Avoiding Electricity Theft using

Smart Meters in Smart Grid

By

Muhammad Anas

Registration Number: CIIT/FA10-REE-041/ISB

MS Thesis

In

Electrical Engineering

COMSATS Institute of Information Technology

Islamabad - Pakistan

Spring, 2012

COMSATS Institute of Information Technology

Avoiding Electricity Theft usingSmart Meters in Smart Grid

A Thesis Presented to

COMSATS Institute of Information Technology Islamabad

In Partial fulfilment

of the requirement of the degree of

MS (Electrical Engineering)

By

Muhammad Anas

CIIT/FA10-REE-041/ISB

Spring, 2012

ii

Avoiding Electricity Theft using Smart Meters in Smart Grid.

A Post Graduate Thesis submitted to the Department of Electrical Engineering

as partial fulfilment of the requirement for the award of Degree of M.S (Electrical

Engineering).

Name Registration NumberMuhammad Anas CIIT/FA10-REE-041/ISB

Supervisor:

Dr. Nasrullah Khan

Professor,

Department of Electrical Engineering,

COMSATS Institute of Information Technology (CIIT)

Islamabad Campus

June,2012.

iii

Final Approval

This Thesis titled

Avoiding Electricity Theft using

Smart Meters in Smart Grid

By

Muhammad AnasCIIT/FA10-REE-041/ISB

Has been approved

For COMSATS Institute of Information Technology, Islamabad Campus.

External Examiner:Name:

Supervisor:Dr.Nasrullah Khan/ Professor

Department of Electrical Engineering, Islamabad Campus.

Co-Supervisor:Dr.Nadeem Javaid/ Assistant Professor

Department of Electrical Engineering, Islamabad Campus.

HOD:Dr.Shafayat Abrar/ Associate Professor

Head of Department of Electrical Engineering, Islamabad Campus.

iv

Declaration

I Muhammad Anas Registration number: FA10-REE-041/ISB hereby declare thatI have produced the work presented in this thesis, during the scheduled period ofstudy. I also declare that I have not taken any material from any source exceptreferred to wherever due that amount of plagiarism is within acceptable range. Ifa violation of HEC rule on research has occured in this thesis, I shall be liable topunishable action under the plagiarism rules of the HEC.

Date: Signature of the student:

Muhammad AnasFA10-REE-041/ISB

v

Certificate

It is certified that Muhammad Anas, FA10-REE-041/ISB has carried out all thework related to this thesis under my supervision at the Department of ElectricalEngineering, COMSATS Institute of Information Technology, Islamabad Campusand the work fulfills the requirement for award of MS degree.

Date: Supervisor:

Dr.Nasrullah Khan/ Professor,Department of ELectrical Engineering,CIIT Islamabad Campus.

Head Of Department:

Dr.Shafayat Abrar/ Associate Professor,HoD Electrical Engineering.

vi

DEDICATION

Dedicated to my Loving Parents.

vii

ACKNOWLEDGEMENTS

I am heartily grateful to my supervisor, Dr. Nasrullah Khan, whose patient en-couragement, guidance and really nice to me from the beginning to the final levelenabled me understanding of the thesis.

I offer my profound regards, blessing and express my deepest sense of gratitudeto my co-supervisor, Dr. Nadeem Javaid for his noble guidance, tremendous co-operation and help me in any respect during the completion of my thesis.

I wish to express my sincere thanks to my father, who guided me and helped mein my mathematical work. I very much honors all my fellows and friends whohelped me and discussed issues with me in a very good way.

Special thanks to my co-supervisor, Dr. Nadeem Javaid, who offered much as-sistance regarding publications in my current thesis. I deeply appreciate yoursupport. Thank you so much. I am also thankful to all my good teachers fromwhom I learned many things including studies and real guidance of everyday life.

Muhammad AnasFA10-REE-041/ISB

viii

ABSTRACT

Global energy crises are increasing every moment. World is trying to shift fromnon-renewable energy resources towards renewable energy resources. Every onehas the major attention towards more and more energy production and savingit, that is to minimize loss or miss use of electrical energy. Electricity can beproduced through many ways. In hydro power plants, after electricity production,it is synchronized on a single bus bar, than allowed for transmission from theswitch yard. Main theme is to study losses in electrical system. Generation andtransmission losses are considered technical. They can be calculated easily. Whereas i am interested to find non-technical or commercial losses. To find out non-technical losses, ways and methods of non-technical losses are important to know.Causes and effects of electricity theft is one other important point. If governmentprovide subsidy and incentives to its users commercial losses can be minimized toa great deal.

There are different kinds of energy meters. Smart meter can be the best option tominimize electricity theft, because of its high efficiency, accurate and precise resultsand excellent resistance towards many of theft ideas in other energy meter, that isit has high security than other electromechanical meters. Behind Smart meters aninfrastructure must be present to support smart meters, that is to handle the datasafely for further process of billing etc., to the grid or utility system. Data can besent through wireless and wired connections. Under ground fiber optic cable can beused for data transmission. Using different methods of regression model, includingfitting regression line model, non-parametric test, Spearman’s rank correlationcoefficient test, Karl Pearson’s correlation test, and hypothesis testing methods.I have compiled practical data through these methods, compared results of thesedifferent methods. As there are other different classification techniques as well,like optimum path forest tree based algorithm, support vector machine(Linear orRadial basis function), genetic algorithm and linear programming techniques etc.

ix

Contents

1 Introduction 1

1.1 Overview of problem . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Goals And Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Major Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Smart Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.5 Other Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.5.1 Multi-tarif meters . . . . . . . . . . . . . . . . . . . . . . . . 6

1.5.2 Time of Use Meters . . . . . . . . . . . . . . . . . . . . . . . 6

1.5.3 Pre-payment meters . . . . . . . . . . . . . . . . . . . . . . 7

1.5.4 Energy meters in Pakistan . . . . . . . . . . . . . . . . . . . 8

2 Electricity Theft Issues, Methods, and Data Communication to

Utility 10

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.1 Electromechanical Meters . . . . . . . . . . . . . . . . . . . 11

2.2 Related Work and Motivation . . . . . . . . . . . . . . . . . . . . . 12

2.3 Losses Due To Electricity Theft . . . . . . . . . . . . . . . . . . . . 13

2.3.1 Theft in Electromechanical Meters . . . . . . . . . . . . . . 18

2.3.2 Theft in smart meters . . . . . . . . . . . . . . . . . . . . . 19

2.3.3 Engineered ways of Theft . . . . . . . . . . . . . . . . . . . 21

2.4 To Communicate Data To Utility Safely . . . . . . . . . . . . . . . 21

2.5 Causes And Effects Of Electricity Theft . . . . . . . . . . . . . . . 24

3 Regression Based Technique for Estimating Electricity Theft 26

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2 Related Work and Motivation . . . . . . . . . . . . . . . . . . . . . 28

3.3 Techniques for Estimating Electricity Theft . . . . . . . . . . . . . 28

3.3.1 Fitting a Regression line . . . . . . . . . . . . . . . . . . . . 29

3.3.2 Non-Parametric Statistical Methods . . . . . . . . . . . . . . 32

3.3.2.1 Spearman Rank Correlation Coefficient Test . . . . 33

x

3.3.3 Karl Pearson’s Approximation . . . . . . . . . . . . . . . . . 36

3.3.4 Hypothesis Testing in Regression Model . . . . . . . . . . . 37

3.4 Linear Support Vector Machine . . . . . . . . . . . . . . . . . . . . 39

4 Conclusion 44

References 44

xi

List of Figures

1.1 Power Flow in Advanced Metering Infrastructure . . . . . . . . . . 3

1.2 Smart meter basic Configuration . . . . . . . . . . . . . . . . . . . 5

1.3 Single Phase Electronic multi tariff Meter [20] . . . . . . . . . . . . 6

1.4 Peak and off Peak timings in Pakistan . . . . . . . . . . . . . . . . 7

1.5 Basic Time of use meter [21] . . . . . . . . . . . . . . . . . . . . . . 7

1.6 Prepay Electromechanical meter [22] . . . . . . . . . . . . . . . . . 8

2.1 To find lambda using lambda-iteration method . . . . . . . . . . . . 15

2.2 Month wise Graphical Representation of losses in a populated city

in year 2010-2012. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 Neutral Grounded . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4 Communicating Data To Utility . . . . . . . . . . . . . . . . . . . . 23

