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A STUDY OF POWER FACTOR IMPACT ON ELECTRICAL INSTALLATIONS IN
AJAOKUTA STEEL COMPANY LIMITED, NIGERIA
By
OLORUNDARE, Akinwale Joseph
AAU/SPS/FET/ELE/M.Eng/11/03768
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING,
SCHOOL OF POSTGRADUATE STUDIES,
AMBROSE ALLI UNIVERSITY,
EKPOMA, NIGERIA.
AUGUST, 2018
i
A STUDY OF POWER FACTOR IMPACT ON ELECTRICAL INSTALLATIONS IN
AJAOKUTA STEEL COMPANY LIMITED, NIGERIA
By
OLORUNDARE, Akinwale Joseph
AAU/SPS/FET/ELE/M.Eng/11/03768
HND (Kwara Poly), PGD Eng (Ekpoma)
A THESIS IN THE DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING, SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES,
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF
MASTERS DEGREE (M.Eng) IN ELECTRICAL POWER/MACHINES, AMBROSE
ALLI UNIVERSITY, EKPOMA, NIGERIA.
AUGUST, 2018
ii
DECLARATION
I hereby declare that this research work was done by OLORUNDARE Akinwale Joseph and
to the best of my knowledge, this research work has not been submitted elsewhere for the award
of Masters of Engineering or any other degree or diploma.
…….………………………………….. ………………………………..
OLORUNDARE Akinwale Joseph Date
AAU/SPS/FET/ELE/M.Eng/11/03768
i
CERTIFICATION
This is to certify that this study was carried out by OLORUNDARE Akinwale Joseph with
Matriculation number AAU/SPS/FET/ELE/M.Eng/11/03768, in the Department of Electrical
and Electronics Engineering, School of Postgraduate Studies, Ambrose Alli University,
Ekpoma.
…………………………….. …………………………
Engr. Dr. Osahenvemwen, O. A. Date
Supervisor
Department of Electrical and Electronics Engineering,
Faculty of Engineering and Technology,
Ambrose Alli University,
Ekpoma, Nigeria.
…………………………….. …………………………
Engr. Dr. Okundamiya, M. S. Date
Head of Department
Department of Electrical and Electronics Engineering,
Faculty of Engineering and Technology,
Ambrose Alli University,
Ekpoma, Nigeria.
..............Signed.................... ………………………
External Examiner Date
ii
DEDICATION
I dedicate this project work to our Lord Jesus Christ and my family.
iii
ACKNOWLEDGEMENT
I return all glory and honor to God Almighty for the successful completion of this project work
which is the climax of the M.Eng. programme. My profound gratitude goes to
Engr. Dr. A. O. Osahenvemwen my project supervisor for every support they have given me
to complete the work on time. I am highly indebted to him for finding time from his tight
schedule of work to read through and to correct the work and also to have discussion of the
work with me. His labour of love shall never go unrewarded.
Personally I am grateful to the Head of Department, Electrical and Electronics Engineering,
Engr. Dr. M. S. Okundamiya for his encouragements. My special regard and respect goes to
the Postgraduate Coordinator, Engr. Dr. O. Omorogiuwa for his effort to make sure that the
project is completed on time. I am equally thankful to all my lecturers and the staff of the
Department of Electrical and Electronics Engineering, Ambrose Alli University, Ekpoma.
Especially Prof. Engr. A. M. O. Obiazi, Prof. Engr. R. E. Okonigene, Prof. Engr. G. I. Ighalo,
Engr. Dr. C.E Ojeabu, Engr. J. B. Erua and many others I could not mention. I am grateful to
Engr. Dr. M. J. E. Evbogbai, who was my Lecturer and supervisor until he left for a new calling.
The Lord will reward him abundantly for his advice on the project title.
My special thanks goes to my wife, Morenike Olorundare for standing by me in all aspect of
life and to the entire members of my family for their support, prayers, love, cares and
inspirations. I am grateful to all who have contributed in one way or the other to the successful
completion of the project work especially, Engr. Abraham Adekunle Adegbile, Francis
Alegbeleye, Abraham Ojogbane for helping to type the project work.
iv
My thanks also goes to my co-students especially, Engr. Rotimi Makanjuola Shola for his
encouragement and advice, all the staff of Water Facilities, Utilities Department of Ajaokuta
Steel Company Limited. May God bless you all. I am grateful to Mr. Nwekwo Enerst. FCS,
the Head of Utilities Department, for his understanding. I thank God for His infinite journey
mercy and protection throughout the programme.
v
ABSTRACT
Power factor is related to power flow in electrical systems and measures how effective an
electrical power system is used. In order to efficiently use a power system, the power factor
should be as close to unity as possible. This implies that the flow of reactive power should be
kept to a minimal. Maintaining a high power factor is crucial to obtaining the best possible
economic advantage for both Utilities and Industrial users. Operating a power system at a low
power factor is a concern for both electrical utility and industry since it increases the magnitude
of current in the system which may damage or shorten the life span of the equipment and also
increase copper loss which is capable of lowering the system efficiency due to increase in
reactive power. Industrial loads are mostly inductive and hence operate at low power factor.
Several methods can be used for improving power factor in order to reduce the reactive power
(kVA) demands of the load and power loss from the power supply system. Therefore the study
of the power factor impact on the electrical installations of Ajaokuta power system is to analyze
the effect of improving power factor of its electrical installation network beyond 0.8 being the
power factor of various induction motors as investigated using the recirculating system No. 3
(Pump House No 3). The research approach used to implement this study is through simulation
and calculations considering the use of bank of capacitors because it is the most common
method of power factor correction. The result of the three investigations carried out shows that
when power factor is improved there will be a reduction in the energy charges to the Ajaokuta
steel plant. The plant was able to save 2 million one hundred and seventy five thousand five
hundred and fifty eight naira (2,175,558) only. This amount was just for one substation out of
400 substations in the plant.
vi
CONTENTS
Page
TITLE PAGE i
CERTIFICATION ii
ACKNOWLEDGEMENT iii
ABSTRACT iv
TABLE OF CONTENT v
LIST OF FIGURES xii
LIST OF TABLE xv
LIST OF ABBREVIATION xvi
CHAPTER ONE: INTRODUCTION
1.1 Background To The Study 1
1.2 Justification Of The Study 5
1.3 Objective Of The Study 7
1.4 Scope And Limitation 7
1.4.1 Scope 7
1.4.2 Limitation 7
1.5 Methodology 8
1.6 Thesis Arrangement 11
CHAPTER TWO: LITERATURE REVIEW
2.1. Power System 12
2.1.1 Types Of Power 14
vii
2.1.2 Power System Loads 15
2.1.4 Power Factor 17
2.1.5 Definitions 19
2.2.0 Meaning of Power Factor 20
2.2.1 Relevance of Power Factor 21
2.2.2 Effects of Power Factor 23
2.3.0 Capacitance and Capacitor 25
2.4.0 Phasor Representation of an Alternating Quantity 26
2.5.0 Phasor Representation of Quantities Differing in Phase 27
2.5.1 Addition and Subtraction of Sinusoidal Alternating Quantities 28
2.5.2 Subtraction of Phasor 29
2.5.3 Phasor Additions 30
2.5.3.1 Important Formulae 32
2.6.0 Understanding Power Factor 34
2.6.1 Typical Utility Billing Structure 36
2.7.0 Low Power Factor 37
2.7.1 Power Quality 37
2.7.2 Sources of Power Quality Disturbance 38
2.7.2.0 Unpredictable Events 38
2.7.2.2 Point of Supply (Generation) 38
2.7.2.3 The Transmission System 39
2.7.2.4 The Distribution System 39
2.7.2.5 The Customer 39
2.7.3.0 Manufacturing Regulation 40
2.7.3.1 Standard 40
viii
2.7.3.2 Operating Conditions 40
2.7.4.0 Line Voltage 41
2.7.4.1 Resistive Loads 41
2.7.4.2 Inductive Load 42
2.7.4.3 Cos ∅ In Pf 42
2.8.0 Improving Power Factor 43
2.8.1 Advantages of Improved Power Factor 43
2.8.2 Disadvantages of Low Power Factor 44
2.8.3 Effects of Low Power Factor 46
2.8.4 Causes of Low Power Factor 47
2.9.0 Methods of Power Factor Correction 48
2.9.1 Static Capacitor 49
2.9.2 Synchronous or High Power Factor Machine 52
2.9.3 Synchronous Motors 52
2.9.4 Synchronous Condensers 53
2.9.5 Phase Advancer 55
2.9.6 Synchronous-Induction Motor 56
2.9.7 High Power Factor Motors 56
2.9.8 Location of Power Factor Correction Equipment 56
CHAPTER THREE: METHOD AND MATERIALS
3.1 Test and Experiment Method 57
3.2 Site and Location of Study 57
3.3 The Experimental Procedure 60
3.4 Capacitors 61
3.4.1 Advantages of Capacitor 61
ix
3.6.0 Proecdure 63
3.6.1 Measurement and Calculations 63
3.6.2 Alternatively 63
3.7 Construction 64
3.8 How to Calculate the Size of Capacitor 66
3.9 Experiment No: 1 66
3.10 Experiment No: 2 68
3.11 Experiment No: 3 69
CHAPTER FOUR: RESULT AND DISCUSSION
4.1 Result of Experiment No: 1 73
4.2 Analysis of Experiment No: 1 73
4.3 Result of Experiment No: 2 74
4.4 Graph of Experiment No: 2 75
4.5.1 Graph of Experiment No: 3 before Improving Power Factor 76
4.6 Analysis of Experiment No: 3 79
4.8 Findings of the Study 79
4.9 Contribution to Knowledge 80
CHAPTER FIVE: CONCLUSIONS AND RECOMMENDATION
5.1 Conclusions 81
5.2 Recommendations 82
REFERENCES 83
x
LIST OF FIGURES
Page
Fig 1.1 Electronic Configuration of A Hydrogen Atom 3
Fig 1.2 132kV Transmission Substation Power Network of Ajaokuta
Steel Company 9
Fig 1.3 Experimental Block Diagram 10
Fig 1.4 Research Stage By Stage Analysis of Power Factor 10
Fig 2.1 Simple DC Circuit 2
Fig 2.2 A/C Waveform 13
Fig 2.3 Negative Phase Shift 13
Fig 2.4 Positive Phase Shift 14
Fig 2.5 Purely Reactive Circuit 16
Fig 2.6 Purely Inductive Circuit 16
Fig 2.7 Reactive and Inductive Circuit 17
Fig 2.8 The Power Triangle 18
Fig 2.9 Graphical Representation of Power Factor Relationship 21
Fig 2.10 Phasor Representation of an A/C Quantity 26
xi
Fig 2.11 Phasor Representation of an Alternating Quantity 27
Fig 2.12 Addition of Phasors 29
Fig 2.13 Phasor Diagram and Waveform Representing Voltage and Current 30
Fig 2.14 Addition of Phasor Representation 30
Fig 2.15 Diagrammatic Representation of Phasor Subtraction 32
Fig 2.16 Power Factor Triangle 43
Fig 2.17 Leading Power Factor 43
Fig 2.18 Star Connected Capacitors 49
Fig 2.19 Delta Connected Capacitors 49
Fig 2.20 Series Connection of Capacitors 50
Fig 2.21 Parallel Connection of Transformer to Reduce Reaction 51
Fig 2.22 Phasor Diagram 53
Fig 3.1 Location of Ajaokuta on World Map 58
Fig 3.2 132KV Ajaokuta Transmission Substation 59
Fig 3.3 Experimental Procedure 60
Fig 3.4 Experimental Activities 60
Fig 3.5 Individual Motor Compensation 62
Fig 3.6 Power Factor Correction Unit 63
xii
Fig 3.7 Power Triangle 64
Fig 3.8 Leading Power Factor Correction Triangle 65
Fig 3.9 Lagging Power Factor Correction Triangle 65
Fig 3.10 Transmission System without the Capacitor Bank 67
Fig 3.11 Transmission System with Capacitor Bank 68
Fig 3.12 Transmission System without Capacitor for Experiment No: 3 70
Fig 3.13 Transmission System with Capacitor for Experiment No: 3 71
Fig 4.1 Power Factor against Motor Load Factor 75
Fig 4.2 Power Factor against Time before Improvement 76
Fig 4.3 Reactive Power against Time 77
Fig 4.4 Apparent Power against Time 77
Fig 4.5 Real Power against Time 78
Fig 4.6 Current against Time 78
xiii
LIST OF TABLES
Page
Table 2.1 Deducing the Power Parameters 15
Table 2.2 Typical Un-Improve Power Factor by Industry 35
Table 3.1 Record of Activities at Pump House No: 3 Between April 2015 and
May 2017 68
Table 3.2 Load and the Power Factor Value 69
Table 3.3 Before Correction 72
Table 3.4 After Correction 72
Table 4.1 Result of Experiment No:1 73
Table 4.2 Load and the Power Factor Value 74
xiv
LIST OF ABBREVIATIONS AND SYMBOLS
∅ Phi
A Ampere
AC Alternating Current
ASCL Ajaokuta Steel Company Limited
C Capacitance
CT current Transformer
DS Distribution Station
EMF Electromagnetic force
f frequency
Fig Figure
h Hour
H.V High Voltage
Hz Hertz
I Current
J Joules
kV kilovolt
kVA kilovolt Ampere
kVAR kilovolt Ampere (reactive)
kW kilowatt
LV Low voltage
xv
NERC National Electricity Regulatory Commission
Ɵ Phase Angle
P True/Active/Real Power (KW)
P.F Power Factor
PFC Power Factor Correction
Ph3 Pump House No.3
Q Reactive/inductive KVAR
RCS Recirculating System
RMS Root Mean Square
S Apparent Power KVA
S seconds
TCN Transmission Company of Nigeria
TS Transformer Station
V Volts
VT or PT voltage Transformer or Potential Transformer
W Watts
μF micro farad
𝜋 Pi
1
CHAPTER ONE
INTRODUCTION
1.1 Background to the Study
The background of any study provides the fundamental framework and basic concepts for the
true knowledge and proper understanding of the study, through presentation of facts and
qualitative analysis, with the basic principles and laws paramount to the study. In the course of
this study, the center of attention is power factor which is a function of energy. These frame
work or the fundamental principles and laws borders on the scientific study and universal
concepts of matter, space and time in relation with man and his immediate environment
(Mohammed, 2013).
