EE013 Alternating Current Th Inst

7/25/2019 EE013 Alternating Current Th Inst

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SRI LANKA INSTITUTE of ADVANCED TECHNOLOGICAL EDUCATION

Training Unit

Alternating CurrentTheory

No: EE 013

INDUSTRIETECHNIKINDUSTRIETECHNIK

ELECTRICAL and ELECTRONIC

ENGINEERING

Instructor Manual


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Training UnitAlternating Current

Theoretical Part

No.: EE 013

Edition: 2008Al l Rights Reserved

Editor: MCE Industrietechnik Linz GmbH & CoEducation and Training Systems, DM-1Lunzerst rasse 64 P.O.Box 36, A 4031 Linz / Aus triaTel. (+ 43 / 732) 6987 - 3475Fax (+ 43 / 732) 6980 - 4271Website: www.mcelinz.com


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ALTERNATING CURRENT

CONTENTS Page

LEARNING OBJECTIVES...................................................................................................4

1 GENERAL ....................................................................................................................5

1.1

Formula for induced voltage ................................................................................6

1.2

Generator principle ..............................................................................................6

1.3 Cycle, duration of cycle........................................................................................8

1.4 Frequency............................................................................................................8

1.4.1

Frequency and speed of generator................................................................10

1.4.2

Waveform and phasor diagram......................................................................11

1.4.3 Angular Velocity (angular speed)...................................................................14

1.4.4

Maximum Value, Effective Value ...................................................................15

2

RESISTANCE IN AN ALTERNATING CURRENT CIRCUIT......................................17

2.1 Ohmic Resistance..............................................................................................17

2.2

Inductive Reactance (reactive impedanceXL[]) .............................................17

2.3 Capacitive reactance .........................................................................................19

2.3.1 Capacitor on direct current:............................................................................19

2.3.2

Capacitor on alternating voltage ....................................................................22

3

ALTERNATING CURRENT POWER .........................................................................24

3.1 Pure ohmic load .................................................................................................24

3.2

Pure reactive load ..............................................................................................25

3.3 Mixed load (resistance and reactance) ..............................................................26

3.4 Power triangle ....................................................................................................27

3.5 Current triangle ..................................................................................................28

4

CONNECTION OF RESISTANCE AND REACTANCE..............................................31

4.1 Series connection ..............................................................................................31

4.1.1

Series connection of RandXL .......................................................................31

4.1.2 Series connection of RandXC.......................................................................33

4.1.3 Series connection of R, XLandXC.................................................................35

4.1.4 Particular Case...............................................................................................38


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4.2 Parallel Connection............................................................................................39

4.2.1

Parallel Connection of RandXL.....................................................................39

4.2.2 Parallel connection of R and XC ....................................................................42

4.2.3 Parallel connection of R,XLandXC...............................................................43

4.2.4 Particular case ...............................................................................................45

5 RESONANT CIRCUITS..............................................................................................46

5.1

Series resonant circuit .......................................................................................47

5.2

Parallel resonant circuit......................................................................................48

6 COMPENSATION (POWER FACTOR CORRECTION) ............................................49

6.1

Phase compensation .........................................................................................49

6.2

Series compensation .........................................................................................50

6.3 Shunt compensation ..........................................................................................51

6.3.1

Single reactive-power correction....................................................................51

6.3.2 Group power-factor correction ....................................................................... 51

6.3.3

Central power-factor compensation ...............................................................52

7

INTERFERENCE SUPPRESSION.............................................................................53

7.1 Interference Suppression on a drill ....................................................................53

7.2 Interference suppression on switches................................................................54

7.3

Interference suppression using choke coils .......................................................54

8

THREE-PHASE CURRENT .......................................................................................55

8.1 Production of three-phase current .....................................................................55

8.2

Interconnection ..................................................................................................56

8.2.1 Star connection ..............................................................................................56

8.2.2 Delta connection ............................................................................................58

8.3 Three-phase power in balanced circuits ............................................................60

8.4

Rotating field......................................................................................................62


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ALTERNATING CURRENT

LEARNING OBJECTIVES

The trainee should...

describe the production of alternating current

list and define the characteristics of an alternating quantity

draw the waveform diagram from the phasor diagram and vice versa

describe the behaviour of a resistance in an alternating current circuit

calculate inductive reactance values

calculate capacitive reactance values

represent graphically and numerically the relationship between effective power,

reactive power and apparent power

evaluate current and power values in an alternating current circuit

solve calculations for series circuits numerically and with phasor diagrams

solve calculations for parallel circuits numerically and with phasor diagrams

solve calculations involving resonant circuits

list the characteristics of resonant circuits

solve calculations for power factor correction

state the characteristics of different forms of power factor correction

describe methods of radio interference suppression

describe how three-phase current is produced

calculate line and phase quantities in the star and delta connections

calculate three-phase power values

describe the production of a rotating field


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ALTERNATING CURRENT

1 GENERAL

Alternating current voltages are produced in a generator by induction. This is caused

either by windings rotating in a magnetic field or by magnetic fields turning around fixed

windings.

