Forecasting of Photovoltaic Power using Extreme

Learning Machine
T. T. Teo, T. Logenthiran, W. L. Woo,
School of Electrical and Electronic School of Electrical and Electronic School of Electrical and Electronic
Engineering, Engineering, Engineering,
Newcastle University, Singapore Newcastle University, Singapore Newcastle University, Singapore
t.t.teo@newcastle.ac.uk t.logenthiran@newcastle.ac.uk lok.woo@newcastle.ac.uk

Abstract - This paper aims to forecast the photovoltaic power, affecting the stability of the grid. The operation of a power
which is an important and challenging function of energy grid involves matching the supply and load. This difference
management system for grid planning, scheduling, maintenance between supply and load is seen as disturbance to the grid. The
and improving stability. Forecasting of photovoltaic power using grid frequency is usually maintained at 50Hz or 60Hz. If load
Artificial Neural Network (ANN) is the main focus of this paper. is greater than supply, the frequency falls and if load is lesser
The training algorithm used for ANN is Extreme Learning than supply, the frequency rises. The stability of the grid relies
Machine (ELM). Accurate forecast of Renewable Energy Sources on maintaining this frequency. During a generator failure, load
(RES) is important for grid operators. It can help the grid will be greater than supply, if this load is not match quickly, it
operators to anticipate when there will be a shortage or surplus
will lead to the failure of other generators.
of RES and make the necessary generation planning. Therefore, a
real and accurate data were used to train and test the developed There are typically two type of power generator: Base load
ANN. In this paper, MATLAB is used to create and implement generators and peak load generators. Base load generator such
the neural network model. Simulation studies were carried out on as thermal power generator will supply the minimum required
the developed model and simulation results show that, the load over 24 hours. They will be operating at all time and shut
proposed neural network model forecasts the photovoltaic power down only for maintenance. They tend to take a longer time to
with high accuracy. generate enough heat and steam to turn the turbine. They are
unable to match the rapid changing load during the peak
Index Terms -- Photovoltaic, Forecasting, Artificial neural
network, Extreme learning machine, Energy management
period. The operating cost of such generator is inexpensive.
system, Renewable energy resources Peak load generator such as gas turbine generator, which burns
natural gas, operates for a few hours at a time. The startup
I. INTRODUCTION time is fast and it can adjust the power generated quickly. It is
ideal for matching the load during peak period. However the
The world energy demand has increased steadily over the operating cost of such generator is expensive.
years. However with the finite supplies of fossil fuels and
strong evidence of its negative environmental impact, energy Traditional grid is load-dominant. The supply will
policies have shifted towards balancing economic constantly try to match the load. However with the increased
competitiveness, energy security and environmental penetration of RES, there may be a shift towards a generation-
sustainability, also known as ‘Energy Trilemma’. This creates dominant grid. There may be instances where the supply is
the necessity to look for alternate source of energy that is higher than the load. When this happens, shutting down the
cleaner and more sustainable. peak load generator may not be sufficient to reduce the supply
and adjusting the power of base load generators is not
Majority of the world energy supplies are non-renewable possible. This will result in the need to quickly detach RES
and is responsible for majority of the emitted greenhouse from the grid to prevent a grid collapse.
gases. The Kyoto Protocol is a legally binding agreement that
industrialized nations agree to reduce their emissions of Forecasting the output power of RES is important for grid
