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| {{two other uses|the electrical device|the media and toy franchise|Transformers}}
| | Winnifred may be the name people use to call her though she doesn't really love being called like which. What I love doing is canoeing but Dislike have time lately. Debt collecting is her profession for any time but her promotion never comes. Puerto Rico is since it is place I've been residing about. See what's new on his website here: http://haarausfallstoppen.bloggg.org<br><br> |
| [[File:Polemount-singlephase-closeup.jpg|thumb|right|Pole-mounted [[distribution transformer]] with [[center tap|center-tapped]] secondary winding used to provide '[[Split-phase electric power|split-phase]]' power for residential and light commercial service, which in North America is typically rated 120/240 volt.<ref name="Knowlton (1949)">{{cite book|last=Knowlton|first=A.E. (Ed.)|title=Standard Handbook for Electrical Engineers|edition=8th|year=1949|publisher=McGraw-Hill|page=597, Fig. 6–42}}</ref><ref name="Mack (2006)">{{cite book|last=Mack|first=James E.|coauthors=Shoemaker, Thomas|booktitle=The Lineman's and Cableman's Handbook|title=Chapter 15 - Distribution Transformers|year=2006|publisher=McGraw-Hill|location=New York|isbn=0071467890|pages=15–1 to 15–22|url=http://books.mcgraw-hill.com/downloads/products/0071467890/0071467890_ch15.pdf|edition=11th}}</ref>]]
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| A '''transformer''' is generally a four-terminal device that is capable of transforming an [[alternating current]] (AC) input voltage into a relatively higher or lower AC output voltage. A transformer usually consists of two closely coupled coils that are designed to transfer energy by [[inductive coupling]] between its winding circuits. A typical transformer has two or more coils that share a common laminated [[magnetic core|iron core]]. One of the coils is referred to as the ''primary'' (containing N<sub>p</sub> turns), while the other coil is called the ''secondary'' (containing N<sub>S</sub> turns). Primary coils are defined as those coils whose current is driven by an external alternating-current source, whereas secondary coils are defined as those coils whose voltage is induced by the varying magnetic field produced by the primary coil. The voltage applied to the primary coil is simply equal to the voltage applied to the secondary coil multiplied by the ratio of the number of turns of primary coil to that of secondary coil.
| | Also visit my web blog ... [http://haarausfallstoppen.bloggg.org für haarwachstum] |
| {{TOC limit|limit=4}}
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| ==Simplified operation==
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| When fluctuating [[electric current|current]] flows through the ''primary'' winding (or coil) of a transformer, a varying [[magnetic flux]] is induced in the transformer's [[Magnetic core|core]], which generates a varying magnetic flux through the ''secondary'' winding. This varying magnetic flux [[electromagnetic induction|induces]] a varying [[electromotive force|electromotive force (emf)]] or [[voltage]] in the secondary winding, which in turn produces a current through the secondary winding. Thus, a transformer is not designed to raise or lower [[direct current]] (DC) voltages, for the reason that a 'steady' (DC) current is incapable of transferring (or inducing) a current into the secondary winding.
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| ==Invention==
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| The invention of transformers during the late 1800s allowed for longer-distance, cheaper, and more energy efficient [[electric power transmission|transmission]], [[electric power distribution|distribution]], and utilization of [[electric power|electrical energy]]. In the early days of commercial electric power, the main energy source was direct current (DC), which operates at low-voltage high-current. According to [[Joule's Law]], energy losses are directly proportional to the square of current. This law revealed that even a tiny decrease in current or rise in voltage can cause a substantial lowering in energy loses and costs. Thus, the historical pursuit for a high-voltage low-current electricity transmission system took shape. Although high voltage transmission systems offered many benefits, the future fate of high-voltage alternating current still remained unclear for several reasons: high-voltage sources had a much higher risk of causing severe electrical injuries; many essential appliances could only function at low voltage. Regarded as one of the most influential electrical innovations of all time, the introduction of transformers had successfully reduced the safety concerns associated with alternating current and had the ability to lower voltage to a value that was required by most essential appliances. <ref name=hughes>{{cite book |url=http://books.google.com/?id=g07Q9M4agp4C&pg=PA122&lpg=PA122&dq=westinghouse+%22universal+system%22|pages=119–122|author=Thomas P. Hughes|title=Networks of Power: Electrification in Western Society, 1880–1930|publisher=Johns Hopkins University Press|location=Baltimore|isbn=0-8018-4614-5 |year=1993|authorlink=Thomas P. Hughes}}</ref>
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| Transformers are highly beneficial for three fundamental reasons: [[voltage converter|voltage conversion]]; [[Isolation transformer|isolation protection]]; and [[impedance matching]]. In terms of voltage conversion, transformers can step-up voltage/step-down current from generators to high-voltage transmission lines, and step-down voltage/step-up current to local distribution circuits or industrial customers. The step-up transformer is used to increase the secondary voltage relative to the primary voltage, whereas the step-down transformer is used to decrease the secondary voltage relative to the primary voltage. Transformers range in size from thumbnail-sized used in microphones to units weighing hundreds of tons interconnecting the [[power grid]]. A broad range of [[transformer types|transformer designs]] are used in electronic and electric power applications, including miniature, audio, isolation, high-frequency, power conversion transformers, etc.
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| ==Basic principles==
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| ===The ideal transformer===
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| [[Image:TR Ideal.jpg|thumb|280px|right|Ideal transformer circuit diagram]]
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| The ideal condition assumptions are:
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| * The windings of the transformer have negligible resistance, so R<sub>P</sub>= R<sub>S</sub>= 0, where R<sub>P</sub> represents the resistance of the primary winding and R<sub>S</sub> represents the resistance of the secondary winding. Thus, there is no [[copper loss]] in the winding, and hence no voltage drop.
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| * Flux is confined within the [[Magnetic core|core]]. Therefore, it is the same [[flux]] that links both the windings.
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| * Permeability of the core is infinitely high which implies that zero mmf (current) is required to set up the flux and that the flux in the core due to the primary winding must be equal and opposite to the flux due to the secondary winding.
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| * The core does not incur any [[Magnetic core#Core loss|hysteresis]] or [[Magnetic core#Core loss|eddy current loss]]. Hence, no core losses.
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| If the secondary is an open circuit, an ideal transformer will not allow the flow of primary current.
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| Consider the ideal, lossless, perfectly-coupled transformer shown in the circuit diagram at right having primary and secondary windings with N<sub>P</sub> and N<sub>S</sub> turns, respectively.
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| The ideal transformer induces secondary voltage ''E''<sub>S</sub> =''V''<sub>S</sub> as a proportion of the primary voltage ''V''<sub>P</sub> = ''E''<sub>P</sub> and respective winding turns as given by the equation
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| :<math>
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| \frac{V_\text{P}}{V_{\text{S}}} = \frac{E_\text{P}}{E_\text{S}} = \frac{N_\text{P}}{N_\text{S}}
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| =a</math>,
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| where,
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| :- ''V''<sub>P</sub>/''V''<sub>S</sub> = ''E''<sub>P</sub>/''E''<sub>S</sub> = a is the ''voltage ratio'' and ''N''<sub>P</sub>/''N''<sub>S</sub> = a is the winding ''turns ratio'', the value of these ratios being respectively higher and lower than unity for step-down and step-up transformers,.<ref name="Winders (2002)">{{cite book| last = Winders| first = John J., Jr.| title = Power Transformer Principles and Applications| pages = 20–21| year = 2002| publisher = CRC}}</ref><ref name="Hameyer *2001)">{{cite conference|last=Hameyer|first=Kay|title= §3.2 'Definition of Transformer Ratio' in Section 3 - Transformers|booktitle=Electrical Machines I: Basics, Design, Function, Operation|publisher=RWTH Aachen University Institute of Electrical Machines|year=2001|page=27}}</ref>{{efn|"The turn ratio of a transformer is the ratio of the number of turns in the high-voltage winding to that in the low-voltage winding",<ref>Knowlton, §6-13, p. 552</ref> common usage having evolved over time from 'turn ratio' to 'turns ratio',}}{{efn|A step-down transformer converts a high voltage to a lower voltage while a step-up transformer converts a low voltage to a higher voltage, an [[isolation transformer]] having 1:1 turns ratio with output voltage the same as input voltage.}}
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| :- ''V''<sub>P</sub> designates source impressed voltage,
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| :- ''V''<sub>S</sub> designates output voltage, and,
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| :- ''E''<sub>P</sub> & ''E''<sub>S</sub> designate respective emf induced voltages.{{efn|As each ideal transformer winding's impressed voltage equals its induced voltage, induced voltages are omitted for clarity in the next four equations.}}
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| According to the equation shown above, when the number of turns in the primary coil is greater than the number of turns in the secondary coil, the secondary voltage must be less than the primary voltage. On the other hand, when the number of turns in the primary coil is less than the number of turns in the secondary, the secondary voltage must be greater than the primary voltage.
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| Any [[impedance (electrical)|load impedance]] <math>Z_L</math> connected to the ideal transformer's secondary winding causes current to flow without losses from primary to secondary circuits, the resulting input and output [[volt-ampere|apparent power]] therefore being equal as given by the equation
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| :<math>
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| I_P \times V_P = I_S \times V_S
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| </math>.
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| Combining the two equations yields the following ideal transformer identity
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| :<math>
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| \frac{V_P}{V_S} = \frac{I_S}{I_P} = \frac{N_P}{N_S}=a</math>.
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| This formula is a reasonable approximation for the typical commercial transformer, with voltage ratio and winding turns ratio both being inversely proportional to the corresponding current ratio.
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| The load impedance <math>Z_L</math> is defined in terms of secondary circuit voltage and current as follows
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| :<math>Z_L = \frac{V_L}{I_L}=\frac{V_S}{I_S}</math>.
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| The apparent impedance <math>Z_L^\prime</math> of this secondary circuit load ''referred'' to the primary winding circuit is governed by a squared turns ratio multiplication factor relationship derived as follows<ref name="flanagan_p2.1"/><ref name="Tcheslavski (2008)">{{cite conference|last=Tcheslavski|first=Gleb V.|title=Slide 13 Impedance Transformation in Lecture 4: Transformers|accessdate=17 April 2013|booktitle=ELEN 3441 Fundamentals of Power Engineering|publisher=Lamar University (TSU system member)|year=2008}}</ref>
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| :<math>Z_L^\prime=\frac{V_P}{I_P}=\frac{aV_S}{I_S/a}=a^2\times\frac{V_S}{I_S}=a^2\times{Z_L}</math>.
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| For an ideal transformer, the power supplied in the primary and the power dissipated by the load are both equal to the following equation:<ref name="The World of Physics">{{Cite web
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| |title= The World of Physics
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| |publisher= [Thomas Nelson and Sons Ltd]
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| |author= John Avison
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| |year= 1989
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| |pages= 300–320
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| }}</ref><ref name="New Understanding: Physics for Advanced Level">{{Cite web
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| |title= New Understanding: Physics for Advanced Level (4th Edition)
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| |publisher= [Stanley Thornes (Publishers) Ltd]
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| |author= Jim Breithaupt
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| |year= 2000
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| |pages= 300–320
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| }}</ref>
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| :<math>
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| P = \frac{V^2_{\text{S}}}{R_{\text{L}}} = \frac{{N^2_{\text{S}}}{V^2_{\text{p}}}}{{N^2_{\text{p}}}{R_{\text{L}}}}
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| </math>
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| The primary current is equal to the following equation:<ref name="The World of Physics" /><ref name="New Understanding: Physics for Advanced Level" />
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| :<math>
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| I_{\text{p}} = \frac{P_{\text{R}}}{V_{p}} = \frac{{N^2_{\text{S}}}{V_{\text{p}}}}{{N^2_{\text{p}}}{R_{\text{L}}}}
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| </math>
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| The equivalent resistance on the source from the load sections and transformer is equal to the following equation:<ref name="The World of Physics" /><ref name="New Understanding: Physics for Advanced Level" />
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| :<math>
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| R_{\text{eq}} = \frac{V_{\text{p}}}{I_{\text{p}}} = \left(\frac{N_{\text{p}}}{N_{\text{S}}}\right)^2 {R_{\text{L}}}
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| </math>
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| ====Induction law====
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| The transformer is based on two principles: first, that an electric current can produce a [[magnetic field]] and second that a changing magnetic field within a coil of wire induces a voltage across the ends of the coil (electromagnetic induction). Changing the current in the primary coil changes the magnetic flux that is developed. The changing magnetic flux induces a voltage in the secondary coil.
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| Referring to the two figures here, current passing through the primary coil creates a magnetic field. The primary and secondary coils are wrapped around a core of very high [[Permeability (electromagnetism)|magnetic permeability]], usually [[iron]],{{efn|Transformer winding coils are usually wound around [[Magnetic core|ferromagnetic core]]s but can also be [[Transformer#Cores|air-core]] wound.}} so that most of the magnetic flux passes through both the primary and secondary coils. Any secondary winding connected load causes current and voltage induction from primary to secondary circuits in indicated directions.