3.1 Capacitor coupled voltage transformer [www.wikipedia.com] . . . . 28

3.2 Regression Line fitted on Data of 2010-2011 . . . . . . . . . . . . . 33

3.3 Regression Line fitted on Data of 2011-2012 . . . . . . . . . . . . . 34

3.4 Linear data classification . . . . . . . . . . . . . . . . . . . . . . . . 40

3.5 Linear data classification with slack variables . . . . . . . . . . . . . 43

xii

List of Tables

2.1 Energy Losses in year 2010 till 2012, Data taken from Lahore Elec-

tric Supply Company . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1 Energy Losses in a populated city of Lahore Pakistan in year 2010

till 2012[www.lesco.gov.pk] . . . . . . . . . . . . . . . . . . . . . . . 30

3.2 Regional Progressive energy Losses as updated on 29-02-2012 on

www.lesco.gov.pk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3 Showing ranking of data . . . . . . . . . . . . . . . . . . . . . . . . 36

xiii

Chapter 1

Introduction

1

1.1 Overview of problem

As Pakistan is an economically week country and we cannot beer any type of

loss in our economic resources due to any reason that may be frauds, corruption,

stealing which can damage our country. Every individual has to do something

for his/her country for its well being. I have discussed the problem of electricity

theft in many aspects. We must know electricity flow for studying theft in a

power generation point, while transmitting it through high power lines, or while

distribution. Generally theft is carried out at distribution level, however it is

possible to steal electricity at any stage. For that extra knowledge and experience

is needed, as stealing at transmission level is very risky. Because Power is generated

at low voltage it is stepped up at power generation level. Maximum voltage

bearing system in Pakistan is 500kV. So voltage is stepped up to 500kV in step

up transformer at transformer deck in a power generation system. Then this

power is transferred to the switch yard, from where it can be ready to send it

for transmission through high energy power lines. Power transmission has many

stages, it can be transmitted in 500kV, 220kV, 133kV, 66kV, even 33kV, but 66kV

and 33kV are almost obsolete now a days, because of system up gradation. Few of

grid stations of 66kV and 33kV are still in a working condition in Azad Kashmir.

As electricity in usable form must have the specific voltage value that is 220V

in Pakistan because all devices are made for this specification to work on, while

current drawing capacity of every device is different. This is the reason due to

which theft is generally performed at distribution level, where voltage is already

stepped down to 220V. Following is the power flow diagram which tells the whole

story explained above.

There are different kinds of transformers for different purposes, as at power gen-

eration step up transformer is used, at primary grid station where input voltage is

500kV and output voltage can be any voltage like 220kV, 133kV, or 220V, depend-

ing on the situation different power transformers are used. These are all step down

transformers, varying capability of stepping voltage down. Power transmission is

done in three phase three wire system, while distribution of power is generally

done in three phase four wire system, which are shown in above figure 1.1.

1.2 Goals And Objectives

In Electric power system development and usage of IT based system instead of

manual system is need of the day, because of its efficiency, stability, accuracy and

2

Figure 1.1: Power Flow in Advanced Metering Infrastructure

timely operations. It has many advantages as less men power and effort is required

to operate the whole system. it is cost effective because once system is installed

it will work for a larger period of time, though it would need maintenance but

not as frequently as now a days manual system requires. Thus we can say that

it is cost effective as well. Time is one other factor which is more important,

and we can save that as well, if we have smart meters installed instead manual

electromechanical meters. This system would be error free, that is chances of error

will be minimum. Smart meters can be controlled remotely from a grid station

or utility. Its reading will be accurate and precise, because clerical mistakes will

also be minimized, that is delayed meter reading by the meter readers, unable to

take certain meter readings, incorrect meter readings, and rounding of data by the

meter readers. Reading taken automatically are more accurate and precise than

a manual meter readings, that is they are free of errors. Data will not be lost in

3

case of installing a smart meters. Processing of that data for further process like

billing process it will also be in time and accurate. Remote security can also be

established, and billing can be made even if employees are on leave, and billing

process will not be effected. Data stored at the servers in the utility can be further

easily used in experiments and research work, because it is easy to manipulate.

1.3 Major Functions

Major functions performed if existing system is changed to the advanced system

of power grid, called smart grid. Smart grid consists of advanced metering in-

frastructures, which includes smart meters. This system has function of remote

controlling and monitoring from grid or utility, that is remote on/ off of any de-

vices at homes or at industry, or we can turn the smart meter off completely if it

is assumed that meter is being miss used, an illegal means of electricity is being

taken. We can record meter readings on a cell phones, if we use GSM. We can still

perform on/off operations from a cell phones through SMS messages, and through

emails as well. We can update the data on a web site as well from control centers

in the utility grid.

1.4 Smart Meter

A smart meter record consumption of power every after one hour and communicate

that information to the distribution company for billing purpose. It performs

following main functions:

• Register electricity both generated and consumed.

• Offer possibility to read meter both remotely and locally.

• Have the ability to read nearby or consumer premises gas and water meters.

• Control electricity consumed by consumer.

• Switch the consumer of remotely.

Smart meters communicate by means of modem. Power line carrier (PLC), wire-

less modem (GSM/GPRS) and ADSL are the communication interfaces which

connect home appliance and display of the meter. Display is used to show energy

consumption and corresponding cost. From the above discussion it is quite clear

that smart metering provide following benefits such as:

4

• Reliability of supply.

• Variable tarif scheme to attract the attention of new customers.

• Metering cost be reduced.

• Power saving.

• Detection of power theft and fraud.

Domestic, commercial and industrial users waste energy and use energy too much

of their sanctioned load. This misuse of energy can be controlled by smart meter-

ing. Because if the power flow exceeds for a certain time then smart meter will

cut of the power supply and restored when the power comes to its prescribed lim-

its. This feature will greatly help to accomplish the government goals regarding

energy.

The great challenge faced by the distribution companies is to replace all old me-

ters by smart meters and also to update their system. Because in smart metering

continuously data being received, processed and transmit. If smart metering is

done then distribution companies easily find/locate the region where power con-

sumption is high and easily controlled or managed. Smart metering easily reduces

the cost of meter reading, billing collection and labor to disconnect the faulty

consumer. It will also improve billing accuracy, tighter billing and collection and

reduce power theft.

Basic configuration of smart meter is shown below in figure 1.2:

Figure 1.2: Smart meter basic Configuration

5

1.5 Other Meters

Instead of electromechanical meters and smart meters certain other kind of meters

are also used

1.5.1 Multi-tarif meters

Distribution companies think that it is not cost effective to charge from the con-

sumer at the same rate during a period of high demand as they charge the con-

sumer during a period of low demand. They decided to charge the consumer at

different rates during different period of time. Thus multi-tariff meters are intro-

duced to charge different amount for different period of time. They are mostly

industrial meters. Generally they are introduced at the premises where load is

above 5 KW. These multi-tariff meters have ”peak” and ”off-peak” tariff register.

Such type of meters are also called time of use (TOU) meters. These have time

register and also have other register in it. Single Phase electronic multi tariff meter

is shown below in figure 1.3.

Figure 1.3: Single Phase Electronic multi tariff Meter [20]

1.5.2 Time of Use Meters

Time of use (TOU) meters basically divide the day according to the load demand.

