**What is the K-factor?**

K-factor for an electrical network primarily relates to non-linear loads and is defined as a number representing the effect of harmonics on the heating of the transformer. For calculating the K-factor all the harmonics up to a predefined limit are considered. For industrial loads of induction motors, up to 25thharmonic currents are considered but the limit can be up to 50th. The formula for calculating the K factor of a network is-^{[1]}

As from the formula, while calculating the K-factor, the harmonic current is getting multiplied by the square of its number. So for higher-order harmonics, getting multiplied by the square of their number even small harmonic current will give considerable effects on the K-factor. To avoid these misleading results, it is acceptable to consider only up to the 25th harmonic ^{[2]}.

For a linear network, the K factor will always be 1. As the harmonic content increases in the current, the K factor moves upwards from 1. Electronic ballasts, induction motors, UPS, and all diode-based switching circuits come under non-linear loads causing harmonics.

**Significance of K factor-**

K factor of the electrical distribution network is the reason why transformers need to be de-rated. While supplying the non-linear loads, harmonic currents flow in the transformer, and to protect the windings and transformer oil from overheating, load on it needs to be reduced.

Due to harmonics of non-linear loads, magnitude of eddy currents flowing in the transformer increases. These eddy currents flowing in the core of the transformer cause additional heating losses. Other than the heat, the harmonic current flowing in the core of the transformer also causes disturbance in the magnetic field, which results in vibrations in the transformer and audible noise.

The general transformers without mentioned K factor are capable of supplying the non-linear loads but their limit is unknown. Thus the reliability for such loads is low. The alternate is of using K rated transformer, these are tagged with a K-factor number and are suitable for supplying loads of equal K factor or less. These transformers are larger in size for better heat dissipation as compare to general transformers. The K rated transformers comes for K=4, 9, 13,20,30,40. Higher the K rating of the transformer higher is its capacity for feeding non-linear loads ^{[3]}.

The transformer carrying nonlinear loads will need better room cooling as a fully loaded transformer feeding nonlinear loads will produce 10% more heat in BTU as compare to linear loads ^{[4]}. If not ventilated, oil temperature might rise above relay setting temperature, which will trip the whole system.

Calculating total losses for a transformer- considering the K factor, the total load losses of a transformer are given by PTLL= PDC (1+ K(PEC)) ^{[4]}

Where PDC is I2R losses, PEC is total eddy current losses and K is the K factor of the transformer.

**Over-Current protection problem associated with non-linear loads-**

While supplying non-linear loads from a transformer, it needs to be de-rated. De-rating implies that the transformer will be carrying a load current below its rated current but the protection circuit needs to be designed while keeping in mind the harmonic currents. If relays of the protection circuit are made to operate overload current, it will give false tripping for any harmonic current superimposed overload current. To avoid false tripping if relay settings are changed in accordance with rated current, it will not trip for initial fault conditions. Thus for both measures, the protection system of the transformer suffers.

**K-rated Transformers-**

K factor transformers have additional heat dissipation capability for handling the effects of non-linear loads. K rating should be provided by the manufacturer by testing the transformer’s heating characteristics while supplying non-linear loads.

Double Neutral has used for the K-rated transformers as for harmonic currents flowing in the system, the triple harmonics shows additive nature and flow through neutral. A neutral current of as high as 100% of the load current is observed under non-linear loads ^{[2]}.To avoid the neutral burn out, double neutral conductor is used in K rated transformers.

Secondary windings of a K rated transformers are also modified to incorporate harmonic currents. A number of small insulated conductors are used to avoid skin effect and there are stranded if necessary for balancing magnetic circuit.

**Avoiding the misconceptions about K factor-**

As harmonics are vector quantity, for a number of non-linear loads connected from a single point K factor is not the mean of the K factors for singular loads. On contrary, harmonics tend to cancel out each other and the resultant K factor of the system is low. ^{[5]}

K-rated transformers do not improve the efficiency of the system or reduce the harmonics but they are used only for heat dissipation produced by harmonics.

A transformer of K=4 can supply loads with higher K rating for a short period of time. Though the heat generated will be high but a period of relatively low load will give the transformer time to dissipate the extra heat generated.

The spectrum of K factor can be analyzed to decide about the requirement of a K rated transformer. Harmonic content at a particular time is not sufficient in itself to calculations but its analyses over time give the system irregularities and need for improvement.

At Zenatix, we collect the K-factor parameter at distribution level metering. Collecting the averaged out data every 30 seconds provides accurate and consistent data to constantly monitor and put checks in case of irregularity. As the transformer is a critical part of the electrical power distribution system and its overheating can result in spilling of all the oil through the diaphragm and tripping of the power circuit, it is advised to use proper checks to avoid extreme conditions. Further for identifying and eliminating the root cause behind high K-factor, Zenatix recommends metering at individual load level which will be effective in capturing other losses as well.

**Case Study**

K factor data for two of the Zenatix clients is presented for illustration purposes. We are collecting the data every 30 seconds and as K-factor is the numerical sum of a number of contributing factors, we get the average of the values over 30 seconds. For getting more consolidated results, we are taking the mean of the readings for every hour. For the purpose of case study, the clients can be referred as client1 and client2. As the transformer’s efficiency and heating of both winding and oil depend upon the current, we can plot the K-factor values for current. Below are the two plots showing the current K-factor for both the clients.

When K-factor went too high for a specific period of time, the transformer’s temperature will rise and its efficiency will drop as well. Such type of sudden rise indicates a high harmonic current flowing in the transformer. For a regular transformer with no specific K-factor defined, this high value will overheat the winding and oil inside the transformer and can trip the whole supply.

Even when K-factor is staying consistently under 4, it can result in overheating if the ambient temperature is high. Especially during summer season, with improper dissipation of heat from the transformer even low K-factors can result in tripping. For the same purpose it is suggested for the transformers to be installed with proper ventilation.

**Figure’s Detail**

**Fig.1-** Plot of one of the Zentix customers with high in K-Factor.

**Fig.2-** Plot of one of the Zentix customers with low K-Factor.

**References-**

[1] http://www.electrotechnik.net/2010/04/k-factor-for-harmonics.html

[3] http://www.xitrontech.com/assets/002/5787.pdf

[4] The Institute of Electrical & Electronic Engineers, “Recommended Practice for establishing Transformer capabilities when supplying Non-sinusoidal Load Currents”, ANSIIIEEE C57.110-1986, New York, 1986

[5] GE electrical distribution and control- Q/A on K factor.

[6] A Study of K-Factor Power Transformer Characteristics by Modeling Simulation, ETASR – Engineering, Technology & Applied Science Research