Harmonics in power system and metering
by Surendra Jhalora
Synopsis
The issue of harmonics is debated at various
levels. Harmonics are generated in the system.
Generally the effect of harmonics is studied in
voltage or current. The current harmonics flow in
the system generates voltage harmonics which
results into power harmonics. Power harmonics
are than measured by energy meters. The flow of
power harmonics and it effect on the energy
measurement is discussed in this paper. Though
current harmonics are high, power harmonics
are very small and contribution to energy is
insignificant. The power harmonics direction is
opposite to fundamental power flow at the
source of harmonics so total power measured is
less than fundamental power. The linear loads
consumes harmonics power from the system.
Introduction
A well designed power plant generates sinusoidal
alternating current electrical power, thus a utility
delivers sinusoidal power or fundamental power to
consumers. The loads at consumer end are
nonlinear in nature and cause distortion in the
wave shape and generate other components at
frequencies that are integral multiples of the
fundamental frequency. The combined wave shape
of all the frequencies is not a sinusoidal wave shape
and make an irregular shape but of repetitive
nature. The repetitive deviation of either the
voltage or current waveform from a pure sinusoid is
usually referred as harmonic distortion. The
combined wave shape is a complex wave shape and
can be decomposed by Fourier transform method.
The distortion components can be submultiples of
the fundamental frequencies in a power system
and cause distortion in the sinusoidal wave shape
and are called harmonic distortion but generally
the integer multiples are referred as harmonic
components and are harmonic distortion. The
harmonic components may be different in current
and voltage waveforms.
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How the harmonics are generated
Harmonics are generated by any load, which draws current not proportional to
the voltage applied. Most loads are somewhat nonlinear, but some generate
more and higher level harmonics than others. These include the following and
many more types of loads
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Static power converters using thyristor or SCRs to control the drives
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Arc furnaces, Arc welding sets and ovens
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Ballast in high power discharge, mercury vapor lamps, high-pressure
sodium vapor lamps and metal Halide lighting etc.
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Switching or phase controlled AC to DC power supplies, battery chargers
and UPS for computers and computer-controlled machines.
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Transformers operating near saturation
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Solid state frequency converters for induction heating and cyclo converters
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Induction furnaces and electrolysis plants
Harmonic current, voltage and power
The sinusoidal voltages or fundamental value of voltage is defined by the
equation
' E=Em Sin wt
' I=Im Sin wt
Em and Im are the peak values. The RMS values and peak values has a ratio of
0.707.
Let the complex voltage waveform be represented by the equation
'E = E1m Sin wt+E2m Sin 2wt + E3m Sin 3wt + E4m Sin 4wt +…+ Enm Sin nwt
is applied to a circuit. Let the equation of the resultant current wave be
'I= I1m Sin (wt+1) +E2m Sin (2wt+2) + E3m Sin (3wt+3) + E4m Sin (4wt+4)
+…+ Enm Sin(nwt+n)
The instantaneous value of the power in the circuit is p=ei watt
For obtaining the values of this product, we will multiply every term of the
voltage wave, in turn, by every term in the current wave. The average power
supplied during a cycle would be equal to the sum of the average values over
one cycle of each individual product term. Hence total power supplied by a
complex wave is the sum of the average power supplied by each harmonic
component acting independently.
Total power is
P= E1I1cos1 + E2I2 Cos 2 + E3I3 Cos 3 + ……EnIn Cosn
The first component is the fundamental power and other components are
harmonic components. Hence the total power is a sum of fundamental power
and harmonic power. The direction of flow of individual component should be
considered appropriately.
A complex waveform consisting offundamental and third harmonics is shown
in the figure below.
Harmonics in three phase system
In three-phase system, harmonics may be
produced in the same way as in the single-phase
systems. In the three phase systems following need
to be considered
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All the third harmonics are equal in all phases of
the circuit and they are in time phase.
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All harmonics, which are not multiples of three,
have a phase displacement of 120 degree so that
they can be dealt in the usual manner.
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The 5th, 11th and 17th harmonics have a negative
phase sequence of R, Y, and B.
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The 7th, 13th and 19th harmonics have a positive
phase rotation of R, Y, and B.
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In case of three phase transformers, the
production of harmonics will be affected by the
method of connection and the type of
construction employed.
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When primary is connected in delta, in each
phase the third harmonics current will be in
phase and so produce circulating current round
the mesh with the result that there will be no
third harmonic current in the line current.
