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58-503: The first deliveries for STB started in 2009. Initially, the trams were manufactured in the LF-CH version, with direct current motors with chopper , and since 2012 in the LF-CA version, with inverter and alternating current motors. A five-section vehicle design of 100% low floor and 29 m (95 ft) length was also proposed as Bucur LF2. This European tramway-related article

116-409: 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}

174-510: A rectifier , which contains electronic elements (usually) or electromechanical elements (historically) that allow current to flow only in one direction. Direct current may be converted into alternating current via an inverter . Direct current has many uses, from the charging of batteries to large power supplies for electronic systems, motors, and more. Very large quantities of electrical energy provided via direct-current are used in smelting of aluminum and other electrochemical processes. It

232-438: A vacuum as in electron or ion beams . The electric current flows in a constant direction, distinguishing it from alternating current (AC). A term formerly used for this type of current was galvanic current . The abbreviations AC and DC are often used to mean simply alternating and direct , as when they modify current or voltage . Direct current may be converted from an alternating current supply by use of

290-543: A DC circuit. However, most such circuits have a DC solution. This solution gives the circuit voltages and currents when the circuit is in DC steady state . Such a circuit is represented by a system of differential equations . The solution to these equations usually contain a time varying or transient part as well as constant or steady state part. It is this steady state part that is the DC solution. There are some circuits that do not have

348-403: 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

406-407: A DC solution. Two simple examples are a constant current source connected to a capacitor and a constant voltage source connected to an inductor. In electronics, it is common to refer to a circuit that is powered by a DC voltage source such as a battery or the output of a DC power supply as a DC circuit even though what is meant is that the circuit is DC powered. In a DC circuit, a power source (e.g.

464-453: A battery system to ensure power is maintained for subscriber lines during power interruptions. Other devices may be powered from the telecommunications DC system using a DC-DC converter to provide any convenient voltage. Many telephones connect to a twisted pair of wires, and use a bias tee to internally separate the AC component of the voltage between the two wires (the audio signal) from

522-423: A battery, capacitor, etc.) has a positive and negative terminal, and likewise, the load also has a positive and negative terminal. To complete the circuit, positive charges need to flow from the power source to the load. The charges will then return to the negative terminal of the load, which will then flow back to the negative terminal of the battery, completing the circuit. If either the positive or negative terminal

580-413: A catalyst to produce electricity and water as byproducts) also produce only DC. Light aircraft electrical systems are typically 12 V or 24 V DC similar to automobiles. Transformer In electrical engineering , a transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits . A varying current in any coil of

638-464: A changing magnetic flux encircled by the coil. 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

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696-524: A direct current source . The DC solution of an electric circuit is the solution where all voltages and currents are constant. Any stationary voltage or current waveform can be decomposed into a sum of a DC component and a zero-mean time-varying component; the DC component is defined to be the expected value, or the average value of the voltage or current over all time. Although DC stands for "direct current", DC often refers to "constant polarity". Under this definition, DC voltages can vary in time, as seen in

754-670: 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

812-493: 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

870-432: 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

928-433: 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

986-468: 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

1044-422: 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

1102-436: Is a stub . You can help Misplaced Pages by expanding it . This Romania -related article is a stub . You can help Misplaced Pages by expanding it . Direct current Direct current ( DC ) is one-directional flow of electric charge . An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors , insulators , or even through

1160-554: Is also used for some railways , especially in urban areas . High-voltage direct current is used to transmit large amounts of power from remote generation sites or to interconnect alternating current power grids. Direct current was produced in 1800 by Italian physicist Alessandro Volta 's battery, his Voltaic pile . The nature of how current flowed was not yet understood. French physicist André-Marie Ampère conjectured that current travelled in one direction from positive to negative. When French instrument maker Hippolyte Pixii built

1218-482: Is an AC device which uses a rectifier to produce DC for battery charging. Most highway passenger vehicles use nominally 12  V systems. Many heavy trucks, farm equipment, or earth moving equipment with Diesel engines use 24 volt systems. In some older vehicles, 6 V was used, such as in the original classic Volkswagen Beetle . At one point a 42 V electrical system was considered for automobiles, but this found little use. To save weight and wire, often

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1276-519: 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

1334-402: 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

1392-435: Is commonly found in many extra-low voltage applications and some low-voltage applications, especially where these are powered by batteries or solar power systems (since both can produce only DC). Most electronic circuits or devices require a DC power supply . Domestic DC installations usually have different types of sockets , connectors , switches , and fixtures from those suitable for alternating current. This

