Editing Transformer (section)

===Energy losses===
Transformer energy losses are dominated by winding and core losses. Transformers' efficiency tends to improve with increasing transformer capacity.<ref name="De Keulenaer2001">{{harvnb|De Keulenaer|Chapman|Fassbinder|McDermott|2001|}}</ref> The efficiency of typical distribution transformers is between about 98 and 99 percent.<ref name="De Keulenaer2001"/><ref>{{Cite book| last1 = Kubo| first1 = T.|last2 = Sachs| first2 = H.| last3 = Nadel| first3 = S.| title = Opportunities for New Appliance and Equipment Efficiency Standards| publisher = [[American Council for an Energy-Efficient Economy]] | at = p. 39, fig. 1| year = 2001|url=http://www.aceee.org/research-report/a016| access-date = June 21, 2009}}</ref>

As transformer losses vary with load, it is often useful to tabulate [[no-load loss]], full-load loss, half-load loss, and so on. Hysteresis and [[eddy current]] losses are constant at all load levels and dominate at no load, while winding loss increases as load increases. The no-load loss can be significant, so that even an idle transformer constitutes a drain on the electrical supply. Designing [[energy efficient transformer]]s for lower loss requires a larger core, good-quality [[Electrical steel|silicon steel]], or even [[Electrical steel#Amorphous steel|amorphous steel]] for the core and thicker wire, increasing initial cost. The choice of construction represents a [[trade-off]] between initial cost and operating cost.<ref name="Heathcote1998-41">{{harvnb|Heathcote|1998|pp=41–42}}</ref>

Transformer losses arise from:
; Winding joule losses
:Current flowing through a winding's conductor causes [[joule heating]] due to the [[electrical resistance|resistance]] of the wire. As frequency increases, skin effect and [[proximity effect (electromagnetism)|proximity effect]] causes the winding's resistance and, hence, losses to increase.
;[[magnetic core#Core loss|Core losses]]
:; Hysteresis losses
::Each time the magnetic field is reversed, a small amount of energy is lost due to [[Magnetic hysteresis|hysteresis]] within the core, caused by motion of the [[magnetic domain]]s within the steel. According to Steinmetz's formula, the heat energy due to hysteresis is given by
:::<math>W_\text{h}\approx\eta\beta^{1.6}_{\text{max}}</math> and,
::hysteresis loss is thus given by
:::<math>P_\text{h}\approx{W}_\text{h}f\approx\eta{f}\beta^{1.6}_{\text{max}}</math>
::where, ''f'' is the frequency, ''η'' is the hysteresis coefficient and ''β''<sub>max</sub> is the maximum flux density, the empirical exponent of which varies from about 1.4 to 1.8 but is often given as 1.6 for iron.<ref name="Heathcote1998-41"/> For more detailed analysis, see [[Magnetic core#Core losses|Magnetic core]] and [[Steinmetz's equation]].
:; Eddy current losses
:: [[Eddy current]]s are induced in the conductive metal transformer core by the changing magnetic field, and this current flowing through the resistance of the iron dissipates energy as heat in the core. The eddy current loss is a complex function of the square of supply frequency and inverse square of the material thickness.<ref name="Heathcote1998-41"/> Eddy current losses can be reduced by making the core of a stack of laminations (thin plates) electrically insulated from each other, rather than a solid block; all transformers operating at low frequencies use laminated or similar cores.
; Magnetostriction related transformer hum
: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 as [[magnetostriction]], the frictional energy of which produces an audible noise known as [[mains hum]] or "transformer hum".<ref name="PF (nd)">{{cite web|title=Understanding Transformer Noise|url=http://www.federalpacific.com/literature/drytrans/10transformernoise.pdf|publisher=FP|access-date=30 January 2013|url-status=dead|archive-url=https://web.archive.org/web/20060510231426/http://www.federalpacific.com/literature/drytrans/10transformernoise.pdf|archive-date=10 May 2006}}</ref> This transformer hum is especially objectionable in transformers supplied at [[utility frequency|power frequencies]] and in [[high-frequency]] [[flyback transformer]]s associated with television [[cathode-ray tube|CRTs]].
; {{anchor|stray}} Stray losses
:Leakage inductance is by itself largely 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.<ref name="nailen">{{Cite journal| last = Nailen| first = Richard| title = Why We Must Be Concerned With Transformers| journal = Electrical Apparatus| date = May 2005|url=http://www.blnz.com/news/2008/04/23/must_concerned_with_transformers_9639.html| url-status = dead| archive-url=https://web.archive.org/web/20090429031651/http://www.blnz.com/news/2008/04/23/must_concerned_with_transformers_9639.html| archive-date = 2009-04-29}}</ref>
; Radiative
:There are also radiative losses due to the oscillating magnetic field but these are usually small.
;Mechanical vibration and audible noise transmission
:In addition to magnetostriction, the alternating magnetic field causes fluctuating forces between the primary and secondary windings. This energy incites vibration transmission in interconnected metalwork, thus amplifying audible transformer hum.<ref name="Pansini1999-23">{{harvnb|Pansini|1999|p=23}}</ref>