Symmetrical Components

 SYMMETRICAL COMPONENTS

An unbalanced system of n related phasors can be resolved into n systems of balanced phasors called symmetrical components of the original phasors.

These symmetrical components are balanced. They are equal in length and the angle between them are also equal.

In the Electrical Power System, The Symmetrical Components used, has the Positive Sequence component, the negative Sequence component and the zero Sequence components.

The characteristic of these components are as follows:

The Positive Sequence component,

The Positive Sequence components consist of three phasors equal in magnitude displaced from each other by 120^o in phase and having the same phase sequence as the original Phasors. ,

The negative Sequence component,

The negative Sequence components consist of three phasors equal in magnitude displaced from each other by 120^o in phase and having a phase sequence opposite that of the original Phasors. ,

The Zero Sequence component,

 The Zero Sequence Components consist of three phasors equal in magnitude with zero phase displacement from each other.

V(a) = V(a1)+V(a2)+V(a0)                (i)

V(b) = V(b1)+V(b2)+V(b0)               (ii)

V(c) = V(c1)+V(c2)+V(c0)                (iii)

Positive Sequence Component   abc(phase sequence of original phasors) ------- abc (phase sequence of symmetrical components)

Negative Sequence Component   abc(phase sequence of original phasors) --------  acb(phase sequence of symmetrical components)

1=> +ve

2=> -ve

0=> zero

In symmetrical Component Analysis, ‘a’ causes a rotation of 120^o

In circuit analysis, ‘j’ causes a 90^o rotation

In complex number notation ‘i’ causes a 90^o rotation

In numerical analysis and number notation and representation ‘-1’ causes a 180^o rotation

A rotation of 90o + 90o  is achieved by multiplying ‘ j x j ’ which causes a 180^o rotation j² = -1.

With this understanding,

a = 1/120 = 1e^j2π/3 = -0.5 + j0.866

apply ‘a’ twice to achieve a 240^o rotation

when ‘a’ is applied three times the phasor is rotated 360o

Hence

a² = 1/240 = 1e^j4π/3 = -0.5 - j0.866

a³ = 1/360 = 1e^j2π = 1/0^o = 1

V(b1) = a²V(a1)

V(b2) = aV(a2)

 V(b0) = V(a0)

V(c1) = aV(a1)

V(c2) = a²V(a²)

V(c0) = V(a0)

V(a) = V(a1) + V(a2) + V(a0)

V(b) = a²V(a1) + aV(a2) + V(a0)

V(c) =aV(a1) + a²V(a2) + V(a0)

 

A      =

 

A^-1       =

 

A^-1   = 1/3                                                                              A^-1       =  1/3

 

                                      

V(a0) = 1/3 (V(a) + V(b) + V(c))

V(a10) = 1/3 (V(a) + aV(b) + a²V(c))

V(a20) = 1/3 (V(a) + a²V(b) + aV(c))

Let us take a look at the effect of Symmetrical Components on the Impedance with respect to the Electrical Power System.

V(abc) = Z(abc)I(abc)

Where

Z(abc)  3x3 matrix giving the self and mutual impedances in and between phases

However

V(abc) = [A]V(012)

I(abc) = [A]I(012)

[A]V(012) = Z(abc)[A]I(012)

Or

V(012) = [A]^-1Z(abc)[A]I(012)

Let us define

Z(012) = [A]^-1Z(abc)[A]

V(012) = Z(012)I(012)

Power Considerations

We shall apply the Reversal Rule of Matrix Algebra.

The Reversal Rule of Matrix Algebra.

The Reversal Rule Of Matrix Algebra states that the transpose of the Product of two matrices is equal to the Product of the transpose of the matrices in reverse order hence :

[AV]^T  =  V^TA^T

Complex Power can be expressed as follows in the Electrical Power System:

S(3φ) = V(a)I^*(a) + V(b)I^*(b)+ V(c)I^*(c)

Let ‘t’  =>   transpose (interchange of rows and columns in a matrix  v^*(i,j) = v(j,i) )

Let ’^*’ =>   conjugate (the mirror image along the x axis of the complex plane of a complex number or phasor )

In Matrix Notation, This can be written as:

S(3φ) = Vt(abc)I^*(abc)

           = {[A]V(012)}t{[A]I(012)} ^*

           = V(012)tAtA^*I^*(012)

 

                                       A^t  A^*  = 

 

                                                         =

                                        

Therefore

S(3φ)  =  3V(012)t I^* (012)

S(3φ)   =  3(V(0)I^*(0)V(1)I^*(1)V(2)I^*(2))

Notice that there are no cross terms or mixed quantities in the expression for S(3φ). This is useful when equivalent circuits are being considered.

Symmetrical Components are very important in the Analysis of the Electrical Power System.

