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109-414: Transformers are used to change AC voltage levels, such transformers being termed step-up or step-down type to increase or decrease voltage level, respectively. Transformers can also be used to provide galvanic isolation between circuits as well as to couple stages of signal-processing circuits. Since the invention of the first constant-potential transformer in 1885, transformers have become essential for

218-507: A cycle ). In certain applications, like guitar amplifiers , different waveforms are used, such as triangular waves or square waves . Audio and radio signals carried on electrical wires are also examples of alternating current. These types of alternating current carry information such as sound (audio) or images (video) sometimes carried by modulation of an AC carrier signal. These currents typically alternate at higher frequencies than those used in power transmission. Electrical energy

327-406: A > 1. By the law of conservation of energy , apparent , real and reactive power are each conserved in the input and output: where S {\displaystyle S} is apparent power and I {\displaystyle I} is current . Combining Eq. 3 & Eq. 4 with this endnote gives the ideal transformer identity : where L {\displaystyle L}

436-403: A balanced signaling system, so that the two wires carry equal but opposite currents. Each wire in a twisted pair radiates a signal, but it is effectively cancelled by radiation from the other wire, resulting in almost no radiation loss. Coaxial cables are commonly used at audio frequencies and above for convenience. A coaxial cable has a conductive wire inside a conductive tube, separated by

545-431: A current source provides a constant current, as long as the load connected to the source terminals has sufficiently low impedance. An ideal current source would provide no energy to a short circuit and approach infinite energy and voltage as the load resistance approaches infinity (an open circuit). An ideal current source has an infinite output impedance in parallel with the source. A real-world current source has

654-448: A dielectric layer. The current flowing on the surface of the inner conductor is equal and opposite to the current flowing on the inner surface of the outer tube. The electromagnetic field is thus completely contained within the tube, and (ideally) no energy is lost to radiation or coupling outside the tube. Coaxial cables have acceptably small losses for frequencies up to about 5 GHz. For microwave frequencies greater than 5 GHz,

763-477: A power plant , energy is generated at a convenient voltage for the design of a generator , and then stepped up to a high voltage for transmission. Near the loads, the transmission voltage is stepped down to the voltages used by equipment. Consumer voltages vary somewhat depending on the country and size of load, but generally motors and lighting are built to use up to a few hundred volts between phases. The voltage delivered to equipment such as lighting and motor loads

872-402: A wall socket . The abbreviations AC and DC are often used to mean simply Alternating Current and Direct Current , respectively, as when they modify current or voltage . The usual waveform of alternating current in most electric power circuits is a sine wave , whose positive half-period corresponds with positive direction of the current and vice versa (the full period is called

981-401: A DC component flowing in the windings. A saturable reactor exploits saturation of the core to control alternating current. Knowledge of leakage inductance is also useful when transformers are operated in parallel. It can be shown that if the percent impedance and associated winding leakage reactance-to-resistance ( X / R ) ratio of two transformers were the same, the transformers would share

1090-440: A compromise between low frequency for traction and heavy induction motors, while still allowing incandescent lighting to operate (although with noticeable flicker). Most of the 25 Hz residential and commercial customers for Niagara Falls power were converted to 60 Hz by the late 1950s, although some 25 Hz industrial customers still existed as of the start of the 21st century. 16.7 Hz power (formerly 16 2/3 Hz)

1199-490: A direct current does not create electromagnetic waves. At very high frequencies, the current no longer flows in the wire, but effectively flows on the surface of the wire, within a thickness of a few skin depths . The skin depth is the thickness at which the current density is reduced by 63%. Even at relatively low frequencies used for power transmission (50 Hz – 60 Hz), non-uniform distribution of current still occurs in sufficiently thick conductors . For example,

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1308-437: A form of dielectric waveguides, can be used. For such frequencies, the concepts of voltages and currents are no longer used. Alternating currents are accompanied (or caused) by alternating voltages. An AC voltage v can be described mathematically as a function of time by the following equation: where The peak-to-peak value of an AC voltage is defined as the difference between its positive peak and its negative peak. Since

