It is a general practice to have some means of adjustment to maintain constant voltage at the output terminals by compensating for the variations of the input voltage. This is done by tapping out or adding turns to the primary or input winding and maintaining the volts per turn, and thus the output voltage.

This operation is usually performed when the transformer is de-energized; this is called off-circuit tap changing. In dry type transformers, the usual method is to bring out the tap terminals on the outer surface of the coil or on a terminal board, where the linking to obtain the required turns is done manually with the unit de-energized.

It is possible, though not usual, to have tap switches similar to those used in liquid- filled units. Until recently, dry-type transformers were never supplied with under-load-tap-changing equipment. This was due to the fact that under-load tap changing involves breaking of load current at full voltage, thereby requiring switching equipment with capabilities comparable to those of circuit breakers.

To do this in air was cumbersome, bulky, and extremely expensive. But with the increased capacities and voltages of dry- type transformers, the demand for such equipment has increased, and recently voltage regulators became commercially available.

Two different approaches are used to provide underload voltage regulation. One takes the traditional approach of the liquid-filled units by providing motor-driven selector switches combined with a spring activated vacuum diverter switch.

The other approach uses a separate regulator winding feeding a buck/boost transformer connected in series with the primary winding. Voltage regulation is achieved by means of low-voltage vacuum contactors that modify the tap settings of the regulating winding of the buck/boost transformer, circumventing high-voltage switching equipment.

The contactors are usually controlled by programmable logic controllers (PLC). In cases where high speed response is required, the second approach has successfully used thyristors in place of vacuum contactors, thereby achieving a cycle switching.



Oriented (anisotropic) silicon-steel laminations.
The iron cores of conventional transformers consist of anisotropic silicon-steel laminations with lamination thickness ranging from 0.1 mm to 0.4 mm. In a transformer, the flux travels mostly within the limbs in the with-grain direction, and in the cross-grain direction only near the corners and lamination joints of transformer cores; thus oriented steel sheets are used.

The with- and cross-grain structure of oriented steel is determined by the rolling direction of the sheets during manufacture. Each side of a lamination is coated with insulating material so that no eddy currents can flow between laminations.

The coating does not significantly interfere with the passage of flux. The magnetic resistance, or reluctance, is only slightly increased and is taken into account via the iron-core stacking factor ϕFe = #(iron cross section of all laminations of core)/(cross section of entire core including insulation between laminations).

The stacking factor is in the range of 0.93 ≤ ϕFe ≤ 0.97 for 60 Hz units. For anisotropic electrical silicon steel the relative permeability is larger (and thus the magnetization required is smaller) in the with-grain direction (direction of rolling) than in the cross-grain direction. Similarly, the core losses are small in the with-grain direction and relatively large in the cross-grain direction.

Amorphous (glass-type) cores.
Amorphous magnetic materials either are obtained by quenching the molten material at high cooling rates or are manufactured by deposition techniques in a vacuum. The quenching process does not permit the forming of a crystalline structure, and therefore amorphous magnetic materials have a structure similar to glass.

The cores of transformers with amorphous alloy (AMTs) can be fabricated in the same manner as those made of oriented-silicon-steel. METGLAS (trademark of the Allied Signal Co) cores are 30% heavier than comparable oriented silicon-steel cores, but the no-load losses in amorphous alloy wound cores are only 30% of those in comparable oriented-siliconsteel wound cores.

However, the rated power efficiencies of present-day designs of AMTs and silicon-steel pole transformers with wound cores are about the same. For example, the rated power efficiencies of 20 kVA and 50 kVA wound-core AMTs at unity power factor are ηpower = 98.26% and 98.59%, respectively, while that of a 25 kVA oriented-silicon-steel wound core (10) at unity power factor is ηpower = 98.31%. The fabrication cost for AMTs with wound cores is higher than that for oriented silicon-steel wound cores.



Single-phase transformers can be connected to form three-phase transformer banks for stepping voltages up or down in three-phase systems. Four common configurations for connecting transformers in three-phase systems are delta–delta, wye–wye, wye–delta, and delta–wye.

The first three are shown in Fig. 3-9. The delta–wye is not shown because it is simply the reverse of the wye–delta connection.

Delta–delta connection
The delta–delta connection, shown in Fig. 3-9a, is widely used for moderate voltages. This connection has the advantage of remaining operational in what is known as the open delta or V connection if one transformer is damaged or taken out of service, leaving the remaining two functional.

