Utility frequency - Knowledge (XXG)

1512:, for example, can be made smaller because the magnetic core can be much smaller for the same power level. Induction motors turn at a speed proportional to frequency, so a high-frequency power supply allows more power to be obtained for the same motor volume and mass. Transformers and motors for 400 Hz are much smaller and lighter than at 50 or 60 Hz, which is an advantage in aircraft and ships. A United States military standard 235:. For very slow prime mover speeds, it would be costly to build a generator with enough poles to provide a high AC frequency. As well, synchronizing two generators to the same speed was found to be easier at lower speeds. While belt drives were common as a way to increase speed of slow engines, in very large ratings (thousands of kilowatts) these were expensive, inefficient, and unreliable. After about 1906, generators driven directly by 3439: 665: 4018: 1532: 159:. When large central generating stations became practical, the choice of frequency was made based on the nature of the intended load. Eventually improvements in machine design allowed a single frequency to be used both for lighting and motor loads. A unified system improved the economics of electricity production, since system load was more uniform during the course of a day. 844:. Industrial plants and mines in North America and Australia sometimes were built with 40 Hz electrical systems which were maintained until too uneconomic to continue. Although frequencies near 40 Hz found much commercial use, these were bypassed by standardized frequencies of 25, 50 and 60 Hz preferred by higher volume equipment manufacturers. 1506:, military equipment, and hand-held machine tools. Such high frequencies cannot be economically transmitted long distances; the increased frequency greatly increases series impedance due to the inductance of transmission lines, making power transmission difficult. Consequently, 400 Hz power systems are usually confined to a building or vehicle. 45: 903:(VDE), in the first standard for electrical machines and transformers in 1902, recommended 25 Hz and 50 Hz as standard frequencies. VDE did not see much application of 25 Hz, and dropped it from the 1914 edition of the standard. Remnant installations at other frequencies persisted until well after the Second World War. 754:

that frequency was chosen. The operation of Tesla's induction motor, licensed by Westinghouse in 1888, required a lower frequency than the 133 Hz common for lighting systems at that time. In 1893 General Electric Corporation, which was affiliated with AEG in Germany, built a generating project at

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that limits the RoCoF. Since the IBRs are not electromechanically coupled into the power grid, a system with high VRE penetration might exhibit large RoCoF values that can cause problems with the operation of the system due to stress placed onto the remaining synchronous generators, triggering of the

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In Japan, the western part of the country (Nagoya and west) uses 60 Hz and the eastern part (Tokyo and east) uses 50 Hz. This originates in the first purchases of generators from AEG in 1895, installed for Tokyo, and General Electric in 1896, installed in Osaka. The boundary between the two

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decided to standardize on a higher frequency to permit operation of both electric lighting and induction motors on the same generating system. Although 50 Hz was suitable for both, in 1890 Westinghouse considered that existing arc-lighting equipment operated slightly better on 60 Hz, and so

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In practice, the exact frequency of the grid varies around the nominal frequency, reducing when the grid is heavily loaded, and speeding up when lightly loaded. However, most utilities will adjust generation onto the grid over the course of the day to ensure a constant number of cycles occur. This is

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had standardized on 50 Hz. Much of Southern California operated on 50 Hz and did not completely change frequency of their generators and customer equipment to 60 Hz until around 1948. Some projects by the Au Sable Electric Company used 30 Hz at transmission voltages up to 110,000

722: Hz were used on different systems. For example, the city of Coventry, England, in 1895 had a unique 87 Hz single-phase distribution system that was in use until 1906. The proliferation of frequencies grew out of the rapid development of electrical machines in the period 1880 through 1900. 111:

During the development of commercial electric power systems in the late-19th and early-20th centuries, many different frequencies (and voltages) had been used. Large investment in equipment at one frequency made standardization a slow process. However, as of the turn of the 21st century, places that

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rate to be the same as the local mains supply frequency. This helped to prevent power line hum and magnetic interference from causing visible beat frequencies in the displayed picture of early analogue TV receivers particularly from the mains transformer. Although some distortion of the picture was

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Even by the middle of the 20th century, utility frequencies were still not entirely standardized at the now-common 50 Hz or 60 Hz. In 1946, a reference manual for designers of radio equipment listed the following now obsolete frequencies as in use. Many of these regions also had 50-cycle,

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Smaller power systems, not extensively interconnected with many generators and loads, will not maintain frequency with the same degree of accuracy. Where system frequency is not tightly regulated during heavy load periods, system operators may allow system frequency to rise during periods of light