1417-459: A higher voltage requires less loss-producing current than for the same power at a lower voltage. Power is often transmitted at hundreds of kilovolts on pylons , and transformed down to tens of kilovolts to be transmitted on lower level lines, and finally transformed down to 100 V – 240 V for domestic use. High voltages have disadvantages, such as the increased insulation required, and generally increased difficulty in their safe handling. In

1526-670: 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

1635-946: A lighting system where sets of induction coils were installed along a high voltage AC line. Instead of changing voltage, the primary windings transferred power to the secondary windings which were connected to one or several 'electric candles' (arc lamps) of his own design, used to keep the failure of one lamp from disabling the entire circuit. In 1878, the 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. Alternating current systems can use transformers to change voltage from low to high level and back, allowing generation and consumption at low voltages but transmission, possibly over great distances, at high voltage, with savings in

1744-492: A nameplate that indicate the phase relationships between their terminals. This may be in the form of a phasor diagram, or using an alpha-numeric code to show the type of internal connection (wye or delta) for each winding. The EMF of a transformer at a given flux increases with frequency. By operating at higher frequencies, transformers can be physically more compact because a given core is able to transfer more power without reaching saturation and fewer turns are needed to achieve

1853-431: A number of approximations. 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 reactance by simple summation as two series impedances. Transformer equivalent circuit impedance and transformer ratio parameters can be derived from

1962-431: 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. Later designs constructed

2071-512: A single center-tapped transformer giving two live conductors, is a common distribution scheme for residential and small commercial buildings in North America. This arrangement is sometimes incorrectly referred to as "two phase". A similar method is used for a different reason on construction sites in the UK. Small power tools and lighting are supposed to be supplied by a local center-tapped transformer with

2180-417: A single equivalent impedance. The internal resistance of an ideal voltage source is zero; it is able to supply or absorb any amount of current. The current through an ideal voltage source is completely determined by the external circuit. When connected to an open circuit, there is zero current and thus zero power. When connected to a load resistance , the current through the source approaches infinity as

2289-465: A transformer design to limit the short-circuit current it will supply. Leaky transformers may be used to supply loads that exhibit negative resistance , such as electric arcs , mercury- and sodium- vapor lamps and neon signs or for safely handling loads that become periodically short-circuited such as electric arc welders . Air gaps are also used to keep a transformer from saturating, especially audio-frequency transformers in circuits that have

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2398-422: A varying magnetic flux in the transformer core, which is also encircled by the secondary winding. This varying flux at the secondary winding induces a varying electromotive force or voltage in the secondary winding. This electromagnetic induction phenomenon is the basis of transformer action and, in accordance with Lenz's law , the secondary current so produced creates a flux equal and opposite to that produced by

2507-513: A very high, but finite output impedance . In the case of transistor current sources, impedance of a few megohms (at low frequencies) is typical. Since no ideal sources of either variety exist (all real-world examples have finite and non-zero source impedance), any current source can be considered as a voltage source with the same source impedance and vice versa. Voltage sources and current sources are sometimes said to be duals of each other and any non ideal source can be converted from one to

2616-555: A voltage of 55 V between each power conductor and earth. This significantly reduces the risk of electric shock in the event that one of the live conductors becomes exposed through an equipment fault whilst still allowing a reasonable voltage of 110 V between the two conductors for running the tools. A third wire , called the bond (or earth) wire, is often connected between non-current-carrying metal enclosures and earth ground. This conductor provides protection from electric shock due to accidental contact of circuit conductors with

2725-403: A wire that is made of a non-perfect conductor (a conductor with finite, rather than infinite, electrical conductivity) pushes the alternating current, along with their associated electromagnetic fields, away from the wire's center. The phenomenon of alternating current being pushed away from the center of the conductor is called skin effect , and a direct current does not exhibit this effect, since

2834-470: Is 230 × R × W × 2 {\displaystyle 230\times R\times W\times 2} , that is 460 RW. During the course of one cycle (two cycle as the power) the voltage rises from zero to 325 V, the power from zero to 460 RW, and both falls through zero. Next, the voltage descends to reverse direction, -325 V, but the power ascends again to 460 RW, and both returns to zero. Alternating current