It is particularly very useful in the analysis of unbalanced faults as a result of the unbalanced phasors associated with them.

God Loves Us All

For God so loved the world that He gave His only begotten Son that whosoever believeth in Him shall not perish but have everlasting life. Seek ye first the kingdom of God and His righteousness and every other thing shall be added unto you. You are the light of the world. Let your light so shine before men that they may see your good works and glorify your father in heaven. Let not your heart be troubled believe in God believe also in our Lord Jesus Christ.  Jesus died to save us from our sins.  

Past Question Papers in Electrical Power Engineering

These Questions have been Obtained with the Express Permission of the Lecturer Teaching the Course

ENUGU STATE UNIVERSITY OF SCIENCE AND TECHNOLOGY ESUT

DEPARTMENT OF ELECTRICAL/ELECTRONICS ENGINEERING

SECOND SEMESTER EXAMINATION 2011/2012 SESSION            MASTERS CLASS

ELECTROMAGNETIC FIELD THEORY AND ELECTRICAL MACHINE DYNAMICS (EEE 770)

TIME: 1Hr 30Min (Answer All Questions)

NB: IF you have not done any continuous assessment, write down what you have learnt in about 120 words first.

BASIC CONCEPTS

Explain the characteristics and behavior of the Electrical Frequency on the Rotor of an induction motor. What are the main types of induction motors and how are they constructed? What is an Induction Motor? How does it Work? What is the difference between an induction motor and a synchronous machine? Explain the concept of slip. What is slip speed? How is torque developed in an induction motor? Compare the principle of operation of the transformer and the induction Motor. Explain the concept of rotating transformer. What happens as the induction motor approaches synchronous speed? What is the maximum possible speed of an induction Motor and why? Explain the Power flow in an induction motor. What is the efficiency of an induction motor? How does a thyristor work? What is Maxwell's equation? What is the relevance of Maxwell's equation in the study and investigation of fields and waves? Show that the continuity equation is imbedded in the Maxwell's equation. What is directional derivative? What is the curl? What is the gradient of a scalar function? What is the del? What is the divergence of a vector?

APPLICATION

You are responsible for setting up a new Vehicle assembly plant in Nigeria. What motors would you recommend for the various drives and why? How would you control the various drive systems and why? What kind of switches would you use and why? What would be the switching response of the entire assembly and why? What kind of load would this present to the Electrical Power System and how would you make provision for it? What are the applications of Power Electronics in Machine dynamics? Illustrate an induction motor equivalent circuit.

CALCULATIONS

A 200V 10hp four-pole 50Hz Y- connected induction motor has a full-load slip of 4 percent. Answer the following questions about this machine and explain your work:

a)      What is the synchronous speed of the motor?

b)      What is the rotor speed of the motor?

c)       What is the rotor frequency of this motor at the rated load?

d)      What is the shaft torque of the motor at the rated load?

A 450V 50hp three phase induction motor is drawing 50A at 0.8 p.f. lagging. The Stator copper losses are 1.82kW, and the rotor copper losses are 500W, the core losses are 1500W, and the stray losses are negligible. Find the following quantities and explain your work.  Explain in some considerable detail, how the induction motor converts Electrical energy to Mechanical energy. 

a)      The air-gap Power P(AG)

b)       The Power Converted P(conv)

c)       The output Power P(out)

d)      The efficiency of the motor

Do Good Always

Either make the tree good, and his fruit good or else make the tree corrupt, and his fruit  corrupt: for the tree is known by his fruit.

O generation of vipers, how can ye being evil , speak good things? For out of the abundance of the heart the mouth speaketh. A good man out of the treasure of the heart brings forth good things: and an evil man out of the evil treasures bring forth evil things.

But I say unto you that every idle word that men shall speak, they shall give account thereof in the day of judgement. For by thy words thou shall be justified, and by thy words thou shalt be condemned

For whosoever shall do the will of of my Father which is in heaven, the same is my brother, and sister, and mother. Jesus said I will have mercy, and not sacrifice,

For the Son of Man is Lord even of the sabbath day. How much then is a man better than a sheep? Wherefore it is lawful to do well on the sabbath day.    

INTRODUCTION TO POWER ELECTRONICS

POWER ELECTRONICS

Power Electronics is an area of study and specialization that aims at applying the speed and other desirable properties of Electronic devices in Electrical Power Systems Engineering.

Over the years, it has been found out that the Thyristors are reliable Power Electronic devices which are fast and are able to withstand high voltages and currents.

In this study, the Thyristor shall be investigated with a view of determining its characteristics and how it can be applied in practice to realize desirable Power Electronics Components, Circuits and Devices.

Areas Of Interect

Types of Converters
Converters are Power Semiconductor Systems used for rectifying, inverting, or otherwise modulating the Power Output of an AC or DC energy source.

