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electric power transmission
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{{Redirect|Electric transmission|vehicle transmissions|diesel-electric transmission}}{{Use mdy dates|date=April 2014}}File:500kV 3-Phase Transmission Lines.png|thumb|500 kV Three-phase electric power Transmission Lines at Grand Coulee DamGrand Coulee DamElectric power transmission is the bulk movement of electrical energy from a generating site, such as a power plant, to an electrical substation. The interconnected lines which facilitate this movement are known as a transmission network. This is distinct from the local wiring between high-voltage substations and customers, which is typically referred to as electric power distribution. The combined transmission and distribution network is known as the "power grid" in North America, or just "the grid". In the United Kingdom, India, Myanmar, Malaysia and New Zealand, the network is known as the "National Grid".A wide area synchronous grid, also known as an "interconnection" in North America, directly connects a large number of generators delivering AC power with the same relative frequency to a large number of consumers. For example, there are four major interconnections in North America (the Western Interconnection, the Eastern Interconnection, the Quebec Interconnection and the Electric Reliability Council of Texas (ERCOT) grid). In Europe one large grid connects most of continental Europe.Historically, transmission and distribution lines were owned by the same company, but starting in the 1990s, many countries have liberalized the regulation of the electricity market in ways that have led to the separation of the electricity transmission business from the distribution business.JOURNAL,weblink A Primer on Electric Utilities, Deregulation, and Restructuring of U.S. Electricity Markets, United States Department of Energy Federal Energy Management Program (FEMP), May 2002, pdf, October 30, 2018,

System

Most transmission lines are high-voltage three-phase alternating current (AC), although single phase AC is sometimes used in railway electrification systems. High-voltage direct-current (HVDC) technology is used for greater efficiency over very long distances (typically hundreds of miles). HVDC technology is also used in submarine power cables (typically longer than 30 miles (50 km)), and in the interchange of power between grids that are not mutually synchronized. HVDC links are used to stabilize large power distribution networks where sudden new loads, or blackouts, in one part of a network can result in synchronization problems and cascading failures.(File:Electricity grid simple- North America.svg|thumb|400px|left|Diagram of an electric power system; transmission system is in blue)Electricity is transmitted at high voltages (115 kV or above) to reduce the energy loss which occurs in long-distance transmission. Power is usually transmitted through overhead power lines. Underground power transmission has a significantly higher installation cost and greater operational limitations, but reduced maintenance costs. Underground transmission is sometimes used in urban areas or environmentally sensitive locations.A lack of electrical energy storage facilities in transmission systems leads to a key limitation. Electrical energy must be generated at the same rate at which it is consumed. A sophisticated control system is required to ensure that the power generation very closely matches the demand. If the demand for power exceeds supply, the imbalance can cause generation plant(s) and transmission equipment to automatically disconnect or shut down to prevent damage. In the worst case, this may lead to a cascading series of shut downs and a major regional blackout. Examples include the US Northeast blackouts of 1965, 1977, 2003, and major blackouts in other US regions in 1996 and 2011. Electric transmission networks are interconnected into regional, national, and even continent wide networks to reduce the risk of such a failure by providing multiple redundant, alternative routes for power to flow should such shut downs occur. Transmission companies determine the maximum reliable capacity of each line (ordinarily less than its physical or thermal limit) to ensure that spare capacity is available in the event of a failure in another part of the network.

