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4.1
IV. HARMONICS IN POWER SYSTEMS
4.1 Introduction
Power system harmonics have been presented since the invention of AC as a means of power
transmission. However, harmonic problems became more critical mainly due to the
substantial increase of non-linear loads due to the technological advances, such as the use of
power electronic circuits and devices, in ac/dc transmission links or loads in the control of
power systems using power electronics or microprocessor controllers. Prior to the appearance
of power semiconductors, the main sources of waveform distortion were electric arc furnaces,
the accumulated effect of fluorescent lamps and to a lesser extent electrical machines and
transformers.
Sources of harmonics can be classified as:
Traditional harmonic sources
Transformers
Rotating Machines (Motors and generators)
Arcing devices: Arc furnaces and fluorescent lamps
Modern (power electronic) harmonic sources
Electronic controls and switch-mode power supplies and office electronic
equipment
Thyristor-controlled devices (Electronic and Power Electronic Devices)
Rectifiers
Inverters
Static VAR compensators
Cycloconverters
HVDC power transmission systems
Surge arresters
Photovoltaic systems,
Electronic ballasts,
Welding machines,
Electrical Communication systems.
4.2 Transformers
Coils that have iron core will cause harmonics in electrical power systems. Transformers are
the most commons between those. As being one of the most important elements in power
systems, transformers are the oldest nonlinear elements known. The magnetization
characteristic of a transformers core is non-linear and will produce harmonics as it issaturated.
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The equivalent circuit of a transformer is given below. Here Rp and Xp shows the primary
circuit resistance and the leakage reactance, Rs and Xs shows the secondary resistance andleakage reactance that is transferred (referred) to the primary respectively. RFe is the
resistance which symbolizes the iron losses and IFe is the current related to this losses. In
parallel to this resistance, Xm shows the magnetization reactance and Im is the related current
passes through.
At no-load conditions:
ttN
Edt
N
e
dt
dNtEev mmm
coscossin
11
1111
A sinusoidal primary voltage produces a sinusoidal flux at no-load. The primary current,
however, will not be purely sinusoidal, because the flux is not linearly proportional to the
magnetizing current. The magnetizing current harmonics often rise to their maximum levels in
the early hours of the morning, in example, when the system is lightly loaded and the voltage
high.
For 3-phase transformers, let,
I1: Effective value of the fundamental component of a nonlinear and balanced load current
w1: angular frequency for the fundamental frequency
The instantaneous value of the fundamental component of the load current for phases a,b and
c is equal to
)3/2sin(2)(,)3/2sin(2)(,)sin(2)( 111111 tItitItitIti cba
For the nth harmonic component, instantaneous value of the phase currents will be
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4.3
)3/2sin(2)(,)3/2sin(2)(,)sin(2)( 111 ntnItintnItitnIti ncnnbnnan
For triplen harmonics; k=1,2,3, and n=3k
)3sin(2)()()( 13333 tkItititi kkckbka
As seen from the equation above, under balanced load and network conditions, triplen
harmonic components of the phase currents are equal to each other.
a) Star-Connected Transformers:
The Transformers Star Point is connected to Earth:
The current flows through the neutral conductor will be zero because of the sum of thebalanced fundamental component currents belong to the three phases is zero. This
situation is not valid for triplen harmonics. The sum of the three phase currents flows
through the neutral conductor as shown in the figure below.
The triplen harmonics may cause extra heat on the neutral conductor so during the
consideration of the neutral conductors cross section, triplen harmonics should taken intoaccount.
All the remaining harmonics besides the triplen ones have 120
of phase difference so
that their sum will be zero at the star point. As easily be seen, if the star point of thetransformer is connected to Earth, triplen harmonics passes to the secondary circuit
(network).
Transformers Primary Circuit Star Point is Disconnectedfrom Earth:
Triplen harmonics cannot pass to the secondary circuit as the star point of the primary
circuit is not connected to Earth.
b) Delta-Connected Transformers:
Primary Circuit is Delta-Connected:
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4.4
Triplen harmonics occur in magnetization currents but they cannot get out of the delta
connected coils. Other harmonic components pass to the network side.
Secondary Circuit is Delta-Connected:As the total current at the nodal points of the delta connection is equal to zero, triplen
harmonics do not flow through the network.
If the nonlinear load is unbalanced, whatever the transformer design is, triplen harmonics
will also flow through the network.
4.3. Rotating Machine Harmonics
Rotating machines produce harmonic due to the field distribution of salient poles, the
magnetic permeance is related with slots and the saturation of the main circuit. These
harmonics induce an electromotive force (emf) on the stator windings at a frequency equal to
the ratio of speed/wavelength. The resultant distribution of magnetomotive forces (mmfs) in
the machine produces harmonics that are a function of speed. Additional harmonic currents
can be created upon magnetic core saturation.
Harmonics produced by a synchronous generator will not be taken into consideration if the
generators power rating is smaller than 1000 kVA. If the magnetic flux of the field system isdistributed perfectly sinusoidal around the air gap, the e.m.f. generated in each full-pitched
armature coil is 2f
sin wt volts per turn. Where
is the total flux per pole and f is
frequency related to the speed and pole pairs. However the flux is never exactly distributed in
this way, particularly in salient pole machines.
