But such clean waveforms typically only exist in a laboratory. Harmonics have been
around for a long time and will continue to do so. In fact, musicians have been aware
of such since the invention of the first string or woodwind instrument. Harmonics
(called overtones in music) are responsible for what makes a trumpet sound like a
trumpet, and a clarinet like a clarinet.
Electrical generators try to produce electric power where the voltage waveform has only
one frequency associated with it, the fundamental frequency. In the North America, this
frequency is 60 Hz, or cycles per second. In European countries and other parts of the
world, this frequency is usually 50 Hz. Aircraft often uses 400 Hz as the fundamental
frequency. At 60 Hz, this means that sixty times a second, the voltage waveform
increases to a maximum positive value, then decreases to zero, further decreasing to a
maximum negative value, and then back to zero. The rate at which these changes
occurs is the trigometric function called a sine wave, as shown in figure 1. This
function occurs in many natural phenomena, such as the speed of a pendulum as it
swings back and forth, or the way a string on a voilin vibrates when plucked.
Figure 1. Sine Wave
The frequency of
the harmonics are
different, depending on the fundamental frequency. For example, the 2nd harmonic on
-1.1
-0.9
-0.7
-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
0.9
1.1 a 60 Hz system is 2*60 or 120 Hz. At 50Hz, the second harmonic is 2* 50 or 100Hz.
300Hz is the 5th harmonic in a 60 Hz system, or the 6th harmonic in a 50 Hz system.
Figure 2 shows how a signal with two harmonics would appear on an oscilloscope-type
display, which some power quality analyzers provide.
Figure 2.
Fundamental
with two
harmonics
In order to be able to analyze complex signals that have many different frequencies
present, a number of mathematical methods were developed. One of the more popular
is called the Fourier Transform. However, duplicating the mathematical steps required
in a microprocessor or computer-based instrument is quite difficult. So more
compatible processes, called the FFT for Fast Fourier Transform, or DFT for Discrete
Fourier Transform, are used. These methods only work properly if the signal is
composed of only the fundamental and harmonic frequencies in a certain frequency
range (called the Nyquist frequency, which is one-half of the sampling frequency). The
frequency values must not change during the measurement period. Failure of these
rules to be maintained can result in mis-information.
For example, if a voltage waveform is comprised of 60 Hz and 200 Hz signals, the FFT
cannot directly see the 200 Hz. It only knows 60, 120, 180, 240,..., which are often
called bins. The result would be that the energy of the 200 Hz signal would appear
partially in the 180Hz bin, and partially in the 240 Hz bin. An FFT-based processer
could show a voltage value of 115V at 60 Hz, 18 V at the 3rd harmonic, and 12 V at the
4th harmonic, when it really should have been 30 V at 200 Hz.
These in-between frequencies are called interharmonics. There is also a special
category of interharmonics, which are frequency values less than the fundamental
frequency value, called sub-harmonics. For example, the process of melting metal in
an electric arc furnace can result large currents that are comprised of the fundamental ,
interharmonic, and subharmonic frequencies being drawn from the electric power grid.
These levels can be quite high during the melt-down phase, and usually effect the
voltage waveform.
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0.1
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1.1
1.3 Why Worry About Them
The presence of harmonics does not mean that the factory or office cannot run
properly. Like other power quality phenomena, it depends on the stiffness of the
power distribution system and the susceptability of the equipment. As shown below,
there are a number of different types of equipment that can have misoperations or
failures due to high harmonic voltage and/or current levels. In addition, one factory
may be the source of high harmonics but able to run properly. This harmonic pollution
is often carried back onto the electric utility distribution system, and may effect facilities
on the same system which are more susceptible.
Some typical types of equipment susceptible to harmonic pollution include:
- Excessive neutral current, resulting in overheated neutrals. The odd triplen
harmonics in three phase wye circuits are actually additive in the neutral. This is
because the harmonic number multiplied by the 120 degree phase shift between
phases is a integer multiple of 360 degrees. This puts the harmonics from each of the
three phase legs in-phase with each other in the neutral, as shown in Figure 3.
