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## PowerPedia:Alternating current

Lasted edited by Andrew Munsey, updated on June 15, 2016 at 2:04 am.

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An alternating current (AC) is an There was an error working with the wiki: Code[5] and direction vary cyclically, as opposed to Direct current, whose direction remains constant. The usual There was an error working with the wiki: Code[30] of an There was an error working with the wiki: Code[31] circuit is a There was an error working with the wiki: Code[32], as this results in the most efficient transmission of energy. However in certain applications different waveforms are used, such as triangular or square waves.

Used generically, AC refers to the form in which There was an error working with the wiki: Code[6] and There was an error working with the wiki: Code[7] signals carried on electrical There was an error working with the wiki: Code[33] are also examples of alternating current. In these applications, an important goal is often the recovery of There was an error working with the wiki: Code[34] encoded (or There was an error working with the wiki: Code[35]) onto the AC signal.

#### History

William Stanley designed one of the first practical devices to transfer AC power efficiently between isolated circuits. Using pairs of coils wound on a common iron core, his design, called an Induction coil, was an early precursor of the modern Transformer. The system used today was devised by many contributors including Nikola Tesla, There was an error working with the wiki: Code[36], There was an error working with the wiki: Code[37], There was an error working with the wiki: Code[38], and There was an error working with the wiki: Code[39] from There was an error working with the wiki: Code[40] to There was an error working with the wiki: Code[41]. AC systems overcame the limitations of the Direct current system used by There was an error working with the wiki: Code[42] to distribute electricity.

The first long-distance Electric power transmission of alternating current took place in There was an error working with the wiki: Code[43] near There was an error working with the wiki: Code[44], followed a few months later in Germany. Thomas Edison strongly advocated the use of Direct current (DC), having many patents in that technology, but eventually alternating current came into general use (see There was an error working with the wiki: Code[45]).

The first modern commercial power plant using three-phase alternating current was at the Mill Creek hydroelectric plant near There was an error working with the wiki: Code[46] in 1893. Its designer was Almirian Decker, a brilliant young engineer. Decker's innovative design incorporated 10,000 volt three phase transmission and established the standards for the complete system of generation, transmission and motors used today. And through the use of alternating current, There was an error working with the wiki: Code[47] of There was an error working with the wiki: Code[48] was able to solve many of the problems associated with Electricity generation and transmission.

#### Transmission, distribution, and domestic power supply

In There was an error working with the wiki: Code[8] transmission systems contrast with the more common alternating-current systems as a means for the bulk transmission of electrical power over long distances. However, these tend to be more expensive and less efficient than transformers, and did not exist when There was an error working with the wiki: Code[9], There was an error working with the wiki: Code[10] and Nikola Tesla were designing their power systems.

Use of a higher voltage leads to more efficient transmission of power. The power losses in a conductor are a product of the square of the current and the Electrical resistance of the conductor, described by the formula P= I^2R . This means that when transmitting a fixed power on a given wire, if the current is doubled, the power loss will be four times greater. Since the power transmitted is equal to the product of the current, the voltage and the There was an error working with the wiki: Code[11] ( P = IV \cos \phi), the same amount of power can be transmitted with a lower current by increasing the voltage. Therefore it is advantageous when transmitting large amounts of power to distribute the power with high voltages (often hundreds of kilovolts). However, high voltages also have disadvantages, the main ones being the increased insulation required, and generally increased difficulty in their safe handling. In a Power plant, power 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 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.

There was an error working with the wiki: Code[12] electrical generation is very common. Three separate coils in the generator There was an error working with the wiki: Code[49] are physically offset by an angle of 120° to each other. Three current waveforms are produced that are equal in magnitude and 120° There was an error working with the wiki: Code[50] to each other.

If the load on a three-phase system is balanced equally between the phases, no current flows through the There was an error working with the wiki: Code[51]. Even in the worst-case unbalanced (linear) load, the neutral current will not exceed the highest of the phase currents. For three-phase at low (normal mains) voltages a four-wire system is normally used. When stepping down three-phase, a transformer with a Delta primary and a Star 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 There was an error working with the wiki: Code[13] and the neutral or two phases and the neutral are taken to the property. For larger installations all three phases and the neutral are taken to the main distribution panel. From the three-phase main panel, both single and three-phase circuits may lead off.