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When the primary is connected in 4wire star, the
third harmonic current will flow through line
and return through neutral wire. And in case of 3
wire star connection, third harmonics current is
not returning there fore the line voltages will
contain third harmonic components.
Metering and flow of harmonics
The Diagram of metering point and load is shown
below
A
Zs
The nonlinear load draws a current with a complex waveform. The complex
current wave shape will cause drop across the Zl and Zs. Consider the Zs and Zl
as linear impedances, the drop will be same as complex current wave shape.
The voltage at point B is Vg minus the complex voltage drop across the two
impedances. Thus the harmonic power has negative sign as compared to the
fundamental power.
The total power is the sum of fundamental power and harmonic power thus
the total power measured by the meter M2 is fundamental power consumed
minus the harmonic power generated. The harmonic power is flowing from the
load to the utility and meters will measure less total power.
The complex current waveform will distort the voltage at the point A but the
magnitude of distortion will be less as compared to the point B. The linear load
will draw current proportional to the voltage. Thus it will draw some complex
current due to the drop in the voltage due to complex current waveform. The
complex current is in phase with the voltage applied thus the total power
measured by the meter M1 is the fundamental power consumed by the load
plus complex or harmonic power fed due to voltage at the point B. Thus the
harmonic energy is flowing from the utility to the consumer and the power
metered is more than the power actually consumed in the load.
Lets consider a simple mathematics to illustrate the above. 50% third
harmonic current is generated by a load causes 10% drop in the voltage. The
harmonic power is 10*50/100=5%. Thus Total power will be 95% of the
fundamental power actually consumed in the nonlinear load. Thus a Total
power meter will measure 5% less than a Fundamental power meter. The 10%
drop will cause 10% harmonic current to flow in the linear load thus total
power is 10*10/100=1%. Thus a total power will measure 1% more power than a
fundamental power meter.
Some experiments have been conducted to prove the explanation and the
results is shown in the table below
B
Zl
Meter M1
Meter M2
Linear load
Nonlinear
The simple and common power system
connections can be used to understand the flow of
harmonic power in the system due to nonlinear
loads.
Vg is the generator of the utility, which
generates fundamental power. The Zs is the source
impedance and Zl is the distribution network
impedance, which a load see from the load end.
The Zl causes drop in the voltage due to load
current. Meter M2 measures power drawn by the
nonlinear load. The voltage distortion at the point
marked A and B depends on the impedances Zs and
Zl. The linear load is connected in the system and
power drawn by the linear load is measured by
meter M1.
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The fundamental power is generated by the generator and transmitted to
the load via Zs and Zl. the harmonic current causes distortion in the voltage at
the points A and B. The distortion in the voltage will depend on the
impedances. And the magnitude of harmonics currents.
The fundamental values are considered as 100% and other harmonic
components are presented corresponding to fundamental values.
The table below shows flow of harmonics corresponding to harmonics in
voltage and current harmonics above.
these results are taken by simulating the loads and high line impedances to
enlarge the effect of harmonics.
3P3W and 3P4W measurement
The harmonics appear differently in the way the
connections are done. 3phase 4 wire connected
meter will measure the voltages phase to neutral
and 3p3w meter measure the phase voltages thus
both the meter will perceive different harmonics
under the same harmonics flow in the system. The
harmonics measurement is different in different
type of connection as illustrated above in three
phase systems. Thus the total power measured will
also be different for the same harmonics in the
system.
Conclusion
It is evident form the test results and study done
by various engineers across the world that the
harmonics are generated by non linear loads.
The generated harmonics flows back to the
system and causes heating in the lines,
transformers and capacitors. The resonance
due to harmonics is quite common which leads
to excessive RMS current and more loading than
actual useful power transferred or delivered.
The total power measurement is always less
than the fundamental power measurement. The
consumer generating harmonics is metered less
if total power is metered and consumers who are
not generating the harmonics are absorbing
harmonics and metered more than what is
c o n s u m e d . To t a l p o w e r a n d e n e r g y
measurements system rewards consumers
generating harmonics and polluting the
electrical system and penalizes innocent and
fair consumers.
The non-linear consumers are increasing and
are more than the linear consumers. The loss of
revenue is much more due to harmonics
generation than the gain in revenue due to
harmonics power consumed when the total
power is measured.
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