Overhead transmission

(File:High Voltage Lines in Washington State.tif|thumb|upright=0.75|left|3-phase high-voltage lines in Washington State, "Bundled" 3-ways){{multiple image
|direction = vertical
|align = right
|width = 225
|image1=Electric power transmission line.JPG
|image2=Sample cross-section of high tension power (pylon) line.jpg
|caption1=Four-circuit, two-voltage power transmission line; "Bundled" 2-ways
|caption2=A typical ACSR. The conductor consists of seven strands of steel surrounded by four layers of aluminium.
}}High-voltage overhead conductors are not covered by insulation. The conductor material is nearly always an aluminum alloy, made into several strands and possibly reinforced with steel strands. Copper was sometimes used for overhead transmission, but aluminum is lighter, yields only marginally reduced performance and costs much less. Overhead conductors are a commodity supplied by several companies worldwide. Improved conductor material and shapes are regularly used to allow increased capacity and modernize transmission circuits. Conductor sizes range from 12 mm2 (#6 American wire gauge) to 750 mm2 (1,590,000 circular mils area), with varying resistance and current-carrying capacity. For normal AC lines thicker wires would lead to a relatively small increase in capacity due to the skin effect (which causes most of the current to flow close to the surface of the wire). Because of this current limitation, multiple parallel cables (called bundle conductors) are used when higher capacity is needed. Bundle conductors are also used at high voltages to reduce energy loss caused by corona discharge.Today, transmission-level voltages are usually considered to be 110 kV and above. Lower voltages, such as 66 kV and 33 kV, are usually considered subtransmission voltages, but are occasionally used on long lines with light loads. Voltages less than 33 kV are usually used for distribution. Voltages above 765 kV are considered extra high voltage and require different designs compared to equipment used at lower voltages.Since overhead transmission wires depend on air for insulation, the design of these lines requires minimum clearances to be observed to maintain safety. Adverse weather conditions, such as high wind and low temperatures, can lead to power outages. Wind speeds as low as {{convert|23|kn|km/h}} can permit conductors to encroach operating clearances, resulting in a flashover and loss of supply.Hans Dieter Betz, Ulrich Schumann, Pierre Laroche (2009). Lightning: Principles, Instruments and Applications. Springer, pp. 202–203. {{ISBN|978-1-4020-9078-3}}. Retrieved on 13 May 2009.Oscillatory motion of the physical line can be termed gallop or flutter depending on the frequency and amplitude of oscillation.

Underground transmission

Electric power can also be transmitted by underground power cables instead of overhead power lines. Underground cables take up less right-of-way than overhead lines, have lower visibility, and are less affected by bad weather. However, costs of insulated cable and excavation are much higher than overhead construction. Faults in buried transmission lines take longer to locate and repair. In some metropolitan areas, underground transmission cables are enclosed by metal pipe and insulated with dielectric fluid (usually an oil) that is either static or circulated via pumps. If an electric fault damages the pipe and produces a dielectric leak into the surrounding soil, liquid nitrogen trucks are mobilized to freeze portions of the pipe to enable the draining and repair of the damaged pipe location. This type of underground transmission cable can prolong the repair period and increase repair costs. The temperature of the pipe and soil are usually monitored constantly throughout the repair periodweblink" title="www.nytimes.com/2001/09/16/us/after-attacks-workers-con-edison-crews-improvise-they-rewire-truncated-system.htmweblink">weblink{5B2369A6-97FC-4613-AD8B-91E23D41AC05}NYSPSC case no. 13-E-0529 Underground lines are strictly limited by their thermal capacity, which permits less overload or re-rating than overhead lines. Long underground AC cables have significant capacitance, which may reduce their ability to provide useful power to loads beyond {{convert|50|mi|abbr=off}}. DC cables are not limited in length by their capacitance, however, they do require HVDC converter stations at both ends of the line to convert from DC to AC before being interconnected with the transmission network.