greenhouse gases by 5% compared to the year 1990. The 6 operators. It can help the grid operators to anticipate when
greenhouse gases are carbon dioxide, methane, nitrous oxide, there will be a shortage or surplus of RES and make the
sulfur hexafluoride, hydrofluorocarbons (HFCs) and necessary generation planning. It is useful for power system
perfluorocarbons (PFCs). scheduling, energy storage management and maintenance.
Grid operators also need to participate in the wholesale
The sun continuously delivers ͳǤʹ ൈ ͳͲହ terawatts to earth, electricity market.
far exceeding 13 terawatt, the entire power demand of the
earth [1]. The cost of manufacturing photovoltaic panel and 4 April 2013, Germany grid operator forecasted a day-
installation cost has fallen dramatically [2]. Despite this ahead PV of 20GW. However the actual PV for the day is
abundance of solar energy and lower cost, it accounts for less 11.2GW. This resulted in a shortage of 8.8GW, which must be
than 1% of the world energy production [3]. met by the grid operator. This resulted in an instability in the
grid. Germany is unable to balance the grid independently and
There are several challenges in integrating RES with had to be supported by neighboring countries [4]. This
existing grid. Most of the RES are intermittent in nature. The highlighted the importance of accurate forecast.
power produce depends on the weather condition, thus
 In this paper, a methodology for forecasting photovoltaic retaining its generalization and universal approximation
power using ANN with ELM as the training algorithm is capabilities.
presented. The developed forecasting model has been verified
by some simulation studies. The rest of this paper is organized C. Single Hidden Layer Feed Forward Networks with
as follows: Section II presents an overview of the literature Random Hidden Nodes
available on forecasting using ANN. Section III explains the Set: Training set Input and Actual Output [(X), (Y)]
proposed methodology used to implement ANN. Section IV
discuss the simulations and results. Section V provides the Set: No. Of Hidden Nodes [K]
discussion. Finally, the paper is concluded in section VI. Set: Activation Function [g(.)]
II. BACKGROUND INFORMATION 1. Randomly assigns weight and bias [(W), (b)]
A. ANN Architecture
2. Calculate the Hidden Layer Matrix [H]
The ANN is inspired by the biological architecture of the
brain. The model proposed in this paper is a Single Layer 3. Analytically determine output weight [β]
Feed-forward Network (SLFN) that consists of input layer,
hidden layer and output layer. Each layer contains many nodes 4. Evaluate the performance of training ELM
and a weighted line that interconnects each node between each Set the input variable(s) as a matrix, X
layer.
ܺଵଵ ‫ڮ‬ ܺଵ௝ (1)
The number of input nodes represents the number of
ܺൌ቎ ‫ڭ‬ ‫ڮ‬ ‫ ڭ‬቏
lagged observations that are fed into the network. Each input
ܺ௡ଵ ‫ڮ‬ ܺ௡௝
nodes is fully interconnected with the nodes in the hidden ௡ൈ௝
layer. This interconnection is called input layer weights. The
layer between the input layer and output layer is the hidden Where, n is the number of samples and j is the number of
layer. Nodes in each hidden layer are also fully interconnected variables.
with all the nodes in the output layer. This interconnection is And set the actual output as a vector, Y
called the output layer weights. The weights can be adjusted
using different training algorithm. The number of output nodes ܻ ൌ ሾܻଵ ‫ڮ‬ ܻ௡ ሿ் (2)
represents the horizon of forecast. It is capable of modeling Set a positive integer for K. Set an infinitely differentiable
the complex relationship between the input(s) and output(s).
function for g(.)
There are five major parameters that require user
intervention and have appeared repeatedly in the literature: 1. Randomly generate an input weight matrix W that inter-
connects the input nodes to the hidden nodes.
1. Size and division of dataset [5], [6]
ܹଵଵ ‫ܹ ڮ‬ଵ௞ (3)
2. Number of hidden layer and hidden nodes [7]-[10] ܹൌ൥ ‫ڭ‬ ‫ڮ‬ ‫ ڭ‬൩
3. Activation function [5], [8]-[10] ܹ௝ଵ ‫ܹ ڮ‬௝௞ ௝ൈ௞