Scientific investigation of the characteristic nature and behavioural pattern of matter, with
reference to space and time, often reveals that the study of energy which is the ability to do
work. The source of this energy is the sun. This primary form of energy is called solar energy.
Scientific investigations provide evidences to the study of energy. The facts are preserved by
the law of its conservation, which states that energy cannot be created nor destroyed but can
only be changed from one form to another or transferred from one point of location to another
(Ubi, 2013). The unit of energy is Joule (J) i.e. Newton-meter (N-m). Energy generated or
expended per second is known as power. The unit of power is Joule per second (J/s), Watts
(W), Volt-ampere (VA), or Volt-ampere reactive (VAR). These units define the various types of
electrical power, which are: Real or Active power in Watts (W),
Reactive power in volt, ampere-reactive (VAR), Apparent power measured in Volt-ampere (VA)
which is a combination of both true and reactive power.
2
The effectiveness of ac power is determined by power factor. It is a function of the phase angle
of ac current or voltage. Usually, power factor P.F, has a value range from 0 to 1. That is 0 ≤
P.F ≤ 1. The closer the value of P.F to unity, the more efficient the system becomes. It is the
ratio of the active power to apparent power given by,
𝑃. 𝐹 = 𝑇𝑟𝑢𝑒(𝑜𝑟 𝑎𝑐𝑡𝑖𝑣𝑒)𝑃𝑜𝑤𝑒𝑟,𝑊
𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑃𝑜𝑤𝑒𝑟,𝑉𝐴 = 𝑐𝑜𝑠 ∅ (1.1)
where, Ø = Phase angle of the electrical quantity (i.e. voltage or current).
The knowledge of the primary concepts of energy forms the basic understanding of electricity
and the power factor with its implications, relevance, problems and corrective measures. There
are different types of energy, and these are: Solar, Electrical, Chemical, Mechanical, Potential,
Kinetic, Internal, Atomic, Nuclear, Heat, Light, Sound, and Electronic (Constantin, 2011). In
the content of this study, electrical energy is the major focus due to its relationship with the
subject matter which is power factor problems, investigation, analysis, implication and
correction. As far as power system delivery is concerned the power factor of electrical
generation, transmission and distribution system is of great relevance. It is a function of
electrical charges. These charges however, move or flow as particles called electrons.
The flow or movement of these particles is known as current. Electrons are sub divisional
particles of an atom. This atom according to atomic theory is the smallest particle of an element
or a substance that can take part in any chemical reaction. An element is a substance that can
exist separately. Chemical reaction is the chemical combination or disintegration. That is,
chemical fusion or fusion of two or more elements or substances to form a compound. The
entire study of electricity depends on the process of migration, movement, transfer or flow of
electrons from one particular atom of an element or substance to another and the electrical force
causing the flow or substance. Figure 1.1 shows the electronic configuration of Hydrogen (H)
3
atom. The flow or movement of electrons is caused by electric forces which are due to potential
differences between electrically charged particulars.
Figure. 1.1: The Electrons Configuration of a Hydrogen Atom (Theraja, 2004)
In electric power delivery system certain limitations are obvious to its generation, transmission,
distribution and utilization. Prominent among these limiting factors is power factor problem.
Power factor provides a condition that explains the relationship between active or true and
apparent power of an electrical system. It is a ratio of true power to that of the apparent power.
For cost efficiency and effectiveness of power system, depends on the knowledge and
understanding of power factor. This is necessary for designers, manufacturers and users of
electrical equipment. This power factor is a function of the phase angle difference between
alternating quantities such as voltage V and current I. When alternating current was first
introduced, learned scientist claimed that it was impossible to deliver energy by such a means
(Muljadiet al, 2000 and Sun et al, 1980). Their argument was based on the idea that power
transfer would only take place during the first half of the cycle and then would be transferred
back during the second half of the cycle. Though, there was element of truth in their observation
as they overlooked the basic relationship of power dissipation given by the equation.
Power, p = I2R,
where I = instantaneous current.
R = Resistance of the conductor
Electron
Shell or orbit
Nucleus containing proton and
Neutron
4
The square of the current means that the power dissipated is real for both cycles irrespective of
the polarity of the current value. The square of the current means that the power dissipated is
real for both cycles irrespective of the polarity of the current value. However, it was only the
resistance element of the system that dissipates the energy from the circuit. Inductors and
capacitors do not dissipate energy which supports their claims. These inductors and capacitors
are often referred to as reactors in electrical circuits. They are so called because they produce
reactive or intangible power instead of real, true or tangible power (Muljadiet al,
2000).Capacitors are reactors; they store electric charges in the form of voltages by the law of
conservation of energy. Inductors use electricity current to produce magnetic flux as excitation
field. This magnetic flux can be stored in some metallic magnetic material, resistors dissipates
electric energy in the form of heat or light by this principle of conservation of energy
(Constantin, ‘2011).
In view of the above explanation and understanding of tangible and intangible components of
power the idea of power factor was conceived and then introduced to determine the effective
value of electrical power in an alternating current (or voltage) Circuit system. This power factor
is a function of the phase angle, difference between the two quantities of current and voltage
produced in an alternating system. Electrical power quantity is a broad field which covers all
aspects of power systems engineering, from transmission and distribution, to end user
problems. It has civil and construction engineers and manufacturers. For these problems to be
addressed, electric producer must understand the sensitivity of end user equipment to the
quality of voltage. Consumers must also learn to control the quality of their loads. Studies show
that the best and most efficient solution to power quality problems is to control them at their
source (Haesegawa et al, 2012).
5
1.2 Justification for the Study
Edomah (2016) of Pan Atlantic University declared that poor power factor is really becoming
and increasing phenomenon. Studies revealed that most companies particularly multinationals
in Nigeria. Ajaokuta Steel Plant inclusive does not pay enough attention to the effect of poor
power factor on their plant and equipment, let alone the economic implications. The result has
always been high production and maintenance cost, huge amount of fund is also wasted yearly
due to equipment damage caused by poor power factor (Edomah, 2016)
Pabla (2011) wrote that the electricity sector is currently experiencing many changes such as
the impact of high end technologies, environmental issues, privatization of the power utilities,
rising tariff and power shortages. The sector is reinventing itself to overcome these challenges
and also anticipating growth with the institution of electricity reforms. (Pabla, 2011).
Evaluation of transmission losses and efficiency, has become imperative to improve the power
sector, losses associated with the transformer design, such as the joule effect where energy is
lost as heat in the conductor (a copper wire, magnetic losses where energy dissipate into a
magnetic field and the dielectric effect where energy is absorbed in the insulating material
(Harpuneetet al., 2012, Ubi, 2013). Also losses are experienced in the distribution cables due
to undersize distribution power cable, Corona Loss, Dielectric, Radiation Losses and Skin
effect loss (Theraja, 2004).
Another aspect that introduced losses is the electric load (nonlinear) loads is associated with
voltage and current harmonics which increase power losses and negative impact on electric
utility distribution systems (Ubi, 2013). The nonlinear load generated by refrigerator, air-
conditioner, electric motors etc introduces inefficiencies into the electricity supply network by
drawing additional currents, called "inductive reactive currents". Although these currents
produce no useful power, they increase the load on the supplier’s switchgear and distribution
6
network and on the consumer's switchgear & cabling. The inefficiency is expressed as the ratio
of useful power to total power (kW/kVA), known as Power Factor (Harpuneet, 2012). Power
factor improvement is an important aspect of Electric Grids design and operation. Different
researchers provided technical measures to improve losses at customer premise by increasing
the power factor to unity value. This can be achieved by the following methods; such has the
Static Capacitors, Synchronous motors and Phase advancers (Solomon et al, 2012) Tsinkovich
(2013), focused on the capacitor bank evaluation problem for power factor improvement of an
industrial plant’s distribution network containing non-linear load.
It is shown that the choice of the capacitor bank depends on the current harmonic spectrum
consideration. The estimation of the equivalent circuit for the whole current harmonic spectrum
and for the first current harmonic only has been carried out with the use of the classical ways
of electric circuit analysis. The capacitors bank is most efficient in power factor correction
technique with high Economic benefits; therefore this power correction is deployed in this
study, carried out in Ajaokuta Steel Plant. The power factor correction technique based on
capacitors will increase the power factor low value to high power factor. This project is
committed to improve the quality of power factor, although some of the consumers or users
may be ignorant but maximizing the quality of supply will enhance the behaviour of operating
machines. Ajaokuta Steel Plant being a large area with high concentration of various sizes and
different types of electrical induction machines is faced with the problem of poor power factor.
Therefore, this project is to investigate the problems using relevant works done before as
references with a view to correct the poor power factor for the most efficient and economic use
of electric power supply to the Steel Plant.
Ajaokuta steel plant has about 400N0s 11/0.415kV transformer stations, with reactors installed
at the 132KV supply point. All the 11/0.415kV stations are yet to be connected with power
7
factor improvement devices. Hence, the huge amount of energy charges being paid by the
company. It has now become imperative to investigate the effect of power factor on the
electrical installations in Ajaokuta and come up with a scheme to improve the existing power
factor to a higher value, in order to reduce energy bills.
1.3 Objectives of the Study
The overall aim of this study is to determine the cause and effect of poor power factor and its
remedy in Ajaokuta Steel Company power system network.
The Specific Objectives are to: -
(a) collect power factor data from transmission stations 10TS10 and Electric motors at
water system No. 3 of Ajaokuta Steel Company Limited;
(b) investigate the cause and the effect of poor power factor, the economic implication and
the cost on the electrical installations in the integrated Ajaokuta Steel Plant; and
(c) develop a scheme or technique to be used to improve the power factor of the electrical
installation of Ajaokuta Steel Plant without affecting the amount of power delivered.
1.4 Scope and Limitation of the Study
The scope of this study is to develop a scheme to investigate and analysis a method of a cost
reduction of Ajaokuta Power System Network. The project work is currently limited to the
investigation of the power factor problems and correction of the Ajaokuta Steel Company
Limited, using 10TS10 power system of the Recirculation System No.3 as a case study
1.5 Methodology
Ajaokuta steel company limited electrical power installations will be used to generate data bank
for the investigation, analyze and correction of power factor.
(a) Workshop and laboratory analysis for confirmation of data collected.
(b) Useful information and data will be collected from internet
8
(c) Design a system using power factor as basis of power stability and economic use of
electricity.
(d) Discuss and analyze the issue relating to power factor problems and their correction
method.
(e) Testing, discussion and amendment of result.
Site and Location of Study
Ajaokuta Steel Plant is located in the north central region of Nigeria; it is about 30km from
Lokoja in Kogi State of Nigeria. The Steel Plant is an integrated Steel Plant established by the
Federal Government of Nigeria. The land area is about 1,800 hectares (18 millions square
meters). The erection of Ajaokuta power system network commenced in 1981 and was
completed and commissioned in 1987.
Figure 1.2: Geographical Location of Aajaokuta Nigeria
The power system of the Steel Plant consists of a thermal power plant /thermal blower station
(TPP/TBS) which can produce a total of 110 MW from a two generators of 55 MW each, to
produce an alternative source of power. The main source of power to Ajaokuta Steel Plant is a
dedicated 132kV power line from Benin transmission station.
9
Figure. 1.3: 132 kV Transmission substation Power Network of Ajaokuta Steel Company.
The Iron and Steel Plant comprises a large and varied complex of raw material, processing iron
and steel making, steel and finishing as well as product treatment department. This services
and utilities consume a fairly large amount of electrical power. This project is to investigate
the effect of power factor on the electrical power consumed, by proffering the best option from
an effective power system in order to reduce the energy charges.
