# Stability Factor: K-Factor

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• #10955
Steven Mill
Participant

K-Factor determines the total harmonic current which a transformer can withstand without going beyond its specified temperature threshold limits. Under normal circumstances the value of K-Factor ranges from 1-50. It is the load that determines the K-Factor of the specific transformer. For example in the case of linear loads K-Factor of 1 is used whereas in worst harmonic conditions K-Factor of 50 is advisable. K-Factor rating indicates the tendency of a transformer to supply rated KVA output to a load of specified harmonic content.

Most harmonic systems use transformers with K-Factor of 13. Transformers using K-Factor values are said to be K-rated. The purpose of K-rated transformers is to tackle the problems associated with inductive and nonlinear loads which include industrial loads such as motors. These types of loads are known as harmonic generating loads. Harmonics; are multiples of fundamental frequency which when increased beyond ordinary limits result in overheating of the system. Likewise, in a transformer harmonics produce excessive heat which could result in fire or in some extreme cases violent explosions. Most of these hazardous cases occur in non K-rated transformers which lack Harmonic Protection. Harmonics result in decreased life of any electrical system. In order to tackle overheating issues in conventional non K-rated transformers, K-rated transformers are designed in such a way to mitigate the effects of harmonics and to dissipate the heat from the transformer to the environment as quickly as possible. The image underneath delineates the effects of harmonics on a conventional sine wave.

#### Working Of K-rated Transformer

The working principle of K-rated transformers involves the use of a double sized neutral conductor with their alignment changed. Some K-rated transformers use more than one conductor. K-rated transformers could be used at places where the loads are either inductive or nonlinear. Most of these places include heavy industries, offices, automation factories and many other places where harmonic generating loads are present. Normally at consumer ends where the loads have harmonic content less than 75%, a transformer with K-Factor of 13 could be used. For loads with Total Harmonic Distortion greater than 75%, a transformer with K-Factor of 20 is used.

#### Need For K-rated Transformers

Due to continuous increase of consumer end loads such as computers, Uninterrupted Power Supplies, Switch Mode Power Supplies, VFD’s and various small household motors the problem of harmonics has grown much severe. All of these loads are nonlinear and cause unnecessary loading of the Power System due to irregular demand of current and variable impedance during their voltage cycle. As a result these loads result in the generation of increased harmonic currents which at the end result in producing more heat in power distribution equipment which include distribution transformers.

This is where the importance of using K-factor transformers arises. K-Factor is a measure to determine how much a transformer could be overrated or de-rated to sustain a specified load.

#### Rules to Follow

There are some specific rules set by IEEE which must be followed before choosing a specific K-Factor value for a specific load. These include:

1. For loads with Harmonic Currents less than 15% a standard non K-rated transformer could be used
2. For loads with Harmonic Currents up to 35% a K-4 rated transformer should be used
3. For loads with Harmonic Currents up to 75% a K-13 rated transformer should be used
4. For loads with Harmonic Currents greater than 75% a K-20 rated transformer should be used

K-Factor transformer or K-rating is used to tackle the overheating of transformers due to excessive harmonic currents produced by nonlinear loads. K-Factor neither improves the quality of Power System nor does it increase the efficiency of Power System. An added advantage of K-Factor transformers is that these transformers prevent insulation breakdown by uniformly distributing the stress across the transformer’s winding. This results in longevity of transformer.

Did this introduction to K-Factor draw your interest? Please let us know by posting a comment.

#13223
Spir Georges GHALI
Participant

Dear;

It’s very good and important to mention the effects of Harmonics on the Transformers, but I have some remarks that are :

– I think the percentages of Harmonics currents mentioned in this topic mean the percentage of the “ THD-I ” ( Total Harmonic Distortion of Current ). If not, please clarify.

– It’s known that the effect of K-Factor is to over-size the Transformer’s power, but what is the formula between the K-Factor and the Transformer’s power ?

– You mention that “ the inductive loads like Motors are known as harmonic generating loads ”, but most of motors especially “ Squirrel Cage Motors ”, and after the transient running case are always “ Linear Loads ”, but for these loads the Harmonic currents can be generated or not depending on the kind of running equipment used to run these motors. ( for exp. Contactors with Thermal relays doesn’t generate any harmonic, VFD equipment generates harmonics ).

– It’s mentioned that “ the working principal of K-rated Transformers involves the use of a double sized neutral conductor ”, but in general, depending on the Harmonics Currents value or percentage, we over-size “ double or even more ” the cables’ sections of Phases & Neutral “, and also depending on the value or percentage of the “ Third multiple Harmonics ” and the “ Unbalance current’s value ” we decide the final section of neutral conductor.

– It’s mentioned that “ K-rated Transformers could be used at places where the loads are either inductive or nonlinear ”, and as known, some inductive loads generate harmonics but not all inductive loads.

