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Solar Power Forecasting Using Weather Type
Clustering and Ensembles of Neural Networks
Mashud Rana
Australian Energy Research Institute
The University of New South Wales
Sydney, NSW, Australia
md.rana@unsw.edu.au
Irena Koprinska
School of Information Technologies
The University of Sydney
Sydney, NSW, Australia
irena.koprinska@sydney.edu.au
Vassilios G Agelidis
Australian Energy Research Institute
The University of New South Wales
Sydney, NSW, Australia
vassilios.agelidis@unsw.edu.au
Abstract—We consider the task of forecasting the electricity
power generated by a photovoltaic solar system, for the next day
at halfhourly intervals. The forecasts are based on previous
power output and weather data, and weather prediction for the
next day. We present a new approach that forecasts all the power
outputs for the next day simultaneously. It builds separate
prediction models for different types of days, where these types are
determined using clustering of weather patterns. As prediction
models it uses ensembles of neural networks, trained to predict the
power output for a given day based on the weather data. We
evaluate the performance of our approach using Australian
photovoltaic solar data for two years. The results showed that our
approach obtained MAE=83.90 kW and MRE=6.88%,
outperforming four other methods used for comparison.
Keywords—solar power forecasting; time series prediction;
renewable energy; clustering; ensembles of neural networks
I. I
NTRODUCTION
Solar power produced by solar PhotoVoltaic (PV) systems is
one of the most promising types of renewable energy. The
installation of PV systems around the world, both small rooftop
and large PV plants, has increased 100 times since 2000 and is
expected to reach 540 GW in 2019 [1]. This growth is driven by
government legislations to increase the electricity supply from
renewable sources and also by the reduced cost of PV systems,
their easy maintenance and operation.
However, the variable and intermittent nature of the solar
power makes its integration into the electricity grid difficult. The
power generated from PV systems is highly variable as it
depends on the solar irradiance and other meteorological
conditions. The uncertainty in solar power generation may lead
to unnecessary increase in the spinning reserve and operational
costs. This motivates the need for accurate forecasting of the
generated solar power at different time intervals to ensure the
stability of the grid by balancing the demand and supply, while
keeping the costs low.
Different approaches for forecasting the power generated
from PV systems have been proposed. They are based on
statistical methods such as liner regression and autoregressive
moving average [24], and machine learning methods such as
Neural Networks (NNs) [27], nearest neighbour [2, 4, 5] and
Support Vector Regression (SVR) [8, 9]. Most of the previous
work focused on developing general prediction method for all
types of weather conditions. In this paper we develop
specialized prediction models for different types of weather
patterns. We firstly use clustering to understand the weather
characteristics of the different days and determine groups of
days with similar weather patterns. We then develop a separate
prediction model for each type of days that uses as inputs the
weather data for a given day and predicts the PV power output
for this day.
Our contributions can be summarized as follows:
• We propose a new approach for forecasting the half
hourly PV power output for the next day from previous
PV power and weather data, and weather prediction for
the next day. In contrast to previous approaches, it
predicts all power outputs simultaneously, not
iteratively from previous predicted values.
• Our approach develops separate prediction models for
different types of days. It firstly clusters the previous
weather data to find groups of days with similar weather
patterns. An appropriate number of clusters is
determined by a method based on the CalinskiHara
basz, Silhouette and DaviesBouldin measures. It then
builds a separate prediction model for each cluster using
our proposed ensemble of NNs. The NN ensemble is
trained to use as inputs the weather data for a given day
and predict the PV power output for this day. To make
a prediction for the next day, our approach uses the
weather forecast for the next day as an input.
• We conduct a comprehensive evaluation of our
approach using two years of Australian PV power data
from a 1.22 MW PV plant and compare its performance
with four other methods. We also assess the benefit of
using an ensemble of NNs instead of a single NN and
analyse the effectiveness of the method for selecting the
number of clusters.
The paper is organized as follows. Section II reviews the
previous research on solar power forecasting. Section III
provides a problem statement and explains the experimental
setup. Sections IV and V describe our proposed approach and
the methods used for comparison. Section VI presents and
discusses the results. Section VII summarizes the main results
and concludes the paper.
II. P
REVIOUS
W
ORK
There are two main groups of approaches for solar power
forecasting: (1) indirect, that firstly predict the solar irradiance
and then convert it to power output, and (2) direct, that directly
predict the solar power output. Our approach falls in the second
group, which is also the more recent. Hence, in this section we
briefly review the previous work in the second group  direct
forecasting.