2943-405: Is a two-terminal device that maintains a fixed voltage drop across its terminals. It is often used as a mathematical abstraction that simplifies the analysis of real electric circuits. If the voltage across an ideal voltage source can be specified independently of any other variable in a circuit, it is called an independent voltage source. Conversely, if the voltage across an ideal voltage source

3052-515: Is an electric current that periodically reverses direction and changes its magnitude continuously with time ranging between some maximum and minimum values, in contrast to direct current (DC), which flows only in one direction. Alternating current is the type of electric current through which electric power is delivered to businesses and residences, and it is the type of electric current that consumers typically use when they plug kitchen appliances , televisions , fans and electric lamps into

3161-518: 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 caused in switching or by lightning. 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

3270-400: 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

3379-530: Is called Litz wire . This measure helps to partially mitigate skin effect by forcing more equal current throughout the total cross section of the stranded conductors. Litz wire is used for making high-Q inductors , reducing losses in flexible conductors carrying very high currents at lower frequencies, and in the windings of devices carrying higher radio frequency current (up to hundreds of kilohertz), such as switch-mode power supplies and radio frequency transformers . As written above, an alternating current

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3488-468: Is determined by some other voltage or current in a circuit, it is called a dependent or controlled voltage source . A mathematical model of an amplifier will include dependent voltage sources whose magnitude is governed by some fixed relation to an input signal, for example. In the analysis of faults on electrical power systems , the whole network of interconnected sources and transmission lines can be usefully replaced by an ideal (AC) voltage source and

3597-505: Is distributed as alternating current because AC voltage may be increased or decreased with a transformer . This allows the power to be transmitted through power lines efficiently at high voltage , which reduces the energy lost as heat due to resistance of the wire, and transformed to a lower, safer voltage for use. Use of a higher voltage leads to significantly more efficient transmission of power. The power losses ( P w {\displaystyle P_{\rm {w}}} ) in

3706-439: Is double of the one of the voltage's. To illustrate these concepts, consider a 230 V AC mains supply used in many countries around the world. It is so called because its root mean square value is 230 V. This means that the time-averaged power delivered P average {\displaystyle P_{\text{average}}} is equivalent to the power delivered by a DC voltage of 230 V. To determine

3815-424: Is given by the universal EMF equation: 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 exiting the secondary winding's 'dot' end. Three-phase transformers used in electric power systems will have

3924-466: Is ideal; all have a non-zero effective internal resistance, and none can supply unlimited current. However, the internal resistance of a real voltage source is effectively modeled in linear circuit analysis by combining a non-zero resistance in series with an ideal voltage source (a Thévenin equivalent circuit ). Most sources of electrical energy (the mains , a battery ) are modeled as voltage sources. An ideal voltage source provides no energy when it

4033-410: Is loaded by an open circuit (i.e. an infinite impedance ), but approaches infinite energy and current when the load resistance approaches zero (a short circuit ). Such a theoretical device would have a zero ohm output impedance in series with the source. A real-world voltage source has a very low, but non-zero internal resistance and output impedance , often much less than 1 ohm. Conversely,

4142-469: Is made of electric charge under periodic acceleration , which causes radiation of electromagnetic waves . Energy that is radiated is lost. Depending on the frequency, different techniques are used to minimize the loss due to radiation. At frequencies up to about 1 GHz, pairs of wires are twisted together in a cable, forming a twisted pair . This reduces losses from electromagnetic radiation and inductive coupling . A twisted pair must be used with

4251-512: Is probably by Guillaume Duchenne , inventor and developer of electrotherapy . In 1855, he announced that AC was superior to direct current for electrotherapeutic triggering of muscle contractions. Alternating current technology was developed further by the Hungarian Ganz Works company (1870s), and in the 1880s: Sebastian Ziani de Ferranti , Lucien Gaulard , and Galileo Ferraris . In 1876, Russian engineer Pavel Yablochkov invented

4360-446: Is standardized, with an allowable range of voltage over which equipment is expected to operate. Standard power utilization voltages and percentage tolerance vary in the different mains power systems found in the world. High-voltage direct-current (HVDC) electric power transmission systems have become more viable as technology has provided efficient means of changing the voltage of DC power. Transmission with high voltage direct current

