Transformer

{{Side box|style=width:100%;max-width:30em|text= Ideal transformer equations By Faraday's law of induction: {{NumBlk|:|V_\text{P} = -N_\text{P} \frac{\mathrm{d}\Phi}{\mathrm{d}t}|{{efn|With turns of the winding oriented perpendicularly to the magnetic field lines, the flux is the product of the magnetic flux density and the core area, the magnetic field varying with time according to the excitation of the primary. The expression \mathrm{d}\Phi/\mathrm{d}t, defined as the derivative of magnetic flux \Phi with time t, provides a measure of rate of magnetic flux in the core and hence of EMF induced in the respective winding. The negative sign in eq. 1 and eq. 2 is consistent with Lenz's law and Faraday's law in that by convention EMF "induced by an increase of magnetic flux linkages is opposite to the direction that would be given by the right-hand rule."}}|Attr=style="margin-left:1.6em;width:unset !important;"}} {{NumBlk|:|V_\text{S} = -N_\text{S} \frac{\mathrm{d}\Phi}{\mathrm{d}t}||Attr=style="margin-left:1.6em;width:unset !important;"}} where V is the instantaneous voltage, N is the number of turns in a winding, dΦ/dt is the derivative of the magnetic flux Φ through one turn of the winding over time (t), and subscripts P and S denote primary and secondary. Dividing eq. 1 by eq. 2: {{NumBlk|:|Turns ratio =\frac{V_\text{P}}{V_\text{S}} = \frac{N_\text{P}}{N_\text{S}}=a||Attr=style="margin-left:1.6em;width:unset !important;"}} where for a step-up transformer a 1. gives the ideal transformer identity: {{NumBlk|:|\frac{V_\text{P}}{V_\text{S}} = \frac{I_\text{S}}{I_\text{P}}=\frac{N_\text{P}}{N_\text{S}}=\sqrt{\frac{L_\text{P}}{L_\text{S}}}=a||Attr=style="margin-left:1.6em;width:unset !important;"}} where L_\text{P} is the primary winding self-inductance and L_\text{S} is the secondary winding self-inductance. By Ohm's law and the ideal transformer identity: {{NumBlk|:|Z_\text{L}=\frac{V_\text{S}}{I_\text{S}}||Attr=style="margin-left:1.6em;width:unset !important;"}} {{NumBlk|:|Z'_\text{L}=\frac{V_\text{P}}{I_\text{P}}=\frac{aV_\text{S}}{I_\text{S}/a}=a^2\frac{V_\text{S}}{I_\text{S}}=a^2{Z_\text{L}}||Attr=style="margin-left:1.6em;width:unset !important;"}} where Z_\text{L} is the load impedance of the secondary circuit and Z'_\text{L} is the apparent load or driving point impedance of the primary circuit, the superscript ' denoting impedance referred to the primary. }} Ideal transformer An ideal transformer is linear, lossless, and perfectly coupled. Perfect coupling implies infinitely high core magnetic permeability and winding inductance and zero net magnetomotive force (i.e. ''i'p'n''p − ''i's'n''s = 0). Core loss and reactance is represented by the following shunt leg impedances of the model: • Core or iron losses: RC • Magnetizing reactance: XM. RC and XM are collectively termed the magnetizing branch of the model. 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. The finite permeability core requires a magnetizing current IM 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. Conversely, frequencies used for some railway electrification systems 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 electric traction motors. Consequently, the transformers used to step down the high overhead line voltages were much larger and heavier for the same power rating than those required for the higher frequencies. 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 large transformer at other than its design frequency may require assessment of voltages, losses, and cooling to establish if safe operation is practical. Transformers may require protective relays to protect the transformer from overvoltage at higher than rated frequency. One example is in traction transformers used for electric multiple unit and high-speed train service operating across regions with different electrical standards. The converter equipment and 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). At much higher frequencies the transformer core size required drops dramatically: a physically small transformer can handle power levels that would require a massive iron core at mains frequency. The development of switching power semiconductor devices made switched-mode power supplies (SMPSs) viable, to generate a high frequency, then change the voltage level with a small transformer. Transformers for higher frequency applications, such as SMPSs, typically use core materials with much lower hysteresis and eddy-current losses than those for 50/60 Hz. Primary examples are iron-powder and ferrite cores. The lower frequency-dependent losses of these cores often is at the expense of flux density at saturation. For instance, ferrite saturation occurs at a substantially lower flux density than laminated iron. Large power transformers are vulnerable to insulation failure due to transient voltages with high-frequency components, such as those caused by switching or by lightning. Energy losses Transformer energy losses are dominated by winding and core losses. Transformers' efficiency tends to improve with increasing transformer capacity. The efficiency of typical distribution transformers is between about 98 and 99 percent. As transformer losses vary with load, it is often useful to tabulate no-load loss, full-load loss, half-load loss, and so on. Hysteresis and eddy current losses are constant at all load levels and dominate at no load, while winding loss increases as load increases. The no-load loss can be significant, so that even an idle transformer constitutes a drain on the electrical supply. Designing energy efficient transformers for lower loss requires a larger core, good-quality silicon steel, or even amorphous steel for the core and thicker wire, increasing initial cost. The choice of construction represents a trade-off between initial cost and operating cost. Transformer losses arise from: ; Winding joule losses :Current flowing through a winding's conductor causes joule heating due to the resistance of the wire. As frequency increases, skin effect and proximity effect cause the winding's resistance and, hence, losses to increase. ;Core losses :; Hysteresis losses ::Each time the magnetic field is reversed, a small amount of energy is lost due to hysteresis within the core, caused by motion of the magnetic domains within the steel. According to Steinmetz's formula, the heat energy due to hysteresis is given by :::W_\text{h}\approx\eta\beta^{1.6}_{\text{max}} and, ::hysteresis loss is thus given by :::P_\text{h}\approx{W}_\text{h}f\approx\eta{f}\beta^{1.6}_{\text{max}} ::where, f is the frequency, η is the hysteresis coefficient and βmax 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. This transformer hum is especially objectionable in transformers supplied at power frequencies and in high-frequency flyback transformers associated with television CRTs. ; Stray losses :Leakage inductance is by itself largely lossless, since energy supplied to its magnetic fields is returned to the supply with the next half-cycle. However, any leakage flux that intercepts nearby conductive materials, such as the transformer's support structure, will give rise to eddy currents and be converted to heat. ; Radiative :There are also radiative losses due to the oscillating magnetic field, but these are usually small. ;Mechanical vibration and audible noise transmission :In addition to magnetostriction, the alternating magnetic field causes fluctuating forces between the primary and secondary windings. This energy incites vibration transmission in interconnected metalwork, thus amplifying audible transformer hum. ==Construction==

