and robust RNN to forecast hourly
solar irradiance. We applied univariate and multivariate GRU models using historical solar irradiance,
exogenous meteorological variables, and cloud cover data to forecast solar irradiance in Phoenix,
Arizona. The proposed is compared with LSTM, another popular deep learning model. We further
analyze the performance of models to forecast multiple time steps into future, how the models perform
with cloud cover variable, and how the performance of different models vary across a given day, over
the year, and days with high variability in irradiance. Our primary motivation for this work is to be able
to find a model that can continuously produce real-time forecasts based on publicly available weather
data. Therefore, we also study the computational performance of various models. Overall, multivariate
deep learning methods perform better than univariate models. There is significant performance
improvement with including cloud cover in the multivariate models. We observe from Phoenix dataset
that multivariate LSTM has slightly less error compared to multivariate GRU, but multivariate GRU
has less training and prediction time compared to multivariate LSTM. There is not much difference
between per month MAPE and RMSE between multivariate GRU and multivariate LSTM.
In our future work, we would like to improve irradiance forecasting performance that would
further help grid operators to manage uncertainty associated with solar power. This includes using
better quality cloud cover data in the model, techniques to further improve the performance of the
model, and finally, evaluating the utility of these models to help grid operators manage the variability
of irradiance under different conditions. The proposed deep learning methods could be further
improved by incorporating more detailed cloud cover related features [
31
] as well as higher resolution
GHI data. The data used in our experiments includes hourly GHI data which is freely available from
NREL [
32
], but many solar installations collect one-minute resolution data [
33
] that could be used
to potentially improve the model performance. On days where there is no cloud cover, both models
performed exceptionally; however, on days with cloud cover, both models fail to accurately predict
future solar irradiance. Rather than having one static model to predict non-cloudy and cloudy days,
we could potentially use ensemble methods or concept drift methods to reduce over-fitting on days
where there is high variability in cloud cover [
34
]. Moreover, more research is needed in not only
reducing the forecast error, but also maximizing the utility of irradiance forecasts. The use of variables,
namely back-of-module temperature and DNI, could be used to predict solar power plant production.

Energies 2019,12, 4055 11 of 13
Being able to predict solar power plant production using DNI and back-of-module temperature would
allow power grid operators to calculate future production directly, further reducing the margin of error.
Author Contributions:
Conceptualization, R.G. and T.L.C.; Methodology, J.W. and R.G.; Software, J.W. and
M.H.; Validation, M.H. and J.W.; Formal analysis, J.W.; Investigation, J.W.; Resources, R.G.; Data curation, J.W.;
Writing—original draft preparation, J.W.; Writing—review and editing, T.L.C. and R.G.; Visualization, J.W.;
Supervision, R.G.; Project administration, R.G.; Funding acquisition, R.G.
Funding: This research was funded by NSF grants CNS-1429526 and CNS-1650551.
Acknowledgments:
We thank the anonymous reviewers for their insightful comments and suggestions that
helped us improve the overall quality of the paper.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript:
ARIMA Autoregressive Integrated Moving Average
DHI Diffuse Horizontal Irradiance
DNI Direct Normal Irradiance
FFNN Feedforward Neural Network
GRU Gated Recurrent Unit
GHI Global Horizontal Irradiance
HMM Hidden Markov Model
ISCCP International Satellite Cloud Climatology Project
LSTM Long Short-Term Memory
MAPE Mean Absolute Percentage Error
NOAA National Oceanic and Atmospheric Administration
NWP Numerical Weather Prediction
PV Photovoltaic
RMSE Root Mean Squared Error
RNN Recurrent Neural Network
SVR Support Vector Regression
References
1.
Diagne, M.; David, M.; Lauret, P.; Boland, J.; Schmutz, N. Review of solar irradiance forecasting methods
and a proposition for small-scale insular grids. Renew. Sustain. Energy Rev. 2013,27, 65–76. [CrossRef]
2.
Kreith, F. Principles of Sustainable Energy Systems; Mechanical and Aerospace Engineering Series; CRC Press:
London, UK, 2013.
