ERBFNN based Electricity Load and Price
Asra Raﬁ, Sana Mujeeb and Nadeem Javaid*
COMSATS University Islamabad, Islamabad 44000, Pakistan
*Correspondence: email@example.com, www.njavaid.com
Abstract—The power grid has attracted a lot of attention
recently, due to its innovations and technologies. Sophisticated
and efﬁcient techniques are used to manage energy demand
and supply operations in the modern power grids. Efﬁcient
energy management based on load and price forecasting is the
focus of the power utility. In this paper, hour-ahead electricity
load and price is predicated on the basis of peak load hours
using Enhanced Radial Basis Neural Network (ERBFNN). Firstly,
Decision Tree (DT) and Recursive Feature Elimination (RFE)
techniques are used for feature selection. Then, auto correlation
is used for feature extraction. For comparison, Feed Forward
Neural Network (FFNN) and Radial Basis Neural Network
(RBFNN) are examined. To evaluate the efﬁciency of the proposed
model, four performance metrics are used, i.e., Mean Absolute
Error (MAE), Root Mean Square Error (RMSE), Mean Square
Error (MSE) and Mean Absolute Percentage Error (MAPE).
Performance of the proposed model is evaluated on the historical
load data of New York Independent System Operator (NYISO).
Experimental results show proposed model achieves higher fore-
casting accuracy (89%) as compared to RBFNN (84%) and Feed
Forward Neural Network (FFNN) (80%).
Index Terms—Smart Grid, ERBFNN, RBFNN, FFNN, Elec-
tricity Load and Price Forecasting.
A Smart Grid (SG) system is a power network that is
a combination of digital automation technology and electric
network to: control smart meters, automate consumers billing
data, identifying power device crash and send out repair team
to the accurate location. It facilitates electricity consumers
in an sustainable, reliable, secure and economical manner as
compared to the traditional grid that is almost obsolete in
the modern world. SG develops an interactive environment
between energy consumers and utility (power generation and
distribution company). The objective of transferring from tra-
ditional grid to SG is to minimize the gap between generation
and consumption of electricity. The demand for electricity is
rising at an alarming rate with the growth of world population
and excessive use of appliances. Many SGs are developed
around the globe that are generating big volume of data. The
data regarding energy market operations, i.e., consumption,
price, generation, etc. is generated by the SG. Energy market
utilities use this data to perform analysis to take important
decisions for the electricity market operations management
and planning. Utilities require better knowledge of consumer
behavior, electricity demand, consumption and power failures.
Data analytic follows a series of actions to inspect data
objects in data sets and give useful information for decision
making. Classiﬁcation, clustering, regression is broader level
techniques used to perform Data Analytic on data. The clus-
tering is a method of unsupervised learning to group similar
data objects. Functional clustering  and Linear clustering
 algorithms are used for forming clusters in smart grid.
Regression analysis uses methods for modeling relationships
between variables. Quantile regression , Linear regression
 are regression techniques implemented for load and price
forecasting in smart grid.
A. Motivation and Contributions
The Feed Forward Neural Network (FFNN) and Radial
Basis Neural Network (RBFNN) are widely used for electricity
load and price prediction. In paper , FFNN is implemented
for building’s energy demand forecasting. The learning rate for
a network is set high which leads to the problem of unstable
learning of nonlinear network. That cause problem of model
overﬁtting. In paper , short-term load is predicted using
RBFNN with the introduction of clustering idea. The authors
used k-means for ﬁnding center, which results computational
complexity. In this paper, FFNN, RBFNN and ERBFNN are
implemented to forecast electricity load and price accurately.
The major contributions of this paper are:
1: The reﬁned features are extracted from data, using a
feature extractor that is a combination of Decision Tree (DT),
Recursive Feature Elimination (RFE) and autocorrelation
2: The proposed forecaster, ERBFNN is tuned by increasing
number of output dimensions and network parameter optimiza-
tion to achieve high accuracy.