Cores ; 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. 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. 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. 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. 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. The transformer universal EMF equation can be used to calculate the core cross-sectional area for a preferred level of magnetic flux. Thin laminations are generally used on high-frequency transformers, with some very thin steel laminations able to operate up to 10 kHz. 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. Overcurrent protection devices such as fuses must be selected to allow this harmless inrush to pass. On transformers connected to long, overhead power transmission lines, induced currents due to geomagnetic disturbances during solar storms can cause saturation of the core and operation of transformer protection devices. 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 VHF band, cores made from non-conductive magnetic ceramic materials called ferrites are common. A strip construction ensures that the 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. Air cores A transformer can be produced by placing the windings near each other, an arrangement termed an "air-core" transformer. An air-core transformer eliminates loss due to hysteresis in the core material. Air cores are also used for resonant transformers such as tesla coils, where they can achieve reasonably low loss despite the low magnetizing inductance. Windings Black: Primary winding Red: Secondary winding The electrical conductor 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. For small transformers, in which currents are low and the potential difference between adjacent turns is small, the coils are often wound from enameled magnet wire. Larger power transformers may be wound with copper rectangular strip conductors insulated by oil-impregnated paper and blocks of pressboard. 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. 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. 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. Large transformers are filled with transformer oil that both cools and insulates the windings. Transformer oil is often a highly refined mineral oil that cools the windings and insulation by circulating within the transformer tank. The mineral oil and 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. 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. However, the long life span of transformers can mean that the potential for exposure can be high long after banning. Some transformers are gas-insulated. Their windings are enclosed in sealed, pressurized tanks and often cooled by nitrogen or sulfur hexafluoride gas. Insulation Insulation must be provided between the individual turns of the windings, between the windings, between windings and core, and at the terminals of the winding. Inter-turn insulation of small transformers may be a layer of insulating varnish on the wire. A layer of paper or polymer films may be inserted between layers of windings, and between primary and secondary windings. A transformer may be coated or dipped in a polymer resin to improve the strength of windings and protect them from moisture or corrosion. The resin may be impregnated into the winding insulation using combinations of vacuum and pressure during the coating process, eliminating all air voids in the winding. In the limit, the entire coil may be placed in a mold, and resin cast around it as a solid block, encapsulating the windings. Large oil-filled power transformers use windings wrapped with insulating paper, which is impregnated with oil during assembly of the transformer. Oil-filled transformers use highly refined mineral oil to insulate and cool the windings and core. Construction of oil-filled transformers requires that the insulation covering the windings be thoroughly dried of residual moisture before the oil is introduced. Drying may be done by circulating hot air around the core, by circulating externally heated transformer oil, or by vapor-phase drying (VPD), where an evaporated solvent transfers heat by condensation on the coil and core. For small transformers, resistance heating by injection of current into the windings is used. Bushings Larger transformers are provided with high-voltage insulated 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. ==Classification parameters==