4.4 Arcing Devices
The voltage-current characteristics of electric arcs are highly non-linear. Following an arc
ignition the voltage decreases due to the short-circuit current, the value of which is only
limited by the power system impedance. The main harmonic sources in this category are the
electric arc furnaceand discharge type lighting with magnetic ballasts.
Arc furnaces may range from small units of a few ton capacities, power rating 2
3 MVA, to
larger units having 400-ton capacity and power requirement of 100 MVA. The harmonics
produced by electric arc furnaces are not definitely predicted due to variation of the arc feed
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4.5
material. The arc current is highly nonlinear, and reveals a continuous spectrum of harmonic
frequencies of both integer and non-integer order. The arc furnace load gives the worst
distortion, and due to the physical phenomenon of the melting with a moving electrode and
molten material, the arc current wave may not be the same from cycle to cycle.
There is a vast difference in the harmonics produced between the melting and refining stages.
As the pool of molten metal grows, the arc becomes more stable and the current becomes
steady with much less distortion. Figure below, shows erratic rms arc current in a supply
phase during the scrap melting cycle, and table below, shows typical harmonic content of two
stages of the melting cycle in a typical arc furnace. The values shown in this table cannot be
generalized.
Both the odd and the even harmonics are produced. Arc furnace loads are harsh loads on the
supply system, with attendant problems of phase unbalance, flicker, harmonics, impact
loading, and possible resonance.
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4.6
Discharge lighting is highly nonlinear and gives rise to considerable odd-ordered harmonic
currents. This effect is illustrated in figures below, which shows the current waveform and
harmonic spectrum of a high-efficiency lamp.
This effect is particularly important in the case of fluorescent lamps, given the large
concentration of this type of lighting. Additional magnetic ballasts are needed to limit the
current to within the capability of the fluorescent tube and stabilize the arc. These type of
lamps shows nonlinear voltage-current characteristics because of their negative resistance
property.
Also the lighting ballasts connected to the lamp may produce large harmonic distortions and
third harmonic currents in the neutral. The newer rapid start ballast has a much lowerharmonic distortion and can be filtered with a filter circuit implementation. Table below
shows the harmonic spectrum of a fluorescent lamp with magnetic ballast. Harmonic currents
are shown as the percentage of the fundamental component.
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4.7
Harmonic Order (n)
1 3 5 7 9 11 13 15 17 19 21
%In/I1 100 19,9 7,4 3,2 2,4 1,8 0,8 0,4 0,1 0,2 0,1
Lighting circuits often involve long distances and have very little load diversity. With
individual power factor correction capacitors, the complex LC circuit can approach a
condition of resonance.
4.4. Electronic and Power Electronic Devices/Systems
The increasing use of the power electronic devices in which the voltage and/or the frequency
are varied to adapt to specific industrial and commercial processes has made power converters
the most widespread source of harmonics in distribution systems. Converters can be grouped
into the following categories:
Small power rectifiers used in residential entertaining devices, including TV sets and
personal computers, battery chargers
Medium-size power converters like those used in the manufacturing industry for motor
speed control and in the railway industry.
Large power converters like those used in the metal smelter industry and in HVDCtransmission systems.
Single-Phase Rectifiers
Rectifiers are used in all sorts of power system and power electronic subsystems to convert
AC power to DC power. In low-power applications using single-phase power, rectifiers are
used as the front-end of switching power supplies and small motor drives. A single-phase,
full-wave rectifier is shown below.
Two cases can be analyzed separately, namely, continuous conduction mode and
Discontinuous conduction mode. Waveforms for continuous conduction mode are givenbelow.
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As L line current approaches to a square wave. For this idealized case, the first harmonichas amplitude 1.0, the third harmonic has amplitude 1/3, the fifth harmonic has amplitude 1/5,
and so on. Note that the line current drawn by this rectifier circuit is very harmonic-rich, with
a THD of 48.3 percent.
Waveforms for discontinuous conduction mode are given below. As L0 line currentapproaches to impulse functions. Typical THD values are around 130%.
Example: Assume that a 120-V AC source consumes a DC load of 5 A through a single-phase
full-wave rectifier with and a capacitive output filter. With a 1000 F bus capacitor,
the load voltage ripple is about 25-V peak-peak. Load voltage and line currents are
shown below.
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4.9
Example: In order to decrease the ripples in DC voltage of the previous example to 4 V, filter
capacitance is increased to 10000 F. The waveforms for the new system areshown below.
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4.10
Harmonic contents of the two configurations are given below.
Harmonic
order
Line current Magnitude of the
system with C = 1000 F
Line current Magnitude of the
system with C = 10000 F
13
5
7
9
11
13
15
17
19
21
2325
27
100.094.0
69.0
48.0
30.0
22.0
21.0
20.0
16.5
13.4
12.5
12.011.0
10.0
100.0100.0
98.0
95.0
90.0
82.5
77.5
70.0
65.0
63.0
50.0
45.038.0
33.0
THD 140 % 265 %
Three-Phase Rectifiers (The six-pulse rectifier)
A typical application using a three-phase, six-pulse rectifier is an adjustable speed drive.