4469-563: Is still used in some European rail systems, such as in Austria , Germany , Norway , Sweden and Switzerland . Off-shore, military, textile industry, marine, aircraft, and spacecraft applications sometimes use 400 Hz, for benefits of reduced weight of apparatus or higher motor speeds. Computer mainframe systems were often powered by 400 Hz or 415 Hz for benefits of ripple reduction while using smaller internal AC to DC conversion units. A direct current flows uniformly throughout

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4578-405: Is the instantaneous voltage , N {\displaystyle 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 denotes primary and secondary. Combining the ratio of eq. 1 & eq. 2: where for a step-up transformer a < 1 and for a step-down transformer

4687-422: Is therefore V peak − ( − V peak ) = 2 V peak {\displaystyle V_{\text{peak}}-(-V_{\text{peak}})=2V_{\text{peak}}} . Below an AC waveform (with no DC component ) is assumed. The RMS voltage is the square root of the mean over one cycle of the square of the instantaneous voltage. The relationship between voltage and

4796-425: Is used to transmit information , as in the cases of telephone and cable television . Information signals are carried over a wide range of AC frequencies. POTS telephone signals have a frequency of about 3 kHz, close to the baseband audio frequency. Cable television and other cable-transmitted information currents may alternate at frequencies of tens to thousands of megahertz. These frequencies are similar to

4905-417: Is winding self-inductance. By Ohm's law and ideal transformer identity: 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). A varying current in the transformer's primary winding creates

5014-400: The 'real' transformer model's equivalent circuit shown below does not include parasitic capacitance. However, the capacitance effect can be measured by comparing open-circuit inductance, i.e. the inductance of a primary winding when the secondary circuit is open, to a short-circuit inductance when the secondary winding is shorted. The ideal transformer model assumes that all flux generated by

5123-814: 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 Ganz 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

5232-466: 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 I M 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

5341-463: The transmission , distribution , and utilization of alternating current electric power. A wide range of transformer designs is encountered in electronic and electric power applications. Transformers range in size from RF transformers less than a cubic centimeter in volume, to units weighing hundreds of tons used to interconnect the power grid . Ideal transformer equations By Faraday's law of induction: where V {\displaystyle V}

5450-715: The AC system at the Grosvenor Gallery power station in 1886 for the London Electric Supply Corporation (LESCo) including alternators of his own design and open core transformer designs with serial connections for utilization loads - similar to Gaulard and Gibbs. In 1890, he designed their power station at Deptford and converted the Grosvenor Gallery station across the Thames into an electrical substation , showing

5559-413: The biggest difference being that waveguides have no inner conductor. Waveguides can have any arbitrary cross section, but rectangular cross sections are the most common. Because waveguides do not have an inner conductor to carry a return current, waveguides cannot deliver energy by means of an electric current , but rather by means of a guided electromagnetic field . Although surface currents do flow on

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5668-401: The burden of current: If an exact duplicate of voltage is connected in parallel to the original one, either one of them will provide half of the electric current that the original voltage source would provide. For the remainder of the circuit, nothing has changed: These two voltage sources together provide the same voltage, and the same current as the original one alone. No real voltage source

5777-537: The city of Pomona, California , which was 14 miles away. Meanwhile, the possibility of transferring electrical power from a waterfall at a distance was explored at the Grängesberg mine in Sweden. A 45  m fall at Hällsjön, Smedjebackens kommun, where a small iron work had been located, was selected. In 1893, a three-phase 9.5  kv system was used to transfer 400 horsepower a distance of 15  km , becoming

5886-755: 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. The transformer universal EMF equation can be used to calculate the core cross-sectional area for a preferred level of magnetic flux. 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, but are more laborious and expensive to construct. Thin laminations are generally used on high-frequency transformers, with some of very thin steel laminations able to operate up to 10 kHz. Alternating current Alternating current ( AC )

5995-454: 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. 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

6104-414: The corresponding current ratio. The load impedance referred to the primary circuit is equal to the turns ratio squared times the secondary circuit load impedance. The ideal transformer model neglects many basic linear aspects of real transformers, including unavoidable losses and inefficiencies. (a) Core losses, collectively called magnetizing current losses, consisting of (b) Unlike the ideal model,