Types of Converters

AC Voltage Controller:
Converts Fixed Voltage AC  to variable Voltage AC
Rectifiers (Uncontrolled)
Converts Fixed Voltage AC to Fixed Voltage DC
Rectifiers (Controlled)
Converts Fixed Voltage AC to Variable Voltage DC
DC to DC Converter (Chopper)
Converts Fixed Voltage DC to Variable Voltage DC
Inverters (Uncontrolled)
Converts Fixed Voltage DC to Fixed Voltage AC
Inverters (Controlled)
Converts Fixed Voltage DC to variable Voltage AC

Cycloconverters
ConvertsFixed frequency AC toVariable frequency, variable Voltage AC


Thyristors and their Applications

Switches
Rectification
DC to DC Convertion (Chopper)
Inverters

Thyristors can be used instead of :

Mecury - arc rectifiers
relays and Contactors
Rheostats and Motor Starters
Autotransformers
Mechanical Speed Changers
etc,

Application

Electric drives for rapid-transit systems
Rolling-mill drives
Multiple-drive Systems for textile and paper mills
Machine tool control
Aircraft Power Supply
UPS
DC Power Transmission etc.

Diode and Thyristors

Current passes from anode to cathode of a diode but not in the opposite direction

In the case of a thyristor, when a small current is passed from the gate terminal to the cathode, the thyristor will conduct, provided that the anode is at a higher potential than the cathode.

Once conduction starts, the gate circuit looses control. The device then continues to conduct until the potential of the anode becomes equal to or less than that of the cathode for a brief interval. At the end of which the gate circuit is once again in control.

Where possible, seperate the Cathode-gate circuit from Cathode external circuit.

Anode - Cathode Resistance
The anode - Cathode Resistance of a diode or of a thyristor in the conducting state is very low but not zero. Hence large anode current produce heat. Hence heat sink is used to remove the heat and sefeguard the device.

Switch

A switch presents either infinit or zero resistance to current. It is desirable to have a switch which is capable of instantenous transition from one state to another. The thyristor or the diode can be used as a switch. Eg. an ideal diode.

The diode conducts if source voltage v is positive. The anode - cathode voltage v(AK) is then zero.
The diode does not conduct if the source voltage is negative, then v(AK) is also negative

The operating point of the diode may lie on the +ve axis of i(A) in the range 0>=v(AK)>=-2V

Holy

Holy
Be ye holy for I am holy says the Lord God

Illumination

Illumination
Law of Inverse Square:

The amount of Light which falls on one unit of the area of these surfaces is inversely proportional to the square of the distance from the source. The brightness of the surface as it appears to the eye when viewed from a fixed distance depends on the amount of light that falls on it.

A stronger light will be placed further away from the surface than a weaker one to produce the same effect.

Candela
Candela: Unit of Light source measurrement.

Luminous Intensity (Symbol I)
This has to do with the strength of a source of Light and is measured in Candelas. This is a measure of the rate at which a source of Light is sending out Luminous energy in a given direction.

Luminous Flux (O) measured in Lumen

A divergent beam (cone or Pyramid)

Consider a surface, a distance d from the source, half way the beam length.

The light incident on a unit surface area of the surface is inversely proportional to the square of the distance.

Hence:

AI/d2 = O

Given an area 'A' and a luminous intensity I, the amount of light incident on the area 'A' is proportional to AI/d2

If A and d are measured in  SI unit meter. this amount of light, referred to as luminous flux is measured in lumens.

When unity = 1 lumen.

This is the amount of light falling on a unit area 1m2 illuminated by a source with luminous intensity of 1 Candela placed a unit distance 1m away.

God is good to Us

THE FIRST GENERAL EPISTLE OF JOHN

CHAPTER 1
1 That which was from the beginning, which we have heard, which we have seen with our eyes, which we have looked upon, and our hands have handled, of the Word of life;
2 (For the life was manifested, and we have seen [it], and bear witness, and shew unto you that eternal life, which was with the Father, and was manifested unto us;)
3 That which we have seen and heard declare we unto you, that ye also may have fellowship with us: and truly our fellowship [is] with the Father, and with his Son Jesus Christ.
4 And these things write we unto you, that your joy may be full.
5 This then is the message which we have heard of him, and declare unto you, that God is light, and in him is no darkness at all.
6 If we say that we have fellowship with him, and walk in darkness, we lie, and do not the truth:
7 But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin.
8 If we say that we have no sin, we deceive ourselves, and the truth is not in us.
9 If we confess our sins, he is faithful and just to forgive us [our] sins, and to cleanse us from all unrighteousness.
10 If we say that we have not sinned, we make him a liar, and his word is not in us.