– As mentioned, the K-Factor Value’s range is from “ 1 ” to “ 50 ”, and also, the rules mentioned the K-Factor Transformers that should be used depending on the Harmonic Current, ( exp. for Harmonics Currents more than 75% the “ K-20 Transformers ” should be used ) but, at which levels or where the values “ K-30  or  K-35 Transformers ” or more should be used ?

– The K-Factor value is the percentage of Harmonics current’s percentage to fundamental current, but this percentage’s value can be only known after industries’ running, so, what the Electrical Engineers Designers should do at designing step ? For this point, the IEC determines a curve that helps the Electrical Engineers Designers to define the transformer’s powers that should be used depending on the percentage of “ Non Linear Loads ”.

#12791
Anonymous
Guest

IT IS VERY VITAL PHENOMINON FOR THE SUBJECT MATTER OF K-FACTOR TO OVER SIZE TRANSFORMERS.

#13000
Steven Mill
Participant

Spir Georges GHALI, sorry for the late reply and thank you for your interesting remarks.

@Spir Georges GHALI said:
Dear;

It’s very good and important to mention the effects of Harmonics on the Transformers, but I have some remarks that are :

– I think the percentages of Harmonics currents mentioned in this topic mean the percentage of the “ THD-I ” ( Total Harmonic Distortion of Current ). If not, please clarify.

Yes these percentages are of THD. Sorry If that confused you.

– It’s known that the effect of K-Factor is to over-size the Transformer’s power, but what is the formula between the K-Factor and the Transformer’s power ?

Normally in order to calculate the K-Factor you keep into account two things the KVA & load Harmonic Current. So accordingly the K-Factor would be:

K – Factor = KVA * IL

As IL is the load harmonic content so you can easily calculate the K-Factor value to be used.

– You mention that “ the inductive loads like Motors are known as harmonic generating loads ”, but most of motors especially “ Squirrel Cage Motors ”, and after the transient running case are always “ Linear Loads ”, but for these loads the Harmonic currents can be generated or not depending on the kind of running equipment used to run these motors. ( for exp. Contactors with Thermal relays doesn’t generate any harmonic, VFD equipment generates harmonics ).

I was specifically referring to induction motors which are widely used in industry as compared to squirrel cage motors which are most suited for small tasks. Very rare have I seen squirrel cage motors used in industry. Induction motors generate harmonics and come in the domain of non-linear loads. Also in industries the Switch mode power supplies & DC rectifiers also add to the non-linearity of the system.

– It’s mentioned that “ the working principal of K-rated Transformers involves the use of a double sized neutral conductor ”, but in general, depending on the Harmonics Currents value or percentage, we over-size “ double or even more ” the cables’ sections of Phases & Neutral “, and also depending on the value or percentage of the “ Third multiple Harmonics ” and the “ Unbalance current’s value ” we decide the final section of neutral conductor.

Yes you are right about conductor size. It depends on the harmonic currents value. I also wrote in the article that Some K-rated transformers use more than one conductor. Normally you don’t need a transformer with K-factor rating more than K-4 or K-13 in industries which are coherent to the design specs presented in the article.

– As mentioned, the K-Factor Value’s range is from “ 1 ” to “ 50 ”, and also, the rules mentioned the K-Factor Transformers that should be used depending on the Harmonic Current, ( exp. for Harmonics Currents more than 75% the “ K-20 Transformers ” should be used ) but, at which levels or where the values “ K-30  or  K-35 Transformers ” or more should be used ?

Transformer size increase as you increases the value of K-Factor & so does the heat tolerance due to harmonic currents. Normally transformers of K-Factor 30, 40 & 50 are used where harmonic currents are somewhere b/w 125-150%. These are worst harmonic conditions. As mentioned before the size of transformer increases with the increase in K-Factor so the optimal K-Factor should be chosen which would be a tradeoff between transformer size & its heat tolerance. Normally the K-50 transformers are very expensive & much larger in size so manufacturers recommend a transformer of K-30 with modified designs as a replacement.

#13002
Spir Georges GHALI
Participant

Dear Mr. Steven ;

first, thanks for your reply, and be sure for me there’s no any confusion.

Please let me clarify the following :

– The percentages of Harmonics are certainly ” THD-I “ ( Total Harmonics Distortion of Current ) and not ” THD-V

– The mentioned formula between ” K-Factor ” and ” the Transformer’s Power ” is ” K-Factor = S ( kVA ) * IL ” as IL is the load harmonic, please let me clarify the following points :

• This formula is ” linear “, but the relation between K-Factor and the Transformer’s Power is not a linear.
• As I mentioned, there’s a Curve ( not linear ) between ” the Percentage of Non-linear Loads compared with the total installed loads ” and the ” Derating Factor “, when we obtain this factor, we use the following formula : S(new) = S / Derating Factor. Noting that I use this curve during designing step of any site if the derating of transformer is necessary, and if you want, send me your e-mail to send it you.

– About the type of used motors : from my experience, most of LV motors even till 300kW are Squirrel Cage Motors. noting that all Motors are Induction Motors. Please clarify if there’s another kind, and what?

#13049
Anonymous
Guest

how to calculate load harmonic content