3 Fasa Circuits
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SIRKUIT 3 FASA
(Balanced 3-phase )Semester Genap 2009/2010Prodi Teknik Elektro
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Consider the complex roots of unity:
Find all the roots of:
Then find the sum of the roots
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Balanced ComplexNumbers
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Balanced ComplexNumbers
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It is evident from above that the sum of any threeroots of the cube-root of any complex number isabsolutely zero.
This is the essence of a balanced three phasesystem and indeed the most powerful tool in powertransmission.
The results below are self-evident.
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Let us use the above discovery and
KCL: Suppose we have three currents such that
o
o o i1 = I0
, i2 = I120
, i3 = I240
If
we decide to sup ply i1 , i2 , i3 to a load ;
as shown below we make int eresting conclusions :
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Balances 3-phase Currents
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Balances 3-phase Currents Clearly,
I n = i1 + i2 + i3
But, i1 + i2 + i3 = 0
I n = 0
I n = 0; needless to have neutral wire
There is always NO neutral wire
in a balanced 3 phase system
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Advantages of balanced 3-phase supply
1.The elimination of a neutral wire is clearly thebiggest saving.
2. If we wanted to supply the same amount ofpower using single phases, we would have used 6wires! But we have managed with just 3 of them.
3. The fact that line voltages are higher means thatthe line currents are lower hence reduced I2Rlosses.
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Line & Phase Values
In practice, when a 3-phase system is used, we dohave both the currents & voltages as 3- phase. Theirvalues may be given as phase or line values.
Let us consider a balanced 3-phase voltage system.
Just as we did in the case of currents, the voltage isgiven by:
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Line & Phase Values It is however usual to measure voltage between
one phase & another phase. So the value is that ofone phase with respect to the other. Since it ismeasured between one phase & another it is
referred as the line voltage.
The line voltages must the phasor differences asshown below:
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Line & Phase Values
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Phasors for Phase & LineVoltages
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Phase & Line Voltages The following conclusions are made:
1. The line voltages also constitute a balanced 3-phase system.
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Line & Phase Values Please note that:
1. In a 3-phase system; the line values
(voltage & current) are the ones specified.
2. It is very dangerous to touch any two line wire
(because of much higher voltages). 3. All valuesare rms.
4. Red, Yellow, Blue representv.v1 , v2 , v3
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Line & Phase Values While it is easy to identify phase & line voltages;
caution is taken on phase & line currents.
It is easier to assume that phase & line currents arethe same.
S & D l 3 h
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Star & Delta 3-phrepresentation
There are two distinct ways of representing 3- phasevoltages/currents;
Star or Delta. [Star is sometimes called Wye].
Let us re-draw the phasors for 3-phase voltages.
S & D l 3 h
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Star & Delta 3-phrepresentation
S & D l 3 h
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Star & Delta 3-phrepresentation
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It is noted that:
A Star connection has a neutral point (n) and canbe accessed when need arises. But the Deltaconnection does not have one.
Hence in a Delta connection only the line voltagescan be measured. But in the Star connection bothline & phase voltages are measurable.
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Star-Star connection Supply-load connections
Sumber Beban
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Star-Delta connection Supply-load connections
I3
I2
I1i1
i2
i3
n
Sumber
Beban
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Line & Phase currents In the star connection; the line current=phase
current.
But in Delta connection; the line current DOES NOTequal to phase current e.g.
i1 I1
But we may use KCL to find the relationshipsbetween line and phase currents.
i1 I1 + I3 = 0
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Power in 3-phase We know that is 1-phase;
Power= VI cos But in 3 phase;
Total power
= 3VI cos ;
where V, I are phase values. Total power=
where VL , I L are line values (assume I = I L )
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3-phase ExercisesExercise 1:
v1 (t ) = Vsin(wt) =reference voltage;
express v2 (t ), v3 (t) as sin e functions.
Exercise 2 :
A 2MW,11kV,3 phase source uses 80% of its capacity to sup ply a load.
determine the current if power factor is 0.5
Exercise 3:
A 0.6MW, 416V, 3-phase, 50Hz load has a power factorof 0.5. Determine the necessary capacitors and showtheir connections so as to improve the power factor to0.9.
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Solution 1
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Solution 2
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Solution 3
The power factor improvement is done byconnecting a capacitor between @ phase & theneutral point.
[Though it is possible to connect a capacitorbetween phases but then the capacitors are moreexpensive because of the higher (line) voltages].
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Star-Star connection Supply-load connections
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Solution 3
Since @ capacitor is connected across a phase &neutral; phase voltages must be used.
We are at liberty to use the phasor diagramstudied earlier
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Solution 3
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Solution 3
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Solution 3
In pratice use nearest orhigher valuable availableon market
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Question 4
A 440V, 3-ph, Y-connected source has two loadsconnected as:
One load is balanced in @ phase with
Z=10+j5. The second load is balanced in @ phasewith
Z=15+j0. (i) Find the average power to @ load.
(ii) Find the total power delivered.
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Total load =(10+j5)+(15+j0)=25+j5=Z
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Latihan Soal
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Soal 1
Diket A = 5 + j3 dan B = 8300
Hitung;
1. A + B 2. AB
3. A * B
4. A / B
Dalam bentuk vektor dan komplexs
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Soal 2
2 buah watt meter dipasang pada supply dengansystem 3 kawat 3 phase. Jika tegangan beban 400V dan arus 20 A, hitung
A. Pembacaan watt meter saat faktor daya = 1
B. Pembacaan watt meter saat faktor daya =
0.5
C. Pembacaan watt meter saat faktor daya = 0
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Soal 3
Suatu sistem 3 phase 4 kawat mempunyai bebanZa = 10L00 , Zb = 20L300 dan Zc =
10L-300 . Beban tersebut dihubungkan bintang dandisupply tegangan 400 V, 50 Hz. Hitung arus yangmengalir pada masing- masing fasa dan arusnetralnya.
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Soal 4
Sistem 400 Volt ( fasa ke fasa ), 3 fasa, 50 Hzmensupply beban yang seimbang dengan besarbeban 8 + j6 ohm. Hitung daya keseluruhan yang
disupply dan faktor daya dari arus yang ditarik darisumber
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LATIHAN SOAL
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Soal 5
3 impedansi yang mempunyai nilai yang sama,tahanan 8 ohm dan reaktansi 6 ohm, dihubungkanpada suulay 200 V, 3 phase.
Hitung daya yang dibutuhkan jika
Dihubung bintang
Dihubung delta/ segitiga
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Soal 6
Suatu beban yang dihubung bintang denganimpedansi 8+j6 ohm dihubungkan dengan supply100 V dan 3 phase. Hitung nilai kapasitor yang harus
dipasang jika ingin merubah faktor dayanyamenjadi 0.9
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