History

(File:New York utility lines in 1890.jpg|thumb|New York City streets in 1890. Besides telegraph lines, multiple electric lines were required for each class of device requiring different voltages)In the early days of commercial electric power, transmission of electric power at the same voltage as used by lighting and mechanical loads restricted the distance between generating plant and consumers. In 1882, generation was with direct current (DC), which could not easily be increased in voltage for long-distance transmission. Different classes of loads (for example, lighting, fixed motors, and traction/railway systems) required different voltages, and so used different generators and circuits.BOOK,weblink 119–122, Thomas P. Hughes, Networks of Power: Electrification in Western Society, 1880–1930, Johns Hopkins University Press, Baltimore, 0-8018-4614-5, 1993, Thomas P. Hughes, JOURNAL, Guarnieri, M., 2013, The Beginning of Electric Energy Transmission: Part One, IEEE Industrial Electronics Magazine, 7, 1, 57–60, 10.1109/MIE.2012.2236484, harv, Due to this specialization of lines and because transmission was inefficient for low-voltage high-current circuits, generators needed to be near their loads. It seemed, at the time, that the industry would develop into what is now known as a distributed generation system with large numbers of small generators located near their loads.JOURNAL,weblink Electricity Transmission: A primer, National Council on Electricity Policy, pdf, The transmission of electric power with alternating current (AC) became possible after Lucien Gaulard and John Dixon Gibbs built what they called the secondary generator, an early transformer provided with 1:1 turn ratio and open magnetic circuit, in 1881.The first long distance AC line was {{convert|34|km|abbr=off}} long, built for the 1884 International Exhibition of Turin, Italy. It was powered by a 2 kV, 130 Hz Siemens & Halske alternator and featured several Gaulard secondary generators with their primary windings connected in series, which fed incandescent lamps. The system proved the feasibility of AC electric power transmission on long distances.A very first operative AC line was put into service in 1885 in via dei Cerchi, Rome, Italy, for public lighting. It was powered by two Siemens & Halske alternators rated 30 hp (22 kW), 2 kV at 120 Hz and used 19 km of cables and 200 parallel-connected 2 kV to 20 V step-down transformers provided with a closed magnetic circuit, one for each lamp. Few months later it was followed by the first British AC system, which was put into service at the Grosvenor Gallery, London. It also featured Siemens alternators and 2.4 kV to 100 V step-down transformers – one per user – with shunt-connected primaries.JOURNAL, Guarnieri, M., 2013, The Beginning of Electric Energy Transmission: Part Two, IEEE Industrial Electronics Magazine, 7, 2, 52–59, 10.1109/MIE.2013.2256297, harv, (File:William-Stanley jr.jpg|thumbnail|left|Working for Westinghouse, William Stanley Jr. spent his time recovering from illness in Great Barrington installing what is considered the world's first practical AC transformer system.)Working from what he considered an impractical Gaulard-Gibbs design, electrical engineer William Stanley, Jr. developed what is considered the first practical series AC transformer in 1885.Great Barrington 1886 - Inspiring an industry toward AC power Working with the support of George Westinghouse, in 1886 he installed demonstration transformer based alternating current lighting system in Great Barrington, Massachusetts. Powered by a steam engine driven 500 V Siemens generator, voltage was stepped down to 100 Volts using the new Stanley transformer to power incandescent lamps at 23 businesses along main street with very little power loss over 4000 feet.ethw.org - William Stanley, Jr. This practical demonstration of a transformer and alternating current lighting system would lead Westinghouse to begin installing AC based systems later that year.1888 saw designs for a functional AC motor, something these systems had lacked up till then. These were induction motors running on polyphase current, independently invented by Galileo Ferraris and Nikola Tesla (with Tesla’s design being licensed by Westinghouse in the US). This design was further developed into the modern practical three-phase form by