If it is operated this way, the bank still delivers three-phase currents and voltages in their correct phase relationships. However, the capacity of the bank is reduced to 57.7 percent of the value obtained with all three transformers in service.

Wye–wye connection
In the wye–wye connection, shown in Fig. 3-9b, only 57.7 percent (or 1/1.73) of the line voltage is applied to each winding, but full line current flows in each transformer winding. The drawback to this connection is that power circuits supplied from a wye–wye bank generate serious electromagnetic interference, which could interrupt nearby communications circuits.

Because of this and other disadvantages, the wye–wye connection is seldom used. However, the wye–wye connection can be used to interconnect two delta systems and provide suitable neutrals for grounding both of them.

Delta–wye and wye–delta connections 
The delta–wye connection (not shown) is suitable for stepping up voltages because the voltage is increased by the transformer ratio multiplied by a factor of 1.73. Similarly, the wye–delta connection, shown in Fig. 3-9c, is used for stepping down voltages.

The high-voltage windings of most transformers operating at more than 100 kV are wye-connected. To match the polarities correctly in a wye connection, the H and X markings must be connected symmetrically.

In other words, if an H1 or X1 terminal is connected to the neutral, then all of the H1 or X1 terminals must be connected to the neutral and the remaining H2 or X2 terminals must be brought out as the line connections, as shown in Fig. 3-9b.

By contrast, in a delta connection, H1 must always be connected to H2 and X1 to X2, and the line connections must be made at these junctions, as shown in Fig. 3-9a.

When a large number of single-phase loads are to be served from a three-phase transformer bank, the wye connected low-voltage winding is recommended because the single-phase loads can be balanced evenly on all phases.



The following technical terms apply to transformers.

BIL: An abbreviation for basic impulse level, a dielectric strength test. Transformer BIL is determined by applying a high-frequency square-wave voltage with a steep leading edge between the windings and between the windings and ground.

The BIL rating provides the maximum input kV rating that a transformer can withstand without causing insulation breakdown. The transformer must also be protected against natural or man-made electrical surges. The NEMA standard BIL rating is 10 kV.

Exciting current: In transformers, the current in amperes required for excitation. This current consists of two components: (1) real in the form of losses (no load watts) and (2) reactive power in kvar. Exciting current varies inversely with kVA rating from approximately 10 percent at 1 kVA to as low as 0.5 percent at 750 kVA.

Eddy-current losses: Contiguous energy losses caused when a varying magnetic flux sets up undesired eddy currents circulating in a ferromagnetic transformer core.

Hysteresis losses: Continuous energy losses in a ferromagnetic transformer core when it is taken through the complete magnetization cycle at the input frequency.

Insulating transformer: A term synonymous with isolating transformer, to describe the insulation or isolation between the primary and secondary windings. The only transformers that are not insulating or isolating are autotransformers. Insulation system temperature: The maximum temperature in degrees Celsius at the hottest point in the winding.

Isolating transformer: See insulating transformer. Shielded-winding transformer: A transformer with a conductive metal shield between the primary and secondary windings to attenuate transient noise.

Taps: Connections made to transformer windings other than at its terminals. They are provided on the input side of some high-voltage transformers to correct for high or low voltages so that the secondary terminals can deliver their full rated output voltages.

Temperature rise: The incremental temperature rise of the windings and insulation above the ambient temperature.

Transformer impedance: The current-limiting characteristic of a transformer expressed as a percentage. It is used in determining the interrupting capacity of a circuit breaker or fuse that will protect the transformer primary.

Transformer voltage regulation: The difference between the no-load and full-load voltages expressed as a percentage. A transformer that delivers 200 V at no load and 190 V at full load has a regulation of 5 percent.



Although transformer oil is a highly refined product, it is not chemically pure. It is a mixture principally of hydrocarbons with other natural compounds which are not detrimental. There is some evidence that a few of these compounds are beneficial in retarding oxidation of the oil.

Although oil is not a “pure” substance, a few particular impurities are most destructive to its dielectric strength and properties. The most troublesome factors are water, oxygen, and the many combinations of compounds which are formed by the combined action of these at elevated temperatures.

A great deal of study has been given to the formation of these compounds and their effects on the dielectric properties of oil, but there apparently is no clear relation between these compounds and the actual dielectric strength of the transformer insulation structure.

