Transcript AC Electricity - UniMAP Portal

AC Electricity
Muhajir Ab. Rahim
School of Mechatronic Engineering
Universiti Malaysia Perlis
Contents
1. Introduction
2. AC Sinusoidal Waveform
3. Measurement of AC Sinusoidal
Waveform
4. Nonsinusoidal Waveforms
Contents
1. Introduction
2. AC Sinusoidal Waveform
3. Measurement of AC Sinusoidal
Waveform
4. Nonsinusoidal Waveforms
Learning Objectives in
Introduction
1. Able to describe the difference between
DC and AC voltage and current.
2. Able to represent the sources of DC and
AC voltage and current.
3. Understand the concept of operation of
AC generator
Introduction
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In 1887 direct current (DC) was
king. At that time there were 121
Edison power stations scattered
across the United States
delivering DC electricity to its
customers.
But DC had a great limitation -namely, that power plants could
only send DC electricity about a
mile before the electricity began to
lose power.
In the late 1880s, George
Westinghouse introduced his
system based on high-voltage
alternating current (AC), which
could carry electricity hundreds of
miles with little loss of power.
DC Current vs. AC Current (1/2)
• Direct current (DC) flows in one direction the
circuit.
• Alternating current (AC) flows first in one
direction then in the opposite direction.
The same definitions apply to alternating voltage (AC voltage):
• DC voltage has a fixed polarity.
• AC voltage switches polarity back and forth.
DC Current vs. AC Current (2/2)
• There are numerous sources of DC and AC
current and voltage. However: Sources of DC
are commonly shown as a cell or battery:
• Sources of AC are commonly shown as an AC
generator:
Switch is off,
circuit is open,
no current flow,
lamp is off
Switch is on to DC,
Circuit is closed,
Current is flowing in one direction,
Lamp is on
Switch is on to AC,
Circuit is closed,
Current is flowing back and forth,
Lamp is on
The purpose of a generator is to
convert motion into electricity.
The wire passing through a magnetic field
causes electrons in that wire
to move together in one direction.
When the loop is spinning,
it's moving across the field first in one direction
and then in the other,
which means that the flow of electrons
keeps changing
Comparison of DC and AC loops and rings
This is Brighton Electric Light Station in 1887.
Stationary steam engines drive tiny
direct current (DC) generators
by means of leather belts
Tesla's alternating current (AC)
induction motor was simple in
concept and could be made
sufficiently small to power
individual machines in factories
Contents
1. Introduction
2. AC Sinusoidal Waveform
3. Measurement of AC Sinusoidal
Waveform
4. Nonsinusoidal Waveforms
Learning Objectives in
AC Sinusoidal Waveform
1. Able to describe the shape and main
features of a AC sinusoidal waveform.
2. Able to calculate the instantaneous value
of a current or voltage sine waveform,
given the maximum value and angular
displacement
The Sinusoidal
AC Waveform (1/2)
• The most common AC waveform is a sine (or sinusoidal)
waveform.
• The vertical axis represents the amplitude of the AC current or
voltage, in amperes or volts.
• The horizontal axis represents the angular displacement of the
waveform. The units can be degrees or radians.
The Sinusoidal
AC Waveform (2/2)
• The sine waveform is accurately
represented by the sine function of plane
trigonometry: y = rsinθ where:
y = the instantaneous amplitude
r = the maximum amplitude
θ = the horizontal displacement
Instantaneous Current
i = Ipsinθ
where,
i = instantaneous current in amperes
Ip= the maximum, or peak, current in amperes
θ = the angular displacement in degrees or radians
Instantaneous Voltage
v = Vpsinθ
where
v = instantaneous voltage in volts
Vp = the maximum, or peak, voltage in volts
θ = the angular displacement in degrees or radians
Contents
1. Introduction
2. AC Sinusoidal Waveform
3. Measurement of AC Sinusoidal
Waveform
4. Nonsinusoidal Waveforms
Learning Objectives in Measurement
of AC Sinusoidal Waveform (1/2)
Amplitude of AC Sinusoidal Waveform
• Able to define the terms peak and peak-to-peak as they apply to AC sinusoidal
waveforms.
• Able to convert between peak and peak-to-peak values.
• Able to describe the meaning of root-mean-square (RMS) as it applies to AC
sinusoidal waveforms.
• Able to convert between RMS values and peak values.
• Able to describe the meaning of average values of a AC sinusoidal waveform.
• Able to convert between averages values and peak values.
• Able to describe how instantaneous values for voltage and current differ from peak,
RMS, and averages values.
Period and Frequency of AC Sinusoidal Waveform
• Able to define the period of a AC waveform.
• Able to cite the units of measure for the period of a waveform.
• Able to define the frequency of a waveform.
• Able to cite the units of measure for the frequency of a waveform.
• Able to convert between values for the period and frequency of a waveform
Learning Objectives in Measurement
of AC Sinusoidal Waveform (2/2)
Phase Angle
• Able to describe the meaning of phase angle.
• Able to expand the formula for instantaneous sine voltage and
current to include a phase angle, then apply the formula to sketch
accurate sinusoidal waveforms.