Example:

The movement of the permanent magnet causes the magnetic flux in the coil to change.

According to the law of induction, a change of flux in a coif induces a voltage in the coil.

This voltage is dependent on the number of turns of the coil and on the rate of change of

flox.


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1.1 Formula for induced voltage

1.2 Generator principle

A loop of wire rotated in a constant magnetic field.An induced voltage is generated by the change of flux within the loop or by "cutting"

magnetic flux lines.

The induced voltage is led away through two slip rings.

The voltage direction is determined using the "right-hand rule". (Palm of the hand towards

the North Pole, thumb pointing in the direction of movement, fingertips pointing in the

direction of the current.)

= B x A


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As the area A varies with the position of the conductor loop, this causes a change of flux

inside the coil which in turn causes the induction of a voltage.

Position 1, 3 of the conductor loop:

No change of flux, no intersecting of the lines of force and therefore no induction.

Position 2, 4:

Movement of the conductor loop vertically to the lines of force; maximum rate of flux

change, greatest induction.


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1.3 Cycle, duration of cycle

A cycle is a complete sinusoidal oscillation, consisting of a positive (+) and a negative (-)

half cycle.

Revolution of the conductor loop from N to S up to N 360 = 1 cycle.

Duration of a cycle. Time needed for the conductor loop from N - S -

N = time for the duration of a cycle.

Symbol = T

Unit = seconds (s)

1.4 Frequency

Symbol = f

Unit = Hertz (Hz)

Usual standard frequencies:


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Central Europe - 50 Hz

U.S.A. - 60 Hz

Austrian Federal Railways - 16.6 Hz (from 50/3 simpler speed change of the

drive units)

Higher frequencies are stated in kilohertz

(kHz ... 103Hz) or megahertz (MHz ... 106Hz).

Other means of notation

c/s or cps cycles per second

Calculation example:

How long is the time for cycle for f = 50 Hz?

Draw the waveform of a sinusoidal oscillation = 60 Hz from


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1.4.1 Frequency and speed of generator

Following voltage curves are obtained at the same number of revolution:


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This shows that, in order to generate a certain frequency, machines with a higher number

of poles run slower than machines with a lower number of poles.

Calculation examples:

At what speed is a 2 pole generator running to generate

a) 50 Hz? b) 16 2/3 Hz?

1.4.2 Waveform and phasor diagram

These diagrams are used to represent sinusoidal alternating voltages and currents

graphically.


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A phasor is a line of length proportional to the peak value of the sinus curve; which rotates

anti-clockwise around its initial position (zero angle) at a given speed (frequency).

1 revolution = 360 = 1 cycle

The instantaneous value at any time is given by the projection of the phasor on the

vertical axis (perpendicular to the time axis)

V= peak value of the voltage

v= instantaneous value, momentary value of the voltage

Calculation using trigonometry

One can then deduce the instantaneous value:

= angle of intersection

v= Vx sin


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The peak value of voltage (F = 50 Hz) is 100 V.

Represent graphically and numerically the voltage after 4 ms.

a)

b) Scale: 20 V = 1cm ( therefore 100 V = 5 cm)


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1.4.3 Angular Velocity (angular speed)

The angular speed is equal to the arc of an angle covered during a given time unit. R is

the frequency expressed in radians per second.

Example:

What angular frequency for = 50 Hz?

= 2 x x f = 2 x 3.14 x 50 = 314


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1.4.4 Maximum Value, Effective Value

The effective value of an alternating current (Ieffor Irms) is equal to the value of the direct

current which will produce the same average power.

Since power is proportional to the square of the current (P = I R),

then:

The effective current is the square root of the mean value of the squared values of

instantaneous current. This is often called the root mean square current (rms value or

Irms). Measuring instruments for alternating current are normally calibrated in terms of the

effective values. Oscilloscopes will show instantaneous values and peak values.