The remaining sections of this article are described as follows:
ANN and its types are discussed in Section 2. In Section 3,
the implemented classiﬁer are discussed. In Section 4 Proposed
scheme is described in detail. Results and Simulations are part
of Section 5. While in Section 6 Performance Evaluation is
done . In the last section the article is concluded precisely.
II. ARTIFICIAL NEURAL NETWORK
ANN is inspired by the biological neural behavior of the
brain. It is the computational modeling of natural neural
network’s learning activity. ANN architectures are classiﬁed
as Feed Forward (FF) networks and feedback or Back Propa-
gation (BP) networks.
FFNN is a classiﬁer used to forecast, hour-ahead price and
load of electricity. There are three layers in FFNN: input layer,
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one hidden layer and an output layer. An inputs set is fed
to hidden layer and weights are assigned to each input for
processing. Features and their corresponding values (Hours)
are given to the network as input and predicted load and price
are taken as ﬁnal output.
’Hi’ belongs to hidden layer, ‘W’ belongs to Weight matrix,
and ‘I’ belong to inputs, where ‘B’ is bias for leveling the
weighted sum. In the equation (1), it is shown that one input
matrix and another weight matrix transform into vector form
to generate a multiplicative vector. The weights vector matrix
is multiplied by an input vector matrix; this gives a single
matrix. This resultant matrix is then added to the bias matrix
of two columns b1, b2. An important thing to consider here
is that bias matrix must also be transformed into vector to
perform matrix addition. Bias addition in FFNN is required
to overcome the problem of having zero values in weighted
sum. This result of vector sum is passed through an activation
function called signed to get output which become input for
Output =σ(Wij Hi+Bi)(2)
In the equation (2), it is shown that Weights vector matrix Wij
is multiplied by a hidden layer vector matrix Hi, this gives a
single matrix. This resultant matrix is then added to the bias
vector matrix. This given output given is passed to sigmoid
function to get forecast results of hour-ahead load and price
Any number passed from the sigmoid function equation (3)
gives output in the range of [0, 1]. Sigmoid function squashes
the large value in to 0 to 1 range.
RBFNN is a type of Artiﬁcial Neural Network (ANN). It is
widely used network used in pattern recognition, classiﬁcation
and regression. RBFNN in RBFNN is used as activation
function. RBFNN may contain single layer or multiple layer
according to the implementation perspective. The weights
are updated iteratively in back propagation. The weights are
learned for computing a weighted sum for output layer is
At the input layer six features are passed for load prediction
and seven features are passed for price prediction. The per-
formance of a network is evaluated on different parameters.
It is an enhanced version of RBFNN. ERBFNN is a machine
learning, Neural network and RBFNN is as activation function
of this network. This Neural network is used with Support
Vector Machine (SVM) as a kernel function for classiﬁcation
in data analysis. This classiﬁer is used to forecast electricity
Load and price. There are three basic layers in this network:
An input layer, hidden layers and output layer. These are
used for function approximation in general, so the output that
ERBFNN returns is real value. At the input layer every neuron
or unit corresponds to the predictor variable in our data. Each
neuron in the hidden layer consist of radial basis function, e.g.
Gaussian function on the hidden layer. Gaussian function is
also known as a transfer function. That function is centered on
a point with the similar dimensions as the predictor variables.
More speciﬁcally Load and price prediction is done by using
5 and 6 features respectively, Each Gaussian function which
is centered on a point is a 5 and 6 dimensional and it has
components according to the features passed to network at the
input layer. The output layer is a weighted sum of the outputs
from the hidden layer. Target value is also known as target
variable. While predicting Load and Price the feature TWI load
and TWI Price are target variables respectively. There are 6
features as a predictor varied so RBFNN have 6 dimensional
activation function on the hidden layer. We ﬁnd a distance
from new point which is a query point to the center of each
neuron. RBFNN applies to that distance to compute weights
for each neuron. The next neuron is evaluated on the basis of
its less inﬂuence on prediction. When a point is far from the
center point, then it has less inﬂuence.