The operating shops and equipment will be used at different time to determine the power
consumed by an electric motor before a power factor correction and power consumed by the
same motor after the correction. The experimental block diagram employed in this project work
is shown in Figure.1.4
10
Figure 1.4: Experimental Block Diagram
(a) It involves Experimentation, Simulation of the power supply from 10DS to 10TS10 in
Recirculating Water System of No. 3 of Ajaokuta Steel Company Limit
(b) Analysis and calculation of the power factor of electrical load of the Recirculating
system of No. 3 as stated in Fig. 1.5
(c) Data collection through measurement of the power factor based on the power dissipated
to the electrical load.
(d) Observe the result of the data collected then extract the related findings and identify the
relationship between the power factor component and the electrical load. The power
factor of the Electrical load is evaluated
10DS 10TS10 Load
RCS
Capacitor Bank
11
Figure. 1.5: Research stage by stage analysis of power factor
Feasibility study on PF at RCS
NO.3 Ajaokuta
Evaluate power factor and justify
the characteristics related to the
load
Analysis the power factor of the
load when connected to the
capacitor bank
Analysis power factor when load is
not connected to the Capacitor
Bank
Determine power factor of the
electrical load on 10TS10
12
Design Methods
(i) Analytical Method and Record
(a) Use of formula
𝐾𝑉𝐴𝑅𝑐𝑎𝑝 = 𝐾𝑉𝐴𝑅𝑠𝑦𝑠 − 𝐾𝑉𝐴𝑅𝑛𝑒𝑤 𝑎𝑛𝑑 𝐾𝑉𝐴𝑅 = 2𝜋𝑓𝑐𝑉2 × 10−9 1.1
(b) Use of graphs
(c) Use of diagrams
(d) Calculations
(ii) Design and modelling method
1.6: Thesis Arrangement
The arrangement of this thesis involves the introduction which comprises justification, aim and
objective of the study, and limitation and scope of the study. Chapter two involves literature
review, theoretical background and past related study on power factor. Chapter three present
details methodology with explanation of all the experimental procedure and data presentation.
Chapter four presents the analysis, result, discussion, findings and contribution to knowledge.
While chapter five presents conclusion and recommendations.
13
CHAPTER TWO
LITERATURE REVIEW
2.1 Power System
The electrical power in a circuit is the amount of energy expended over time. Voltage or
“potential” is the force necessary to move electrons through a material. Current is the rate of
flow of these electrons per second through the material with that voltage applied. By taking the
force (voltage) multiplied by the rate (current), the end result is energy expended over time.
This quantity is power. Thus electrical power is voltage multiplied by current:
P = V × I where power (P) is in watts, voltage (V) is in volts and current (I) is in amps
In a DC circuit, analysis is simple because voltage and current are maintained at a constant
level. The circuit in Figure 1 shows a 9VDC source connected to a 100Ω resistor. The current
flowing through the circuit is: (Donnelly, 1981).
Figure. 2.1: Simple DC Circuit
I = 9V/100Ω = 0.09A = 90mA
This means that the power dissipated at the load is:
P = 0.09A × 9V = 0.81W
In an AC system, the current and voltage are constantly changing in amplitude (Figure 2.2).
14
Therefore, the power will also constantly change depending on the value of the current or
voltage at any given point in time.
Figure. 2.2: AC Waveform
To make things even more complicated, the peaks and valleys of the current and voltage wave
forms will not always match up. When the current and voltage waveforms line up, they are said
to be “in phase.” In the case that they do not match up, the waveforms are said to be “out of
phase” or “phase shifted.” A purely resistive circuit will cause no phase shift. A purely
capacitive or inductive circuit will cause a 90 degree phase shift. A capacitor will cause a
negative phase shift while an inductor causes a positive phase shift (Figure 2.3).
Active Power
Reactive Power
Apparent Power
Figure. 2.3: Negative Phase Shift
15
Apparent Power
Reactive Power
Active Power
Fig 2.4: Positive Phase Shift
Since a purely resistive circuit produces no phase shift between voltage and current power is
maximized. This is known as the true power and it is the power that performs work. True power
is measured in Watts (W). Conversely, a purely capacitive or inductive circuit will draw current
that does no work. Power that performs no work is known as reactive power and it is measured
in Volt Amps Reactive (VAR). Reactive power is undesirable because, like true power, it
generates current which in turn produces energy loss in the form of heat on the conductors. As
a result, it is important to know how much true power vs. reactive power exists in a system.
Taking these two values into account, the overall output is known as apparent power and it is
measured in Volt Amps (VA) (Donnelly, 1981).
2.1.1 Types of Power
The actual amount of power being used, or dissipated, in a circuit is called true power. It is
measured in watts and is symbolized mathematically by a capital letter P. True power is a
function of the circuit’s dissipative elements, such as resistance (R). Reactive loads such as
induction and capacitors dissipate no power, but the fact that they drop voltage and draw current
gives the perception that they do dissipate power. This “dissipated power” is called the reactive
power and is measured in Volt-Amps-Reactive (VAR). Reactive power is represented by the
capital letter Q, and is a function of a circuit’s reactance (X).
16
The combination of true power and reactive power is called apparent power. It is the product
of a circuit’s voltage and current, without reference to phase angle. Apparent power is measured
in the unit of Volt-Amps (VA) and is symbolized by the capital letter S. Apparent power is a
function of a circuit’s total impendence (Z).
There are equations relating the three types of power to resistances, reactance, and impedance
(all using scalar quantities)
Table 2.1: used for deducing the power parameters
2.1.2. Power System Loads
Power system loads consists of resistive, inductive, and capacitive loads. Examples of resistive
loads are incandescent lighting and electric heaters. Examples of inductive loads are induction
motors, transformers, and reactors. Examples of capacitive loads are capacitors, variable or
fixed capacitor banks, motor starting capacitors, generators and synchronous motors
(Donnelly, 1981)
Inductive capacitive loads are opposite in nature. Equal amount of inductive and capacitive
loads within the same system will offset each other leaving only real power. This is defined as
a power factor of 1 or unity. When a unity power factor is achieved the real power (kW) or
demand is equal to the apparent power (kVA). Achieving a unity power factor will provide the
most efficient power system (Hughes, 1980).
𝑃 = 𝑇𝑟𝑢𝑒 𝑃𝑜𝑤𝑒𝑟 𝑃 = 𝐼2𝑅 𝑃 =
𝑉2
𝑅
𝑄 = 𝑅𝑒𝑎𝑐𝑐𝑡𝑖𝑣𝑒 𝑃𝑜𝑤𝑒𝑟 𝑄 = 𝐼2𝑋 𝑄 =
𝑉2
𝑋
𝑆 = 𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑃𝑜𝑤𝑒𝑟 𝑆 = 𝐼2𝑍, 𝑆 =
𝑉2
𝑍
𝑆 = 𝑉𝐼
17
In a purely resistive circuit, all circuit power is dissipated by the resistor, voltage and current
in phase with each other, and the true power is equal to the apparent power. In a purely reactive
circuit, no circuit power is dissipated by the load. Rather, power is alternately absorbed from
and returned to the AC source. Voltage and current are 90° out of phase with each other, and
the reactive power is equal to the apparent power. In a circuit containing of both resistance and
reactance, there will be more power dissipated by the load than returned, but some power will
definitely be dissipated and some will merely be absorbed and returned, but some power will
definitely be dissipated and some will be out of phase by a value somewhere between 0° and
90°. The apparent power is vector sum of the true power and the reactive power (Okoro, 2010)
I
AC source R
No reactance
Figure 2.5: Purely Reactive Circuit
I
AC source L
No Resistance
Figure 2.6: Purely Inductive Circuit
18
I
R
AC source
L
Resistance and induced load
Figure 2.7: Resistive and Inductive Circuit
2.1.3. Power Factor
In power systems, wasted energy capacity, also known as poor power factor, is often
overlooked. It can result in poor reliability, safety problems and higher energy cost. The lower
your power factor, the less economically your system operates. Power factor is the ratio
between the real power and the apparent power drawn by an electrical load. Like all ratio
measurements it is a unit-less quantity and can be represented mathematically as:
𝑃. 𝐹 = 𝑇𝑟𝑢𝑒𝑃𝑜𝑤𝑒𝑟
𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡𝑃𝑜𝑤𝑒𝑟 =
𝐾𝑊
𝐾𝑉𝐴 (2.1)
Where PF is the power factor, kW is the real power that actually does the work, kVA is the
apparent power and kVAR (not include in the equation) is the reactive power. In an inductive
load, such as motor, active power performs the work and the reactive power creates the
19
electromagnetic field. The three types of power relates to each other in a trigonometric form in
the Figure 2.7.
Figure 2.7: The Power Triangle
For the purely resistive circuit, the power factor is 1 (perfect), because the reactive power
equals zero. Here, the power triangle would look like a horizontal line, because the opposite
(reactive power) side would have zero length. (David et al, 1995).The same could be side for
a purely capacitive circuit. If there are no dissipative (resistive) components in the circuit, then
the true power must be equal to zero, making any power in the circuit purely reactive. The
power triangle for a purely capacitive circuit would again be a vertical line (pointing down
instead of up as it was for the purely inductive circuit). Power factor can be an important aspect
to consider in an AC circuit because any power factor is less than one means that the circuit
wiring has to carry more current than what would be necessary with zero reactance in the circuit
to deliver the same amount of (true) power to the resistive load. The poor factor makes for an
inefficient power delivery system (David et al, 1995). Poor power factor can be corrected,
paradoxically, by adding another load to the circuit drawing an equal and opposite amount of
reactive power, to cancel out the effective reactance, so we have to add a capacitor in parallel
Apparent Power (S)
Phase Angle ()
Reactive Power (Q)
True Power (P)
20
to bring the circuit’s total impendence equal to its total resistance (to make the impendence
phase angle equal, or at least closer to zero) (Pabla, 2011).
Power factor measures how efficient the current is being converted into real work with a low
power factor; more electrical current is required to provide the same amount of real power. All
the current causes dissipation in a distribution system. These losses can be modeled as (loss=
I² R), where R is the resistance. A power factor of 1 will result in the most efficient loading of
the supply; a load with a power factor of 0.5 will result in higher losses in the distribution
system. The reactive load of an industrial power system typically consists of large number of
AC induction motors. This can cause the total load to 50% inductive. Large inductive loads
cause the apparent power to be 25% 0r 41% higher than the real power. If the utility billing is
based on real power (kW) only, the utility provide up to 41% more capacity than what they are
billing for. Since it takes more capacity and is more expensive to serve a customer with a low
power factor, that customer has to pick up the higher electric rate
2.1.5: Definitions
AC power flow has three components:
(a) Real power or active power (P), expressed in watts (W)
(b) Apparent power (S), usually expressed in volt-amperes (VA)
(c) Reactive power (Q), usually expressed in reactive volt-amperes (var)
The VA and var are non-SI units mathematically identical to the Watt, but are used in
engineering practice instead of the Watt in order to state what quantity is being expressed. The
SI explicitly disallows using units for this purpose or as the only source of information about a
physical quantity as used. The power factor is defined as the ratio of real power to apparent
power. As power is transferred along a transmission line, it does not consist purely of real
power that can do work once transferred to the load, but rather consists of a combination of
21
real and reactive power, called apparent power. The power factor describes the amount of real
power transmitted along a transmission line relative to the total apparent power flowing in the
line.
2.2.6. Meaning of Power Factor
Power factor is the percentage of electricity that is being used to do useful work. It is defined
as the ratio of ‘active or actual power’ used in the circuit measured in watts or kilowatts (W or
kW), to the ‘apparent power’ expressed in volt-amperes or kilo volt-amperes (VA or kVA).The
apparent power also referred to as total power delivered by utility company has two
components.
1) ‘Productive Power’ that powers the equipment and performs the useful work. It is
measured in kW (kilowatts)
2) ‘Reactive Power’ that generates magnetic fields to produce flux necessary for the
operation of induction devices (AC motors, transformer, inductive furnaces, ovens etc.). It is
measured in kVAR (kilovolt-Ampere-Reactance).
Reactive Power produces no productive work. An inductive motor with power applied and no
load on its shaft should draw almost nil productive power, since no output work is being
accomplished until a load is applied. The current associated with no-load motor readings is
almost entirely "Reactive" Power. As a load is applied to the shaft of the motor, the "Reactive”
Power requirement will change only a small amount. The ‘Productive Power’ is the power that
is transferred from electrical energy to some other form of energy (i.e. such as heat energy or
mechanical energy). The apparent power is always in excess of the productive power for
inductive loads and is dependent on the type of machine in use. The working power (kW) and
22
reactive power (kVAR) together make up apparent power, which is measured in kilovolt-
amperes (kVA). Graphically it can be represented as: (Gupla, 2011).
