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Load and Price Forecasting Based

on Enhanced Logistic Regression

in Smart Grid

Aroosa Tahir1, Zahoor Ali Khan2, Nadeem Javaid3(B

), Zeeshan Hussain2,

Aimen Rasool2, and Syeda Aimal2

1Sardar Bhadur Khan Women University Quetta, Quetta 87300, Pakistan

2Computer Information Science, Higher Colleges of Technology, Fujairah 4114, UAE

3COMSATS University Islamabad, Islamabad 44000, Pakistan

nadeemjavaidqau@gmail.com

http://www.njavaid.com/

Abstract. Smart Grid (SG) is a modern electricity grid that enhance

the eﬃciency and reliability of electricity generation, distribution and

consumption. It plays an important role in modern energy infrastruc-

ture. Energy consumption and generation have ﬂuctuating behaviour

in SG. Load and price forecasting can decrease the variation between

energy generation and consumption. In this paper, we proposed a model

for forecasting, which consists of feature selection, extraction and classi-

ﬁcation. With the combination of Fast Correlation Based Filter (FCBF)

and Recursive Feature Elimination (RFE) is used to perform feature

selection to minimize the redundancy. Furthermore, Mutual Informa-

tion technique is used for feature extraction. To forecast electricity load

and price, we applied Naive Bayes (NB), Logistic Regression (LR) and

Enhanced Logistic Regression (ELR) techniques. Our proposed technique

ELR beats other techniques in term of forecasting accuracy of load and

price. The load forecasting accuracy of ELR, LR and NB techniques

are 80%, 82% and 85%, while price forecasting accuracy are 78%, 81%

and 84%. Locational Marginal Price of Pennsylvania, Jersey, Maryland

(LBM-PJM) market data used in our proposed model. Forecasting per-

formance is assessed by using RMSE, MAPE, MAE and MSE. Simu-

lation results show that our proposed technique ELR is perform better

than other techniques.

Keywords: Smart Grid ·Naive Bayes ·Logistic Regression ·

Fast Correlation Based Filter ·Recursive Feature Elimination ·

Mutual Information

1 Introduction

Traditional Grid (TG) is an interconnection of many elements such as trans-

mission lines, distribution lines and diﬀerent types of load. They are located far

from power consumption areas, so power consumption transmitted from long

c

Springer Nature Switzerland AG 2019

L. Barolli et al. (Eds.): EIDWT 2019, LNDECT 29, pp. 221–233, 2019.

https://doi.org/10.1007/978-3-030-12839-5_21

222 A. Tahir et al.

transmission lines. Traditional power grid is old version of Smart Grid (SG).

SG precisely manage distribution, consumption and generation of energy which

introduce communication and control of technology in power grid [1]. Smart grid

helps the consumers to use electricity in secure manner. The new generation is

attached against the SG due to extensive shortage of energy during summer. It

suggest electricity consumers for load transferring and storage that can overcome

their power consumption cost [2]. SG creates connection between consumer and

utility. Customer consumes operation in SG for decreasing price by load shifting

and energy storage. Consumer can manage their demand of energy on Demand

Side Management (DSM) according to price variation [3]. Customer has choice

to minimize their electricity cost through energy control and shifting the load.

Consumer can switch the load and oﬀ depending on the electricity pricing. Com-

petitive market takes advantage from load and price forecasting. Many valuable

operational decisions are depends on load predication such as power reliability

analysis, maintenance planning and generation scheduling. Consumer takes part

in operation of SG that shifts the load from on-peak hours to oﬀ-eak hours.

In this paper, we highlight the electricity load and price problems, to solve

these problems we used many techniques. Machine learning methods works excel-

lent on data analytics, they categorize the data into training and testing step

by step. Feature selection is an important operation for classiﬁcation and selects

important features. However, Feature selection have many common problems

in the process is that redundancy of selected feature is not minimizing. Fast

Correlation Based Filter (FCBF) and Recursive Feature Elimination (RFE) are

used as a solution of feature selection problem. Mutual Information (MI) feature

extraction method is used for feature reduction. We use two techniques Naive

Bayes (NB) and Logistic Regression (LR) classiﬁers that have better capability

of non-linear estimation and self learning. We proposed Enhance (ELR) classi-

ﬁer that suitable for load and price forecasting. These methods are capable for

extract the complex data representation with better prediction. ELR has better

computation power when comparing it with LR. The objective of our paper is

to predict Load and price accurately using data analytics in the smart grid. For

this problem we use NB, LR and ELR to predict the best results of electricity

load and price forecasting.