Long et al. [5] compared the performance of NNs, SVR, k
nearest neighbour and linear regression for predicting the hourly
PV power output from 1 to 3 days ahead, using both previous
power output and meteorological data. They applied a variable
selection algorithm based on clustering and cross validation to
find a subset of important variables. Different scenarios were
considered and it was found that different algorithms perform
best in each of them, achieving best Mean Absolute Percentage
Error (MAPE) of 30% for 1 day ahead and 40% for 3 days ahead
forecasts. The evaluation was done using data for two years from
a power plant in Macau.
Pedro and Coimbra [2] studied four different univariate
methods for direct prediction of the solar power produced by a
PV plant from previous solar power values: autoregressive
integrated moving average, knearest neighbour, NN trained
with the backpropagation algorithm and NN trained with a
genetic algorithm. They predicted the PV power 1 and 2 hours
ahead and conducted an evaluation using data for two years from
a 1MW plant in California. The two NNbased methods were
found to be the most accurate prediction methods.
Rana et al. [8] considered the task of 2Dinterval forecasting
for solar power produced by PV systems. While most of the
existing approaches focus on point forecasting, they considered
a special type of interval forecasting  predicting a range of
expected values for a future time interval. Their approach uses
previous solar power and meteorological data as inputs and SVR
as prediction algorithm. The results showed that it provided
accurate predictions for different data sampling rates and
interval lengths.
Mandal et al. [7] predicted the hourly PV output for the next
day using previous PV output data, which was decomposed
using wavelet transform, and also using weather data (solar
irradiance and temperature). As a prediction algorithm they
applied a Radial Basis Function Neural Network (RBFNN). An
evaluation was conducted for 12 days from different seasons,
obtaining MAPE results in the range of 4.25% and 13.81%. It
was also shown that the wavelet RBFNN outperformed the
standard nonwavelet RBFNN.
Chu et al. [4] described a twostage approach for 515 min
ahead power output prediction in 5 min intervals. They firstly
generate initial predictions by applying three methods – an
autoregressive moving average, knearest neighbour and
deterministic model based on cloud tracking. In the second
stage, these initial forecasts were improved by using a NN that
takes as inputs the initial forecast and the seven most recent
actual PV power outputs. The results showed an improvement
in all initial forecasts, with best MAE=20.727.1 kW for 515
min ahead forecasting.
Rana et al. [10] proposed NNbased methods for predicting
the halfhourly PV power output for the next day based on
previous PV power data only, without using any weather data.
The best results were achieved by an iterative method, which
forecasts one step ahead, and uses the previous forecasts to make
predictions for all points from the forecasting horizon.
Chen et al. [6] predicted the hourly PV power output for the
next day using the power output from the previous day and the
weather forecast for the next day. They classified the days into
three groups (sunny, cloudy and rainy) and built a separate
RBFNN prediction model for each group. The inputs of the
RBFNN were the average PV power from the previous day and
the weather forecasts for the next day (average daily values for
solar irradiance, wind speed, humidity and temperature). A Self
Organising Map (SOM) was used to learn the characteristics of
the three types of days based on the weather predictions for solar
irradiance and cloudiness. To forecast the PV output for a new
day, the SOM was firstly used to output the type of the day, and
then the RBNN model for this type of day was used to generate
the prediction. An evaluation was conducted for 12 days using
data from a power plant in Wuhan, China, and showing
promising MAPE results: 9.45% for sunny, 9.88% for cloudy
and 38.12% for rainy days.
Shi et al. [9] followed a similar approach. They classified the
days into four types (clearsky, cloudy, foggy and rainy) and
built a separate SVR prediction model for each type that was
trained on historical data. To predict the PV power output for a
new day, the day was firstly mapped to one of the types based
on the weather forecast and then the respective prediction model
was used. The inputs to the prediction model were the historical
PV output data at 15 min intervals from the nearest day with the
same classification, and the predicted daily temperature for the
next day from the weather report (minimum, maximum and
average). The results showed RMSE from 1.57 % sunny days to
2.52% for foggy days using data from a power plant located in
South China.
