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 Current

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)

Conductor Motion

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

Magnetic

Conductor Motion

Magnetic Field

Answers: Direction of induced EMF

Magnetic Field

No Induced EMF – travels parallel to flux

Direction of relative motion of

Polarity of magnetic field poles?

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

Polarity of magnetic

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Direction of relative motion of

Polarity of magnetic field poles?

Direction of relative motion of magnetic

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

Polarity of magnetic field poles?

Fleming’s Right-Hand Rule (for Generators): A single conductor formed into a loop

Front View

Top ViewConductor Loop

Magnetic Field

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 VPk or VMaxFor a Current waveform, symbol IPk or Imax

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 = VmaxSinθ

v is the instantaneous value of the sinewave at a specified pointVmax 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 VRMS = 0.707 Vmax

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

Period, or Periodic Time

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

Symbol t, measured in Seconds (s)

The number of cycles per second

Symbol ƒ, measured in Hertz (Hz)

ƒ = 1/t

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AC Waveform: Horizontal Axis

one cyclePeriodic 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).

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AC Waveform: Electrical Degrees

θ = tinstantaneous x 3600

tperiodic

AC Waveform: Exercises

value of 230V and a frequency of 50Hz,

calculate the instantaneous values of voltage at the following points:

356mS

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AC Waveform: Answers to Exercises

Step 1: Find VMax

AC Waveform: Answers to Exercises

NON-Sinusoidal Waveforms

NON-Sinusoidal Waveforms

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

Average formulas are NOT valid.

To determine the values and shape of a 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 = Vmax/ VRMS

For a pure sinusoidal waveform, the crest factor would be 1.41

NON-Sinusoidal Waveforms

waveforms

Form Factor = VRMS / Vave

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

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

Max voltage of waveform (VMax)

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 “out-of-phase: leading”.

The amount of “Lag” or “Lead” is expressed as a phase angle.

Determining the out-of-phase relationship between waveforms is a critical part of electrical theory.

Phase Relationships between Sinusoidal Waveforms

OUT-OF-PHASE => LAG

Waveform ‘I’ LAGS the reference waveform ‘V’ by Ø (phi)

The Phase Angle (Ø) is 90oE Lag

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Phase Relationships between Sinusoidal Waveforms

OUT-OF-PHASE => LEAD

Waveform ‘I’ LEADS

the reference waveform ‘V’ by Ø (phi)

The Phase Angle (Ø) is 90oE 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

Waveform Relationship Exercises

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Waveform Relationship Exercises

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Practical Exercise: AC Waveforms

connecting, measuring, and analysing the multiple waveforms of electrical circuits.