The period of high demand is called peak hour and during this period, the dis-

tribution company charge consumer at high rate. The remaining period is called

6

off peak and during this period consumer is charged at relatively low rate. The

basic purpose of this is that the consumer automatically controls the consumption

of electricity and pay accordingly. The peak and off peak hours in Pakistan are

listed in table above:

Figure 1.4: Peak and off Peak timings in Pakistan

Figure 1.5: Basic Time of use meter [21]

1.5.3 Pre-payment meters

The distribution companies install prepayment meters at such a premise, where

they think that the consumer will creates problem in billing. Some consumers

wish to install prepayment meters because it will greatly help them to manage

the budget. In such type of meters, advance mode of payment is made just like

in mobile phones. When the amount for which you purchase electricity vanished/

end then the relay will cut of the supply. Prepayment meters are of three types:

7

• Smart card meters.

• Key meters.

• Token meters.

The tariff of these prepayment meters is much high because it includes fixing and

maintenance charges and also it includes the cost of collection of money from pay

points or from post offices.

Figure 1.6: Prepay Electromechanical meter [22]

1.5.4 Energy meters in Pakistan

Our distribution companies take energy meters from both national and interna-

tional companies. Some of the major energy meter supplier companies are as

follows:

• Pak-Elektron Limited.

• MicroTech Industries (Pvt.) Ltd.

• Syed Bhai (Pvt.) Ltd.

• Creative Engineering Group Lahore.

8

• S.B. Electronics and Control Engineering.

• ESCORT Pakistan Ltd. Lahore

9

Chapter 2

Electricity Theft Issues, Methods,

and Data Communication to

Utility

10

2.1 Introduction

Electricity is generated through many ways, is synchronized on a single bus bar

of the grid for transmission. Before utilization of electricity, it passes from certain

phases. It is first generated, step upped in transformer deck, passed from switch

yard for transmission through power lines. After transmission it is distributed for

utilization to the customers. This energy needs to be billed as well. Usually two

types of devices are mainly used for billing procedure.

1. Electromechanical KWh meters.

2. Smart meters.

2.1.1 Electromechanical Meters

Electromechanical meters consists of following parts:

• Counting mechanism

• Serious Electromagnet.

• Shunt Electromagnet

• Brake magnet

• Aluminium rotor disk.

Shunt electromagnet is wound with a fine wire of many turns and is connected

across the supply so that the current flow through it is proportional to the supply

voltage. Since the coil of the shunt magnet has large number of turns and the

reluctance of its magnetic circuit is very small due to the presence of small air gap

which makes the coil highly inductive. Thus the current lags the supply voltage

by 90o. In comparison to its series magnet its wound with a heavy wire of few

turns and is connected in series with the load so that it carries the load current.

Since the coil of series magnet is highly non inductive so that angle of lead or lag

is determined by the load.

Our energy is strained to the utmost now a day, so using energy efficiently is

one of the issues which need urgent attention. That is why electricity is to be

dealt with great care. As for as knowledge is concerned there is no such password

which can not be cracked but best password is the one which is being cracked in

a larger period of time. This is one basic reason that whole world is shifting from

analog devices to digital devices. That is why analog electromechanical meters

are being substituted by smart meters. Digital devices provide better security and

11

controlling options. The better detection and controlling of losses is one of the

reasons for substitution of smart meters.

Every thing occurs for a reason, so the reason for this substitution is losses in

electrical systems. There are mainly two types of losses.

1. Technical losses.

2. Non-Technical/Commercial losses.

In developing countries electricity theft is a common practice specially in remote

areas, as they do not pay utility bills to a government company in case of electricity

and gas as well. To solve this problem governments must think of an idea to provide

help in terms of subsidy to manage this issue.

2.2 Related Work and Motivation

In [1,3] authors explained theft control very well in a sense that they proposed a

model. In this model they calculated NTL in external control section, and if NTL

> 5%, legal customers are disconnected for some interval. Harmonic generator is

operated in this time period, which destroys the electrical equipment of all the

illegal consumers. Reconnect normal supply for genuine customers. Although this

is a good model that electricity theft is an issue that one can make equipments

of an illegal users starts malfunctioning. However this model can be improved to

stop functioning of the equipment of an illegal users, weather using smart meters

or any other technique.

S. McLaughlin et al. explained some of the energy theft in Advanced Metering

Infrastructure (AMI), proposed an idea of a communication architecture from

smart meter to grid using meter to meter communication. For boosting the data

signals using collectors and receptors. It defines this procedure in a network known

as Backhaul network, used to transport data to utility. However energy theft in

smart meters can be a technical person, if he removes the µ-controller from his

meter. It will not be able to measure readings and send it to utility for further

process.

In [4,5] authors elaborated ways of communication, in how many ways we can

transmit the data of smart meter to utility. S. S. S. R Depuru and et. al. shown

how an electromechanical meter works and why is smart meter better than elec-

tromechanical meter.

In [6] central observer meter is placed, which is cost effective because a smart meter

12

is placed at secondary side of transformer. It used matrix based approach in excel

to show electricity theft case and normal case. Where as if large amount of data

has to be managed than larger matrices will be required. Memory requirements

will increase, time consumption to solve large matrices will increase.

[8,9] have some mathematical modeling techniques which helps to detect and con-

trol electricity theft using some classifiers. [8] discussed a Graphical User Interface

(GUI) based software implemented in Malayesia.

2.3 Losses Due To Electricity Theft

Electricity theft is basically an illegal way of getting the energy for different uses,

resulting in loss for utility companies. Losses consist of technical and non technical

losses. There are about $25 billion of losses annually in the world [1]. Losses can

actually be computed by finding the energy supplied, subtracting the amount of

energy billed/paid [3]. If we want to calculate non-technical losses (NTL) simply

one way of calculating it is to calculate technical losses. We can evaluate it as

follows.

Total Energy Losses = Energy Supplied−Bills paid (2.1)

Total Energy Losses = NTL + TL (2.2)

Combining equation 1 and 2, we get

NTL = Energy Supplied−Bills Paid− TL (2.3)

In data 1 shown below in table 2.1. losses occurred monthly in Lahore Pakistan

in the year 2011-12 till February [7]. Percentage losses are calculated as:

Percentage Loss =

(Received V alue− Sold V alue

Received V alue

)∗ 100

As we are intrusted in calculating NTL, we can generally find it from equation 2.3,

as if we have smart meters installed, we would be having data of Energy supplied

recorded in control centers, and bill payments by the consumers, the only factor

left with us unknown in the equation is TL. Now we have to find technical losses

by numerous ways but we can find it by using Lagrang function.

Lagrange function can also be the method to study load flow in electrical power

system toward distribution. Lagrange basic function without losses can be given

as:

13

£ =N∑i=0

Fi + λϕ (2.4)

Where £ is Lagrang function,∑N

i=0 Fi is a cost function, λ is a Lagrangian mul-

tiplier.

ϕ = 0 =

[Pd −

N∑i=0

Pgi

](2.5)

£ =N∑i=0

Fi + λ

[Pd −

N∑i=0

Pgi

](2.6)

d£

dPgi

=dFi

dPgi

− λ = 0 (2.7)

Taking derivative of equation 2.6 to solve it for the generation cost of certain

operating unit, we get equation 2.7, equating it to zero. It can be the approach

for finding technical losses in one way as if we consider above equation 2.6 including

losses it will be given as:

£ =N∑i=0

Fi + λ

[Pd + PL −

N∑i=0

Pgi

](2.8)

Now taking derivative of equation 2.8, we get the following equation in terms of

losses.

d£

dPgi

=dFi

dPgi

− λ

(1− ∂PL

∂Pi

)= 0 (2.9)

dFi

dPgi

+ λ∂PL

∂Pi

− λ = 0 (2.10)

dFi

dPgi

+ λ∂PL

∂Pi

= λ (2.11)

∂PL

∂Pi

= 1− dFi

λdPgi

(2.12)

Integrating both sides, we get the following to find out TL = PL.

