The Autotransformer and Transformer Parameters

The Autotransformer

This differs from the ordinary transformer in that the winding of the autotransformer are electrically connected as well as being coupled by mutual flux.

There is a type of autotransformer called a Variac (VARIAC) which is used to regulate the voltage applied to a particular device from ‘0’ to a certain maximum value Vmax . In the starting of induction motors, variacs are used to start IM (Induction Motors) of rating 5hp and above. This is in order to limit the high surge of current (Starting Current) which usually occurs when the motor is started direct-on-line. Induction Motors of Low horse powers hp<5 are usually started direct-on-line.

Determination of Transformer Parameters
a) Open Circuit Test: The high voltage winding is on open circuit and the low Voltage winding is connected to a variable voltage supply, at normal frequency. The primary is assumed to be the low voltage winding.

The input current and power and the voltage across the open circuit winding are measured for a range of applied voltages up to 125% of the rated voltage.

Then at rated voltage,

Iron Losses Pi = V2g ie g = pi/V2;

Open circuit admittance y = I/V,

Magnetising Susceptance b = √(y2 – g2)

b) Short Circuit Test : The low voltage winding is short circuited through an ammeter and the high voltage winding is connected to a variable voltage supply at normal frequency. The high voltage winding is assumed to be the primary winding.

The input current and power and voltage across the high voltage winding are measured for a range of short circuit currents up to 125% of the rated current.

Cupper loss Pc = I2R, Total
Resistance R = Pc/I2
Short circuit Impedance Z = V/I
Total leakage reactance X = √(Z2 – R2)

Let Us Study The Bible Together Today. {Acts 8}

Bible Study1

Acts 8

Vs 1 Saul was consenting unto his death (the death of Stephen)
There was persecution. The people (early Christians) were scattered as a result of that except the apostles.
Vs 2 devout men carried and buried Stephen.
Vs 3 Saul Put people in Prison
Vs 4 The Christians preached the gospel as they scattered.
Vs 5 Philip preached Christ in Samaria
Vs 6 People believed
Vs 7 Philip cast out unclean spirit in the name of God through Jesus Christ Our Lord.
Vs 8 Salvation brings Joy. When the people got saved, they rejoiced.
Vs 9 -12 Here Simon’s activities were documented which were not very good deeds. He deceived many by them. The preaching of the gospel made the people to repent and believe God through Jesus Christ.
Vs 13 Simon repented.
Vs 14 Jerusalem sent Peter and John to Samaria on their repentance.
Vs 15 -17 Peter and John Prayed and they repented and received the Holy Spirit. The Holy Spirit dwells in a repented heart. There is a need for repentance.
Vs 18 Simon offered money to buy the Holy Ghost.
Things of God are neither bought nor sold. They are freely given by God by grace through Jesus Christ our Lord and savior.
Vs 20 Here Peter rebuked him and said Your money perish with you.
Vs 21-23 You do not buy the things of God.
Vs 24 Simon begged for forgiveness.
Vs 25 They returned to Jerusalem and Preached as they returned.
Vs 26 The Holy Spirit directs Philip towards the south unto the way that goeth down from Jerusalem unto Gaza which is a desert.
Vs 27 He Obeyed.
Vs 28 He ministered to the Ethiopian Eunuch
Vs 29 The Holy Spirit directs Philip. We should be receptive to the directives of the Holy Spirit. We should Put every Spirit to the test to know if it is of God. Jesus Christ is the Standard and the Bible is the Reference. Pray to God always for understanding.
Vs 30 He obeyed. Trust and Obey God.
Isaiah 53 : 7, 8
He asked him Understandest thou what thou readest?
Vs 32 – 33
These passages talked about Jesus Christ and His work of salvation.
Vs 34 -35 Philip explained
Vs 37 He Believed and was baptized. – I believe that Jesus Christ is the son of God.
Vs 39 When Philip finished his assignment, the Spirit took Philip and the Ethiopan rejoiced
Vs 40 Philip continued preaching elsewhere. – at Azotus, Caesarea. We should be sensitive to the Spirit of God and allow the Spirit of God to lead us and direct us in all we do to the glory of God.