Mikhail Dolivo-Dobrovolsky and Charles Eugene Lancelot Brown.Arnold Heertje, Mark Perlman Evolving Technology and Market Structure: Studies in Schumpeterian Economics, page 138 Practical use of these types of motors would be delayed many years by development problems and the scarcity of poly-phase power systems needed to power them.Carlson, W. Bernard (2013). Tesla: Inventor of the Electrical Age. Princeton University Press. {{ISBN|1-4008-4655-2}}, page 130Jonnes, Jill (2004). Empires of Light: Edison, Tesla, Westinghouse, and the Race to Electrify the World. Random House Trade Paperbacks. {{ISBN|978-0-375-75884-3}}, page 161.The late 1880s and early 1890s would see a financial merger of many smaller electric companies into a few larger corporations such as Ganz and AEG in Europe and General Electric and Westinghouse Electric in the US. These companies continued to develop AC systems but the technical difference between direct and alternating current systems would follow a much longer technical merger. Due to innovation in the US and Europe, alternating current's economy of scale with very large generating plants linked to loads via long distance transmission was slowly being combined with the ability to link it up with all of the existing systems that needed to be supplied. These included single phase AC systems, poly-phase AC systems, low voltage incandescent lighting, high voltage arc lighting, and existing DC motors in factories and street cars. In what was becoming a universal system, these technological differences were temporarily being bridged via the development of rotary converters and motor-generators that would allow the large number of legacy systems to be connected to the AC grid.BOOK, Thomas, Parke Hughes, Networks of Power: Electrification in Western Society, 1880-1930, JHU Press, 1993, 120–121, BOOK, Raghu, Garud, Arun, Kumaraswamy, Richard, Langlois, Managing in the Modular Age: Architectures, Networks, and Organizations, John Wiley & Sons, 2009, 249, These stopgaps would slowly be replaced as older systems were retired or upgraded.File:Tesla polyphase AC 500hp generator at 1893 exposition.jpg|thumb|right|Westinghouse alternating current polyphase generators on display at the 1893 World's Fair in Chicago, part of their "Tesla Poly-phase System". Such polyphase innovations revolutionized transmission]]The first transmission of single-phase alternating current using high voltage took place in Oregon in 1890 when power was delivered from a hydroelectric plant at Willamette Falls to the city of Portland 14 miles downriver.JOURNAL, Argersinger, R.E., 1915, Electric Transmission of Power, General Electric Review, XVIII, 454, The first three-phase alternating current using high voltage took place in 1891 during the international electricity exhibition in Frankfurt. A 15 kV transmission line, approximately 175 km long, connected Lauffen on the Neckar and Frankfurt.Kiessling F, Nefzger P, Nolasco JF, Kaintzyk U. (2003). Overhead power lines. Springer, Berlin, Heidelberg, New York, p. 5Voltages used for electric power transmission increased throughout the 20th century. By 1914, fifty-five transmission systems each operating at more than 70 kV were in service. The highest voltage then used was 150 kV.Bureau of Census data reprinted in Hughes, pp. 282–283By allowing multiple generating plants to be interconnected over a wide area, electricity production cost was reduced. The most efficient available plants could be used to supply the varying loads during the day. Reliability was improved and capital investment cost was reduced, since stand-by generating capacity could be shared over many more customers and a wider geographic area. Remote and low-cost sources of energy, such as hydroelectric power or mine-mouth coal, could be exploited to lower energy production cost.The rapid industrialization in the 20th century made electrical transmission lines and grids a critical infrastructure item in most industrialized nations. The interconnection of local generation plants and small distribution networks was greatly spurred by the requirements of World War I, with large electrical generating plants built by governments to provide power to munitions factories. Later these generating plants were connected to supply civil loads through long-distance transmission.Hughes, pp. 293–295{{clear left}}