14

PL =

∫ (1− dFi

λdPgi

)Pi (2.13)

Further we can find the value of λ using lambda iteration method, the flow chart

for finding lambda is given below:

Figure 2.1: To find lambda using lambda-iteration method

As i mentioned earlier that Lagrangian function method can be used for load flow

analysis for economic dispatch of power from utility to the distribution or con-

sumer level. Certain other methods are also used for economic dispatch including

Gradient search method, Newton‘s method, and dynamic programming methods.

Several methods are used to identify electricity theft using certain mathematical

methods like Support Vector Machine LINEAR (SVM-LINEAR), Support Vector

Machine- Radial Basis Function (SVM-RBF), Artificial Neural Network- Multi

Layer Perceptrons (ANN-MLP), Optimum Path Forest classifier (OPF) [8]. SVM

is a regression based technique, in which dependent and independent variables are

considered. It defines certain parameters to define a graph or compare it to the

standard data or graph. In this method special kind of theft are recognized. If

there occurs an abrupt change in load flow it notify that change and store that

data as faulty one [7].

Their is one other technique ANN-MLP which is based on modeling techniques,

obeys some of non-linear statistical modeling or tree diagram. Other part of it is

MLP which is a type of linear classifier and selects better output among outputs

15

from its input.

Ramos, C. C. O et al. proposed OPF based technique [8]. It is an approach in

which better output is replaced for the previous value selected to reach to identify

theft. It needs no parameters to be assumed. Its training phase operation is very

fast, an overview is tested by [8] and showed that an OPF has a higher hit rate of

theft and having more accuracy than SVM-LINEAR, SVM-RBF, and ANN-MLP

[8].

16

Table

2.1:Energy

Losses

inyear2010till2012,Data

takenfrom

Lahore

ElectricSupply

Company

Month

sJuly

Aug

Sept

Oct

Nov

Dec

Jan

Feb

2010-2011

Energ

y(M

KW

H)

Rece

ived

1764.81

1777.29

1518.89

1461.89

1136.25

1179.97

1169.85

1058.03

Sold

1508.41

1513.76

1311.82

1282.98

1047.91

1060.11

1057.74

1009.38

PercentageLosses

14.53

14.83

13.63

12.24

7.77

10.16

9.58

4.60

2011-2012

Energ

y(M

KW

H)

Rece

ived

1693.09

1768.82

1570.68

1509.01

1199.71

1179.12

1127.43

1140.52

Sold

1449.12

1510.51

1365.99

1329.63

1106.89

1115.94

1024.03

1085.20

PercentageLosses

14.41

14.60

13.03

11.89

7.74

5.36

9.17

4.85

Decrease

0.12

0.22

0.60

0.35

0.04

4.80

0.41

-0.25

17

July Aug Sep Oct Nov Dec Jan Feb1000

1200

1400

1600

1800

Rec

eive

d va

lues

vs

Sol

d va

lues

(a) Data of 2010−2011

July Aug Sep Oct Nov Dec Jan Feb1000

1200

1400

1600

Rec

eive

d va

lue

vs s

old

valu

es

(b) Data of 2011−2012

Figure 2.2: Month wise Graphical Representation of losses in a populated city in year2010-2012.

Decrease or difference between 2010-2011 and 2011-2012 can be found out by

subtracting the value of the present year from the previous year in table 2.1. and

graphically shown in figure 2.2. 1

There are certain methods of stealing electricity. The core reason of stealing is

lack of awareness amongst the peoples, due to which this unpleasant act is being

performed in different areas of the world. Meter tempering can be done in elec-

tromechanical meters and smart meters as well. Tempering in electromechanical

meter is explained in detail below.

2.3.1 Theft in Electromechanical Meters

Few methods of stealing electricity are

• Taking connections directly from distribution lines.

• Grounding the neutral wire.

• Putting a magnet on electromechanical meter like neodymium [1].

• Inserting some disc to stop rotating of the coil.

1Area of a city = 684 sq mile , Population of city = 11,000,000

18

• Hitting the meter to damage the rotating coil [2].

• Interchanging input output connections.

But these disputed issues can be minimized by using the smart meters. Even

in smart meter, one can take connections directly from distribution system but

smart meters have the ability to record zero reading. It inform the utility system

by sending data through different techniques. These techniques include bluetooth,

Power Line Carrier (PLC), Internet protocols. Session Initiation Protocol (SIP)

can be used for controlling of Voice over Internet Protocol (VoIP), Zigbee 802.15.4

can be used in Home Area Networks (HANs) [4].

In second point if we ground neutral wire then energy meter assume the circuit

is not complete and does not measure reading. As we know that moving coil in

electromechanical meter can be easily affected by magnetic field lines. So if we put

a magnet on electromechanical meter its magnetic field effects the coil motion and

cause it to move slow, or even stop if magnet is strong magnet like neodymium. If

someone insert an x-ray disc in electromechanical meter, it also interact with coil

and affect its performance. Hitting meter shows same results by damaging coil in

electromechanical meter. In last point interchanging input output connections in

electromechanical meter starts moving in reverse direction, which is also a method

to produce less reading, till end of the month.

2.3.2 Theft in smart meters

Smart grid is a very generalized word, it includes diverse kind of sub-infrastructures.

One of the important infrastructures is AMI discussed in [2]. Due to many ad-

vantages of AMI, every community has the desire to install this system for its

ease. AMI is an infrastructure which has many function but it can also be used

to control electricity theft. AMI is an infrastructure and smart meter is an entity

which can be placed at each and every home/industry, replacing electromechanical

Kilo-Watt hour (KWh) meters.

AMI provides a new sensor based approach. If sensors are installed in the electrical

equipment, then AMI can be useful in a way that utility or power distributing

companies can predict load of a specific area. This is useful for utility in a way that

they will design a correct and efficient load flow to certain area. This technique

is efficient to save many of economic issues for installing an infrastructure for any

area.

Smart meter is a digital device, uses µ-controller and certain other digital instru-

19

Lamp 1 Lamp 2

Energy Meter

Phase

Neutral

Main Switch

Incom

ing E

lect

ricity

To E

nerg

y M

ete

r

Outg

oin

g E

lect

ricity

T

o U

ser

Neutral Grounded

Figure 2.3: Neutral Grounded

ments. Function of smart meter includes.

1. Self billing.

2. Avoid outages in HAN’s.

3. Remote connect and disconnect.

4. Remote authentication like sending control messages

While authenticating, data tempering occurs, using software hacking. False au-

thentication can be used to authenticate the password and hack the data from

smart meter.

Some hardware hacking, specially designed for fraud purposes are also designed

by professionals like descrambler boxes, which reads data from smart meters and

are used for illegal purposes.

Time of use capability is also present in AMI, like billing during peak load must

be little higher than billing in an off peak load timings.

Methods mentioned for electricity theft in electromechanical meter can be applied

to smart meters as well, except putting magnet of neodymium, inserting disc, or

hitting it, by this mechanical shock the meter does not work properly.

One of the objections from consumer is that smart meters are used as a spy at our

homes. It discloses privacy of our homes, which is not ethically viable. It emits

certain kind of radiations which are toxic and dangerous to humans life. It also

interferes radio frequency and create problems in radio transmissions to people.

Mobile police also uses radio frequency which is interrupted by emission of smart

meters [2].

20

2.3.3 Engineered ways of Theft

Some of the sophisticated ways of stealing electricity [3] are

1. Tempering the current transformers (CT) secondary side of the energy me-

ter,it is generally insulated. where CT’s are used to measure current flowing

through it. If any one temper CT, then it will not be able to measure cor-

rect current passing from energy meter to the consumer or it will record slow

readings.

2. Internal calibration of electromechanical energy meter is not correct; the coil

used in it is not calibrated correctly.

3. In three phase meters if neutral is kept open, and only one out of three

phases is used, than electromechanical meter assume that no energy is flow-

ing through it to the customer. These kind of thefts are easily detected in

smart meter by an option of “EL” glowing.