1.1 Motivation

After reviewing papers [4,5], existing forecasting method have following motiva-

tions:

•Data analytics is not taken in the discussion of load and price forecasting

method. Performance Matrix is taken on the electricity price data which is

not enough large that minimize prediction.

•Intelligent methods such as ANN, SVM, DE and DWT have limited general-

ization capacity, they have ﬁtting problem.

•Non-linear and other patterns of energy price is critical to predict with tra-

ditional data. The usage of data analytics make it feasible that generates the

pattern of data and predicts accuracy.

Data Analytics Load and Price Forecasting in Smart Grid 223

•Automatically feature selection and extraction can eﬃciently extract and

select useful hidden patterns in the data (Table 1).

Table 1. List of abbreviations

Abbreviation Full f o r m

ARMA Auto Regressive Moving Average

AI Artiﬁcial Intelligence

ANN ArtiﬁcialNeuralNetwork

DSM Demand Side Management

DE Diﬀerential Evaluation

DWT Discrete Wavelet Transformation

ELR Enhanced Logistic Regression

FCBF Fast Correlation based Filter

LR Logistic Regression

MI Mutual Information

MAPE Mean Average Percentage Error

MSE Mean Square Error

MAE Mean Absolute Error

MLR Multi Linear Regression

NB Naive Bayes

RFE Recursive Feature Elimination

RMSE Root Mean Square Error

SG Smart Grid

SVM Support Vector Machine

SNN Shallow Neural Network

SVR Support Vector Regression

TG Traditional Grid

1.2 Problem Statement

There is high variation between energy generation and consumption [6]. There is

no proper strategy of energy generation, which leads to extra energy generation.

To avoid spare energy generation, we perform forecasting. With the help of load

and price forecasting, generation of energy can be controlled with in the limits.

1.3 Contributions

This paper have major contributions such as:

•We implement a framework for achieving accurate load and price forecasting

by using the data analytics in SG.

224 A. Tahir et al.

•Feature selection, extraction and classiﬁcation is proposed in our model to

solve the addressed problem.

•In feature selection, we combine FCBF and RFE which gives us importance

of feature selection. MI is used for feature extraction.

•Naive Bayes and LR classiﬁers are used for forecasting.

•However, we enhance LR to beat these two techniques.

•We have use the real world energy load and price data which performs better

simulation that have better results.

2 Related Work

In the paper [1] Data Analytics Demand response technique propose for res-

idential load. Data analytics scheme tested on PJM and Open Energy Infor-

mation and show that it minimizing the load. In this paper author forecast

day-ahead price forecasting, which contain six year long dataset and four auto

regressive expert model transformed price [2]. ANN present for price forecast-

ing, the focus is on the selection and preparation of fundamental data that has

eﬀect on electricity price [4]. In this paper [5], author admit the eﬀect of data

integrity attacks on the accuracy of four representative load forecasting model

such as Multiple Linear regression (MLR), Support Vector Regression (SVR),

ANN and Fuzzy Integration Regression (FIR). These models used to generate

one-year-ahead forecasting to provide the comparison of their forecast error. The

concepts of interaction for feature selection is introduce as Mutual Information

(MI) and Interaction Gain (IG). These techniques measure the feature relevancy

and redundancy, measures the load and price by merging them [6]. In [7] author

reduce the energy purchase from wholesale market at the high price with operat-

ing Behind The Meter Storage System (BESS). MI use for feature selection and

Intra Rolling Horizon (IRH) and Pre-Dispatch Price use for prediction. Forecast-

ing the electricity price, three models are used to merge the Random Forest (RF)

and Relief-F algorithm based on Gray Correlation Analysis (GCA) for feature

selection to eliminate the feature redundancy [8].

Kernel Function and Principle Component Analysis (KPCA) used for feature

extraction. Author use Diﬀerential Evaluation (DE) for price forecasting, which

based on Support Vector Machine (SVM) classiﬁer. Author hybrid the Discrete

Wavelet Transformation (DWT), Empirical Mode Decomposition (EMD) and

Random Vector Functional Link Network (RVFL) Techniques to forecast the

short term load [9]. In paper [10], ﬁlter the feature by Stacked De-noising Auto-

Encoder (SDAs) from energy load to train the SVR for prediction. The day-

ahead load forecasting compare SVR and ANN, validates the performance for

improvement. Author combine the Kernel Extreme Learning Machine (KELM)

based on self-adapting (SAPSO) and (ARMA) [11]. Their experimental result

show that developed method has more accurate prediction. Multi variation MI

and SVR used for feature selection and price prediction [12].