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Relation

The peak value of an alternating voltage is 1.414 times greater than the effective value

which is recorded on a meter.

For a frequency of 50 H1z, the peak value is reached 100 times a second. Insulation must

be made to withstand the peak voltage.

Example:

How high is the peak value for V = 220 V?


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2 RESISTANCE IN AN ALTERNATING CURRENT CIRCUIT

2.1 Ohmic Resistance

Effective resistances (i.e. incandescent lamp, heating elements) have the same effect in

an alternating current circuit as in a direct current circuit, that is, current and voltage are

"in phase".

The zero values and the maximum values of Vand Ioccur at the same time.

Calculation:

2.2 Inductive Reactance (reactive impedanceXL[])

Inductive reactance is caused by the self-induction of a coil.

The self-induced voltage ES, which opposes the applied voltage, is at its highest when the

rate of change of flux (proportional to rate of change of current) is at its greatest, i.e. at the

zero values of and I.


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The voltage is 0 when and I have reached their highest value and will therefore be

momentarily stationary.

The following, simplified phasor diagram can be obtained:

In the case of pure inductance, the current tags behind the voltage by 90.

The reactive impedance of a coil depends on its inductance L.

Ldepends on the number of turns of the coil and on the core material.


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Current Calculation

Example:

Calculate the current in a coil of 20 mH when the supply is

a) 100 V 50 Hz

b) 100 V 16 2/3 Hz

The inductive reactance increases as the frequency increases.

The current is reduced (choked) by the Insertion of an inductance in a circuit.

It is for this reason that the coils are called "choke coils".

XLis a frequency-dependent quantity.

2.3 Capacitive reactance

2.3.1 Capacitor on direct current:

Structure:

2 metal plates with a dielectric (insulating) material between them. When direct voltage is

applied, a charging current flows for a short time, after which the direct current is blocked.The capacitor is able to store its charge. When a load is connected to a charged

capacitor, a discharge current will flow for a short time.


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Definition:

A capacitor has a capacitance of 1 Farad when a charge of 1 coulomb (A.s) produces a

potential difference at the terminals of 1 V.

1 Farad is too large a unit for practical purposes and the following units are used:

Microfarad - F - 10-6F

Nanofarad - nF - 10-9F

Picofarad - pF - 10-12F

The capacitance depends on the plate separation distance, the plate area and the

dielectric material.

Time constant:

is the time during which the capacitor is charged 63 % of the applied voltage.

After 5 x , the capacitor is fully charged.


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Example:

How long is the charging process for a 5 F capacitor connected to direct current in series

with a resistor of 200 k?


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2.3.2 Capacitor on alternating voltage

When an alternating voltage is applied to a capacitor, it charges during the rise of voltage.

During the voltage drop, it discharges through the mains network, that is to say, current

flows when the rate of change of voltage is at its highest (at the current Zero).

Phase shift:

The current leads the voltage by 90.

The reactance of a capacitor depends on the capacitance and on the frequency.


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Example:

Calculate the current in a capacitance

C= 50 F with the applied voltage of:

a) 100 V 50 Hz

b) 100 V 500 Hz

Summary:

Direct current is blocked, high-frequency alternating current flows freely. A capacitive

reactance is frequency-dependent and decreases as the frequency rises.


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3 ALTERNATING CURRENT POWER

Direct Current

P = V x I = effective power

Alternating Current

The power is deduced from the effective values of current and voltage.

3.1 Pure ohmic load

No phase shift between current and voltage.

The instantaneous value of the power can be deduced from the instantaneous values of V

and I

As in mathematics:

+ x + = +

- x - = -

+ x - = -

(any number) x 0 = 0


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The power is only positive, i.e. it always runs from a generator to a load. It runs in pulses

at twice mains frequency (i.e. for f= 50 Hz there are 100 power pulses per second).

The effective value of the power can be calculated as follows:

3.2 Pure reactive load

At a phase shift of 90 between V and I (inductive or capacitive), reactive power is

consumed.

For example:

Inductive load


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There is a series of equal positive and negative power impulses at twice mains frequency.

Power is alternately taken from the supply and then fed back to it.

The total effective power is 0.

A wattmeter would not indicate anything, the meter remains at zero.

Reactive power causes current in the lines and consequently, power losses. It is therefore

undesirable. Reactive power is kept to a minimum by using power factor correction.

3.3 Mixed load (resistance and reactance)

The phase angle is less than 90. In the example shown, = 30 inductive.


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The effective power indicated on the wattmeter is smaller than the apparent power

obtained by multiplying Vand I.