There was an error working with the wiki: Code[14] systems, with a single centre-tapped transformer giving two live conductors, is a common distribution scheme for residential and small commercial buildings in North America. 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 a voltage of 55V between each power conductor and the earth. This significantly reduces the risk of There was an error working with the wiki: Code[52] in the event that one of the live conductors becomes exposed through an equipment fault whilst still allowing a reasonable voltage for running the tools.

A There was an error working with the wiki: Code[15] is often connected between non-current carrying metal enclosures and earth ground. This conductor provides protection from electrical shock due to accidental contact of circuit conductors with the case of portable appliances and tools.

#### AC power supply frequencies

The There was an error working with the wiki: Code[16] varies by country most electric power is generated at either 50 or 60 Hz. See There was an error working with the wiki: Code[53]. Some countries have a mixture of 50 Hz and 60 Hz supplies, notably Japan.

A low frequency eases the design of low speed electric motors, particularly for hoisting, crushing and rolling applications, and commutator-type There was an error working with the wiki: Code[54]s for applications such as There was an error working with the wiki: Code[55]s, but also causes a noticeable flicker in incandescent lighting and objectionable flicker of There was an error working with the wiki: Code[56]s. 16.7 Hz power (approx. ? of the mains frequency) is still used in some European rail systems, such as in There was an error working with the wiki: Code[57], Germany, There was an error working with the wiki: Code[58], There was an error working with the wiki: Code[59] and There was an error working with the wiki: Code[60].

Off-shore, textile industry, marine, computer There was an error working with the wiki: Code[61], aircraft, and spacecraft applications sometimes use 400 Hz, for benefits of reduced weight of apparatus or higher motor speeds.

#### Effects at high frequencies

A direct, constant, current flows uniformly throughout the cross-section of the (uniform) wire that carries it. With alternating current of any frequency, the current is forced towards the outer surface of the wire, and away from the center. This is due to the fact that an There was an error working with the wiki: Code[17] There was an error working with the wiki: Code[18] (the metal which makes up the wire) do not allow propagation of electromagnetic waves. This phenomenon is called There was an error working with the wiki: Code[62].

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 There was an error working with the wiki: Code[19]s. For example, the skin depth of a copper conductor is approximately 8.57mm at 60 Hz, so high current conductors are usually hollow to reduce their mass and cost.

Since the current tends to flow in the periphery of conductors, the effective cross-section of the conductor is reduced. This increases the effective AC There was an error working with the wiki: Code[63] of the conductor, since resistance is inversely proportional to the cross-sectional area in which the current actually flows. The AC resistance often is many times higher than the DC resistance, causing a much higher energy loss due to skin effect There was an error working with the wiki: Code[64] (also called I2R loss).

##### Techniques for reducing AC resistance

For low to medium frequencies, conductors can be divided into stranded wires, each insulated from one other, and the individual strands specially arranged to change their relative position within the conductor bundle. Wire constructed using this technique is called There was an error working with the wiki: Code[20] There was an error working with the wiki: Code[21] and There was an error working with the wiki: Code[65] Transformers.

##### Techniques for reducing radiation loss

As written above, an alternating current is made of There was an error working with the wiki: Code[22] of There was an error working with the wiki: Code[66]. Energy that is radiated represents a loss. Depending on the frequency, different techniques are used to minimize the loss due to radiation.

##### Twisted pairs

At frequencies up to about 1 GHz, wires are paired together in cabling to form a There was an error working with the wiki: Code[67] in order to reduce losses due to There was an error working with the wiki: Code[68] and There was an error working with the wiki: Code[69]. A twisted pair must be used with a balanced signalling system, where the two wires carry equal but opposite currents. The result is that each wire in the twisted pair radiates a signal that is effectively cancelled by the other wire, resulting in almost no electromagnetic radiation.

##### Coax cables

At frequencies above 1 GHz, unshielded wires of practical dimensions lose too much energy to radiation, so There was an error working with the wiki: Code[23] a more efficient medium for transmitting energy.

##### Waveguides

There was an error working with the wiki: Code[24] are similar to coax cables, as both consist of tubes, with the biggest difference being that the waveguide has no inner conductor. Waveguides can have any arbitrary cross section, but rectangular cross section are the most common. With waveguides, the energy is no longer carried by an Electric current, but by a guided Electromagnetic field. Waveguides have dimensions comparable to the wavelength of the alternating current to be transmitted, so are only feasible at microwave frequencies.