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| {{clear}}
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| [[Image:Transformer3d col3.svg|thumb|400px|Ideal transformer and induction law]]
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| The voltage induced across the secondary coil may be calculated from Faraday's law of induction, which states that:
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| :<math>
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| V_\text{S} = E_\text{S} = N_\text{S} \frac{\mathrm{d}\Phi}{\mathrm{d}t}.
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| </math>
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| where ''V''<sub>s</sub> = ''E''<sub>s</sub> is the instantaneous voltage, ''N''<sub>s</sub> is the number of turns in the secondary coil, and dΦ/dt is the [[derivative]]{{efn|The expression dΦ/dt, defined as the derivative of magnetic flux Φ with time t, provides a measure of rate of magnetic flux in the core and hence of emf induced in the respective winding.}} of the magnetic flux Φ through one turn of the coil. If the turns of the coil are oriented perpendicularly to the magnetic field lines, the flux is the product of the [[magnetic flux density]] ''B'' and the area ''A'' through which it cuts. The area is constant, being equal to the cross-sectional area of the transformer core, whereas the magnetic field varies with time according to the excitation of the primary. Since the same magnetic flux passes through both the primary and secondary coils in an ideal transformer,<ref name="flanagan_p2.1">{{cite book|last=Flanagan|first=William M.|title=Handbook of Transformer Design & Applications|year=1993|publisher=McGraw-Hill|isbn=0-07-021291-0|edition=2nd|pages=1–2}}</ref> the instantaneous voltage across the primary winding equals
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| :<math>
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| V_\text{P} = E_\text{P} = N_\text{P} \frac{\mathrm{d}\Phi}{\mathrm{d}t}.
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| </math>
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| Taking the ratio of the above two equations gives the same voltage ratio and turns ratio relationship shown above, that is,
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| :<math>\frac{V_\text{P}}{V_\text{S}} = \frac{E_\text{P}}{E_\text{S}} = \frac{N_\text{P}}{N_\text{S}}=a</math>.
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| The changing magnetic field induces an emf across each winding.<ref name="Heathcote (1998)">{{cite book| last = Heathcote| first = Martin| title = J & P Transformer Book| edition = 12th| pages = 2–3| isbn = 0-7506-1158-8| publisher = Newnes| date = Nov 3, 1998}}</ref> The primary emf, acting as it does in opposition to the primary voltage, is sometimes termed the [[Counter-electromotive force|counter emf]].<ref name="calvert">{{cite web| last = Calvert| first = James| title = Inside Transformers| publisher = University of Denver| year = 2001| url = http://www.du.edu/~jcalvert/tech/transfor.htm| accessdate = May 19, 2007}}</ref> This is in accordance with [[Lenz's law]], which states that induction of emf always opposes development of any such change in magnetic field.
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| As still lossless and perfectly-coupled, the transformer still behaves as described above in [[transformer#The ideal transformer|the ideal transformer]].
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| ====Polarity====
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| [[File:Instrument Transformer.jpg|thumb|180px|Instrument transformer, with polarity dot and X1 markings on LV side terminal]]
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| A [[dot convention]] is often used in transformer circuit diagrams, nameplates or terminal markings to define the relative polarity of transformer windings. Positively-increasing instantaneous current entering the primary winding's dot end induces positive polarity voltage at the secondary winding's dot end.<ref name="Ula (2005)">{{cite conference|last=Parker|first=M. R|coauthors=Ula, S.; Webb, W. E.|editor-first=Jerry C.|editor-last=Whitaker|booktitle=The Electronics Handbook|title=§2.5.5 'Transformers' & §10.1.3 'The Ideal Transformer'|year=2005|publisher=Taylor & Francis|isbn=0-8493-1889-0|pages=172, 1017|url=http://books.google.ca/books?id=FdSQSAC3_EwC&pg=PA1017&lpg=PA1017&dq=transformer+polarity+dot+convention&source=bl&ots=V_ULeEEk6t&sig=SFYhwdztWIVTr1yK6hQc-LOKL44&hl=en&sa=X&ei=37E_Uf-DDsipqgHtpIHwBA&ved=0CEAQ6AEwAw#v=onepage&q=transformer%20polarity%20dot%20convention&f=false|edition=2nd}}</ref><ref name="Nagrath (2010)">{{cite book|coauthors=Nagrath, I.J.|first=D.P.|last= Kothari|title=§3.7 'Transformer Testing' in Chapter 3 - Transformers|year=2010|publisher=Tata McGraw-Hill|isbn=978-0-07-069967-0|page=73|url=http://books.google.com/?id=fR1rNJhBbmcC&pg=PA72&lpg=PA72&dq=dot+convention+polarity+of+transformer#v=onepage&q=dot%20convention%20polarity%20of%20transformer&f=false|edition=4th}}</ref><ref name="Brenner (1959)">{{cite conference|coauthors=Javid, Mansour|last=Brenner|first=Egon|title=§18.1 'Symbols and Polarity of Mutual Inductance' in Chapter 18 - Circuits with Magnetic Circuits|booktitle=Analysis of Electric Circuits|year=1959|publisher=McGraw-Hill|pages=589–590|url=http://books.google.ca/books/about/Analysis_of_electric_circuits.html?id=V4FrAAAAMAAJ&redir_esc=y}}</ref>{{efn|ANSI/IEEE C57.13, ANS Requirements for Instrument Transformers, defines polarity as the 'designation of the relative instantaneous directions of the currents entering the primary terminals and leaving the secondary terminals during most of each half cycle', the word 'instantaneous' differentiating from say phasor current.<ref name="Crompton (ND)">{{cite web|title=Polarity Markings on Instrument Transformers|url=http://www.cromptonusa.com/Polarity%20on%20Transformers.pdf|accessdate=13 April 2013}}</ref>}}{{efn|Transformer polarity can also be identified by terminal markings H0,H1,H2... on primary terminals and X1,X2, (and Y1,Y2, Z1,Z2,Z3... if windings are available) on secondary terminals. Each letter prefix designates a different winding and each numeral designates a termination or tap on each winding. The designated terminals H1,X1, (and Y1, Z1 if available) indicate same instantaneous polarities for each winding as in the dot convention.<ref name="GE Digital (ND)">{{cite web|title=Connections - Polarity|url=http://www.gedigitalenergy.com/products/buyersguide/ct_sc.pdf|accessdate=13 April 2013}}</ref>}}
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| ===The real transformer===
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| ====Real transformer deviations from ideal====
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| The ideal model neglects the following basic linear aspects in real transformers:
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| :Core losses collectively called magnetizing current losses consisting of:<ref name="Say (1984)"/>
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| :*Hysteresis losses due to nonlinear application of the voltage applied in the transformer core
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| :*Eddy current losses due to joule heating in core are proportional to the square of the transformer's applied voltage.
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| :Whereas the ideal windings have no impedance, the windings in a real transformer have finite non-zero impedances in the form of:
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| :*Joule losses due to resistance in the primary and secondary windings<ref name="Say (1984)">{{cite book| last = Say| first = M. G.| title = Alternating Current Machines| edition = 5th| isbn = 0-470-27451-4| publisher = Halsted Press| year = 1984}}</ref>
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| :*Leakage flux that escapes from the core and passes through one winding only resulting in primary and secondary reactive impedance.
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| Imagine that a source voltage is applied across the real transformer's primary terminals while the secondary terminals are open circuited. In order to make sense of these associations, the real transformer must be viewed as a simple inductor with an impedance as displayed in the equation below:
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| :<math>\ Z_P = j\omega {L_P}</math>
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| As a result, the primary current should be out of phase with the primary voltage by 90° such that the primary current is lagging the primary voltage. Moreover, the primary voltage should be out of phase with the induced voltage by 180º.
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| The real transformer's primary current can be determined by using the following equation:
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| :<math>
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| {I_{\text{P}}} = {{V_{\text{P}}}/{Z_{\text{P}}}}
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| </math>.
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| ====Leakage flux====
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| {{Main|Leakage inductance}}
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| [[Image:Transformer flux.gif|left|thumb|301px|Leakage flux of a transformer]]
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| 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.<ref name="mclaren">{{cite book
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| | last = McLaren | first = P. G.
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| | title = Elementary Electric Power and Machines
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| | pages = 68–74
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| | isbn = 0-13-257601-5
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| | year = 1984}}</ref> Such flux is termed ''leakage flux'', and results in [[leakage inductance]] in [[series and parallel circuits|series]] with the mutually coupled transformer windings.<ref name="calvert"/> Leakage flux results in energy being alternately stored in and discharged from the magnetic fields with each cycle of the power supply. It is not directly a power loss (see [[transformer#Stray losses|Stray losses]] below), but results in inferior [[voltage regulation]], causing the secondary voltage not to be directly proportional to the primary voltage, particularly under heavy load.<ref name="mclaren"/> Transformers are therefore normally designed to have very low leakage inductance. Nevertheless, it is impossible to eliminate all leakage flux because it plays an essential part in the operation of the transformer. The combined effect of the leakage flux and the electric field around the windings is what transfers energy from the primary to the secondary.<ref>{{cite conference|last=Edwards|first=J.|coauthors=Saha, T. K.|title=Power Flow in Transformers Via the Poynting Vector|booktitle=AUPEC 2000 Proceedings|url=http://www.itee.uq.edu.au/~aupec/aupec00/edwards00.pdf|year=2000|publisher=Queensland University of Technology}}</ref>
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| In some applications increased leakage is desired, and long magnetic paths, air gaps, or magnetic bypass shunts may deliberately be introduced in a transformer design to limit the [[Short circuit|short-circuit]] current it will supply.<ref name="calvert"/> Leaky transformers may be used to supply loads that exhibit [[negative resistance]], such as [[electric arc]]s, [[mercury vapor lamp]]s, and [[neon sign]]s or for safely handling loads that become periodically short-circuited such as [[arc welding|electric arc welders]].<ref name="Say, p. 485">Say, p. 485</ref>
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| Air gaps are also used to keep a transformer from saturating, especially audio-frequency transformers in circuits that have a DC component flowing in the windings.<ref>{{cite book|last=Terman|first=Frederick E.|title=Electronic and Radio Engineering| edition=4th |year=1955|publisher=McGraw-Hill|location=New York|pages=15}}</ref>
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| Knowledge of leakage inductance is also useful when transformers are operated in parallel. It can be shown that if the percent impedance (Z) and associated winding leakage reactance-to-resistance (X/R) ratio of two transformers were hypothetically exactly the same, the transformers would share power in proportion to their respective volt-ampere ratings (e.g. 500 [[Kilovolt-ampere|kVA]] unit in parallel with 1,000 kVA unit, the larger unit would carry twice the current). However, the impedance tolerances of commercial transformers are significant. Also, the Z impedance and X/R ratio of different capacity transformers tends to vary, corresponding 1,000 kVA and 500 kVA units' values being, to illustrate, respectively, Z ~ 5.75%, X/R ~ 3.75 and Z ~ 5%, X/R ~ 4.75.<ref name="Knowlton, p. 585-586">Knowlton, pp. 585-586</ref><ref name="Haymeyer (2001)">{{cite web|last=Haymeyer|year=2001|first=Kay|title=Electrical Machines I: Basics, Design, Function, Operation|publisher=RWTH Aachen University Institute of Electrical Machines|page=39}}</ref>
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| ====Equivalent circuit====
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| {{See also|Induction motor#Steinmetz equivalent circuit|l1=Steinmetz equivalent circuit}}
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| Referring to the diagram, a practical transformer's physical behavior may be represented by an [[equivalent circuit]] model, which can incorporate an ideal transformer.<ref name="daniels">{{cite book
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| | last=Daniels
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| | first= A. R.
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| | title=Introduction to Electrical Machines
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| | pages=47–49}}</ref>
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| Winding joule losses and leakage reactances are represented by the following series loop impedances of the model:
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| * Primary winding: ''R''<sub>P</sub>, ''X''<sub>P</sub>
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| * Secondary winding: ''R''<sub>S</sub>, ''X''<sub>S</sub>.
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| In normal course of circuit equivalence transformation, ''R''<sub>S</sub> and ''X''<sub>S</sub> are in practice usually referred to the primary side by multiplying these impedances by the turns ratio squared, (''N''<sub>P</sub>/''N''<sub>S</sub>)<sup> 2</sup> = a<sup>2</sup>.
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| [[Image:TREQCCT.jpg|thumb|500px|Real transformer equivalent circuit]]
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| Core loss and reactance is represented by the following shunt leg impedances of the model:
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| * Core or iron losses: ''R''<sub>C</sub>
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| * Magnetizing reactance: ''X''<sub>M</sub>.
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| ''R''<sub>C</sub> and ''X''<sub>M</sub> are collectively termed the ''magnetizing branch'' of the model.