The mean value of the power decreases in direct proportion to the increase in the phase

shift angle .

3.4 Power triangle

This is a phaser representation of effective power, apparent power and reactive power.

Effective power P= energy consumption in the resistance; measured using a wattmeter.

Reactive power Q= consumed by pure inductances or capacitances.

reactive current (current in quadrate with voltage)


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Apparent power S:

This is the power which a load appears to consume, the product of voltage - current,

independent of their phase position. Effective and reactive power values are included in

the apparent power.

Measurement using a volt-ampere meter or Pythagoras:

Output data for electric machines is indicated on their rating plates.

Motor:

Effective power delivered at the shaft in kW

Generator, transformer:

Apparent power delivered in kVA

3.5 Current triangle

Phasor representation of effective current, reactive current and total current.


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Effective current IW

This is the part of the total current which flows to produce the effective power (energy). IW.

is in phase with the voltage.

Reactive current IQ

Reactive current lags behind the voltage by 90 (for an inductive lad) or leads by 90 (for

capacitive lad).

Conversion of cos to sin

Total current = apparent current I

Consumed by the load: Iconsists of IWand IQ.


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A single-phase alternating current motor has an output of 1.5 kW. The rating plate gives

the following additional data:


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4 CONNECTION OF RESISTANCE AND REACTANCE

4.1 Series connection

XLandXCcause a phase shift. A simple addition with Ris therefore not possible.

4.1.1 Series connection of RandXL


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Graphic solutions:

Always start with the common value, i.e. in the case of a series connection with I.

Example of calculation:


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In practice, there are no pure inductances. Each coil has a resistive component.

Equivalent electric circuit of a coil:

4.1.2 Series connection of RandXC

.


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Example:


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4.1.3 Series connection of R,XLandXC


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Graphic solution:


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Calculation Example:


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4.1.4 Particular Case

XL and XC are equally large; they cancel each other in their effect. The circuit then

appears as purely resistive. Series resonance occurs. In this condition, the voltages

across the reactances may be larger than the applied voltage.

The current is high, due to the fact that it is only limited by the resistance (Z = R).

Graphic Solution:

Calculation of the resonant frequency:


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4.2 Parallel Connection

4.2.1 Parallel Connection of RandXL


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Graphic Solution:


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4.2.2 Parallel connection of R and XC

Resistance triangle:

Graphic solution:


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4.2.3 Parallel connection of R,XLandXC

XLand XCoppose each other, that is to say, ILand ICare in opposition and partly annul

one another.

IX= IC- ILor IL- IC, depending on whether the capacitive or inductive current dominates.

Graphic solution: ie.: IL> IC


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4.2.4 Particular case

XLandXCare equally large - ILand ICcancel each other.

Z = R; parallel resonance occurs.

Currents in the reactances may be greater than the total current.

The calculation of the resonant frequency is the same as for the series connection.


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5 RESONANT CIRCUITS

An electric resonating circuit consists of a coil and a capacitor. Without a constant supply

of energy, damped oscillations can occur.

The damping is caused by the ohmic resistances which will exist in every resonant circuit.

These resistances change electrical energy into heat. In a resonant circuit, electrical

energy is transformed into magnetic energy and vice versa.

The periodic time and the frequency of the oscillations are constant.

natural frequency of oscillation.

The frequency depends on the components used and not on the magnitude of the applied

voltage.

Resonance: XL=XC


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5.1 Series resonant circuit

Phasor diagrams:

Resonance curve:

Smallest impedance (pure resistance) in the resonant case, increased voltage across the

reactances.


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5.2 Parallel resonant circuit

At resonance, highest impedance (pure resistance), therefore smallest current.Currents in reactances may be greater than the total current.


Calculate the resonant frequency of a series resonant circuit with

L= 200 mH and C= 20 F.


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6 COMPENSATION (POWER FACTOR CORRECTION)

6.1 Phase compensation

In the mains network, the loads such as motors, transformers etc., are mainly inductive.

Therefore, the feeders must carry this reactive current.

This means greater total current - the feeder must have a greater cross sectional area and

additional expense is necessary.

The inductive reactive output can be cancelled by a capacitive reactive .load

(compensated).

Output triangle:

The power remains the same, the reactive load and apparent power decrease.

Compensating capacitors should be as close to the load as possible.


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Calculating the capacitor output:

The capacitance can then be deduced

Power factor correction (a resonance phenomenon) is usually carried out to increase cos

to cos = 0.9 to 0.95 and more rarely to increase cos to unity.