##### Fiber optics

At frequencies greater than 200 GHz, waveguide dimensions become impractically too small, and the There was an error working with the wiki: Code[25] in the waveguide walls become large. Instead, There was an error working with the wiki: Code[70], 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 by alternating voltages. An AC voltage v can be described mathematically as a There was an error working with the wiki: Code[26] of time by the following equation:

:v(t)=V_{peak}\cdot\sin(\omega t),

where

:Vpeak is the peak voltage (unit: Volt),

:? is the There was an error working with the wiki: Code[71] (unit: There was an error working with the wiki: Code[72]), and

:t is the time (unit: There was an error working with the wiki: Code[73]).

Since angular frequency is of more interest to mathematicians than to engineers and technicians, this is commonly rewritten as:

:v(t)=V_{peak}\cdot\sin(2\pi f t),

where

:f is the Frequency (unit: There was an error working with the wiki: Code[74]).

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 sin(x) is +1 and the minimum value is &minus1, an AC voltage swings between +Vpeak and &minusVpeak. The peak-to-peak voltage, usually written as Vpp or VP-P, is therefore (+Vpeak) &minus (&minusVpeak) = 2 &times Vpeak.

AC voltage is usually expressed as a There was an error working with the wiki: Code[75] (RMS) value, written Vrms. For a sinusoidal voltage:

:V_{rms}=\frac{V_{peak}}{\sqrt{2}}

Vrms is useful in calculating the power consumed by a load. If a DC voltage of VDC delivers a certain power P into a given load, then an AC voltage of Vpeak will deliver the same average power P into the same load if Vrms = VDC. Because of this fact, RMS is the normal means of measuring AC voltage.

##### Example

To illustrate these concepts, consider a 240 V AC mains supply. It is so called because its There was an error working with the wiki: Code[27] value is (at least nominally) 240 V. This means that it has the same heating effect as 240 V DC. To work out its peak voltage (amplitude), we can modify the above equation to:

:

V_{peak}=\sqrt{2}\ V_{rms}

For our 240 V AC, the peak voltage Vpeak is therefore 240 V &times ?2, which is about 339 V. The peak-to-peak value VP-P of the 240 V AC mains is even higher: 2 &times 240 V &times ?2, or about 679 V.

Note that non-sinusoidal waveforms have a different relationship between their peak magnitude and effective (RMS) value. This is of practical significance when working with non-linear circuit elements that produce harmonic currents, such as There was an error working with the wiki: Code[76].

The There was an error working with the wiki: Code[77] (including the UK) has now officially harmonized on a supply of 230 V 50 Hz. However, it made the tolerance bands very wide at ±10%. Some countries actually specify stricter standards than this for example, the UK specifies 230 V +10% &minus6%. Most supplies to the old standards therefore conform to the new one and do not need to be changed.

#### Related Items

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Electricity

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#### External articles and references

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General

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, Pages 22-24

"AC/DC: What's the Difference?". Edison's Miracle of Light, American Experience. (There was an error working with the wiki: Code[80])

"AC-DC: Inside the AC Generator". Edison's Miracle of Light, American Experience. (PBS)

Kuphaldt, Tony R., "Lessons In Electric Circuits : Volume II - AC". March 8, 2003. (Design Science License)

Nave, C. R., "Alternating Current Circuits Concepts". HyperPhysics.

"Alternating Current (AC)". Magnetic Particle Inspection, Nondestructive Testing Encyclopedia.

"Alternating current". Analog Process Control Services.

Hiob, Eric, "An Application of Trigonometry and Vectors to Alternating Current". British Columbia Institute of Technology, 2004.

"Introduction to alternating current and transformers". Integrated Publishing.

"Wind Energy Reference Manual Part 4: Electricity". Danish Wind Industry Association, 2003.

Chan. Keelin, "Alternating current Tools". JC Physics, 2002.

"Measurement -> ac". Analog Process Control Services.

Williams, Trip "Kingpin", "Understanding Alternating Current, Some more power concepts".

Professor Mark Csele's tour of the 25 Hz Rankine generating station

50/60 hertz information

AC circuits Animations and explanations of vector (phasor) representation of RLC circuits

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

There was an error working with the wiki: Code[1], Wikipedia: The Free Encyclopedia. Wikimedia Foundation.

Newsgroups

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