Figure 1 illustrates a balanced sinusoidal supply constellation consisting of three line-neutral electromotive forces holding equal magnitudes and a stage difference of 120i‚° . Figure 2 nevertheless illustrates an imbalanced constellation wherein there may be a difference in either the magnitude of the three electromotive forces or in the stage difference between the electromotive forces [ 1 ] .
There are several grounds for this imbalance to happen. These are
aˆ? Incomplete heterotaxy of transmittal lines
aˆ? Open delta transformer connexions
aˆ? Single-phase tonss
aˆ? Blown fuses on capacitance Bankss
aˆ? Railway grip tonss
If a balanced three-phase burden is connected to an imbalanced supply ( electromotive force ) constellation, it leads to an imbalance in the currents drawn by the burden. Practically, it is impracticable for the supply constellations to be absolutely balanced and hence it is really of import to seek to minimise the degree of imbalance every bit much as possible so as to cut down its effects on consumer tonss [ 2 ] .
1.2 Theory of Symmetrical Components
The Theory of Symmetrical Components mathematically represents a set of balanced vectors in footings of a set of imbalanced vectors or vice-versa. These balanced vectors are classified as:
Positive Sequence Components
Negative Sequence Components
Zero Sequence Components
In a absolutely balanced system both the negative and zero sequence systems do non be. Figure 3 below shows the different symmetrical constituents of an imbalanced system of electromotive forces [ 5 ] .
The physical significance of these constituents is as follows. When a three-phase initiation motor is supplied with a positive sequence set of electromotive forces, it rotates in the counter-clockwise way. However, the way of rotary motion becomes clockwise if the three-phase initiation motor is supplied with negative sequence electromotive forces alternatively. Since the zero sequence constituents are co-phasal and have no stage difference between them, they are unable to bring forth a rotating magnetic field to run the motor. Hence, the supply of nothing sequence electromotive forces to the motor consequences in no rotary motion at all [ 6 ] .
See the undermentioned equations:
Where, i?? is the stage rotary motion operator defined to revolve a phasor vector frontward by 120 grades or radians, i.e.
From the above set of equations, we get
Therefore, we can stand for an imbalanced set of vectors ( VP ) in footings of a balanced set of vectors ( VS ) by utilizing the forward transmutation:
Alternately, we can besides stand for the set of balanced vectors in footings of the imbalanced set of vectors by utilizing the rearward transmutation:
1.3 Induction Motor
1.3.1 Operating rule
Operation of 3-phase initiation motors is based upon the application of Faraday ‘s Law and the Lorentz Force on a music director.
Let us see a series of music directors of length L represented by bars A and B in figure 4 whose appendages are shorted. A lasting magnet with its north pole confronting the music directors travels at a velocity V above the music directors ensuing in a magnetic field across the music directors.
Figure 4 Operating rule of an initiation motor
The undermentioned sequence of events takes topographic point:
( a ) Harmonizing to Faraday ‘s Law
This electromotive force ( E ) is induced in each music director as a consequence of it being cut by the flux.
( B ) Circulating currents are produced due to the induced electromotive force which travel in a cringle through the bars and around the music directors.
( degree Celsius ) Harmonizing to Lorentz force, the current-carrying music directors experience a mechanical force since they lie in a magnetic field.
( vitamin D ) The mechanical force Acts of the Apostless in the way of the magnetic field and drags the music director along with the field [ 9 ] .
A 3-phase initiation motor has two chief parts:
( a ) A stator whose twists are housed in slots on the stator ‘s internal perimeter. The stator is made up of a steel frame that supports a nothingness, cylindrical nucleus of stacked laminations.
( B ) A rotor, with rotor slots for the rotor twist, besides composed of punched laminations.
There are two-types of rotor twists:
( a ) Squirrel-cage twists, which are the most common and bring forth a squirrel-cage initiation motor. The squirrel coop rotor consists of Cu bars, slightly longer than the rotor, which are distressed into the slots. The appendages are welded to copper terminal rings, so that all the bars are short-circuited.