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Another use of this side effect is as a forensic tool. When a recording is made that captures audio near an AC appliance or socket, the hum is also incidentally recorded. The peaks of the hum repeat every AC cycle (every 20 ms for 50 Hz AC, or every 16.67 ms for 60 Hz AC). The

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Rotating-machine frequency changers used to convert between 25 Hz and 60 Hz systems were awkward to design; a 60 Hz machine with 24 poles would turn at the same speed as a 25 Hz machine with 10 poles, making the machines large, slow-speed, and expensive. A ratio of 60/30 would

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can be used to step down high transmission voltages to lower customer utilization voltage. The transformer is effectively a voltage conversion device with no moving parts and requiring little maintenance. The use of AC eliminated the need for spinning DC voltage conversion motor-generators that

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was found to work well on frequencies around 50 to 60 Hz, but with the materials available in the 1890s would not work well at a frequency of, say, 133 Hz. There is a fixed relationship between the number of magnetic poles in the induction motor field, the frequency of the alternating

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Today, AC power network operators regulate the daily average frequency so that clocks stay within a few seconds of the correct time. In practice the nominal frequency is raised or lowered by a specific percentage to maintain synchronization. Over the course of a day, the average frequency is

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Several factors influence the choice of frequency in an AC system. Lighting, motors, transformers, generators, and transmission lines all have characteristics which depend on the power frequency. All of these factors interact and make selection of a power frequency a matter of considerable

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or other generation-load mismatch, then adjacent generators would observe a decrease in frequency but a counterbalancing increase in outward tieline power flow, giving no ACE. They would thus make no governor adjustments in the (presumed) brief period before the failed region recovered.

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Real-time frequency meters for power generation in the United Kingdom are available online – an official one for the National Grid, and an unofficial one maintained by Dynamic Demand. Real-time frequency data of the synchronous grid of Continental Europe is available on websites such as

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for 60 Hz distribution. Converters for production of DC from alternating current were available in larger sizes and were more efficient at 25 Hz compared with 60 Hz. Remnant fragments of older systems may be tied to the standard frequency system via a rotary converter or

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allowed international trade in electrical equipment. Much later, the use of standard frequencies allowed interconnection of power grids. It was not until after World War II – with the advent of affordable electrical consumer goods – that more uniform standards were enacted.

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In the early days of electrification, so many frequencies were used that no single value prevailed (London in 1918 had ten different frequencies). As the 20th century continued, more power was produced at 60 Hz (North America) or 50 Hz (Europe and most of Asia).

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exact frequency of the hum should match the frequency of a forensic recording of the hum at the exact date and time that the recording is alleged to have been made. Discontinuities in the frequency match or no match at all will betray the authenticity of the recording.

1000:, intended to bring the whole country under 50 Hz within eight years. The law did not work, and in the early 1960s it was decided that Brazil would be unified under 60 Hz standard, because most developed and industrialized areas used 60 Hz; and a new law 2107:

As of 2017, regulations for some grids required the power plants to tolerate RoCoF of 1–4 Hz/s, the upper limit being a very high value, an order of magnitude higher than the design target of a typical older gas turbine generator. Testing high-power (multiple

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power transmission had been definitively selected. Westinghouse would have selected a low frequency of 30 Hz to drive motor loads, but the turbines for the project had already been specified at 250 RPM. The machines could have been made to deliver

807: Hz. Eventually a compromise of 25 Hz, with 12-pole 250 RPM generators, was chosen. Because the Niagara project was so influential on electric power systems design, 25 Hz prevailed as the North American standard for low-frequency AC. 819:

study concluded that 40 Hz would have been a good compromise between lighting, motor, and transmission needs, given the materials and equipment available in the first quarter of the 20th century. Several 40 Hz systems were built. The

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frequencies originated in the 19th century practice that gave frequencies in terms of alternations per minute, instead of alternations (cycles) per second. For example, a machine which produced 8,000 alternations per minute is operating at

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Small, temporary frequency changes are an unavoidable consequence of changing demand, but dramatic, rapid frequency shifts often signal that a distribution network is near capacity limits. Exceptional examples have occurred before major

2140:). It is usually produced by motor and transformer core laminations vibrating in time with the magnetic field. This hum can also appear in audio systems, where the power supply filter or signal shielding of an amplifier is not adequate. 1659:(NERC) discussed a proposed experiment that would relax frequency regulation requirements for electrical grids which would reduce the long-term accuracy of clocks and other devices that use the 60 Hz grid frequency as a time base. 116:, and those that now use 60 Hz tend to use 100–127 V. Both frequencies coexist today (Japan uses both) with no great technical reason to prefer one over the other and no apparent desire for complete worldwide standardization. 1780:

load to maintain a daily average frequency of acceptable accuracy. Portable generators, not connected to a utility system, need not tightly regulate their frequency because typical loads are insensitive to small frequency deviations.