EL is an option in smart meter, whose Light Emitting Diode (LED) when flashes

shows certain points, such as the miss match between the phase and neutral current

is detected by Earth Leakage (EL) LED.

• “EL” glows in smart meter means either neutral of your home is connected

to the neutral of your neighbors or vice versa.

• Phase of your home is connected to the phase of your neighbors or vice versa.

• Neutral is connected to the ground.

If this “EL” LED flashes, it will also be visible to the utility, so utility can check

the problem manually to control theft.

2.4 To Communicate Data To Utility Safely

Communicating to utility follows a step wise procedure. Smart meter has the

ability to measure the energy flowing through it, records the values using micro

controller. it updates the values in its registers, but if there occurs any problem in

wireless data transfer, it will re-check wireless device. Resolve the issue and and

re-update data in smart meter as shown in fig. 2. One of the technical way of theft

is to make a meter read slow. If partial electricity is taking by an illegal means,

and high energy consumption devices like motors are operated by that electricity.

These theft can be examined and checked physically to make all devices operate

through legal connection. After that data will be transferred to utility with out

21

letting an intruder to hack it or distort it, through descrambler boxes etc. This

data transfer is also an important phase, and it needs attention. Next is to store

data at server and make it available for technical computation, that is billing

procedure, etc.

Smart meter has the ability to measure reading time and again, and send it through

different techniques like wireless data transfer using different protocols. Bluetooth

is one of the method through which we can collect the data from smaller distances

such as we can use Bluetooth for HAN as a metering device which follows standard

protocols of Bluetooth that is 802.15.1. Broadband Power Line communication

(BPL) is another way of communication to the grid, it has certain protocols like

Transmission Control Protocol/ Internet Protocol (TCP/IP). It is an advanced

form of Power Line Communication (PLC), and it uses a radio frequency spectrum.

It causes hurdles in radio communication is one of disadvantage of BPL. Using

wired data lines we can also communicate the data from certain industry or home

to some central device like smart meter and then send the data wirelessly to the

server at utility using Wi-Fi, WiMAX, which follows the standards 802.11g [4].

There are certain other protocols like SIP which supports Voice over Internet

Protocol (VoIP), this protocol controls the video and audio data as well. SIP

also controls few of the other protocols like Transmission Control Protocol (TCP),

Hyper Text Transfer Protocols (HTTP), User Datagram Protocol (UDP). SIP is

a very common protocol and dals with many of other protocols. Zigbee is one

other protocol which can be used for HAN. It uses standards of 802.15.4. Global

System for Mobile communication (GSM), General Packet Radio Server (GPRS)

can be another way to send the data to utility using them [5].

By discussing all these ways of communication there will be a problem of huge

data transfer through these networks. In wired and wireless services which are

using currently IPv4. It uses total of 232 addresses, equivalent to 4294967296.

These addresses are insufficient to control all devices of all homes of the world

including industries etc. On the other hand we have IPv6 which has a total of 128

bits or 32 hex digit code means 2128 addresses in which there is 48 bit for the node

address only, it has a lot of addresses, and we can use them to fulfil requirement

of the said scenario. There is one other approach to transmit the data known as

Power Line Carrier (PLC). If it is applied through optical fiber then this would

be a once and for all investment, and is called as Overhead Power Ground Wire

(OPGW).

It would be feasible for controlling the whole of the data if we use one way com-

munication or two way communication from or towards utility. In two way com-

22

Smart

Meter

Update

Reading

Missing

Slow

Reading

Data Transfer

Data Storage

Record at

Utility Server

Problem in

Wireless Data

Transfer

Re-Check

YesTaking Partial

Electricity By

Illegal Means

Check internal

connections

Physically

Turning off

High energy

Devices

Yes

No

No

Figure 2.4: Communicating Data To Utility

23

munication we have an advantage of turning on and off the smart meter of any

home or industry. Bandim. C. J, et al. proposed an idea of low cost methodol-

ogy of sending the data to the utility, by placing a smart meter on the secondary

side of the distribution transformer, which monitors data of home meters locally,

records the readings, sends data through wireless device, and communicate two

way communication with utility.

2.5 Causes And Effects Of Electricity Theft

Theft is a serious crime, creating short fall, increase of load, decrease of frequency,

which is not acceptable and causing load shedding, increase of tariff on the legal

customers[1].The main reason behind electricity theft are low literacy rate and lack

of awareness. Circular debt is one of the serious consequences of the electricity

theft. It can be explained as electricity power is produced through many ways like

from oil, turbines are operated and produce electricity. So now if oil is supplied

to the utility for their use to run turbines for electricity generation. While utility

is not paying to the oil suppliers, and utility is producing electricity from that oil,

and selling it to customers. Then losses come into act non paying customers, and

theft are also very dangerous, this is what it means that they are not paying the

utility back. So this is the issue which is called as circular debt.

In the third world countries, people are mostly not able to pay their utility bills.

Government can also help deserving people by avoiding the electricity theft thus

providing subsidy to minimize per unit cost. For further improvement in electri-

cal power system respective government needs to give incentives to the capable

people to focus on their own electricity production, like emerging technology for

production of electricity from solar cells, wind power, hydel etc. Fulfil their own

use and sell it to the utility for their own good as well, and be benefited from the

Utility by synchronizing their systems successfully.

Power flow mechanism in AMI shown in fig. 4. can briefly be described as power

is generated at hydro power plants. As control rooms and control sections are

very important part of each and every portion of electricity power generation,

primary substation, and secondary substation. Power generation plant is very

important part, because whole of electricity is generated at power plants from

water. Head is one important issue. Water head and turbine size are mechanical

portions. Which also needs to be controlled. These all controls are present for

power generation plants on mimic board in control room. Water level is also to

be noticed, flow of water through gates. Water reservoirs are kept in water bays

24

for running turbine at peak hours. For control at power generation and control

at remote areas Supervisory Control and Data Acquisition System (SCADA)is

used. Distributed Control Systems (DCS) is also used for control and supervision

at power generation plants. Power flows towards primary substation through

transmission lines where it is maintained on the grid in control room.

At Primary substation electricity is stepped down to certain limit. Where elec-

tricity could be stolen at any point. At generation less electricity production and

waste of water is also a theft. Where system has the ability to produce more

electricity, than they were producing. Electricity can also be watched on its way

to primary substation. It is quite possible that it could be stolen in a way that is

why control centers are deployed and data is observed time to time. After primary

distribution it is transmitted to secondary substation, where data comes from the

end users, through smart meters or PLC. Home appliances can be controlled using

Zigbee.

25

Chapter 3

Regression Based Technique for

Estimating Electricity Theft

26

3.1 Introduction

According to law of conservation of energy, energy can neither be created nor

destroyed, but only it can be changed from one form to another form. Electricity

is a form of electrical energy, and is obtained from a lot of methods. Now every area

of population has its own seasonal and environmental conditions. Due to which

one can decide the way of getting electricity for prescribed area which would be

efficient and sufficient. The energy planning for certain area can be managed

by different statistical methods and optimization techniques. Computations are

performed to utilize our economic resources in a best way.

Electricity usage is also a main problem to be considered. As, different types of

losses are also constituted with the distribution of electricity to the consumers.

Mainly losses are of two types; technical and non-technical losses. Technical losses

include core or iron losses(hysteresis and Eddy-current losses), copper or electrical

losses etc. Where as non-technical losses include losses that are unauthorized or

illegal means of getting electricity also called stray load losses.

In this thesis, I first collected data of non-technical losses from utility using smart

meters, which are more suitable to minimize the possibility of electricity theft,as

compared to other devices. Then we applied different estimation methods to cal-

culate the variation and dispersion in the data. In [10-12], authors discussed differ-

ent probability and regression analysis based techniques to estimate non-technical

losses. In this thesis, I mainly used regression based approach, Spearman’s rank

test, sign test etc., and also studied how linear support vector machine is used to

classify electricity theft.

