part 10 emachines eep 3243
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ELECTRICAL MACHINE
EEP 3243
Lt Cdr Ong Khye Liat RMN
2 Mac 2010
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RECAP/ADDITION
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Voltage and Current Relationships in 3Ø
Phase current = line current. Phase current = line current/3
Phase voltage = line voltage/3 Phase voltage = line voltage
Same total apparent power
Voltage across the elements are 120o out of phase
Current across the elements are 120o out of phase
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Type of Connection
Delta-delta Connection
Delta-wye Connection
Wye-delta Connection Wye-wye Connection
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Open Delta Connection
I t is mainly used in emergency situation when 1 of the delta-delta connection becomes defective and has to be removed.
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Cont.
Open delta connectionis seldom used as theload capacity of the
installed transformer bank is only 86.6% of the installed
transformer capacity.
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PROBLEM 1
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3-Phase Transformer
T ransformers for 3-phase circuits can be constructed in
2 ways.
± 3 single phase transformer connected in a 3 phasebank.
± Make 3 phase transformer consisting of 3 sets of windings wrapped on a common core.
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Cont.
T he majority of three phase transformers aremostly in the form of core-type construction. Asmall or medium rated transformer is usually of
three-legged core-type.
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The schematic of three phase
core-type magnetic paths U nder balanced condition,the currents in 3 phases areequal in magnitude, with
angles 120° apart. Accordingly, the vector formfluxes in three phases are120° apart and summed to
zero at the yoke. T here is no need of a return path for the flux.
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Cont. I f there is some unbalance in the
terminal voltage, the sum of the 3 phase fluxes (residual flux), will not be zero and it has to return
through a path out of thetransformer magnetic core.
T his means the residual flux at thetop yoke has to pass through a
huge air gap and the tank to thebottom yoke.
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Cont. T he path through the air gap and
the tank has low permeability and, thus, high magnetic reluctance.
I n order to overcome theshortcoming of three-legged transformers in unbalanced condition, a fourth leg is added tothe transformer core.
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Four-legged core-type transformer
T he fourth leg provides a path for thezero-sequence magnetic flux.
For a four-legged transformer, thezero sequence magnetic reluctance issmall and the zero sequenceimpedance is large.
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Cont. T he top and bottom yokes
generally are designed tocarry one per unit of zerosequence flux in the fourth
leg. I n order to reduce the height
of the yoke on a large rated transformer for
transportability, a fifth leg isadded to the four-legged transformer.
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Five-legged core-type transformer
T he zero sequence performance of afive legged transformer is similar tothat of a four-legged transformer,which is approximately the positivesequence leakage impedancebetween the windings until theapplied voltage saturates either theyokes or the end legs.
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Cont.
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Cont.
A 3-phase transformer always cheaper and smaller than 3 single phase transformer for the samecapacity.
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3 Phase Transformer Calculation
S ame way as for a single-phase transformer. S teps as following:
± Assume that the primary and secondary windings areboth connected in wye. I n wye connection theimpedance per phase is understood to be the line-to-neutral impedance. T he voltage per phase is simply theline voltage divided by ¥3 and the current per phase is
equal to the line current.
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Cont.
Consider only single phase of this transformer bank. Primary voltage of this single phase transformer is theline-to-neutral voltage of incoming line.
S econdary voltage of this transformer is line-to-neutral
voltage of the outgoing line. T he nominal power rating of this transformer in the
rating of the 3 phase transformer bank. T he load on this transformer is the load on the
transformer bank.
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PROBLEM 2
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The per-unit system for
3P
hase Transformers S olving circuits containing transformers can be
quite a tedious operation because of the need torefer all the different voltage levels on different sides of the transformers in the system to acommon level.
T he per unit system can simplify the calculation.
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Cont.
T he per unit system can simplify the calculation.
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Cont.
A transformer has no effect on the base apparent power of the system, since the apparent power intoa transformer equals the apparent power out of thetransformer.
T he per unit system applies just as well to 3 phasetransformers as to single phase transformer.
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Cont.
I f the total base voltampere value of thetransformer bank is called S base, then the basevoltampere value of one of the transformer, S 1Ø,base,
is
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Voltage Regulation
With primary voltage held constant at its rated value,the voltage regulation (in %) is
Where
E NL = secondary voltage at no load
E FL = secondary voltage at full-load
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Cont.
I f the transformer equivalent circuit is in the per-unit system, then voltage regulation can beexpressed as
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Cont.
T he relationship between the base linevoltage/current and base phase voltage/current of the transformer depends on the connection of windings.
I f the windings are connected in delta, V L,base = V Ø,base
and I L,base = ¥3 I Ø,base.
While the windings are connected in wye,
V L,base = ¥3 V Ø,base and I L,base = I Ø,base.
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PROBLEM 3&4
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Cont.
As we slide contract P form phase B toward phase C,voltage E AP changes both in
amplitude and phase. T his simple phase shifter
only can only be used insmall load application.
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Cont.
By moving the contract P, we obtain the sameopen circuit voltages
and phase shiftswhether theautotransformer delivers a current to the
load or not.
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Cont.
Contract P 1, P 2 and P 3move in tandem enablesto create a 3 phase
source whose phaseangle changes stepwiseand the voltagesmagnitude vary from E line
to 0.5 E line.
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Phase Shift Transformer
A special 3 phase autotransformer shifts the phaseangle between incoming and outgoing line without changing the voltage ratio.
T he angle may be leading or lagging, and isusually variable between zero and 20 o.
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Cont.T he basic power rating of this transformer depends upon the apparent power carried by the transmission line and the phase shift. For angles
lessthan 20 o,
S T = 0.025 S L max
where,
S T = basic power rating of 3 phase transformer bank (VA),
S L = apparent power carried by the transmission line (VA),
max = maximum transformer phase shift ( o ),
0.025 = an approximate coefficient.
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Cont.
T he basic principle of obtaining a phase shift is toconnect 2 voltages in series that are generated by 2 different phases.
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Cont.
T hus, voltage E 1b generated by phase B is connected in series with E PN generated by phase A. T he values of E PN and E 1b are selected so that the output voltage is
equal to the input voltage while obtaining the desired phase angle.
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3 Phase to 2 Phase Transformation
T he voltages in a 2 phase system are equal but
displaced by 90 o.
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Cont.
U se a single phase autotransformer having taps at 50% and 86.6%T he ratio of transformation is fixed and given by E AB /E AT =
100/86.6 = 1.1547 .
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Cont. U se scott connection
± Consists of 2 identical single phasetransformers, one having a 50% tapand other 86.6% tap on primary.
± T he ratio of transformation is givenby E AB /E 12 .
± Has advantage of isolating the 3 phase and 2 phase systems.
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END OF PART 10
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