Oil will dissolve in true solution a very small quantity of water, about 70 ppm at 25 C and 360 ppm at 70 C. This water in true solution has relatively little effect on the dielectric strength of oil. If, however, acids are present in similar amounts, the capacity of oil to dissolve water is increased, and its dielectric strength is reduced by the dissolved water. Small amounts of water in suspension cause severe decreases in dielectric strength.

The primary reason for concern over moisture in transformer oil, however, may not be for the oil itself but for the paper and pressboard which will quickly absorb it, increasing the dielectric loss and decreasing the dielectric strength as well as accelerating the aging of the paper.

It is generally recognized today that the best answer to the problem of air and water is to eliminate them and keep them out. For this purpose, in American practice, transformer tanks are completely sealed. About three basic schemes are used in sealed transformers to permit normal expansion and contraction of oil (0.00075 per unit volume expansion per degree Celsius) as follows:

1. A gas space above the oil large enough to absorb the expansion and contraction without excessive variation in pressure. Some air may unavoidably be present in the gas space at the time of installation but soon the oxygen mostly combines with the oil without causing significant deterioration, leaving an atmosphere which is mostly nitrogen.

2. A nitrogen atmosphere above the oil maintained in a range of moderate positive pressure by a storage tank of compressed nitrogen and automatic valving. This scheme has the advantage that the entrance of air or moisture is prevented by the continuous positive internal pressure, and the disadvantage of somewhat higher cost.

3. A constant-pressure oil-preservation system consisting of an expansion tank with a flexible synthetic rubber diaphragm floating on top of the oil. This scheme has the advantages that the oil is never in contact with the air and there is always atmospheric pressure and not a variable pressure on the oil. The disadvantage is the higher cost. A number of mechanical variations and elaborations of this general idea have been devised.

It is now generally recommended that the constant-pressure oil-preservation system of item 3 be employed on all high-voltage power transformers (345 kV and above) and on all large generator step-up transformers. This is a consequence of unfavorable experience with transformers having gascushion systems, which inherently operate with large quantities of the cushion gas in solution in the hot oil under load.

If the oil is suddenly cooled (reduction of ambient temperature or load), the oil volume contracts and the static pressure of gas over the oil drops rapidly, allowing free gas bubbles to come out of solution throughout the insulation system. The dielectric strength of the oil and cellulose insulation system is drastically weakened when it has free gas inclusions, and this has occasionally led to electrical failure of operating transformers.



ANSI/IEEE C57.12.90 specifies the method for measuring the average sound level of a transformer. The measured sound level is the arithmetic average of a number of readings taken around the periphery of the unit. For transformers with a tank height of less than 8 ft, measurements are taken at one-half tank height.

For taller transformers, measurements are taken at one-third and two-thirds tank height. Readings are taken at 3-ft intervals around the string periphery of the transformer, with the microphone located 1 ft from the string periphery and 6 ft from fan-cooled surfaces.

The ambient must be at least 5 and preferably 10 dB below that of the unit being measured. There should be no acoustically reflecting surface, other than ground, within 10 ft of the transformer. The A weighting network is used for all standard transformer measurements regardless of sound level.

NEMA Publication TR 1 contains tables of standard sound levels. For oil-filled transformers, from, 1000 to 100,000 kVA, self-cooled (400,000 kVA, forced-oil-cooled) standard levels are given approximately by

Equation L = 10 log E K

where E equivalent two-winding, self-cooled kVA (for forced-oil-forced-air-cooled units, use 0.6  kVA), K constant, from Table 10-3, and L = decibel sound level.

Example. A transformer rated 50,000 kVA self-cooled, 66,667 kVA forced-air-cooled, 83,333 kVA forced-oil-forced-air-cooled, at 825 kV BIL, would have standard sound levels of 78, 80, and 81 dB on its respective ratings.

Public Response to Transformer Sound.
The basic objective of a transformer noise specification is to avoid annoyance. In a particular application, the NEMA Standard level may or may not be suitable, but in order to determine whether it is, some criteria must be available.

One such criterion is that of audibility in the presence of background noise. A sound which is just barely audible should cause no complaint.

Studies of the human ear indicate that it behaves like a narrowband analyzer, comparing the energy of a single frequency tone with the total energy of the ambient sound in a critical band of frequencies centered on that of the pure tone. If the energy in the single-frequency tone does not exceed the energy in the critical band of the ambient sound, it will not be significantly audible.

This requirement should be considered separately for each of the frequencies generated by the transformer core. The width of the ear-critical band is about 40 Hz for the principal transformer harmonics. The ambient sound energy in this band is 40 times the energy in a 1-Hz-wide band.