1480:. In the 19th century, frequencies as low as 8 Hz were contemplated for operation of electric railways with commutator motors. Some outlets in trains carry the correct voltage, but using the original train network frequency like 995:

Initially in Brazil, electric machinery were imported from Europe and United States, implying the country had both 50 Hz and 60 Hz standards according to each region. In 1938, the federal government made a law,

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popularized the practice in a series of articles, arguing that load-frequency control minimized the adjustment necessary for changes in load. In particular, Cohn supposed that all regions of the grid shared a common

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Mathematically, the derivative can vary with location as long as each generation control system has only one neighbor generating plant. That is only possible on a grid with the unrealistically few one or two

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Generators can only be interconnected to operate in parallel if they are of the same frequency and wave-shape. By standardizing the frequency used, generators in a geographic area can be interconnected in a

3214: 918:. In the 1950s, many 25 Hz systems, from the generators right through to household appliances, were converted and standardized. Until 2006, some 25 Hz generators were still in existence at the 151:, so as to economize on transformer materials and to reduce visible flickering of the lamps, but would pick a lower frequency for systems with long transmission lines or feeding primarily motor loads or 2022: 930:

to provide power for large industrial customers who did not want to replace existing equipment; and some 25 Hz motors and a 25 Hz power station exist in New Orleans for floodwater pumps. The

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Since, for a given power level, the dimensions of a transformer are roughly inversely proportional to frequency, a system with many transformers would be more economical at a higher frequency.

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Because of the cost of conversion, some parts of the distribution system may continue to operate on original frequencies even after a new frequency is chosen. 25 Hz power was used in

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measures the frequency of the interconnections within the North American power grid, as well as in several other parts of the world. These measurements are displayed on the FNET website.

2188:, and other changes to set design helped minimise the effect and some countries now use a vertical rate that is an approximation to the supply frequency (most notably 60 Hz areas). 1892: 892:

starting in 1926 compelled the standardization of frequencies among the many interconnected electrical service providers. The 50 Hz standard was completely established only after

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frequency changer. These allow energy to be interchanged between two power networks at different frequencies, but the systems are large, costly, and waste some energy in operation.

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If an incandescent lamp is operated on a low-frequency current, the filament cools on each half-cycle of the alternating current, leading to perceptible change in brightness and

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In the United Kingdom, a standard frequency of 50 Hz was declared as early as 1904, but significant development continued at other frequencies. The implementation of the

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In the early incandescent lighting period, single-phase AC was common and typical generators were 8-pole machines operated at 2,000 RPM, giving a frequency of 133 hertz.

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Generators operated by slow-speed reciprocating engines will produce lower frequencies, for a given number of poles, than those operated by, for example, a high-speed steam

1579:. The target frequency is then adjusted by up to ±0.01 Hz (±0.02%) from 50 Hz as needed, to ensure a long-term frequency average of exactly 50 Hz × 60 1748:. During a severe failure of generators or transmission lines, the ensuing load-generation imbalance will induce variation in local power system frequencies. Loss of an 198:. Open arc lamps made an audible buzz on alternating current, leading to experiments with high-frequency alternators to raise the sound above the range of human hearing. 2081: 3243: 2848: 2841: 1656: 1606: 919: 3290: 2565: 2112:) equipment for RoCoF tolerance is hard, as a typical test setup is powered off the grid, and the frequency thus cannot be arbitrarily varied. In the US, the 3963: 602:

Direct-current power was not entirely displaced by alternating current and was useful in railway and electrochemical processes. Prior to the development of

2579: 1473:'s traction power systems in the United States. Other AC railway systems are energized at the local commercial power frequency, 50 Hz or 60 Hz. 793: Hz power suitable for heavy commutator-type motors, but the Westinghouse company objected that this would be undesirable for lighting and suggested 3223: 3205: 1915:

traditionally has a negative value, so that when the frequency is lower than the target, area power production should increase; its magnitude is usually

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also depends on a synchronous AC clock motor to maintain the correct speed of its internal "tone wheel" generator, thus keeping all notes pitch-perfect.

