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Leakage flux

Leakage flux of a transformer

Main article:Leakage inductance

The ideal transformer model assumes that all flux generated by the primary winding links all the turns of every winding, including itself. In practice, some flux traverses paths that take it outside the windings.[17]Such flux is termedleakage flux, and results inleakage inductanceinserieswith the mutually coupled transformer windings.[16]Leakage results in energy being alternately stored in and discharged from themagnetic fieldswith each cycle of the power supply. It is not directly a power loss (see"Stray losses"below), but results in inferiorvoltage regulation, causing the secondary voltage to fail to be directly proportional to the primary, particularly under heavy load.[17]Transformers are therefore normally designed to have very lowleakage inductance.

However, in some applications, leakage can be a desirable property, and long magnetic paths, air gaps, or magnetic bypass shunts may be deliberately introduced to a transformer's design to limit theshort-circuitcurrent it will supply.[16]Leaky transformers may be used to supply loads that exhibitnegative resistance, such aselectric arcs,mercury vapor lamps, andneon signs; or for safely handling loads that become periodically short-circuited such aselectric arc welders.[18]Air gaps are also used to keep a transformer from saturating, especially audio-frequency transformers in circuits that have a direct current flowing through the windings.

Effect of frequency

The time-derivative term inFaraday's Lawshows that the flux in the core is theintegralof the applied voltage Hypothetically an ideal transformer would work with direct-current excitation, with the core flux increasing linearly with time. In practice, the flux would rise to the point wheremagnetic saturationof the core occurred, causing a huge increase in the magnetizing current and overheating the transformer. All practical transformers must therefore operate with alternating (or pulsed) current.[

Transformer universal EMF equation

If the flux in the core issinusoidal, the relationship for either winding between itsrmsVoltage of the windingE, and the supply frequencyf, number of turnsN, core cross-sectional areaaand peakmagnetic flux densityBis given by the universal EMF equation:

The EMF of a transformer at a given flux density increases with frequency.[By operating at higher frequencies, transformers can be physically more compact because a given core is able to transfer more power without reaching saturation, and fewer turns are needed to achieve the same impedance. However properties such as core loss and conductorskin effectalso increase with frequency. Aircraft and military equipment employ 400 Hz power supplies which reduce core and winding weight

Operation of a transformer at its designed voltage but at a higher frequency than intended will lead to reduced magnetizing current; at lower frequency, the magnetizing current will increase. Operation of a transformer at other than its design frequency may require assessment of voltages, losses, and cooling to establish if safe operation is practical. For example, transformers may need to be equipped with "volts per hertz" over-excitationrelaysto protect the transformer from overvoltage at higher than rated frequency.

Knowledge of natural frequencies of transformer windings is of importance for the determination of the transient response of the windings to impulse and switching surge voltages.

Energy losses

An ideal transformer would have no energy losses, and would be 100% efficient. In practical transformers energy is dissipated in the windings, core, and surrounding structures. Larger transformers are generally more efficient, and those rated for electricity distribution usually perform better than 98%.[22]

Experimental transformers usingsuperconductingwindings achieving efficiencies of 99.85%, While the increase in efficiency is small, when applied to large heavily-loaded transformers the annual savings in energy losses are significant.

A small transformer, such as a plug-in"wall-wart" or power adaptertype used for low-power consumer electronics, may be no more than 85% efficient, with considerable loss even when not supplying any load. Though individual power loss is small, the aggregate losses from the very large number of such devices is coming under increased scrutiny.

The losses vary with load current, and may be expressed as "no-load" or "full-load" loss. Windingresistancedominates load losses, whereashysteresisandeddy currentslosses contribute to over 99% of the no-load loss. The no-load loss can be significant, meaning that even an idle transformer constitutes a drain on an electrical supply, which encourages development of low-loss transformers (also seeenergy efficient transformer).

Transformer losses are divided into losses in the windings, termedcopper loss, and those in the magnetic circuit, termediron loss. Losses in the transformer arise from:

Winding resistance

Current flowing through the windings causesresistive heatingof the conductors. At higher frequencies,skin effectandproximity effectcreate additional winding resistance and losses.

Hysteresis losses

Each time the magnetic field is reversed, a small amount of energy is lost due tohysteresiswithin the core. For a given core material, the loss is proportional to the frequency, and is a function of the peak flux density to which it is subjected

Eddy currents

Ferromagneticmaterials are also goodconductors, and a solid core made from such a material also constitutes a single short-circuited turn throughout its entire length.Eddy currentstherefore circulate within the core in a plane normal to the flux, and are responsible forresistive heatingof the core material. The eddy current loss is a complex function of the square of supply frequency and inverse square of the material thickness

Magnetostriction

Magnetic flux in a ferromagnetic material, such as the core, causes it to physically expand and contract slightly with each cycle of the magnetic field, an effect known asmagnetostriction. This produces the buzzing sound commonly associated with transformers and in turn causes losses due to frictional heating in susceptible cores.

Mechanical losses

In addition to magnetostriction, the alternating magnetic field causes fluctuating electromagnetic forces between the primary and secondary windings. These incite vibrations within nearby metalwork, adding to thebuzzing noise, and consuming a small amount of power

Stray losses

Leakage inductance is by itself lossless, since energy supplied to its magnetic fields is returned to the supply with the next half-cycle. However, any leakage flux that intercepts nearby conductive materials such as the transformer's support structure will give rise to eddy currents and be converted to heat.

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