Figure 2.9: Graphical representation of kW, kVAR & kVA
𝑃𝑜𝑤𝑒𝑟𝐹𝑎𝑐𝑡𝑜𝑟 = 𝐾𝑊 (𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑒𝑃𝑜𝑤𝑒𝑟)
𝐾𝑉𝐴 (𝑇𝑜𝑡𝑎𝑙𝑃𝑜𝑤𝑒𝑟) (2.2)
The cosine of the phase angle between the kVA and the KW components represents the power
factor of the load, kVAR represents the non-productive reactive power and is lagging phase
angle. The Relationship between kVA, kW and kVAR is non-linear and is expressed kW =
2kVA
2.2.1. Relevance of Power Factor
The study of power factor would be meaningless and irrelevant without the problem of
reactance (inductive and capacitance) which exists as energy losses or wattles energy in power
system. This is because reactance accounts for the losses incurred in an electrical power system
as a result of the power equipment. This reactive power provides the basis for the determination
of the efficiency and effectiveness of the power circuit system. The higher the value of the
power factor, the more is the efficiency of the system. Power factor is caused by
I. A negative phase angle (shift) produced as a result of energy stored up in the system
as charges in capacitors or accumulators
KVAR
KW (Productive Power)
KVA KVA KVAR
23
II. By a positive phase angle (shift) produced as a result of mechanical energy dissipated
as magnetism or excitation current by magnetizing voltage and current in the power
system circuits in inductors.
The energy loss due to capacitive reactance is as a result of the effects of the stored up
capacitive energy in the capacitors in the form of charges as static electricity of opposing
magnitude while the energy loss due to inductive reactance is simply the effect of inductive
energy expressed as magnetism inductors for excitation fields in induction machines such as:-
1. Alternating Current (or voltage)
2. Generator and electric motor in addition to electronic fitters.
Power factor is the relationship between working (active) power and total power consumed
(apparent power). Essentially, power factor is a measurement of how effectively electrical
power is being used. A higher power factor represents a more effective use of electrical power.
A distribution system’s operating power is composed of two parts: Active (working) power
and reactive (nonworking magnetizing) power. The active power performs the useful work –
the reactive power does not. Reactive power only function is to develop magnetic fields
required by inductive loads (Donnelly, 1981).
Low power factor means poor electrical efficiency. The lower the power factor, the higher the
apparent power drawn from the distribution network. When low power factor is not corrected,
the utility must provide the nonworking reactive power in addition to the working active power.
This results in the use of larger generators, transformers, bus bars, wires, and other distribution
system devices that otherwise would not be necessary. As the utility’s capital expenditures and
operating costs are going to be higher, they are going to pass these higher expenses to industrial
users in the form of power factor penalties and higher utility bills (Edomah, 2010).
24
Studies show that the best and most efficient solution to power quality problems is to control
them at their source. This can be done by a careful selection of loads, and control and mitigation
of single-time disturbances and harmonics before connecting loads to power systems. The
following sections will focus on the impact of poor power quality, the need for continuous
monitoring of poor power quality, and the economic benefits for monitoring poor power quality
voltage changes can range from small voltage fluctuations of short duration to a complete
outage for an extended period of time. Under voltage occurs when voltage decreases outside
normal rated tolerance. An under voltage is often referred to as sag when the duration is two
seconds or less. Over voltages occur when voltage increases above normal rated tolerance. An
over voltage is referred to a swell when the disturbance lasts two seconds or less. Over voltages
and swells can upset sensitive electronic equipment, and cause damage in some cases (Niel,
1981).
2.2.2. Effects of Power Factor:-
a) The need of larger cables to run the 1000W motor if the power factor is 0.5 because of
the larger current required in this low power factor load.
b) Higher capacity switches will be needed.
c) Bigger transformer would equally be required for such supplies.
d) Instruments must be larger with a greater increase in transmission losses ( R).
e) There will be an ineffectiveness use of generators by the supplier since the maximum
intensity does not match the maximum power (watts) used.
f) Loss of productivity by the supplier since more resources (Coal, Water, Gas etc)
required producing the same amount of real power.
g) There will be poor voltage regulation and large voltage drop.
Voltage drop, v = IZ
25
If the power factor is low, there will be large voltage drop which will cause low voltage
regulation. Therefore keeping voltage drop in the particular limit we need to install extra
voltage regulators. This is because the apparent power increases with the increasing current of
the system circuit as the power factor decreases to zero or negative values.
(1) The electricity sector is currently experiencing many changes, such as the impact of
high-end technologies, environmental issue, privatization of the power utilities, rising tariff and
power shortages. Hence the sector is reinventing itself to overcome these challenges and
anticipating growth with the institution of electricity reforms as applied to Ajaokuta Steel
Company, Limited.
(2) A lot of power system network designers seem to pay little or no attention to the serious
problem caused by leading and lagging power factor and the innocent consumers that purchase
and utilize the electrical/gadgets are ignorant of the implication of leading and lagging effects
of power factor. This project is committed to improve the quality of power factor, though some
of the consumers or users may be ignorant, but maximizing the quality of supply will enhance
the behavior of operating machines (Bhalia. 2012).
(3) The constant abuse of electricity supply due to ignorance of the knowledge, and right
application of power factor in Nigeria today is on the increase, because of the surge in social-
economic and industrial development in the country. As a result, there is a corresponding
demand and wastage of electricity. Therefore the idea of economical use of this essential and
crucial commodity becomes, an issue of great concern and most urgent (Neil, 1981).
(4) The power factor at which equipment operates is an economically important feature, all
efforts must be made to generate quality power.
(5) Demand for electricity is raising fast and sub-transmission and distribution capacity
development need to keep pace. The challenges of present day are:
(a) Rising cost of electricity
26
(b) Poor reliability and quality of power
(c) Improper regulatory frame work for renewable energy.
(d) Poor quality materials particularly distribution transformers and energy meters.
(e) Energy inefficiency
(f) Wasteful expenditure on procurement of substandard electrical equipment.
(6) From previous results and knowledge of power factor, its values normally exist from
0≤ pf ≤ 1 since the higher the value of power factor the lower the losses in electric power
systems, the justification of the study would depend absolutely on the reduction of reactive
power to the least possible value and increase of power factor to maximum possible values.
This set target is achievable with the use of inductors and capacitors (Gupta, 2011).
2.3. Capacitance and Capacitor:
If two similar capacitors are connected in parallel the capacitance is double that of one
capacitor. However, the effect of connecting the two similar capacitors in parallel is merely to
double the area of each plate. In general, the capacitance of a capacitor is proportional to the
area of the plates. On the other hand, if two similar capacitors are connected in series, it follows
from expression that the capacitance is halved. This implies that the thicknesses of the
insulation between the plates that are connected to the supply have been doubled (Bhalia,
2012). Hence, the capacitance of a capacitor is inversely proportional to the distance between
the plates, and the above relationships may be summarized as;
𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 ∝ 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑃𝑙𝑎𝑡𝑒𝑠
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑃𝑙𝑎𝑡𝑒𝑠 (2.4)
By considering the space between the charged plates of a capacitor, the above expression can
be clarified. In this space, the charges set up electric fields. The study of such electric fields is
known as electrostatics.
27
2.4. Phasor Representation of an Alternating Quantity.
Figure 2.10 shows a representation of an alternating quantity.
Figure 2.10: phasor representation of Alternating current.
Suppose OA in the above figure X to represent to scale the maximum value of an alternating
quantity say, voltage or current, i.e.
OA = Im or Vm (2.5)
Also, suppose OA to rotate anticlockwise about o at a uniform angular velocity, ω. This is
purely a conventional directional which has been universally adopted. An arrow head is drawn
at the outer end of the phasor when two or more phasor coincide. Figure 2.10, shows OA when
it has rotated through an angle from the position occupied when the current or voltage was
passing through its zero value or applied at the point, respectively. If AB and AC are drawn
perpendicularly to the horizontal and vertical axes respectively, then
OC = AB = OAsin θ (2.6)
= Im sin θ, in terms of current
= I, that is the value of the current at that particular instance.
Hence, the projection of OA on the vertical axis represents to scale the instantaneous value of
the current. That is, when = 900, the projection is OA, that is, when = 1800, the projection
is zero and corresponds to the current passing through zero from a positive to a negative value.
28
When , the phasor is in positive OA, and the projection = OD = OA, = , and
when = 3600, the projection is again zero and corresponds to the current passing through
zero from a negative to a positive value. It follows that OA rotates through one revolution or 2
in one cycle of the current wave (Okoro, 2010).
If F is the frequency in hertz, then OA rotates through F revolutions of 2 radians in 1s.
Hence the angular velocity or speed of OA is 2𝜋𝑓 radians per seconds and is denoted by the
symbol ω. That is,
𝜔 = 2𝑓 𝑟𝑎𝑑
𝑠 (2.7)
If the time taken by OA in figure 2.0, to rotate through an angle radian is one (1) second
(s), then, Angular velocity X time
𝜔𝑡 = 2𝜋𝑓𝑡 = 𝐼𝑚 sin 𝜔𝑡 (2.8)
We can therefore express the instantaneous value of the current as
𝑖 = 𝐼𝑚 sin 𝜔𝑡 = 𝐼𝑚 sin 2𝜋𝑓𝑡 (2.9)
2.5. Phasor Representation of Quantities Differing in Phase.
Figure: 2.11: shows the phasor diagram and waveform representation of voltage and current.
29
Consider the representation of two quantities such as voltage and current by a
diagram in Figure 2.11, with voltage leading the current by an angle ∅.
After the phasor have rotated through an angleƟ,they occupy positions OA, and OB,
respectively, with OB still leading by the same angle ∅, and the voltage are again given by the
projection of OA, and OB on the vertical axis as shown by the horizontal dotted lines.
If the instantaneous value of the currents represented by
𝑖 = 𝐼𝑚 sin 𝜃 (2.10)
Then, the instantaneous value of the voltage is represented by 𝑣 = 𝑉𝑚 sin(𝜃 + 𝜙)
The current in the figure Y is said to lag the voltage by angle 𝜙 or the voltage is said to lead
the current by an angle∅. The phase difference angle 𝜙 between the twophasors remain
constant, irrespective of their position (Okoro 2010)
2.5.1. Addition and Subtraction of Sinusoidal Alternating Quantities:-
Addition of PhasorSuppose OA and OB in Figure 2.12, are phasors representing to scale the
maximum values of say, two voltages or two maximum current values having the same
frequency but different phase by an angle∅. If the parallelogram AOCB is completed and the
diagonal OC is drawn, with OA, OB and OC projected on to the vertical axis, then for the
position so shown in Figure 2.12
Instantaneous value of OA = OD
Instantaneous value of OB = OE and
Instantaneous value of OC = OF
Since, AC is parallel and equal to OB, DF=OE
30
OF = OD + DF = OD + OE
That is, the instantaneous value of OC equals the sum of the instantaneous values of OA and
OB. Hence, OC represents the maximum value of the resultant voltage to the scale that OA and
OB represent the maximum values of the separate voltages. Therefore OC is termed the
sum of OA and OB, and this is evident that OC is less than the arithmetic sum of OA
and OB except when the latter are in phase with each other. This is the reason why it is seldom
correct in ac work to add voltages or currents together arithmetically (Okoro, 2010)
Fig 2.12: shows Addition of phasor.
2.5.2: Subtraction of Phasors:-
If voltage OB is to be subtracted from OA, then OB is produced backwards so that OB is equal
and opposite of OB as shown in Figure 2.13.
31
Fig 2.13: shows the diagrammatic representation for phasor subtraction.
The diagonal OD of the parallelogram drawn on OA and OB represents the phasor difference
of OA and OB.For simplicity, OA can be represented by A and B, bold letters being used to
indicate the appropriate phasor. It follows that
C = A + B and D = A – B
2.5.3: Phasors Addition:-
The instantaneous values of two alternating voltages are represented respectively by
(i) 𝑉1 = 60 sin 𝜃 𝑣𝑜𝑙𝑡𝑠 𝑎𝑛𝑑 (2.11)
(ii) 𝑉2 = 40 sin(𝜃 − 𝜋3⁄ )𝑣𝑜𝑙𝑡𝑠 (2.12)
Then, to derive expression for the instantaneous value of the sum and the difference of the
voltages.
32
Figure 2.14: shows addition of phasor for the given example (a)
It is usual to draw the Phasors in the position corresponding to 0 that is, OA in figure A
above is drawn to scale along the x- axis to represent 60V, and OB is drawnπ
8 radians or 600
behind OA to represents 40V. The diagonal OC of the parallelogram drawn on OA and OB
represents the sum of OA and OB. By measure OC = 87V and angle ф between OC
and the x- axis is 23.50, namely 0.41radians. Hence instantaneous, sum of the two voltages are
given by
𝑣 = 87 sin(𝜃 − 0.41) 𝑉
This is equivalent of line OE in Figure 2.14
Vertical component of OA = O
Vertical component of OB = BD =-40 cos 600
=-34.64V
Resultant vertical component = -34.64V = CE
This is equivalent to line CE in Figure 2.14.
33
The minus sign merely indicates that the resultant vertical component is below the horizontal
reference Phasor OA.
Hence, the maximum value of resultant voltage is
𝐶 = √802 + (−43.642) = 87.2𝑉
If ф is the phase difference between OC and OA
Tan 𝜙 =𝐸𝐶𝑂𝐸⁄ = -
34.64
80=-0.433
𝜙 =−23. 40=−0.4 𝑟𝑎𝑑𝑖𝑎𝑛𝑠
And, instantaneous value of resultant voltage is 87.2 sin(𝜃 − 0.41) 𝑉
The construction for subtracting OB from OA is obvious from Figure 2.15. by
measurement,𝑂𝐶 = 53𝑉 𝑎𝑛𝑑 𝜙 = 410 = 0.715 𝑟𝑎𝑑.