In little motors, the bars and end-rings are die- dramatis personae in aluminum to organize an built-in block.
( B ) Conventional 3-phase twists prepared of insulated wire for particular applications, which produce a wound-rotor initiation motor.
A lesion rotor has a 3-phase twist, similar to the stator twist.
The rotor twist terminuss are linked to three faux pas rings which rotate with the rotor. The faux pas rings/brushes allow peripheral resistances to be attached in series with the twist.
The external resistances are chiefly used through start-up – under standard running fortunes the twists are short- circuited superficially. Figure 5 below shows the assorted constituents of an initiation motor [ 9 ] .
Figure 5 Components of an initiation motor
( a ) Locked rotor: When the rotor is at a deadlock, the field rotates at a rate of return ( comparative to the rotor ) equivalent to the supply rate of return. This induces a immense electromotive force – hence immense currents billow inside the rotor, bring forthing a strapping torsion.
( B ) Acceleration: When unrestricted, the rotor accelerates rapidly. As velocity additions, the comparative rate of return of the magnetic field lessenings. As a consequence, the induced electromotive forces and currents decrease rapidly as the motor accelerates.
( degree Celsius ) Synchronous velocity: The comparative rate of return of the revolving field is nil, so the induced currents and electromotive forces are besides nil. Therefore, the torsion is nil excessively. It concludes, that initiation motors are incapable of making synchronal speed due to losingss such as clash.
( vitamin D ) Motor under burden: The motor velocity decreases until the comparative rate of return is large plenty to bring forth equal torsion to stabilise the burden torsion [ 7 ] .
1.3.4 Faux pas
The difference between the synchronal velocity and rotor velocity can be expressed as a per centum of synchronal velocity, known as the faux pas.
s = faux pas,
Ns = synchronal velocity ( revolutions per minute ) ,
N = rotor velocity ( revolutions per minute )
aˆ? At no-load, the faux pas is about zero ( & lt ; 0.1 % ) .
aˆ? At full burden, the faux pas for big motors seldom exceeds 0.5 % . For little
motors at full burden, it seldom exceeds 5 % .
aˆ? The faux pas is 100 % for locked rotor.
The rate of return induced in the rotor depends on the faux pas [ 9 ] :
fR = rate of return of electromotive force and current in the rotor
f = rate of return of the supply and stator field
s = faux pas
1.3.5 Power Flow Equations
Efficiency by definition, is the ratio of end product / input power:
Rotor Cu losingss:
Motor torsion [ 7 ] :
Figure 6 Power flow in an initiation motor
1.3.6 Effectss of Voltage Unbalance
The greatest consequence of electromotive force imbalance is on three-phase initiation motors. Three stage initiation motors are one of the most widespread tonss on the system and are observed in big Numberss peculiarly in industrial environments. When a three-phase initiation motor is supplied by an imbalanced system the attendant line currents show an extent of imbalance that is legion times the electromotive force imbalance. This can be explained with reference to the two contra-rotating Fieldss established when the motor is subjected to voltage imbalance.
In relation to the positive sequence set of electromotive forces if the motor faux pas is:
Ns – synchronal velocity
Nr – the rotor velocity
Then the faux pas matching to the negative sequence set of electromotive forces would be
Slip s2 can be expressed in footings of faux pas s1 and hence,
As the positive sequence faux pas s1 is normally really little ( close to zero ) the negative sequence faux pas s2 would be really big ( close to 2 ) . From the basic theory of initiation motors the electric resistance of an initiation motor is really dependent on the faux pas where at high faux pas ( eg. at start or under locked rotor conditions ) it is little and conversely at low faux pas it is really big. Hence it can be about stated that the ratio of the positive sequence electric resistance to negative sequence electric resistance is given by:
As the positive sequence current is given by
and the negative sequence current is given by
it can be rapidly shown that:
As an illustration, a motor with a locked rotor current that is 6 times the running current would give rise to a really important 30 % imbalance in the motor line current if the electromotive force imbalance is 5 % [ 10 ] .
chapter 2 Problem Description
To Investigate the Theory of Symmetrical Components applied to a three-phase initiation motor working under imbalanced status.