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| Core losses are caused mostly by hysteresis and eddy current effects in the core and are proportional to the square of the core flux for operation at a given frequency.<ref name="Say, pp. 142–143">Say, pp. 142-143</ref> The finite permeability core requires a magnetizing current ''I''<sub>M</sub> to maintain mutual flux in the core. Magnetizing current is in phase with the flux, the relationship between the two being non-linear due to saturation effects. However, all impedances of the equivalent circuit shown are by definition linear and such non-linearity effects are not typically reflected in transformer equivalent circuits.<ref name="Say, pp. 142–143"/> With [[sinusoidal]] supply, core flux lags the induced emf by 90°. With open-circuited secondary winding, magnetizing branch current ''I''<sub>0</sub> equals transformer no-load current.<ref name="daniels"/>
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| | |
| The resulting model, though sometimes termed 'exact' equivalent circuit based on [[linearity]] assumptions, retains a number of approximations.<ref name="daniels"/> Analysis may be simplified by assuming that magnetizing branch impedance is relatively high and relocating the branch to the left of the primary impedances. This introduces error but allows combination of primary and referred secondary resistances and reactances by simple summation as two series impedances.
| |
| | |
| Transformer equivalent circuit impedance and transformer ratio parameters can be derived from the following tests: [[open circuit test|Open-circuit test]],{{efn|A standardized open-circuit or unloaded transformer test called the [[Epstein frame]] can also be used for the characterization of magnetic properties of soft magnetic materials including especially electrical steels.<ref>[http://webstore.iec.ch/webstore/webstore.nsf/mysearchajax?Openform&key=60404-2&sorting=&start=1&onglet=1 IEC Std 60404-2 Magnetic Materials - Part 2: Methods of Measurement of the Magnetic Properties . . .]</ref>}} [[short circuit test|short-circuit test]], winding resistance test, and transformer ratio test.
| |
| | |
| ==Basic transformer parameters and construction==
| |
| | |
| ===Effect of frequency===
| |
| <div style="float:right; padding:1em; margin:0 0 0 1em; width:300px; border:1px solid; background:ivory;">
| |
| {{anchor|Transformer universal emf equation}}
| |
| '''Transformer universal emf equation'''
| |
| | |
| If the flux in the core is purely [[sinusoidal]], the relationship for either winding between its '''[[root mean square|rms]] voltage''' ''E<sub>rms</sub>'' of the winding, and the supply frequency ''f'', number of turns ''N'', core cross-sectional area ''a'' in m<sup>2</sup> and peak magnetic flux density ''B<sub>peak</sub>'' in Wb/m<sup>2</sup> or T (tesla) is given by the universal emf equation:<ref name="Say (1984)"/>
| |
| | |
| <math> E_\text{rms} = {\frac {2 \pi f N a B_\text{peak}} {\sqrt{2}}} \! = 4.44 f N a B_{{peak}}</math>
| |
| | |
| If the flux does not contain even [[harmonics]] the following equation can be used for '''half-cycle average voltage''' ''E''<sub>avg</sub> of any waveshape:
| |
| | |
| <math> E_\text{avg}= 4 f N a B_\text{peak} \!</math>
| |
| </div>
| |
| The time-derivative term in Faraday's Law shows that the flux in the core is the [[integral]] with respect to time of the applied voltage.<ref name="dixon">{{Cite conference | first = Lloyd
| |
| | last = Dixon
| |
| | booktitle = Magnetics Design Handbook
| |
| | title = Power Transformer Design
| |
| | url = http://focus.ti.com/lit/ml/slup126/slup126.pdf
| |
| | year=2001
| |
| | publisher = Texas Instruments}}</ref> Hypothetically an ideal transformer would work with direct-current excitation, with the core flux increasing linearly with time.<ref name="billings">{{cite book
| |
| | last=Billings
| |
| | first=Keith
| |
| | title=Switchmode Power Supply Handbook
| |
| | publisher=McGraw-Hill
| |
| | year=1999
| |
| | isbn = 0-07-006719-8
| |
| }}</ref> In practice, the flux rises to the point where [[saturation (magnetic)|magnetic saturation]] of the core occurs, causing a large increase in the magnetizing current and overheating the transformer. All practical transformers must therefore operate with alternating (or pulsed direct) current.<ref name="billings"/>
| |
| | |
| The emf of a transformer at a given flux density increases with frequency.<ref name="Say (1984)"/> 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 conductor [[skin effect]] also increase with frequency. Aircraft and military equipment employ 400 Hz power supplies which reduce core and winding weight.<ref>{{cite web | title = 400 Hz Electrical Systems | work = Aerospaceweb.org | url = http://www.aerospaceweb.org/question/electronics/q0219.shtml | accessdate = May 21, 2007}}</ref> Conversely, frequencies used for some [[railway electrification system]]s were much lower (e.g. 16.7 Hz and 25 Hz) than normal utility frequencies (50 – 60 Hz) for historical reasons concerned mainly with the limitations of early [[traction motor|electric traction motors]]. As such, the transformers used to step-down the high over-head line voltages (e.g. 15 kV) were much heavier for the same power rating than those designed only for the higher frequencies.
| |
| | |
| [[File:Power Transformer Over-Excitation.gif|thumb|Power transformer over-excitation condition caused by decreased frequency; flux (green), iron core's magnetic characteristics (red) and magnetizing current (blue).]]
| |
| | |
| Operation of a transformer at its designed voltage but at a higher frequency than intended will lead to reduced magnetizing current. At a 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-excitation [[protective relay|relays]] to protect the transformer from overvoltage at higher than rated frequency.
| |
| | |
| One example of state-of-the-art design is traction transformers used for [[electric multiple unit]] and [[High-speed rail|high-speed]] train service operating across the country border and using different electrical standards, such transformers' being restricted to be positioned below the passenger compartment. The power supply to, and converter equipment being supply by, such traction transformers have to accommodate different input frequencies and voltage (ranging from as high as 50 Hz down to 16.7 Hz and rated up to 25 kV) while being suitable for multiple AC asynchronous motor and DC converters & motors with varying harmonics mitigation filtering requirements.
| |
| | |
| Large power transformers are vulnerable to insulation failure due to transient voltages with high-frequency components, such as caused in switching or by lightning.<ref name="Gururaj (1963)">{{cite journal| last=Gururaj| first=B.I.| title=Natural Frequencies of 3-Phase Transformer Windings| journal=IEEE Transactions on Power Apparatus and Systems|volume=82| issue=66|date=June 1963| pages=318–329| doi=10.1109/TPAS.1963.291359| url=http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?isnumber=4072786&arnumber=4072800&count=25&index=12}}</ref>
| |
| {{Clear}}
| |
| | |
| ===Energy losses===
| |
| A 'theoretical' (or 'ideal') transformer does not experience energy losses (i.e., its 100% efficient), so the power dissipated by its load would be equal to the power supplied by its primary source. Contrarily, a 'practical' (or 'real') transformer does experience energy losses (its typically 95 to 99% efficient) due to a variety of loss mechanisms, including winding resistance, winding capacitance, leakage flux, core losses, and [[Magnetic core#Core loss|hysteresis loss]]. Larger transformers are generally more efficient, and those rated for electricity distribution usually perform better than 98%.<ref>{{Cite book
| |
| | last = Kubo
| |
| | first = 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]] | page = 39
| |
| | year = 2001
| |
| | url = http://www.aceee.org/research-report/a016
| |
| | accessdate = June 21, 2009}}</ref>
| |
| | |
| Experimental transformers using [[superconductivity|superconducting]] windings achieve efficiencies of 99.85%.<ref>{{Cite journal
| |
| | last = Riemersma
| |
| | first =H.
| |
| | title = Application of Superconducting Technology to Power Transformers
| |
| | journal = IEEE Transactions on Power Apparatus and Systems | volume = PAS-100
| |
| | issue = 7
| |
| | year=1981
| |
| | url = http://md1.csa.com/partners/viewrecord.php?requester=gs&collection=TRD&recid=0043264EA&q=superconducting+transformer&uid=790516502&setcookie=yes
| |
| | doi = 10.1109/TPAS.1981.316682
| |
| | page = 3398
| |
| | last2 = Eckels
| |
| | first2 = P.
| |
| | last3 = Barton
| |
| | first3 = M.
| |
| | last4 = Murphy
| |
| | first4 = J.
| |
| | last5 = Litz
| |
| | first5 = D.
| |
| | last6 = Roach
| |
| | first6 = J.}}</ref>
| |
| The increase in efficiency can save considerable energy, and hence money, in a large heavily loaded transformer; the trade-off is in the additional initial and running cost of the superconducting design.
| |
| | |
| As transformer losses vary with load, it is often useful to express these losses in terms of no-load loss, full-load loss, half-load loss, and so on. [[Hysteresis]] and [[eddy current]] losses are constant at all loads and dominate overwhelmingly at no-load, variable winding [[electrical resistance|joule losses]] dominating increasingly as load increases. The no-load loss can be significant, so that even an idle transformer constitutes a drain on the electrical supply and a running cost. Designing transformers 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 so that there is a [[trade-off]] between initial cost and running cost (also see [[energy efficient transformer]]).<ref name="Heathcote, pp. 41-42">Heathcote, pp. 41-42</ref>
| |
| | |
| Transformer losses arise from:
| |
| ; '''Winding joule losses'''
| |
| :Current flowing through winding conductors causes [[joule heating]]. As frequency increases, skin effect and [[proximity effect (electromagnetism)|proximity effect]] causes winding 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 hysteresis within the core. According to Steinmetz's formula, the heat energy due to hysteresis is given by
| |
| :::<math>W_h\approx\eta\beta^{1.6}_{max}</math>, and,
| |
| ::hysteresis loss is thus given by
| |
| :::<math>P_h\approx{W}_hf\approx\eta{f}\beta^{1.6}_{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="Heathcote, pp. 41-42"/><ref>Knowlton, pp. 49 (§2.67) & 323 (§4.279)</ref><ref name=EE-Reviewonline.com>{{cite web|last=EE-Reviewonline.com|title=Steinmetz's Formula for Magnetic Hysteresis|url=http://www.ee-reviewonline.com/index.php?option=com_content&view=article&id=534%3Asteinmetzs-formula-for-magnetic-hysteresis&catid=65%3Amagnetic-circuits&Itemid=44|accessdate=7 February 2013}}</ref>
| |
| :; '''Eddy current losses'''
| |
| ::[[Ferromagnetic]] materials are also good [[electrical conductor|conductors]] and a core made from such a material also constitutes a single short-circuited turn throughout its entire length. [[Eddy current]]s therefore circulate within the core in a plane normal to the flux, and are responsible for [[resistive heating]] of the core material. The eddy current loss is a complex function of the square of supply frequency and inverse square of the material thickness.<ref name="Heathcote, pp. 41-42"/> Eddy current losses can be reduced by making the core of a stack of 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 [[Mains hum|transformer hum]].<ref name="Winders (2002)"/><ref name="PF (nd)">{{cite web|title=Understanding Transformer Noise|url=http://www.federalpacific.com/literature/drytrans/10transformernoise.pdf|publisher=FP|accessdate=30 January 2013}}</ref> This transformer hum is especially objectionable in transformers supplied at [[utility frequency|power frequencies]]{{efn|Transformer hum's fundamental noise frequency is two times that of the power frequency as there is an extension and a contraction of core laminations for every cycle of the AC wave and a transformer's audible hum noise level is dominated by the [[fundamental frequency|fundamental noise frequency]] and its first triplen [[harmonic series (mathematics)|harmonic]], i.e., by the 100 & 300 Hz, or 120 & 360 Hz, frequencies.<ref name="PF (nd)"/>}} and in [[high-frequency]] [[flyback transformer]]s associated with PAL system [[Cathode ray tube|CRT]]s.
| |
| ; '''Stray losses''' <div id="stray"/>
| |
| :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}}</ref> 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 [[Mains hum|transformer hum]].<ref name="Pansini (1999)">{{cite book
| |
| | last = Pansini
| |
| | first = Anthony J.
| |
| | title = Electrical Transformers and Power Equipment
| |
| | isbn = 0-88173-311-3
| |
| | publisher = Fairmont Press
| |
| | page = 23
| |
| | year = 1999}}</ref>
| |
| | |
| ===Core form and shell form transformers===
| |
| [[File:Transformer winding formats.jpg|thumb|225px|right| Core form = core type; shell form = shell type]]
| |
| Closed-core transformers are constructed in 'core form' or 'shell form'. When windings surround the core, the transformer is core form; when windings are surrounded by the core, the transformer is shell form. Shell form design may be more prevalent than core form design for distribution transformer applications due to the relative ease in stacking the core around winding coils.<ref name="Del Vecchio (2002)"/> Core form design tends to, as a general rule, be more economical, and therefore more prevalent, than shell form design for high voltage power transformer applications at the lower end of their voltage and power rating ranges (less than or equal to, nominally, 230 kV or 75 MVA). At higher voltage and power ratings, shell form transformers tend to be more prevalent.<ref name="Del Vecchio (2002)"/><ref name="Knowlton, p. 562"/><ref name="HRTSG (2005)">{{cite web|last=Hydroelectric Research and Technical Services Group|title=Transformers: Basics, Maintenance, and Diagnostics|url=http://permanent.access.gpo.gov/lps113746/Trnsfrmr.pdf|publisher=U.S. Dept. of the Interior, Bureau of Reclamation|accessdate=Mar 27, 2012|page=12}}</ref><ref name="EM 1110-2-3006 (1994)">{{cite conference|last=EM 1110-2-3006|booktitle=Engineering and Design - Hydroelectric Power Plants Electrical Design|title=Chapter 4 - Power Transformers
| |
| |year=1994|publisher=U.S. Army Corps of Engineers|page=4-1|url=http://140.194.76.129/publications/eng-manuals/em1110-2-3006/c-4.pdf}}</ref> Shell form design tends to be preferred for extra high voltage and higher MVA applications because, though more labor-intensive to manufacture, shell form transformers are characterized as having inherently better kVA-to-weight ratio, better short-circuit strength characteristics and higher immunity to transit damage.<ref name="EM 1110-2-3006 (1994)"/>
| |
| | |
| ==Construction==
| |
| | |
| ===Cores===
| |
| | |
| ====Laminated steel cores====
| |
| [[Image:Transformer.filament.agr.jpg|thumb|220px|Laminated core transformer showing edge of laminations at top of photo]]
| |
| | |
| [[File:Power Transformer Inrush Current.gif|thumb|Power transformer inrush current caused by residual flux at switching instant; flux (green), iron core's magnetic characteristics (red) and magnetizing current (blue).]]