CHAPTER 2
1 My little children, these things write I unto you, that ye sin not. And if any man sin, we have an advocate with the Father, Jesus Christ the righteous:
2 And he is the propitiation for our sins: and not for our's only, but also for [the sins of] the whole world.
3 And hereby we do know that we know him, if we keep his commandments.
4 He that saith, I know him, and keepeth not his commandments, is a liar, and the truth is not in him.
5 But whoso keepeth his word, in him verily is the love of God perfected: hereby know we that we are in him.
6 He that saith he abideth in him ought himself also so to walk, even as he walked.
7 Brethren, I write no new commandment unto you, but an old commandment which ye had from the beginning. The old commandment is the word which ye have heard from the beginning.
8 Again, a new commandment I write unto you, which thing is true in him and in you: because the darkness is past, and the true light now shineth.
9 He that saith he is in the light, and hateth his brother, is in darkness even until now.
10 He that loveth his brother abideth in the light, and there is none occasion of stumbling in him.
11 But he that hateth his brother is in darkness, and walketh in darkness, and knoweth not whither he goeth, because that darkness hath blinded his eyes.
12 I write unto you, little children, because your sins are forgiven you for his name's sake.
13 I write unto you, fathers, because ye have known him [that is] from the beginning. I write unto you, young men, because ye have overcome the wicked one. I write unto you, little children, because ye have known the Father.
14 I have written unto you, fathers, because ye have known him [that is] from the beginning. I have written unto you, young men, because ye are strong, and the word of God abideth in you, and ye have overcome the wicked one.
15 Love not the world, neither the things [that are] in the world. If any man love the world, the love of the Father is not in him.
16 For all that [is] in the world, the lust of the flesh, and the lust of the eyes, and the pride of life, is not of the Father, but is of the world.
17 And the world passeth away, and the lust thereof: but he that doeth the will of God abideth for ever.
18 Little children, it is the last time: and as ye have heard that antichrist shall come, even now are there many antichrists; whereby we know that it is the last time.
19 They went out from us, but they were not of us; for if they had been of us, they would [no doubt] have continued with us: but [they went out], that they might be made manifest that they were not all of us.
20 But ye have an unction from the Holy One, and ye know all things.
21 I have not written unto you because ye know not the truth, but because ye know it, and that no lie is of the truth.
22 Who is a liar but he that denieth that Jesus is the Christ? He is antichrist, that denieth the Father and the Son.
23 Whosoever denieth the Son, the same hath not the Father: [(but) he that acknowledgeth the Son hath the Father also].
24 Let that therefore abide in you, which ye have heard from the beginning. If that which ye have heard from the beginning shall remain in you, ye also shall continue in the Son, and in the Father.
25 And this is the promise that he hath promised us, [even] eternal life.
26 These [things] have I written unto you concerning them that seduce you.
27 But the anointing which ye have received of him abideth in you, and ye need not that any man teach you: but as the same anointing teacheth you of all things, and is truth, and is no lie, and even as it hath taught you, ye shall abide in him.
28 And now, little children, abide in him; that, when he shall appear, we may have confidence, and not be ashamed before him at his coming.
29 If ye know that he is righteous, ye know that every one that doeth righteousness is born of him.

CHAPTER 3
1 Behold, what manner of love the Father hath bestowed upon us, that we should be called the sons of God: therefore the world knoweth us not, because it knew him not.
2 Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is.
3 And every man that hath this hope in him purifieth himself, even as he is pure.
4 Whosoever committeth sin transgresseth also the law: for sin is the transgression of the law.
5 And ye know that he was manifested to take away our sins; and in him is no sin.
6 Whosoever abideth in him sinneth not: whosoever sinneth hath not seen him, neither known him.
7 Little children, let no man deceive you: he that doeth righteousness is righteous, even as he is righteous.
8 He that committeth sin is of the devil; for the devil sinneth from the beginning. For this purpose the Son of God was manifested, that he might destroy the works of the devil.
9 Whosoever is born of God doth not commit sin; for his seed remaineth in him: and he cannot sin, because he is born of God.
10 In this the children of God are manifest, and the children of the devil: whosoever doeth not righteousness is not of God, neither he that loveth not his brother.
11 For this is the message that ye heard from the beginning, that we should love one another.
12 Not as Cain, [who] was of that wicked one, and slew his brother. And wherefore slew he him? Because his own works were evil, and his brother's righteous.
13 Marvel not, my brethren, if the world hate you.
14 We know that we have passed from death unto life, because we love the brethren. He that loveth not [his] brother abideth in death.
15 Whosoever hateth his brother is a murderer: and ye know that no murderer hath eternal life abiding in him.
16 Hereby perceive we the love [of God], because he laid down his life for us: and we ought to lay down [our] lives for the brethren.
17 But whoso hath this world's good, and seeth his brother have need, and shutteth up his bowels [of compassion] from him, how dwelleth the love of God in him?
18 My little children, let us not love in word, neither in tongue; but in deed and in truth.
19 And hereby we know that we are of the truth, and shall assure our hearts before him.
20 For if our heart condemn us, God is greater than our heart, and knoweth all things.
21 Beloved, if our heart condemn us not, [then] have we confidence toward God.
22 And whatsoever we ask, we receive of him, because we keep his commandments, and do those things that are pleasing in his sight.
23 And this is his commandment, That we should believe on the name of his Son Jesus Christ, and love one another, as he gave us commandment.
24 And he that keepeth his commandments dwelleth in him, and he in him. And hereby we know that he abideth in us, by the Spirit which he hath given us.

