Topic 1 sinusoidal alternating voltage and current topic a1

Bài giảng ngành Điện: Giải các bài toán trong mạch điện điện thế thấp một pha và ba pha (Phần A) gồm các chủ đề sau Solve problems in single and threephase low voltage circuits Part A Content Topic 1 Sinusoidal Alternating Voltage and Current_Topic_A1 Topic 2 Phasors_Topic_A2.ppt Topic 3 Resistance in AC Circuits_Topic_A3 Topic 4 Inductance in AC Circuits_Topic_A4 Topic 5 Capacitance in AC Circuits_Topic_A5 Topic 6 AC Circuit Analysis_Topic_A6 Topic 7 Resonance_Topic_A7 Topic 9 Harmonics_Topic_B9

 Sinusoidal Alternating Voltage and Current

 Phasor Representation of Voltage and

Solve Problems in Single and

Three Phase Low Voltage

Circuits

Solve problems in single and three-phase low

voltage circuits

Topic 1: Sinusoidal Alternating Voltage and Current

Generation of a Voltage

Fleming’s Right-Hand Rule (for generators)

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Nathan CondieCopyright  2003 McGraw-Hill Australia Pty Ltd

PPTs t/a Electrical Principals for the Electrical Trades 5e by Jenneson

Slides prepared by Anne McLean

Fleming’s Right-Hand Rule (for generators)

S

S

Conductor Motion

In each of the following examples, determine the direction of induced EMF

Magnetic

S

S

Conductor Motion

Magnetic Field

Motion

Answers: Direction of induced EMF

Magnetic Field

Motion

No Induced EMF – travels parallel to flux

N S

S N

Further exercises using Fleming’s Right-Hand Rule (for Generators)

?

?

Polarity of magnetic

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N S

S N

Direction of relative motion of magnetic

field?

Answers: Fleming’s Right-Hand Rule (for Generators)

S N

Polarity of magnetic

field poles?

Fleming’s Right-Hand Rule (for Generators):

A single conductor formed into a loop

Front View

Top View

Conductor Loop Magnetic

Field

Poles

North

South North

South

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Copyright  2003 McGraw-Hill Australia Pty Ltd

PPTs t/a Electrical Principals for the Electrical Trades 5e by Jenneson

Slides prepared by Anne McLean

Generation of an AC Voltage

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AC Waveform: Vertical Axis

 The height the waveform reaches above (or below) the horizontal axis represents its AMPLITUDE Amplitude is expressed as a:

 Peak or Maximum Value

 The distance from the zero value to the highest value on the curve (either above or below the horizontal axis)

 For a Voltage waveform, symbol V Pk or V Max

 For a Current waveform, symbol I Pk or I max

 Peak-to-Peak Value

 The distance between the top (crest) and bottom (trough) of the

waveform

 For a Voltage waveform, symbol V P-P

 For a Current waveform, symbol I P-P

V P-P =2V Pk

AC Waveform: Vertical Axis

 The value at any point along the waveform

 For Voltage waveform, symbol “v” (lowercase)

 For Current waveform, symbol “i” (lowercase)

Sine Wave Onlyv = Vmax Sinθ

Where

v is the instantaneous value of the sinewave at a specified point

Vmax is the maximum value of the sinewave

Sin is a function applied to the phase angle

Θ is the phase angle in degrees Electrical (indicates the rotation of loop)

AC Waveform: Vertical Axis

 RMS Value (Root-Mean-Square)

 Represents the EFFECTIVE value of the AC waveform.

 An RMS value represents the DC equivalent in terms of

electrical energy potential.

 The RMS value of an alternating current (AC) waveform will cause the same heat dissipation as that value of direct current (DC).

Sine Wave Only V RMS = 0.707 V max

ALL AC values given are considered to be RMS values, unless

otherwise specified

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Copyright  2003 McGraw-Hill Australia Pty Ltd

PPTs t/a Electrical Principals for the Electrical Trades 5e by Jenneson

Slides prepared by Anne McLean

AC Waveform: Vertical Axis

Instantaneous values

AC Waveform: Horizontal

Axis

waveform

 Period, or Periodic Time

 The time taken for the AC waveform to complete one full cycle (360 o E)

 Symbol t, measured in Seconds (s)

 Frequency

 The number of cycles per second

 Symbol ƒ, measured in Hertz (Hz)

ƒ = 1/t

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AC Waveform: Horizontal

Axis

one cycle Periodic Time

one cycle

one cycle

Periodic time is measured between two EQUIVALENT points of the

waveform

AC Waveform: Electrical

Degrees

oscilloscopes where the horizontal axis is

normally given as a time base (in seconds) rather than as an angle (in degrees)

any specified time value will need to be

converted to an angle (Electrical Degrees)

AC Waveform: Exercises

value of 230V and a frequency of 50Hz,

calculate the instantaneous values of voltage

at the following points:

 2mS

 5mS

 11mS

 356mS

NON-Sinusoidal Waveforms

NON-Sinusoidal Waveforms

sinusoidal

effect of some loads, a sinusoidal waveform may become NON-sinusoidal

Average formulas are NOT valid.

 To determine the values and shape of a

non-sinusoidal waveform, two factors are used.

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NON-Sinusoidal Waveforms

Non-sinusoidal (Flat-topped) AC Waveform

RMS Value

NON-Sinusoidal Waveforms

Non-sinusoidal (Peaky) AC Waveform

RMS Value

Crest Factor = V max / V RMS

For a pure sinusoidal waveform, the crest factor would be

1.41

NON-Sinusoidal Waveforms

waveforms

Form Factor = V RMS / V ave

For a pure sinusoidal waveform, the Form Factor would be 1.11

If the waveform’s Form Factor is GREATER than 1.11,

waveform is more “PEAKY”

If the waveform’s Form Factor is LESS than 1.11, the

waveform is more “FLAT-TOPPED”

NON-Sinusoidal Waveforms

 Exercises

 An inverter producing a 230V, 50Hz NON-sinusoidal waveform has a stated crest factor of 1.6 Determine the following:

 Max voltage of waveform (V Max )

 How does this Vmax of this waveform compare to a 230V purely

sinusoidal waveform?

 How would this affect the insulation rating required by loads?

 An light dimmer device produces a 230V RMS NON-sinusoidal waveform with a form factor of 2.9 If an analogue voltmeter was used to measure the voltage in of the waveform, determine the value of voltage that would be indicated.

Sinusoidal Waveforms (cont.)

Phase Relationships between

Sinusoidal Waveforms

 In any electrical circuit, there may exist more than ONE waveform.

 Depending on the loads in the circuit, these

waveforms often may or may not oscillate together – they may be “in-phase”, “out-of-phase: lagging”, or

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Phase Relationships between

Sinusoidal Waveforms

 IN-PHASE

 Waveform ‘I’ is

IN-PHASE with the

reference waveform ‘V’

 The “Phase Angle” (Ø)

is zero (no lag or lead)]

 Ø = 0 o E

 “ 0 E” stands for “Degrees

Electrical”

Phase Relationships between

 Waveform ‘I’ LEADS

the reference waveform

‘V’ by Ø (phi)

 The Phase Angle (Ø) is

90 o E Lead

Phase Relationships between

Sinusoidal Waveforms

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To Convert a Time Difference

(lag or lead) to a Phase Angle

waveforms is often only indicated, on an

oscilloscope, as a time difference lead or lag

determined by comparing two equivalent

points on the waveforms eg “zero-cross up”

Ø = tLag or Lead x 3600

tperiodic

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Practical Exercise: AC

Waveforms

connecting, measuring, and analysing the

multiple waveforms of electrical circuits