Subject Of Previous
Articles

Article

Glossary of
Sizing Power and Distribution Transformers,


Resources
used to calculate basic ratings of power and distribution transformers


the selection
factors for the Power and Distribution Transformers


Applicable
calculations procedures for sizing of power and distribution transformers


1 Applicable
procedures for calculating power and distribution transformer ratios,
2 Applicable
procedures for calculating power transformer efficiency,
3 Applicable
procedures for calculating power transformer voltage regulation,
4 Special Cases
In Transformers Sizing Calculations: Secondary Unit Substations


Special Cases
In Transformers Sizing Calculations: Paralleled Transformers


Note: I’d like
from all of you to review our course “EP3: Electrical Procurement – Transformers Course” to be more
familiar with the contents of our new articles about the Power and
Distribution Transformers sizing calculations.


Today, we
will explain other special cases for Power and Distribution Transformers
sizing calculations; KFactor Transformers.

Special
Cases In Transformers Sizing Calculations
3
KFactor Transformers

Linear
Vs. Nonlinear Loads
Linear Loads:
A load that
does not affect the input waveform, which is a pure sinewave, composed of a
fundamental frequency (e.g. 60 hz) component with no multiple frequencies. Typical linear
loads are resistive heating and induction motors.
Nonlinear
Loads:
A load that
distorts the input sinewave such that the resultant waveform is composed of a
fundamental frequency (e.g. 60 hz) component and multiple frequency
components (e.g. 120 hz, 180 hz,..etc) called harmonics. Examples of these
loads used in offices are: computers, fax machines, copiers, printers, cash
registers, UPS systems, and solidstate ballasts. In industrial plants, nonlinear
loads are such
as variable speed drives, HID lighting, solidstate starters and solidstate
instruments.
See Fig.1
Fig.1:
voltage and current waveforms for nonlinear loads.

Harmonics
As defined by
ANSI / IEEE Std. 519, 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. which called odd harmonics (3rd, 5th, 7th ,...,
25th,...). See Table1.
Table1:
Harmonics

The
Effect of Nonlinear Loads on the Electrical Power Systems
Nonlinear
loads produce harmonic currents which flow from the load towards the power
source following the path of least impedances result in harmonic voltage
drops which are observed as harmonic voltage distortion. The voltage
distortions could become very severe when the power systems inductive and
capacitive impedances become equal, a condition of parallel resonance.
The Problems Caused By
Harmonic Currents Include:

KFactor
K4, K9, K13,
K20, K30, K40, K50
Fig.2:
UL Label for Kfactor Transformers

Diversity
of Harmonics
Each nonlinear load
generates harmonics independently with the magnitude and phase angle of each
harmonic depending on the design of the circuit and the instantaneous
loading. When several loads are connected in parallel, for example, a number
of personal computers on an office floor, the overall sum of each harmonic
will be less than the sum of the individual magnitudes. See Fig.3.
Fig.3: Diversity
of Harmonics
In other words, the
Kfactor of the overall load is less than that which would be expected from measurement
of all the individual items. Similarly, when there are linear loads present,
the overall Kfactor is reduced because the harmonic load is a smaller
proportion of the total load.

KFactor
or Factor K?
There are two approaches
in selecting a transformer feeding nonlinear loads as follows:
The figures produced by
each method are numerically different; ‘factor K’ is a total rating factor
while ‘Kfactor’ is a multiplier (although a derating factor can be derived
from it). The fact that both methods use K as a designation can lead to
confusion when talking to suppliers.
Disadvantage
of using Derated Transformers (factor K) instead of KFactor Transformer
The use of
derated standard transformers instead of KFactor Transformers carries some
disadvantage as under:

Sizing Methods
of Transformers for NonLinear Loads
We have three methods for
Sizing Transformers for NonLinear Loads as follows:
Method#1: ANSI / IEEE C57.110 has
a procedure for derating standard distribution transformers for nonlinear
loading but We will explain this method later since it is more
complicated.
Method#2: Underwriters’
Laboratories method where the appropriate KFactor for a transformer with nonlinear
loads can be calculated as follows:
K
= Σ
(Ih)^{2}
(h)^{2}
Where:
Ih = RMS Current at
Harmonic h
h = Harmonic Order, i.e.
3rd, 5th, 7th, etc.
Fig.4:
Kfactor calculations by UL
Method#3: Estimating
KFactor from Tables
1 List the kVA value for
each load category to be supplied. Next, assign a Kfactor designation that
corresponds to the relative level of harmonics drawn by each type of load.
Refer to Table2.
2 Multiply the kVA of
each load or load category times the Index of Load Krating (I_{LK})
that corresponds to the assigned Kfactor rating. This result is an indexed
kVAI_{LK} value.
KVA x I_{LK}
= kVAI_{LK}
2 Tabulate the total
connected load kVA for all load categories to be supplied.
4 Next, addup the kVAI_{LK}
values for all loads or load categories to be supplied by the transformer.
5 Divide the grand total
kVAI_{LK} value by the total k_{VA} load to be supplied.
This will give an average I_{LK} for that combination of loads.
Total
kVAI_{LK}/ Total kVA = average I_{LK}
6 From Table2 find the
Kfactor rating whose I_{LK} is equal to or greater than the
calculated I_{LK}.
Table2:
Estimating KFactor
Notes:

In the next article, we will explain KFactor/Factor K Calculators used in sizing transformers with nonlinear loads. So, please keep following.
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