2928: 739:(descended from a company founded by Edison in Germany) built the first German generating facility to run at 50 Hz. At the time, AEG had a virtual 179:. Both devices operate well on DC, but DC could not be easily changed in voltage, and was generally only produced at the required utilization voltage. 2390: 821: 744: 2168: 1438: 2703: 1466: 3234: 2157: 2146: 1969: 2511: 1564: 1470: 2688: 2192: 825: 640: 2958: 609:, rotary converters were used to produce DC power from AC. Like other commutator-type machines, these worked better with lower frequencies. 4021: 2812: 2117: 1652: 1024: 631:

over long lines favors lower frequencies. The effects of the distributed capacitance and inductance of the line are less at low frequency.

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In some cases, where most load was to be railway or motor loads, it was considered economic to generate power at 25 Hz and install

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and their standard spread to the rest of Europe. After observing flicker of lamps operated by the 40 Hz power transmitted by the

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Traction power may be derived from commercial power supplies by frequency converters, or in some cases may be produced by dedicated

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used 40 Hz to transmit power 175 km in 1891. A large interconnected 40 Hz network existed in north-east England (the

750: 1621:, a correction of ±0.02 Hz (0.033%) is applied. Time error corrections start and end either on the hour or on the half-hour. 2909: 1847: 1016: 931: 3751: 3676: 3547: 1552: 1752:

causes system frequency to increase (due to excess generation) upstream of the loss, but may cause a collapse in frequency or

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Electricity Supply in the United Kingdom: A Chronology from the beginnings of the industry to 31 December 1985 Fourth Edition

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discovered that solar plants could respond to the signal faster than traditional generators, because they did not need to

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was declared in 1964. Brazil underwent a frequency conversion program to 60 Hz that was not completed until 1978.

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current, and the rotation speed; so, a given standard speed limits the choice of frequency (and the reverse). Once AC

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In Mexico, areas operating on 50 Hz grid were converted during the 1970s, uniting the country under 60 Hz.

840:, still produces electric power at 40 Hz and supplies power to the local 60 Hz transmission system through 239:

favored higher frequencies. The steadier rotation speed of high-speed machines allowed for satisfactory operation of

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too low, depending on the system's disturbance tolerance and the severity of protection measures). These initiate

1667: 1568: 1086: 988: 923: 81: 2806:"Western Electricity Coordinating Council Regional Reliability Standard Regarding Automatic Time Error Correction" 762:

using 50 Hz, but changed to 60 Hz a year later to maintain market share with the Westinghouse standard.

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C. Linder (2002), "Umstellung der Sollfrequenz im zentralen Bahnstromnetz von 16 2/3 Hz auf 16,70 Hz (English:

2212: 1421: 209:-type motors do not operate well on high-frequency AC, because the rapid changes of current are opposed by the 1355:

Canada (Southern Ontario), Panama Canal Zone(*), France, Germany, Sweden, UK, China, Hawaii, India, Manchuria

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have simplified these designs, but the installed base at 25 Hz was too large to be economically opposed.

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By about 1900, European manufacturers had mostly standardized on 50 Hz for new installations. The German

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motors are common in AC household appliances and power tools, they are small motors, less than 1 kW. The

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present, it went mostly un-noticed because it was stationary. The elimination of transformers by the use of

2092: 2083:), usually measured in Hz per second, Hz/s. The importance of this parameter increases when the traditional 1640: 1618: 1610: 1372:

Lots Road Power station, Chelsea, London (for London Underground and Trolley busses after conversion to DC)

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to coordinate generators connected the network. The practice arose because the frequency of a mechanical

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became common, it was important to standardize frequency for compatibility with the customer's equipment.

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Switching the frequency in train electric power supply network from 16 2/3 Hz to 16,70 Hz

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Regulation of power system frequency for timekeeping accuracy was not commonplace until after 1916 with

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Power frequencies as high as 400 Hz are used in aircraft, spacecraft, submarines, server rooms for

1477: 774:, built by Westinghouse in 1895, were 25 Hz, because the turbine speed had already been set before 240: 206: 172: 1796:

for power provision or consumption to surrounding areas. The automatic generation scheme described in

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in the late 1920s, and projects in Italy used 42 Hz. The oldest continuously operating commercial

3537: 3299: 1737: 759: 736: 2515: 3908: 3741: 3641: 3616: 3569: 3378: 3368: 3333: 2600:, copyright American Technical Book Company 1897, published by P.F. Collier and Sons New York, 1902 1904: 1829: 775: 659: 77: 2929:"First Solar Proves That PV Plants Can Rival Frequency Response Services From Natural Gas Peakers" 2756: 3782: 3393: 3057: 2892: 2659: 2313: 1699: 1675: 691: 647: 191: 143:

In the late 19th century, designers would pick a relatively high frequency for systems featuring