| |
| | |
| Transformers for use at power or audio frequencies typically have cores made of high permeability [[silicon steel]].<ref name="Hindmarsh (1984)">{{cite book|last=Hindmarsh|first=J.|title=Electrical Machines and Their Applications.|year=1984|publisher=Pergamon Press|location=Oxford|isbn=0-08-030573-3|pages=29–31}}</ref> The steel has a permeability many times that of [[free space]] and the core thus serves to greatly reduce the magnetizing current and confine the flux to a path which closely couples the windings.<ref>{{cite book
| |
| | last = Gottlieb
| |
| | first = Irving
| |
| | title = Practical Transformer Handbook
| |
| | publisher = Newnes
| |
| | isbn = 0-7506-3992-X
| |
| |page = 4
| |
| | year = 1998}}</ref> Early transformer developers soon realized that cores constructed from solid iron resulted in prohibitive eddy current losses, and their designs mitigated this effect with cores consisting of bundles of insulated iron wires.<ref name="allan"/> Later designs constructed the core by stacking layers of thin steel laminations, a principle that has remained in use. Each lamination is insulated from its neighbors by a thin non-conducting layer of insulation.<ref name="k&k_p36-7">{{cite book
| |
| | last = Kulkarni|first= S. V.| coauthors= Khaparde, S. A.| title = Transformer Engineering: Design and Practice
| |
| | isbn = 0-8247-5653-3
| |
| | publisher = CRC
| |
| | date = May 24, 2004
| |
| | pages = 36–37}}</ref> The universal transformer equation indicates a minimum cross-sectional area for the core to avoid saturation.
| |
| | |
| The effect of laminations is to confine eddy currents to highly elliptical paths that enclose little flux, and so reduce their magnitude. Thinner laminations reduce losses,<ref>Hindmarsh, pp. 29-31</ref> but are more laborious and expensive to construct.<ref name="McLyman (2004)">{{cite book
| |
| | last = McLyman
| |
| | first = Colonel Wm. T.
| |
| | isbn = 0-8247-5393-3
| |
| | publisher = CRC
| |
| | title = Transformer and Inductor Design Handbook
| |
| | pages = Chap. 3, pp. 9–14
| |
| | nopp = true
| |
| | year = 2004}}</ref> Thin laminations are generally used on high-frequency transformers, with some of very thin steel laminations able to operate up to 10 kHz.
| |
| | |
| [[Image:Laminering av kärna.svg|thumb|upright|left|Laminating the core greatly reduces eddy-current losses]]
| |
| | |
| One common design of laminated core is made from interleaved stacks of [[E-shaped]] steel sheets capped with [[I-shaped]] pieces, leading to its name of 'E-I transformer'.<ref name="McLyman (2004)"/> Such a design tends to exhibit more losses, but is very economical to manufacture. The cut-core or C-core type is made by winding a steel strip around a rectangular form and then bonding the layers together. It is then cut in two, forming two C shapes, and the core assembled by binding the two C halves together with a steel strap.<ref name="McLyman (2004)"/> They have the advantage that the flux is always oriented parallel to the metal grains, reducing reluctance.
| |
| | |
| A steel core's [[remanence]] means that it retains a static magnetic field when power is removed. When power is then reapplied, the residual field will cause a high [[inrush current]] until the effect of the remaining magnetism is reduced, usually after a few cycles of the applied AC waveform.<ref name="Harlow (2004a)">{{cite conference|last=Sim|first=H. Jim|coauthors=Digby; Scott H.|booktitle=The Electric Power Engineering Handbook|year=2004|publisher=CRC Press|title=§2.1 Power Transformers in Chap. 2 - Equipment Types|editor-last=James H. Harlow (ed.); L. L. Grigsby (Series ed.)|isbn=0-8493-8578-4|url=http://www.uncp.edu.pe/newfacultades/ingenieriasarqui/newelectrica/phocadownload/descargas/E%20BOOK%20Electric%20Power%20Transformer%20Engineering.pdf|edition=Online|page=§2.1.7 & §2.1.6.2.1|url=http://www.uncp.edu.pe/newfacultades/ingenieriasarqui/newelectrica/phocadownload/descargas/E%20BOOK%20Electric%20Power%20Transformer%20Engineering.pdf}}</ref> Overcurrent protection devices such as [[fuse (electrical)|fuses]] must be selected to allow this harmless inrush to pass. On transformers connected to long, overhead power transmission lines, induced currents due to [[Geomagnetically induced current|geomagnetic disturbances]] during [[Geomagnetic storm|solar storms]] can cause saturation of the core and operation of transformer protection devices.<ref>{{Cite journal
| |
| | last = Boteler
| |
| | first = D. H.
| |
| | last2 = Pirjola | first2= R. J.
| |
| | last3 = Nevanlinna | first3 = H.
| |
| | title = The Effects of Geomagnetic Disturbances On Electrical Systems at the Earth's Surface
| |
| | journal = Advances in Space Research
| |
| | doi = 10.1016/S0273-1177(97)01096-X
| |
| | volume = 22
| |
| | pages = 17–27
| |
| | year = 1998}}</ref>
| |
| | |
| Distribution transformers can achieve low no-load losses by using cores made with low-loss high-permeability silicon steel or [[Amorphous#Metallic glass|amorphous (non-crystalline) metal alloy]]. The higher initial cost of the core material is offset over the life of the transformer by its lower losses at light load.<ref>{{cite journal
| |
| | last =Hasegawa
| |
| | first = Ryusuke
| |
| | title = Present Status of Amorphous Soft Magnetic Alloys
| |
| | journal =Journal of Magnetism and Magnetic Materials
| |
| | volume =215-216
| |
| | pages = 240–245
| |
| | date = June 2, 2000
| |
| | doi = 10.1016/S0304-8853(00)00126-8 }}</ref>
| |
| | |
| ====Solid cores====
| |
| Powdered iron cores are used in circuits such as switch-mode power supplies that operate above mains frequencies and up to a few tens of kilohertz. These materials combine high magnetic permeability with high bulk electrical [[resistivity]]. For frequencies extending beyond the [[Very high frequency|VHF band]], cores made from non-conductive magnetic [[ceramic]] materials called [[ferrite (magnet)|ferrites]] are common.<ref name="McLyman (2004)"/> Some radio-frequency transformers also have movable cores (sometimes called 'slugs') which allow adjustment of the [[coupling coefficient]] (and [[bandwidth (signal processing)|bandwidth]]) of tuned radio-frequency circuits.
| |
| | |
| ====Toroidal cores====
| |
| [[Image:Small toroidal transformer.jpg|thumb|right|Small toroidal core transformer]]
| |
| Toroidal transformers are built around a ring-shaped core, which, depending on operating frequency, is made from a long strip of [[silicon steel]] or [[permalloy]] wound into a coil, powdered iron, or [[ferrite (magnet)|ferrite]].<ref>McLyman, Chap. 3 p. 1</ref> A strip construction ensures that the [[grain boundary|grain boundaries]] are optimally aligned, improving the transformer's efficiency by reducing the core's [[reluctance]]. The closed ring shape eliminates air gaps inherent in the construction of an E-I core.<ref name="Say, p. 485"/> The cross-section of the ring is usually square or rectangular, but more expensive cores with circular cross-sections are also available. The primary and secondary coils are often wound concentrically to cover the entire surface of the core. This minimizes the length of wire needed, and also provides screening to minimize the core's magnetic field from generating [[electromagnetic interference]].
| |
| | |
| Toroidal transformers are more efficient than the cheaper laminated E-I types for a similar power level. Other advantages compared to E-I types, include smaller size (about half), lower weight (about half), less mechanical hum (making them superior in audio amplifiers), lower exterior magnetic field (about one tenth), low off-load losses (making them more efficient in standby circuits), single-bolt mounting, and greater choice of shapes. The main disadvantages are higher cost and limited power capacity (see [[transformer#Classification parameters|Classification parameters]] below). Because of the lack of a residual gap in the magnetic path, toroidal transformers also tend to exhibit higher inrush current, compared to laminated E-I types.
| |
| | |
| Ferrite toroidal cores are used at higher frequencies, typically between a few tens of kilohertz to hundreds of megahertz, to reduce losses, physical size, and weight of inductive components. A drawback of toroidal transformer construction is the higher labor cost of winding. This is because it is necessary to pass the entire length of a coil winding through the core aperture each time a single turn is added to the coil. As a consequence, toroidal transformers rated more than a few kVA are uncommon. Small distribution transformers may achieve some of the benefits of a toroidal core by splitting it and forcing it open, then inserting a bobbin containing primary and secondary windings.
| |
| | |
| ====Air cores====
| |
| [[File:AirCoreSymbol.png|100px|thumb|[[Electronic symbol]] for Air Cores]]
| |
| A physical core is not an absolute requisite and a functioning transformer can be produced simply by placing the windings near each other, an arrangement termed an 'air-core' transformer. The air which comprises the magnetic circuit is essentially lossless, and so an air-core transformer eliminates loss due to hysteresis in the core material.<ref name="calvert"/> The leakage inductance is inevitably high, resulting in very poor regulation, and so such designs are unsuitable for use in power distribution.<ref name="calvert"/> They have however very high [[bandwidth (signal processing)|bandwidth]], and are frequently employed in radio-frequency applications,<ref>{{cite web
| |
| | first = Reuben
| |
| | last = Lee
| |
| | title = Air-Core Transformers
| |
| | work = Electronic Transformers and Circuits
| |
| | url = http://www.vias.org/eltransformers/lee_electronic_transformers_07b_22.html | accessdate=May 22, 2007}}</ref> for which a satisfactory coupling coefficient is maintained by carefully overlapping the primary and secondary windings. They're also used for [[Resonant inductive coupling|resonant transformers]] such as Tesla coils where they can achieve reasonably low loss in spite of the high leakage inductance.
| |
| | |
| ===Windings===
| |
| [[Image:Transformer-hightolow smaller.jpg|thumb|right|250px|Windings are usually arranged concentrically to minimize flux leakage.]]
| |
| {{main|Windings}}
| |
| The [[electrical conductor|conducting material]] used for the windings depends upon the application, but in all cases the individual turns must be electrically insulated from each other to ensure that the current travels throughout every turn.<ref name="Dixon (1997)">{{cite journal|last=Dixon|first=L.H., Jr.|url=http://focus.ti.com/lit/ml/slup197/slup197.pdf| title=Eddy Current Losses in Transformer Windings|year=1997|publisher=Texas Instrument|pages=R2–1–to–R2–10}}</ref> For small power and signal transformers, in which currents are low and the potential difference between adjacent turns is small, the coils are often wound from [[enameled wire|enamelled magnet wire]], such as Formvar wire. Larger power transformers operating at high voltages may be wound with copper rectangular strip conductors insulated by oil-impregnated paper and blocks of [[Transformerboard|pressboard]].<ref name="cegb_1982">{{cite book
| |
| | author=Central Electricity Generating Board
| |
| | title=Modern Power Station Practice
| |
| | year = 1982
| |
| |publisher = Pergamon Press}}</ref>
| |
| | |
| [[Image:transformer min stray field geometry.svg|thumb|left|250px|
| |
| Cut view through transformer windings.
| |
| White: insulator.
| |
| Green spiral: [[Electrical steel|Grain oriented silicon steel]].
| |
| Black: Primary winding made of [[oxygen-free copper]].
| |
| Red: Secondary winding.
| |
| Top left: Toroidal transformer.
| |
| Right: C-core, but E-core would be similar. The black windings are made of film.
| |
| Top: Equally low capacitance between all ends of both windings. Since most cores are at least moderately conductive they also need insulation.
| |
| Bottom: Lowest capacitance for one end of the secondary winding needed for low-power high-voltage transformers.
