Technical
Harmonics / K-factor Ratings
Non-Linear Loads
When a sinusoidal voltage is applied to a
linear load, the resultant current
waveform takes on the shape of a sine
wave as well. Typical linear loads are
resistive heating and induction motors.
In contrast, a non-linear load either:
▪ Draws current during only part of the
cycle and acts as an open circuit for
the balance of the cycle,
or
Changes
the impedance during the
▪
cycle, hence the resultant waveform is
distorted and no longer conforms to a
pure sine wave shape
In recent years, the use of electronic
equipment has mushroomed in both
offices and industrial plants. These
electronic devices are powered by
switching power supplies or some type
of rectifier circuit. Examples of these
devices used in offices are: computers,
fax machines, copiers, printers, cash
registers, UPS systems, and solid-state
ballasts. In industrial plants, one will find
other electronic devices such as variable
speed drives, HID lighting, solid-state
starters and solid-state instruments. They
all contribute to the distortion of the
current waveform and the generation of
harmonics. As the use of electronic
equipment increases and it makes up a
larger portion of the electrical load, many
concerns are raised about its impact on
the electrical power supply system.
Voltage of Current Waveform for Linear Loads (Sine Wave)
Typical Current Waveform of Switching Power Supply
A Non-Linear Current and Its Fundamental, Plus 3rd and 5th Harmonic Components
18
TECHNICAL
Harmonics
As defined by ANSI / IEEE Std. 519-1992,
harmonic components are represented
by a periodic wave or quantity having a
frequency that is an integral multiple of
the fundamental frequency. Harmonics
are voltages or currents at frequencies
that are integer multiples of the
fundamental (60 Hz) frequency: 120 Hz,
180 Hz, 240 Hz, 300 Hz, etc. Harmonics
are designated by their harmonic number,
or multiple of the fundamental frequency.
Thus, a harmonic with a frequency of 180
Hz (three times the 60 Hz fundamental
frequency) is called the 3rd harmonic.
Harmonics superimpose themselves on
the fundamental waveform, distorting it
and changing its magnitude. For instance,
when a sine wave voltage source is
applied to a non-linear load connected
from a phase-leg to neutral on a 3-phase,
4-wire branch circuit, the load itself will
draw a current wave made up of the
60 Hz fundamental frequency of the
voltage source, plus 3rd and higher order
odd harmonic (multiples of the 60 Hz
fundamental frequency), which are all
Selection
Figure 30 — Effect of Harmonics on Current Waveform
generated by the non-linear load. Total
Harmonic Distortion (THD) is calculated
as the square root of the sum of the
squares of all harmonics divided by the
normal 60 Hz value.
THD=
冑
( (( ( ( (
( (
IRMS
60 HZ
2
IRMS
2
180 HZ
IRMS
60 HZ
IRMS
N
2
2
Therefore, it is the percentage amount of
odd harmonics (3rd, 5th, 7th ,..., 25th,...)
present in the load which can affect the
transformer, and this condition is called a
“Non-Linear Load” or “Non-Sinusoidal
Load”. To determine what amount of
harmonic content is present, a K-Factor
calculation is made instead of using the
THD formula. The total amount of
harmonics will determine the percentage
of non-linear load, which can be specified
with the appropriate K-Factor rating.
This yields an RMS value of distortion as
a percentage of the fundamental 60 Hz
waveform.
Siemens Power Distribution & Control, SPEEDFAX™ 2007-2008 Product Catalog
18-17
Technical
Harmonics / K-factor Ratings
Typical Symptoms of Harmonic
Problems
▪ Distribution / lighting transformers
overheating even when measured load
current is within transformer rating
▪ Neutral cable / bus overheating even
with balanced load
▪ Fuses blowing and circuit breakers
tripping at currents within rating
Effect Of Harmonics On Transformers
Non-sinusoidal current generates extra
losses and heating of transformer coils
thus reducing efficiency and shortening
the life expectancy of the transformer.