Wij =RBF (distance)(4)
In equation (4), Wij belongs to weights of neuron which are
calculated by passing points distance to the RBF. At the hidden
layer there are four neurons and activation function is applied
to every neuron. The output of that function is the weighted
input to ﬁnal predicted output at the output layer.
In equation (5), Wibelongs to weights and hi(x)belongs
to activation function. For each function on the hidden layer
distances and corresponding weights are computed. f(x) is
predicted output at output layer. The forward pass in the
network model means computation done at the network layer
is in forward manner and features are taken at input layers
are passed to the hidden layer where their weights of each
neuron are computed and for this purpose distance is computed
from centered point to each point. RBFNN is then applied
in a forward manner on each distance value and as a result
of this process, we found weights of each neuron. After this
step weighted sum is computed. This weighted sum is then
multiplied by the activation function to get input for the output
layer. Backward pass of network works inn opposite manner
as compared to a forward pass. The computation of Weighted
sum and application of activation function is done at hidden
layer and weights are updated in backward pass.
III. PROPOSED SCHEME
The proposed model is implemented in four main stages:
pre-processing of data, training ERBFNN, validation of net-
work, forecasting load and price on test data. The proposed
system model is shown in the Figure.1.
A. Data Preprocessing
The data are gathered from energy market is pre-processed
in 2 steps: Feature Selection, Feature Extraction.
Fig. 1: Proposed System Model
1) Dataset:The historic data of New York Independent
System Operator (NYISO)  is used for the prediction of
price and load of electricity. This proposed model has been
used peak hours’ load data for two months, April-May, 2016
for forecasting hour-ahead load and price of electricity.
B. Feature Engineering
Two techniques are used for feature selection. First, features
are selected from feature space using classiﬁcation technique
named Decision tree (DT). DT Algorithm is used in feature
selection phase to eliminate redundancy among features. For
this purpose, we split data into two sets: one is called training
set and other is known as test set. The training data is passed
through the DT classiﬁer. DT classiﬁer calculates importance
of each feature. Figure 2.shows importance of features calcu-
lated by DT.
RFE technique is used for dimensionality reduction from
selected features. RFE is used to select features on the basis
of weights, assigned to every feature. First, the weights are
estimated by DT classiﬁers and importance of each feature is
obtained. Then, the least important features are pruned from
available data set of features. That procedure is recursively
repeated on the pruned or remaining set until the desired
number of features found according to threshold set in the
code. Then importance of each feature return by DT. The
feature with least coefﬁcient or importance value is pruned
by RFE. Wind speed is eliminated by RFE to reduce dimen-
sionality as it is least important feature when predicting load
of electricity. On the other side when target get changed from
Load to Price then Humidity is also pruned by RFE along with
wind speed. Most important features for price forecasting are
Actual Load, Temperature,Pressure and Wind Direction are
passed to next stage of preprocessing. Features are extracted
by normalization. Auto correlation is a technique used by
proposed system to extract features.
By using technique named Auto correlation (AC), correlated
features are extracted on the basis of similarity between
observations. Then the model is ﬁt on the remaining features.
These features will become input for network. DNN has shown
promising results in load and price prediction. So a DNN
based technique ERBFNN is proposed. At this level data is
normalized in such way that no feature got eliminated as all
the features selected by DT and RFE are important. At this
stage, data is normalized and transformed to pass to the neural
C. ERBFNN Training and Forecasting
Data is partitioned again into training and testing at this
stage. ERBFNN is trained on training data and then validated
on test data which is also known as unseen set of data set.