1450-427: Is disconnected, the circuit will not be complete and the charges will not flow. In some DC circuit applications, polarity does not matter, which means you can connect positive and negative backwards and the circuit will still be complete and the load will still function normally. However, in most DC applications, polarity does matter, and connecting the circuit backwards will result in the load not working properly. DC

1508-412: Is distributed to a substation, which utilizes a rectifier to convert the power to direct current. The term DC is used to refer to power systems that use only one electrical polarity of voltage or current, and to refer to the constant, zero-frequency, or slowly varying local mean value of a voltage or current. For example, the voltage across a DC voltage source is constant as is the current through

1566-425: 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

1624-447: Is mostly due to the lower voltages used, resulting in higher currents to produce the same amount of power . It is usually important with a DC appliance to observe polarity, unless the device has a diode bridge to correct for this. Most automotive applications use DC. An automotive battery provides power for engine starting, lighting, the ignition system, the climate controls, and the infotainment system among others. The alternator

1682-421: Is rarely attempted; 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

1740-405: 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

1798-419: 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

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1856-468: 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

1914-464: 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}

1972-448: The DC component of the voltage between the two wires (used to power the phone). High-voltage direct current (HVDC) electric power transmission systems use DC for the bulk transmission of electrical power, in contrast with the more common alternating current systems. For long-distance transmission, HVDC systems may be less expensive and suffer lower electrical losses. Applications using fuel cells (mixing hydrogen and oxygen together with

2030-407: The circuit voltages and currents are independent of time. A particular circuit voltage or current does not depend on the past value of any circuit voltage or current. This implies that the system of equations that represent a DC circuit do not involve integrals or derivatives with respect to time. If a capacitor or inductor is added to a DC circuit, the resulting circuit is not, strictly speaking,

2088-456: 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

2146-400: 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

2204-440: 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

2262-448: 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

2320-654: The first dynamo electric generator in 1832, he found that as the magnet used passed the loops of wire each half turn, it caused the flow of electricity to reverse, generating an alternating current . At Ampère's suggestion, Pixii later added a commutator , a type of "switch" where contacts on the shaft work with "brush" contacts to produce direct current. The late 1870s and early 1880s saw electricity starting to be generated at power stations . These were initially set up to power arc lighting (a popular type of street lighting) running on very high voltage (usually higher than 3,000 volts) direct current or alternating current. This

2378-424: 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

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2436-461: 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)

2494-412: The ideal model, 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

2552-445: 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

2610-455: 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

2668-662: 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

2726-512: The metal frame of the vehicle is connected to one pole of the battery and used as the return conductor in a circuit. Often the negative pole is the chassis "ground" connection, but positive ground may be used in some wheeled or marine vehicles. In a battery electric vehicle , there are usually two separate DC systems. The "low voltage" DC system typically operates at 12V, and serves the same purpose as in an internal combustion engine vehicle. The "high voltage" system operates at 300-400V (depending on

2784-444: 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

2842-401: 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

2900-439: 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

2958-428: The raw output of a rectifier or the fluctuating voice signal on a telephone line. Some forms of DC (such as that produced by a voltage regulator ) have almost no variations in voltage , but may still have variations in output power and current. A direct current circuit is an electrical circuit that consists of any combination of constant voltage sources, constant current sources, and resistors . In this case,

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3016-436: 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

3074-423: 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

3132-637: 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

3190-415: The transformer produces a varying magnetic flux in the transformer's core, which induces a varying electromotive force (EMF) across any other coils wound around the same core. Electrical energy can be transferred between separate coils without a metallic (conductive) connection between the two circuits. Faraday's law of induction , discovered in 1831, describes the induced voltage effect in any coil due to

3248-464: The vehicle), and provides the power for the traction motors . Increasing the voltage for the traction motors reduces the current flowing through them, increasing efficiency. Telephone exchange communication equipment uses standard −48 V DC power supply. The negative polarity is achieved by grounding the positive terminal of power supply system and the battery bank. This is done to prevent electrolysis depositions. Telephone installations have

3306-406: Was followed by the widespread use of low voltage direct current for indoor electric lighting in business and homes after inventor Thomas Edison launched his incandescent bulb based electric " utility " in 1882. Because of the significant advantages of alternating current over direct current in using transformers to raise and lower voltages to allow much longer transmission distances, direct current

3364-477: Was replaced over the next few decades by alternating current in power delivery. In the mid-1950s, high-voltage direct current transmission was developed, and is now an option instead of long-distance high voltage alternating current systems. For long distance undersea cables (e.g. between countries, such as NorNed ), this DC option is the only technically feasible option. For applications requiring direct current, such as third rail power systems, alternating current

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