6213-499: The cost of conductors and energy losses. A bipolar open-core power transformer developed by Lucien Gaulard and John Dixon Gibbs was demonstrated in London in 1881, and attracted the interest of Westinghouse . They also exhibited the invention in Turin in 1884. However, these early induction coils with open magnetic circuits are inefficient at transferring power to loads . Until about 1880,

6322-514: The cross-section of a homogeneous electrically conducting wire. An alternating current of any frequency is forced away from the wire's center, toward its outer surface. This is because an alternating current (which is the result of the acceleration of electric charge ) creates electromagnetic waves (a phenomenon known as electromagnetic radiation ). Electric conductors are not conducive to electromagnetic waves (a perfect electric conductor prohibits all electromagnetic waves within its boundary), so

6431-411: The cross-sectional area. A conductor's AC resistance is higher than its DC resistance, causing a higher energy loss due to ohmic heating (also called I R loss). For low to medium frequencies, conductors can be divided into stranded wires, each insulated from the others, with the relative positions of individual strands specially arranged within the conductor bundle. Wire constructed using this technique

6540-476: The design of electric motors, particularly for hoisting, crushing and rolling applications, and commutator-type traction motors for applications such as railways . However, low frequency also causes noticeable flicker in arc lamps and incandescent light bulbs . The use of lower frequencies also provided the advantage of lower transmission losses, which are proportional to frequency. The original Niagara Falls generators were built to produce 25 Hz power, as

6649-439: 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: Closed-core transformers are constructed in 'core form' or 'shell form'. When windings surround

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6758-504: The electrical system to a safe state. All bond wires are bonded to ground at the main service panel, as is the neutral/identified conductor if present. The frequency of the electrical system varies by country and sometimes within a country; most electric power is generated at either 50 or 60  Hertz . Some countries have a mixture of 50 Hz and 60 Hz supplies, notably electricity power transmission in Japan . A low frequency eases

6867-518: The electromagnetic wave frequencies often used to transmit the same types of information over the air . The first alternator to produce alternating current was an electric generator based on Michael Faraday 's principles constructed by the French instrument maker Hippolyte Pixii in 1832. Pixii later added a commutator to his device to produce the (then) more commonly used direct current. The earliest recorded practical application of alternating current

6976-445: The equivalent circuit shown are by definition linear and such non-linearity effects are not typically reflected in transformer equivalent circuits. With sinusoidal supply, core flux lags the induced EMF by 90°. With open-circuited secondary winding, magnetizing branch current I 0 equals transformer no-load current. The resulting model, though sometimes termed 'exact' equivalent circuit based on linearity assumptions, retains

7085-414: The experiments; 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 wound around a ring core of iron wires or else surrounded by a core of iron wires. In both designs, the magnetic flux linking the primary and secondary windings traveled almost entirely within the confines of

7194-469: The first commercial application. In 1893, Westinghouse built an alternating current system for the Chicago World Exposition . In 1893, Decker designed the first American commercial three-phase power plant using alternating current—the hydroelectric Mill Creek No. 1 Hydroelectric Plant near Redlands, California . Decker's design incorporated 10 kV three-phase transmission and established

7303-447: The fixed voltage independent of the load resistance or the output current . However, a real-world voltage source cannot supply unlimited current. A voltage source is the dual of a current source . Real-world sources of electrical energy, such as batteries and generators , can be modeled for analysis purposes as a combination of an ideal voltage source and additional combinations of impedance elements. An ideal voltage source

7412-422: The following series loop impedances of the model: In normal course of circuit equivalence transformation, R S and X S are in practice usually referred to the primary side by multiplying these impedances by the turns ratio squared, ( N P / N S ) = a. Core loss and reactance is represented by the following shunt leg impedances of the model: R C and X M are collectively termed

7521-455: The following tests: open-circuit test , short-circuit test , winding resistance test, and transformer ratio test. If the flux in the core is purely sinusoidal , the relationship for either winding between its rms voltage E rms of the winding, and the supply frequency f , number of turns N , core cross-sectional area A in m and peak magnetic flux density B peak in Wb/m or T (tesla)