Bulk power transmission

File:Transmissionsubstation.jpg|thumb|A transmission substation decreases the voltage of incoming electricity, allowing it to connect from long distance high voltage transmission, to local lower voltage distribution. It also reroutes power to other transmission lines that serve local markets. This is the PacifiCorp Hale Substation, Orem, UtahOrem, UtahEngineers design transmission networks to transport the energy as efficiently as feasible, while at the same time taking into account economic factors, network safety and redundancy. These networks use components such as power lines, cables, circuit breakers, switches and transformers. The transmission network is usually administered on a regional basis by an entity such as a regional transmission organization or transmission system operator.Transmission efficiency is greatly improved by devices that increase the voltage (and thereby proportionately reduce the current), in the line conductors, thus allowing power to be transmitted with acceptable losses. The reduced current flowing through the line reduces the heating losses in the conductors. According to Joule's Law, energy losses are directly proportional to the square of the current. Thus, reducing the current by a factor of two will lower the energy lost to conductor resistance by a factor of four for any given size of conductor.The optimum size of a conductor for a given voltage and current can be estimated by Kelvin's law for conductor size, which states that the size is at its optimum when the annual cost of energy wasted in the resistance is equal to the annual capital charges of providing the conductor. At times of lower interest rates, Kelvin's law indicates that thicker wires are optimal; while, when metals are expensive, thinner conductors are indicated: however, power lines are designed for long-term use, so Kelvin's law has to be used in conjunction with long-term estimates of the price of copper and aluminum as well as interest rates for capital.The increase in voltage is achieved in AC circuits by using a step-up transformer. HVDC systems require relatively costly conversion equipment which may be economically justified for particular projects such as submarine cables and longer distance high capacity point-to-point transmission. HVDC is necessary for the import and export of energy between grid systems that are not synchronized with each other.A transmission grid is a network of power stations, transmission lines, and substations. Energy is usually transmitted within a grid with three-phase AC. Single-phase AC is used only for distribution to end users since it is not usable for large polyphase induction motors. In the 19th century, two-phase transmission was used but required either four wires or three wires with unequal currents. Higher order phase systems require more than three wires, but deliver little or no benefit.File:ElectricityUCTE.svg|thumb|left|The synchronous grids of the European UnionEuropean UnionThe price of electric power station capacity is high, and electric demand is variable, so it is often cheaper to import some portion of the needed power than to generate it locally. Because loads are often regionally correlated (hot weather in the Southwest portion of the US might cause many people to use air conditioners), electric power often comes from distant sources. Because of the economic benefits of load sharing between regions, wide area transmission grids now span countries and even continents. The web of interconnections between power producers and consumers should enable power to flow, even if some links are inoperative.The unvarying (or slowly varying over many hours) portion of the electric demand is known as the base load and is generally served by large facilities (which are more efficient due to economies of scale) with fixed costs for fuel and operation. Such facilities are nuclear, coal-fired or hydroelectric, while other energy sources such as concentrated solar thermal and geothermal power have the potential to provide base load power. Renewable energy sources, such as solar photovoltaics, wind, wave, and tidal, are, due to their intermittency, not considered as supplying "base load" but will still add power to the grid. The remaining or 'peak' power demand, is supplied by peaking power plants, which are typically smaller, faster-responding, and higher cost sources, such as combined cycle or combustion turbine plants fueled by natural gas.Long-distance transmission of electricity (hundreds of kilometers) is cheap and efficient, with costs of US$0.005–0.02 per kWh (compared to annual averaged large producer costs of US$0.01–0.025 per kWh, retail rates upwards of US$0.10 per kWh, and multiples of retail for instantaneous suppliers at unpredicted highest demand moments). Thus distant suppliers can be cheaper than local sources (e.g., New York often buys over 1000 MW of electricity from Canada).WEB, NYISO Zone Maps,weblink New York Independent System Operator, 10 January 2014, Multiple local sources (even if more expensive and infrequently used) can make the transmission grid more fault tolerant to weather and other disasters that can disconnect distant suppliers.(File:Electicaltransmissionlines3800ppx.JPG|thumb|A high-power electrical transmission tower, 230 kV, double-circuit, also double-bundled)Long-distance transmission allows remote renewable energy resources to be used to displace fossil fuel consumption. Hydro and wind sources cannot be moved closer to populous cities, and solar costs are lowest in remote areas where local power needs are minimal. Connection costs alone can determine whether any particular renewable alternative is economically sensible. Costs can be prohibitive for transmission lines, but various proposals for massive infrastructure investment in high capacity, very long distance super grid transmission networks could be recovered with modest usage fees.