Electricity is being generated it is transmitted in 500kV lines and in some countries

it is transmitted through 700kV lines primarily. After long transmission lines it

is stepped down to 220kV lines and then 132kV lines passing through specific

grid stations. Electricity theft in very high voltage and high voltage transmission

lines which is not an easy job to do. It requires a trained personal because our

equipments at home or equipments in industry works on 220V of supply on its

input. Coupling Capacitor Voltage Transformer (CCVT’s) are used for theft on

high voltage transmission lines. It is a simple transformer having three main parts

capacitor, inductor and a transformer which is used to step down a voltage to a

usable range. If theft is taking place on 220kV single phase, disturbance will occur

in transmission lines, and increase of capacitive losses will occur in transmission

lines.

27

Figure 3.1: Capacitor coupled voltage transformer [www.wikipedia.com]

3.2 Related Work and Motivation

In paper [10], authors used a data sets in the form of windows and performed

certain operation on that data to extract their results. Detection of electricity

theft is explained in a way that data samples will be selected first and decision

will be taken that which sample should be tested on which particular method that

is on decision trees, baysien approach or on Karl Pearson’s approach. As a result

theft can be detected during theft processes. They will be merged and refiltered

on the bases of which inspection will be carried out. However, Karl Pearson’s

approach explains relationship of chi square distribution and discrete multinomial

distribution, which is not explained by the authors.

Technical losses in low voltage distribution systems are evaluated by the authors

in [11]. They used regression analysis to estimate electricity theft defining certain

data sets. They considered some data to be independent and some of data which

will depend on the independent variable. Sixteen (16) data sets are defined in

this work in total and checked that data on seven (7) different variables. However

correlation coefficients are not discussed clearly in [11]. In [12] authors discussed

a project of MIDAS.

3.3 Techniques for Estimating Electricity Theft

In this section, to detect special kind of patterns different mathematical mod-

els are discussed. There are certain classifiers that can also be used for detec-

tion. They includes Support Vector Machine LINEAR (SVM-LINEAR), Support

Vector Machine- Radial Basis Function (SVM-RBF), Artificial Neural Network-

Multi Layer Perceptrons (ANN-MLP), Optimum Path Forest classifier (OPF).

28

The ANN-MLP is based on modeling techniques, obeys some of non-linear statis-

tical modeling or tree diagram. Other part of it is MLP which is a type of linear

classifier and selects better output among outputs from its input. [13] proposed

OPF based technique. It is an approach in which better output is replaced for the

previous value selected to identify theft. Advantages of OPF are[13]:

• It needs no parameters to be assumed.

• Its training phase operation is very fast, and has a higher hit rate of theft,

having more accuracy than ANN-MLP.

Certain other programming methods are also used which are Quadratic Program-

ming (QP) and Genetic Algorithm (GA).

3.3.1 Fitting a Regression line

29

Table

3.1:Energy

Losses

inapopulatedcity

ofLahore

Pakistanin

year2010till2012[www.lesco.gov.pk]

Month

sJuly

Aug

Sept

Oct

Nov

Dec

Jan

Feb

Energ

y(M

kW

H)

Rece

ived

1764.81

1777.29

1518.89

1461.89

1136.25

1179.97

1169.85

1058.03

2010-2011

Sold

1508.41

1513.76

1311.82

1282.98

1047.91

1060.11

1057.74

1009.38

PercentageLosses

14.53

14.83

13.63

12.24

7.77

10.16

9.58

4.60

Energ

y(M

kW

H)

Rece

ived

1693.09

1768.82

1570.68

1509.01

1199.71

1179.12

1127.43

1140.52

2011-2012

Sold

1449.12

1510.51

1365.99

1329.63

1106.89

1115.94

1024.03

1085.20

PercentageLosses

14.41

14.60

13.03

11.89

7.74

5.36

9.17

4.85

Decrease

0.12

0.22

0.60

0.35

0.04

4.80

0.41

-0.25

30

We can test data using linear regression model using non parametric test. There

are two types of tests; parametric tests and non-parametric tests. In a former test

we know about the parameters of data including mean and standard deviation etc.

After performing non parametric tests, we can process the data and obtain results.

In later non parametric tests we do not know about any parameter of the data i.e.,

mean and standard deviation. In particular, we take them as parameters of any

statistical data that might be a sample data or a population data. In method of

regression analysis through non parametric test, we would find the average values

of variable x and y. Where x is the data taken for energy generated by power

house or energy consumed, and y specifies values of energy paid back to the utility

in the form of bills. The correlation between x and y is given as:

ρ =σxy

σxσy

(3.1)

where, ρ denotes the coefficient of correlation, σx specifies the standard deviation

of x and σy is the standard deviation of y. We can also right this equation as

follows:

ρ =Cov(x, y)

σxσy

(3.2)

Covariance shows dispersion in data. There are differences between covariance

and coefficient of correlation. One of them is, coefficient of correlation is a unit

less quantity, because it is a ratio, and its range varies from -1 to +1. Covariance

has units and it is based on standard deviation. Covariance can be calculated as:

Cov(x, y) = E[(x− x)(y − y)] (3.3)

where, E is an expectation. The general equation to find out standard equation

is:

σ2 =

∑x2

N−(∑

x

N

)2

(3.4)

Fig. 1 shows data of 2010-11 power consumed to the power sold in a electric

supply company for one year. We fitted a straight line on this data which shows a

regression fitting on the prescribed data. It basically explains deviation from the

fitted straight line which shows deviation i.e., theft values, that specifies dispersion

from the fitted line.

Suppose we have two variables x and y. we can plot them against each other to

obtain a scatter diagram. However if we plot values of x against y we get regression

line. For regression line we will first find a parameter a as follows:

y = a+ bx (3.5)

31

or

y = a+ bx (3.6)

Therefore,

a = y − bx (3.7)

From here we will find the value of a. To find a parameter b the following equation

is given as:

b =n∑

xy − (∑

x)(∑

y)

n∑

x2 − (∑

x)2(3.8)

Putting values in above equation to get value of b. Hence, the estimated regression

line of y on x is:

y = a+ bx (3.9)

R =

√n∑

xy − (∑

x)(∑

y)√[n

∑y2 − (

∑y)2][n

∑(x2)− (

∑x)2]

(3.10)

where, R2 is the coefficient of determination.

Explained V ariation = σ(y − y)2 (3.11)

Total V ariation =∑

(y − y)2 (3.12)

R2 =σ(y − y)2∑(y − y)2

(3.13)

The variability among the value of dependent variable y, called the total variation.

Coefficient of determination which measure the proportion of variability in values

of the dependent variable y, which is explained by its linear relation with the

independent variable x is defined by the ratio R2. Therefore, 96.3 % of y values

on x values are explained, means 3.7% of electricity is being stolen in data used

of 2010-11, shown in Table.1. 1

Non parametric regression based technique is quite a simple technique, however

its results are similar with other computational methods. It can be used for a

large data sets of any utility system, because of its simplicity.

3.3.2 Non-Parametric Statistical Methods

Non-parametric tests are considered to be very good methods for testing hypoth-

esis. Computations involved in these techniques are very quick and easy to carry

out. Second advantage of using non-parametric test is to be clarified from an

1Area of a city = 684 sq mile , Population of city = 11,000,000

32

1000 1100 1200 1300 1400 1500 1600 1700 1800900

1000

1100

1200

1300

1400

1500

1600

Power Consumed

y

Fitting a Regression line

y = 236.783 + 0.69904 * x

Figure 3.2: Regression Line fitted on Data of 2010-2011

example that if we have two judges and they will have to decide first five best

cement industries. Non-parametric methods can be used to find weather there is

an agreement between the two judges or not. Third advantage of using these kinds

of methods is use of less restrictive assumptions than parametric methods. One

of non-parametric methods are used to estimate electricity theft in certain data

as follows.