CHAPTER 4
1 Beloved, believe not every spirit, but try the spirits whether they are of God: because many false prophets are gone out into the world.
2 Hereby know ye the Spirit of God: Every spirit that confesseth that Jesus Christ is come in the flesh is of God:
3 And every spirit that confesseth not that Jesus Christ is come in the flesh is not of God: and this is that [spirit] of antichrist, whereof ye have heard that it should come; and even now already is it in the world.
4 Ye are of God, little children, and have overcome them: because greater is he that is in you, than he that is in the world.
5 They are of the world: therefore speak they of the world, and the world heareth them.
6 We are of God: he that knoweth God heareth us; he that is not of God heareth not us. Hereby know we the spirit of truth, and the spirit of error.
7 Beloved, let us love one another: for love is of God; and every one that loveth is born of God, and knoweth God.
8 He that loveth not knoweth not God; for God is love.
9 In this was manifested the love of God toward us, because that God sent his only begotten Son into the world, that we might live through him.
10 Herein is love, not that we loved God, but that he loved us, and sent his Son [to be] the propitiation for our sins.
11 Beloved, if God so loved us, we ought also to love one another.
12 No man hath seen God at any time. If we love one another, God dwelleth in us, and his love is perfected in us.
13 Hereby know we that we dwell in him, and he in us, because he hath given us of his Spirit.
14 And we have seen and do testify that the Father sent the Son [to be] the Saviour of the world.
15 Whosoever shall confess that Jesus is the Son of God, God dwelleth in him, and he in God.
16 And we have known and believed the love that God hath to us. God is love; and he that dwelleth in love dwelleth in God, and God in him.
17 Herein is our love made perfect, that we may have boldness in the day of judgment: because as he is, so are we in this world.
18 There is no fear in love; but perfect love casteth out fear: because fear hath torment. He that feareth is not made perfect in love.
19 We love him, because he first loved us.
20 If a man say, I love God, and hateth his brother, he is a liar: for he that loveth not his brother whom he hath seen, how can he love God whom he hath not seen?
21 And this commandment have we from him, That he who loveth God love his brother also.

CHAPTER 5
1 Whosoever believeth that Jesus is the Christ is born of God: and every one that loveth him that begat loveth him also that is begotten of him.
2 By this we know that we love the children of God, when we love God, and keep his commandments.
3 For this is the love of God, that we keep his commandments: and his commandments are not grievous.
4 For whatsoever is born of God overcometh the world: and this is the victory that overcometh the world, [even] our faith.
5 Who is he that overcometh the world, but he that believeth that Jesus is the Son of God?
6 This is he that came by water and blood, [even] Jesus Christ; not by water only, but by water and blood. And it is the Spirit that beareth witness, because the Spirit is truth.
7 For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one.
8 And there are three that bear witness in earth, the Spirit, and the water, and the blood: and these three agree in one.
9 If we receive the witness of men, the witness of God is greater: for this is the witness of God which he hath testified of his Son.
10 He that believeth on the Son of God hath the witness in himself: he that believeth not God hath made him a liar; because he believeth not the record that God gave of his Son.
11 And this is the record, that God hath given to us eternal life, and this life is in his Son.
12 He that hath the Son hath life; [and] he that hath not the Son of God hath not life.
13 These things have I written unto you that believe on the name of the Son of God; that ye may know that ye have eternal life, and that ye may believe on the name of the Son of God.
14 And this is the confidence that we have in him, that, if we ask any thing according to his will, he heareth us:
15 And if we know that he hear us, whatsoever we ask, we know that we have the petitions that we desired of him.
16 If any man see his brother sin a sin [which is] not unto death, he shall ask, and he shall give him life for them that sin not unto death. There is a sin unto death: I do not say that he shall pray for it.
17 All unrighteousness is sin: and there is a sin not unto death.
18 We know that whosoever is born of God sinneth not; but he that is begotten of God keepeth himself, and that wicked one toucheth him not.
19 [And] we know that we are of God, and the whole world lieth in wickedness.
20 And we know that the Son of God is come, and hath given us an understanding, that we may know him that is true, and we are in him that is true, [even] in his Son Jesus Christ. This is the true God, and eternal life.
21 Little children, keep yourselves from idols. Amen.