Grid input

At the power stations, the power is produced at a relatively low voltage between about 2.3 kV and 30 kV, depending on the size of the unit. The generator terminal voltage is then stepped up by the power station transformer to a higher voltage (115 kV to 765 kV AC, varying by the transmission system and by the country) for transmission over long distances.In the United States, power transmission is, variously, 230 kV to 500 kV, with less than 230 kV or more than 500 kV being local exceptions.For example, the Western System has two primary interchange voltages: 500 kV AC at 60 Hz, and ±500 kV (1,000 kV net) DC from North to South (Columbia River to Southern California) and Northeast to Southwest (Utah to Southern California). The 287.5 kV (Hoover to Los Angeles line, via Victorville) and 345 kV (APS line) being local standards, both of which were implemented before 500 kV became practical, and thereafter the Western System standard for long distance AC power transmission.

Losses

Transmitting electricity at high voltage reduces the fraction of energy lost to resistance, which varies depending on the specific conductors, the current flowing, and the length of the transmission line. For example, a {{convert|100|mile|abbr=on}} span at 765 kV carrying 1000 MW of power can have losses of 1.1% to 0.5%. A 345 kV line carrying the same load across the same distance has losses of 4.2%.American Electric Power, Transmission Facts, page 4:weblink For a given amount of power, a higher voltage reduces the current and thus the resistive losses in the conductor. For example, raising the voltage by a factor of 10 reduces the current by a corresponding factor of 10 and therefore the I^2 R losses by a factor of 100, provided the same sized conductors are used in both cases. Even if the conductor size (cross-sectional area) is decreased ten-fold to match the lower current, the I^2 R losses are still reduced ten-fold. Long-distance transmission is typically done with overhead lines at voltages of 115 to 1,200 kV. At extremely high voltages, more than 2,000 kV exists between conductor and ground, corona discharge losses are so large that they can offset the lower resistive losses in the line conductors. Measures to reduce corona losses include conductors having larger diameters; often hollow to save weight,California Public Utilities Commission Corona and induced currents or bundles of two or more conductors.Factors that affect the resistance, and thus loss, of conductors used in transmission and distribution lines include temperature, spiraling, and the skin effect. The resistance of a conductor increases with its temperature. Temperature changes in electric power lines can have a significant effect on power losses in the line. Spiraling, which refers to the way stranded conductors spiral about the center, also contributes to increases in conductor resistance. The skin effect causes the effective resistance of a conductor to increase at higher alternating current frequencies.Transmission and distribution losses in the USA were estimated at 6.6% in 1997,WEB,weblink Where can I find data on electricity transmission and distribution losses?, 19 November 2009, Frequently Asked Questions – Electricity, U.S. Energy Information Administration, 29 March 2011, 6.5% in 2007 and 5% from 2013 to 2019.WEB,weblink How much electricity is lost in electricity transmission and distribution in the United States?, 9 January 2019, Frequently Asked Questions – Electricity, U.S. Energy Information Administration, 27 February 2019, In general, losses are estimated from the discrepancy between power produced (as reported by power plants) and power sold to the end customers; the difference between what is produced and what is consumed constitute transmission and distribution losses, assuming no utility theft occurs.As of 1980, the longest cost-effective distance for direct-current transmission was determined to be {{convert|7000|km|mi|abbr=off}}. For alternating current it was {{convert|4000|km|mi|abbr=off}}, though all transmission lines in use today are substantially shorter than this.WEB,weblink Present Limits of Very Long Distance Transmission Systems, L., Paris, G., Zini, M., Valtorta, G., Manzoni, A., Invernizzi, N., De Franco, A., Vian, 1984, CIGRE International Conference on Large High Voltage Electric Systems, 1984 Session, 29 August – 6 September, Global Energy Network Institute, 29 March 2011, pdf, 4.98 MBIn any alternating current transmission line, the inductance and capacitance of the conductors can be significant. Currents that flow solely in ‘reaction’ to these properties of the circuit, (which together with the resistance define the impedance) constitute reactive power flow, which transmits no ‘real’ power to the load. These reactive currents, however, are very real and cause extra heating losses in the transmission circuit. The ratio of 'real' power (transmitted to the load) to 'apparent' power (the product of a circuit's voltage and current, without reference to phase angle) is the power factor. As reactive current increases, the reactive power increases and the power factor decreases. For transmission systems with low power factor, losses are higher than for systems with high power factor. Utilities add capacitor banks, reactors and other components (such as phase-shifting transformers; static VAR compensators; and flexible AC transmission systems, FACTS) throughout the system help to compensate for the reactive power flow, reduce the losses in power transmission and stabilize system voltages. These measures are collectively called 'reactive support'.

Transposition

Current flowing through transmission lines induces a magnetic field that surrounds the lines of each phase and affects the inductance of the surrounding conductors of other phases. The mutual inductance of the conductors is partially dependent on the physical orientation of the lines with respect to each other. Three-phase power transmission lines are conventionally strung with phases separated on different vertical levels. The mutual inductance seen by a conductor of the phase in the middle of the other two phases will be different than the inductance seen by the conductors on the top or bottom. An imbalanced inductance among the three conductors is problematic because it may result in the middle line carrying a disproportionate amount of the total power transmitted. Similarly, an imbalanced load may occur if one line is consistently closest to the ground and operating at a lower impedance. Because of this phenomenon, conductors must be periodically transposed along the length of the transmission line so that each phase sees equal time in each relative position to balance out the mutual inductance seen by all three phases. To accomplish this, line position is swapped at specially designed transposition towers at regular intervals along the length of the transmission line in various transposition schemes.

Subtransmission

File:Cavite, Batangas jf0557 11.jpg|thumb|175px|A 115 kV subtransmission line in the Philippines, along with 20 kV distribution lines and a street light, all mounted in a wood subtransmission pole ]](File:Wood Pole Structure.JPG|thumb|173px|115 kV H-frame transmission tower)Subtransmission is part of an electric power transmission system that runs at relatively lower voltages. It is uneconomical to connect all distribution substations to the high main transmission voltage, because the equipment is larger and more expensive. Typically, only larger substations connect with this high voltage. It is stepped down and sent to smaller substations in towns and neighborhoods. Subtransmission circuits are usually arranged in loops so that a single line failure does not cut off service to a large number of customers for more than a short time. Loops can be "normally closed", where loss of one circuit should result in no interruption, or "normally open" where substations can switch to a backup supply. While subtransmission circuits are usually carried on overhead lines, in urban areas buried cable may be used. The lower-voltage subtransmission lines use less right-of-way and simpler structures; it is much more feasible to put them underground where needed. Higher-voltage lines require more space and are usually above-ground since putting them underground is very expensive.There is no fixed cutoff between subtransmission and transmission, or subtransmission and distribution. The voltage ranges overlap somewhat. Voltages of 69 kV, 115 kV, and 138 kV are often used for subtransmission in North America. As power systems evolved, voltages formerly used for transmission were used for subtransmission, and subtransmission voltages became distribution voltages. Like transmission, subtransmission moves relatively large amounts of power, and like distribution, subtransmission covers an area instead of just point-to-point.Donald G. Fink and H. Wayne Beaty. (2007), Standard Handbook for Electrical Engineers (15th Edition). McGraw-Hill. {{ISBN|978-0-07-144146-9}} section 18.5