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| Bottom left: Reduction of [[leakage inductance]] would lead to increase of capacitance.
| |
| ]]
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| | |
| High-frequency transformers operating in the tens to hundreds of kilohertz often have windings made of braided [[Litz wire]] to minimize the skin-effect and proximity effect losses.<ref name="dixon"/> Large power transformers use multiple-stranded conductors as well, since even at low power frequencies non-uniform distribution of current would otherwise exist in high-current windings.<ref name="cegb_1982"/> Each strand is individually insulated, and the strands are arranged so that at certain points in the winding, or throughout the whole winding, each portion occupies different relative positions in the complete conductor. The transposition equalizes the current flowing in each strand of the conductor, and reduces eddy current losses in the winding itself. The stranded conductor is also more flexible than a solid conductor of similar size, aiding manufacture.<ref name="cegb_1982"/>
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| | |
| The windings of signal transformers minimize leakage inductance and stray capacitance to improve high-frequency response. Coils are split into sections, and those sections interleaved between the sections of the other winding.
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| | |
| Power-frequency transformers may have [[Tap (transformer)|taps]] at intermediate points on the winding, usually on the higher voltage winding side, for voltage adjustment. Taps may be manually reconnected, or a manual or automatic switch may be provided for changing taps. Automatic on-load [[tap changer]]s are used in electric power transmission or distribution, on equipment such as [[arc furnace]] transformers, or for automatic voltage regulators for sensitive loads. Audio-frequency transformers, used for the distribution of audio to public address loudspeakers, have taps to allow adjustment of impedance to each speaker. A [[Center tap|center-tapped transformer]] is often used in the output stage of an audio power [[amplifier]] in a [[Push-pull converter|push-pull circuit]]. Modulation transformers in [[Amplitude modulation|AM]] transmitters are very similar.
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| | |
| Dry-type transformer winding insulation systems can be either of standard open-wound 'dip-and-bake' construction or of higher quality designs that include [[vacuum|vacuum pressure impregnation]] (VPI), [[vacuum|vacuum pressure encapsulation]] (VPE), and [[Transformer types#Cast resin tranformer|cast coil encapsulation]] processes.<ref name="Lane (2007)">{{cite web|last=Lane|first=Keith (2007)|title=The Basics of Large Dry-Type Transformers|url=http://ecmweb.com/content/basics-large-dry-type-transformers|publisher=EC&M|accessdate=29 January 2013}}</ref> In the VPI process, a combination of heat, vacuum and pressure is used to thoroughly seal, bind, and eliminate entrained air voids in the winding polyester resin insulation coat layer, thus increasing resistance to corona. VPE windings are similar to VPI windings but provide more protection against environmental effects, such as from water, dirt or corrosive ambients, by multiple dips including typically in terms of final epoxy coat.<ref>Heathcote, pp. 720–723</ref>
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| | |
| ===Cooling===
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| [[Image:Drehstromtransformater im Schnitt Hochspannung.jpg|thumb|180px|right|Cutaway view of liquid-immersed construction transformer. The conservator (reservoir) at top provides liquid-to-atmosphere isolation as coolant level and temperature changes. The walls and fins provide required heat dissipation balance.]]
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| {{see also|Arrhenius equation}}
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| To place the cooling problem in perspective, the accepted rule of thumb is that the life expectancy of insulation in all [[electric machine]]s including all transformers is halved for about every 7°C to 10°C increase in [[operating temperature]], this life expectancy halving rule holding more narrowly when the increase is between about 7°C to 8°C in the case of transformer winding cellulose insulation.<ref name="Harlow (2004b)">{{cite conference|last=Tillman|first=Robert F.|booktitle=The Electric Power Engineering Handbook|year=2004|publisher=CRC Press|title=§3.4 Load and Thermal Performance in Chap. 3 - Ancillary Topics|editor-last=James H. Harlow (ed.); L. L. Grigsby (Series ed.)|isbn=0-8493-8578-4|url=http://www.uncp.edu.pe/newfacultades/ingenieriasarqui/newelectrica/phocadownload/descargas/E%20BOOK%20Electric%20Power%20Transformer%20Engineering.pdf|edition=Online|page=§3.4.8}}</ref><ref name="Walling (2007)">{{cite conference|last=Walling|first=Reigh|coauthors=Shattuck; G. Bruce|title=Distribution Transformer Thermal Behaviour and Aging in Local-Delivery Distribution Systems|conference=19th International Conference on Electricity Distribution|date=May 2007|volume=Paper 0720|url=http://www.gepower.com.cindmz.gecompany.com/prod_serv/plants_td/en/downloads/cired_dist_transformer.pdf|accessdate=11 February 2013}}</ref><ref name="Kimberly (web)">{{cite web|last=Kimberly|first=E.E.|title=Permissible Temperatures for Insulation|url=http://www.vias.org/kimberlyee/ee_14_11.html|accessdate=12 February 2013}}</ref>
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| | |
| Small dry-type and liquid-immersed transformers are often self-cooled by natural convection and [[radiation]] heat dissipation. As power ratings increase, transformers are often cooled by forced-air cooling, forced-oil cooling, water-cooling, or combinations of these.<ref>Pansini, p. 32</ref> Large transformers are filled with [[transformer oil]] that both cools and insulates the windings.<ref name="willis">{{cite book
| |
| | last = Willis
| |
| | first = H. Lee
| |
| | title = Power Distribution Planning Reference Book
| |
| | publisher = CRC Press
| |
| | year = 2004
| |
| | page = 403
| |
| | isbn = 0-8247-4875-1 }}</ref> Transformer oil is a highly refined [[mineral oil]] that cools the windings and insulation by circulating within the transformer tank. The mineral oil and [[electrical insulation paper|paper]] insulation system has been extensively studied and used for more than 100 years. It is estimated that 50% of power transformers will survive 50 years of use, that the average age of failure of power transformers is about 10 to 15 years, and that about 30% of power transformer failures are due to insulation and overloading failures.<ref name="Hartley (2003)">{{cite conference|last=Hartley|first=William H. (2003)|title=Analysis of Transformer Failures|url=http://www.bplglobal.net/eng/knowledge-center/download.aspx?id=191|conference=36th Annual Conference of the International Association of Engineering Insurers|accessdate=30 January 2013|page=7 (fig. 6)}}</ref><ref name="Hartley (~2011)">{{cite web|last=Hartley|first=William H. (~2011)|title=An Analysis of Transformer Failures, Part 1 – 1988 through 1997|url=http://www.hsb.com/TheLocomotive/AnAnalysisOfTransformerFailuresPart1.aspx|publisher=The Locomotive|accessdate=30 January 2013}}</ref> Prolonged operation at elevated temperature degrades insulating properties of winding insulation and dielectric coolant, which not only shortens transformer life but can ultimately lead to catastrophic transformer failure.<ref name="Harlow (2004b)"/> With a great body of empirical study as a guide, [[transformer oil testing]] including [[dissolved gas analysis]] provides valuable maintenance information. This underlines the need to monitor, model, forecast and manage oil and winding conductor insulation temperature conditions under varying, possibly difficult, power loading conditions.<ref name="Prevost (2006)">{{cite web|last=Prevost|first=Thomas A. et al.|title=Estimation of Insulation Life Based on a Dual Temperature Aging Model|url=http://www.weidmann-solutions.cn/huiyi/Seminar%202006%20New%20Mexico/2006prevostpaperyes.pdf|publisher=Weidmann|accessdate=Mar 30, 2012|page=1|date=Nov 2006}}</ref><ref name="Sen (2011)">{{cite web|year=2011|last=Sen|first=P.K. et al.|title=PSERC Pub. 11-02 Transformer Overloading and Assessment of Loss-of-Life for Liquid-Filled Transformers|url=http://www.pserc.wisc.edu/documents/publications/reports/2011_reports/Sen_T-25_Final_Report_Feb_2011.pdf|publisher=Power Systems Engineering Research Center, Arizona State University|accessdate=11 January 2013}}</ref>
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| Building regulations in many jurisdictions require indoor liquid-filled transformers to either use dielectric fluids that are less flammable than oil, or be installed in fire-resistant rooms.<ref name="energie">{{cite journal | last= De Keulenaer|first= H. et al | title = The Scope for Energy Saving in the EU Through the Use of Energy-Efficient Electricity Distribution Transformers | publisher=Institution of Engineering and Technology | year = 2001 | url = http://www.seai.ie/Archive1/Files_Misc/REP009THERMIEFinalreport.pdf}}</ref> Air-cooled dry transformers can be more economical where they eliminate the cost of a fire-resistant transformer room.
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| | |
| The tank of liquid filled transformers often has radiators through which the liquid coolant circulates by natural convection or fins. Some large transformers employ electric fans for forced-air cooling, pumps for forced-liquid cooling, or have [[heat exchangers]] for water-cooling.<ref name="willis"/> An oil-immersed transformer may be equipped with a [[Buchholz relay]], which, depending on severity of gas accumulation due to internal arcing, is used to either alarm or de-energize the transformer.<ref name="Harlow (2004a)"/> Oil-immersed transformer installations usually include fire protection measures such as walls, oil containment, and fire-suppression sprinkler systems. Another protection means consists in [http://www.electricenergyonline.com/?page=show_article&article=362 fast depressurization systems] which are activated by the first dynamic pressure peak of the shock wave, avoiding transformer explosion before static pressure increases. Many explosions are reported to have been avoided thanks to this technology.<ref>http://www.prweb.com/releases/2013/6/prweb10836945.htm</ref>
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| | |
| [[Polychlorinated biphenyl]]s have properties that once favored their use as a [[coolant|dielectric coolant]], though concerns over their [[Persistent organic pollutant|environmental persistence]] led to a widespread ban on their use.<ref>{{Cite web
| |
| | authorlink = [[Agency for Toxic Substances and Disease Registry]]
| |
| | title = ASTDR ToxFAQs for Polychlorinated Biphenyls
| |
| | year = 2001
| |
| | url = http://www.atsdr.cdc.gov/toxfaqs/tf.asp?id=140&tid=26
| |
| | accessdate = June 10, 2007 }}</ref> Today, non-toxic, stable [[silicone]]-based oils, or [[fluorocarbon|fluorinated hydrocarbons]] may be used where the expense of a fire-resistant liquid offsets additional building cost for a transformer vault.<ref name="energie"/><ref name="kulk-khap pp. 2-3">Kulkarni, pp. 2-3</ref> PCBs for new equipment was banned in 1981 and in 2000 for use in existing equipment in United Kingdom<ref name="AFBI (2011)">{{cite conference|last=AFBI|title=9. Contaminants|booktitle=State of the Seas Report|year=2011|publisher=Agri-Food and Biosciences Institute & Northern Ireland Environment Agency|isbn=9977 and 178-1-907053-20-7|page=71|url=http://www.afbini.gov.uk/sots-contaminants.pdf}}</ref> Legislation enacted in Canada between 1977 and 1985 essentially bans PCB use in transformers manufactured in or imported into the country after 1980, the maximum allowable level of PCB contamination in existing mineral oil transformers being 50 ppm.<ref>{{cite book | last= McDonald|first= C. J.|coauthors=Tourangeau, R. E.| title=PCBs, Question and Answer Guide Concerning Polychlorinated Biphenyls| publisher=Government of Canada: Environment Canada Department | year=1986| isbn=0-662-14595-X| url=https://www.ec.gc.ca/Publications/C7F1F416-C632-4D11-BDD4-C823690C2651/PCBsQuestionandAnswerGuideConcerningPolychlorinatedBiphenyls.pdf | accessdate=Nov 7, 2007}}</ref>
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| Some transformers, instead of being liquid-filled, have their windings enclosed in sealed, pressurized tanks and cooled by [[nitrogen]] or [[sulfur hexafluoride]] gas.<ref name="kulk-khap pp. 2-3"/>
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| | |
| Experimental power transformers in the 500-to-1,000 kVA range have been built with [[liquid nitrogen]] or [[liquid helium|helium]] cooled [[superconductivity|superconducting]] windings, which eliminates winding losses without affecting core losses.<ref name="Mehta (1997)">{{cite journal|last=Mehta|first=S.P.|coauthors=Aversa, N.; Walker, M.S.|title=Transforming Transformers [Superconducting windings]|journal=IEEE Spectrum|date=Jul 1997|volume=34|issue=7|pages=43–49|doi=10.1109/6.609815|url=http://www.superpower-inc.com/files/T141+IEEE+Spectrum+XFR.pdf|accessdate=14 November 2012}}</ref><ref>Pansini, pp. 66–67</ref>
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| | |
| ===Insulation drying===
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| | |
| Construction of oil-filled transformers requires that the insulation covering the windings be thoroughly dried of residual moisture before the oil is introduced. Drying is carried out at the factory, and may also be required as a field service. Drying may be done by circulating hot air around the core, or by vapor-phase drying (VPD) where an evaporated solvent transfers heat by condensation on the coil and core.