The sound level for a 1-Hz bandwidth is known as the “spectrum level” and is used as a reference. The sound level of the 40-Hz band is 16 dB (10 log 40) greater than the sound level of the 1-Hz band. Thus, a pure tone must be raised 16 dB above the ambient spectrum level to be barely audible.

The transformer sound should be measured at the standard NEMA positions with a narrow-band analyzer. If only the 120- and 240-Hz components are significant, an octave-band analyzer can be used, since the 75- to 150-Hz and 150- to 300-Hz octave bands each contain only one transformer frequency. The attenuation to the position of the observer can be determined.

The ambient sound should be measured at the observer’s position. For each transformer frequency component, the ambient spectrum level should be determined. An octave-band reading of ambient sound can be converted to spectrum level by the equation

S = B - 10 log C

where B decibels octave-band reading, C hertz octave bandwidth, and S decibels spectrum level.



The delta-delta, the delta-Y, and the Y-Y connections are the most generally used; they are illustrated in figure below. The Y-delta and delta-delta connections may be used as step-up transformers for moderate voltages.

                      Standard 3-phase/3-phase transformer systems.
The Y-delta has the advantage of providing a good grounding point on the Y-connected side which does not shift with unbalanced load and has the further advantage of being free from third-harmonic voltages and currents; the delta-delta has the advantage of permitting operation in V in case of damage to one of the units.

Delta connections are not the best for transmission at very high voltage; they may, however, be associated at some point with other connections that provide  means for properly grounding the high voltage system; but it is better, on the whole, to avoid mixed systems of connections. The delta-Y step-up and Y-delta step-down connections are without question the best for high voltage transmission systems.

They are economical in cost, and provide a stable neutral whereby the high-voltage system may be directly grounded or grounded through resistance of such value as to damp the system critically and prevent the possibility of oscillation.

The Y-Y connection (or Y-connected autotransformer) may be used to interconnect two delta systems and provide suitable neutrals for grounding both of them. A Y-connected autotransformer may be used to interconnect two Y systems which already have neutral grounds, for reasons of economy.

In either case, a delta-connected tertiary winding is frequently provided for one or more of the following purposes. In stabilization of the neutral, if a Y-connected transformer (or autotransformer) with a delta connected tertiary is connected to an ungrounded delta system (or poorly grounded Y system), stability of the system neutral is increased.

That is, a single-phase short-circuit to ground on the transmission line will cause less drop in voltage on the short-circuited phase and less rise in voltage on the other two phases. A 3-phase three-leg Y-connected transformer without delta tertiary furnishes very little stabilization of the neutral, and the delta tertiary is generally needed.

Other Y connections offer no stabilization of the neutral without a delta tertiary. With increased neutral stabilization, the fault current in the neutral on single-phase short circuit is increased, and this may be needed for improved relay protection of the system.

Third-harmonic components of exciting current find a relatively low impedance path in a delta tertiary on a Y-connected transformer, and less of the third-harmonic exciting current appears in the connected transmission lines, where it might cause interference with communication circuits. Failure to provide a path for third-harmonic current in Y-connected 3-phase shell-type transformers or banks of single-phase transformers will result in excessive third-harmonic voltage from line to neutral.

The bank of a 3-phase, three-legged core-type Y-connected transformer acts as a delta winding with high impedance to the other windings. As a consequence, there is very little third-harmonic line-to-neutral voltage and a separate delta tertiary is not needed to reduce it. An external load can be supplied from a delta tertiary. This may include synchronous or static capacitors to improve system operating conditions.



Tap-changing equipment is sometimes used in a loop system, for phase-angle control, for the purpose of obtaining minimum losses in the loop due to unequal impedances in the various portions of the circuit.

Transformers used to derive phase-angle control do not differ materially, either mechanically or electrically, from those used for in phase control. In general, phase-angle control is obtained by interconnecting the phases, that is, by deriving a voltage from one phase and inserting it in another.

The simple arrangement given in figure below illustrates a single core delta-connected autotransformer in which the series windings are so interconnected as to introduce into the line a quadrature voltage.

One phase only is printed in solid lines so as to show more clearly how the quadrature voltage is obtained. The terminals of the common winding are connected to the midpoints of the series winding in order that the in phase voltage ratio between the primary lines ABC and secondary lines XYZ is unity for all values of phase angle introduced between them.

As large high-voltage systems have become extensively interconnected, a need has developed to control the transfer of real power between systems by means of phase-angle-regulating transformers.

