Alternating current

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v t e

Alternating current (AC) is an

The usual

of an AC carrier signal. These currents typically alternate at higher frequencies than those used in power transmission.

Transmission, distribution, and domestic power supply

Electrical energy is distributed as alternating current because AC

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 (${\displaystyle P_{\rm {w}}}$) in the wire are a product of the square of the current ( I ) and the (R) of the wire, described by the formula:

${\displaystyle P_{\rm {w}}=I^{2}R\,.}$

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,

${\displaystyle P_{\rm {t}}=IV\,.}$

Consequently, power transmitted at 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.

electric generation plants and consumers. The lines in the picture are located in eastern Utah

.

High voltages have disadvantages, such as the increased insulation required, and generally increased difficulty in their safe handling. In a

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 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.

. 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 the supply side. For smaller customers (just how small varies by country and age of the installation) only a

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

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 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.

AC power supply frequencies

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.

Low frequency

A low frequency eases the design of electric motors, particularly for hoisting, crushing and rolling applications, and commutator-type

. 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 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^[

.

High frequency

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.^{[citation needed]}

Effects at high frequencies

A direct current flows uniformly throughout the cross-section of a homogeneous

, and a direct current does not exhibit this effect, since 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

ohmic heating

(also called I²R loss).

Techniques for reducing AC resistance

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 is called

.

Techniques for reducing radiation loss

As written above, an alternating current is made of

electromagnetic waves

. Energy that is radiated is lost. Depending on the frequency, different techniques are used to minimize the loss due to radiation.

Twisted pairs

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 a balanced signalling 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

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

dissipate power). At higher frequencies, the power lost to this dissipation becomes unacceptably large.

Fiber optics

At frequencies greater than 200 GHz, waveguide dimensions become impractically small, and the

fiber optics

, which are a form of dielectric waveguides, can be used. For such frequencies, the concepts of voltages and currents are no longer used.

Mathematics of AC voltages

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:

${\displaystyle v(t)=V_{\text{peak}}\sin(\omega t)}$,

where

• ${\displaystyle V_{\text{peak}}}$ is the peak voltage (unit: volt),
• ${\displaystyle \omega }$ is the
  radians per second
  ).
  The angular frequency is related to the physical frequency, ${\displaystyle f}$ (unit: hertz), which represents the number of cycles per second, by the equation ${\displaystyle \omega =2\pi f}$.
• ${\displaystyle t}$ is the time (unit: second).

The peak-to-peak value of an AC voltage is defined as the difference between its positive peak and its negative peak. Since the maximum value of ${\displaystyle \sin(x)}$ is +1 and the minimum value is −1, an AC voltage swings between ${\displaystyle +V_{\text{peak}}}$ and ${\displaystyle -V_{\text{peak}}}$. The peak-to-peak voltage, usually written as ${\displaystyle V_{\text{pp}}}$ or ${\displaystyle V_{\text{P-P}}}$, is therefore ${\displaystyle V_{\text{peak}}-(-V_{\text{peak}})=2V_{\text{peak}}}$.

Root mean square voltage

Below an

) is assumed.

The RMS voltage is the square root of the mean over one cycle of the square of the instantaneous voltage.

Power

The relationship between voltage and the power delivered is:

${\displaystyle p(t)={\frac {v^{2}(t)}{R}}}$,

where ${\displaystyle R}$ represents a load resistance.

Rather than using instantaneous power, ${\displaystyle p(t)}$, 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 ${\displaystyle V_{\text{rms}}}$, because

${\displaystyle P_{\text{average}}={\frac {{V_{\text{rms}}}^{2}}{R}}.}$

Power oscillation

${\displaystyle {\begin{aligned}v(t)&=V_{\text{peak}}\sin(\omega t)\\i(t)&={\frac {v(t)}{R}}={\frac {V_{\text{peak}}}{R}}\sin(\omega t)\\p(t)&=v(t)i(t)={\frac {(V_{\text{peak}})^{2}}{R}}\sin ^{2}(\omega t)={\frac {(V_{\text{peak}})^{2}}{2R}}\ (1-\cos(2\omega t))\end{aligned}}}$

For this reason, AC power's waveform becomes Full-wave rectified sine, and its fundamental frequency is double of the one of the voltage's.