Features of training set are passed to the network. ERBFNN
consist of three basic layers: Input layer, Hidden layer and
output layer. ERBFNN take features or predictor variables
as input at input layer.At hidden layer of the network four
neurons are used and each neuron is passed through At this
stage distance from center of each neuron to the query point is
calculated. Each distance is passed to the RBFNN to compute
weights of every neuron.The output at this stage given by
hidden layer is a weighted sum of neurons that will be passed
to the output layer which process it and return predicted load
of price as ﬁnal output. ERBFNN is trained for load and
price separately. While predicting load, TWI actual Load is
used as target variable and network will return predicted load
in result.Beside this, TWI Zonal LBMP is taken as a target
variable to predict hour ahead price. The steps of proposed
model are listed bellow:
•Step 1: The historical Load and Price data as input
vectors are passed to the network after pre-processing
of data.This data is divided into train set and test set.
•Step 2: ERBFNN model is trained on training data set
and tested on unseen data set. Root Mean Square Error
(RMSE) is calculated to compute the error rate of network
•Step 3: In this step Network model is tuned on training
set and results are generated.
•Step 4: The ﬁnalized efﬁcient model of network is tested
on the test records and hour ahead Load and price are
Algorithm 1 Algorithm of ERBFNN
1: Input: x1,...,xm
2: I(i1,2, .., I)number of neurons
3: J(j1,2, .., I)dimension of the output
4: B(β1, .., βj )bias parameters
5: wij Weight of the ith neuron and jth output
6: wij Weight of the ith neuron and jth output
7: While ( true )
8: initializing all ERB F N N popul ation
9: find the best weights wij
10: keep calculating best possible weights
12: σ(r)=exp(−α, |x−c|2)
13: End while
14: self.X ←X
17: return K.exp(−self.betas ∗K.sum(H∗∗2, axis =1))
18: baseconfig =super(ER BF Layer, self ).getconf ig()
19: Output: ERB F N N output(Y1, .., Y j).
IV. RESULTS AND SIMULATIONS
This section includes results of simulations which are com-
puted at different stages of implementation. As Two schemes
named FFNN and RBFNN are benchmark schemes of this
proposed scheme so their results are also discussed in this
A. Data Description
The historic data of price and load of NYISO  market is
used. The data of peak hours of two months, April-May, 2016
is used for forecasting hour-ahead load and Price of electricity.
B. Features Importance in Forecasting
Features in any data set are very importance for dealing with
data. For using these features efﬁciently without redundancy
importance of each feature must be available. The importance
of each feature is calculated and on the basis of threshold value
important features are selected. The importance of ﬁgures is
shown both in tabular and graphical format. In the ﬁgure.2,
importance of each feature is represented using plots and it
clearly shows that electricity load forecasting is dependent on
different features, which includes Humidity, Pressure, Temper-
ature, Wind direction and Wind speed.
Fig. 2: Features Importance in Load prediction.
Fig. 3: Features Importance in Price Prediction.
Figure.3 shows that each feature has its importance. Elec-
tricity Price forecasting is dependent on different features,
which includes Actual Load, Pressure, Temperature and Wind
direction. Feature importance is calculated at this stage when
price is taken as target variable. It is shown that actual load
and temperature are the most important features along with
pressure and wind direction, which have greater importance as
compared to wind speed and humidity having least importance.
The load predicted by ERBFNN classiﬁer outperform bench-
mark schemes. The hour ahead Price is predicted by ERBFNN
on the basis of peak hours data of historic price provided by
NYISO. Load prediction by ERBFNN is shown in ﬁgure 6.
This classiﬁer performed with higher accuracy in comparison
with FFNN and RBFNN. Load data is partition in to feature
training set and feature test set. Model is trained on 75
percent of record and, is tested on remaining 25 percent. Price
prediction by ERBFNN is shown in ﬁgure 9. Electricity Price
data is taken as target variable and is divided into label train
and test. Actual Price and Load are shown in blue line and
predicted price and Load can be observed in red lines.
FFNN is a classiﬁer which is implemented to forecast Load
and Price separately. The Load of Energy market is forecasted
on hourly basis using FFNN. The hour ahead Price of Energy
market is forecasted on the basis of peak hours using FFNN.
