Solution To Harmonics
"True or False"
Question #1: True
Question #2: False
Question #3: True & False (While there is some additional
heating due to losses caused by harmonic magnetic flux flowing in the
transformer iron core, it is not significant enough to cause the derating
of a transformer. It is the losses in the transformer coil windings
that account for derating a transformer when it supplies a highly harmonic
load. See detailed explanation below.)
Harmonics usually begin with the generation of harmonic CURRENTS that are produced
by non linear loads.
Linear loads such as resistors and for the most part motors (though not motor
drives such as ASD's) draw a current that is pretty much sinusoidal (i.e. a sine wave).
Non linear loads draw AC currents that are distorted waveforms. That is, they are
distorted in that they do not look like the mathematically perfect sine waveform.
When a non linear load utilizes current in a distorted wave shape, the actual
distorted wave of current is made up of a conglomeration of pure sine waves. This
amalgamation of sine waves can be broken up into component parts that consist of
- the fundamental frequency component which has its normal 60 Hz frequency and RMS
value of current, and
- a series of harmonics which are a series of pure sine waves.
Each harmonic sine wave has a frequency that is an integral multiple of 60 Hz
(such as a 3rd order harmonic - 3 x 60 or 180 Hz, or a 5th order harmonic that has a
frequency of 5 x 60 or 300 Hz). Each harmonic sine wave also has its own RMS value and its
own phase angle. (The RMS value of a harmonic is usually expressed as a percentage of the
fundamental's RMS value.)
You can think of harmonics as a rainbow of colors in the light spectrum. With
light all you see is the distorted waveform i.e. the white light. But the white light can
be broken up by a prism into its component colors which are analogous to the harmonic
series. Each source of light, such as a mercury vapor lamp or a high pressure sodium lamp,
has its own unique series of harmonic colors. Mercury lamps have more blues while HP
sodium has more yellow and orange. The amount of each color is analogous to the RMS value
of each harmonic.
You can also think of harmonics as the base, treble, and midrange frequencies in a
musical sound. The sound can be broken down into its harmonic components with each sound
having its own unique spectrum or series of harmonics.
Any distorted waveform of current has its own unique series of harmonics. It is
these harmonic currents that may cause operational problems on your power system.
ALL HARMONICS BEGIN WITH DISTORTED CURRENTS DRAWN BY NON LINEAR LOADS.
In fact, when we analyze a system for harmonic problems, the non linear load (or
loads) is considered the source of the harmonics (not the service entrance transformer)
and the load is modeled as a series of current sources (one for each harmonic) that inject
harmonic currents into your power system from the non linear load's location.
These harmonic currents will travel throughout your power system in the paths of
least impedance. Since these harmonics oscillate at higher than 60 Hz frequencies, they
affect the impedance of any capacitors and inductive reactance (line, motor, transformer
impedances) that is seen by the harmonic.
For example, a capacitor bank has a reactance, Xc, equal to:
So if the capacitor has a reactance of 1 ohm at 60 Hz, then at 300 Hz (5 x 60) the
reactance of the capacitor is only 0.2 ohms. Energize the capacitor with a 120 volts at 60
Hz and Ohm's Law dictates that 120 amps will flow. But energize this same capacitor with a
120 volt, 5th order harmonic (300 Hz), and 600 amps will flow.
Obviously, the fusing that protects a capacitor bank can be sensitive to the
unexpected flow of high frequency harmonics. In fact, the nuisance blowing of capacitor
fuses (or even breaker trips for no reason) are a sure sign of harmonic problems.
When harmonic currents flow through the impedances of your power system, they can
generate harmonic voltage drops which will distort the voltage supply as seen by other
loads. If this supply voltage, which now has a harmonic voltage component, is placed
across a linear load, the linear load will draw a distorted current with the same level of
harmonic distortion as the distorted voltage.
If you do measure a supply voltage with harmonic distortion in it, 99 times out of
a 100, you can bet that some non linear load in your plant is causing the distortion, by
injecting a harmonic current into some high impedance path.
High impedance paths can be caused by harmonic resonances that occur due to the
series or parallel combination of source impedance (e.g. transformer reactance), line
reactance, and capacitor bank reactance as seen by the injected harmonic current.