Design Considerations For Residential Houses, Multistory, Multiflat Buildings; Office Blocks, Factories and Public Buildings.

Design Considerations for Residential Houses, Multistory, Multiflat buildings; Office Blocks, factories and Public Buildings.

Some of the design considerations are outlined below. It should be noted that the experience of the engineer is very important in design.

Architectural and Structural Drawings

In most projects, the Electrical Engineer forms part of a design team. This team include other Service Engineers and the Architect, Other members of the team provide information which the engineer utilizes for his design. The Architectural and Structural Drawings which are used by the Electrical Engineer for Electrical Services design work. Some of the information provided by these drawings include the nature, location and intended use of the bulding of interest. The location of beams and columns, and cantelivers. Other details which would be of interest to the engineer and which will influence the design consequently.

Luminous Level, and Electrical Facilities to be installed or provided for.

A good understanding of the proposed project would enable the Engineer determine the appropriate Electrical facilities to be installed or provided for within the limits of available resources. This calls for good client - consultant relationship for proper understanding of the needs of the client as well as the recommendations of the consultant. The luminous requirement of the various parts of the building is also determined.  

Selection of Fittings, Luminares, Cables and other Facilities.


Load Analysis


Protection and Control

Bill of Quantities

Supervision
Tests

Certificates

Commissioning

Defect Liability Period

The Will of God

The Will of God
Jesus said My meat is to do the will of Him that sent me and to finish His work. Verily verily I say unto you,  The hour is coming , and now is , when the dead shall hear the voice of the son of God : and they that hear shall live. Verily, verily, I say unto you, He that heareth my word, and believeth on Him that sent me , hath everlasting life, and shall not come into condemnation; but is passed from death unto life. And this is the Father's will which sent me, that of all which he hath given me I should lose nothing, but should raise it up again at the last day. And this is the will of him that sent me, that every one which seeth the Son, and beliveth on Him, may have everlasting life: and I will raise him up at the last day.ne ;  

STATE ESTIMATION

STATE ESTIMATION

State Estimation is a study of the Electrical Power System which enables us to estimate the state of the Electrical Power System at any given time using state variables which may or may not be measurable, observable or accessible. The state of a system is described by a set of state variables, which at time t(0) contains all information about the system which has any influence on the future (t>t(0)) system behaviour. For a given physical system a number of different state variables can be chosen, for example temperature, positions, speeds, voltages, currents, etc. Aconvinient choice is the selection of a minimum set of variables, thus obtaining a minimum, but sufficient, set of state variables. It is important to emphasize that the state variables are not necessarily directly accessible, measurable or observable.

The system model that is used for the Electrical Power System is a node based model, ie. only the conditions in the nodes are described by the model. In such a model, Power - flows, nodal voltages, line  - impedances etc. are the interesting variables. The choice of state variables is rather obvious: If the line -impedances are known, all other values are uniquely defined by the set of complex nodal voltages. Thus the state variables are the absolute voltage magnitudes of the nodes, and the angles between the nodes.

The state variables are the variables that are directly calculated by the state estimation function. All other variables, such as Power - Flows, can then be calculated from the set of State Variables.

SCADA   :   Supervisory Control And Data Acquisition.

There are various steps to be performed before any State Estimation can be initiated. The measurements can also be more or less pre-checked. The allocation of measurements can leave several lines or zones empty of measurements. There may be no measurements available from a certain part of the Power System due to, eg. , a failure in a communication link to an RTU. (Remote Terminal Unit). A necessary condition for the existence of a solution to the state estimation problem is that the system is observable, ie a possibility exists of calculating all state variables from the available measurements. If some part of the Power System is unobservable, the state estimation program must be able to treat this accordingly

:- include all observable parts of the system in the estimation algorithm,
:- exclude the unobservable parts or treat each one separately
- Exclude non-observable part of the system. Use some method to identify what part(s) of the Electrical Power network which must be excluded and perform State Estimation on the rest of the network.
- Include pseudo-measurements to achieve observability. Sometimes it (is) possible to replace real measurements by intelligent "guesses" and go on with the State Estimation.

The first method should be preferred, since it is not advisable to mix real measurements with "guessed" measurements. If, however, many measurements are lost from an important part of the network, the second approach is reasonable.

Another basic necessity for state estimation is that there must be a redundancy in measurements. If we denote the numbeer of measurements by 'm' and the state variables (two times the number of nodes minus 1{sometimes minus 2, where the reference bus or node has two variables eg the voltage magnitude and angle} ie. - the reference angle)by 'n' the redundancy must be greater than one.     

In Practice, it is often 1.5 - 2.0

Redundancy = (m/n ) > 1

Mathematical Formulation of State Estimation

The mathematical formulation of State estimation in Electrical Power Systems is based on the assumption that the Electrical Power System is more or less static.

