Encyclopedia
An
alternating current is an electrical current whose magnitude and direction vary cyclically, as opposed to
direct current, whose direction remains constant. The usual
waveform of an
AC power circuit is a
sine wave, 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
electricity is delivered to businesses and residences. However, audio and
radio signals carried on electrical
wire are also examples of alternating current. In these applications, an important goal is often the recovery of information encoded 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,
George Westinghouse, Lucien Gaulard, John Gibbs, and Oliver Shallenger from 1881 to 1889. AC systems overcame the limitations of
direct current systems, such as that which
Thomas Edison first used to distribute electricity commercially.
The first long-distance
transmission of alternating current took place in 1891 near
Telluride, Colorado, followed a few months later in
Germany. Thomas Edison strongly advocated the use of
direct current , having many patents in that technology, but eventually alternating current came into general use .
The first modern commercial power plant using three-phase alternating current was at the Mill Creek hydroelectric plant near
Redlands, California 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,
Charles Proteus Steinmetz of
General Electric was able to solve many of the problems associated with electricity generation and transmission.
Transmission, distribution, and domestic power supply
AC voltage can be stepped up or down by a
transformer to a different
voltage. Modern High-voltage, direct current electric power 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
Edison,
Westinghouse and
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
resistance of the conductor, described by the formula . 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
cosine of the phase difference f , 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 . 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.
Three-phase electrical generation is very common. Three separate coils in the generator stator are physically offset by an angle of 120° to each other. Three current waveforms are produced that are equal in magnitude and 120°
out of phase to each other.
If the load on a three-phase system is balanced equally between the phases, no current flows through the neutral point. Even in the worst-case unbalanced load, the neutral current will not exceed the highest of the phase currents. For three-phase at low 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 only a
single phase 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.
Three-wire single phase 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
electric shock 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 third wire 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 frequency of the electrical system varies by country; most electric power is generated at either 50 or 60 Hz. See
List of countries with mains power plugs, voltages and frequencies. 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 traction motors for applications such as
railways, but also causes a noticeable flicker in incandescent lighting and objectionable flicker of
fluorescent lamps. 16.7 Hz power is still used in some European rail systems, such as in
Austria,
Germany,
Norway,
Sweden and
Switzerland.
Off-shore, textile industry, marine, computer
mainframe, 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 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 electric charge which accelerates
radiates electromagnetic waves, and materials of high conductivity do not allow propagation of electromagnetic waves. This phenomenon is called skin effect.
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 high power transmission , non-uniform distribution of current still occurs in sufficiently thick conductors. 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 resistance 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 ohmic heating .
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 Litz wire. This measure helps to partially mitigate skin effect by forcing more equal current flow 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 power frequencies, and in the windings of devices carrying higher
radio frequency current , such as switch-mode
power supplies and
radio frequency transformers.
Techniques for reducing radiation loss
As written above, an alternating current is made of electric charge under periodic
acceleration, which causes
radiation of
electromagnetic waves. 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
twisted pair in order to reduce losses due to
electromagnetic radiation and inductive coupling. 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
coaxial cables are used instead. A coaxial cable has a conductive wire inside a conductive tube. The current flowing on the inner conductor is equal and opposite to the current flowing on the inner surface of the outer tube. This causes the electromagnetic field to be completely contained within the tube, and no energy is radiated or coupled outside the tube. Coaxial cables have acceptably small losses for frequencies up to about 20 GHz. For
microwave frequencies greater than 20 GHz, the
dielectric losses become too large, making waveguides a more efficient medium for transmitting energy.
Waveguides
Waveguides 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 ohmic losses in the waveguide walls become large. Instead,
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 by alternating voltages. An AC voltage
v can be described mathematically as a function of time by the following equation:
,
where
- Vpeak is the peak voltage ,
- ? is the angular frequency
...
, and
- t is the time .
Since angular frequency is of more interest to mathematicians than to engineers and technicians, this is commonly rewritten as:
,
where
- f is the frequency .
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 is +1 and the minimum value is −1, an AC voltage swings between +
Vpeak and −
Vpeak. The peak-to-peak voltage, usually written as
Vpp or
VP-P, is therefore − = 2 ×
Vpeak.
AC voltage is usually expressed as a root mean square value, written
Vrms. For a sinusoidal voltage:
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 RMS value is 240 V. This means that it has the same heating effect as 240 V DC. To work out its peak voltage , we can modify the above equation to:
For our 240 V AC, the peak voltage
Vpeak is therefore 240 V × v2, which is about 339 V. The peak-to-peak value
VP-P of the 240 V AC mains is even higher: 2 × 240 V × v2, or about 679 V.
Note that non-sinusoidal waveforms have a different relationship between their peak magnitude and effective value. This is of practical significance when working with non-linear circuit elements that produce harmonic currents, such as
rectifiers.
The
European Union 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% −6%. Most supplies to the old standards therefore conform to the new one and do not need to be changed.
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, Pages 22-24
External links
- "AC/DC: ?". Edison's Miracle of Light, .
- "AC-DC: ". Edison's Miracle of Light, American Experience.
- Kuphaldt, Tony R., "Lessons In Electric Circuits : ". March 8, 2003.
- Nave, C. R., "". HyperPhysics.
- " ". Magnetic Particle Inspection, Nondestructive Testing Encyclopedia.
- "". Analog Process Control Services.
- Hiob, Eric, "". British Columbia Institute of Technology, 2004.
- "". Integrated Publishing.
- "Wind Energy Reference Manual Part 4: ". Danish Wind Industry Association, 2003.
- Chan. Keelin, "". , 2002.
- "". Analog Process Control Services.
- Williams, Trip "Kingpin", ", Some more power concepts".
- "".
-
-
- Animations and explanations of vector representation of RLC circuits
- Blalock, Thomas J., "". The history of various frequencies and interconversion schemes in the US at the beginning of the 20th century
