Contents 1 Transmission, distribution, and domestic power supply
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3.1 Techniques for reducing AC resistance 3.2 Techniques for reducing radiation loss 3.2.1 Twisted pairs 3.2.2 Coaxial cables 3.2.3 Waveguides 3.2.4 Fiber optics 4 Mathematics of AC voltages 4.1 Power
4.2
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6.1 Transformers 6.2 Pioneers 7 See also 8 References 9 Further reading 10 External links Transmission, distribution, and domestic power supply[edit]
Main articles:
A schematic representation of long distance electric power transmission. C=consumers, D=step down transformer, G=generator, I=current in the wires, Pe=power reaching the end of the transmission line, Pt=power entering the transmission line, Pw=power lost in the transmission line, R=total resistance in the wires, V=voltage at the beginning of the transmission line, U=step up transformer.
P w displaystyle P_ rm w ) in the wire are a product of the square of the current (I) and the resistance (R) of the wire, described by the formula P w = I 2 R . 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 will be four times less. The power transmitted is equal to the product of the current and the voltage (assuming no phase difference); that is, P t = I V . 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, and transformed to 100 V – 240 V for domestic use. High voltage transmission lines deliver power from electric generation plants over long distances using alternating current. These lines 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 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 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 was not feasible in the
early days of electric power transmission, as there was then no
economically viable way to step down the voltage of DC for end user
applications such as lighting incandescent bulbs.
Play media A
A direct current flows uniformly throughout the cross-section of a uniform wire. An alternating current of any frequency is forced away from the wire's center, toward its outer surface. This is because the acceleration of an electric charge in an alternating current produces waves of electromagnetic radiation that cancel the propagation of electricity toward the center of materials with high conductivity. 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 power transmission (50 Hz – 60 Hz), non-uniform distribution of current still occurs in sufficiently thick conductors. For example, 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. 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. The AC resistance often is many times higher than the DC resistance, causing a much higher energy loss due to ohmic heating (also called I2R loss). Techniques for reducing AC resistance[edit]
For low to medium frequencies, conductors can be divided into stranded
wires, each insulated from one another, and the relative positions of
individual strands specially arranged 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 throughout the total cross section of the stranded conductors.
A sinusoidal alternating voltage. 1 = Peak, also amplitude, 2 = Peak-to-peak, 3 = Effective value, 4 = Period A sine wave, over one cycle (360°). The dashed line represents the root mean square (RMS) value at about 0.707 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: v ( t ) = V p e a k ⋅ sin ( ω t ) displaystyle v(t)=V_ mathrm peak cdot sin(omega t) , where V p e a k displaystyle displaystyle V_ rm peak is the peak voltage (unit: volt), ω displaystyle displaystyle omega is the angular frequency (unit: radians per second) The angular frequency is related to the physical frequency, f displaystyle displaystyle f (unit = hertz), which represents the number of cycles per second, by the equation ω = 2 π f displaystyle displaystyle omega =2pi f . t displaystyle 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 sin ( x ) displaystyle sin(x) is +1 and the minimum value is −1, an AC voltage swings between + V p e a k displaystyle +V_ rm peak and − V p e a k displaystyle -V_ rm peak . The peak-to-peak voltage, usually written as V p p displaystyle V_ rm pp or V P − P displaystyle V_ rm P-P , is therefore V p e a k − ( − V p e a k ) = 2 V p e a k displaystyle V_ rm peak -(-V_ rm peak )=2V_ rm peak . Power[edit] Main article: AC power The relationship between voltage and the power delivered is p ( t ) = v 2 ( t ) R displaystyle p(t)= frac v^ 2 (t) R 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 r m s displaystyle V_ rm rms , because P t i m e a v e r a g e d = V r m s 2 R . displaystyle P_ rm time~averaged = frac V_ rm rms ^ 2 R . Power oscillation v ( t ) = V p e a k sin ( ω t ) displaystyle v(t)=V_ mathrm peak sin(omega t) i ( t ) = v ( t ) R = V p e a k R sin ( ω t ) displaystyle i(t)= frac v(t) R = frac V_ mathrm peak R sin(omega t) P ( t ) = v ( t ) i ( t ) = ( V p e a k ) 2 R sin 2 ( ω t ) displaystyle P(t)=v(t) i(t)= frac (V_ mathrm peak )^ 2 R sin ^ 2 (omega t)
For an arbitrary periodic waveform v ( t ) displaystyle v(t) of period T displaystyle T : V r m s = 1 T ∫ 0 T [ v ( t ) ] 2 d t . displaystyle V_ mathrm rms = sqrt frac 1 T int _ 0 ^ T [v(t)]^ 2 dt . For a sinusoidal voltage: V r m s = 1 T ∫ 0 T [ V p k sin ( ω t + ϕ ) ] 2 d t = V p k 1 2 T ∫ 0 T [ 1 − cos ( 2 ω t + 2 ϕ ) ] d t = V p k 1 2 T ∫ 0 T d t = V p k 2 displaystyle begin aligned V_ mathrm rms &= sqrt frac 1 T int _ 0 ^ T [ V_ pk sin(omega t+phi )]^ 2 dt \&=V_ pk sqrt frac 1 2T int _ 0 ^ T [ 1-cos(2omega t+2phi )]dt \&=V_ pk sqrt frac 1 2T int _ 0 ^ T dt \&= frac V_ pk sqrt 2 end aligned where the trigonometric identity sin 2 x = 1 − cos 2 x 2 displaystyle sin ^ 2 x= frac 1-cos 2x 2 has been used and the factor 2 displaystyle sqrt 2 is called the crest factor, which varies for different waveforms. For a triangle waveform centered about zero V r m s = V p e a k 3 . displaystyle V_ mathrm rms = frac V_ mathrm peak sqrt 3 . For a square waveform centered about zero V r m s = V p e a k . displaystyle displaystyle V_ mathrm rms =V_ mathrm peak . Example[edit] 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 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: V p e a k = 2
V r m s . displaystyle V_ mathrm peak = sqrt 2 V_ mathrm rms . For 230 V AC, the peak voltage V p e a k displaystyle V_ mathrm peak is therefore 230 V × 2 displaystyle 230Vtimes sqrt 2 , which is about 325 V. During the course of one cycle the
voltage rises from zero to 325 V, falls through zero to
-325 V, and returns to zero.
The Hungarian "ZBD" Team (Károly Zipernowsky, Ottó Bláthy, Miksa Déri), inventors of the first high efficiency, closed-core shunt connection transformer The prototype of the ZBD transformer on display at the Széchenyi
István Memorial Exhibition,
In the autumn of 1884, Károly Zipernowsky,
Westinghouse Early AC System 1887 (US patent 373035) 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 transformer designs similar to Gaulard and Gibbs.[24] In
1890 he designed their power station at Deptford[25] 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.[26]
In the US
Electronics portal Energy portal AC power
Direct current
Electric current
Electrical wiring
Heavy-duty power plugs
Hertz
Mains power systems
References[edit] ^ N. N. Bhargava & D. C. Kulshreshtha (1983). Basic Electronics
& Linear Circuits. Tata McGraw-Hill Education. p. 90.
ISBN 978-0-07-451965-3.
^ National Electric Light Association (1915). Electrical meterman's
handbook. Trow Press. p. 81.
^ The Basics of 400-Hz Power Systems
^ Pixii Machine invented by Hippolyte Pixii, National High Magnetic
Field Laboratory
^ Licht, Sidney Herman., "History of Electrotherapy", in Therapeutic
Further reading[edit] 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[edit] 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". 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.
Chan. Keelin, "
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