Instantaneous difference of the two voltages is given by
𝑉 = 53 sin(𝜃 + 0.715)𝑉
Alternatively, resultant horizontal component is
That is, this is equivalent of OD in Figure 2.15. and, resultant vertical component is given by
Therefore, maximum value of the resultant voltage is given by,
𝑂𝐶 = √402 + 34.642 = 52.9𝑉
34
And,tan 𝜙 = 34.6440⁄ = 0.866.
𝜙 = 40. 90 = 0.714 𝑟𝑎𝑑.
Figure 2.15: Subtraction of phasor in the given example.
2.5.3: Important formulae.
(2.13)
= (2.14)
= frequency. T = period, =
, N = rpm,
. Maximum value of emf generated in a coil rotating in a uniform magnetic field
Constant =
Flux density, in weber ( )
35
rea = in metre squared
Number of turns of coils in series
Speed of rotation in
Angular displacement of the rotating coil.
Phase angle displacement of the rotating coil
0.637 , Amperes = Average value of current
Average heating effect =𝐼2𝑅 = (𝐼1
2 + 𝐼22 + ⋯ + 𝐼𝑛
2)𝑅𝑛⁄ (2.15)
RMS Value is the effective value of current or voltage of an a.c system. This value
produces the same heating effect as d.c of the same value in the same resistance.
Complex Notation:- This is mathematical method used for the analysis of (a)
complicated dc network arrangements and (b) complex ac networks system problems. It is
called operator J, or the j operator.By this technique called j operator, phasors are resolved into
their horizontal and vertical components. The vertical component is then identified with the j
operator. By so doing, complex circuits can readily and easily handled. Complex ac problems
can be solved with the j operator. The techniques can be used to define voltages, current,
impedances and power in an a.c circuits (Theraja, 2008)
2.6. Understanding Power Factor
36
Any industrial process using electric motors (to drive pumps, fans, conveyors, refrigeration
plant etc.) introduces inefficiencies into the electricity supply network by drawing additional
currents, called "inductive reactive currents". Although these currents produce no useful
power, they increase the load on the supplier’s switchgear& distribution network and on the
consumer's switchgear & cabling. The inefficiency is expressed as the ratio of useful power to
total power (kW/kVA), known as Power Factor. The typical ‘un-corrected power factor’ by
different sectors of industry are as follows (Pabla, 2011).
Table 2.2: Typical Un-Improved Power Factor by Industry
S/N INDUSTRY POWER FACTOR
1 Auto Parts 75-80
2 Brewery 75-80
3 Cement 80-85
4 Chemical 65-75
5 Coal mine 65-80
6 Clothing 35-60
7 Electroplating 65-70
8 Foundry 75-80
9 Forging 70-80
10 Hospital 75-80
11 Machine manufacturing 60-65
12 Metalworking 65-70
13 Office Building 80-90
14 Oil Field Pumping 40-60
15 Paint manufacturing 65-70
16 Plastic 75-80
17 Stamping 60-70
18 Steel Works 65-80
37
Typical uncorrected industrial power factor is 0.8. This means that a 1MVA transformer can
only supply 800kW or that a consumer can only draw 80 useful Amps from a 100Amp supply.
To put it the other way, a 3-phase 100kW load would draw 172A per phase instead of the 139A
expected. For inherently low power factor equipment, the utility company has to generate much
more current than is theoretically required. This excess current flows through generators,
cables, and transformers in the same manner as the useful current. If steps are not taken to
improve the power factor of the load, all the equipment from the power station to the
installation sub-circuit wiring, has to be larger than necessary.
This results in increased capital expenditure and higher transmission and distribution losses
throughout the whole network. To discourage these inefficiencies the electricity companies
charge for this wasted power. These charges appear on electricity bills as "reactive power
charges", "kVA maximum demand" or "kVA availability charges". For instance known
information taken from billing about electrical system: kVA = 1000, kW = 800, kVAR = 600,
PF = 0.8
2.6.1. Typical Utility Billing Structure:
i. 90% Billing Structure -Where demand billed is based on 90% of the kVA or 100% of the
KW - Whichever is greater. Because the facility has a power factor of 0.80 they will pay
demand rates on 90% of the kVA 1000 x .90 = 900 kVA because it is the larger number
(900 kVA > 800 kW). Thus the facility is paying a penalty on 100 kVA of unproductive
power. Correcting the facility’s Power Factor to 90% will eliminate this penalty cost.
ii 100% kVA + 100% kW Billing Structure -Where one rate is applied to 100% of the kVA
and another rate is applied to 100% of the kW. Both are then added together to determine
the total demand charged on the bill. If we correct the power factor to unity (kVA = kW or
38
800 kVA = 800 kW) we can recover costs paid on 200 kVA at kVA rates. Assuming an
equal rate is being paid for kVA and kW
Rather than pay demand costs on 1000 kVA + 800 kW = 1800 if the Power Factor = Unity we
will pay demand costs on 800 kVA + 800 kW = 1600. Savings = 1800 -1600 = 200. (More
examples are provided later in this paper). Generally the cost per kVA is greater than the cost
for KW. Thus the savings would be greater by correcting the power factor to unity. The
reactive power charges levied as penalties in the billing should always be regulated. The excess
reactive currents and associated charges can be removed by a well-established technology
called "Power factor correction". Simply put, this technology offsets the inductive reactive
currents by introducing equal and opposite capacitive reactive currents. Typically this can
reduce electricity bills by 5-8%, with a payback period of 12 to 18 months. In addition, the
consumer shall gain from improved supply availability, improve voltage and reduced power
losses (Gupta, 2011).
2.7. Low Power Factor
Electrical power quality is a broad field which covers all aspects of power systems engineering,
from transmission and distribution, to end user problems. It has become a source of concern
for utilities, end users, civil/construction engineers and manufacturers. For these problems to
be addressed, electric utilities must understand the sensitivity of end-user equipment to the
quality of voltage. Consumers must also learn to control the quality of their loads (Theraja,
2008). Studies show that the best and most efficient solution to power quality problems is to
control them at their source. This can be done by a careful selection of loads, and control and
mitigation of single-time disturbances and harmonics before connecting loads to power
systems. The following sections will focus on the impact of poor power quality, the need for
continuous monitoring of poor power quality, and the economic benefits for monitoring poor
power quality.
39
2.7.1. Power Quality
Voltage changes can range from small voltage fluctuations of short duration to a complete
outage for an extended period of time. Under voltage occurs when voltage decreases outside
normal rated tolerance. An under voltage is often referred to as sag when the duration is two
seconds or less. Over voltage occurs when voltage increases above normal rated tolerance
(Okundamiya et al., 2009).
An over voltage is referred to a swell when the disturbance lasts two seconds or less. Over
voltage and swells can upset sensitive electronic equipment, and cause damage in some cases
(Theraja, 2008). Utility companies strive to maintain uniform voltage but disturbances from
outside sources, such as lightning and short circuits, can appear on the sine wave in the form
of surges. Surges can range from a few volts to several thousand volts and last from a few
microseconds to a few milliseconds. While over voltage and under voltage can upset or damage
sensitive electronic equipment, surges are far more destructive (Theraja, 2008).
2.7.2: Sources of Power Quality Disturbances
Power quality disturbances originate from four major sources
(a) Unpredictable events
(b) The electric utility
(c) The consumer/customer
(d) The manufacturers
2.7.2.1. Unpredictable Events
Both electric utilities and end users agree that more than 60% of power quality problems are
generated by natural and unpredictable events. Some of these include faults, lightning surge
propagation, resonance, Ferro-resonance, and Geo-magnetically Induced Currents (GICs) due
to solar flares. These events are considered to be utility related problems
40
2.7.2.2. The Point of Supply (Generation)
Although synchronous machines generate nearly perfect sinusoidal voltages (harmonic content
less than 3%), there are power quality problems originating at generating plants which are
mainly due to maintenance activity, planning, capacity and expansion constraints, scheduling,
events leading to forced outages, and load transferring from one substation to another.
2.7.2.3. The Transmission System
Relatively few power quality problems originate in the transmission system. Typical power
quality problems originating in the transmission system are galloping (under high-wind
conditions resulting in supply interruptions and/or random voltage variations), lightning
(resulting in a spike or transient over voltage), insulator flashover, voltage dips (due to faults),
interruptions (due to planned outages by utility), transient over voltages (generated by capacitor
and/or inductor switching, and lightning), transformer energizing (resulting in inrush currents
that are rich in harmonic components), improper operation of voltage regulation devices (which
can lead to long-duration voltage variations), slow voltage variations (due to a long-term
variation of the load caused by the continuous switching of devices and load), Flexible AC
Transmission System (FACTS) devices and High-Voltage DC (HVDC) systems, corona,
power line carrier signals, Broadband Power Line (BPL) communications, and
Electromagnetic Fields (EMF) (Okakwu et al., 2018).
2.7.2.4. The Distribution System
Typical power quality problems originating in the distribution system are voltage dips, spikes,
and interruptions, transient over voltages, transformer energizing, improper operation of
voltage regulation devices, slow voltage variations, power line carrier signals, BPL, and EMFs.
2.7.2.5. The Customer
Customer loads generate a considerable portion of power quality problems in today’s power
systems. Some end-user related problems are harmonics (Okundamiya, 2016) generated by
41
non-linear loads such as power electronic devices and equipment, renewable energy sources,
FACTS devices, adjustable-speed drives, Uninterruptible Power Supplies (UPS), fax
machines, laser printers, computers, and fluorescent lights), poor power factor (due to highly
inductive loads such as induction motors and air-conditioning units), flicker (generated by arc
furnaces), transients (mostly generated inside a facility due to device switching, electrostatic
discharge, and arcing), improper grounding (causing most reported customer problems),
frequency variations (when secondary and backup power sources, such as diesel engine and
turbine generators, are used), misapplication of technology, wiring regulations, and other
relevant standards.
2.7.3. Manufacturing Regulations
There are two main sources of poor power quality related to manufacturing regulations: The
lack of standards for testing, certification, sale, purchase, installation, and use of electronic
equipment and appliances is a major cause of power quality problems. The proliferation of
“sensitive” electronic equipment and appliances is one of the main reasons for the increase of
power quality problems. The design characteristics of these devices, including computer-based
equipment, have increased the incompatibility of a wide variety of these devices with the
electrical environment.
2.7.3.1 Operating Conditions
Load: The power factor of an electrical motor reaches its maximum value under full load. The
power factor decreases rapidly when the load decreases. Table 2.3, shows the effect of the load
on the power factor of a motor.
42
Table 2.3: The Effect of Load on the Power Factor of a Motor
Motor Load Factor Power Factor
Unloaded 17%
¼ Loaded 55%
½ Loaded 73%
¾ Loaded 80%
Fully Loaded 84%
Overloaded (25%) 86%
2.7.4 Line Voltage: Increasing the line voltage on motors and transformers above the rated
voltage will increase the consumption of reactive energy. The result will be reduction of power
factor. For example, an increase of 10% on the rated voltage can result in 20% reduction of
the power factor (Gupta, 2011). Power factor is simply a name given to the ratio of “actual”
power (active power) being used in a circuit, expressed in watts or more commonly kilowatts
(kW), to the power which is “apparently” being drawn from the mains, expressed in volt-
ampere or more commonly kilo volt-ampere (kV)
All modern industries utilize electrical energy in some form or other. Two basic categories of
load are encountered in alternate current (AC) networks.
2.7.4.1 Resistive Loads
Resistive loads are devices containing only resistance e.g. incandescent lamps, heaters,
soldering irons, ovens, etc. The current drawn from the supply is directly converted into heat
or light. Since the voltage is assumed to be constant, the actual power (kW) being used is
identical to the apparent power (kVA) being drawn from the line. The power factor is therefore
43
unity or 1. In these purely resistive circuits, the current and voltage sin wave peaks occur
simultaneously and are said to be “in phase”.
2.7.4.2. Inductive Loads
All motors and transformers depend on magnetism as the basis of their operation. Magnetism
is a force and in the physical sense is not consumed. In AC motors and transformers, magnetic
forces are only required periodically. Consequently, a permanent magnet cannot be used and
the necessary magnetism is produced by electrical means. The electrical current needed for this
purpose is not fully utilized. Having produced the magnetic force, the current flows back to the
power station again. This current is called the reactive current in contrast to the active current
which performs work and is fully utilized in so doing. Although the reactive current is not
utilized, it imposes a load on the electrical distribution system and supply authorities demand
payment for this load according to specific tariffs.
The current drawn from the supply is made up of two separate kinds of current “power
producing current” and “magnetizing current”. Therefore the current flowing in an AC circuit
(unless corrected) is generally larger than is necessary to supply the power.
2.7.4.3. Cos∅ of Power Factor
Reactive power and active power flow through the motor or transformer. Geometrical
calculation of these two powers yields the apparent power. The ratio of the active and apparent
power is denoted by cos ∅ and indicates what fraction of apparent power flowing is actually
used by the motor (Bhatia 2012).