The most commonly used circuit for this purpose is the two-core, four-winding arrangement. The high-voltage common winding is Y-connected, with reduced insulation at the neutral for economy of design, and a series transformer is employed so that low-voltage-switching equipment may be used.

Phase-shifting regulating transformers; single core delta-connected common winding for low-voltage systems.



Below shows the voltage relations across an autotransformer and switching contacts during a tap changing cycle using an autotransformer designed for 60% circulating current and with 100% load current at 80% power factor flowing through it.

Perfect interlacing between the autotransformer halves is assumed, and the voltage drop due to resistance of the autotransformer winding is neglected.

A study of the figure will disclose the fact that increasing the magnetizing reactance of the autotransformer to reduce the circulating current will

1. Increase the voltage across the full autotransformer winding
2. Increase the voltage to be ruptured
3. Introduce undue voltage fluctuations in the line

Since B-4 and B-3 represent the voltages appearing across the arcing contacts when the bridging position is opened at A and B, the voltage rupturing duty will increase with

1. Increase in voltage between adjacent taps
2. Increase in load
3. Decrease in power factor of the load
4. Decrease in the magnetizing current for which the autotransformer is designed

Vector relations for bridging position AB—voltage across adjacent taps; A-1 and A-2— reactance volts due to load current in only half the autotransformer winding; A-3 and A-4—induced voltage across full auto transformer winding; B-4— voltage ruptured when bridging position is ruptured
at A; B-3—voltage ruptured when bridging position is ruptured at B.



Three factors must be considered in the evaluation of the dielectric capability of an insulation structures —the voltage distribution must be calculated between different parts of the winding, the dielectric stresses are then calculated knowing the voltages and the geometry, and finally the actual stresses can be compared with breakdown or design stresses to determine the design margin.

Voltage distributions are linear when the flux in the core is established. This occurs during all power frequency test and operating conditions and to a great extent under switching impulse conditions (Switching impulse waves have front times in the order of tens to hundreds of microseconds and tails in excess of 1000 μs.)

These conditions tend to stress the major insulation and not inside of the winding. For shorter-duration impulses, such as full-wave, chopped-wave, or front-wave, the voltage does not divide linearly within the winding and must be determined by calculation or low voltage measurement. The initial distribution is determined by the capacitative network of the winding.

For disk and helical windings, the capacitance to ground is usually much greater than the series capacitance through the winding. Under impulse conditions, most of the capacitive current flows through the capacitance to ground near the end of the winding, creating a large voltage drop across the line end portion of the coil.

The capacitance network for shell form and layer-wound core form results in a more uniform initial distribution because they use electrostatic shields on both terminals of the coil to increase the ratio between the series and to ground capacitances.

Static shields are commonly used in disk windings to prevent excessive concentrations of voltages on the line-end turns by increasing the effective series capacitance within the coil, especially in the line end sections.

Interleaving turns and introducing floating metal shields are two other techniques that are commonly used to increase the series capacitance of the coil.

Following the initial period, electrical oscillations occur within the windings. These oscillations impose greater stresses from the middle parts of the windings to ground for long-duration waves than for short-duration waves.

Very fast impulses, such as steep chopped waves, impose the greatest stresses between turns and coil portions. Note that switching impulse transient voltages are two types— asperiodic and oscillatory. Unlike the asperiodic waves discussed earlier, the oscillatory waves can excite winding natural frequencies and produce stresses of concern in the internal winding insulation.

Transformer windings that have low natural frequencies are the most vulnerable because internal damping is more effective at high frequencies. Dielectric stresses existing within the insulation structure are determined using direct calculation (for basic geometries), analog modeling, or most recently, sophisticated finite-element computer programs.

Allowable stresses are determined from experience, model tests, or published data. For liquidinsulated transformers, insulation strength is greatly affected by contamination and moisture. The relatively porous and hygroscopic paper-based insulation must be carefully dried and vacuum impregnated with oil to remove moisture and gas to obtain the required high dielectric strength and to resist deterioration at operating temperatures.

Gas pockets or bubbles in the insulation are particularly destructive to the insulation because the gas (usually air) not only has a low dielectric constant (about 1.0), which means that it will be stressed more highly than the other insulation, but also air has a low dielectric strength.

High-voltage dc stresses may be imposed on certain transformers used in terminal equipment for dc transmission lines. Direct-current voltage applied to a composite insulation structure divides between individual components in proportion to the resistivities of the material.