3.
Law, E.W.; Prasad, A.A.; Kay, M.; Taylor, R.A. Direct normal irradiance forecasting and its application to
concentrated solar thermal output forecasting—A review. Sol. Energy 2014,108, 287–307. [CrossRef]
4.
Yang, D.; Jirutitijaroen, P.; Walsh, W.M. Hourly solar irradiance time series forecasting using cloud cover
index. Sol. Energy 2012,86, 3531–3543. [CrossRef]
5.
Marquez, R.; Coimbra, C.F. Intra-hour DNI forecasting based on cloud tracking image analysis. Sol. Energy
2013,91, 327–336. [CrossRef]
6.
Li, J.; Ward, J.K.; Tong, J.; Collins, L.; Platt, G. Machine learning for solar irradiance forecasting of photovoltaic
system. Renew. Energy 2016,90, 542–553. [CrossRef]
7.
Qing, X.; Niu, Y. Hourly day-ahead solar irradiance prediction using weather forecasts by LSTM. Energy
2018,148, 461–468. [CrossRef]
8.
Wang, Y.; Liao, W.; Chang, Y. Gated recurrent unit network-based short-term photovoltaic forecasting.
Energies 2018,11, 2163. [CrossRef]
9.
Kratochvil, J.A.; Boyson, W.E.; King, D.L. Photovoltaic Array Performance Model; Technical Report; Sandia
National Laboratories: Albuquerque, NM, USA.
10.
De Soto, W.; Klein, S.; Beckman, W. Improvement and validation of a model for photovoltaic array
performance. Sol. Energy 2006,80, 78–88. [CrossRef]

Energies 2019,12, 4055 12 of 13
11.
Perez, R.; Lorenz, E.; Pelland, S.; Beauharnois, M.; Van Knowe, G.; Hemker, K., Jr.; Heinemann, D.; Remund, J.;
Müller, S.C.; Traunmüller, W.; et al. Comparison of numerical weather prediction solar irradiance forecasts
in the US, Canada and Europe. Sol. Energy 2013,94, 305–326. [CrossRef]
12.
Mathiesen, P.; Collier, C.; Kleissl, J. A high-resolution, cloud-assimilating numerical weather prediction
model for solar irradiance forecasting. Sol. Energy 2013,92, 47–61. [CrossRef]
13.
Reikard, G. Predicting solar radiation at high resolutions: A comparison of time series forecasts. Sol. Energy
2009,83, 342–349. [CrossRef]
14.
Dong, Z.; Yang, D.; Reindl, T.; Walsh, W.M. Short-term solar irradiance forecasting using exponential
smoothing state space model. Energy 2013,55, 1104–1113. [CrossRef]
15.
Melzi, F.N.; Touati, T.; Same, A.; Oukhellou, L. Hourly solar irradiance forecasting based on machine
learning models. In Proceedings of the 2016 15th IEEE International Conference on Machine Learning and
Applications (ICMLA), Anaheim, CA, USA, 18–20 December 2016; pp. 441–446.
16.
Heinemann, D.; Lorenz, E.; Girodo, M. Forecasting of solar radiation. In Solar Energy Resource Management
for Electricity Generation from Local Level to Global Scale; Nova Science Publishers: New York, NY, USA, 2006.
17.
Aguiar, L.M.; Pereira, B.; Lauret, P.; Díaz, F.; David, M. Combining solar irradiance measurements,
satellite-derived data and a numerical weather prediction model to improve intra-day solar forecasting.
Renew. Energy 2016,97, 599–610. [CrossRef]
18.
Marquez, R.; Pedro, H.T.; Coimbra, C.F. Hybrid solar forecasting method uses satellite imaging and ground
telemetry as inputs to ANNs. Sol. Energy 2013,92, 176–188. [CrossRef]
19.
Cao, J.C.; Cao, S. Study of forecasting solar irradiance using neural networks with preprocessing sample
data by wavelet analysis. Energy 2006,31, 3435–3445. [CrossRef]
20.