THE ELECTRIC UTILITY IS RARELY RESPONSIBLE FOR ANY HARMONICS THAT IS IN YOUR
It is possible however, that the utility company "looks" like they are
sending harmonics into your facility. But what may actually be happening is that an
industrial or commercial plant down the road from your location is the genuine source of
the offending harmonics. Your neighbor is generating harmonics in their non linear loads,
which are being injected not only into their power system but out of their building and
down the road into your building.
Harmonics make their way onto the utility lines and into other neighboring
facilities when the non linear load injects harmonic currents into the power system. These
currents will flow in the secondary windings of the utility substation transformer and
will cause a harmonic voltage distortion on the transformer's secondary bus. It is the
harmonic current flowing through the impedance of the secondary winding that causes a
harmonic voltage drop on the secondary, and this drop will appear as a voltage distortion
at the transformer's secondary terminals.
All loads that are connected to that transformer's secondary, are energized with
these harmonic voltage distortions and will thus draw distorted harmonic currents.
[NOTE: Another possible source of harmonics that can come from the utility, is
voltage distortion that is caused by the transformer's magnetizing current. It is true
that transformers produce a third order harmonic in their exciting (magnetizing) current.
When this exciting current flows in the primary winding of a utility's downline
distribution transformer, third order harmonic voltage drops will develop on the source
side lines which feed the distribution transformer. Harmonic voltage drops will also
develop in the secondary windings in the upline substation transformer which feeds the
If there are enough downline distribution transformers that are fed off of the
upline substation transformer, the collective exciting current of all the distribution
transformers could add up enough to cause an excessive and unacceptable third order
harmonic voltage distortion. This distortion would be a part of the total voltage
energizing all the distribution transformers and would cause 3rd harmonics to flow into
any plant facility load.
All loads that are connected to the substation transformer's secondary, are
energized with these harmonic voltage distortions and will thus draw distorted harmonic
currents. However this is usually insignificant to the power loads that any transformer
handles and is therefore not normally a concern.]
When harmonics flow through transformers, the transformers will usually heat up
more than you would expect from the same RMS value of a purely fundamental 60 Hz current.
The reason for this extra heat comes from mainly one source. The "eddy
current" losses in the transformer COIL WINDINGS (not the eddy currents in
the iron core
- see below) produce the major portion of excess heat. The higher frequency current
running through the coils causes eddy currents to flow more readily in each of the coil
windings' individual conductors. It is these excess eddy currents in the coil windings'
conductors that are responsible for the excessive heat and for the derating of the
transformers' capability and KVA rating.
Some additional heating occurs due to the additional AC resistance in the coils
when higher frequency current flows through them. Remember, AC resistance increases with
frequency due mainly to skin effect. However, this additional resistance is a smaller part
of the overall overheating of transformers when they supply harmonic currents to non
What does NOT SIGNIFICANTLY add to the overheating of transformers due to the flow of harmonic currents, is the core losses that occur due to the flow of harmonic magnetic flux in the iron core of a transformer.
(Core losses are also known as "iron losses" or "no-load" losses.) Harmonic currents do create harmonic magnetic fluxes in the iron core which will create extra heat. HOWEVER, this is only a small magnetizing flux that does not add significantly to the iron losses of a transformer and is not the loss that accounts for having to derate a transformer.
The ANSI/IEEE Standard C57.110 on "IEEE Recommended Practice for Establishing Transformer Capability When Supplying Nonsinusoidal Load Currents" is the standard from which the "K" Factor method of derating transformers was derived. This standard recognizes that only the current in the windings are major enough to warrant derating a transformer. In this standard's calculations, iron losses are basically ignored since their magnitude just isn't great enough, in comparison to losses in the coil windings, to cause overheating, and thus derating, of the transformer.
Consider a simple transformer; one with an iron core, a primary winding and a secondary winding. When the primary coil is energized by a source voltage (and no load on secondary), the source sends an "exciting current" to the coil which causes a magnetic flux to circulate around the iron core in a closed loop. It is this circulating magnetizing flux which causes the primary coil to have a voltage induced in it, which will equal and oppose the source voltage (also known as the back-emf). Without this flux, the coil could not produce any voltage across it to oppose the source voltage. If this flux is ever reduced, the source will send more current into the coil to restore the original magnetizing flux so that the coil will be able to have its back-emf voltage produced in order to balance (equal & oppose) the applied source voltage. (If the flux is increased, the source will decrease the current sent to the primary.)
This magnetizing flux (referred to here as no-load or original magnetizing flux) is the flux that induces a voltage in the secondary coil. (No load meaning that the secondary circuit is open, with no load attached.)