Three Phase Transformers And Three Winding Transformers

Three Phase transformers

Three phase transformers usually have all three phases on one iron structure and can be connected in Y(Star) – Δ(Delta), Δ(Delta) – Y(Star). Other possible connections are Y – Y and, Δ – Δ where the first symbol refers to the connection of the primary windings and the second symbol refers to the connection of the secondary winding.

Three Winding transformers.

Some transformers have three windings: primary, secondary and tertiary windings. It is possible to measure three impedances by the standard short circuit tests as follows

Zps = Leakage impedance measured in primary with secondary short circuited and tertiary open.
Zpt = Leakage impedance measured in primary with tertiary short circuited and secondary open
Zst = Leakage impedance measured in secondary with tertiary short circuited and primary open

We note that

Zps = Zp + Zs
Zpt = Zp + Zt {*}
Zst = Zs + Zt

Where Zp, Zs and Zt are the impedances of the primary, secondary and tertiary windings referred to the primary circuit and Zps, Zpt, Zst are the measured impedances referred to the primary circuit.

Solving the equation {*} simultaneously will yield

Zp = ½ (Zps + Zpt – Zst)
Zs = ½ (Zps + Zst – Zpt)
Zt = ½ (Zpt + Zst – Zps)

The impedance of the three windings are connected in star to represent the equivalent circuit of a three winding transformer with magnetizing current neglected.

Parental Responsibility

Parental Responsibility
Let us take a look at Jesus Christ and His Parents and learn from them.
Luke 2: 41 – 52
Vs 41 – 45 The parents of Jesus Christ took Jesus Christ to the temple. As parents, where do you take your children? Kindly take your children to God. Introduce your children early to our Lord Jesus Christ. Make an effort to go regularly to Church with your children. Go together with them. Study the word of God together and pray together. Grow up with your children and help them as they grow up.

Vs 46 They sought Him for 3 days till they found Him. Be patient with your children. Seek them for Jesus Christ until you find them. Do not give up on them. Pray for them spend time with them and talk with them. Seek them for three days until you find them. Search the scriptures with them.

Remind them that Jesus Christ was found in the Temple. Where will you and your children be found when people look for you?

Vs 47 Jesus Christ Had both understanding and answers. When you patiently bring up your children in the way of the Lord, people will be surprised at what they will turn out to be.
Vs 48 The parents of Jesus Christ were amazed when they saw Him. The mother pointed out what they had to pass through to ensure His safety looking for Him and sorrowing. Be patient with your children. Do not be discouraged. If they do the right thing, encourage them the more. Direct them towards where they will learn more about our Lord Jesus Christ. Be patient with them. Correct them in Love. Pray for them.
Vs 49 Jesus went about His Fathers Business. As a father or a mother, what is your business? What do you encourage your children to do. Do what is right in the sight of God and God will bless your children as they do the same.
Vs 50 They did not understand. Sometimes we do not understand. Sometimes others do not understand us. God understands. Be patient even when you do not understand your children. Talk to God about them and be patient. Be patient with God as He works out His purpose in their lives. Be patient with them as they respond to the work of the Holy Spirit in them.
Vs 51 Jesus went with then and was subject unto them. Encourage your children to obey you. On your own part, obey God. Believe in our Lord Jesus Christ and it shall be well with you. You shall be saved. You and your house hold.
Vs 52 God blessed Him. God blessed Jesus Christ. Jesus Christ increased in stature and in wisdom and in favour with God and man. God will bless you and God will bless your children. Trust God and obey God. Believe in God and Believe in our Lord Jesus Christ too.

Parental Responsibility

Parental Responsibility
Let us take a look at Jesus Christ and His Parents and learn from them.
Luke 2: 41 – 52
Vs 41 – 45 The parents of Jesus Christ took Jesus Christ to the temple. As parents, where do you take your children? Kindly take your children to God. Introduce your children early to our Lord Jesus Christ. Make an effort to go regularly to Church with your children. Go together with them. Study the word of God together and pray together. Grow up with your children and help them as they grow up.