4. Number of input parameters [6], [8]-[11] 2. Calculate the hidden layer matrix H by multiplying input
matrix X with input weight matrix W.
5. Performance evaluation
The literature offers little guidance on the size and division ‫ ܪ‬ൌ ܹܺ (4)
of dataset; the number of hidden nodes is determined Multiply the hidden layer matrix H with activation function
heuristically; unclear choice of activation function; vague g(.) to get the hidden layer output matrix ‫ܪ‬௢௨௧
number of input samples and finally no agreement on method
to evaluate the performance. ‫ܪ‬௢௨௧ ൌ ݃ሺ‫ܪ‬ሻ (5)
B. Extreme Learning Machine 3. Solve for ߚ
In the research paper [12], Huang et al. proposed a new The output layer weights ߚ interconnects hidden layer output
training algorithm that does not require iterative tuning while matrix ‫ܪ‬௢௨௧ to the output vector ܻ෠. The output of the ELM is
guaranteed to reach global minima. This paper made a major
contribution to reduce the training time compared to gradient- ܻ෠ ൌ ‫ܪ‬௢௨௧ ߚ (6)
descent based training algorithm. The paper concluded that
ELM training speed is generally faster than gradient-descent And there exist a ߚ such that
based training algorithm. It can avoid choosing additional ‫ܪ צ‬௢௨௧ ߚመ െ ܻ ‫צ‬ൌ ‹ ‫ܪ צ‬௢௨௧ ߚ െ ܻ ‫צ‬ (7)
parameters such as the learning rate and stopping criterion. ఉ
Empirical evidence shows that ELM has good generalization
The smallest norm least squares solution can be obtain
and universal approximation capabilities [12]. It is stated that
the smallest norm of weights will have better generalization ߚ ൌ ‫ܪ‬௢௨௧ ற ܻ (8)
performance which can be attain with ELM [13]. It addresses
the long training time of Back Propagation (BP) [14] while
Where, ‫ܪ‬௢௨௧ற
is the Moore-Penrose generalized inverse of B. Number of Hidden Layer and Hidden Nodes
‫ܪ‬௢௨௧ , which can be calculated through orthogonal projection. The number of hidden layer can be set to one and
sufficiently approximate to any continuous nonlinear function
ற
‫ܪ‬௢௨௧ ൌ ሺ‫ܪ ்ܪ‬ሻିଵ ‫் ܪ‬ (9) [9]. However, one hidden layer network may require a large
number of hidden nodes, which may not be computationally
III. PROPOSED ANN ARCHITECTURE efficient and tends to have poor performance. The choice of
A. Size and Division of Dataset the number of hidden nodes is crucial to the performance of
The sizes of the dataset used in the literatures are different the model. Too few and it may not generalize (under fit) and
and it is typically separated into training set and testing set. too many and it may over fit. It is shown that the number of
The training set is used to train the model and testing set is nodes is chosen heuristically to determine the optimum
used to evaluate the performance of the model [5]. The number [8]-[10].
literature offers little guidance on the division of dataset. The C. Activation Function
sizes of the dataset have an impact on the performance of the Activation function introduces a degree of nonlinearly to
model. There is no definite way to determine the optimum size the data. There is no explanation to the choice of activation
of dataset. Intuitively, larger dataset will contain more noise function and no comparison with other activation function [5],
than smaller dataset; however smaller dataset may not contain [8]-[10]. The literature does not have a consensus on the
enough information to uncover the underlying relationship choice of activation function.
between the input and output. The size of dataset is also
constrained by the availability of the data. [6] Shows that x Logistic Function
increasing the training data will improve the performance.
ͳ (11)
The dataset has been acquired from 8th June 2014 to 6th ݃ሺ‫ݔ‬ሻ ൌ
ͳ ൅ ݁ ି௫
July 2014.
x Hyperbolic Tangent
x Ambience Temperature, Degree Celsius, °C
݁ ௫ െ ݁ ି௫ (12)