Transmission grid exit

At the substations, transformers reduce the voltage to a lower level for distribution to commercial and residential users. This distribution is accomplished with a combination of sub-transmission (33 to 132 kV) and distribution (3.3 to 25 kV). Finally, at the point of use, the energy is transformed to low voltage (varying by country and customer requirements – see Mains electricity by country).

Advantage of high-voltage power transmission

{{See also|ideal transformer}}High-voltage power transmission allows for lesser resistive losses over long distances in the wiring. This efficiency of high voltage transmission allows for the transmission of a larger proportion of the generated power to the substations and in turn to the loads, translating to operational cost savings.(File:Power split two resistances.svg|thumb|Electrical grid without a transformer.)(File:Transformer power split.svg|thumb|Electrical grid with a transformer.)In a very simplified model, assume the electrical grid delivers electricity from a generator (modelled as an ideal voltage source with voltage V, delivering a power P_V) to a single point of consumption, modelled by a pure resistance R, when the wires are long enough to have a significant resistance R_C.If the resistance are simply in series without any transformer between them, the circuit acts as a voltage divider, because the same current I=frac{V}{R+R_C} runs through the wire resistance and the powered device. As a consequence, the useful power (used at the point of consumption) is:
P_R= V_2times I = Vfrac{R}{R+R_C}timesfrac{V}{R+R_C} = frac{R}{R+R_C}timesfrac{V^2}{R+R_C} = frac{R}{R+R_C} P_V
Assume now that a transformer converts high-voltage, low-current electricity transported by the wires into low-voltage, high-current electricity for use at the consumption point. If we suppose it is an ideal transformer with a voltage ratio of a (i.e., the voltage is divided by a and the current is multiplied by a in the secondary branch, compared to the primary branch), then the circuit is again equivalent to a voltage divider, but the transformer-consumption branch has an apparent resistance of a^2 R. The useful power is then:
P_R= V_2times I_2 = frac{a^2Rtimes V^2}{(a^2 R+R_C)^2} = frac{a^2 R}{a^2 R+R_C} P_V
For a>1 (i.e. conversion of high voltage to low voltage near the consumption point), a larger fraction of the generator's power is transmitted to the consumption point and a lesser fraction is lost to Joule heating.

Modeling and the transmission matrix

(File:Transmission Line Black Box.JPG|thumb|350px|"Black box" model for transmission line)Oftentimes, we are only interested in the terminal characteristics of the transmission line, which are the voltage and current at the sending and receiving ends. The transmission line itself is then modeled as a "black box" and a 2 by 2 transmission matrix is used to model its behavior, as follows:
begin{bmatrix} V_mathrm{S} I_mathrm{S}end{bmatrix}

begin{bmatrix} A & B C & Dend{bmatrix}begin{bmatrix} V_mathrm{R} I_mathrm{R}end{bmatrix}The line is assumed to be a reciprocal, symmetrical network, meaning that the receiving and sending labels can be switched with no consequence. The transmission matrix T also has the following properties:
  • det(T) = AD - BC = 1
  • A = D
The parameters A, B, C, and D differ depending on how the desired model handles the line's resistance (R), inductance (L), capacitance (C), and shunt (parallel, leak) conductance G. The four main models are the short line approximation, the medium line approximation, the long line approximation (with distributed parameters), and the lossless line. In all models described, a capital letter such as R refers to the total quantity summed over the line and a lowercase letter such as c refers to the per-unit-length quantity.

Lossless line

The lossless line approximation is the least accurate model; it is often used on short lines when the inductance of the line is much greater than its resistance. For this approximation, the voltage and current are identical at the sending and receiving ends.(File:Losslessline.jpg|thumb|Voltage on sending and receiving ends for lossless line)The characteristic impedance is pure real, which means resistive for that impedance, and it is often called surge impedance for a lossless line. When lossless line is terminated by surge impedance, there is no voltage drop. Though the phase angles of voltage and current are rotated, the magnitudes of voltage and current remain constant along the length of the line. For load > SIL, the voltage will drop from sending end and the line will “consume” VARs. For load 

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