Vs 46 They sought Him for 3 days till they found Him. Be patient with your children. Seek them for Jesus Christ until you find them. Do not give up on them. Pray for them spend time with them and talk with them. Seek them for three days until you find them. Search the scriptures with them.

Remind them that Jesus Christ was found in the Temple. Where will you and your children be found when people look for you?

Vs 47 Jesus Christ Had both understanding and answers. When you patiently bring up your children in the way of the Lord, people will be surprised at what they will turn out to be.
Vs 48 The parents of Jesus Christ were amazed when they saw Him. The mother pointed out what they had to pass through to ensure His safety looking for Him and sorrowing. Be patient with your children. Do not be discouraged. If they do the right thing, encourage them the more. Direct them towards where they will learn more about our Lord Jesus Christ. Be patient with them. Correct them in Love. Pray for them.
Vs 49 Jesus went about His Fathers Business. As a father or a mother, what is your business? What do you encourage your children to do. Do what is right in the sight of God and God will bless your children as they do the same.
Vs 50 They did not understand. Sometimes we do not understand. Sometimes others do not understand us. God understands. Be patient even when you do not understand your children. Talk to God about them and be patient. Be patient with God as He works out His purpose in their lives. Be patient with them as they respond to the work of the Holy Spirit in them.
Vs 51 Jesus went with then and was subject unto them. Encourage your children to obey you. On your own part, obey God. Believe in our Lord Jesus Christ and it shall be well with you. You shall be saved. You and your house hold.
Vs 52 God blessed Him. God blessed Jesus Christ. Jesus Christ increased in stature and in wisdom and in favour with God and man. God will bless you and God will bless your children. Trust God and obey God. Believe in God and Believe in our Lord Jesus Christ too.

Introduction To Conventional And Renewable Energy Resources For Power Generation

Introduction To Conventional And Renewable Energy Resources For Power Generation.
In order to generate electrical energy we have to depend on sources such as coal, natural gas, hydro(water), and nuclear energy. These can be classified as follows:

A) Fossil Fuels
1) Coal
2) Oil
3) Natural gas
4) Substitute fuels eg. coal liquefaction and coal gasification
5) Oil from shale
6) Oil from tar sand

B) Nuclear Energy
1) Fission Reactors
2) Breeder Reactors
3) Fusion Reactors

C) Natural Sources
1) Hydro electric Power
2) Geothermal
3) Wind
4) Solar – Solar thermal, Photovoltaic
5) Ocean – Ocean thermal, Ocean current, tidal

Conventional Energy Sources
The conventional Energy Sources are as those that have been in use for over a century and which are considered less risky. Examples are hydroelectric power stations, fossil fueled power stations.

The following block diagrams highlight the process of Energy Conversion in the nuclear , Fossil fueled and hydro power stations.

Fossil Fuel – Boiler — Heat Energy – Steam Turbine – Mechanical Energy - Generator  Electrical Energy

Water in Reservoir – Hydraulic Turbine – Mechanical Energy - Generator  Electrical Energy

Heat From Nuclear Reactor –Steam Generator — Heat Energy – Steam Turbine – Mechanical Energy - Generator  Electrical Energy

Bible Study

Bible Study

Mathew 15

Vs 1 Scribes and Pharasees came to Jesus Christ
Vs 2 They asked Him: Why disciples transgress traditions of elders because they wash not their hands when they eat bread.
Vs 3 He answered and said unto them why do ye also transgress the commandment of God by your tradition?
Vs 4 Honour thy Father and Mother
Vs 5 Excuse: People use excuses or make excuses why they will not honour their parents.
Vs 6 They by so doing, They make the commandment of God of no effect by their tradition.
Vs 7 Ye hypocrites well did Esaias prophesy of you saying.
Vs 8 This people draweth nigh unto me with their mouth and honoureth me with their lips; but their heart is far from me.
Vs 9 In vain they do worship God. Teaching for doctrine the commandments of Men
Vs 11 Not that which goeth into the mouth defileth a man – but that which cometh out of the mouth, this difileth a man.
Vs 12 The Pharasees were offended
Vs 14 Blind Leaders of the Blind – both fall into the ditch