In general the resistivity of an insulating material is not a constant but varies over a range of 100:1 or more, depending on temperature, dryness, contamination, and stress. Insulation design of high-voltage dc transformers in particular require extreme care.



The core loss (no-load loss) of a power transformer may be obtained from an empirical design curve of watts per pound of core steel (Fig. below). Such curves are established by plotting data obtained from transformers of similar construction.

The basic loss level is determined by the grade of core steel used and is further influenced by the number and type of joints employed in construction of the core. Figure 10-1 applies for 9-mil-thick M 3-grade steel in a single-phase core with 45” mitered joints.

Loss for the same grade of steel in a 3-phase core would usually be 5% to 10% higher. Exciting current for a power transformer may be established from a similar empirical curve of exciting volt-amperes per pound of core steel.

The steel grade and core construction are the same as for Fig. 10-1. The exciting current characteristic is influenced primarily by the number, type, and quality of the core joints, and only secondarily by the grade of steel.

Because of the more complex joints in the 3-phase core, the exciting volt-amperes will be approximately 50% higher than for the single-phase core. The exciting current of a transformer contains many harmonic components because of the greatly varying permeability of the steel.
For most purposes, it is satisfactory to neglect the harmonics and assume a sinusoidal exciting current of the same effective value. This current may be regarded as composed of a core-loss component in phase with the induced voltage (90DEG ahead of the flux) and a magnetizing component in phase with the flux.

Sometimes it is necessary to consider the harmonics of exciting current to avoid inductive interference with communication circuits. The harmonic content of the exciting current increases as the peak flux density is increased.

Performance can be predicted by comparison with test data from previous designs using similar core steel and similar construction. The largest harmonic component of the exciting current is the third.

Higher-order harmonics are progressively smaller. For balanced 3-phase transformer banks, the third harmonic components



The effects of harmonics on transformers are

• Increased copper losses
• Increased iron losses
• Possibly resonance between transformers
• windings and line capacitance
• Insulation stress
• Neutral overheating due to triplen harmonics

The copper losses and iron losses in the presence of harmonics can be computed. The application
of general equations assumes that the transformer is a linear device which it is not. However, for normal, operating conditions and normal levels of harmonics, this is a reasonable approximation.

However, the increase of hysteresis losses due to harmonics is only a fraction of the eddy current losses. Voltage harmonics result in higher transformer voltage, therefore higher insulation stress. This is not a problem since most transformers are insulated for much higher voltage levels than the overvoltages due to usual levels of harmonics.

There is a certain degree of interaction between voltage and current harmonics for transformers designed to operate near the saturation point (knee of the saturation curve). It is possible a small level of voltage harmonic to generate a high level of current harmonics. This phenomenon depends on specific harmonic and phase relationship to the fundamental.

To address the overheating of transformers due to harmonics, the ANSI/IEEE published a standard C57.110-1998, “Recommended practice for establishing transformer capability when supplying nonsinusoidal load currents,” which was reaffirmed in 2004. This standard establishes methods for determining derating factors for transformer capability to carry nonsinusoidal load currents.

In 1990, Underwriters Laboratory (UL) established the method for testing transformers that serve nonlinear loads. The UL test addresses coil heating due to nonlinear loads and overheating of the neutral conductor by assigning a “K“ factor to the transformer. The K-factor is meant to apply to transformers serving general nonlinear loads. UL has devised the K-factor method for labeling and rating the ability of dry-type transformers to withstand the effects of harmonics.

The K-factor rating indicates the transformer’s ability to tolerate the additional heating caused by harmonics. The K-factor is based on the methodology similar to that discussed in the ANSI/IEEE C57.110 standard. The K-factor can be calculated as the sum of the product of each harmonic current squared and that harmonic number squared for all harmonics from the fundamental to the highest harmonic of consequence.

When K-factor is multiplied by the stray losses of the transformer, the result represents the total stray losses in the transformer caused by harmonic currents. To obtain the total load losses, the total stray losses are then added to the load losses. It should be obvious that the K-factor for linear loads (absence of harmonics) is 1.

Also, the K-factor does not mean that the transformer can eliminate harmonics. Harmonics increase heating losses in all transformers, and some of these losses are deep within the core and windings and some are closer to the surface. Oil-filled transformers react differently to the increased heat and are better able to cool whereas dry-type transformers are more susceptible to the harmonic current effects and are so labeled. The UL test addresses coil heating due to nonlinear loads and overheating of the neutral conductor.
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