Assume that we have a system which is characterised by "n" state variables which completely describe the "System State". The state variables are denoted by 'X'.  'X' is merely a vector which holds all state variables X= x(i) where i = 1,2,3,4........,n.

The 'm' measurements are denoted by 'z'. However, each measurement is corrupted by noise. If the noise is denoted by 'v' the expression relating the measurement to the state can be formulated. The relationship is denoted by h.

Z(1) = h(1){x(1),x(2),.......,x(n)} + v(1)

ie.

Z(1) = h(1){x} + v(1)
.
.
.
.
Z(m) = h(m){x} + v(m)


More compactly we can write

Z = h{x} + v

If h(x) is linear,

Z = HX + V

where: H is independent of the state variables x(i). H is called the Measurement Matrix.

Worship God only
Jesus helps us to over come temptations. Man shall not live by bread alone , but by every word that proceedeth out of the mouth of God. Thou shall not tempt the Lord thy God. Thou shall worship the Lord thy God and only Him shall thou serve. For what is a man advantaged if he gain the whole world, and loose himself, or be cast away? For whosoever shall  be ashamed of me and of my words, of him shall the Son of Man be ashamed, when he shall come in His glory, and in His Fathers and of the Holy Angels. And there came a voice out of the cloud saying, This is my beloved Son: hear Him.  

THE JOY OF THE LORD IS MY STRENGTH

The Joy of the Lord is my strength. Jesus Christ is the bread of life; the  fountain of life and the living water. Jesus Christ is the Rock of ages. Jesus Christ is the I Am That I AM. Jesus Christ is the begining and the end .He is the alpha and the Omega. He is the Lamb that was slain. He is the Lion of the tribe of Judah. Trust Him . He is trust worthy. He is faithful. He is Holy. He is Just. He is merciful. He is Love. His tender mercies endureth forever. He is good. He is God. He is almighty. His loving kindness is for evermore. Worthy is the Lamb that was slain. Jesus Christ is the Lamb of God that taketh away the sins of the whole world. He died and rose from the dead that you and I may live forevermore. He shed His blood to pay for our sins that we may be made perfect, holy and just before God. Believe in our LOrd Jesus Christ today and you shall be saved.

STABILITY STUDIES

Stability Studies in Electrical Power Systems Engineering
Stability studies is the ability of the Electrical Power System to return to normal operation after a disturbance.
There are three main types of stability studies carried out in the Electrical Power System. The are the Transient Stability studies, the Dynamic Stability Studies and Steady State stability studies.

Transient Stability Studies deals with the ability of the Electrical Power System to retain synchronism following major disturbances such as transmission system faults, sudden load changes, loss of generating units or line switching.

Dynamic and Steady-State Stability studies deal with a few machines undergoing slow or gradual changes in operating conditions.

Steady-State Stability Problems use very simple generator model which treats the generator as a constant voltage source. While the dynamic stability studies uses a model in which the excitation system and turbine-governing system are represented along with synchronous machine models which make provision for flux-linkage variation in the machine air-gap.

The Stability of the System is examined under incremental variations about an equilibrum point.

The Non-Linear differential and algebraic equations for the system can be replaced by a set of linear equations which are then solved by methods of linear analysis to determine whether the machine or machines will remain in synchronism following small changes from the operating point.

Transient Stability Studies involve large disturbances which do not allow the linearization process to be used and the non-linear differential and algebraic equation must be solved by direct method or by iterative step-by-step procedure.

Transient Stability Studies can be subdivided into first-swing and multiswing stability Problems.

The first-swing Stability is based on a reasonably simple generator model without representation of control system. Usually te time period under study is the first second following a system fault. If the machines of the system are found to remain in synchronism within the first seconds; the system is said to be stable. Multiswing Stability Problems extended over a longer study period and therefore must consider effects of generator control systems which affect machine performance during the extended time period. Machine models of greater sophistication must be represented to reflect proper behaviour.

In all Stability Studies, the objective is to determine whether, or not the rotors of the machines being perturbed, return to constant speed operation. 

YOU ARE THE SALT OF THE EARTH

For everyone  shall be salted with fire, and every sacrifice shall be salted with salt.  Salt  is good : but if the salt have lost his saltness, wherewith will ye  season it? Have salt  in yourselves, and have peace one with another. If thine eye offend thee, pluck it out: it is better for thee to enter into the kingdom of God with one eye, than having two eyes to be cast into hell fire: Where their worm dieth not, and the fire is not quenched. Ye  are the light of the world 

FEAR NOT

Fear thou not; for I am with thee: be not dismayed; for I am thy God: I will strengthen thee; yea, I will help thee; yea, I will uphold thee with the right hand of my righteousness. But rather seek ye the kingdom of God; and all these things shall be added unto you. Fear not, little flock; for it is your Father's good pleasure to give you the kingdom.

