TTL Tekim - Class 04

8/10/2019 TTL Tekim - Class 04

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Class 4

Impedance & Three-phase System

Firmansyah Nur Budiman

Lab. Transmisi & Distribusi

Jurusan Teknik Elektro & Teknologi Informasi FT UGM


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Complex Number

B

A

B

ABABA

jBBB

jAAA

.

)sin(cos

)sin(cos

Polar form

Rectangular form

A

)sin(cos jA


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Complex Number

Example of Use:

Load 1:

TL light220 V, 40 W, pf = 0.4

Load 2:

Induction motor

220 V, 200 W, pf = 0.7

Find I, I1, I

2!


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Complex Number

VV 00220

01

1

0

4.6645.0

45.04.0220

40

4.664.0cos

I

AI

02

2

0

6.453.1

3.17.0220

200

6.457.0cos

I

AI

Load 1: Load 2:

0

21

9.5073.1)93.091.0()42.018.0(

jjI

III


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Complex Power

Complex power:

Apparent power:

where

Therefore, apparent power is the magnitude

of complex power, or

*VIjQPS

22QPS

sin

cos

IVQ

IVP

SS


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Impedance

Individual passive components:


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Impedance

Combination:


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Impedance

X

B

ZY

1

1

Y= admittance [Mho, Siemens]

X= reactance [Ohm]

B= suseptance [Mho, Siemens]


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Three-phase System

Single-phase electricity:

Three-phase electricity:


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Three-phase System

)240cos()(

)120cos()(

cos)(

0

0

tVtv

tVtv

tVtv

Mcn

Mbn

Man

)240cos()(

)120cos()(

)cos()(

0

0

tIti

tIti

tIti

Mc

Mb

Ma

Important properties:

Voltage & current:

0

0

CBA

CNBNAN

III

VVV


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Three-phase System

Advantages:

(1) Three-phase motors, generators, and

transformers are simpler, cheaper, and more

efficient.

(2) Three-phase transmission lines can deliver

more power for a given weight and cost.

(3) The voltage regulation of 3-phase

transmission lines is better.


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Three-phase System

Instantaneous power:

Note: this power is independent of time

cos2

3)( MMIV

tp


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Power in Single-phase System

0 90 180 270 360 450 540

-10

-5

0

5

10 va(t)

ia(t)

Angle (degree)

0 90 180 270 360 450 5400

10

20

30

40

50p

a(t)

Angle (degree)


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Power in Two-phase System

0 90 180 270 360 450 540

-10

-5

0

5

10 va(t)

ia(t)

Angle (degree)

0 90 180 270 360 450 540

-10

-5

0

5

10 vb(t)

ib(t)

Angle (degree)

0 90 180 270 360 450 5400

10

20

30

40

50

pa(t)

Angle (degree)

pb(t)

0 90 180 270 360 450 5400

10

20

30

40

50p

total(t)

Angle (degree)


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Power in Three-phase System

0 120 240 360 4800

10

20

30

40

50p

a(t)

Angle (degree)

pb(t) p

c(t)

0 120 240 360 480

0

25

50

75

100

ptotal

(t)

Angle (degree)


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Power in Three-phase System

Power in single-phase circuit:

Power in three-phase circuit:

IVS LN1

IVS LN31


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Example

The 3-phase generator shown is connected to

three 20load resistors. If the effective

voltage in each phase is 120V, calculate:

(a)Power dissipated in each resistor

(b)Power dissipated in 3-phase load

(c)Peak powerPmdissipated in eachresistor

(d)Total 3-phase power compared to Pm


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Wye Connection


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Wye Connection

Voltage relationship:

cabcabLL VVVV ,,

cnbnancabcab VVVVVV 333


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Examples

A 3-phase 60Hz generator, connected in wye,generates a line (line-to-line) voltage of 23900V.Calculate:

(a) Line-to-neutral voltage(b) Voltage induced in individual winding

(c) Time interval between positive peak voltage

of phase A and positive peak voltage ofphase B

(d) Peak value of line voltage


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Examples

A 3-phase generator generates a line voltage of

865V, and each load resistor has an impedance

of 50. Calculate:

(a)Voltage across each resistor

(b)Current in each resistor

(c)Total power output of generator


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Delta Connection

321 333 IIIIII cba


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Summary


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Examples

Three identical impedances are connected in

delta across a 3-phase 550V line. If the line

current is 10A, calculate:

(a) Current in each impedance

(b) Value of each impedance


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Examples

A manufacturing plant draws a total of 415kVA

from a 2400V(line-to-line) 3-phase line. If the

plant power factor is 87.5% lagging, calculate:

(a) Impedance of the plant, per phase

(b) Phase angle between line-to-neutral voltage

and line current

(c) Phasor diagram for the plant


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Homeworks

(1) A 3-phase motor connected to a 600V line drawsa line current of 25A. Calculate the apparentpower supplied to the motor!

(2) A 3-phase heater dissipates 15kW whenconnected to a 208V, 3-phase line.a) What is the line current if the resistors areconnected in wye?

b) What is the line current if the resistors areconnected in delta?

c) If the resistors are known to be connected inwye, calculate the resistance of each


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Homeworks

(3) Three 15resistors and three 8reactors areconnected as shown below.

If the line voltage is 530V, calculate:

a) Active, reactive, and apparent powersupplied to the 3-phase load

b) Voltage across each resistor

Documents

TTL Tekim - Class 04