7630-564: The inner walls of the waveguides, those surface currents do not carry power. Power is carried by the guided electromagnetic fields. The surface currents are set up by the guided electromagnetic fields and have the effect of keeping the fields inside the waveguide and preventing leakage of the fields to the space outside the waveguide. Waveguides have dimensions comparable to the wavelength of the alternating current to be transmitted, so they are feasible only at microwave frequencies. In addition to this mechanical feasibility, electrical resistance of

7739-511: The iron core, with no intentional path through air (see toroidal cores ). The new transformers were 3.4 times more efficient than the open-core bipolar devices of Gaulard and Gibbs. The Ganz factory in 1884 shipped the world's first five high-efficiency AC transformers. 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. The ZBD patents included two other major interrelated innovations: one concerning

7848-445: 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

7957-612: The limitations of the direct current system. In 1886, the ZBD engineers designed 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. The reliability of the AC technology received impetus after the Ganz Works electrified a large European metropolis: Rome in 1886. Building on the advancement of AC technology in Europe, George Westinghouse founded

8066-453: The load power in proportion to their respective ratings. However, the impedance tolerances of commercial transformers are significant. Also, the impedance and X/R ratio of different capacity transformers tends to vary. Referring to the diagram, a practical transformer's physical behavior may be represented by an equivalent circuit model, which can incorporate an ideal transformer. Winding joule losses and leakage reactance are represented by

8175-411: The load resistance approaches zero (a short circuit). Thus, an ideal voltage source can supply unlimited power. If two ideal independent voltage source are directly connected in parallel , they must have exactly the same voltage; Otherwise, it creates a fallacy in logic, similar to writing down the equation 1 = 2 {\displaystyle 1=2} . Voltage sources in parallel shares

8284-429: The losses (due mainly to the dielectric separating the inner and outer tubes being a non-ideal insulator) become too large, making waveguides a more efficient medium for transmitting energy. Coaxial cables often use a perforated dielectric layer to separate the inner and outer conductors in order to minimize the power dissipated by the dielectric. Waveguides are similar to coaxial cables, as both consist of tubes, with

8393-657: 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. Transformers for use at power or audio frequencies typically have cores made of high permeability silicon steel . The steel has

8502-419: The lower speed is preferable for larger machines. If the load on a three-phase system is balanced equally among the phases, no current flows through the neutral point . Even in the worst-case unbalanced (linear) load, the neutral current will not exceed the highest of the phase currents. Non-linear loads (e.g. the switch-mode power supplies widely used) may require an oversized neutral bus and neutral conductor in

8611-484: The main street of Great Barrington. The spread of Westinghouse and other AC systems triggered a push back in late 1887 by Thomas Edison (a proponent of direct current), who attempted to discredit alternating current as too dangerous in a public campaign called the " war of the currents ". In 1888, alternating current systems gained further viability with introduction of a functional AC motor , something these systems had lacked up till then. The design, an induction motor ,

8720-538: The maximum value of sin ⁡ ( x ) {\displaystyle \sin(x)} is +1 and the minimum value is −1, an AC voltage swings between + V peak {\displaystyle +V_{\text{peak}}} and − V peak {\displaystyle -V_{\text{peak}}} . The peak-to-peak voltage, usually written as V pp {\displaystyle V_{\text{pp}}} or V P-P {\displaystyle V_{\text{P-P}}} ,

8829-469: The metal chassis of portable appliances and tools. Bonding all non-current-carrying metal parts into one complete system ensures there is always a low electrical impedance path to ground sufficient to carry any fault current for as long as it takes for the system to clear the fault. This low impedance path allows the maximum amount of fault current, causing the overcurrent protection device (breakers, fuses) to trip or burn out as quickly as possible, bringing

8938-425: The non-ideal metals forming the walls of the waveguide causes dissipation of power (surface currents flowing on lossy conductors dissipate power). At higher frequencies, the power lost to this dissipation becomes unacceptably large. At frequencies greater than 200 GHz, waveguide dimensions become impractically small, and the ohmic losses in the waveguide walls become large. Instead, fiber optics , which are

9047-435: 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

9156-431: The peak voltage (amplitude), we can rearrange the above equation to: For 230 V AC, the peak voltage V peak {\displaystyle V_{\text{peak}}} is therefore 230  V × 2 {\displaystyle 230{\text{ V}}\times {\sqrt {2}}} , which is about 325 V, and the peak power P peak {\displaystyle P_{\text{peak}}}