From the above literature review, we can see that approaches
such as [6, 9] that group the days based on their weather
characteristics and then build separated prediction model for
each group show very promising results. In this paper we further
extend this class of approaches in several ways. Firstly, while in
previous work the grouping of the days is done manually, we
apply a clustering algorithm where each day is represented as a
feature vector of weather conditions. The resulting clusters are
not predefined but depend on the data characteristics, which
makes our method applicable to PV plants with different
weather conditions, located at different geographic areas. We
also show how to automatically select a good number of clusters
by applying clustering evaluation measures. Secondly, while
previous work uses PV power output for a previous day and
weather forecast for the next day as inputs to the prediction
models, we show that it is sufficient to use only the weather
forecast for the next day. Thirdly, we evaluate this type of
methods on data from a different geographic location
(Australia), and show its effectiveness.
III. P
ROBLEM
S
TATEMENT AND
E
XPERIMENTAL
S
ETUP
A. Problem Statement
Given:
(1) a time series of previous solar power output from a PV
plant up to the day : =[
,
,
,…,
], where
=[
,
,
,…,
] represents the power profile for
day , i.e. observations of the power output measured
at halfhourly intervals.
(2) a time series of previous weather data for the location of
the PV plant up to day d: =[
,
,
,…,
,],
where
is the weather data for day i.
is a 12
dimensional vector of the maximum, minimum and
average daily solar irradiance (SI), ambient temperature
(T), humidity (H) and wind speed (WS),
=
[
,
,
,
,
,
,
,
,
,
,
,
].
(3) predicted weather data
for day d+1, e.g. obtained
from the Bureau of Meteorology.
Goal:
Forecast
, the PV halfhourly solar power profile for
the next day +1
The main idea of our method is to use
to find the
weather type for the new day and then to apply the trained
prediction model for this type of days to generate the PV
output prediction.
B. Solar Power and Weather Data
We use solar power data collected from the Australia’s
largest flatpanel PV system, located at the St Lucia campus of
the University of Queensland in Brisbane. This PV system
consists of 5004 polycrystalline silicon solar panels installed on
the roofs of four building and has a maximum generation
capacity of 1.22 MW. The data is publicly available at [11].
The data is measured in 1 minute intervals for all 24 hours
of the day, for two complete years  from 1 January 2013 to 31
December 2014. We only consider data between 7am and 5pm.
Outside this 10hour interval the solar power is almost zero or
not available for most of the days due to absent or very low solar
irradiance. Thus, there are 438,000 data points (2 years × 365
days × 10 hours per day × 60 observations per hour). There was
a small number of missing values  1,518 missing values which
is about 0.35%. Each missing value was replaced by the average
of the previous 5 observations.
We aggregated the original 1min measurements into 30min
measurements by calculating the mean value of every 30 1min
measurements. The 30min length is the typical interval used for
making transactions at electricity markets in Australia and other
countries. Thus, the total number of measurements in the 30min
dataset is 14,600 (2 years × 365 days × 10 hours per day × 2
observations per hour).
The power generated by a PV system is considerably
influenced by the weather conditions. As an example Fig. 1
shows the halfhourly power profiles for three days  13th, 15th
and 20th of April, 2013. These three days represent a typical
rainy, cloudy and sunny day, respectively. We can observe that
the power profiles for the three days differ considerably. For
clear sunny days, the power output from a PV system is the
highest and typically follows a bell shaped curve as the one
shown. For cloudy and rainy days, the power profile show
highly random fluctuations in line with the changes in the solar
irradiance and other meteorological conditions.
Fig. 1. Solar power output for different weather conditions: a sunny day (20
April, 2013), cloudy day (15 April, 2013) and rainy day (13 April, 2013)
In addition to the solar irradiance, the other weather
variables that significantly influence the PV power output are
ambient temperature, relative humidity and wind speed [12]. We
collected data from all these four sources, from a weather station
located at the PV site. As with the PV power data, the weather
data was originally measured at 1min intervals and then
aggregated to form a 30min dataset. The small number of
missing values (7,871 measurements = 1.8% of all data) were
replaced using the same method as for the solar power data.
To represent the weather profile of a given day, we use
summary statistics for the day– the daily maximum, minimum
and average solar irradiance, temperature, humidity and wind
speed.
We normalize all the data (PV power and weather) to the
range [0,1].
C. Training, Validation, and Testing Data
The PV power and weather data were divided into three non
overlapping subsets: training, validation and testing. As
recommended in [13], the split was 50%25%25%,
respectively. Table I gives more details about the three subsets.