These two methods also measure relation between price and load. Index

bad sample matrix (IBSM), Optimize Algorithm (OA) and Dynamic Choos-

ing (DCANN) are proposed for day-ahead price forecasting [13]. Proposed new

Data Analytics Load and Price Forecasting in Smart Grid 225

feature strategy for short term load forecasting [17], uses for feature selection are

MI and Neural Network (NN) which remove unnecessary and redundant candi-

dates input. Data analysis is the way of predicting future value, if future stock

price will decreases or increases [18]. To predict the future price used prediction

Table 2. Summary of related work

Techniques used Objectives Dataset Achievement Limitation

DA [1]Peak load

Reduction by

analyzing the

consumption

data of SH

PJM and open

energy

information

Load forcasting Tra d in g o f u se r

satisfaction in

response to the

price for further

boost the saving

MAP, SVT [2]Price prediction EPEX, PJM,

Nord Pool

Electricity price

forecasting

Redundancy in

feature are not

describe

ANN [4]Develop ANN

model for

electricity

forecasting from

existing ANN

model

European Power

Exchange

(EPEX)

Price forecasting Measured on

historical data

and represented

by connection

weight

MLR, SVR, ANN [5]Retrive load

forecasting

Global electricity

forcasting

competition 2012

Load fecasting Data intergrated

attack in other

similer

forecasting feild

NN, SCA, MI [6]Short term Price

prediction

PJM Price forecasting Redundant

feature not

removed

IRH, MI [7]Eﬃcient for price

forecasting

Ontario’s

electricity market

Price Redundant

feature not

removed

DWT, EM I, RVFL [8]Load prediction

of time series

AEMO Load forecasted No good results

for long term

data

RF, Relief-f, GCA,

KCPA, DE-S VM [9]

Price prediction HSEC Price forecasted KPCA cannot

model non-linear

data

SDAs, SVR, ANN [10]Compare SVR

and ANN and

forecast load

City or State of

U.S

Load forecasting Feature reduction

do not remove

SAPSO, ARMA,

KELM [11]

Price forecasting PJM Price forecasted Big data is not

used

IG, MI [12]Best Feature

selection

PJM Price forecasted More reduction

of features,

decreases the

accuracy score

Multi variate MI,

SVR [13]

Feature selection

and price

prediction

AEMO Measure relation

b/w price and

load, Price

forecasted

Redundancy in

features not

eliminated

IBSM, OA, DCANN

[14]

Find the best

parameter

PJM, AEM Price forecasting Limited for both

dataset

NB, ANN [17]Predict future

Price using

prediction

concept

Logs from yahoo

ﬁnance and store

in stock market

Price forecasting This method can

not be use for big

data

BR, NN, TB, GPR,

MLR [18]

Predict future

cooling load

WSHP Load forecasting Error arise

because of

weather change

226 A. Tahir et al.

concept. NB classiﬁer use for prediction concept. Six performance indicators were

made for use to assess the prediction performance of 6 models [19]. In simulation

results display that precision of TB, GPR, NN, MLR and MAPE are compare

for load forecasting (Table 2).

3SystemModel

Our proposed system consist of many steps such as: preprocessing of data and

splitting by training and testing, feature selection by RFE and FCBF, Feature

extraction by MI, and forecasting of load and price oerformed by three techniques

NB, LR and ELR shown in Fig. 1.

Fig. 1. System model

3.1 Preprocessing

For electricity load and price forecasting, it is necessary to collect load and

price data that reﬂect the power usage of real world. In propose system model,

Locational Marginal Price Pennsylvania, Jersey, Maryland (LBMP PJM) 2015

to 2017 market dataset is used for load and price forecasting [20]. Three years

data is used and divided month wise, i.e. January 2015, January 2016, January

2017 etc. this dataset is a regional transmission organization, which is managed

by system operator, also responsible for whole sale energy market operations.

Data is categorized into three steps as training, validation, and testing. First

three weeks of month are used as training and last week for testing.