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| For small transformers, resistance heating by injection of current into the windings is used. The heating can be controlled very well, and it is energy efficient. The method is called low-frequency heating (LFH) since the current used is at a much lower frequency than that of the power grid, which is normally 50 or 60 Hz. A lower frequency reduces the effect of inductance, so the voltage required can be reduced.<ref>{{cite book|last=Fink|first= Donald G.|coauthors= Beatty, H. Wayne (Eds.)|year=1978|title=Standard Handbook for Electrical Engineers|edition= 11th|publisher= McGraw Hill|isbn=0-07-02974-x |pages=10–38 through 10–40}}</ref> The LFH drying method is also used for service of older transformers.<ref name=Figueroa>{{cite web|last=Figueroa|first=Elisa et al|title=Low Frequency Heating Field Dry-Out of a 750 MVA 500 kV Auto Transformer|url=http://www.electricity-today.com/et/issue0109/transformer_field_dry-out.pdf|publisher=Electricity Today|date=Jan/Feb 2009|accessdate=Feb 28, 2012}}</ref>
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| | |
| ===Bushings===
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| Larger transformers are provided with high-voltage insulated [[Bushing (electrical)|bushings]] made of polymers or porcelain. A large bushing can be a complex structure since it must provide careful control of the [[electric field gradient]] without letting the transformer leak oil.<ref>{{cite book
| |
| | last = Ryan
| |
| | first= Hugh M.
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| | title = High Voltage Engineering and Testing
| |
| | isbn = 0-85296-775-6
| |
| | publisher = Institution Electrical Engineers
| |
| | pages = 416–417
| |
| | year = 2001}}</ref>
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| | |
| ==Classification parameters==
| |
| Transformers can be classified in many ways, such as the following:
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| * ''[[Power rating|Power capacity]]'': From a fraction of a volt-ampere (VA) to over a thousand MVA.
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| * ''Duty of a transformer'': Continuous, short-time, intermittent, periodic, varying.
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| * ''Frequency range'': [[Utility frequency|Power-frequency]], [[audio frequency|audio-frequency]], or [[radio frequency|radio-frequency]].
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| * ''Voltage class'': From a few volts to hundreds of kilovolts.
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| * ''Cooling type'': Dry and liquid-immersed - self-cooled, forced air-cooled; liquid-immersed - forced oil-cooled, water-cooled.
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| * ''Circuit application'': Such as power supply, impedance matching, output voltage and current stabilizer or circuit isolation.
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| * ''Utilization'': [[Pulse transformer|Pulse]], [[Electricity distribution|power, distribution]], [[rectifier]], [[arc furnace]], amplifier output, etc.''.
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| * ''Basic magnetic form'': Core form, shell form.
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| * ''Constant-potential transformer descriptor'': Step-up, step-down, [[Isolation transformer|isolation]].
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| * ''General winding configuration'': By [[Vector group|EIC vector group]] - various possible two-winding combinations of the phase designations delta, wye or star, and [[zigzag transformer|zigzag or interconnected star]];{{efn|For example, the [[delta-wye transformer]], by far the most common commercial three-phase transformer, is known as the Dyn11 vector group configuration, Dyn11 denoting D for delta primary winding, y for wye secondary winding, n for neutral of the wye winding, and 11 for relative phase position on the clock by which the secondary winding leads the primary winding, namely, 30° leading.}} other - [[autotransformer]], [[Scott-T transformer|Scott-T]], [[zigzag transformer|zigzag grounding transformer winding]].<ref name="Lawhead (2006)">{{cite web|last=Lawhead|first=Larry|coauthors=Hamilton, Randy; Horak, John|title=Three Phase Transformer Winding Configurations and Differential Relay Compensation|pages=8–10|url=http://basler.com/downloads/3phXfmrs.pdf|publisher=Georgia Tech 60th Protective Relay Conference|year=2006|accessdate=Feb 23, 2012}}</ref><ref name="Beeman (1955)">{{cite book|last=Beeman|first=Donald (Ed.)|title=Industrial Power Systems Handbook|year=1955|publisher=McGraw-Hill|pages=349–364}}</ref><ref name=Brown>{{cite web|last=Brown|first=BIll|title=Section 6 Grounding Systems|url=http://static.schneider-electric.us/assets/consultingengineer/appguidedocs/section6_0307.pdf|publisher=Schneider|accessdate=18 January 2013|pages=9–12}}</ref><ref name="Beltz (2000)">{{cite conference|last=Beltz|first=Robert|coauthors=Peacock, Ian; Vilcheck, William|url=http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=854186&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D854186|title=Application Considerations for High Resistance Ground Retrofits in Pulp and Paper Mills|conference=Pulp and Paper Industry Technical Conference|year=2000|pages=33–40|doi=10.1109/PAPCON.2000.854186}}</ref>
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| * ''Rectifier phase-shift winding configuration'': 2-winding, 6-pulse; 3-winding, 12-pulse; . . . n-winding, [n-1]*6-pulse; polygon; etc..
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| {{Clear}}
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| ==Types==
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| For more details, see [[Transformer types]] or specific main articles, as shown.
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| | |
| A wide variety of transformer designs are used for different applications, though they share several common features. Important common transformer types include:
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| *''[[Autotransformer]]'': Transformer in which part of the winding is common to both primary and secondary circuits.<ref name="Knowlton, p. 549-550">Knowlton, §6-7, pp. 549-550</ref>
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| *''[[Capacitor voltage transformer]]'': Transformer in which capacitor divider is used to reduce high voltage before application to the primary winding.
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| *''[[Distribution transformer|Distribution transformer, power transformer]]'': International standards make a distinction in terms of distribution transformers being used to distribute energy from transmission lines and networks for local consumption and power transformers being used to transfer electric energy between the generator and distribution primary circuits.<ref name="Knowlton, p. 549-550"/><ref name="IEEE PES TC (2011)">{{cite web|last=IEEE PES TC (Fall 2011)|title=Discussion of Class I & II Terminology|url=http://grouper.ieee.org/groups/transformers/subcommittees/standardsc/F11-Class1-Class2Discussion.pdf|publisher=IEEE PES Transformer Committee|accessdate=27 January 2013|page=slide 6}}</ref>{{efn|While the above formal definition, derived from standards such as IEEE C57.12.80, applies to large transformers, it is not uncommon in colloquial, or even trade, parlance for small general-purpose transformers to be referred to as 'power' transformers, for distribution transformers to be referred to as 'power distribution' transformers, and so on.}}
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| *''[[Quadrature booster|Phase angle regulating transformer]]'': A specialised transformer used to control the flow of real power on three-phase electricity transmission networks.
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| *''[[Scott-T transformer]]'': Transformer used for phase transformation from three-phase to [[two-phase electric power|two-phase]] and vice versa.<ref name="Knowlton, p. 549-550"/>
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| *''[[Transformer types#Polyphase transformer|Polyphase transformer]]'': Any transformer with more than one phase.
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| *''Grounding transformer'': Transformer used for grounding three-phase circuits to create a neutral in a three wire system, using a wye-delta transformer,<ref name="Beeman (1955)"/><ref>Knowlton, §12-341, fig. 12-95, p. 1085</ref> or more commonly, a [[zigzag transformer|zigzag grounding winding]].<ref name="Beeman (1955)"/><ref name="Beltz (2000)"/><ref name="Knowlton, p. 549-550"/>
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| *''[[Transformer types#Leakage transformers|Leakage transformer]]'': Transformer that has loosely coupled windings.
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| *''[[Transformer types#Resonant transformer|Resonant transformer]]'': Transformer that uses resonance to generate a high secondary voltage.
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| *''[[Transformer types#Audio transformer|Audio transformer]]'': Transformer used in audio equipment.
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| *''[[Transformer types#Output transformer|Output transformer]]'': Transformer used to match the output of a valve amplifier to its load.
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| *''[[Transformer types#Instrument transformer|Instrument transformer]]'': Potential or [[current transformer]] used to accurately and safely represent voltage, current or phase position of high voltage or high power circuits.<ref name="Knowlton, p. 549-550"/>
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| | |
| ==Applications==
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| [[Image:Melbourne Terminal Station.JPG|300px|thumb|left|An [[electrical substation]] in [[Melbourne]], [[Australia]]
| |
| showing 3 of 5 220kV/66kV transformers, each with a capacity of 150 MVA.<ref name="AEMO (2012">{{cite web|last=AEMO et al. (2012)|url=http://jemena.com.au/Assets/What-We-Do/Assets/Jemena-Electricity-Network/Planning/Western%20metropolitan%20Melbourne%20transmission%20connection%20and%20subtransmission%20capacity.pdf#page=11|title=Joint Consultation Paper - Western Metropolitan Melbourne Transmission Connection and Subtransmission Capacity|accessdate= and [http://www.webcitation.org/6DQTNt5E7 archived] 4 January 2013|page=11}}</ref>]]
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| [[Image:Transformer-Limestone-Generating-Station.JPG|thumb|right|Transformer at the [[Limestone Generating Station]] in [[Manitoba]], [[Canada]]]]
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| | |
| Transformers are used to increase voltage before transmitting electrical energy over long distances through [[wire]]s. Wires have [[Electrical resistance|resistance]] which loses energy through joule heating at a rate corresponding to square of the current. By transforming power to a higher voltage transformers enable economical transmission of power and distribution. Consequently, transformers have shaped the [[Electrical power industry|electricity supply industry]], permitting generation to be located remotely from points of [[electrical load|demand]].<ref>Heathcote, p. 1</ref> All but a tiny fraction of the world's electrical power has passed through a series of transformers by the time it reaches the consumer.<ref name="nailen"/>
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| | |
| Transformers are also used extensively in [[Consumer electronics|electronic products]] to step-down the supply voltage to a level suitable for the low voltage circuits they contain. The transformer also electrically isolates the end user from contact with the supply voltage.
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| | |
| Signal and audio transformers are used to couple stages of [[amplifier]]s and to match devices such as [[microphone]]s and [[record player]]s to the input of amplifiers. Audio transformers allowed [[telephone]] circuits to carry on a [[Hybrid coil|two-way conversation]] over a single pair of wires. A [[balun]] transformer converts a signal that is referenced to ground to a signal that has [[Balanced line|balanced voltages to ground]], such as between external cables and internal circuits.
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| | |
| ==History==
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| | |
| ===Discovery of induction phenomenon===
| |
| [[Image:Induction experiment.png|thumb|270px|Faraday's experiment with induction between coils of wire<ref>{{cite book|url=http://books.google.com/books?id=JzBAAAAAYAAJ&pg=PA285| last=Poyser| first=Arthur William|year=1892|title=Magnetism and Electricity: A Manual for Students in Advanced Classes| location=London and New York|publisher= Longmans, Green, & Co.| page= 285, fig. 248| accessdate= Aug 6, 2009}}</ref>]]
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| | |
| The principle behind the operation of a transformer, electromagnetic induction, was discovered independently by [[Michael Faraday]] and [[Joseph Henry]] in 1831. However, Faraday was the first to publish the results of his experiments and thus receive credit for the discovery.<ref name="HenryNAS">{{cite web |url=http://www.nas.edu/history/members/henry.html |title=Joseph Henry|authorlink=Joseph Henry|accessdate=Nov 30, 2006 |work=Distinguished Members Gallery, National Academy of Sciences}}</ref> The relationship between emf and magnetic flux is an equation now known as [[Faraday's law of induction]]:
| |
| | |
| :<math> |\mathcal{E}| = \left|{{d\Phi_B} \over dt}\right|</math>.
| |
| | |
| where <math>|\mathcal{E}|</math> is the magnitude of the emf in volts and Φ<sub>''B''</sub> is the magnetic flux through the circuit in [[Weber (unit)|webers]].<ref name="Chow171">{{cite book|url=http://books.google.com/books?id=dpnpMhw1zo8C&pg=PA171&dq=isbn%3D0763738271+%22Time-Dependent+Magnetic+fields+and+Faraday%27s+Law+of+Induction%22&cd=1#v=onepage&q=&f=false|last= Chow|first= Tai L. |year=2006|title=Introduction to Electromagnetic Theory: A Modern Perspective| location=Sudbury, Mass.| publisher=Jones and Bartlett Publishers| page= 171| isbn=0-7637-3827-1}}</ref>
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| | |
| Faraday performed the first experiments on induction between coils of wire, including winding a pair of coils around an iron ring, thus creating the first [[Toroid (geometry)|toroidal]] closed-core transformer.<ref>{{cite journal|last=Faraday|first=Michael|year=1834|title=Experimental Researches on Electricity, 7th Series|authorlink=Michael Faraday|journal=Philosophical Transactions of the Royal Society|volume=124|pages=77–122|doi=10.1098/rstl.1834.0008|url=http://archive.org/details/philtrans08694360}}</ref> However he only applied individual pulses of current to his transformer, and never discovered the relation between the turns ratio and emf in the windings.