2.1 LAB EXPERIMENT
The public presentation of a 3 stage initiation motor was observed under both balanced and imbalanced operating conditions. The undermentioned stairss were undertaken to accomplish the coveted consequence:
No load trial under balanced status
No load trial under imbalanced status
Blocked rotor trial under balanced status
Measurement of stator opposition
Load trial under balanced status
Load trial under imbalanced status
Calculation of positive & A ; negative sequence currents
Determination of machine parametric quantities
Calculation of positive & A ; negative sequence torsion
( a ) No Load Test – Balanced Operation
Table 1 No burden trial ( balanced ) observations
V0 = 415 V
I0 = 2.41 Angstrom
P0 = 0.27 kilowatt
( B ) No Load Test – Unbalanced Operation
Table 2 No burden trial ( imbalanced ) observations
V1 = 415 V
I1 = 3.66 Angstrom
P1 = 0.32 kilowatt
( degree Celsius ) Blocked Rotor Test
Table 3 Blocked rotor trial observations
VBR = 80 V
IBR = 2.8 Angstrom
PBR= 0.146 kilowatt
( vitamin D ) Weaving Resistance Measurement
Table 4 Weaving opposition measuring observations
V ( V )
I ( A )
Average Value of R1 = 11.93i?-
R1 ( eq. ) = 7.95i?-
( vitamin E ) Load Test – Balanced Operation
Table 5 Load trial ( balanced ) observations
V2= 415 V
I2 = 3.36 Angstrom
P2= 1.51 kilowatt
n = 1464 revolutions per minute
( degree Fahrenheit ) Load Test – Unbalanced Operation
Table 6 Load trial ( imbalanced ) observations
V3= 415 V
I3 = 5.45A
P3= 1.66 kilowatt
n1 = 1444 revolutions per minute
( g ) Machine Nameplate Evaluations
Table 7 Machine nameplate evaluations
3 Phase Induction Motor
P = 2.2 kilowatt
P = 2 kilowatt
V = 415 V
V = 220 V
ns = 1500 revolutions per minute
n = 1500 revolutions per minute
I = 4.8 Angstrom
I = 9A
2.3.1 machine parametric quantities [ 4 ]
( a ) Positive Sequence Current
( B ) Negative Sequence Current
Positive Sequence Torque [ 3 ]
Figure 7 Positive sequence tantamount circuit
( B ) Negative Sequence Torque [ 3 ] Figure 8 Negative sequence equivalent circuit
Chapter 3 consequences
Percentage decrease in torsion due to negative sequence constituent
Percentage decrease in velocity due to negative sequence constituent
Chapter 4 Decision
When one of the stages of an initiation motor is all of a sudden blown ( single-phasing ) , we are faced with what is fundamentally a current imbalance job.
As a consequence of this current imbalance, a negative sequence current is developed. This current produced a negative sequence torsion, which acts as a burden torsion in the way antonym to the normal positive sequence electro magnetic torsion.
As a consequence, the net torsion lessenings, ensuing in a bead in velocity, i.e. the negative sequence torsion acts as a practical burden. Hence, burden additions and velocity must drop even if the machine is running on free shaft.
The effects of negative sequence constituent on public presentation of initiation motor are:
aˆ? The motor takes longer clip to run up.
aˆ? It increases the thermic emphasis in the motor which leads to loss in life.
aˆ? The net torsion is reduced and if full burden is still demanded, so the motor is forced to run at a higher faux pas, therefore increasing the rotor losingss and heat dissipation.
aˆ? The decrease in the extremum torsion reduces the ability of motor to sit through dips and droops, therefore impacting the stableness of the full system.
Premature failure can merely be prevented by derating of the machine to
let it to run within the thermic restrictions [ 8 ] .