• Able to define the terms leading and lagging as they apply to
sinusoidal waveforms.
AC Sinusoidal Power Waveform
• Able to sketch voltage, current, and power sine waveforms on the
same axis.
• Able to explain why the power waveform is always positive as long
as current and voltage are in phase.
• Able to cite the fact that average power is equal to the product of
RMS current and RMS voltage
Amplitude of AC Waveform
• Peak and peak-to-peak values are most often used
when measuring the amplitude of ac waveforms directly
from an oscilloscope display.
Peak and
Peak-to-Peak Voltage
• Peak voltage is the voltage measured from the baseline of an ac
waveform to its maximum, or peak, level.
• Unit: Volts peak (Vp)
Symbol: Vp
• For a typical sinusoidal waveform, the positive peak voltage is equal
to the negative peak voltage.
• Peak-to-peak voltage is the voltage measured from the maximum
positive level to the maximum negative level.
• Unit: Volts peak-to-peak (Vp-p)
Symbol: Vp-p
• For a typical sinusoidal waveform, the peak-to-peak voltage is equal
to 2 times the peak voltage.
Conversion between Vp and Vp-p
• Convert Vp to Vp-p:
Vp-p = 2 Vp
• Convert Vp-p to Vp :
Vp =0.5 Vp-p
Exercise
1. What is the peak-to-peak value of a
sinusoidal waveform that has a peak
value of 12 V? Ans: 24 V
2. What is the peak value of a sine wave
that has a peak-to-peak value of 440 V?
p-p
Ans: 220 Vp
RMS Voltage (1/2)
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AC levels are assumed to be expressed as Root Mean Square, (RMS)
values unless clearly specified otherwise.
The RMS value is also referred to as the effective value.
Unit: Volts (V)
Symbol: Vrms
The RMS voltage of a sinusoidal waveform is equal to 0.707 times its peak
value.
Vrms = 0.707Vp
RMS Voltage (2/2)
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The RMS value of a sinusoidal voltage is actually a measure of the heating effect of
the sine wave.
For example, when a resistor is connected across an AC (sinusoidal) voltage source,
as shown in Figure (a), a certain amount of heat is generated by the power in the
resistor. Figure (b) shows the same resistor connected across a DC voltage source.
The value of the AC voltage can be adjusted so that the resistor gives off the same
amount of heat as it does when connected to the DC source.
In a DC circuit, applying 2 V to a 1 Ω resistance produces 4 W of power.
In an AC circuit, applying 2 Vrms to a 1Ω resistance produces 4 W of power
RMS voltages are expressed without a + or - sign.
Sinusoidal AC
Source
DC
Source
Conversion between Vp to Vrms
• Convert Vp to Vrms:
Vrms = 0.707Vp
• Convert Vrms to Vp :
Vp =1.414Vrms
Exercise
1. Determine the RMS value of a waveform
that measures 15 Vp. Ans: 10.6 V
2. Determine the peak value of 120 V. (Hint:
Ans: 170 V
Assume 120 V is in RMS)
p
Average Voltage
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Average voltage is the average value of all the values for one half-cycle of
the waveform.
Unit: Volts average (Vave)
Symbol: Vave
The average voltage of a sinusoidal waveform is equal to 0.637 times its
peak value. Vave = 0.637Vp
The average voltage is determined from just one half-cycle of the waveform
because the average value of a full cycle is zero.
Average voltages are expressed without a + or - sign
Conversion between Vp to Vave
• Convert Vp to Vave:
Vave = 0.637Vp
• Convert Vave to Vp:
Vp =1.57Vave
Exercise
1. Determine the average value of a
waveform that measured 16 Vp. Ans: 10.2 V
ave
2. What is the peak value of a waveform
that has an average value of 22.4 V?
Ans: 35.2 Vp
Period of a Waveform
• The period of a waveform is the time required for
completing one full cycle.
• Math symbol: T
Unit of measure: seconds (s)
• One period occupies exactly 360º of a sine waveform.
Frequency of a Waveform
• The frequency of a waveform is the number of cycles
that is completed each second.
• Math symbol: f
Unit of measure: hertz (Hz)
• This example shows four cycles per second, or a
waveform that has a frequency of 4 Hz
Conversion between
Period and Frequency
• Period to Frequency f = 1/T
• Frequency to Period T = 1/f
Frequency (f) is in hertz (Hz)
Period (T) is in seconds (s)
Exercise
1. A certain sine waveform has a frequency
of 100 Hz. What is the period of this
waveform? Ans: 10 ms
2. What is the frequency of a waveform that
has a period of 200 ms? Ans: 5 kHz
Phase Angle
• The phase angle of a waveform is angular
difference between two waveforms of the same
frequency.
• Math symbol: θ
Unit of measure: degrees or radians
• Two waveforms are said to be in phase when
they have the same frequency and there is no
phase difference between them.
• Two waveforms are said to be out of phase
when they have the same frequency and there is
some amount of phase shift between them.
Leading Phase Angles
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A leading waveform is one that is
ahead of a reference waveform of
the same frequency.