6.2 Series compensation

Cis connected to the load in series; i.e. to a fluorescent lamp.

Disadvantage - danger of excess voltage at Land C


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6.3 Shunt compensation

Used especially on three-phase systems

Disadvantage:

If high-frequency control signals are sent over the mains network (centralized multi-station

control system), they are short-circuited by the low reactance of the capacitor and thus

rendered ineffective.

6.3.1 Single reactive-power correction

Each load is individually compensated. According to TAEV, the capacitor should be

capable of discharging to a safe voltage within 60 seconds.

6.3.2 Group power-factor correction

Several loads running simultaneously are compensated together.


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6.3.3 Central power-factor compensation

If needed, several capacitors may be connected in parallel. A control device switches the

capacitors on or off depending on the reactive consumption.



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7 INTERFERENCE SUPPRESSION

Brush sparking on commutator motors, lose contacts, switches, sparking plugs, gas-

discharge lamps etc. all act as sources of interference. Interference voltages may be fed

back into the mains network and become superimposed on the supply voltage or radiated

from the equipment and wires to cause interference on radio and television receivers.

Suppression is carried out as close to the source of interference as possible, using anti-

interference capacitors connected in parallel with the equipment. Special interference

suppression capacitors for radios are connected between the live conductors and

between the conductors and the earth (casing).

7.1 Interference Suppression on a drill

Suppression is most effective if the capacitive reactance is very small at the interfering

frequency.


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7.2 Interference suppression on switches

- by connecting CR combinations in parallel with the switch contacts.

7.3 Interference suppression using choke coils

- usually in connection with capacitors as filtering units.

Marking of noise-suppressed appliances according to VE:

The letter informs you of the remaining level of interference.

N = normal i.e. for residential areas.


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8 THREE-PHASE CURRENT

A three phase circuit consists of three interconnected AC circuits. The three alternating

voltages in these three circuits are equal in magnitude but displaced by phase angles of

120 from each other.

A phase angle of 360 is equivalent to two pole pitches 1 pole pitch is the angular

separation between the axes of two adjacent magnetic poles in an electrical machine.

8.1 Production of three-phase current

In the three-phase generator, three windings, each electrically displaced by 120, are

successively cut the magnetic field of the rotating magnet.

This creates three alternating currents with phase displacements of 120 (= 1/3 cycle).


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The sum of the three currents and voltages is 0 at all times. For this reason the three

alternating voltages can be interconnected

Designation:

8.2 Interconnection

8.2.1 Star connection

U2, V2, W2 form the star point. The neutral conductor (neutral wire) is attached to this

point.


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Relations:

Example:

Phasor diagrams:


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When the phases are unequally loaded, the current flows in the neutral wire. The

magnitude of the current is obtained by adding the phasors.

The phasor diagram is no longer closed. The phasor sum flows in the neutral conductor.

8.2.2 Delta connection


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Phasor diagram for a symmetrical load:

The delta connection should only be used for symmetrical loads. An unbalanced load

causes a displacement of the current star:

8.3 Three-phase power in balanced circuits

In order to calculate the power, always use the line currents and voltages.


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Three equal resistances R = 20 each are connected to a three phase supply 380/220 V

~ 50 Hz

a) in a star connection

b) in a delta connection

calculate the effective power for a) and b).

a)

Each R is on 220 V, therefore:

Result:


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8.4 Rotating field

If three-phase current flows through three coils which are displaced by 120 in space this

produces a rotating magnetic field.

This field rotates at a constant speed around an axis. In the case of a bipole machine

(which has three field windings) and for f = 50 Hz, the field rotates 3000 times per minute.

The direction of rotation may be changed by reversing two of the lines. The rotating field is

used on three-phase machines.


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EE013Alternating Current

Theoretical Test


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Alternating Current

Test 1

1. Describe the production of alternating current.

2. Explain the term cycle.

3. State the relation between current and voltage in resistances an AC.

4. Calculate the current Iin a 2 mH coil with an applied voltage of 12 V ~ 50 Hz.

5. What is the unit of reactive power?

6. What is the .output recorded on the rating plates of electric machines?

7. R= 10 and L= 32 mH are in series with a supply V= 100V ~ 50 Hz. Calculate the

value of I.

8. R, Land Care in series. State the formula for calculating the total impedance.

9. Draw the impedance curve for a series resonant circuit.

10. The line voltage of a three-phase network connected in 220 V. Calculate the phase

voltage?