When a load is added to the secondary, the load draws current. This current in the secondary coil winding produces its own magnetizing flux which opposes the original no-load flux from the primary. The magnetic flux from the secondary opposes the flux from the primary because the secondary flux circulates in the opposite direction of the primary flux, thus reducing the total flux in the transformer core.
As soon as the secondary load draws current, the total flux in the core is instantaneously decreased since the secondary flux subtracts from the primary flux. This reduction in flux as seen by the primary, causes the induced voltage on the primary coil to "want" to decrease instantaneously. However, since the primary coil is energized from the source voltage, the voltage across the primary coil must remain at the same value of the source voltage. In order to maintain this source voltage across the primary coil, more current from the source will instantaneously flow to produce the magnetizing flux needed to keep the coil at full source voltage.
Note how there is an instantaneous balance between source voltage, primary coil voltage, primary current, secondary current, and magnetic flux. The magnetic flux in a transformer is always the same original no-load magnetizing flux, no matter how much load is added to the secondary. (Transformer iron cores are sized to handle this magnetizing flux produced by the exciting current.)
This is the principle of how a transformer supplies more power when a load is added to the secondary.
[Note that if you added load to the transformer's secondary and IF the additional load current increased the transformer magnetizing flux (WHICH IT DOES NOT), you would very quickly saturate the transformer core.]
Saturating a transformer core means that you can't force any more magnetic flux through the iron core. A certain cross section of an iron core can only hold or accommodate a certain limited amount of lines of magnetic flux. Normally we speak in terms of "magnetic flux density" which is the number of flux lines per unit of cross sectional area. After the iron core has reached its limit of flux lines that it will let pass through it (i.e. it has reached its maximum magnetic flux density), any additional magnetic flux lines must travel around outside the core in the air. When this happens the secondary voltage has reached its theoretically possible peak value since there is no more flux that can circulate around the core and induce voltage in the secondary winding. Saturation will normally occur when you raise the primary voltage above rated value.
So, in practice, no matter how much load you add to the transformer, the magnetizing core flux remains the same as the "no load" original flux.
As a matter of fact, it is this no load flux that is the design parameter for sizing the amount of core steel that is used in the transformer's construction. Transformers are designed so that the amount of no load magnetizing flux lines is below the saturation value of the iron core.
Harmonic Loads & Their Magnetic Flux:
Harmonic currents in a transformer secondary do induce a harmonic magnetic flux into the iron core of a transformer which opposes the original magnetizing flux in the core. However, as with any current in the transformer's secondary circuit, the secondary current's magnetic flux is immediately counteracted by flux from the primary winding, which increases its primary current to maintain the original core flux. (When dealing with harmonics, it is usually easier to envision that it is the secondary that is the source of the harmonics injecting them into the power system.)
When a harmonic load is added to the secondary circuit, its harmonic current creates a harmonic flux in the iron core that flows in a reverse direction to the original no-load flux, thus opposing and decreasing it. (NOTE: The magnetic flux from the secondary opposes the flux from the primary because the secondary flux circulates in the opposite direction of the primary flux, thus reducing the total flux in the transformer core.)
The primary senses a reduction in the core flux caused by this new harmonic flux and increases its primary current (of that harmonic frequency) to "counteract" the harmonic flux and maintain the original no-load magnetizing core flux (albeit with now a residual harmonic component). The primary must increase its current in order to restore the total magnetic flux to a value that will maintain the voltage on the primary coil.
Note how the primary now has to supply a harmonic current. The harmonics have been "injected" into the primary (of course at a smaller magnitude since you have to take into account the transformer turns ratio.) This is normally not desirable since the electrical system ahead of the non-linear load is now experiencing the flow of harmonics. There are methods and equipment that can help prevent or limit this spread of harmonics from happening.
The total magnetizing flux in the iron core, caused by harmonic currents, does not increase with load, just as adding 60 cycle load to the secondary does not increase the total transformer magnetizing flux.
Since the magnetic flux from the harmonic loads is nearly constant, it contributes some heat losses in the iron. However, these losses are not as great as the coil winding losses since as harmonic load increases, the current in the windings increase and thus losses increase. Again it is the winding loss that causes a transformer serving non-linear loads to be
More Transformer Basics:
Normally when an unloaded transformer is connected to its rated 60 Hz voltage
source, the primary winding of the transformer is energized and a small exciting current
flows in the primary winding, even though there is no load on the secondary. The iron core
becomes magnetized due to this no load exciting current.