Load prediction by FFNN is shown in ﬁgure 5. Electricity load
data of two months April-May is divided into two parts:Feature
Training Set and Feature Test set. Training set has large size
because it is passed to the model for training patterns so
that model could perform better on test set, which is smaller
in size. Price prediction by FFNN is shown in ﬁgure 8.
Electricity Price data of two months April-May is divided into
training and testing set. Actual Price is predicted on the basis
of most important feature Actual load along with humidity,
temperature and wind direction.
RBFNN is a classiﬁer which is implemented to forecast load
and price separately. The Load of NYISO market is forecasted
using RBFNN and results are computed. The hour ahead Price
of Energy market is forecasted on the basis of peak hours using
RBFNN. Load prediction by RBFNN is shown in ﬁgure 4.
Electricity load data of two months April-May is divided into
two parts:Feature Training Set and Feature Test set. Model is
trained on 75 percent of record and, is tested on remaining
25 percent. Price prediction by RBFNN is shown in ﬁgure 7.
Electricity Price data is taken as target variable and is divided
into label train and test.
C. Comparison of Forecasting Models
The performance and applicability of proposed model is
validated by implementing two other classiﬁer models FFNN
and RBFNN on same data set. Results are computed from all
three classiﬁers. Results shows that ERBFNN performed better
than then RBFNN with simple linear kernel for both load and
price. Figures 10-11 show the results of hour ahead peak hours
load and price prediction of April-May 2016 respectively using
all three classiﬁers. And it is observed that prediction done by
ERBFNN is more accurate and much closer to the actual load
and price of those month.
V. P ERFORMANCE EVALUATION
The performance of every classiﬁer is evaluated using
performance measures  RMSE, MAPE, MSE, MAE.
A. Comparison of Errors
The MAE, MSE, RMSE and MAPE are calculated for all
classiﬁer: ERBFNN, RBFNN and FFNN. From simulations
results it can be observed that ERBFNN performed accurately
as it produces low error rate during implementation as compare
to FFNN and RBFNN.
TABLE I: Errors of Load
Load Forecasting Errors Price Forecasting Errors
Classiﬁers FFNN RBFNN ERBFNN FFNN RBFNN ERBFNN
MAPE 10.0 11 9 15.0 10 0.3
RMSE 12 13 11 14 13 10.1
MAE 6.8 8 7 6.8 8 7
MSE 3.9 5 3 3.9 5 0
Fig. 4: Load Prediction by RBFNN
Fig. 5: Load Prediction by FFNN
Fig. 6: Load Prediction by ERBFNN
Fig. 7: Price Prediction by RBFNN
Fig. 8: Price Prediction by FFNN
Fig. 9: Price Prediction by ERBFNN
Fig. 10: Load Prediction by FFNN, RBFNN, ERBFNN
Fig. 11: Price Prediction by FFNN, RBFNN, ERBFNN
B. Implementation Details
There are different layers in network model which does
affect the prediction results. Layers contain neurons and accu-
racy of the network model is dependent on number of neurons
used by the network.Several experiments are done to ﬁnalize
the hidden layers, number of units at each layer.As much
number of hidden layers increased the parallel increase in
computational cost and model complexity is also observed.
One hidden layer with four hidden units is added in the
model and performance is evaluated accordingly. The results
of forecasted load and price are shown in ﬁgure 10 and ﬁgure
11 respectively. All the network parameters including learning
rate, Epochs and Batch size are set according to the best
accuracy of the model.The number of iterations are dependent
on the value of epochs.
In this paper, data analytic techniques are used for electricity
load and price forecasting in smart grid. An enhanced, three
staged forecasting model is introduced to forecast energy
load and price accurately. Important features are selected
by DT, discarding the irrelevant features. The dimensionality
reduction of input features results in reduced complexity of
forecasting model. The hyper parameters of RBF kernel func-
tion are tuned for enhancing proposed model’s performance.
Simulation results show that proposed model achieves higher
forecasting accuracy as compared to RBFNN and FFNN.
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