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Alternating Current

Test 2

1. Calculate the speed required to produce a frequency of 50 Hz from a 12 pole

generator.

2. State the formula which gives the angular velocity in an AC circuit.

3. State the effect of applying a direct current and high-frequency alternating current to a

capacitor.

4. What is the meaning of the power factor cos of an AC circuit.

5. A coil consumes 1 A on 10 V direct current .and 0.78 A on 10 V alternating current f=

50 Hz. Calculate the inductance.

6. R,XLandXCare connected in series ifXL=XCstate the effect.

7. What does the term "phase compensation" mean?

8. Sketch the resonance curve of impedance for a parallel resonant circuit.

9. Describe the production of three-phase alternating current.

10. Three equal resistances (10 each) are in connection on V= 380 V. Calculate the

total power absorbed.


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Alternating Current

Test 3

1. Calculate the periodic time of an AC of frequency 2 Hz.

2. State the relationship between current and voltage with inductive reactances.

3. Calculate the reactances of a 33 F capacitor at a frequency of 50 Hz.

4. Draw the waveform of an alternating current leading the voltage by 90.

5. State the formula which gives the effective power in an alternating current circuit.

6. Name the instruments used to measure effective and apparent power.

7. Calculate the resonant frequency of a parallel resonant circuit of

L= 100 mH and C= 360 F.

8. State the disadvantage of parallel compensation (power factor correction)

9. What is the ratio VLto VPand ILto IPin a delta connected lad.

10. Describe the production of a rotating field.


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Alternating Current

Test 4

1. What values of an AC quantity are measured by

a) a meter

b) an oscilloscope

2. State the relationship between current and voltage in a capacitive reactance an

alternating voltage.

3. Calculate the charging time for a 10 F capacitor connected to direct voltage through

a series resistance of 1 M.

4. Sketch the power waveform on the following waveform diagram (v and i given).

5. Draw the power triangle showing how effective power, apparent power and reactive

power are related.

6.R

andX

Care in parallel. State the formula used to calculate the total impedance.


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7. On what does the natural frequency of an oscillatory circuit depend?

8. Under what circumstances is an oscillatory circuit in resonance?

9. Calculate the effective power of a star connected load, where

VP= 127 V, IP5 A, cos = 0.8 .

10. Under what circumstances does current flow in the neutral wire of a three-phase star

connection?


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Alternating Current

Test 1

(Solution)

1. Produced by rotating a conductor loop in a fixed magnetic field or rotating a magnet in

a fixed coil.

2. A cycle is a complete sinusoidal oscillation, consisting of a positive and a negative

half-wave.

3. They are in phase; maximum values and zeros are simultaneous.

4.

5. The var = voltamp reactive

6. Motor: effective output power at the shaft in kW.

Generator, transformer: apparent output power in kVA.

7.

8.


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9.

10.


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Alternating Current

Test 2

(Solution)

1.

2.

3. Direct current is blocked; high-frequency alternating current flows trough freely.

4.

5.

6. XLandXCcancel each other (series resonance). In this instance, voltages appearing

across the reactances may be higher than the total voltage. The current is only limited

by R.

7. Improvement of cos by using compensation capacitors. The inductive reactivepower is cancelled or reduced by capacitive reactive power.


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8.

9. Three coils, each displaced electrically by 120, are cut by the magnetic field of a

rotating magnet. An alternating voltage is induced in each coil successively.

10.


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Alternating Current

Test 3

(Solution)

1.

2. Vleads by 90 or Ilags by 90.

3.

4.

5. P = V x I x cos

6. Effective power P = wattmeter.

Apparent power S = V x I = voltmeter and ammeter


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7.

8. High-frequency control signals of a central multi-station control system are short-

circuited by the low reactance of the capacitor and are thus rendered ineffective.

9.

10. If three-phase current flows through a three-phase winding (three coils each displaced

by 120), it creates a rotating magnetic field.


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Alternating Current

Test 4

(Solution)

1. For meters, the effective value; on the oscilloscope peak or instantaneous values.

2. Ileads Vby 90

3.

4.

5.


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76

6.

7. Only on the component parts, not on the voltage.

8. When the inductive and capacitive reactances are equal (XL= XC)

9.

10. When the individual phases are unequally loaded (unbalanced).

11.


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KEY TO EVALUATION

PER CENT MARK

88 100 1

75 87 2

62 74 3

50 61 4

0 49 5

EE013 Alternating Current Th Inst

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