Ogliari, E.; Niccolai, A.; Leva, S.; Zich, R. Computational intelligence techniques applied to the day ahead
pv output power forecast: Phann, sno and mixed. Energies 2018,11, 1487. [CrossRef]
21. Goodfellow, I.; Bengio, Y.; Courville, A. Deep Learning; The MIT Press: Cambridge, MA, USA, 2016.
22.
Graves, A.; Mohamed, A.R.; Hinton, G. Speech recognition with deep recurrent neural networks.
In Proceedings of the 2013 IEEE International Conference on Acoustics, Speech and Signal Processing
(Icassp), Vancouver, BC, Canada, 26–31 May 2013; pp. 6645–6649.
23.
Zhao, Z.; Chen, W.; Wu, X.; Chen, P.C.; Liu, J. LSTM network: A deep learning approach for short-term
traffic forecast. IET Intell. Transp. Syst. 2017,11, 68–75. [CrossRef]
24.
Chung, J.; Gulcehre, C.; Cho, K.; Bengio, Y. Empirical evaluation of gated recurrent neural networks on
sequence modeling. arXiv 2014, arXiv:1412.3555.
25.
Alzahrani, A.; Shamsi, P.; Dagli, C.; Ferdowsi, M. Solar irradiance forecasting using deep neural networks.
Procedia Comput. Sci. 2017,114, 304–313. [CrossRef]
26.
Abdel-Nasser, M.; Mahmoud, K. Accurate photovoltaic power forecasting models using deep LSTM-RNN.
Neural Comput. Appl. 2019,31, 2727–2740. [CrossRef]
27.
Husein, M.; Chung, I.Y. Day-Ahead Solar Irradiance Forecasting for Microgrids Using a Long Short-Term
Memory Recurrent Neural Network: A Deep Learning Approach. Energies 2019,12, 1856. [CrossRef]
28.
Kumar, S.; Hussain, L.; Banarjee, S.; Reza, M. Energy Load Forecasting using Deep Learning Approach-LSTM
and GRU in Spark Cluster. In Proceedings of the 2018 Fifth International Conference on Emerging
Applications of Information Technology (EAIT), Howrah, India, 12–13 January 2018; pp. 1–4. [CrossRef]
29.
Sorkun, M.C.; Paoli, C.; Incel, D. Time series forecasting on solar irradiation using deep learning.
In Proceedings of the 2017 10th International Conference on Electrical and Electronics Engineering (ELECO),
Bursa, Turkey, 30 November–2 December 2017; pp. 151–155.
30.
Cho, K.; van Merrienboer, B.; Gulcehre, C.; Bougares, F.; Schwenk, H.; Bengio, Y. Learning phrase
representations using RNN encoder-decoder for statistical machine translation. In Proceedings of
the Conference on Empirical Methods in Natural Language Processing (EMNLP 2014), Doha, Qatar,
25–29 October 2014.
31.
Watanabe, T.; Oishi, Y.; Nakajima, T.Y. Characterization of surface solar-irradiance variability using cloud
properties based on satellite observations. Sol. Energy 2016,140, 83–92. [CrossRef]
32.
Sengupta, M.; Weekley, A.; Habte, A.; Lopez, A.; Molling, C. Validation of the National Solar Radiation Database
(NSRDB) (2005–2012); Technical Report; NREL (National Renewable Energy Laboratory (NREL): Lakewood,
CO, 2015.

Energies 2019,12, 4055 13 of 13
33.
Pedro, H.T.; Larson, D.P.; Coimbra, C.F. A comprehensive dataset for the accelerated development and
benchmarking of solar forecasting methods. J. Renew. Sustain. Energy 2019,11, 036102. [CrossRef]
34.
Wojtkiewicz, J.; Katragadda, S.; Gottumukkala, R. A Concept-Drift Based Predictive-Analytics Framework:
Application for Real-Time Solar Irradiance Forecasting. In Proceedings of the 2018 IEEE International
Conference on Big Data (Big Data), Seattle, WA, USA, 10–13 December 2018; pp. 5462–5464.
c
2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).