TEST

Tests
Verification Of Polarity

Check that all single-pole switches, thermostats, and other control devices are in the live side.

The polarity test is also made to ensure that the outer contacts of centre-contact byonet and Edison-type srew lamp-holders are connected to the neutral and that wiring has been correctly connected to plugs and socket-outlets.

Crossed polarity, sometimes termed 'Switched Neutral', is one of the major causes of severe electrical accidents.

Loop Impedance Test

Line-earth and Neutral-earth Loops.

Aim: To ensure that the loop impedance is low enough to ensure and allow sufficient current, in the event of an earth fault, to operate the protective device.

Earth-continuity Conductor

Earth Continuity test on the Continuity Conductor of AC installations.

After allowance has been made for the resistance of the leads, the value V/I when measured b/w two furtherest points of the installation is not to exceed  1 ohm (one ohm) This value is subject to loop impedance measurement which may require lower continuity values.

Earth-Leakage Circuit-Breaker

To test and make sure that it will trip effectively in the event of an earth fault.

Earth-Electrode Resistance

Due to an insufficiently - low earth loop impedance, it may be necessary to check  the actual resistance of the earth electrode to earth.

The electrode is disconnected from all sources of supply other than that used for testing.  It should be realised that the resistance of an electrode to the general mass of the earth depends upon the following:

a) shape and material of electrode
b) dept of soil in which buried
c) resistivity of surrounding soil which may be seasonal and in turn dependent upon moisture content.

Insulation Test

A Poor insulator has a comparatively low insulation value  and vice versa

Certificates

After the tecting and inspection of work done,  a completion and inspection certificate is issued. Periodic testing and inspection is important and must be stressed.

TODAY IS A NEW DAY

Behold I stand at the door, and knock: if any man hear my voice, and open the door, I will come in to him, and will sup with, him, and he with me. To him that overcometh will I grant to sit with me in my throne, even as I taso overcame, and am set down with my father in His throne. He that hath an ear, let him hear what the spirit saith unto the churches. And behold I come quickly; and my reward is with me, to give every man according as his work shall be. I am Alpha and Omega, the beginning and the end, the first and the last. Blessed are they that do this commandments, that they may have right to the tree of life

GRACE

But He giveth more grace. Wherefore He saith, God resisteth the Proud, but giveth grace unto the humble. Submit yourselves therefore to God. Resist the devil, and he will flee from you. Draw neigh to God and he will draw neigh to you. Cleanse your hands, ye sinners; purify your hearts ye double minded. Humble yourselves in the sight of the Lord, and he shall lift you up. Speak not evil one of another, brethren. For that ye ought to say, if the Lord will, we shall live, and do this, or that. But now ye rejoice in your boasting: all such rejoicing is evil. Therefore to him that knoweth to do good, and doeth it not, to him it is sin. Thou shall worship the Lord thy God and Him only shalt thou serve.  

LAMINATIONS

LAMINATIONS

The core of Electrical Machines are made of Laminations of Silicon Steel Sheet. This helps to minimize losses due to hysteresis and eddy current. The transformer, electric motor and generator all have laminations in them for the same reason. Silicon Steel Laminations are cut and shallaced and clamped together under pressure for a compact assembly, and so that they are actually insulated from each other. Observations and experiments carried out have shown that by so doing these losses (eddy current losses and hysteresis losses in the core) are minimized. Most machines eg, Electric motors, transformers and generators hare cores in which windings are made. (In the case of the Electric motor and generator, the stator and the rotor are also laminated) The flux produced by these windings when current passes through them are usually confined in these cores. There is always a loss and flux leakage associated with the magnetizing current in a practical machine. By using laminations made of Silicon Steel, it has been discovered that these losses(due to eddy current and hysteresis) are minimized. This helps to improve the efficiency of the machine.

POWER ELECTRONICS

Power Electronics

Power Electronics is an area of study and specialization that aims at applying the speed and other desirable properties of Electronics and Electronic devices in Power, ie. In Electrical Power Systems Engineering Circuits, devices and Machines.

There are a good number of Power Electronics components and devices such as; Power Diodes, Power Transistors, Diacs, Triacs, MOSFET, Thyristors etc. 


Over the years, it has been found out that Thyristors are reliable Power Electronic devices which are fast and are able to withstand high voltages and currents.


In this study, the Thyristor shall be investigated with a view of determining its characteristics and how it can be applied in practice to realize desirable  objectives as well as other Power Electronics Components and Circuits and Devices.

Areas of Interest.

Types of Converters

Converters are Power Semiconductor Systems used for rectifying , inverting, or otherwise modulating the Power output of an AC or DC energysource.  

God is good

God is good all the time.