x Panel Temperature, Degree Celsius, °C ݃ሺ‫ݔ‬ሻ ൌ
݁ ௫ ൅ ݁ ି௫
x Accumulated Daily Energy, Joules, J
D. Input Parameters
x Irradiance, Watt/meter square, W/ଶ
How to determine the number of input samples remains an
x Power, Watt, W open question. If there are too few or too many input samples
Five sampled variables will be used as the input and power there may be an impact to the performance of the model.
will be used as the output. The data are sampled Intuitively, it should be a representative of the population, i.e.
approximately every 15 minutes. In time-series forecasting, all using one year of historical data to forecast the next year. The
sampled values are required to be equally space (sampled at a number of input samples will make up the row vector of the
fixed interval). Since the data are not sampled at a fixed input matrix. The number of sampled variables such as
interval, it resulted in days where there are 96 samples. The temperature, humidity and irradiance will make up the column
96th sample of that particular day is removed. All samples are vector in the input matrix.
assumed to be sampled at 15 minutes interval. The resulting The literature offers little explanation on the choice of
dataset consist of 95 samples for each day and 2850 samples input variables. It have suggested that additional input
for 30 days. Since the power generated cannot be negative, all variable(s) may improve the performance of the model [8]-
negative values are remapped to 0 and assuming the future [10], conversely as [11] have shown, the model that yields the
power will not surpass the historical maximum power. best performance does not necessary comes from the one that
(10) has the most input variables. However, only varied the number
Ͳǡ ‫ݕ‬ො ൏ Ͳ
of input variables but did not vary the sequence of input [11].
‫ݕ‬ො ൌ ቐ ‫ݕ‬ොǡ ‫ݕ‬ො ൑ ‫ݕ‬௠௔௫ Oudjana et al. calculated the correlation coefficient between
‫ݕ‬௠௔௫ ǡ ‫ݕ‬௠௔௫ ൑ ‫ݕ‬ො the input variable and empirical evidence shows that using
variable with the strongest positive correlation yields better
Where, ‫ݕ‬ො is the estimated output, and y is the actual output. performance [6].
The dataset are divided into three different sets as shown in
E. Performance Measure
Table I.
The performance of the ANN is measured by the root mean
TABLE I. DIVISION OF 3 DATASET square error (RMSE) achieved on the testing set data.
Dataset Training Date (Days) Testing Date (Days) (13)
01 24th June to 1st July (8) 2nd July to 6th July (5) σ௡ୀே ෠
௡ୀ௜ ሺܻ௜ െ ܻ௜ ሻ
ଶ
‫ܧ‬ൌඨ
02 16th June to 1st July (16) 2nd July to 6th July (5) ܰ
03 8th June to 1st July (24) 2nd July to 6th July (5)
Where, E is the error of the model, ܻ෠௜ is the estimated output A. Simulation Studies: Number of Hidden Nodes
of the model, ܻ௜ is the actual output, and N is the total number The 3 dataset are tested and the number of hidden nodes is
of samples. varied from 1 to 500. From Figure 2, as the number of hidden
nodes increases, the training RMSE displayed a downward
IV. SIMULATION AND RESULTS
trend. However, for testing RMSE, after approximately 100
Table I shows the division of training data and 2nd July hidden nodes, it has displayed an upward trend. Both RMSE
2014 to 6th July 2014 are used as the test data in the ANN are fluctuating. At this point it is difficult to identify which
simulations. The actual measured values are compared with division of dataset yields the best performance. However the
the output data from the proposed ANN in order to measure number of hidden nodes is set as 100.
the performance of the ANN.
Before the optimum parameters of the ANN are
established, the parameters are set as shown in Table I. The
simulation is repeated for 500 times and the average training,
testing RMSE and respective standard deviation are recorded.