Three-phase power is full-wave rectified by the six-pulse rectifier. The rectified voltage is
filtered by the high-voltage bus capacitor, generating a DC voltage, which is used by the
subsequent inverter. The three-phase inverter generates the three-phase currents necessary todrive the motor.
Typical waveform for a 6-pulse rectifier is given below.
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If L, then the resulting line current becomes a quasi-square waveform. THD of such awaveform is 31 percent. It is less than of the single phase one due to absence of triplen
harmonics.
Waveforms for discontinuous conduction mode will be as follows.
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4.12
Some useful observations:
1. The absence of triple harmonics.
2. The presence of harmonics of orders 6k+/-1 for integer values of k3. Those harmonics of orders 6k+1 are of positive sequence and those harmonics of
orders 6k-1 are of negative sequence.
4. The rms magnitude of the fundamental frequency is
LI6
5. The rms magnitude of the nth harmonic is ..6
n
IL
Example: A six-pulse 3 diode rectifier operating as a DC power supply has the followingcurrent spectrum.. Calculate the THD and sketch the current waveform.
h 1 5 7 11 13 17 19
Ih % 100 72.3 51.5 16 9 7.5 5.4< Ih -12 -241 -88 16 -235 -172 -42
rmsIrmsrms
h
hI
ITHDII
II
THD
,1
2
,1
2
2
1
*353.11
%1.911
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4.13
The twelve-pulse rectifier
The twelve-pulse rectifier is comprised of two six-pulse rectifiers fed from separate
transformers. One six-pulse is fed from a Y/Y transformer, and the other is fed from a /Y
transformer. The two rectifier voltages are phase shifted 30 than in the six-pulse case. This isbecause the 12-pulse topology eliminates the 5th, 7th, 17th, and 19th harmonics, leaving the
11th, 13th, 23rd, and 25th harmonics.
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Variable Frequency Drives
VFDs are, in reality, power converters. The reason to further address them under a separate
section is because, by themselves, VFDs constitute a broad area of application used in diverseand multiple industrial processes. In a very general context, two types of VFDs can be
distinguished:
those that rectify AC power and convert it back into AC power at variable frequency and
those that rectify AC power and directly feed it to DC motors in a number of industrial
applications.
In both cases, the front-end rectifier, which can make use of diodes, thyristors, IGBTs, or any
other semiconductor switch, carry out the commutation process in which current is transferred
from one phase to the other. This demand of current in slices produces significant currentdistortion and voltage notching right on the source side, i.e., at the point of common coupling.Motor speed variations, which are achieved through firing angle control, will provide
different levels of harmonic content on the current and voltage waveforms.
Variable frequency drive designs also determine where harmonic currents will predominantly
have an impact. For example, voltage source inverters produce complex waveforms showing
significant harmonic distortion on the voltage and less on the current waveforms. On the other
hand, current source inverters produce current waveforms with considerable harmonic
contents with voltage waveforms closer to sinusoidal. None of the drive systems is expected
to show large distortion on both voltage and current waveforms, in line with Finneysobservations.
The Static VAR Compensators (SVC)
Static var compensators (SVCs) are very flexible and have many roles in power systems.
SVCs can be used for power factor correction, flicker reduction, and steady-state voltage
control, and also have the benefit of being able to filter out undesirable frequencies from the
system. SVCs typically consist of a TCR in parallel with fixed capacitors.
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The fixed capacitors are usually connected in ungrounded wye with a series inductor to
implement a filter. The reactive power that the inductor delivers in the filter is small relative
to the rating of the filter (approximately 1 to 2 percent).
The controls in the TCR allow continuous variations in the amount of reactive power
delivered to the system, thus increasing the reactive power during heavy loading periods and
reducing the reactive power during light loading. SVCs can be very effective in controlling
voltage fluctuations at rapidly varying loads. Unfortunately, the price for such flexibility is
high. Nevertheless, they are often the only cost-effective solution for many loads located in
remote areas where the power system is weak. Much of the cost is in the power electronics on
the TCR. Sometimes this can be reduced by using a number of capacitor steps. The TCR then
need only be large enough to cover the reactive power gap between the capacitor stages.
TCR generates the 3th,5th,7th,9th harmonics. Normally three phase TCRs are deltaconnected to prevent the triplen harmonics.
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Another possibility is the use of a thyristor-switched capacitor (TSC). TSCs usually
consist of two to five shunt capacitor banks connected in series with diodes and thyristors
connected back to back. In this case, each capacitor bank is switched on and off by means of
thyristors. With this, a discrete variation of the reactive power can be achieved, but never a
continuous variation as in the TCR.
Cycloconverters
A cycloconverter is actually a variable frequency AC motor drive composed of two, three
phase bridges supplying a single phase output. It converts AC power to a lower frequency ACpower. A typical application of a cycloconverter is as an AC traction motor speed control and
other high-power, lowfrequency applications, generally in the MW range.
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