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| | |
| ===Induction coils===
| |
| [[Image:Faradays transformer.png|thumb|right|Faraday's ring transformer]]
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| [[Image:Induktionsapparat hg.jpg|thumb|Induction coil, 1900, Bremerhavn, Germany]]
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| | |
| The first type of transformer to see wide use was the [[induction coil]], invented by Rev. [[Nicholas Callan]] of [[Maynooth College]], Ireland in 1836. He was one of the first researchers to realize the more turns the secondary winding has in relation to the primary winding, the larger the induced secondary emf will be. Induction coils evolved from scientists' and inventors' efforts to get higher voltages from batteries. Since batteries produce [[direct current|direct current (DC)]] rather than AC, induction coils relied upon vibrating [[electrical contact]]s that regularly interrupted the current in the primary to create the flux changes necessary for induction. Between the 1830s and the 1870s, efforts to build better induction coils, mostly by trial and error, slowly revealed the basic principles of transformers.
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| | |
| ===The first alternating current transformers===
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| By the 1870s, efficient [[Electric generator|generators]] producing [[alternating current|alternating current (AC)]] were available, and it was found AC could power an induction coil directly, without an [[interrupter]].
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| | |
| In 1876, Russian engineer [[Pavel Yablochkov]] invented a lighting system based on a set of induction coils where the primary windings were connected to a source of AC. The secondary windings could be connected to several [[Yablochkov candle|'electric candles']] (arc lamps) of his own design.<ref name=maglab>{{Cite web
| |
| |url=http://www.magnet.fsu.edu/education/tutorials/museum/stanleytransformer.html|title=Stanley Transformer|publisher=[[Los Alamos National Laboratory]]; [[University of Florida]]|accessdate=Jan 9, 2009}}</ref>
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| <ref name=fonveille>{{cite journal|url=http://books.google.com/?id=ksa-S7C8dT8C&pg=RA2-PA283|page=283|journal=[[Nature (journal)|Nature]]|issue=534|volume=21|title=Gas and Electricity in Paris|date=Jan 22, 1880|last=De Fonveille|first=W. |accessdate=Jan 9, 2009|bibcode=1880Natur..21..282D|doi=10.1038/021282b0}}</ref> The coils Yablochkov employed functioned essentially as transformers.<ref name="maglab"/>
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| | |
| In 1878, the [[Ganz Works|Ganz factory]], Budapest, Hungary, began manufacturing equipment for electric lighting and, by 1883, had installed over fifty systems in Austria-Hungary. Their AC systems used arc and incandescent lamps, generators, and other equipment.<ref name="Hughes (1993)">
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| {{Cite book
| |
| | url = http://books.google.com/?id=g07Q9M4agp4C&pg=PA96&dq=Networks+of+Power:+Electrification+in+Western+Society,+1880-1930+ganz#v=onepage&q=
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| | last = Hughes
| |
| | first = Thomas P.
| |
| | title = Networks of Power: Electrification in Western Society, 1880-1930
| |
| | publisher = The Johns Hopkins University Press
| |
| | location = Baltimore
| |
| | year = 1993
| |
| | page = 96
| |
| | accessdate = Sep 9, 2009
| |
| | isbn = 0-8018-2873-2}}</ref>
| |
| | |
| [[Lucien Gaulard]] and John Dixon Gibbs first exhibited a device with an open iron core called a 'secondary generator' in London in 1882, then sold the idea to the [[Westinghouse Electric Corporation|Westinghouse]] company in the United States.<ref name="allan">{{Cite journal | last = Allan | first=D.J.| title = Power Transformers – The Second Century | journal = Power Engineering Journal|year=Jan. 1991|volume=5|issue=1|pages=5–14|url=http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=61984 | doi = 10.1049/pe:19910004}}</ref> They also exhibited the invention in Turin, Italy in 1884, where it was adopted for an electric lighting system.<ref name=FJU1889>{{cite book|url=http://www.archive.org/details/historyoftransfo00upperich|last=Uppenborn|first=F. J.|title=History of the Transformer|publisher=E. & F. N. Spon|location=London|year=1889|pages=35–41}}</ref> However, the efficiency of their open-core bipolar apparatus remained very low.<ref name=FJU1889/>
| |
| | |
| ===Early series circuit transformer distribution===
| |
| Induction coils with open magnetic circuits are inefficient at transferring power to [[Electrical load|loads]]. Until about 1880, the paradigm for AC power transmission from a high voltage supply to a low voltage load was a series circuit. Open-core transformers with a ratio near 1:1 were connected with their primaries in series to allow use of a high voltage for transmission while presenting a low voltage to the lamps. The inherent flaw in this method was that turning off a single lamp (or other electric device) affected the voltage supplied to all others on the same circuit. Many adjustable transformer designs were introduced to compensate for this problematic characteristic of the series circuit, including those employing methods of adjusting the core or bypassing the magnetic flux around part of a coil.<ref name=FJU1889/>
| |
| Efficient, practical transformer designs did not appear until the 1880s, but within a decade, the transformer would be instrumental in the [[War of Currents]], and in seeing AC distribution systems triumph over their DC counterparts, a position in which they have remained dominant ever since.<ref name="Coltman">{{Cite news
| |
| | last = Coltman
| |
| | first = J. W.
| |
| | title = The Transformer
| |
| | newspaper = Scientific American
| |
| | pages = 86–95
| |
| | id = {{OSTI|6851152}}
| |
| |date=Jan. 1988}}</ref>
| |
| | |
| [[Image:Trafo1885.jpg|thumb|225px|right|Shell form transformer. Sketch used by Uppenborn to describe ZBD engineers' 1885 patents and earliest articles.<ref name=FJU1889/>]]
| |
| | |
| [[Image:DBZ trafo.jpg|thumb|225px|right|Core form, front; shell form, back. Earliest specimens of ZBD-designed high-efficiency constant-potential transformers manufactured at the Ganz factory in 1885.]]
| |
| [[Image:ZBD team.jpg|right|thumb|The ZBD team consisted of [[Károly Zipernowsky]], [[Ottó Bláthy]] and [[Miksa Déri]]]]
| |
| | |
| [[Image:StanleyTransformer.png|thumb|225px|right|Stanley's 1886 design for adjustable gap open-core induction coils<ref name=Stanley_adj_gap_ind_coil>{{cite web|last=Stanley|first=William, Jr.|url=http://www.google.com/patents?vid=349611|title=Induction Coil|publisher=U.S. Patent 349 311, issued Sept. 21, 1886|authorlink=William Stanley, Jr.|accessdate=July 13, 2009}}</ref>]]
| |
| | |
| ===Closed-core transformers and parallel power distribution===
| |
| In the autumn of 1884, [[Károly Zipernowsky]], [[Ottó Bláthy]] and [[Miksa Déri]] (ZBD), three engineers associated with the Ganz factory, had determined that open-core devices were impracticable, as they were incapable of reliably regulating voltage.<ref>Hughes, p. 95</ref> In their joint 1885 patent applications for novel transformers (later called ZBD transformers), they described two designs with closed magnetic circuits where copper windings were either a) wound around iron wire ring core or b) surrounded by iron wire core.<ref name=FJU1889/> The two designs were the first application of the two basic transformer constructions in common use to this day, which can as a class all be termed as either core form or shell form (or alternatively, core type or shell type), as in a) or b), respectively (see images).<ref name="Del Vecchio (2002)">{{cite book|last=Del Vecchio|first=Robert M. et al.|title=Transformer Design Principles: With Applications to Core-Form Power Transformers|year=2002|publisher=CRC Press|location=Boca Raton|isbn=90-5699-703-3|pages=10–11, Fig. 1.8|url=http://books.google.com/?id=Lzjs0LNHhVYC}}</ref><ref name="Knowlton, p. 562">Knowlton, p. 562</ref><ref name="Természet Világa">{{cite web|last=Károly|first=Simonyi|title=The Faraday Law With a Magnetic Ohm's Law|url=http://www.termeszetvilaga.hu/kulonsz/k011/46.html|publisher=Természet Világa|accessdate=Mar 1, 2012}}</ref><ref name="Lucas (2000)">{{cite web|last=Lucas|first=J.R.|title=Historical Development of the Transformer|url=http://www.elect.mrt.ac.lk/Transformer_history_2000.pdf|publisher=IEE Sri Lanka Centre|accessdate=Mar 1, 2012}}</ref> The Ganz factory had also in the autumn of 1884 made delivery of the world's first five high-efficiency AC transformers, the first of these units having been shipped on September 16, 1884.<ref name="Halacsy (1961)">{{cite journal|last=Halacsy|first=A. A.|coauthors=Von Fuchs, G. H. | title=Transformer Invented 75 Years Ago|journal=IEEE Transactions of the American Institute of Electrical Engineers|date=April 1961|volume=80|issue=3|pages=121–125|doi=10.1109/AIEEPAS.1961.4500994|url=http://ieeexplore.ieee.org/search/freesearchresult.jsp?newsearch=true&queryText=10.1109%2FAIEEPAS.1961.4500994&x=29&y=16|accessdate=Feb 29, 2012}}</ref> This first unit had been manufactured to the following specifications: 1,400 W, 40 Hz, 120:72 V, 11.6:19.4 A, ratio 1.67:1, one-phase, shell form.<ref name="Halacsy (1961)"/>
| |
| | |
| In both designs, the magnetic flux linking the primary and secondary windings traveled almost entirely within the confines of the iron core, with no intentional path through air (see [[transformer#Toroidal cores|Toroidal cores]] below). The new transformers were 3.4 times more efficient than the open-core bipolar devices of Gaulard and Gibbs.<ref name=Jeszenszky>{{cite web|last=Jeszenszky|first=Sándor|title=Electrostatics and Electrodynamics at Pest University in the Mid-19th Century|url=http://ppp.unipv.it/Collana/Pages/Libri/Saggi/Volta%20and%20the%20History%20of%20Electricity/V%26H%20Sect2/V%26H%20175-182.pdf|publisher=[[University of Pavia]]|accessdate=Mar 3, 2012}}</ref> The ZBD patents included two other major interrelated innovations: one concerning the use of parallel connected, instead of series connected, utilization loads, the other concerning the ability to have high turns ratio transformers such that the supply network voltage could be much higher (initially 1,400 to 2,000 V) than the voltage of utilization loads (100 V initially preferred).<ref name="Ideal (2008)">{{cite web|title=Hungarian Inventors and Their Inventions|url=http://www.institutoideal.org/conteudo_eng.php?&sys=biblioteca_eng&arquivo=1&artigo=94&ano=2008|publisher=Institute for Developing Alternative Energy in Latin America|accessdate=Mar 3, 2012}}</ref><ref name=BUTE-OMIKK-BlathyOtto>{{cite web|title=Bláthy, Ottó Titusz|url=http://www.omikk.bme.hu/archivum/angol/htm/blathy_o.htm|publisher=Budapest University of Technology and Economics, National Technical Information Centre and Library|accessdate=Feb 29, 2012}}</ref> When employed in parallel connected electric distribution systems, closed-core transformers finally made it technically and economically feasible to provide electric power for lighting in homes, businesses and public spaces.<ref name="Bláthy_HPO">{{cite web|title=Bláthy, Ottó Titusz (1860–1939)|url=http://www.hpo.hu/English/feltalalok/blathy.html|publisher=Hungarian Patent Office
| |
| |accessdate= Jan 29, 2004}}</ref><ref>{{cite web|last=Zipernowsky|first=K.|coauthors= Déri, M.; Bláthy, O.T. | url=http://www.freepatentsonline.com/0352105.pdf|title=Induction Coil|publisher=U.S. Patent 352 105, issued Nov. 2, 1886|accessdate=July 8, 2009}}</ref> Bláthy had suggested the use of closed cores, Zipernowsky had suggested the use of [[Shunt (electrical)|parallel shunt connections]], and Déri had performed the experiments;<ref name="Smil">{{cite book|url=http://books.google.com/?id=w3Mh7qQRM-IC&pg=PA71&lpg=PA71&dq=ZBD+transformer|last=Smil|first=Vaclav|title=Creating the Twentieth Century: Technical Innovations of 1867—1914 and Their Lasting Impact|location=Oxford |publisher=Oxford University Press|year=2005|page=71|isbn=9780198037743}}</ref>
