3 Fasa Circuits

7/28/2019 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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S & D l 3 h


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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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3 Fasa Circuits

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