3.3.2.1 Spearman Rank Correlation Coefficient Test

Sometime the actual measurement or counts of individual objects are either not

available or accurate assessments are not possible. They are then arranged in

order according to some characteristics of intrust. Such an ordered arrangement

is called ranking in the order given to an individual or object is called its rank.

The correlation between two such set of ranking is known as rank correlation.

Let a set of n objects are ranked with respect to characteristicA as, x1, x2, ..., xi, ..., xn,

and according to characteristic b as y1, y2, ..., yi, ..., yn. We assume that no two or

more objects are given to the same ranks (that are tied) then obviously xi and yi

33

1100 1200 1300 1400 1500 1600 1700 18001000

1100

1200

1300

1400

1500

1600

Power Consumed

y

Fitting a Regression line

y = 269.1164 + 0.700225 * x

Figure 3.3: Regression Line fitted on Data of 2011-2012

are some two numbers from 1 to n. Both xi and yi are the first n natural numbers,

therefore,

n∑i=1

x =n∑

i=1

y =n∑

i=1

i = 1 + 2 + 3 + ...+ n =n(n+ 1)

2(3.14)

n∑i=1

x2 =n∑

i=1

y2 =n∑

i=1

i2 = 12 + 22 + 32 + ...+ n2 =n(n+ 1)(2n+ 1)

6(3.15)

n∑i=1

(xi − x)2 =n∑

i=1

(yi − y)2 =n∑

i=1

y2i −(∑

yi)2

n(3.16)

=n(n+ 1)(2n+ 1)

6− n(n+ 1)2

4(3.17)

=n(n2 − 1)

12(3.18)

Let, di denotes the difference in ranks assigned to the ith individual i.e.,

di = xi − yi (3.19)

34

2010-2011 2011-2012Months MKWH %age losses MKWH %age losses Dec

Received Sold Received SoldJULY 1764.81 1508 14.5 1693.09 1449.12 14.4 0.1

AUGUST 3542.1 3022.17 14.7 3461.91 2959.64 14.5 0.2SEPTEMBER 5061.99 4333.98 14.4 5032.29 4325.63 14 0.4OCTOBER 6523.88 5616.96 13.9 6541.6 5655.11 13.6 0.3NOVEMBER 7660.33 6664.87 13 7741.31 6762 12.7 0.3DECEMBER 8840.92 7724.98 12.6 8920.43 7830.96 12.2 0.4JANUARY 10010.15 8782.71 12.3 10047.86 8854.99 11.9 0.4FEBRUARY 11068.8 9792.1 11.5 11188.38 9940.19 11.2 0.3MARCH 12319.5 10858.19 11.9APRIL 13589.53 11937.1 12.2MAY 15261.04 13350.51 12.5JUNE 16964.32 14740.85 13.1

Table 3.2: Regional Progressive energy Losses as updated on 29-02-2012 onwww.lesco.gov.pk

and ∑d2i =

∑(xi − yi)

2 (3.20)

=∑

x2i +

∑y2i − 2

∑xiyi (3.21)

Substituting for∑

x2i and

∑y2i , we get

∑d2i =

n(n+ 1)(2n+ 1)

6+

n(n+ 1)(2n+ 1)

6− 2

∑xiyi (3.22)

where, ∑xiyi =

n(n+ 1)(2n+ 1)

6− 1

2

∑d2i (3.23)

The product moment coefficient of correlation between the 2 sets of ranking is

r =

∑xy − (

∑x∑

y)n√

[∑

x2 − (∑

x)2

n][∑

y2 − (∑

y)2

n]

(3.24)

Substitution gives

rs =

[n(n+1)(2n+1)

6− 1

2

∑d2i

]− n(n+1)2

4

n(n2−1)12

(3.25)

rs = 1− 6∑

d2in(n2 − 1)

(3.26)

The formula is usually denoted by rs. In order to have a distinction. It is called

35

Table 3.3: Showing ranking of data

x x Rank y y Rank di di2

1764.81 11 1508.41 11 0 01777.29 12 1513.76 12 0 01518.89 8 1311.82 8 0 01461.89 7 1282.98 7 0 01136.25 2 1047.91 2 0 01179.97 4 1060.11 4 0 01169.85 3 1057.74 3 0 01058.03 1 1009.38 1 0 01250.7 5 1066.1 5 0 01270.03 6 1078.91 6 0 01671.51 9 1413.41 10 -1 11763.28 10 1390.34 9 1 1

Total 2

Spearman’s coefficient of correlation, it is to be noted that∑

d2i has the minimum

value and is zero when the number are in complete arrangement. In case of

disarrangement,∑

d2i will be maximum and is equal to n(n2−1)3

Putting these

value, we get:

rs = 1 , for∑

d2i = 1 (3.27)

and

rs = −1 , for∑

d2i =n(n2 + 1)

3(3.28)

This shows that rs lies between (-1,1). If we solve an example using Spearmen

co-efficient of correlation and result comes out to be 0.8 then we can say that it

indicates high correlation.

Using equation-26, we get,

rs = 1− 6(2)

12(122 − 1)(3.29)

Here, rs = 0.993007, i.e., 99.3% correspondence between the data taken.

3.3.3 Karl Pearson’s Approximation

Karl Pearson has established a relationship between discrete multinomial distri-

bution and chi-square distribution by transforming and making the multinomial

distribution approach a χ2-distribution as “n” approaches infinity. This approxi-

mation is widely used to test agreement between observed data and the expected

(or hypothesized) results. Authors in [10], explained models based on Pearson’s

36

coefficient of correlation.

3.3.4 Hypothesis Testing in Regression Model

To check variation between two sets of data as data is available in the form of

electricity losses. These losses can be estimated by using y. Here, as we have

consumed power available i.e., readings taken from the utility that this much

power is to be distributed in a specific month. Second parameter across this one is

MkWH sold, means that utility is paid back after consumption of electricity. Now

we have to estimate the correlation and interdependence between the two sets of

values. We use analysis of variance to get our desired results. In this method, we

have to assume a hypothesis and test it after words.

While assuming Hypothesis we suppose β = 0, If hypothesis is accepted β will

be equal to zero, but hypothesis can be rejected if β = 0.Now we test β using

t-distribution also called student t-distribution. Using the following equation for

the sets of values.

tc =b− β

Sb

(3.30)

It gives the calculated value for “t”, where “b” is the slope of regression line and

β is used in this hypothesis testing. “Sd” is the standard deviation calculated for

“b”. We can fit level of significance “α” from the above calculated “t” value in a

t-table given in fig. If value for level of significance is lesser for a hypothesis better

the covariance and interdependence between data.

Most frequently, we are intrusted in testing the hypothesis that Ho : β = 0

against H1 : β = 0. It is important to note that testing the hypothesis that β = 0

is equivalent to testing the hypothesis that the variable y is independent of the

variable x (in a linear sense). The test statistics then becomes

tc =b− β

Sb

(3.31)

If we reject Ho : β = 0 we conclude that the two variables are linearly related. If

we accept Ho : β = 0, then two variables are not linearly related. To find “Sb”,

s2b =s2yx∑

(x− x)2=

∑(y − y)2

(n− 2)∑

(x− x)2(3.32)

If we want to check the data using hypothesis testing in regression model we need

following parameters;∑x = 17022.5,

∑y = 14740.87,

37

∑x2 = 24969161.78,

∑xy = 21485177.67

and∑

y2 = 18524679.07

Testing the population regression co-efficient, β = 0

• We state our null and alternative hypothesis as

Ho : β = 0andH1 : β = 0

• The significance level is set at α = 0.01

• The test-statistic, under Ho, is

t =b− β

Sb

=0.69904

Sb

(3.33)

which has a student’s t-distribution with υ = 12 − 2, i.e., 10 degrees of

freedom.