Figure 2.16: Power Factor Triangle
44
2.8. Improving Power Factor
The most practical and economic power factor improvement device is capacitor. As stated
previously, all inductive loads produce inductive reactive power (lagging by a phase angle of
90°).Capacitors on the other hand produce capacitive reactive power, which is the exact
opposite of inductive reactive power. In this instance, the current peak occurs before the voltage
peak, leading by a phase angle of 90°. By careful selection of capacitance required, it is possible
to totally cancel out the inductive reactive power when placed in circuit together (Bhatia, 2012).
Figure 2.17: Leading Reactive Power.
To prevent the continual flow of reactive current back and forth between the load and power
station, a capacitor, which is in effect as active current storage device, is connected in parallel
with the load. The reactive current supplied by the power station and used for the magnetic
force when the load is switched on does not now return to the power station but instead flows
into the capacitor and merely circulates between the latter and the load. Consequently the
distribution lines from the power station are relieved of the reactive current. Capacitors can
therefore be utilized to reduce kVA and electrical cost.
45
2.8.1. Advantages of Improved Power Factor
1. Reduced kVA charges (Electricity bill)
2. Improved plant efficiency
3. Additional loads can be added to the system
4. Reduced overloading of cables, transformers, switchgear, etc.
5. Improved starting torque of motors
6. Reduce fuel requirements to generate power due to lower losses.
7. Reduce Power consumption means less greenhouse gas emission and fossil fuel
depletion by power (Environmental hazard)
8. Extend equipment life (reduce electrical burden on cables and electrical components)
2.8.2 Disadvantages of Low Power factor
The current for a given load supplied at a constant voltage will be higher at a lower power
factor and lower at a higher power factor, for example if load P is to be supplied at terminal
voltage V and at power factor of Cos by a 3 balance system, then load current is given by
,
𝐼𝐿 = 𝑃
√3 . 𝑉 cos ∅ (2.16)
If P and V are constant, the load IL is inversely proportion to power factor, which
implies that the lower the power factor the higher the current. The higher current due to poor
power factor affects the system and result in the following disadvantages.
Rating of generators and transformers are proportional to their output current hence it
is inversely proportional to power factor P.F therefore large generators and transformers are
required to deliver same load but at poor or low power factor.
The cross-sectional area of the bus-bar and the contact surface of the switchgear is
required to be enlarged for the same power to be delivered but at lower power factor.
46
For the same power to be transmitted at low power factor the transmission line or
distributor or cable have to carry more current. The size of the conductor will have to be
increased if current density in the line is to be kept constant, thus more conductor material is
required for the transmission lines, distributors and cable to deliver the same load at low power
factor (Gupta, 2011).
Energy losses are proportional to the square of the current, hence inversely proportional
to the square of the power factor i.e. more energy losses is incurred at lower power factor which
results in poor efficiency.
Low lagging in power factor result in large voltage drop in a generations, transformers,
transmission lines and distributors which results in poor regulations. Hence extra regulating
equipment is required to keep the voltage drop within permissible limits.
Low lagging power factor reduces the handling capacity of all the elements of the
system.
Penalty will be impose on the consumer of electricity by the electric power supply company
on low power factor below 0.95 lagging in electric power bill, the need to improve the power
factor is encouraged (Pabla, 2010).
Power factor correction is achieved by the addition of capacitors in parallel with the connected
motor circuits and can be applied at the starter, or applied at the switchboard or distribution
panel. Capacitors connected at each starter and controlled by each starter is known as "Static
Power Factor Correction" while capacitors connected at a distribution board and controlled
independently from the individual starters is known as "Bulk Correction". When installing
equipment, the following points are normally considered: (Neil, 1981)
1) Reliability of the equipment to be installed
2) Probable life of such equipment
47
3) Capital cost
4) Maintenance cost
5) Running cost
6) Space required and ease of installation
Generally the cost of rotating machinery, both synchronous and phase advancing, makes its
use uneconomical, except where one is using rotating plant for a dual function – drive and
power factor correction. In addition the wear and tear inherent in all rotating machines involves
additional expense for upkeep and maintenance.
Capacitors have none of these disadvantages. Compared with other forms of correction, the
initial cost is very low, upkeep
Costs are minimal and they can be used with the same high efficiency on all sizes of installation.
They are compact, reliable, highly efficient & convenient to install and lend themselves to
individual, group or automatic method of correction. These facts indicate that generally
speaking, power factor correction by means of capacitors is the most satisfactory and
economical methods. The static capacitor owing to its low losses, simplicity and high efficiency
is now used almost universally for power factor correction (Edomah 2010)
2.8.3: Effects of Low Power Factor
The effects of power factors to the Electric Power Supply Company are:
i. Ineffective use of the transmission lines
ii. Ineffective use of generators since the maximum intensity does not match the maximum
power (watts) used
iii. There is loss of productivity since more resources (coal, water, gas etc) will be required
to produce the same amount of real power.
iv. There will be poor voltage regulation and large voltage drop, V = IZ
48
The effects of power factor to the consumer of Electricity are
i. Increase of thermal losses in the installed devices.
ii. Large capacity supply line transformers and power usage. Therefore cost is added.
iii. Increase of the cost of use for electricity
2.8.4: Causes of Low Power Factor
All a.c motors (except over-excited synchronous motors and certain type of commutator
motors) and transformers operate at lagging power factor. The power factor falls with increase
in load to 0.8 at 75% of full-load, 0.7 at 50% (half full load, 0.5 at 25% of full-load and as low
as 0.1 on no-load.
Arc lamps and electric discharge lamps operate at low lagging power factor. Due to increased
supply, main voltage, which usually occurs during low-load period such as lunch hours, night
hours etc. the magnetizing current of inductive reactance increase and power factor of the
electric plant as a whole comes down.
The power factor at which motors operate falls due to improper maintenance and repairs. In
repaired motors, less wire is sometimes used than the originally wire used to wound the motor.
Therefore in such motors, leakage of magnetic flux increase and power factor of the motor
decreases (Gupta 2011)
In case of heavily worn-out bearings, the rotor may scratch at the stator; some metal is
sometimes removed from the rotor by turning, instead of replacing the defective bearing. In
doing so, the air gap between stator and rotor increases and the power factor drops. Industrial
heating furnaces such as arc and induction furnaces operate on lagging power factor (Gupta
2011)
49
The average power factors of some of the common appliances are given Table 2.3.
Table 2.3: Average Power Factor of Some Appliances
S/N Type of Loads Power Factor
1 Incandescent lamps 0.98 - 1.0
2 Fluorescent lamps 0.6 - 0.8
3 Neon lam used for adverts 0.4 - 0.5
4 Arc lamps used in cinema hall 0.4 - 0.5
5 Induction motor 0.5 - 0.85
6 Fractional kw motors 0.4 - 0.75
7 Induction heaters 0.85
8 Resistance furnaces 0.6 - 0.9
9 Arc furnaces 0.85
10 Induction furnaces 0.6
11 Arc welding machine 0.3 - 0.5
12 Resistance welding 0.4 - 0.75
2.9.0: Method of Power Factor Corrections
As already indicated, the low power factor is almost invariably due to inductive nature of load
and therefore the logical corrective method is to connect such devices across the load which
take leading reactive power such as static capacitors, synchronous machines or synchronous
condensers. The leading reactive component of current drawn by the load partly completed.
The power factor of the system will become unity when lagging reactive component of load
current is completely neutralized by the leading reactive component of current drawn by power
factor correcting devices (Gupta 2011)
50
2.9.1 Static Capacitor
By using static capacitor power factor can be improved by connecting the capacitors in parallel
with the equipment operating at lagging power factor, such as induction motor, Fluorescent
tubes. Static capacitors have the advantage of small losses (less than 0.05%) of higher
efficiency (say 99.6%) low initial cost, little maintenance owning to absence of rotating parts,
easy installation being lighter in weight and capability to operate under ordinary atmospheric
conditions.
However, they have drawbacks of short service life of (8 to 10years) getting damaged on over
voltages and uneconomical repair. The current drawn by induction motors or fluorescent tubes
can be resolved into 2 components: the active components, which is in phase with the supplied
voltage and the quadrature or witless component of constant magnitude. The capacitor draw
current-leading the supply voltage by 900 approximately and neutralize the quadrature or
wattles component of current drawn by the equipment across which these are connected. In
case of 3 phase loads capacitors remain connected permanently across the equipment terminals
either in star or delta, as shown in Fig:2.18 and Fig:2.19 (Gupta 2011).
Fig. 2.18: Star connected capacitors Fig. 2.19: Delta connected capacitors.
This capacitors remain connected permanently across the equipment and are across the supply
mains whenever the equipment is switched on. The value of the static capacitors for the
improvement of the power factor can be determined as follows.
3Ɵ
Load
3 Ɵ
Loa
d
51
The leading current required to neutralized the lagging reactive component of the current drawn
by the equipment to give unity power factor is expressed as Ic = IL =
𝐼 sin ∅ = 𝐼 √1 − 𝑐𝑜𝑠2∅ = 𝐼√(1 − 𝑝𝑓)2
The value of capacitor in star is given by
Cs = = (2.17)
Where V is the phase voltage, I is the phase current and F is supply frequency. For a given
kVAR and live voltage the delta value will be one-third of the star value. Power factor can also
be improved by connecting static capacitors in series with the line. Capacitors connected in
series with the line neutralized the line reactance. The capacitors when connected with the
equipment are called the shunt capacitors (Gupta 2011)
Fig 2.20: Series Connection of Static Capacitors with Load
Shunt capacitors are sued in factories, plants and also on transmission lines. Series capacitors
are used in long transmission lines because they provide automatic compensation with the
variation in load. The capacity of these capacitors that neutralized the line reactor is given by
(2.18)
Where f is the frequency and L is the inductance of the line per phase.
c
c
c
3Ɵ
Load
52
The value of reactance required is usually very large but reduced to reasonable value by the
use of a transformer as shown in Fig.2.21
Fig 2.21: Parallel Connecting Transformer to Reduce Reaction
Shunt capacitors are used in rating from 15kVAR to 10,000kVAR. Small capacitors, in a few
hundred rating are used on individual distribution circuits of customers. Capacitor bank of 500
– 3,000kvar ratings are employed in small distribution substations and then with larger rating
at big substations (Gupta 2011)
Three phase capacitor banks can be connected in star earthed, star unearthed or in delta
arrangements ungrounded star connection is preferred because of easier protection. In this
method, the fault current in case of a fault in any unit in one of the phase is restricted by the
capacitor in the sound phases. This results in the use of smaller fuses and less protection
materials. The capacitor must be provided with a suitable discharge device to dissipate the
stored energy and to reduce the residual voltage to a safer value (Okundamiya and Nzeako,
2010).
The discharge resistance is usually incorporated within the unit itself in the case of medium
voltage capacitors and in case of high voltage capacitors, potential transformers of the circuit
breakers are generally utilized as a discharge device (Gupta 2011)
3 Ɵ
Load
53
The reactive output of the capacitance in kVAR is given as
𝑉𝑜𝑙𝑡𝑎𝑔𝑒×𝐿𝑖𝑛𝑒𝐶𝑢𝑟𝑟𝑒𝑛𝑡𝐾𝑉𝐴𝑅
1000𝑜𝑟 2𝜋𝑓𝑐𝑣2 × 10−9𝐾𝑉𝐴𝑅(2.17)
In case of single phase, where V is the line voltage, F is the supply frequency and C is the
capacitance in microfarads. And
√3 𝑉𝑜𝑙𝑡𝑎𝑔𝑒×𝐿𝑖𝑛𝑒𝐶𝑢𝑟𝑟𝑒𝑛𝑡
1000𝐾𝑉𝐴𝑅𝑜𝑟√3 × 2𝜋𝑓𝑐𝑣2 × 10−9𝐾𝑉𝐴𝑅 (2.18)
In case of 3θstar connected circuits and 6𝜋𝑓𝑐𝑣𝐿2 × 10−9 𝐾𝑉𝐴𝑅 in case of 3-phase delta a
connected circuit where VL is the line voltage f is the supply frequency in Hz and c is the
capacitance in between the line terminals.
Thus the corrective capacity of the capacitors is a function of the line voltage and supply
frequency varying in accordance with the square of the voltage and directly with the supply
frequency. The units as manufactured are designed for a variation of voltage ±10% of normal
voltage. It is therefore impossible to overload these units so long as the voltage is normal and
frequencies are maintenance (Gupta 2011)
2.9.2: Synchronous or High Power Factor Machines
Synchronous machines are excited by d.c and the power factor may be controlled by controlling
the field excitation. The various synchronous machines available for power factor correction
comprise synchronous motors, synchronous condensers, synchronous converter, synchronous
phase modifiers, phase advancers and synchronous induction motors (Gupta 2011).
54
2.9.3 Synchronous motors
These motors have characteristics that make them adaptable for a wide range of applications.
The speed is constant, the efficiency is high and uniformed form light loads up to considerable
over-loads and the starting characteristics compared favorably with those in induction motors.