In this example, the blue waveform
(sine wave A) is taken as the
reference because it begins at 0
degrees on the horizontal axis.
Sine wave B is shifted to the right
by 90°.
Thus, there is a phase angle of 90°
between sine wave A and sine
wave B.
In terms of time, the positive peak
of sine wave B occurs later than
the positive peak of sine wave A
because time increases to the right
along the horizontal axis.
In this case, sine wave B is said to
lag sine wave A by 90°. In other
words, sine wave A is said to be
leading sine wave B by 90°
A leads B by 900, or B lags A by 900
Lagging Phase Angles
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A lagging waveform is one that is
behind a reference waveform of
the same frequency.
In this example, the blue waveform
(sine wave A) is taken as the
reference because it begins at 0
degrees on the horizontal axis.
Sine wave B is shown shifted left
by 90° .
There is a phase angle of 90°
between sine wave A and sine
wave B.
In this case, the positive peak of
sine wave B occurs earlier in time
than that of sine wave A.
Therefore, sine wave B is said to
lead sine wave A by 90°. In other
words, sine wave A is said to be
lagging sine wave B by 90°
B leads A by 900, or A lags B by 900
AC Power Waveform (1/2)
• The current and voltage waveforms
are shown in phase. This is typical for
a resistive load. The shaded green
areas represent the corresponding
levels of power.
• The instantaneous value of power is
equal to the instantaneous current
times the instantaneous voltage.
P = IV
where,
P = instantaneous value of power (Watt)
I = instantaneous value of current (Amp)
V = instantaneous value of voltage (V)
AC Power Waveform (2/2)
• Notice that the power waveform is always
positive.
• A positive value of power indicates that the
source is giving power to the load.
• A negative value of power would indicate that
the circuit is returning power to the source
(which will not happen in a resistor circuit).
• The power waveform is always positive because
the values of current and voltage always have
the same sign--both negative or both positive. In
algebra, this means that the product of the two
values is always a positive value.
Average AC Power
• When the current and voltage
waveforms are in phase, the
average power is equal to the
RMS voltage times the RMS
current:
Pave = IRMS x VRMS
• Conventional use allows us to
write this equation more simply
as: P = IV
• It is then assumed that P is an
average value and the other
two terms are RMS values.
Contents
1. Introduction
2. AC Sinusoidal Waveform
3. Measurement of AC Sinusoidal
Waveform
4. Nonsinusoidal Waveforms
Learning Objectives in
Nonsinusoidal Waveforms
• Able to describe the features of a rectangular or
square waveform.
• Able to calculate the total period and frequency
of a rectangular waveform.
• Able to define duty cycle and average voltage
as the terms apply to a rectangular waveform.
• Able to describe the features of a triangular or
sawtooth waveform
Rectangular Waveform (1/3)
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A rectangular waveform is characterized
by flat maximum and minimum levels,
fast-rising and fast-falling edges, and
squared-off corners. Because of the
squared corners, a rectangular waveform
is also called a square waveform
The amplitude of a rectangular waveform
is a measure of the distance between the
minimum and maximum levels--the peakto-peak value. Amplitude is most often
expressed in units of volts, although units
of current and power can be useful at
times.
The period of a rectangular waveform is
the time required to complete one full
cycle. The period is measured in units of
seconds.
Rectangular Waveform (2/3)
• The period of a rectangular waveform
can be further broken down into two
phases:
Time High, TH -- The amount of time for
the higher amplitude level.
Time Low, TL--The amount of time for
the lower amplitude level.
• In these terms, the period of the
waveform can be give by:
T = T H + TL
T = total period of the waveform
TH = time high
TL = time low
Rectangular Waveform (3/3)
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The duty cycle of a square waveform is the ratio of time high to the total period:
duty cycle = TH / T
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It is often expressed as a percentage where:
duty cycle (%) = (TH / T ) x 100
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Rectangular waveforms are sometimes used for regulating the amount of power
applied to a load (such as a motor or lamp). The higher the duty cycle, the greater
the amount of power applied to the load.
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The frequency of a rectangular waveform is given by:
f = 1/T or f = 1/(TH+TL)
•
The average voltage of a square waveform is given by:
Vave = Vp x duty cycle
Exercise
1. For a rectangular waveform, TL = 15 ms
and TH = 10 ms. Calculate:
(a) The total period of the waveform.
(b) The frequency of the waveform.
(c) The duty cycle of the waveform.
Ans: (a) 25 ms, (b) 40 Hz, (c) 0.4 or 40%
Sawtooth Waveform
• A sawtooth waveform is characterized
by one sloping edge and one that
instantaneously returns to the
baseline.
• The slope of a sawtooth waveform is
specified in terms of volts per second
(V/s).
• If Vp is the amplitude and T is the
period of sawtooth waveform, the
slope is give by:
slope = Vp / T
or since T = 1/f:
slope = Vpf
Exercise
1. The amplitude of a sawtooth waveform is
12 V. If the frequency is 100 Hz, what is
the slope? slope = 1200 V/s