The training set was used for determining the optimal
number of clusters and for training of the prediction models. The
validation set was used for selecting the best parameters for the
prediction models, e.g. the architecture of the NN ensemble and
the kernel function of SVR. The testing set was used to evaluate
the accuracy of the prediction models.
0
100
200
300
400
500
600
700
800
900
1000
7:00am
8:00am
9:00am
10:00am
11:00am
12:00pm
1:00pm
2:00pm
3:00pm
4:00pm
PV power output [kW]
Time of the day
Sunny day Cloudy day Rainy day
TABLE I. T
RAINING
,
V
ALIDATION AND
T
ESTING
S
ETS

S
UMMARY
Data set Percentage split Number of
observations
Training set 50% of all data
(100% from 2013)
7,300
Validation set 25% of all data
(50% from 2014)
3,650
Testing set 25% of all data
(50% from 2014)
3,650
Total 100% 14,600
It is important to note the weather data that we used in the
testing set is actual data with added noise, not predicted weather
data. The reason for this is that the weather predictions for 2013
and 2014 were not available from meteorological stations close
to the PV site. To ensure realistic evaluation, we added 10%
noise to the actual weather data in the testing set.
D. Assessment Metrics
To evaluate the predictive accuracy of the forecasting
models, we use two measures: Mean Absolute Error (MAE) and
Mean Relative Error (MRE). These are the two most popular
measures for evaluating the accuracy of solar power prediction.
MAE and MRE are defined as follows:
MAE= 1
1
̂
MRE= 1
1
̂
100%
where:
and ̂
are the actual and predicted power outputs
for day d at time h, respectively; D is the number of instances
(days) in the testing data; H is the total number of predicted
power outputs for a day (H=20 for our task), and R is the range
of the power output.
In addition, when we compare prediction models we also
discuss the improvement in accuracy (MAE and MRE). For
example, the improvement in MAE between prediction models
A and B is calculated as follows:
improvementA,B=
100%
IV. O
UR
A
PPROACH
Our proposed approach is outlined in Fig. 2. It consists of
three main steps: clustering, building of prediction models and
generating the forecasts for new days.
A. Clustering
The generated PV power depends on the solar irradiance and
other weather conditions. As shown in Fig. 1, days with different
weather conditions have different PV power profiles. The first
step of our approach is to analyse the weather data and group the
days into different types based on their weather patterns, so that
the days in the same cluster are similar to each other and
dissimilar to the days from the other clusters.
Each day is represented as a 12dimensional weather vector
of solar irradiance, temperature, humidity and wind speed
=
[
,
,
,
,
,
,
,
,
,
,
,
]and clustered using the k
means algorithm. We chose kmeans as it is simple and effective
clustering algorithm, that has been successfully used for
clustering of energy time series data [14].
Fig. 2. Diagram of the proposed approach
To choose an appropriate number of clusters k, we used three
clustering validity measures – the CalinskiHarabasz index [15],
the Silhouette coefficient [16] and the DaviesBouldin index
[17]. We firstly applied the kmeans algorithm on the training
data by varying the number of clusters k from 2 to 20 and
computed the three measures for each k. We then selected the
best number of clusters based on each measure separately.
Finally, we selected the overall best k by majority voting.
Fig. 3 shows the normalized values of the three measures for
k from 2 to 20. For the CalinskiHarabasz index and Silhouette
coefficient, the best number of clusters is the one with the
highest value, while for the DaviesBouldin index, the best
clustering is the one with the smallest value. Table II shows the
best number of clusters and the corresponding value of the
evaluation index (shown in brackets). We can see that k=2 is
selected as the best number of clusters by all three clustering
evaluation measures. Based on these results, we chose k=2
clusters.
Fig. 3. Clustering evaluation using the CalinskiHarabasz index, Silhouette
coefficient and DaviesBouldin index for different number of clusters
TABLE II. B
EST
N
UMBER OF
C
LUSTERS FOR THE
T
HREE
M
EASURES
Measure Best k Second best k
CalinskiHarabasz index 2 (1.00) 3 (0.90)
Silhouette coefficient 2 (1.00) 3 (0.84)
DaviesBouldin index 2 (0.88) 6 (0.90)
B. Building Prediction Models
We build a separate prediction model for each cluster of
days. As a prediction algorithm we use an ensemble of NNs.
NNs are one of the most popular and successful methods for
forecasting solar power [2, 5, 6] and other energy time series
such as electricity load [18, 19]. However, their performance
greatly depends on the initialisation of weights and the NN
architecture. To reduce this dependency and find a NN with
good architecture and initialization, we apply an ensemble of
NNs instead of a single NN. An ensemble of NNs includes
several NNs whose predictions are combined in some way to
produce the final prediction.