Another desirable characteristic of the synchronous motor is its tendency to maintain a constant
load voltage even if there are variations in the supply voltage. When the line voltage. When the
line voltage increases, the usual practice is to keep the field excitation constant at a value
corresponding to normal full load rating as regards output and power factor. Synchronous
motors are designed for 1.0 – 0.8 leading power factors at full-load. The unity power factor
motor costs less and has a higher efficiency, but if fully loaded it cannot furnish leading reactive
kVA to compensate for lagging reactive kVA in the system.(Gupta 2011)
2.9.4: Synchronous condensers
An over-excited synchronous motor running on no-load is called synchronous condenser or
phase advancers and behave like a capacitor, the capacitive reactance of which depends upon
the motor excitation. Power factor can be improved by using synchronous condensers like
shunt capacitors connected across the supply (Gupta 2011)
I
Fig. 2.22: Phasor diagram
𝐼𝑚
V
𝜙𝑀
𝜙𝐿
𝐼𝐿
55
Phasor IL represents the current drawn by the induction load lagging behind the applied voltage
v by a large angle and phasor Im represents the current drawn by the synchronous condenser
leading the applied voltage v by the angle ∅m the resultant I is the phasor sum of IL and Im and
now angle of lag 𝜙 is much smaller than ϕL to Cos 𝜙 by the use of the synchronous condenser.
In this way the power factor can be made unity even. Synchronous condensers are usually built
in large units and are employed where a large quantity of corrective kVAR (say 5000 kVAR
or more) is required.
The advantages of synchronous condenser over static capacitors as a power factor correction
devices are.
i. A finer control can be obtained by variation in the line voltage
ii. Inherent characteristics of synchronous condensers of stability.
iii. Variations in the line voltage and thereby automatically aid in Regulation.
iv. Possibility of overloading a synchronous condenser for a short period.
v. Improvement in the system stability and reduction of the effect of sudden changes in
load owning to initial of synchronous condenser.
By use of synchronous condensers at intermediate stations, the voltage of the line can be kept
constant at various points along the length thereby increasing the current capacity of the line
and improvement of power factor.
The disadvantages of synchronous condenser over static capacitors are power factor correction
devices are
56
i. Except in size above 5,000kVAR, the cost is higher than that of static capacitor of the
same rating.
ii. Higher maintenance and operational cost
iii. Lower efficiency (say 70% due to losses in rotating parts and heat losses.
iv. Noise is produced in operation
v. An auxiliary equipment is required for starting synchronous condenser
vi. There is the possibility of synchronous condensers falling out of synchronous causing
interruption of supply.
vii. Increase of short circuit when the fault occurs near the synchronous condenser.
Synchronous condensers are largely employed by utilities at large substations for improving
power factor and voltage regulation. Machines up to 100mVAR rating or even higher have
been used. The excitation current is regulated automatically to give a desire voltage level.
2.9.5 Phase Advancers
The power factor of an induction motor falls mainly due to its exciting current drawn from the
a.c supply mains, because exciting currents lags behind the voltage by . It may be improved
by equipping the set with an a.c exciter or phase advancer which supplies this exciting current
to the rotor circuit at slip frequency, such an exciter may be mounted on the same shaft as the
main motor or may be suitably driven from it. Use of phase advancer is not generally
economical in connection with motors below 150kW output but above this size, phase
advancers are frequently employed, shunt and series type of phase advancers are available
57
according to whether the exciting winding of the advancers is connected in parallel of series
with the rotor winding of the induction motor.
There are two main advantage of phase advancer.
i. Lagging kVAR drawn by the motor is considerably reduced due to supply of exciting
ampere-turns at slip frequency.
ii. The phase advancer can be employed where the use of synchronous motor is
admissible.
2.9.6 Synchronous-Induction Motor.
There are special types of motors which operate at certain loads as synchronous motors and at
other load as induction motor.
2.9.7 High Power Factor Motors
Beside synchronous motors or synchronous induction motor other several types of motors
which operate at a power factor of approximately unity such as compensated induction motors.
These motors are more expensive and have higher maintenance cost than ordinary induction
motors.
2.9.8: Locations of Power Factor Correction Equipment
The best location for the power factor correction equipment to be installed is where the
apparatus or equipment responsible for low power factor is operating. Synchronous condenser
are used at load centre where considerable corrective kVAR is required whereas static
capacitors are justifiably used in smaller units and may be placed closer to the point where the
58
load is inductive in nature is installed and thereby relieving the distributors and feeders from
carrying excessive current owning to low power factor.
In case of transmission system, if synchronous condensers are to be used for power factor
improvement then these should be installed at the receiving end so that it is not only the
generators but also the transmission lines are relieved of carrying excessive current due to poor
power factor. However if synchronous condensers are installed near the generators then only
the generators will be relieved from the excessive current components and the transmission
lines will carry the excessive current load.
Osama A. and others, of the Electrical Engineering Department Kuwait University. State of
Kuwait studied and present the advantage of power factor correction for the electrical
distribution network in Kuwait.
Olatinwoo and others of the Department of Electrical and Electronics Engineering, Federal
University of Agriculture Abeokuta, Nigeria carried out the effect of power factor improvement
on switching transients : A case study of FUMMAN Agricultural Product Industry and came
out with an improve power factor from 0.8(lagging) to 0.9098(lagging).
In this study ai have investigated the effect of power factor on the electrical installations in
Ajaokuta steel company limited and I have come up with a power factor that reduced the energy
charging bill, the prevailing power of 0.71 lagging has been improved to 0.9 lagging
59
CHAPTER THREE
METHOD AND MATERIALS
3.1 Site and location of study
Ajaokuta Steel Plant is located in the north central region between latitude and longitude
7.330N, 6.39oE, and about 30km from Lokoja in Kogi State of Nigeria. The Steel Plant is an
integrated Steel Plant established by the Federal Government of Nigeria in 1983. The land area
is about 1,800 hectares (18 millions square meters). The erection of Ajaokuta power system
network commenced in 1981 and was completed and commissioned in 1987.
Figure 3.1: location of Ajaokuta Steel Company LTD.
Ajaokuta Steel Company Limited as an integrated Iron and Steel plant comprises a large and
varied complex of raw material processing, iron and steel making shop, steel shopping and
finishing as well as product treatment departments. Apart from various essential auxiliary
utility services such as calcimine dolomite, big setting and refractory plants, foundries,
maintenance shops, gas, air and steam generating facilities, water treatment and water
circulating system, equipment ventilation systems and various other ancillaries are essential to
the efficient operation of an integrated steel plant. These services and utilities consume a fairly
60
large amount of electrical power. An integrated steel plant with an annual output of about
2.0M.T. Steel, producing section products may have connected load of the order of 30MW.
The designed maximum power demand is 220MW with total energy consumption of
1000WH/annum (Bamigbola 1983).
For the purpose of supply from the National grid Networks, the steel plant is linked with
330/132kV grid substation from Benin – Ajaokuta a single line diagram as shown in Fig 3.2
Fig 3.2: 132kV Transmission Substation Power Supply of Ajaokuta Steel Company Ltd
Ajaokuta.
61
3.3: The Experimental Procedure
The methodology employed in this project work is shown in Fig. 3.2, It involves
Experimentation, Simulation of the power supply from 10DS to 10TS10 in Recirculating Water
System No. 3 of Ajaokuta Steel Company Limited.
Fig 3.3: Experimental Procedure
Analysis and calculation of the power factor of electrical load of the Recirculating system No.
3 as stated above.
Distribution
Station
Transformer
Station
Electric
Motor
Power factor correction Capacitor
62
Fig 3.4: Experimental Activities
3.4: Capacitors
Power factor correction is achieved by the addition of capacitors in parallel with the connected
motor circuits and can be applied at the starter, or applied at the switch board or distribution
panel. Capacitor bank is the simplest method of correcting power factor. Static capacitors are
used to produce capacitive reactance that cancels out the inductive reactance of the lagging
current.
3.4.1: Advantages of capacitors in power factor correction
(a) Reliability
(b) Low capital cost
(c) Operational and maintenance cost are low
Feasibility study on PF at RCS
NO.3 Ajaokuta
Evaluate power factor and
justify the characteristics
Analysis the power factor of
the load when connected to the
capacitor bank
Analysis power factor when
load is not connected to the
Capacitor Bank
Determine power factor of the
electrical load on 10TS10
63
(d) No auxiliary equipment required for starting.
(e) Low losses
(f) Light weight
(g) Easy to install
3.4.2: Disadvantages
(a) It is affected by harmonics
(b) Somehow short life span(8-10 years)
(c) Can get easily damaged due to over voltage.
Two methods of improving power factor using capacitor are:
(a) Individual motor compensation (static capacitor)
N
Fig 3.5: Individual motor compensation
Most effective correction is obtained by connecting individual capacitor directly to the terminal
of each motor. The motor and capacitor can be controlled jointly by the motor switch gear
centralize compensation (automatic capacitor bank).
Capacitor Bank
or Synchronous
64
Variable Capacitor Bank
Fig 3.6: Power Factor Correction Unit
3.6.0: Procedure: -
1. Measurement and calculations
a) Apparent power of the system with an energy meter (kVA)
b) True power of the system with a wattmeter (kW)
c) Calculate the reactive power of the system by subtracting the true power from the
apparent power and the power factor is a ratio of true power to apparent power.
C = kVA – kW = kVAR
𝑃. 𝐹 = 𝐾𝑊
𝐾𝑉𝐴 = cos ∅ (3.1)
Alternatively
a) Check the Name plate of the power system
b) Look for the apparent power of the system as per design, from the Name plate and copy
out
c) Get the power factor from the Name plate
CONTROL
UNIT
65
d) Calculate the true and reactive power
i) i.e. True power = Apparent power x P.F
ii) Reactive power = Apparent power – True power
3.7: Construction
Draw the power Triangle for the power system with
i) Adjacent side (Base) = True Power
ii) Hypotenuse side = Apparent Power
iii) Opposite side = Reactive Power as shown below
Fig 3.7: Power Triangle.
Calculations
𝑎. 𝑃. 𝐹 = 𝑇𝑟𝑢𝑒 𝑃𝑜𝑤𝑒𝑟
𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑃𝑜𝑤𝑒𝑟 =
𝑊
𝑉𝐴 (3.2)
𝑅
𝑍 = cos ∅ (3.3)
b. Determine ∅
∅ = cos−1 𝑅
𝑍 = cos−1 𝑃. 𝐹 (3.4)
a. To determine C
Since reactive power = VIc where I is current in capacitor circuit, we can substitute as follows
i. 𝐼𝐶 = 𝑉𝐴𝑅
𝑉(𝐿𝑖𝑛𝑒) =
𝑉
𝑋𝐶 =
1
2𝜋𝑓𝑐 (3.5)
ii. 𝑋𝑐 = 𝑉
𝐼𝑐 (3.6)
Hence C = 𝑉
2𝜋𝑓𝑐[𝜇𝐹] =
1
2𝜋𝑓𝐿𝑐[𝜇𝐹] (3.7)
VAR
∅ VA W
66
Fig 3.8: Leading power factor correction Triangle.
To determine L
(i) 𝐼𝐿 = 𝑉𝐴𝑅
𝑉(𝐿𝑖𝑛𝑒) =
𝑉
𝑋𝐿 = 2𝜋𝑓𝐿(3.8)
(ii) 𝑋𝐿 = 𝑉
𝐼𝐿 (3.9)
Hence L = 𝐼𝐿
2𝜋𝑓 =
𝑉
2𝜋𝑓𝑋𝐿𝐻𝑒𝑛𝑟𝑦[𝐻]
C
New VA
∅𝟏 ∅𝟐
A B
Old VAR
Fig 3.9: Lagging Power factor Triangle diagram
3.8: How to Calculate the Size of Capacitor
First step is to measure the old apparent power 𝐾𝑉𝐴and the power factor
Calculate the 𝐾𝑉𝐴𝑅of the system by using Pythagoras theorem
𝑘𝑉𝐴𝑅𝑠𝑦𝑠 = kVA2old – 𝑘𝑊2(3.10)
Find the power factor
VAR ∅
67
Calculate the new kVA using target P F,
𝐾𝑉𝐴𝑛𝑒𝑤 =
𝐾𝑊
𝑃𝐹𝑛𝑒𝑤
(3.11)
Calculate 𝐾𝑉𝐴𝑅𝑛𝑒𝑤 once the target Pf is achieved
𝐾𝑉𝐴𝑅𝑛𝑒𝑤 = KVA2new – 𝐾𝑊2 (3.12)
𝐾𝑉𝐴𝑅𝑛𝑒𝑤 is the difference between 𝐾𝑉𝐴𝑅 of system and the added capacitor’s 𝐾𝑉𝐴𝑅
𝐾𝑉𝐴𝑅𝑛𝑒𝑤 = 𝐾𝑉𝐴𝑅𝑠𝑦𝑠 − 𝐾𝑉𝐴𝑅𝑐𝑎𝑝(3.13)
So 𝐾𝑉𝐴𝑅 of the capacitors to be installed is
𝐾𝑉𝐴𝑅𝑐𝑎𝑝 = 𝐾𝑉𝐴𝑅𝑠𝑦𝑠 – 𝐾𝑉𝐴𝑅𝑛𝑒𝑤 (3.14)
3.9: Experiment No. 1
A Transmission station designated as 10TS10 at the Recirculation Water System No.3 (Pump
House No. 3) of Water Facilities of Utilities Department Ajaokuta Steel Company
Limited.10Ts12 is supplied with Power from 10DS distribution through 1600kVA, 11/0.415kV
feeding Low Tension busbar.
