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ERBFNN based Electricity Load and Price

Forecasting

Asra Raﬁ, Sana Mujeeb and Nadeem Javaid*

COMSATS University Islamabad, Islamabad 44000, Pakistan

*Correspondence: nadeemjavaidqau@gmail.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.

I. INTRODUCTION

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 [1] and Linear clustering

[2] algorithms are used for forming clusters in smart grid.

Regression analysis uses methods for modeling relationships

between variables. Quantile regression [3], Linear regression

[4] 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 [5], 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 [6], 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.

A. FFNN

FFNN is a classiﬁer used to forecast, hour-ahead price and

load of electricity. There are three layers in FFNN: input layer,

191

2019 International Conference on Frontiers of Information Technology (FIT)

978-1-7281-6625-4/19/$31.00 ©2019 IEEE

DOI 10.1109/FIT47737.2019.00044

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=σ(WijIi+Bi)(1)

’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

hidden layer.

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

of electricity.

σ=1

1+e−x(3)

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.

B. RBFNN

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

forward pass.

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.

f(x)=

n

i=1

Wihi(x)(5)

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.

192

Fig. 1: Proposed System Model

1) Dataset:The historic data of New York Independent

System Operator (NYISO) [7] 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

network.

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

performance.

193

•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

forecasted.

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

11: Yj←wijσ(||x−ci||)+βj

12: σ(r)=exp(−α, |x−c|2)

13: End while

14: self.X ←X

15: C←K.expanddims(self.centers)

16: H=K.transpose(C−K.transpose(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

section.

A. Data Description

The historic data of price and load of NYISO [8] 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.

humidity

pressure

temperature

wind_direction

wind_speed

0.00

0.05

0.10

0.15

0.20

0.25

Feature Importance

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

194

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 [9] 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

20 40 60 80 100 120

Hours

1100

1200

1300

1400

1500

1600

1700

1800

1900

Load (MW)

Actual

Radial Basis Kernel Network

Fig. 4: Load Prediction by RBFNN

20 40 60 80 100 120

Hours

1100

1200

1300

1400

1500

1600

1700

1800

1900

Load (MW)

Actual

FEED FORWARD NEURAL NETWORK

Fig. 5: Load Prediction by FFNN

20 40 60 80 100 120

Hours

1100

1200

1300

1400

1500

1600

1700

1800

1900

Load (MW)

Actual

Enhanced Radial Basis Kernel Network

Fig. 6: Load Prediction by ERBFNN

20 40 60 80

Hours

10

20

30

40

50

60

70

Price ($)

Actual

Radial Basis Kernel Network

Fig. 7: Price Prediction by RBFNN

195

20 40 60 80

Hours

0

50

100

150

200

250

Price ($)

Actual

FEED FORWARD NEURAL NETWORK

Fig. 8: Price Prediction by FFNN

20 40 60 80

Hours

10

20

30

40

50

60

70

Price ($)

Actual

Enhanced Radial Basis Kernel Network

Fig. 9: Price Prediction by ERBFNN

20 40 60 80 100 120

Hours

1100

1200

1300

1400

1500

1600

1700

1800

Load (MW)

Actual

ERBFNN

RBFNN

FFNN

Fig. 10: Load Prediction by FFNN, RBFNN, ERBFNN

20 40 60 80

Hours

10

20

30

40

50

60

70

Price (

$)

Actual

ENHANCED RBFNN

Radial Basis Kernel Network

FNN

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.

VI. CONCLUSION

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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