9265-610: The power delivered is: where R {\displaystyle R} represents a load resistance. Rather than using instantaneous power, p ( t ) {\displaystyle p(t)} , it is more practical to use a time-averaged power (where the averaging is performed over any integer number of cycles). Therefore, AC voltage is often expressed as a root mean square (RMS) value, written as V rms {\displaystyle V_{\text{rms}}} , because For this reason, AC power's waveform becomes Full-wave rectified sine, and its fundamental frequency

9374-443: The power supply. It is not directly a power loss, but results in inferior voltage regulation , causing the secondary voltage not to be directly proportional to the primary voltage, particularly under heavy load. Transformers are therefore normally designed to have very low leakage inductance. In some applications increased leakage is desired, and long magnetic paths, air gaps, or magnetic bypass shunts may deliberately be introduced in

9483-399: The primary winding links all the turns of every winding, including itself. In practice, some flux traverses paths that take it outside the windings. Such flux is termed leakage flux , and results in leakage inductance in series with the mutually coupled transformer windings. Leakage flux results in energy being alternately stored in and discharged from the magnetic fields with each cycle of

9592-439: The primary winding. The windings are wound around a core of infinitely high magnetic permeability so that all of the magnetic flux passes through both the primary and secondary windings. With a voltage source connected to the primary winding and a load connected to the secondary winding, the transformer currents flow in the indicated directions and the core magnetomotive force cancels to zero. According to Faraday's law , since

9701-492: 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. The direct current systems did not have these drawbacks, giving it significant advantages over early AC systems. In the UK, Sebastian de Ferranti , who had been developing AC generators and transformers in London since 1882, redesigned

9810-435: 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. 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

9919-422: The same magnetic flux passes through both the primary and secondary windings in an ideal transformer, a voltage is induced in each winding proportional to its number of turns. The transformer winding voltage ratio is equal to the winding turns ratio. An ideal transformer is a reasonable approximation for a typical commercial transformer, with voltage ratio and winding turns ratio both being inversely proportional to

10028-414: The same phases with reverse polarity and so can be simply wired together. In practice, higher "pole orders" are commonly used. For example, a 12-pole machine would have 36 coils (10° spacing). The advantage is that lower rotational speeds can be used to generate the same frequency. For example, a 2-pole machine running at 3600 rpm and a 12-pole machine running at 600 rpm produce the same frequency;

10137-411: The skin depth of a copper conductor is approximately 8.57 mm at 60 Hz, so high current conductors are usually hollow to reduce their mass and cost. This tendency of alternating current to flow predominantly in the periphery of conductors reduces the effective cross-section of the conductor. This increases the effective AC resistance of the conductor, since resistance is inversely proportional to

10246-573: The standards for the complete system of generation, transmission and motors used in USA today. The original Niagara Falls Adams Power Plant with three two-phase generators was put into operation in August 1895, but was connected to the remote transmission system only in 1896. The Jaruga Hydroelectric Power Plant in Croatia was set in operation two days later, on 28 August 1895. Its generator (42 Hz, 240 kW)

10355-410: The supply side. For smaller customers (just how small varies by country and age of the installation) only a single phase and neutral, or two phases and neutral, are taken to the property. For larger installations all three phases and neutral are taken to the main distribution panel. From the three-phase main panel, both single and three-phase circuits may lead off. Three-wire single-phase systems, with

10464-627: The task of redesigning the Gaulard and Gibbs transformer for commercial use in United States. On March 20, 1886, Stanley conducted a demonstrative experiment in Great Barrington : A Siemens generator's voltage of 500 volts was converted into 3000 volts, and then the voltage was stepped down to 500 volts by six Westinghouse transformers. With this setup, the Westinghouse company successfully powered thirty 100-volt incandescent bulbs in twenty shops along

10573-426: The theoretical basis of alternating current calculations include Charles Steinmetz , Oliver Heaviside , and many others. Calculations in unbalanced three-phase systems were simplified by the symmetrical components methods discussed by Charles LeGeyt Fortescue in 1918. Voltage source A voltage source is a two- terminal device which can maintain a fixed voltage . An ideal voltage source can maintain