in Melbourne, Australia showing three of five 220 kV – 66 kV transformers, each with a capacity of 150 MVA d transformer in Langley City, Canada Transformers can be classified in many ways, such as the following: • Power rating: From a fraction of a volt-ampere (VA) to over a thousand MVA. • Duty of a transformer: Continuous, short-time, intermittent, periodic, varying. • Frequency range: Power-frequency, audio-frequency, or radio-frequency. • Voltage class: From a few volts to hundreds of kilovolts. • Cooling type: Dry or liquid-immersed; self-cooled, forced air-cooled;forced oil-cooled, water-cooled. • Application: power supply, impedance matching, output voltage and current stabilizer, pulse, circuit isolation, power distribution, rectifier, arc furnace, amplifier output, etc. • Basic magnetic form: Core form, shell form, concentric, sandwich. • Constant-potential transformer descriptor: Step-up, step-down, isolation. • General winding configuration: By IEC vector group, two-winding combinations of the phase designations delta, wye or star, and zigzag; autotransformer, Scott-T • Rectifier phase-shift winding configuration: 2-winding, 6-pulse; 3-winding, 12-pulse; . . ., , [n − 1]·6-pulse; polygon; etc. • K-factor: A measure of how well the transformer can withstand harmonic loads. ==Applications==

in Manitoba, Canada Various specific electrical application designs require a variety of transformer types. Although they all share the basic characteristic transformer principles, they are customized in construction or electrical properties for certain installation requirements or circuit conditions. In electric power transmission, transformers allow transmission of electric power at high voltages, which reduces the loss due to heating of the wires. This allows generating plants to be located economically at a distance from electrical consumers. 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. In many electronic devices, a transformer is used to convert voltage from the distribution wiring to convenient values for the circuit requirements, either directly at the power line frequency or through a switch mode power supply. Signal and audio transformers are used to couple stages of amplifiers and to match devices such as microphones and record players to the input of amplifiers. Audio transformers allowed telephone circuits to carry on a 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 voltages to ground, such as between external cables and internal circuits. Isolation transformers prevent leakage of current into the secondary circuit and are used in medical equipment and at construction sites. Resonant transformers are used for coupling between stages of radio receivers, or in high-voltage Tesla coils. ==History==

Discovery of induction Electromagnetic induction, the principle of the operation of the transformer, was discovered independently by Michael Faraday in 1831 and Joseph Henry in 1832. Only Faraday furthered his experiments to the point of working out the equation describing the relationship between EMF and magnetic flux now known as Faraday's law of induction: : |\mathcal{E}| = \left|{{\mathrm{d}\Phi_\text{B}} \over \mathrm{d}t}\right|, where |\mathcal{E}| is the magnitude of the EMF in volts and ΦB is the magnetic flux through the circuit in webers. Faraday performed early experiments on induction between coils of wire, including winding a pair of coils around an iron ring, thus creating the first toroidal closed-core transformer. 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. Induction coils The first type of transformer to see wide use was the induction coil, invented by Irish-Catholic Rev. Nicholas Callan of Maynooth College, Ireland in 1836. In 1878, the Ganz factory, Budapest, Hungary, began producing 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. In 1882, Lucien Gaulard and John Dixon Gibbs first exhibited a device with an initially widely criticized laminated plate open iron core called a 'secondary generator' in London, then sold the idea to the Westinghouse company in the United States in 1886. They also exhibited the invention in Turin, Italy in 1884, where it was highly successful and adopted for an electric lighting system. Their open-core device used a fixed 1:1 ratio to supply a series circuit for the utilization load (lamps). However, the voltage of their system was controlled by moving the iron core in or out. Early series circuit transformer distribution Induction coils with open magnetic circuits are inefficient at transferring power to 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. below). The new transformers were 3.4 times more efficient than the open-core bipolar devices of Gaulard and Gibbs. 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). 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. Bláthy had suggested the use of closed cores, Zipernowsky had suggested the use of parallel shunt connections, and Déri had performed the experiments; In early 1885, the three engineers also eliminated the problem of eddy current losses with the invention of the lamination of electromagnetic cores. 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 although the term had already been in use by 1882. 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. Westinghouse improvements Building on the advancement of AC technology in Europe, George Westinghouse founded the Westinghouse Electric in Pittsburgh, Pennsylvania, on January 8, 1886. The new firm became active in developing alternating current (AC) electric infrastructure throughout the United States. 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. George Westinghouse had bought Gaulard and Gibbs' patents for $50,000 in February 1886. He assigned to William Stanley the task of redesign the Gaulard and Gibbs transformer for commercial use in United States. 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). This design was first used commercially in the US in 1886 but Westinghouse was intent on improving the Stanley design to make it (unlike the ZBD type) easy and cheap to produce. In 1891, Nikola Tesla invented the Tesla coil, an air-cored, dual-tuned resonant transformer for producing very high voltages at high frequency. Audio frequency transformers ("repeating coils") were used by early experimenters in the development of the telephone. ==See also==