| |
| | |
| Transformers today are designed on the principles discovered by the three engineers. They also popularized the word 'transformer' to describe a device for altering the emf of an electric current,<ref name="Bláthy_HPO"/><ref>{{cite web|url=http://www.kfki.hu/~aznagy/lecture/lecture.htm|last=Nagy|first=Árpád Zoltán|title=Lecture to Mark the 100th Anniversary of the Discovery of the Electron in 1897 (preliminary text)| location=Budapest|year=Oct. 11, 1996|accessdate=July 9, 2009}}</ref> although the term had already been in use by 1882.<ref>{{cite book|title = Oxford English Dictionary|edition=2nd|year=1989|publisher=Oxford University Press}}</ref><ref>{{cite book|url=http://books.google.com/books?id=qt8JAAAAIAAJ| last=Hospitalier|first=Édouard|year= 1882|title=The Modern Applications of Electricity|coauthors= as translated by Julius Maier|location=New York|publisher=D. Appleton & Co.|page=103}}</ref> In 1886, the ZBD engineers designed, and the Ganz factory supplied electrical equipment for, the world's first [[power station]] that used AC generators to power a parallel connected common electrical network, the steam-powered Rome-[[Cerchi]] power plant.<ref>{{cite web|url=http://www.iec.ch/cgi-bin/tl_to_htm.pl?section=technology&item=144| title=Ottó Bláthy, Miksa Déri, Károly Zipernowsky| publisher=IEC Techline| accessdate= Apr 16, 2010}}</ref>
| |
| | |
| Although [[George Westinghouse]] had bought Gaulard and Gibbs' patents in 1885, the [[Edison Electric Light Company]] held an option on the US rights for the ZBD transformers, requiring Westinghouse to pursue alternative designs on the same principles. He assigned to [[William Stanley, Jr.|William Stanley]] the task of developing a device for commercial use in United States.<ref name="Skrabec">{{cite book|last=Skrabec|first=Quentin R.|title=George Westinghouse: Gentle Genius|publisher=Algora Publishing|year=2007|page=102|isbn=978-0-87586-508-9|url=http://books.google.com/?id=C3GYdiFM41oC&pg=PA102}}</ref> Stanley's first patented design was for induction coils with single cores of soft iron and adjustable gaps to regulate the emf present in the secondary winding (see image).<ref name="Stanley_adj_gap_ind_coil"/> This design<ref name="Coltman (2002)">{{cite journal|last=Coltman|first=J.W.;|title=The Transformer [Historical Overview]|journal=Industry Applications Magazine, IEEE|date=Jan–Feb 2002|volume=8|issue=1|pages=8–15|doi=10.1109/2943.974352|url=http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=974352|accessdate=Feb 29, 2012}}</ref> was first used commercially in the US in 1886<ref name="Coltman">{{cite book
| |
| | last = International Electrotechnical Commission
| |
| | authorlink = International Electrotechnical Commission
| |
| | title = Otto Blathy, Miksa Déri, Károly Zipernowsky
| |
| | work = IEC History
| |
| | url = http://www.iec.ch/cgi-bin/tl_to_htm.pl?section=technology&item=144 | accessdate = May 17, 2007}}</ref> but Westinghouse was intent on improving the Stanley design to make it (unlike the ZBD type) easy and cheap to produce.<ref name="Coltman (2002)"/>
| |
| | |
| Westinghouse, Stanley and associates soon developed an easier to manufacture core, consisting of a stack of thin 'E‑shaped' iron plates, insulated by thin sheets of paper or other insulating material. Prewound copper coils could then be slid into place, and straight iron plates laid in to create a closed magnetic circuit. Westinghouse applied for a patent for the new low-cost design in December 1886; it was granted in July 1887.<ref name="Smil"/><ref>{{cite web|last=Westinghouse|first=George, Jr.|url=http://www.google.com/patents/about?id=NmRDAAAAEBAJ&dq=366362|title=Electrical Converter|publisher=U.S. Patent 366 362, issued July 12, 1887|authorlink=George Westinghouse}}</ref>
| |
| | |
| ===Other early transformers===
| |
| In 1889, Russian-born engineer [[Mikhail Dolivo-Dobrovolsky]] developed the first [[three-phase]] transformer at the [[Allgemeine Elektricitäts-Gesellschaft]] ('General Electricity Company') in Germany.<ref>{{cite book|last=Neidhöfer|first= Gerhard|coauthors=in collaboration with VDE "History of Electrical Engineering" Committee|location= Berlin | isbn= 978-3-8007-3115-2|url=http://d-nb.info/990964361|title=Michael von Dolivo-Dobrowolsky and Three-Phase: The Beginnings of Modern Drive Technology and Power Supply |language=German|year=2008|publisher=VDE-Verl.|edition=2}}</ref>
| |
| | |
| In 1891, [[Nikola Tesla]] invented the [[Tesla coil]], an air-cored, dual-tuned resonant transformer for generating very [[high voltage]]s at high frequency.<ref name="PBS">{{cite web|last=Uth|first=Robert|title=Tesla Coil|date=Dec 12, 2000|work=Tesla: Master of Lightning|publisher=PBS.org|url=http://www.pbs.org/tesla/ins/lab_tescoil.html|accessdate=May 20, 2008}}</ref><ref>{{cite web|url=http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PALL&p=1&u=%2Fnetahtml%2FPTO%2Fsrchnum.htm&r=1&f=G&l=50&s1=0454622.PN.&OS=PN/0454622&RS=PN/0454622|last=Tesla|first=Nikola|title=System of Electrical Lighting|publisher=U.S. Patent 454 622, issued June 23, 1891|authorlink=Nikola Tesla}}</ref>
| |
| | |
| <!--[[Audio frequency]] transformers ('[[repeating coil]]s') were used by early experimenters in the development of the [[telephone]].{{Citation needed|date=July 2009}}--->
| |
| | |
| ==See also==
| |
| {{Portal|Energy|Electronics}}
| |
| * [[Magnetization]]
| |
| * [[Inductor]]
| |
| * [[Polyphase system]]
| |
| * [[Load profile]]
| |
| * [[Magnetic core]]
| |
| * [[Geomagnetic storm]]
| |
| * [[Paraformer]]
| |
| * [[Rectiformer]]
| |
| * [[Switched-mode power supply]]
| |
| * [[Electronic symbol]]
| |
| | |
| ==Notes==
| |
| {{Notelist}}
| |
| | |
| ==References==
| |
| {{Reflist|2}}
| |
| | |
| ==Bibliography==
| |
| * {{cite book
| |
| | author=Central Electricity Generating Board
| |
| | authorlink = CEGB
| |
| | title=Modern Power Station Practice
| |
| | publisher=Pergamon
| |
| | year=1982 | isbn=0-08-016436-6}}
| |
| * {{cite book
| |
| | last=Daniels
| |
| | first= A.R.
| |
| | title=Introduction to Electrical Machines
| |
| |publisher=Macmillan
| |
| | year=1985
| |
| | isbn=0-333-19627-9}}
| |
| * {{cite book
| |
| | last = Flanagan
| |
| | first = William M.
| |
| | title = Handbook of Transformer Design & Applications
| |
| | publisher = McGraw-Hill
| |
| | year = 1993
| |
| | edition = 2nd
| |
| | isbn = 0-07-021291-0}}
| |
| * {{cite book
| |
| | last = Gottlieb
| |
| | first = Irving
| |
| | title = Practical Transformer Handbook: for Electronics, Radio and Communications Engineers
| |
| | publisher = Elsevier
| |
| | year = 1998
| |
| | isbn = 0-7506-3992-X
| |
| | url=http://books.google.com/?id=HFFo2TNIu88C&printsec=frontcover#v=onepage&q&f=false}}
| |
| * {{cite book
| |
| |last=Hammond
| |
| |first=John Winthrop
| |
| |title=Men and Volts: The Story of General Electric
| |
| |year=1941
| |
| |url=http://archive.org/details/menandvoltsstory00hammrich
| |
| |publisher=J.B. Lippincott Company
| |
| |pages=see esp. 106–107, 178, 238}}
| |
| * {{cite book
| |
| | first = James
| |
| | last = Harlow
| |
| | title = Electric Power Transformer Engineering
| |
| | publisher = CRC Press
| |
| | year = 2004
| |
| | isbn = 0-8493-1704-5
| |
| | url=http://books.google.com/?id=THO9U9f2m9EC&printsec=frontcover#v=onepage&q&f=false}}
| |
| * {{cite book
| |
| | first = Martin
| |
| | last = Heathcote
| |
| | title = J & P Transformer Book
| |
| | edition = 12th
| |
| | publisher = Newnes
| |
| | year = 1998
| |
| | isbn = 0-7506-1158-8
| |
| | url=http://books.google.com/?id=paPKsOXn5FMC&printsec=frontcover#v=onepage&q&f=false}}
| |
| * {{cite book
| |
| | last=Hindmarsh
| |
| | first=John
| |
| | title=Electrical Machines and Their Applications
| |
| | edition = 4th
| |
| | publisher=Pergammon
| |
| | year=1977
| |
| | location=Exeter
| |
| | isbn=0-08-030573-3}}
| |
| * {{cite book
| |
| | last = Kulkarni
| |
| | first = S.V.
| |
| | coauthors= Khaparde, S.A.
| |
| | title = Transformer Engineering: Design and Practice
| |
| | publisher = CRC Press
| |
| | year = 2004
| |
| | isbn = 0-8247-5653-3
| |
| | url=http://books.google.com/?id=qy4QT0BlV0MC&printsec=frontcover#v=onepage&q&f=false}}
| |
| * {{cite book
| |
| | last = McLaren
| |
| | first = Peter
| |
| | title = Elementary Electric Power and Machines
| |
| | publisher = Ellis Horwood
| |
| | year = 1984
| |
| | isbn = 0-470-20057-X }}
| |
| * {{cite book
| |
| | last = McLyman
| |
| | first = Colonel William
| |
| | title = Transformer and Inductor Design Handbook
| |
| | publisher = CRC
| |
| | year = 2004
| |
| | isbn = 0-8247-5393-3
| |
| | url=http://books.google.com/?id=s_iMztIS8y4C}}
| |
| * {{cite book
| |
| | first = Anthony
| |
| | last = Pansini
| |
| | title = Electrical Transformers and Power Equipment
| |
| | publisher = CRC Press
| |
| | year = 1999
| |
| | isbn = 0-88173-311-3
| |
| | url=http://books.google.com/?id=f77zWwA3oS4C}}
| |
| * {{cite book
| |
| | last = Ryan
| |
| | first = H.M.
| |
| | title = High Voltage Engineering and Testing
| |
| | year = 2004
| |
| | publisher = CRC Press
| |
| | isbn=0-85296-775-6
| |
| | url=http://books.google.com/?id=Jg1xA65n56oC&pg=PA7&dq=High+Voltage+Engineering+and+Testing#v=onepage&q=High%20Voltage%20Engineering%20and%20Testing&f=false}}
| |
| * {{cite book
| |
| | last = Say
| |
| | first = M.G.
| |
| | title = Alternating Current Machines
| |
| | edition = 5th
| |
| | publisher = Pitman
| |
| | year = 1983
| |
| | location = London
| |
| | isbn = 0-273-01969-4}}
| |
| * {{cite book
| |
| | last = Winders, Jr.
| |
| | first = John J.
| |
| | title = Power Transformer Principles and Applications
| |
| | publisher = CRC
| |
| | year = 2002
| |
| | isbn = 0-8247-0766-4
| |
| |url=http://books.google.com/?id=Sf1ppwGI6uYC&printsec=frontcover#v=onepage&q&f=false}}
| |
| | |
| ==External links==
| |
| {{Commons category|Transformers}}
| |
| {{Wikibooks|School Science|How to make a transformer}}
| |
| <!-- NOTE: No commercial links, please, eg to transformer manufacturer websites. They will be removed. -->
| |
| <!-- * [http://www.magnet.fsu.edu/education/tutorials/java/transformer/index.html Transformers Tutorial (Interactive Java applet)] National High Magnetic Field Laboratory -->
| |
| <!--kcoyne@magnet.fsu.edu, NHMFL webmaster, said in Oct 11, 2012 e-mail to me, user cblambert, that tutorials are being converted to Flash or movie format in 'the next few months' -->
| |
| * [http://www.du.edu/~jcalvert/tech/transfor.htm ''Inside Transformers'', composed by J. B. Calvert, from Denver University]
| |
| <!--* [http://www.conformity.com/artman/publish/printer_47.shtml ''Understanding Transformers: Characteristics and Limitations'' from Conformity Magazine] -->
| |
| <!--* [http://www.3phasepower.org/3phasetransformers.htm 3 Phase Transformer Information and Construction — The 3 Phase Power Resource Site]-->
| |
| * {{dmoz|Business/Electronics_and_Electrical/Substation_and_Transmission/|Substation and Transmission}}
| |
| * [http://www.elkor.net/pdfs/AN0305-Current_Transformers.pdf Introduction to Current Transformers]
| |
| * [http://www.phy.hk/wiki/englishhtm/Transformer.htm Transformer (Interactive Java applet)], 'Physics is fun' by Chui-king Ng
| |
| * [http://www.afrotechmods.com/videos/transformer_tutorial.htm HD video tutorial on transformers]
| |
| * [http://www.allaboutcircuits.com/vol_2/chpt_10/6.html Three-phase transformer circuits] from All About Circuits
| |
| * [http://www.transformerscommittee.org/info/Bibliographybooks.pdf Bibliography of Transformer Books] by P.M. Balma, from IEEE Transformer Committee
| |
| * [[:de:Einschalten des Transformators|Einschalten des Transformators]]. German Wikipedia article about transformer inrush current at switch on (in German).
| |
| | |
| {{Electricity delivery}}
| |
| {{Electronic component}}
| |
| | |
| [[Category:Electrical power conversion]]
| |
| [[Category:Hungarian inventions]]
| |
| [[Category:Russian inventions]]<!--<ref name=maglab/>-->
| |
| [[Category:Transformers (electrical)| ]]
| |
| | |
| {{Link GA|de}}
| |
| {{Link FA|tt}}
| |