A single NN, part of the selected NN ensemble, is a
multilayer perceptron NN. Fig. 4 shows its architecture  it has
12 input neurons corresponding to the 12 predicted weather
variables for the next day, 20 output neurons corresponding to
the 20 halfhourly PV power outputs for the next day between
7am and 5 pm, and one hidden layer where the number of hidden
neurons is determined as described below.
Fig. 4. Structure of a single NN, part of the ensemble of NNs
In our proposed ensemble method, we build V ensembles of
NNs and then select the best one. Each ensemble
combines
the predictions of m NNs with the same number of hidden
neurons, but different initialization of the weights. Thus, the
ensemble
combines the prediction of m NNs with 1 hidden
neuron and ensemble
combines the predictions of m NNs
with V hidden neurons. For a given ensemble
, each single NN
is trained separately and after the training is completed, the
ensemble prediction is generated by taking the median of the m
individual NN predictions, as shown in Fig. 5. More specifically,
the power output prediction by an ensemble
for time h for the
next day d+1 is:
=
,
,
,
,…,
,
,
where
,
is the prediction for time h generated by an
ensemble member
, h=1,...,20 and j=1,...,m. In our
experiments we used V=50 and m = 10.
Each ensemble member (single NN) is trained separately on
the training data. After the training is completed, the
performance of the V ensembles is evaluated on the validation
set and the best performing ensemble
, which is the one
with the lowest prediction error (MAE) on the validation set, is
selected and used to predict the testing data.
Our ensemble method is similar to the ensemble method
developed by Adeodato et al. [20]. However, while they first
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Index value
Number of clusters
CalinskiHarabasz index
0.00
0.20
0.40
0.60
0.80
1.00
1.20
234567891011121314151617181920
Index value
Number of clusters
Silhouette coefficient
0.80
0.85
0.90
0.95
1.00
1.05
234567891011121314151617181920
Index value
Number of clusters
DaviesBouldin index
select a good NN architecture and then build an ensemble for it,
we first build ensembles with different architectures and then
select the best one.
As a NN training algorithm we applied the Levenberg
Marquardt algorithm [21]. We chose LM over the standard
steepest gradient descent backpropagation algorithm because of
its faster convergence. The Levenberg Marquardt algorithm
combines the steepest gradient descent and the GaussNewton
algorithm, switching between them based on the complexity of
the error surface. It retains the advantages of both algorithms:
the fast convergence of the GaussNewton algorithm and the
stability of the steepest gradient descent when used with a small
learning rate.
Fig. 5. Combining the predictions of the single NNs (ensemble members) to
generate the ensemble prediction
C. Generating Forecasts for New Days
To generate predictions for the new day d+1, we firstly find
the cluster for the new day by comparing its forecasted weather
profile
with all cluster centroids using a distance measure
(we used Euclidean distance) and determining the shortest
distance. We then use the prediction model for this cluster to
predict the PV power profile for the new day.
V. M
ETHODS
U
SED FOR
C
OMPARISON
We compare the performance of our approach with four
other methods.
The first one (M1) is a nearest neighbour method that
considers similarity in weather patterns. To make a prediction
for the next day d+1, it firstly selects the most similar previous
day in the historical data based on the weather profile. This is
the day s from the same cluster as d+1 that is most similar to
d+1 based on a given distance measure; we used the Euclidean
distance. It then uses the power output for day s as the
predictions for day d+1. More formally, the prediction
=
̂
,̂
,…,̂
is given by
=
,
,…,
where
is the vector of halfhourly power output for the previous day
, such that: (1) both days s and d+1 belongs to same cluster,
and (2) the distance between the weather profiles of the two
days,
and
, is the minimum for all days in the historical
data.
The second method (M2) also uses a nearest neighbour
technique, but it considers both similarity in weather type and
closeness in time, where the similarity in weather type is a
relaxed version than the one used in M1. It assumes that the
power output for the next day d+1 will be similar to the power
output of the most recent day r from the same cluster as d+1.
Thus, the prediction
=̂
,̂
,…,̂
is given by
=
,
,…,
where
is the vector of halfhourly
power output for the previous day , such that: (1) both days r
and d+1 belongs to same cluster, and (2) r is the most recent day
(closest in time) to d+1.