3.2 Methodology

We present two techniques RFE and FCBF method for feature selection. RFE

removes the weakest feature until the speciﬁc number of feature is reached. FCBF

works sequentially, where one feature is selected and then unusable features are

removed by the selected one. FCBF is not use as single algorithm, however

we combine other classiﬁer with RFE for feature selection. MI that measure

the dependency between two variable train for each data, extract the selected

feature and remove the redundancy. After that Feature selection and extraction

have normalized data. The output of all features are combined and classiﬁed by

Data Analytics Load and Price Forecasting in Smart Grid 227

NB and LR, when all weakest features are removed until the speciﬁed feature

is received and then formulate ﬁnal prediction. We enhance LR to get better

result. Proposed model procedure can be concluded as:

•RFL and FCBF use for select the feature and MI to extract each feature into

several inputs.

•NB and LG used as classiﬁer for each obtained sub-series.

•ELR used to comparison with these classiﬁers.

•The load data is split and normalized into categories as train, validation and

test.

•Training data is used for train the network and tested on validation data.

•Errors of prediction are calculated on data for validation.

•When network is tuned then update on new data.

•The network is tested on data, and predict the load and price. Prediction

performance is performed by RMSE, MAPE, MAE, and MSE.

4 Description of Forecasting Techniques

Forecasting the load and price many techniques use such as RFE, MI, FCBF,

NB and LR. Description of these techniques are as follows:

4.1 RFE

RFE is feature selection method that ﬁts the model and remove the weakest fea-

ture until speciﬁc features are receive. RFE used to ﬁnd best number of feature,

cross validation and calculate the diﬀerent feature subset and select the best col-

lection of feature. Feature is selected in RFE by resourcefully considering smaller

set of feature. Firstly RFE model ﬁts on data, after that we have many features

and its importance. We drop the feature with least importance, and then our

model ﬁts on the remaining feature. Process is repeated many times until we get

best feature.

4.2 MI

MI used to detect the most applicable feature with less inessential information

and measure the quality between two random variables [14]. Two random vari-

able are a and b, which can be explained the information of b that we get by

studying a. a and b denoted by (a; b) as continuous variable. Deﬁned as joint

probability distribution P (a; b) and individual probability distribution P(a) and

P(b).

SC =a1,a

2,a

3...an(1)

Where SC is set of conditional value and b is variable for forecasting. Appli-

cability of each input variable aiwith target variable b, which is denoted by

Q(ai).

Q(ai)=|(ai;b)|(2)

228 A. Tahir et al.

For example, if a and b are not dependent to each other, then b does not give

any information about a. so their mutual information can be zero.

4.3 FCBF

FCBF method is used for feature selection. Feature selection involves discrete

expression before calculating the feature. FCBF have two categories ﬁlter and

wrapper method. Filter method depend on the training data that select the fea-

tures without including the training data. The wrapper methods depend upon

the proposed algorithm in the feature selection and used to calculate and deter-

mine that which feature is selected. In ﬁlter method, use learning algorithm

from feature selection is RFE which work with SVM and use eﬃciently because

it show the dependency of them. In wrapped method, we use MI to guide the

search process to weight the feature.

4.4 NB

Naive Bayes is classiﬁcation technique depend on bayes theorem. NB classiﬁer

assume that the existence of speciﬁc feature in a class is separated to the exis-

tence of other feature. Bayes algorithm is used to calculate the posterior property.

NB easy to construct and useful for very large dataset. NB also perform well in

multi class forecasting. When assumption independent holds, NB perform better

than other model such as logistic regression.

4.5 LR

Logistic Regression used for evaluate the dataset in which there are many vari-

able that regulate an outcome. The outcome is measure with binary variable

in which there are only two dependent variables on outcome (true or false).

Algorithm 1. Algorithm of Naive Bayes.

Require: Input: [Training data P]

1: (F=(F1,F

2,F

3......Fn)) value of predict variation in the test data

2: Output: [Class of testing dataset]

3: Read the Training data P

4: Calculate the mean and Standard derivation

5: Predict the variable in each class

6: for i=1toPopulation do

7: Calculate the probability of Fi using distribution of each class;

8: Until the probability of all predictor variable;

9: (F1,F

2, ...Fn) has been calculated;

10: end for

11: end for

12: Calculated the probability of class

13: achieved the greatest result

Data Analytics Load and Price Forecasting in Smart Grid 229

LR generates combination of formulas to predict the logit transformation of the

probability that being the characteristic of interest. LR algorithm use as perfor-

mance baseline because easy to implement many task.

Algorithm 2. Algorithm of Logistic Regression.