Explanation

Vs 17 Food is cast out into the draught as waste after digestion.
Vs 18 When you speak it is from the heart
Vs 19 Man is defiled by sin
Vs 20 Outward ceremonies does not make holy and the lack of it does not defile
Vs 21 Jesus departed – Once Jesus Christ has done His work He departs.
Vs 22 A woman of Canaan – asked Jesus Christ to heal her daughter.
When you have any Problem remember to go to Jesus Christ Pray to God through Jesus Christ our Lord.
Vs 23 Jesus Christ answered her not a word. – At first she was ignored. Do not be discouraged when you pray, have faith.
His disciples asked Him – Jesus Christ to send her away – Do not be discouraged in life. Have faith in God. Trust in God.
Vs 24 Jesus Christ said I am not sent but unto the lost sheep of the house of Israel – answered Jesus Christ
Vs 25 She was not discouraged. She had faith and continued to seek God’s help – Then came she and worshiped Him saying, Lord help me.
Vs 26 He asked and said It is not meet to take the childrens’ bread and cast it to dogs
Vs 27 Truth, Lord yet the dogs eat of the crumbs which fall from their master’s table
Vs 28 Jesus Christ answered and said : great is thy faith be it unto you even as thou wilt and her daughter was made whole from that very hour.
Vs 29 Again Jesus Christ departed and went up into a mountain
Note that once the work is done Jesus Christ moves on He does not stay idle. He moves on to do the next work of God.
Vs 30 Lame – blind – dumb – maimed – and many others
Vs 31 He healed them and they glorified God of Israel .
Who do you attract to yourself? Can you tolerate the sick the weak and the maimed? Can you be willing to help them?
Vs 32 Jesus Christ called His disciples : Are you His disciple; then He will call you.
Vs 33-34 He will give you an assignment. He spoke to them fist. He said: I have compassion on the multitude. He had a dialogue with His disciples.
Vs 35 Jesus Christ commanded the multitude to sit down. He took the seven loaves and the fishes and gave thanks and break them and gave to His disciples, and the disciples to the multitude and they did eat and were filled.

Let us learn to give thanks. Whatever we have , let us give thanks. Learn to give. Jesus asked them to sit down. God loves order.

Vs 37 They did all eat and were filed
Vs 38 4000 men ate besides women and children
Vs 39 He sent away the multitude. And took ship and came into the cast of Magdala

Per Unit System

Per Unit System
The Per – Unit Value of any quantity is defined as the ratio of the quantity to its base value expressed as a decimal.

Voltage, current, kilovoltamperes and impedance are so related that the selection of the base values for any two of them determines the base values for the remaining two.
Base Current, A, = (base kVA1Φ)/base Voltage kVLN

Base Impedance, Z, = (base Voltage VLN)/base Current A
Base Impedance, Z = ((base Voltage kVLN)2 * 1000)/Base kVA1Φ
Base Impedance, Z = (base Voltage, kVLN)2/Base MVA1Φ

Base Power kW = base kVA1Φ
Base Power MW = base MVA1Φ

Per Unit Impedance = (Actual Impedance [Ω]) /Base Impedance [Ω]

To change from per unit impedance on a given base to Per Unit impedance on a new base the following equation applies.

Per Unit Znew = Per-Unit Zgiven(Base kVgiven/Base kVnew)2(BasekVAnew/Base kVAgiven)

Note that this expression has nothing to do with transferring the ohmic value of impedance from one side of the transformer to the other.

Advantages of Per Unit Computations

1. Manufacturers usually specify the impedance of a piece of apparatus in percent or per unit on the base of the nameplate rating
2. The Per-Unit impedances of machines of the same type and widely different rating usually lie within a narrow range though the ohmic values differ materially for machines of different ratings. For this reason, when the impedance is not known definitely, it is generally possible to select from tabulated average values a per-unit impedance which will be reasonably correct. Experience in working with Per-Unit values brings familiarity with the proper values of per-unit impedance for different types of apparatus.
3. When impedance in ohms is specified in an equivalent circuit, each impedance must be referred to the same circuit by multiplying it by the square of the ratio of the rated voltages of the two sides of the transformer connecting the reference circuit and the circuit containing the impedance. The Per-Unit impedance once it is expressed on the base is the same referred to either side of the transformer.
4. The way in which transformers are connected in three phase circuits does not affect the per unit impedances of the equivalent circuit although the transformer connection does determine voltage bases on the two sides of the transformer.