Initial Simulation
Initial Parameters

Simulation 1
a) Size of training data b) Number of hidden nodes

Simulation 2
Activation Function

Simulation 3
Number of input variables Sequence of input
Figure 2. RMSE vs no of hidden nodes for 3 different dataset
Figure 1. Proposed methodology

Fig.1 shows the proposed methodology to determine the B. Simulation Studies: Division of Dataset
network architectural in a systematic manner. After setting the number of hidden nodes as 100, another
simulation is done to further analyze the performance against
Before the suitable network architectural are established, the different division of dataset.
the parameters are set as shown in Table II. The simulation is
repeated for 500 times and the average training, testing RMSE From Table III, Set 3 yields the least RMSE among other
and respective standard deviation are recorded. sets. Set 3 is used for the rest of the simulations.

TABLE II. INITIAL PARAMETERS OF NEURAL NETWORK TABLE III. RMSE AND STANDARD DEVIATION FOR 3 DIFFERENT DATASET

Dataset Set 1 Dataset Set 1 Set 2 Set 3

Activation Function Logistic Activation Function Logistic Logistic Logistic

No. Of Input Variables 4 No. Of Hidden Nodes 100 100 100

No. Of Hidden Nodes 100 Training RMSE 3.4738 3.468 3.5366
Training RMSE 3.4738 Standard Deviation 0.0946 0.0898 0.0798
Standard Deviation 0.0946 Testing RMSE 4.1906 3.9496 3.8574
Testing RMSE 4.1906
Standard Deviation 0.2814 0.096 0.0881
Standard Deviation 0.2814
C. Simulation Studies: Activation Function
The training and testing RMSE in Table II will be used as In previous simulations, the activation function is set as
a benchmark to compare the performance when each logistic function. The efficiency of it and hyperbolic tangent
parameter is changed. The parameter that resulted in the least function will be evaluated.
RMSE will be kept and used when changing the next
parameter. All simulations are done using MATLAB From Table IV, the performance of hyperbolic tangent
v8.3.0532 running on 4.0 GHz CPU. The parameter that yields function is very similar to logistic function.
the least RMSE is highlighted.
 TABLE IV. RMSE AND STANDARD DEVIATION OF DIFFERENT ACTIVATION Table VI shows that Sequence 2 with 2 input variables
FUNCTIONS
yields the least RMSE.
Dataset Set 3 Set 3

Activation Function Logistic Hyperbolic Tangent

No. of Hidden Nodes 100 100

Training RMSE 3.5366 3.5525

Standard Deviation 0.0798 0.0811

Testing RMSE 3.8574 3.8638

Standard Deviation 0.0881 0.0882

D. Simulation Studies: Number of Input Variables and

Sequence of Input
The numbers of input variables and the sequence of input
are challenged. As shown in Table V, there are 5 different
sequences to set the input variables. 5 simulations are done on
each sequence. By varying the number of input variable(s) and
the sequence of input, a total of 25 simulations are done.

TABLE V. 5 SEQUENCE OF INPUT VARIABLES

Figure 3. Output vs Target of Sequence 2 with 2 Input variables
No. Of
Input
Varia-
1 Input 2 Input 3 Input 4 Input 5 Input Table VII shows the gradual improvement in forecasting
ble(s) accuracy after each simulation. Comparing the difference in
Ambi- Accumu- testing RMSE and standard deviation, the biggest
Panel
Sequence ence
Tempera-
Irradi- lated
Power
improvement is seen in Simulation 1, followed by Simulation
1 Tempera- ance Daily 3. In Simulation 1, the sizes of training data were changed and
ture
ture Energy in Simulation 3, the input variable and input sequence were
Ambi- Accumu-
Sequence ence
Panel
Irradi- lated
changed. Empirical evidences have shown that the model
Power Tempera- benefited the most by using a larger training dataset and
2 Tempera- ance Daily
ture having more input variables does not yield better performance.
ture Energy
Accumu- Ambi-
Panel
Sequence lated ence Irradi- TABLE VII. SUMMARY RMSE AND STANDARD DEVIATION
Power Tempera-
3 Daily Tempera- ance
ture
Energy ture Simulation Initial 1 2 3
Accumu- Ambi-
Panel Training RMSE 3.4738 3.5366 3.5366 3.6408
Sequence Irradi- lated ence
Power Tempera-
4 ance Daily Tempera-
ture Standard Deviation 0.0946 0.0798 0.0798 0.0108
Energy ture
Accumu- Ambi-
Panel Testing RMSE 4.1906 3.8574 3.8574 3.5821
Sequence Irradi- lated ence
Tempera- Power
5 ance Daily Tempera- Standard Deviation 0.2814 0.0881 0.0881 0.0295
ture
Energy ture

V. DISCUSSION
TABLE VI. SEQUENCE 2
Cross-Validation was used to estimate how accurate the
No. Of Input RMSE Standard RMSE Standard model will perform in practice. To test the forecasting
Variable(s) Train Deviation Test Deviation
Sequence 2
accuracy of a model, the dataset is divided into training and
testing set. The training set is used to train the model and
1 Input 3.7375 0.0013 3.7082 0.0032 testing set is used to validate the accuracy of the model. The
division of dataset has an impact on the performance of the
2 Input 3.6408 0.0108 3.5821 0.0295 model. When the testing set is small, intuitively the RMSE
will also be smaller since the number of point tested is smaller.
3 Input 3.5211 0.0226 3.6594 0.055
Contrary to the literature, more input variables does not
4 Input 3.3368 0.0435 3.7601 0.0934 yield better performance and every sequence has to be tested
to determine the optimum number of input variable(s) and
5 Input 3.533 0.0791 3.8666 0.096 sequence.
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