10682-637: 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 switch-mode power supplies viable, to generate a high frequency, then change the voltage level with a small transformer. Transformers for higher frequency applications such as SMPS 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-dependant losses of these cores often

10791-403: The upstream distribution panel to handle harmonics . Harmonics can cause neutral conductor current levels to exceed that of one or all phase conductors. For three-phase at utilization voltages a four-wire system is often used. When stepping down three-phase, a transformer with a Delta (3-wire) primary and a Star (4-wire, center-earthed) secondary is often used so there is no need for a neutral on

10900-578: 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 1400 V to 2000 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. The other essential milestone

11009-513: The way to integrate older plants into a universal AC supply system. In the autumn of 1884, Károly Zipernowsky , Ottó Bláthy and Miksa Déri (ZBD), three engineers associated with the Ganz Works of Budapest, determined that open-core devices were impractical, as they were incapable of reliably regulating voltage. Bláthy had suggested the use of closed cores, Zipernowsky had suggested the use of parallel shunt connections , and Déri had performed

11118-415: The windings in a real transformer have non-zero resistances and inductances associated with: (c) similar to an inductor , parasitic capacitance and self-resonance phenomenon due to the electric field distribution. Three kinds of parasitic capacitance are usually considered and the closed-loop equations are provided Inclusion of capacitance into the transformer model is complicated, and is rarely attempted;

11227-477: The wire are a product of the square of the current ( I ) and the resistance (R) of the wire, described by the formula: This means that when transmitting a fixed power on a given wire, if the current is halved (i.e. the voltage is doubled), the power loss due to the wire's resistance will be reduced to one quarter. The power transmitted is equal to the product of the current and the voltage (assuming no phase difference); that is, Consequently, power transmitted at

11336-552: Was independently invented by Galileo Ferraris and Nikola Tesla (with Tesla's design being licensed by Westinghouse in the US). This design was independently further developed into the modern practical three-phase form by Mikhail Dolivo-Dobrovolsky and Charles Eugene Lancelot Brown in Germany on one side, and Jonas Wenström in Sweden on the other, though Brown favoured the two-phase system. A long-distance alternating current transmission

11445-534: Was installed in Telluride Colorado. The first three-phase system was established in 1891 in Frankfurt , Germany. The Tivoli – Rome transmission was completed in 1892. The San Antonio Canyon Generator was the third commercial single-phase hydroelectric AC power plant in the United States to provide long-distance electricity. It was completed on December 31, 1892, by Almarian William Decker to provide power to

11554-498: Was made and installed by the Hungarian company Ganz , while the transmission line from the power plant to the City of Šibenik was 11.5 kilometers (7.1 mi) long, and the municipal distribution grid 3000 V/110 V included six transforming stations. Alternating current circuit theory developed rapidly in the latter part of the 19th and early 20th century. Notable contributors to

11663-596: Was not feasible in the early days of electric power transmission , as there was then no economically viable way to step the voltage of DC down for end user applications such as lighting incandescent bulbs. Three-phase electrical generation is very common. The simplest way is to use three separate coils in the generator stator , physically offset by an angle of 120° (one-third of a complete 360° phase) to each other. Three current waveforms are produced that are equal in magnitude and 120° out of phase to each other. If coils are added opposite to these (60° spacing), they generate

11772-506: Was the introduction of 'voltage source, voltage intensive' (VSVI) systems' by the invention of constant voltage generators in 1885. In early 1885, the three engineers also eliminated the problem of eddy current losses with the invention of the lamination of electromagnetic cores. Ottó Bláthy also invented the first AC electricity meter . The AC power system was developed and adopted rapidly after 1886 due to its ability to distribute electricity efficiently over long distances, overcoming

11881-737: Was used in 1883 for the Metropolitan Railway station lighting in London , while the single-phase 1884 system in Turin , Italy, was the first multiple-user AC distribution system in the world. The Ames Hydroelectric Generating Plant , constructed in 1890, was among the first hydroelectric alternating current power plants. A long distance transmission of single-phase electricity from a hydroelectric generating plant in Oregon at Willamette Falls sent power fourteen miles downriver to downtown Portland for street lighting in 1890. In 1891, another transmission system

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