(b) Aim: To evaluate the effect of improved power factor on a transformer station 10TS10.
(c) Objective: To determine the remedy through correction using capacitor bank to reduce
the high energy consumed, and energy bill.
(d) Method: Capacitor bank is connected to load side of the transformer and measurements
are taken.
(e) Apparatus: Capacitor bank, voltmeter, ammeter and wattmeter.
(f) Procedures: The value of the capacitor bank was calculated, it was connected to the
load side of the transformer, measurement was taken for a period of 12 months (between May,
2016 and April, 2017), and the monthly average value were recorded as shown in Table 3.1.
Readings before the installation of the capacitor bank was copied from the operational logbook
of recirculation system No. 3 (PH3) between May, 2015 and April, 2016.
68
By calculation, the kVAR of the capacitor bank can be known
𝐾𝑉𝐴𝑅 =√(𝐾𝑉𝐴 − 𝐾𝑊)2= √(372 − 280)2=245
𝐾𝑉𝐴𝑅 = 245
To improve PF to 0.95
𝑃𝐹 = 𝐾𝑊
𝐾𝑉𝐴 ⟹ 𝐾𝑉𝐴𝑛𝑒𝑤 =
𝐾𝑊
𝑃𝐹 = 295
𝐾𝑉𝐴𝑅𝑠𝑦𝑠 – 𝐾𝑉𝐴𝑅𝑛𝑒𝑤 = 𝐾𝑉𝐴𝑅𝑐𝑎𝑝 = 160
Table 3.1: Record of activities at Pump House No:3 between April 2016 and March 2017
Period Of
The Year
(month)
Actual
kW
Demand
(kW)
Actual
kVA
Demand
(kVA)
Actual
Power
Factor
(%)
New
Power
Factor
(%)
New kVA
Demand
(kVA)
Reduction
kVA
Demand
(kVA)
April 200 245 82 90 222 23
May 150 244 67 90 167 57
June 125 175 71 90 139 36
July 224 256 88 90 249 7
August 208 289 72 90 231 58
September 210 299 70 90 233 66
October 223 289 77 90 248 41
November 211 278 76 90 234 44
December 204 265 77 90 227 38
January 198 245 81 90 220 25
February 156 198 79 90 173 25
March 201 265 76 90 223 42
69
3.10: Experiment No. 2
Aim: To show that Power factor reaches its maximum value under full load
Object: To consider the effect of load on Power factor of a 30kW motor coupled to a water
pump.
Method: A capacitor bank is connected to the electric motor of the water pump, the gate valve
is gradually operated to vary the load and the power factor values were recorded below.
Materials: Wattmeter, Ammeter Power factor meter volt meter
Table 3.2: Load and the Power Factor Value
3.11: Experiment No. 3
Aim: To show the relationship between power factor and true power (kW), Apparent power
(kVA), reactive power (𝑘𝑉𝐴𝑅) and current (I).
Objective: To determine the effect of improved power factor from 0.75 to 0.95 on induction
motors.
Method: A capacitor bank was connected to the low voltage side of a transformer station
10TS10 at recirculating system No. 3 which supplies power to various capacities of induction
motors. As shown in the Figure 3.10.
Motor Load Factor Power Factor
On – no Load 0.18
25% Loaded 0.56
50% Loaded 0.75
75% Loaded 0.85
Full Load 0.96
25% over load 1.0
70
Fig 3.10: The transmission system without the capacitor bank diagram
Fig 3.12: Transmission system with Capacitor Bank diagram
Readings were taken for twelve hours at an interval on one hour between 20th and 21st April,
2017.
11kV
1600kVA, 11/0.415kVA
Point of
reading 0.415kV
Group of
Motors
Group of
Motors
0.415Kv
11Kv
1600KVA, 11/0.415KVA
Capacitor
Group of
Motors
Group of
Motors
Point of
reading
71
Procedure: Parameters of the transformer were taken as below:
Apparent Power (𝐾𝑉𝐴) = 1600
Power Factor (𝑃𝐹) = 0.75
True Power (𝐾𝑊) = ?
But 𝑃𝐹 = 𝐾𝑊
𝐾𝑉𝐴 (3.16)
𝐾𝑊 = 𝐾𝑉𝐴 × 𝑃𝐹= 1600 × 0.75 = 1200KW.
And 𝐾𝑉𝐴 = 1058
To improve PF to 0.95
𝐾𝑊𝑛𝑒𝑤= KVA × 0.95 = 1440
Then𝐾𝑉𝐴𝑅𝑛𝑒𝑤= 697
𝐾𝑉𝐴𝑅𝑐𝑎𝑝= KVARold – 𝐾𝑉𝐴𝑅𝑛𝑒𝑤 = 360
Since𝐾𝑉𝐴𝑅 output of capacitor when connected in series is given as 2𝜋fcV2 x 10-9.
Where C = capacitance in μF.
∴𝐶 = 𝐾𝑉𝐴𝑅
2𝜋𝑓𝑐𝑣2×10−9 = 360 ×109
2𝜋×50 ×4152 = 6650𝜇𝑓
A 350 𝐾𝑉𝐴𝑅 capacitor was therefore installed to improve the power factor and readings were
taken as shown in Table 3.3 and 3.4 respectively.
72
Table 3.3: Before Correction
Time
Hours PF
P
(kW)
Q
kVAr
S
kVA
I
(A)
6.00 0.77 188 156 244 326
8.00 0.77 272 226 353 471
10.00 0.74 328 298 443 591
12.00 0.75 303 267 404 539
14.00 0.75 303 267 404 539
16.00 0.74 286 260 386 515
18.00 0.76 283 242 372 497
Table 3.4: After Correction
Time
Hours PF
P
(kW)
Q
(kVAR)
S
(KVA)
I
(A)
6.00 0.94 188 68 200 267
8.00 0.96 272 79 283 378
10.00 0.94 328 119 349 465
12.00 0.95 303 100 319 425
14.00 0.94 303 110 322 430
16.00 0.95 286 94 301 401
18.00 0.94 283 103 301 401
73
CHAPTER FOUR
RESULT AND DISCUSSION
4.1 Results of Experiment No 1
Table 4.1: Readings of Experimental Loggings between May 2016 and April 2017
Period Of
The Year
(month)
Actual
kW
Demand
(kW)
Actual
kVA
Demand
(kVA)
Actual
Power
Factor
(%)
New
Power
Factor
(%)
New kVA
Demand
(kVA)
Reduction
kVA
Demand
(kVA)
Money
Saved
(₦)
May 200 245 82 90 222 23 108,307
June 150 244 67 90 167 57 268,413
July 125 175 71 90 139 36 169,524
August 224 256 88 90 249 7 32,963
September 208 289 72 90 231 58 273,122
October 210 299 70 90 233 66 310,794
November 223 289 77 90 248 41 193,069
December 211 278 76 90 234 44 207,196
January 204 265 77 90 227 38 178,942
February 198 245 81 90 220 25 117,725
March 156 198 79 90 173 25 117,725
April 201 265 76 90 223 42 197,778
Average 192.5 254 76 90 213 38.5 2,175,555
4.2: Analysis of results obtained from Experiment
(a) Average Power Factor improved by 15% as it was about 0.76 before correction and it
improved to 0.9
(b) The average rated power (kVA) of the transformer was 9.80% as it was 254 before
correction and it became 213.
74
(c) From the above analysis at N47.09/unit of energy used N2,175,558 was saved.
(d) The installation of the capacitor at the load point reduced the kVA demand. The tariff
charges levied on the basis of energy consumed and the maximum reactive power
demand are accordingly reduced by a reduction on the kVA demand.
4.3: Result of Experiment No. 2
Table 4.2: Load and the Power Factor Value
Motor Load Factor Power Factor
On – no Load 0.18
25% Loaded 0.56
50% Loaded 0.75
75% Loaded 0.85
Full Load 0.96
25% over load 1.0
4.4: Graph of Experiment No:2
75
Fig 4.1: Power Factor against Motor Load Factor
From the graph above the power factor increases as the load is increased. The load is applied
at a constant rate.
0
20
40
60
80
100
120
140
0 0.2 0.4 0.6 0.8 1 1.2
MO
TOR
LO
AD
FA
CTO
R (
%)
POWER FACTOR
76
4.5: After Improvement of Power Factor (Experiment No: 3)
Fig 4.2: Power Factor against Time
0.93
0.935
0.94
0.945
0.95
0.955
0.96
0.965
6 8 10 12 14 16 18
PO
WER
FA
CTO
R
TIME (HRS)
77
Fig 4.3: Reactive Power against Time
0
20
40
60
80
100
120
140
6 8 10 12 14 16 18
REA
CTI
VE
PO
WER
Q(K
VA
R)
TIME (HRS)
78
Fig 4.4: Apparent Power against Time
0
50
100
150
200
250
300
350
400
6 8 10 12 14 16 18
AP
PA
REN
T P
OW
ER S
(KV
A)
TIME (HRS)
79
Fig 4.5: Real Power against Time
0
50
100
150
200
250
300
350
6 8 10 12 14 16 18
PO
WER
P(K
W)
TIME (HRS)
80
Fig 4.6: Current against Time
4.6: Analysis of Experiment No.3
From the graph above
(a) The average power factor was improved by 21% as it was 0.75 before power factor
correction and it became 0.95 after PFC
(b) The average loading on the transformer 10TS10 was reduced by 26%. It was 372 kVA
before power factor connection and it became 296 kVA after power factor correction.
(c) The losses on the table reduced by 36.8% as the average current was 497A before the power
factor correction and it became 395 after power factor correction.
0
50
100
150
200
250
300
350
400
450
500
6 8 10 12 14 16 18
CU
RR
ENT
I(A
)
TIME (HRS)
81
(d) The capacitor compensated by 61% of the consumed reactive power as the average was
245kVAR before the power factor improvement and it became 96kVAR after
improvement.
4.7.0 Findings of the Study
The findings are as listed below:
(a) As a result of installation of capacitor bank to our electrical networks, the equipment
temperature was drastically reduced, resulting in longer life span.
(b) More kVA becomes available in other parts of the plant
(c) There is a reduction in current (A) and kVA drawn from the supplier (PHCN) due to
equalization of magnetizing current.
(d) There will be minimal maintenance requirement if capacitor bank is in a clean
environment.
4.8.0: Contribution to Knowledge
The major contributions to knowledge from this project work are listed below: -
(a) That adequate awareness is passed to management of ASCL on the importance of power
factor.
(b) Result can be used as a basis of research by notable scholars and researchers in Nigeria
and other part of the world.
(c) It will call to order the issue of the abuse of electricity through ignorance and negligence
of power factor.
82
CHAPTER FIVE
CONCLUSION AND RECOMMENDATIONS
5.1 Conclusion
A successful attempt has been made to determine the remedy to the problems of poor power
factor of electrical installation of Ajaokuta Steel Plant Power system network. Three
experiments were considered in the investigation and remedy of the problems, bank of
capacitors were used at the load end of a transformer in an operational section of the Steel
Plant. It was established that huge amount of money can be saved from energy bill when the
power factor was improved. Increase in the power factor of the power network of the
recirculating water system No. 3 of Ajaokuta Steel Company Limited can be done by installing
capacitor banks across the power system to reduce kVA demand and power loss.
Engineering economy has been defined as the field of knowledge which deals with the
economy result of engineering and application of the principles and laws of economics to
engineering understanding. However, attractive a project may be from the technical point of
view, it will be fruitless if it is not financially justified. For a justifiable project the economics
of production and utilization has to be considered, hence the essence of this study is to eliminate
waste in electrical energy and increase the output without the need to install additional
transformer and cables.
Power factor is related to power flow in electrical systems and measures how effectively an
electrical power system is being used. In order to effectively use a power system, the power
factor should be as close to unity as possible. This implies that the flow of the reactive power
should be kept to a minimum. Maintaining a high power factor is crucial to obtaining the best
83
possible economic advantage for both utility and the users. Operating a power system at a low
power factor will increase the magnitude of the current in the system which will damage the
equipment and lowers the efficiency of the system due to increase in reactive power demand.
5.2 Recommendations
Further research work should be carried out to investigate the effect of power factor
improvement on switching transient in Ajaokuta Steel Plant Power system network.
Power system designers must put into consideration the issue of leading and lagging power
factor when designing an electrical network for an industry. Heavy penalty should be place on
any industry operating on low power factor.
The Management of Ajaokuta Steel Company Limited should endeavor to installed capacitor
banks in all the transformer sub-stations to reduce the reactive power demand.
84
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