Transformers with K-factor Classification

Nowadays, in industrial workplaces, the proliferation of solid-state devices (lighting reactors, motor drive and control systems, communications equipments, and other DC motor loads) have created some relevant problems for specification engineering, contractors and business owners. The non-linear nature of the power supplies of models with switching by solid state systems, generate harmonic currents which, in turn, generate additional losses, which make transformers (some of these are large losses within the windings and some are closer to the surface) and the system neutrals overheat and be destroyed.

Effect of harmonics on dry-type transformers

There are several situations that may create conditions for harmonic problems in transformers, including the equipment addition to an existing electrical system, or the addition of enhancement facilities or expansions to an existing power source. Transformers with K-factor specifications are designed to reduce the heating effects of harmonic currents created by non-linear loads. The K-factor rating, assigned to a transformer, is an index of the transformer's ability to support a harmonic index in its load current, remaining within its operating temperature limits. A K-factor specific rating indicates that a transformer can supply, in addition to the nominal KVA load output, a load of a specified amount of harmonic index. In 1990, UL (Underwriters Laboratories) developed the method of calculating K-factor rating to evaluate the ability of transformers to support the harmonic effects. The K-factor does not mean that the transformer can eliminate the harmonics. The UL test is oriented to the heating of the windings, due to the general non-linear loads and overheating of the neutral conductor.

There are two methods of calculating the K-factor:
- The UL method
- The standardised method

The UL method is based on the “rms” effective rated current of the transformer. It is generally used when the effective current is measured or measurable, and is defined as:


Where:
h = harmonic order;

Ih (pu) = rms current of the harmonic expressed in pu (per unit) of the effective rated current of the transformer.

The standardised method is based on the fundamental load current. Harmonic measurements are often made with a harmonic analyzer. Most harmonic analyzers have the output responses of the harmonics in pu (values per unit) of the fundamental current. In consequence, the method would be used. The standardised method is defined as follows:

Where:
Fundamental current in pu (the 1st harmonic = 100%);

Here is an example of the two methods for the same harmonic spectrum of data. For example, we assume that the measures were taken to obtain (pu):
Up to now, industrial literature and comments refer to a limited number of K-factor ratings: K-1, K-4, K-9, K-13, K-20, K-30, K-40.

In theory, a transformer could be designed for other K-factor assessments among these values, as well as for higher values. The commonly referenced classifications are in accordance with ANSI/IEEE C57.110-1986 as follows:

K-1: This is the assessment of any conventional transformer that is designed to support only the heating effects of normal losses and additional eddy losses, resulting from 60Hz with the transformer loaded with sinusoidal current. Such a unit may or may not be designed to support the additional harmonic heating in its load current.

K-4: A transformer with this rating was designed to provide nominal KVA, without overheating, to a load provided by 100% of normal 60Hz frequency, sinusoidal current in the fundamental, and:

- 16% of fundamental current as the 3rd harmonic current;
- 10% of the fundamental current as 5th;
- 7% of the fundamental current as 7th;
- 5.5% of the fundamental current as the 9th;
- Minor percentages through the 25th harmonic.
The number "4" indicates its ability to support four times the eddy current losses of a K-1 transformer.
K-9: A K-9 transformer can support 163% of the harmonic load of a K-4 transformer.
K-13: A K-13 transformer can accommodate 200% of the harmonic load of a K-4 transformer.
K-20, K-30, K-40: The highest number of each of these K-factor ratings indicates the ability to work with successively larger amounts of harmonic load indexes without overheating.
The table below gives the example of K-factor loads

LOAD – K-FACTOR
Lighting with discharge lamps - K-4
UPS with optional inlet filter - K-4
Welding machines - K-4
Induction heating equipment - K-4
PLCs and solid-state controllers (other than variable frequency drives). - K-4
Telecommunication Equipment (for example, PBX) - K-13
UPS without inlet filters - K-13
Supply of general multiwire receptacles, in areas with health-care instruments and school classrooms, etc. - K-13
Circuit sources with multiwire receptacles for inspection and testing equipment in productive sectors or production lines - K-13
Loads of computer servers (Mainframe) - K-20
Solid-state drives for motors (variable frequency drives) - K-20
Supply of circuits with receptacles in important safety areas and rooms for hospital surgery and recovery - K-20

* Re-written with permission from EDI Magazine
The K-factor must be clearly marked on the identification plate of the transformer.