• As, we have already find out the values of a and b, which are “0.6990” and

“236.78”, respectively. Computations for sb.

s2yx =

∑y2 − a

∑y − b

∑xy

n− 2(3.34)

s2yx =18524679− 235.7(14740)− 0.699(21485178)

12− 2(3.35)

syx = 41.9303 (3.36)∑(x− x)2 =

∑x2 − (

∑x)2

n(3.37)∑

(x− x)2 = 822036.4792 (3.38)

sb =syx√∑(x− x)2

(3.39)

sb = 0.04625 (3.40)

t =0.69904

0.04625(3.41)

t = 15.11536 (3.42)

• The critical region is |t| ≥ t0.005(10) = 3.169

• Since the computed value of t=15.11536 falls in the critical region, so we

reject the null hypothesis and may conclude that there is sufficient reason

to say at the 1% level of significance that consumed and sold MKWH are

related.

38

3.4 Linear Support Vector Machine

As, different classifiers can be used for optimization problem. In this section, we

focus on SVM based technique. Its aim is to find a hyperplane that sperate the

data points belong to different groups. In linear SVM, we define certain parameters

on the basis of optimization problem. Training data is tested for optimization

problem, as in [17], Td is given as follows:

Td = (xi + yi) for i = 1, 2, 3...n, yi ε [−1, 1] (3.43)

where, xi are the data points septated into upper class and lower class. -1 shows

the lower and 1 shows upper class. This classified data can be written as:

for yi = 1, wx+ b ≥ 1 (3.44)

for yi = −1, wx+ b ≤ −1 (3.45)

where w is the weight of vectors x, and b represents biased or unbiased hyper

plane, for b = 0 it is called unbiased hyperplane i.e., it is passing from origin [9].

However for b = 0. The distance from origin to the margin line can be measured

as b∥w∥ . Where ∥ ∥ is used for norm. By combining the above constraint equations,

we get,

fy = yi(wxi + b) ≥ 1, fori = 1, ..., n (3.46)

The point xi lying on the boundaries line are called the support vector. X+

represents the vector lying on upper class boundary and X− denotes the vectors

lying on lower class boundary, as shown in Fig. 4. Distance (d) of support vector

X+, X i from hyperplane can be find as.

d =wx+ + b

||w||, (for yi = +1) (3.47)

d =wx− + b

||w||, (for yi = −1) (3.48)

Hyperplane with largest margin can minimize the over fitting problem in training

data. To find hyperplane which separates the classes with largest margin, let

margin is denoted by ρ and is calculated as:

ρ(w, x, b) =wx+ + b

||w||− wx− + b

||w||(3.49)

ρ(w, x, b) =1

∥w∥[(wx+ + b)− (wx− + b)] (3.50)

39

X+

X+

X-

X-

wx+b=0wx

+b=+1

wx+b=-1

Margin

Figure 3.4: Linear data classification

ρ(w, x, b) =2

∥w∥(3.51)

Hence, the hyperplane that optimally separates the data is the one that minimizes

f(x) =∥ w ∥2

2(3.52)

This optimization problem with linear and non linear constraints is solved by the

lagrangian multiplier. Lagrangian function £ is expressed as:

£(xi, α) = f(x) +n∑

i=1

αify (3.53)

where, α represents the lagrangian multiplier and fy represents the constraint

function. All the points can be separated as yi(wxi + b) − 1 > 0 for αi > 0.

Lagrangian form of this problem is given below

£(xi, αi) =∥ w ∥2

2−

n∑i=1

αi[yi(wxi + b)− 1] (3.54)

We can find w and b after taking the partial derivative of the lagrangian function

with respect to w and b. First we solve for w

40

Let, suppose:∂£

∂w= 0 (3.55)

∂£

∂b= 0 (3.56)

∂£

∂w=

∂ ∥w∥22

∂w−

n∑i=1

[∂(αiyiwxi)

∂w+

∂αiyib

∂w− ∂αi

∂w] (3.57)

0 =1

22w −

n∑i=1

(αiyixi) + 0 + 0 (3.58)

w =n∑

i=1

(αiyixi) (3.59)

After taking the partial derivative of lagrangian function with respect to b we get:

n∑i=1

(αiyi) = 0 (3.60)

In all conditions, where yi(wxi + b) = 1 it must be the case αi = 0. Solving for

w, b and all αi, it is still complicated. lagrangian equation with function f(x) and

constraints to be transformed to its dual form, which is easier to solve. Using the

fact ∥w∥2 = wwT , the lagrangian equation can be written as:

£(xi, α) =1

2wwT −

n∑i=1

αi[yi(wTxi + b)− 1] (3.61)

w =n∑

i=1

(αiyixi) (3.62)

wT =n∑

i=1

(αjyjxj) (3.63)

£(xi, α, xj, αj) =1

2

n∑i=1

(αiyixi)n∑

j=1

(αjyjxj)−

n∑i=1

αi(yi(n∑

j=1

(αjyjxj)xi) + b)− 1

(3.64)

41

=1

2

n∑i=1

n∑j=1

(αiαjyiyjxixj)−

n∑i=1

αi(yi(n∑

j=1

(αjyjxj)xi) + b) +n∑

j=1

(αi)

(3.65)

=1

2

n∑i,j=1

(αiαjyiyjxixj)−n∑

i,j=1

(αiαjyiyjxixj)+

b

n∑i=1

αiyi +n∑

j=1

(αi)

(3.66)

As we known∑

i=1

αiyi = o

Put values in above equation

= [1

2− 1]

n∑i,j=1

(αiαjyiyjxixj) + 0 +n∑

j=1

αi (3.67)

= −1

2

n∑i,j=1

(αiαjyiyjxixj) + 0 +n∑

j=1

αi (3.68)

In 1995, Corinna Cortes and Vladimir N. Vapnik proposed an adapted maximum

margin idea which allows for misclassified data points. Soft margin method selects

a hyper plane that splits the data point as clear as possible. This method introduce

the slack variables, ξi, which measures the degree of misclassified data of xi.

fy = yi(wxi + b) ≥ 1− ξi, fori = 1, ..., nandξi ≥ 0 (3.69)

If the function is linear, the optimization problem becomes:

minw,b,ξi [1

2∥ w ∥2 + C

n∑i=1

ξi] (3.70)

where, parameter C control the over fitting problems.

42

X+

X+

X-

X-

wx+b=0wx+b=+1

wx+b=-1

Margin

Slack

variableSlack

variable

Figure 3.5: Linear data classification with slack variables

43

Chapter 4

Conclusion

Whole world has about $25 billion of electricity losses, which is a very high amount.

To cope with this situation the primary and necessary action which can be taken

is by governments. They must provide subsidy in electricity price rates. If gov-

ernment give incentives in a form to allow funds for users, small projects to work

on. In these projects they produce electricity using different favorable methods

for certain area, and pay it back to utility and grid stations.

One major point is to aware people for their good and bad using using media like

television, radio, newspapers etc. In second part of my thesis, that is estimation, I

tested data taken from Lahore electric supply company on regression analysis. As

we fit regression model and plotted our data of Lahore electric supply company

on the model. Some of values shown deviation from the fitted model. They are

basically electricity theft. After finding coefficient of determination that is ”R2”, I

concluded that 96.3 out of 100 values shows interdependence and correlation with

the fitted model, while 3.7% values are theft values. In spearman’s coefficient of

correlation test we get these results as 99.3% as it does not explains all the data

points, correlated with the model. Though it is an easy way to find the correla-

tion between non theft scenario and theft scenario. In Karl Pearson’s coefficient

of correlation, chi-square method and student t-distribution are used to find out

correlation in the data. And in hypothesis testing I first assume null and alter-

native hypothesis. I set up significance level and applied test statistics on null

hypothesis. The critical region value from student t-distribution table is 3.169.

Since the computed value of t = 15.11536 falls in the critical region, so we reject

the null hypothesis and may conclude that there is sufficient reason to say at the

1% level of significance that consumed and sold MKWH are related.

44

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46