Examples of alternating current

To illustrate these concepts, consider a 230 V AC

value is 230 V. This means that the time-averaged power delivered ${\displaystyle P_{\text{average}}}$ is equivalent to the power delivered by a DC voltage of 230 V. To determine the peak voltage (amplitude), we can rearrange the above equation to:

${\displaystyle V_{\text{peak}}={\sqrt {2}}\ V_{\text{rms}}}$

${\displaystyle P_{\text{peak}}={\frac {(V_{\text{rms}})^{2}}{R}}{\frac {(V_{\text{peak}})^{2}}{(V_{\text{rms}})^{2}}}={\text{P}}_{\text{average}}{\sqrt {2}}^{2}={\text{2}}P_{\text{average}}.}$

For 230 V AC, the peak voltage ${\displaystyle V_{\text{peak}}}$ is therefore ${\displaystyle 230{\text{ V}}\times {\sqrt {2}}}$, which is about 325 V, and the peak power ${\displaystyle P_{\text{peak}}}$ is ${\displaystyle 230\times R\times W\times 2}$, 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.

Information transmission

Alternating current 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 the electromagnetic wave frequencies often used to transmit the same types of information over the air.

History

The first

.

In 1876, Russian engineer Pavel Yablochkov invented 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,^[5][6] used to keep the failure of one lamp from disabling the entire circuit.^[5] 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.^[7]

Transformers

Alternating current systems can use

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 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.^[9] In 1890, he designed their power station at Deptford^[10] and converted the Grosvenor Gallery station across the Thames into an electrical substation, showing the way to integrate older plants into a universal AC supply system.^[11]

Pioneers

In the autumn^[ambiguous] 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.^[12] Bláthy had suggested the use of closed cores, Zipernowsky had suggested the use of parallel shunt connections, and Déri had performed the experiments;^[13] 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.^[8] In both designs, the magnetic flux linking the primary and secondary windings traveled almost entirely within the confines of the iron core, with no intentional path through air (see toroidal cores). The new transformers were 3.4 times more efficient than the open-core bipolar devices of Gaulard and Gibbs.^[14] The Ganz factory in 1884 shipped the world's first five high-efficiency AC transformers.^[15] 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.^[15]

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 1400 V to 2000 V) than the voltage of utilization loads (100 V initially preferred).^[16][17] 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.^[18][19] The other essential milestone was the introduction of 'voltage source, voltage intensive' (VSVI) systems'^[20] by the invention of constant voltage generators in 1885.^[21] In early 1885, the three engineers also eliminated the problem of eddy current losses with the invention of the lamination of electromagnetic cores.^[22] Ottó Bláthy also invented the first AC electricity meter.^{[23][24][25][26]}

The AC power system was developed and adopted rapidly after 1886 due to its ability to distribute electricity efficiently over long distances, overcoming 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.^[27] The reliability of the AC technology received impetus after the Ganz Works electrified a large European metropolis: Rome in 1886.^[27]

Building on the advancement of AC technology in Europe,

in Sweden on the other, though Brown favoured the two-phase system.

The

In 1893, Decker designed the first American commercial was 11.5 kilometers (7.1 mi) long on wooden towers, 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 the theoretical basis of alternating current calculations include

in 1918.

See also

References

Further reading

• Willam A. Meyers, History and Reflections on the Way Things Were: Mill Creek Power Plant – Making History with AC, IEEE Power Engineering Review, February 1997, pp. 22–24

External links

Wikimedia Commons has media related to Alternating current.

• "AC/DC: What's the Difference?". Edison's Miracle of Light, American Experience. (
  PBS
  )
• "AC/DC: Inside the AC Generator Archived 2014-12-28 at the Wayback Machine". Edison's Miracle of Light, American Experience. (PBS)
• Kuphaldt, Tony R., "Lessons In Electric Circuits : Volume II – AC". March 8, 2003. (Design Science License)
• Professor Mark Csele's tour of the 25 Hz Rankine generating station
• Blalock, Thomas J., "The Frequency Changer Era: Interconnecting Systems of Varying Cycles". The history of various frequencies and interconversion schemes in the US at the beginning of the 20th century
• AC Power History and Timeline