Challenges Of Growing Up

Challenges Of Growing Up

Jesus Christ was born into a family on earth. Jesus Christ grew up too. Jesus Christ recognized the Authority of His Parents
Jesus Christ knew the Power of God. Jesus went to the Temple and worshiped God.
Jesus Christ Asked questions while He was growing up. Jesus Christ learnt from Doctors.
Luke 2: 42-52

Jesus Christ went about His Fathers Business.
Jesus Christ knew God as Father.
We should know God as Father.
We should go about God’s business
Who is your father and what is his business?
Where do you spend most of your time and what do you spend most of your time doing?
Jesus Christ obeyed His parents.

Jesus increased in stature and in favour with God and man.
Be ye like Jesus Christ and it shall be well with you.
God bless you.

Half Wave Rectifier

Half Wave Rectifier

When a diode is introduced between a sinusoidal voltage source and a linear load circuit, the excitation is no longer a pure sinusoid.
The forced response is no longer determined by the method of sinusoidal steady – state circuit analysis at source frequency. It should however be noted that the excitation provided by an alternating voltage source in series with a diode is however periodic and any such excitation can be represented by the sum of an infinite series of sinusoidal functions of related frequency.

Having done this, the forced response to each significant term of this series may then be determined by sinusoidal steady – state analysis of the appropriate frequency.

Given a linear load circuit, superposition theorem can be used to combine the forced responses to all significant terms.

Similarly, the current supplied by the source to a half-wave rectifier circuit is also non-sinusoidal but periodic.

The fourier series is used to calculate and analyse the waveform of most converters to determine their suitability for the intended use.

If a non-ideal voltage source in the form of a single-phase transformer were employed to excite such a circuit, the direct component of the current would saturate the core of the transformer unless the core were extremely large.

Full – wave single phase and polyphase circuits are not subject to unrealistic limitations and the analysis of the halfwave can be extended to these

In the circuit,
Current will flow when

v – vo > 0 : VAK = 0 [V]
The fourier series expansion of the rectified voltage is given by

vo = Vo + an sin nωt + bn cos nωt [V]

α : firing angle of the diode ie the angle at which it starts to conduct.
Β : extinction angle ie. Angle at which the diode stops conducting

ϒ = β – α (rad)

ϒ: conduction angle ie. Angle during which the diode is conducting ϒ

Active Load: A load which has a voltage source or excitation

Passive Load: A load with no voltage source or excitation.

If a diode is supplying a passive load circuit,

α = 0 and ϒ=β

The magnitude of β depends on the nature of the Load circuit.

The coefficients of the fourier expression is determined for the general case using the expressions below.

Vo =(1/2π)∫ vod(ωt) =(1/2π)∫ vod(ωt) [ V ]

an =(1/π)∫ vosinnωtd(ωt) =(1/π)∫ vosinnωtd(ωt) [ V ]

bn =(1/π)∫ vocosnωtd(ωt) =(1/π)∫ vocosnωtd(ωt) [ V ]

Vo = average value of rectified voltage ie. Dc output voltage

The rms value of the nth harmonic voltage is given by.

vnR = 1/√2[a2n + b2n ]1/2 [V]

The rms value of the rectified voltage is

VR = [(1/2π) ∫ v2od(ωt)]1/2

= [Vo2 + ΣV 2n R ]1/2 [V]

So that the rms value of the harmonic component or ripple voltage is

VRI = [ΣV2n R ]1/2 [V]

= [V2R – V2o ]1/2 [V]

Kv : Voltage ripple factor
Kv = VRI/Vo

Similar equations can be written for the line and load current in the circuit.