The third method (M3) is a persistence model. It considers
the power outputs from the previous day d as the predictions for
the next day d+1, i.e. the predictions for
=
̂
,̂
,…,̂
are given by
=
,
,…,
.
The last method used for comparison (M4) is very similar to
the recently proposed method by Shi et al. [9]. We selected it as
it follows a similar methodology to ours  classifying the days
into different types based on the weather data and then
developing a separate prediction model for each group.
However, there are several important differences between the
method of Shi et al. and our method.
Firstly, we apply a clustering algorithm to group the days
based on their weather conditions and select the optimal number
of clusters based on the data. Shi et al. do not use a clustering
algorithm, they manually assign the days into four clusters
(sunny, cloudy, rainy and foggy) based on the weather report for
the next day. Secondly, as inputs to the prediction model for
each cluster we use only the weather profile for the next day,
while they use in addition the PV power profile for the nearest
day from the same cluster. Thirdly, the weather profile in our
case is defined as a 12dimensional vector using information
from 4 sources (solar irradiance, temperature, humidity and
wind speed) while Shi at al. use a 3dimensional vector from 1
source (temperature). Finally, they apply SVR as prediction
algorithm while we use an NN ensemble.
Our implementation of the method of Shi et al. strictly
follows the algorithm and methodology described in their paper,
except for the manual clustering of days. Since we didn't have
access to weather reports to manually classify the days into
sunny, cloudy, rainy, and foggy, we applied clustering into four
groups. This may have resulted in differences in the grouping of
the days and in performance; this is the reason why we refer to
this method as M4.
VI. R
ESULTS AND
D
ISCUSSION
A. Ovearall Performance
Table III presents the accuracy and training time results for
our approach and the four methods used for comparison. The
MRE results from Table III are also plotted in Fig. 6 for visual
comparison.
The results show that our proposed approach achieved the
highest accuracy (MAE=83.90 kW and MRE=6.88%),
outperforming the methods used for comparison. Our approach
obtained 20.5534.48% improvement in MAE over the methods
used for comparison; the improvement in MRE is also similar.
All pairwise differences in accuracy between our approach and
the other methods are statistically significant at p<=0.01
(Wilcoxon ranksum test).
TABLE III. A
CCURACY AND
T
RAINING TIME
R
ESULTS FOR
A
LL
PREDICTION
M
ODELS
Prediction
model
MAE
[kW]
MRE
[%]
Training time
[min]
Our method 83.90 6.88 10
M1 105.60 8.66 
M2 121.11 9.93 
M3 128.05 10.50 
M4 118.78 9.74 20
Fig. 6. Accuracy (MRE) for all prediction models in ranked order
The second best method was M1, followed by M4 and M2
that perform similarly, and finally M3. The superior
performance of M1 compared to M2 and M3 shows that to
predict the power profile for the next day d+1, the most useful
information is carried out by the previous most similar day s
based on the weather conditions, which may not be the nearest
day in time from the same cluster r or the previous day d. The
better performance of our approach compared M4 (the method
similar to Shi et al. [9] ) shows that it is possible to achieve good
results by using only weather information as inputs to the
prediction models, compared to using weather and previous PV
power information.
B. Performance for Different Times During the Day
In addition to the overall accuracy for the day, we also
computed the accuracy for each half hour of the day (between
7am and 5pm). The goal was to check if there is any time
intervals associated with lower or higher prediction error. Fig. 7
presents the halfhourly accuracy (MRE) for all methods. We
can see that the accuracy curves for all methods follow a similar
trend – the error is comparatively lower in the morning and then
gradually increases reaching its peak between 10 am and 1pm,
and then gradually declining. The higher prediction error in the
middle of the day may be due to the bigger changes in solar
irradiance at that time.
C. Effectiveness of the NN Ensemble
To assess the effectiveness of the NN ensemble, we
compared the performance of our approach with NN ensemble
and a single NN. Apart from this difference, all other
experimental settings were the same, following the procedure
described in Section III.
Using a single NN our approach obtained MAE=86.92 kW
and MRE=7.12%. By comparing these results with the results
using an NN ensemble from Table III, we can see the use of
ensemble resulted in 3.60% and 3.49% improvement in MAE
and MRE respectively. The differences in accuracy between the
NN ensemble and the single NN were found to be statistically
significant at p<=0.01 (Wilcoxon ranksum test).