Figure 3. Additive
Third Harmonics.
- Incorrect reading
meters,
including induction discW-hr meters and averaging type current meters.
- Reduced true PF, where PF= Watts/VA.
- Overheated transformers, especially delta windings where triplen harmonics
generated on the load side of a delta-wye transformer will circulate in the primary side.
Some type of losses go up as the square of harmonic value (such as skin effect and eddy current losses). This is also true for solenoid coils and lighting ballasts.
- Zero, negative sequence voltages on motors and generators. In a balanced system,
voltage harmonics can either be positive (fundamental, 4th, 7th,...), negative (2nd, 5th,
8th...) or zero (3rd, 6th, 9th,...) sequencing values. This means that the voltage at that
particular frequency tries to rotate the motor forward, backward, or neither (just heats
up the motor), respectively. There is also heating from increased losses as in a
transformer.
HARMONIC
FUND
2ND
3RD
4TH
5TH
6TH
7TH
ETC
SEQUENCE
+
-
0
+
-
0
+
.....
Table 3. Harmonic Sequencing Values in Balanced Systems.
- Nuisance operation of protective devices, including false tripping of relays and failure
of a UPS to transfer properly, especially if controls incorporate zero-crossing sensing
circuits.
- Bearing failure from shaft currents through uninsulated bearings of electric motors.
- Blown-fuses on PF correction caps, due to high voltage and currents from resonance
with line impedance.
- Mis-operation or failure of electronic equipment
- If there are voltage subharmonics in the range of 1-30Hz, the effect on lighting is
called flicker. This is especially true at 8.8Hz, where the human eye is most sensitive,
and just 0.5% variation in the voltage is noticeable with some types of lighting.
[2]
Where They Come From
How this electricity is used by the different type of loads can have an effect on purity
of the voltage waveform. Some loads cause the voltage and current waveforms to lose
this pure sine wave appearance and become distorted. This distortion may consist of
predominately harmonics, depending on the type of load and system impedances.
Since this article is about harmonics, we will concentrate on those types of sources.
The main sources of harmonic current are at present the phase angle controlled
rectifiers and inverters. [3] These are often called static power converters. These
devices take AC power and convert it to another form, sometimes back to AC power at
the same or different frequency, based on the firing scheme. The firing scheme refers
to the controlling mechanism that determines how and when current is conducted.
One major variation is the phase angle at which which conduction begins and ends. A typical such converter is the switching-type power supplies found in most personal
computers and peripheral equipment, such as printers. While they offer many benefits
in size, weight and cost, the large increase of this type of equipment over the past
fifteen years is largely responsible for the increased attention to harmonics.
Figure 4 shows how a switching-type power supply works. The AC voltage is converted
into a DC voltage, which is further converted into other voltages that the equipment
needs to run. The rectifier consists of semi-conductor devices (such as diodes) that
only conduct current in one direction. In order to do so, the voltage on the one end
must be greater than the other end. These devices feed current into a capacitor, where
the voltage value on the cap at any time depends on how much energy is being taken
out by the rest of the power supply.
Figure 4. Typical Switching Power Supply.
When the input voltage value is higher than voltage on the capacitor, the diode will
conduct current through it. This results in a current waveform as shown in Figure 5,
and harmonic spectrum in Figure 6. Obviously, this is not a pure sinoidal waveform
with only a 60 Hz frequency component.
Figure 5. Current
Waveform Figure 6. Harmonic Spectrum of Current Waveform Shown in Figure 5.
If the rectifier had only been a half wave rectifier, the waveform would only have every
other current pulse, and the harmonic spectrum would be different, as shown in Figure
7.
Figure 7. Harmonic Spectrum of Half-Wave Rectifier.
Fluorescent lights can be the source of harmonics, as the ballasts are non-linear
inductors. The third harmonic is the predominate harmonic in this case. (See Table 3)
As previously mentioned, the third harmonic current from each phase in a four-wire wye
or star system will be additive in the neutral, instead of cancelling out Some of the
newer electronic ballasts have very significant harmonic problems, as they operate
somewhat like a switch