The coefficients an , bn determine the magnitude of the
harmonic components. From the data of the coefficients, we
can obtain two spectra related to these coefficients:
1.Magnitude spectrum: shows the magnitude of different
2.Phase spectrum: shows the phase of different
1.Linear time invariant loads :application of sinusoidal voltage
results in sinusoidal current. They display a constant steady
Eg: Incandescent lighting, Transformers and Rotating
machines under normal operating conditions.
2.Non-Linear loads : application of sinusoidal voltage results
in a non-sinusoidal current. They do not exhibit constant
impedance during the entire period. Also non-linear loads
may draw even a discontinuous current.
Sources of Harmonics
☞Adjustable drive systems
☞Switching Mode Power Supplies
☞Computers, TV sets
☞Wind & Solar power generation
☞Battery charging & Fuel cells
☞Fluorescent lighting, Electronic ballasts
☞Inrush Current Harmonics
☞Rotating machines (slot , mmf)
Effects of Harmonics
☞Increased Cu loss leading to Excessive heating.
☞Voltage distortion in weak system.
☞Harmonic voltages increase hysteresis and eddy
current losses, also additional I2R losses mainly in
Converter transformers.(Transformer derating)
☞Power factor also deteriorates.
☞Phenomenon of Flicker.
☞Excessive neutral currents.
☞Effects measuring instruments.
☞Misoperation of relays.(False tripping of ground
relay due to triplen harmonics)
☞Parallel resonance between Cable capacitance and
system inductances, incase of long cables.
☞Introduces Electromagnetic interference in adjacent
signal or control cables via radiated and conducted
Methods to mitigate Harmonics
Filters are used to suppress harmonics as well as to support
3.Operation with higher pulse number.
4.Using K-factor transformers.
1.Single tuned filter:
Based on series resonance of RLC circuit. The circuit is
designed to resonate at the frequency equal to the frequency
of the component which needs to be filtered.
It is confined to a particular frequency.
2.Double tuned filter:
This filter is tuned to two frequencies equal to the frequency of
the significant harmonic components in the magnitude
3.High pass filters:
These filters are designed such that all the components of
frequencies higher than a particular frequency are filtered.
Passive filters are cheap, easy design and reliable.
But they cause resonance problems, fixed reactive power
compensation and large size.
Active power filters are Power electronic converters to inject
harmonic currents into the system.
They can eliminate voltage and current harmonics;
compensate for reactive power. No resonance problems, can
support variable reactive power compensation.
Expensive, complex control.
Active power filters can be classified as:
1.Based on type of power electronic converter:
a)Current source converter(CSC)
b)Voltage source converter(VSC)
2.Based on topology of converter:
a) Shunt filter
Voltage source converter
Current source converter
Active shunt filter
The harmonic current is supplied by the shunt active filter
locally at the point where it is connected. The converter is
issued control signals based on monitored values of current.
This will ensure that the current drawn from PCC will be
sinusoidal and other loads are unaffected.
Active Series filter
Voltages are injected in order to reduce the harmonics, by
controlling the Converter.
Hybrid active filter
It is a combination of series active filter and shunt
It is essential to know the effects of the
harmonics, sources of the harmonics for a power
engineer to ensure that the systems will work well
within the safety zone, owing to standards.
Also, the various harmonic mitigation techniques
discussed are to be understood well for a design
engineer to protect the power system from
☞Power system Harmonics- Jos Arrillaga, Neville R. Watson.
☞Control of Harmonics in Electrical Power systems,
from American Bureau of Shipping(ABS).
☞POWER SYSTEM ANALYSIS, Short circuit load flow and
Harmonics-J. C. Das
☞IEEE transactions on Power Apparatus & Systems, Power
system Harmonics: An Overview, Vol.PAS102, No.8, August1983.
☞ IEEE transactions on Power Apparatus &
Systems, vol.PAS-104, No.9, 1985. The effects of Power
system Harmonics on Power system equipment and Loads.