Power And Distribution Transformers Sizing Calculations – Part Seven


Subject Of Previous Articles
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 “EP-3: Electrical Procurement – Transformers Courseto 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; K-Factor Transformers.


Special Cases In Transformers Sizing Calculations
3- K-Factor 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 solid-state ballasts. In industrial plants, nonlinear loads are such as variable speed drives, HID lighting, solid-state starters and solid-state instruments. See Fig.1
Fig.1: voltage and current waveforms for nonlinear loads.


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 Table-1.
Frequency in Hz
Table-1: 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:
  1. Overheating of cables, especially the neutral conductor, but if normal wiring sizing methods are employed, then the derating for wiring for harmonics is minimal and can be ignored,
  2. Overheating and vibration in induction motors,
  3. Increased losses in transformers due to stray magnetic losses in the core, and eddy current and resistive losses in the windings. eddy current losses are of most concern when harmonics are present, because they increase approximately with the square of the frequency,
  4. Where power factor capacitors are fitted, harmonic currents can damage them and care must be taken to avoid resonance with the supply inductance.


  • When transformer supply a non-sinusoidal load current with the same rms value than rated current, DC losses remain constant but winding eddy losses increase due to the higher frequency of the harmonics, as a result, winding temperature rise increases and temperature limits can be exceed.
  • So, K Factor rating is used to define the transformer’s ability to withstand the additional heating generated by the harmonic current.
  • K-Factor is a ratio between the additional losses due to harmonics and the eddy losses at 60 Hz. Note that K-Factor transformers do not eliminate harmonic distortion; they withstand the non-linear load condition without overheating.
  • K-Factor transformers are designed to be operated fully loaded with any harmonic load having K-Factor equal to or less than its K-rating. For example, a K-13 transformer can be fully loaded with any harmonic load having a K-Factor up to K-13. If the load has a K-Factor greater than 13, then the transformer cannot be safely operated at full load and would require derating.
  • The great advantage of a ‘K-rated’ transformer is that it will have been designed with harmonic loads in mind and care will have been taken to keep losses low. For example:
  1. Eddy current losses will have been reduced by the use of stranded conductors,
  2. Magnetic losses will have been reduced by the use of low loss steels,
  3. The neutral point connections are usually brought out individually, so that the star point has a 300% current rating
  • Standard Industry K-Factor Transformer Ratings:
             K-4, K-9, K-13, K-20, K-30, K-40, K-50
  • The larger the K Factor, the more harmonics are present. Linear loads, for example, have a K Factor of 1.
  • No UL listing for K Factor means transformer is rated only for linear loads.
  • UL listing requires label stating: “Suitable for non-sinusoidal current loads with K Factor not to exceed x ”. (x= 4, 9, 13, 20, 30, 40 or 50).see Fig.2.
Fig.2: UL Label for K-factor Transformers


Diversity of Harmonics
Each non-linear 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 K-factor 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 K-factor is reduced because the harmonic load is a smaller proportion of the total load.


K-Factor or Factor K?
There are two approaches in selecting a transformer feeding non-linear loads as follows:
  1. In the United States, Underwriters Laboratories used to calculate the factor increase in eddy current loss and specify a transformer designed to cope; this is known as ‘K-Factor’.
  2. in Europe, transformer manufacturers used to estimate by how much a standard transformer should be de-rated so that the total loss on harmonic load does not exceed the fundamental design loss; this is known as ‘factor K’.
The figures produced by each method are numerically different; ‘factor K’ is a total rating factor while ‘K-factor’ is a multiplier (although a de-rating 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 De-rated Transformers (factor K) instead of K-Factor Transformer
The use of de-rated standard transformers instead of K-Factor Transformers carries some disadvantage as under:
  1. The de-rated transformer nameplate indicates greater capacity. Initially, the transformer may be operated at reduced loading. But in the future, additional loads may be increased without reference back to the initial de-rating. This may lead to overloading and consequent failure.
  2. Because the transformer is oversized, the primary over-current protection level may be too high to protect the secondary, but if the protection level is reduced, the inrush current may cause tripping. Larger overcurrent protection may be required for the oversized (de-rated) standard transformer resulting in larger conductor requirements with the associated higher feeder costs.
  3. The transformers designed specifically for nonlinear loads minimize losses due to harmonic currents. They operate with the nonlinear loads more efficiently and generate less heat that need to be dissipated.
  4. There is also a potential maintenance problem for oversized (de-rated) transformers.


Sizing Methods of Transformers for Non-Linear Loads
We have three methods for Sizing Transformers for Non-Linear Loads as follows:
Method#1: ANSI / IEEE C57.110 has a procedure for de-rating standard distribution transformers for non-linear loading but We will explain this method later since it is more complicated.
Method#2: Underwriters’ Laboratories method where the appropriate K-Factor for a transformer with non-linear loads can be calculated as follows:
K = Σ (Ih)2 (h)2
Ih = RMS Current at Harmonic h
h = Harmonic Order, i.e. 3rd, 5th, 7th, etc.
Fig.4: K-factor calculations by UL
Method#3: Estimating K-Factor from Tables
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-2.
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.
2- 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-2 find the K-factor rating whose ILK is equal to or greater than the calculated 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
Electric Discharge Lighting (HID)
UPS with Optional Input Filter
Induction Heating Equipment
PLCs and Solid State Controls
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
Main-Frame Computer Loads
Solid State Motor Drives (variable speed drives)
Multiwire Receptacle Circuits in Critical Care Areas in Hospitals
Multiwire Receptacle Circuits in Industrial, Medical and Educational Laboratories
Multiwire Receptacle Circuits in Commercial Office Spaces
Small Main-Frames (mini and micro)
Table-2: Estimating K-Factor
  • The problem associated with calculating K- Factor is selecting the range of harmonic frequencies that should be included. Some use up to 15th harmonic, others up to 25 th harmonic, and still others include up to 50th harmonic.
  • For the same load, each of these calculations can yield significantly different K-Factors, because even very small current levels associated with higher harmonics, when multiplied by the harmonic number squared, can yield significantly to the K-Factor.
  • Based on the underlying assumptions of ANSI / IEEE C57.II0, it seems reasonable to limit the K-Factor calculation to harmonic currents less than 25 th harmonic.
  • In establishing standard transformer K-Factor rating; UL chose ratings of 1, 4, 9, 13, 20, 30, 40 and 50. From a practical viewpoint individual loads with K-Factors greater than 20 are infrequent.
  • For example, At best office areas with some nonlinear loads and large computer rooms normally have observed K-Factors of 4 to 9. Areas with high concentrations of single phase computers and terminals have observed K- Factors of 13 to 17.

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




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