Coil losses increase with the higher
harmonic frequencies due to higher eddy
current loss in the conductors.
Furthermore, on a balanced linear power
system, the phase currents are 120
degrees out of phase and offset one
another in the neutral conductor. But with
the “Triplen” harmonics (multiple of 3)
the phase currents are in phase and they
are additive in this neutral conductor. This
may cause installations with non-linear
loads to double either the size or number
of neutral conductors.
TECHNICAL
18
Table 17.5
K-Factor Ratings
100%
NonLinear
Load
50%
Total KFactor
Load Valve
4.0
100%
100%
13.0
K20
100%
125%
20.0
K30
100%
150%
30.0
Type
Linear
Load
K4
K13
Selection
Sizing Transformers for Non-Linear
Loads
ANSI / IEEE C57.110-1986 has a
procedure for de-rating standard
distribution transformers for non-linear
loading. However this is not the only
approach. A transformer with the
appropriate K-Factor specifically designed
for non-linear loads can be specified.
K-Factors
K-Factor is a ratio between the additional
losses due to harmonics and the eddy
losses at 60 Hz. It is used to specify
transformers for non-linear loads. Note
that K-Factor transformers do not
eliminate harmonic distortion; they
withstand the non-linear load condition
without overheating.
Calculating K-Factor Loads
1. List the kVA value for each load
category to be supplied. Next, assign a
K-factor designation that corresponds
to the relative level of harmonics
drawn by each type of load. Refer to
Table 21.5.
2. Multiply the kVA of each load or load
category times the Index of Load
K-rating (ILK) that corresponds to the
assigned K-factor rating. This result is
an indexed kVA-ILK value.
KVA x ILK = kVA-ILK.
Table 17.7
Index of Load K-Ratings
K-Factor
K1
ILK
K4
25.82
K9
44.72
K13
57.74
80.94
K30
123.54
K40
208.17
3. Tabulate the total connected load kVA
for all load categories to be supplied.
4. Next, add-up the kVA-ILK values for all
loads or load categories to be supplied
by the transformer.
5. Divide the grand total kVA-ILK value by
the total kVA load to be supplied. This
will give an average ILK for that combination of loads. Total kVA-ILK/ Total
kVA = average ILK.
6. From Table 21.6 find the K-factor rating
whose ILK is equal to or greater than
the calculated ILK.
Estimating K-Factor Loads햲
K-Factor
ILK
Incandescent Lighting
Electric Resistance Heating
Motors (without solid state drives)
Control Transformers / Electromagnetic Control Devices
Motor-Generators (without solid state drives)
Standard Distribution Transformers
K1
0.00
Electric Discharge Lighting (HID)
UPS with Optional Input Filter
Welders
Induction Heating Equipment
PLCs and Solid State Controls
K4
25.82
K13
57.74
Main-Frame Computer Loads
Solid State Motor Drives (variable speed drives)
Multiwire Receptacle Circuits in Critical Care Areas in Hospitals
K20
80.94
Multiwire Receptacle Circuits in Industrial, Medical and Educational Laboratories
Multiwire Receptacle Circuits in Commercial Office Spaces
Small Main-Frames (mini and micro)
K30
123.54
Telecommunications Equipment (PBX)
UPS without Input Filtering
Multiwire Receptacle Circuits in General Care Areas of Health Care Facilities,
Schools, etc.
Multiwire Receptacle Circuits Supplying Testing Equipment on an Assembly Line
/
0.0
K20
Description
Measurement of Harmonics
For existing installations, the extent of
the harmonics can be measured with
appropriate instruments commonly
referred to as “Power Harmonic
Analyzers”. This service is offered by
many consulting service organizations.
For new construction, such information
may not be obtainable. For such
situations, it is best to assume the worse
case condition based on experience with
the type and mix of loads.
18-18
Table 17.6
Typical loads and K-Factor values for estimating purposes only.
Siemens Power Distribution & Control, SPEEDFAX™ 2007-2008 Product Catalog