This exciting current is actually composed of three things:
- an inrush current that occurs the instant a transformer is energized but decays in
magnitude and time.
(The inrush current is a complicated function that occurs due to the residual
magnetic flux in the iron core being "out of synch" with the magnetic flux that
would flow the instant on the voltage sine wave when the transformer is energized. Fusing
for a transformer is sized and selected so that a fuse will not operate or melt during the
inrush. We will not pursue the subject of inrush current further.)
- a small current due to the AC resistance in the primary winding (which does not
concern us here).
- a magnetizing current that sets up the original magnetizing flux within the
This "original" no load magnetizing flux circulates around the core
(reversing its direction 60 times a second in keeping with the magnetizing current) and
circulates through both primary and secondary windings. It is this magnetizing flux which
induces a voltage in the secondary winding.
It is also this "no load" magnetizing flux which also produces two types
of core losses: hysteresis loss and eddy current loss.
The hysteresis loss is due to the alternating magnetizing flux which causes the
iron's inherent magnetic dipole molecules to rotate back and forth. These molecular dipole
magnets (dipole meaning having a North and a South pole) line up with the magnetic flux as
it alternates. As the molecules rotate in the magnetic field, the friction between them
heats up the iron core causing an energy loss. This loss of energy as heat due to the
friction generated by rotating magnetic dipole molecules of iron is referred to as
The second type of loss due to the magnetizing flux is caused by eddy currents in
the iron core. (Here we are NOT referring to the eddy currents in the coil windings - see
explanation in preceding paragraphs.) These eddy currents produce resistive losses in the
form of heat in the core.
When the magnetizing flux flows and alternates, this changing of flux (in
magnitude and direction which again is in keeping with the magnetizing current) causes
eddy currents to flow in the iron core. Eddy currents are like little tornadoes or
whirlpools of currents that spin in a circle within the iron core. (The transformer's
magnetic flux flows through the center of the eddy current circles. The magnetic field
produced by the eddy currents acts to oppose the transformer's changing magnetic flux.)
The iron core is laminated to help reduce the flow of the eddy currents. Still the
deed is done and some eddy current does flow causing resistive (I squared R) losses.
When a load is added to the transformer secondary circuit, the load draws a
current which will produce a magnetic flux in the core that opposes AND THEREFORE REDUCES
the primary winding's exciting current magnetizing flux (admittedly, we are using a lot of
adjectives to describe this original flux!)
The primary instantly senses this reduction of flux and allows more primary
current to flow in order to restore the magnetizing flux back to its original no load
So as load increases, secondary current increases, magnetic flux from the
secondary current opposes and reduces the core flux, primary winding current increases to
oppose this reduction in core flux and to restore the original value of flux, and thus the
transformer draws more current from the generator in order to supply the secondary with
So again, no matter what the secondary current does, the primary counteracts it.
This is why the harmonic currents in the secondary are opposed instantly by
increases in the primary current, so that any magnetic flux injected into the iron core by
the harmonic is negated by a like amount of current from the primary.
(NOTE: Remember that in a transformer there is a turns ratio and the amount of
current that the primary supplies is really the amount necessary to make the PRIMARY
AMPERE - TURNS equal the SECONDARY AMPERE - TURNS.)
In conclusion, harmonics do not add significantly enough to the iron core losses to warrant derating of a transformer. Thus, it is the coil winding losses that account for the majority of heat losses and for having to derate transformers when they serve highly non-linear, harmonic-rich loads.
Some may ask the question, why do non linear loads from switched mode power
supplies (SMPS) clip the peak of the voltage sine wave? The reasoning they would use is
that the highly distorted, high current peaks of a SMPS causes the transformer core to
saturate thus limiting the secondary voltage to a point where the top peak of the
secondary voltage sine wave is squashed so that the voltage takes on a "flat
This is an erroneous deduction even if it is quite convincing.
The reason for the flat topping has more to do with sharply peaked currents trying
to flow through the power system's impedance which causes a large voltage drop that in
turn causes the flat topping of the sine wave. The sharp peaks of current occur in time on
the voltage sine wave when the voltage itself is trying to reach its normal peak. The
large rush of current at this point in time on the sine wave causes the voltage drop that
keeps the voltage sine wave from reaching its natural crest value on the sine wave.
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