As expected, the training time of our approach using an NN
ensemble is higher than using a single NN  10 mins (2 models
× 10 NNs × 30 sec) for NN ensemble compared to 1 mins (2
models × 1 NN × 30 sec) for a single NN. The longer training
time for the ensemble is still acceptable for both offline and
online (e.g. daily) training of the prediction models. Once the
training is completed, both prediction methods are very fast at
predicting the new instances.
Fig. 7. Accuracy (MRE) during the day at halfhourly intervals for all
prediction models
Hence, we can conclude that: (i) our approach for forecasting
the 1day ahead halfhourly PV power profile shows very
promising accuracy, significantly outperforming the methods
used for comparison; (ii) the use of ensemble of NNs instead of
single NN in our approach was found to be beneficial in terms
of accuracy and with acceptable training time requirements.
D. Performance for Different Number of Clusters
To examine the effectiveness of our approach to
automatically select the number of clusters k based on the three
clustering evaluation measures (CalinskiHarabasz, Silhouette
and DaviesBouldin), we conducted a posteriori analysis of the
sensitivity our approach to the parameter k. More specifically,
we evaluated and compared the accuracy of our approach using
different number of clusters.
Table IV shows the accuracy results obtained by varying k
from 2 to 6. We can see that the highest accuracy was achieved
with k=2 clusters (MAE=83.90 kW and MRE=6.88), followed
by second best number of clusters, k=3 (MAE=84.08 and
MRE=6.89). The accuracy results for k=4 to 6 are similar; MAE
and MRE are in the range of 86.7887.26 MW and 7.117.15%
respectively. Overall, the improvement in accuracy between k=2
and k=3 to 6 is 0.213.85%, and all of these differences (except
the difference between k=2 and k=3) are statistically significant
at p<=0.01 (Wilcoxon ranksum test).
0.00
2.00
4.00
6.00
8.00
10.00
Our method M1 M4 M2 M3
MRE [%]
0
2
4
6
8
10
12
14
16
7:00am
7:30am
8:00am
8:30am
9:00am
9:00am
10:00am
10:30am
11:00am
11:30am
12:00pm
12:30pm
1:00pm
1:30pm
2:00pm
2:30pm
3:00pm
3:30pm
4:00pm
4:30pm
MRE [%]
Prediction time
Our method M1
M2 M3
M4
TABLE IV. A
CCURACY OF
O
UR
A
PPROACH
U
SING
D
IFFERENT
N
UMBER
OF
C
LUSTERS
,
K
Number of
clusters k
MAE
[kW]
MRE
[%]
2 83.90 6.88
3 84.08 6.89
4 87.26 7.15
5 86.78 7.11
6 86.99 7.13
Thus, we can conclude that our approach was able to
automatically select an appropriate number of clusters to group
the days based on their weather patterns.
VII. C
ONCLUSTION
We considered the task of forecasting the halfhourly PV
solar power profile for the next day from previous PV power and
weather data, and weather prediction for the next day. We
presented a new approach that predicts all 20 power outputs for
the next day simultaneously by combining clustering with NN
ensembles. Our approach firstly clusters the previous weather
data to determine groups of days with similar weather patterns.
To find an appropriate number of clusters, it applies three
clustering evaluation measures. It then builds a separate NN
ensemble prediction model for each cluster that uses as inputs
the weather data for a given day and predicts the PV power
output for this day. To make a prediction for the next day, it uses
the weather forecast for the next day as an input.
We conducted an evaluation using Australian solar power
data for two years. Our approach identified two clusters and was
able to make accurate predictions achieving MAE=83.90 and
MRE=6.88%, with acceptable computational cost (10 min
training time), and hence is a promising approach for practical
applications. The results also showed that our proposed
approach considerably and statistically significantly
outperformed four other methods used for comparison,
achieving an improvement in accuracy from 20.55% to 34.48%.
We found that the use of ensemble of NNs was beneficial –
it improved the accuracy (MRE) with 3.60% compared to using
a single NN. By analysing the results for different number of
clusters, we found that the proposed use of the three clustering
evaluation measures selected an appropriate number of clusters
for our data.
In future work we plan to study the application of pattern
sequence similarity algorithms which utilise similarity between
sequences of cluster labels [14, 18]. We will also investigate if
feature selection [22] applied to both power and weather data
can improve the results. Another direction for future work is
selecting the best prediction algorithm for a given solar dataset
or different days and times of the day, by investigating methods
based on metalearning [23].
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