Require: Input: [Initialize the prediction as t=0 tow=0]

1:

2: for t=1,2,3, ...n do

3: Compute the prediction gradient for (Xi);

4: For each example (Xi,Y

i);

5: For each non Zero feature of Xi with index (Xj);

6: if j is not w, set w[j]=0 then

7: set w[j]=w[j]+((Yi−Pi)Xj);

8: end if

9: end if

10: Update F

11: end for

12: end for

13: iterate to the next step until it is time to stop

14: Output: [of the feature is W.]

5 Results

Simulation results performed by python, daily electricity load data of LBM PJM

are taken of three year as input data for simulator. To achieve the accuracy of

load and price forecasting we are using three years electricity load and price data.

FCBF and RFE are used for feature selection. We apply these two techniques

which give us feature importance, control and grade of our feature. Every feature

in feature selection have sequence like vector. After feature selection we apply MI

for feature extraction. Mutual information measure the dependency between two

variables that used for training the data. To remove the redundancy of selected

feature we use MI. Feature that has eﬀect on exact point are removed. After that

load and price data is normalized, Then we apply NB, LR and ELR classiﬁer on

Fig. 2. Normalized load and price

230 A. Tahir et al.

load and price data. Data is divided into month wise and split into categories i.e.

train, validate and test. After that network is tuned and validated, then network

is tested the data. When we test the data then load and price is forecast.

5.1 Load Forecast

Firstly load data is used for training the forecast model. Data is splitting into

training and testing in which training is 225% and testing is 75%. Figure 2shows

normalized load and price forecasting. Figure 3(a) Show one week prediction,

Fig. 3(b) Show one month prediction and Fig.3(c) show all nine months (January

2015 to March 2015, January 2016 to March 2016 and January 2017 to March

2017) prediction. All the similar months data are trained in the same pattern. we

are comparing NB, LR with ELR for better prediction. Accuracy of NB is 80%,

LG 82% and ELR 85% shows that our proposed technique ELR beats other two

techniques.

5.2 Price Forecast

Price data is taken to forecast the price. Figure 4(a) Show one week prediction,

Fig. 4(b) Show one month prediction and Fig.4(c) show all nine months (January

2015 to March 2015 etc.) prediction. All the similar months of the data are

trained in the same pattern. These graphs show that ELR performing better

than NB and LR. Accuracy of these techniques show that NB has 78%, LG 81%

and ELR 84%.

Fig. 3. Fig (a) shows one week prediction, ﬁg (b) shows one month prediction, ﬁg (c)

shows nine months prediction

Fig. 4. Fig (a) shows one week prediction, ﬁg (b) shows one month prediction, ﬁg (c)

shows nine month prediction

Data Analytics Load and Price Forecasting in Smart Grid 231

6 Performance Evaluation

To measure the performance of load and price four indicators are used as: Root

Mean Square Error (RMSE), Mean Average Percentage Error (MAPE), Mean

Square Error (MSE) and Mean Absolute Error (MAE). Figure 5(a) shows the

comparison of load prediction and Fig. 5(b) shows the comparison of price pre-

diction. MSE has the lowest error value in ELR i.e., 0.784 in price forecasting

and 0.723 in load forecasting. Formulas of MAPE, RMSE MSE and MAE are

given in Eqs. 3,4,5and 6.

MAPE =1

T

T

n=1

|(s−Ys)|(3)

RMSE =

1

T

TM

tm=1

(Av −Fv)2(4)

MSE =1

T

TM

tm=1

(Av −Fv)2(5)

MAE =N

n=1 |(Fv−Av)|

N(6)

Where AVis test value at time t and Fvis predicted value at time t. MSE has

less error than MSE, MAE and RMSE. Experimental results show that ELR

have better because it shows less error than other performance matrics.

Fig. 5. Error value comparison of load and price

7 Conclusion

In this paper, three year LBM-PJM 2015 to 2017 market data is taken for forecat-

ing the load and price. The proposed model comprises form data preprocessing,

selection, extraction and classiﬁcation. We combine FCBF and RFE for feature

232 A. Tahir et al.

selection and MI for Extraction. After selection of our selected feature, we fore-

cast load and price with NB, LR and ELR techniques. We compare our proposed

technique ELR with NB and LR to get better result. Experimental results prove

the eﬀectiveness of proposed ELG technique in forecasting. ELR beats other tech-

niques in term of forecasting accuracy. ELR, LR and NB techniques accuracy is

84%, 82% and 80%. Numerical results show that ELG based forecasting model

has lesser in MSE and MAPE than NB and LG. The feasibility of proposed ELR

model is conﬁned by its performance that is well known in our data.

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