2816: 2279: 2257: 2870:"Power-grid experiment could confuse clocks – Technology & science – Innovation – NBC News" 2048: 4087: 3933: 3813: 3063: 2978: 2684: 2639: 2494: 2451: 2275: 2253: 2207: 2180: 2096: 1749: 1462: 1443:

Other power frequencies are still used. Germany, Austria, Switzerland, Sweden, and Norway use

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Very early isolated AC generating schemes used arbitrary frequencies based on convenience for

603: 3169: 3882: 3823: 3527: 3522: 3499: 3408: 3348: 2443: 2426: 2137: 1757: 1671: 972: 833: 816: 195: 152: 61: 2514:. Louisiana Department of Transportation and Development. September 5, 2005. Archived from 2347:, Transactions AIEE January 1918, reprinted in the Baltimore Amateur Radio Club newsletter 1698:(AGC) maintains scheduled frequency and interchange power flows by adjusting the generator 17: 3913: 3872: 3850: 3731: 3701: 3666: 3626: 3428: 3261: 3183: 3026: 2101: 1930: 1916: 1769: 1683: 1540: 1388:

Czechoslovakia, Hungary, Italy, Monaco(*), Portugal, Romania, Yugoslavia, Libya (Tripoli)

1130: 881: 220: 69: 2545:, 4th Ed., Westinghouse Electric Corporation, East Pittsburgh Pennsylvania, 1950, no ISBN 1694:

of the generated current; excess force deposits rotational energy, increasing frequency.

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Where regions are marked (*), this is the only utility frequency shown for that region.

732:, there is little certitude in the details of the history of 60 Hz vs. 50 Hz. 4063: 3938: 3928: 3726: 3338: 2994: 2936: 2676: 1789: 1721: 1380:

Jamaica, Belgium, Switzerland, UK, Federated Malay States, Egypt, Western Australia(*)

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it is typically 60 Hz. Current usage by country or region is given in the list of

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systems also used 415 Hz power systems within a computer room. Robert B. Hickey,

2252:, Industry Applications Magazine, IEEE, Sep/Oct 2000, Volume 6, Issue 5, Pages 12–14, 243:

in rotary converters. The synchronous speed N in RPM is calculated using the formula,

4128: 3958: 3746: 3631: 3611: 3542: 3532: 3489: 3373: 3328: 2267:, AIEE Transactions, Volume 31, 1912, pages 955–983, and discussion on pages 974–978. 2025: 1939: 1765: 1556: 927: 687: 236: 85: 2272:

Electrification of a Major Steel Mill – Part II Development of the 25 Hz System

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Synchronous speeds of AC motors for some current and historical utility frequencies

4108: 4103: 3978: 3953: 3818: 3787: 3601: 3403: 1745: 1548: 893: 683: 664: 38: 2611: 4113: 3803: 3771: 3564: 3552: 3472: 3398: 3388: 3318: 2121: 1934: 1725: 1703: 1576: 1513: 1509: 943: 618: 144: 1531: 3766: 3761: 3574: 3557: 3413: 2619:(2nd ed.). New York: Federal Telephone and Radio Corporation. p. 26. 2177: 2084: 2042: 1717: 1020: 848: 210: 2643: 1756:(due to excess load) downstream of the loss. Consequently many power system 1563:

maintained at a nominal value within a few hundred parts per million. In the

1461: Hz or 16.7 Hz. A frequency of 25 Hz is used for the Austrian 140:

importance. The best frequency is a compromise among competing requirements.

4077: 4032: 3482: 3477: 3363: 3323: 2532:, private printing, Chicago 1915, available on the Internet Archive, page 72 2222: 2133: 1923: 1773: 1691: 606: 73: 31: 2770: 3062:. IEE Control Engineering. Stevenage: Peter Peregrinus. pp. 193–198. 2743: 3596: 1919: 1822: 1793: 1713: 1709: 1551:

demonstrated the concept of clocks synchronized by line frequency at the

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Owen, Edward (1997-11-01). "The Origins of 60-Hz as a Power Frequency".

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AC-powered appliances can give off a characteristic hum, often called "

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Tie-line bias LFC was known since 1930s, but was rarely used until the

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LFC incorporates power transfer between different areas, known as "net

1801: 1753: 939: 935: 907: 232: 113: 2136:", at the multiples of the frequencies of AC power that they use (see 3512: 2897:(International Student ed.). Tata-McGraw Hill. pp. 562–565. 2877: 2095:(IBR). The design of a synchronous generator inherently provides the 1584: 1580: 951: 947: 911: 2638:(in German), vol. Book 12, Munich: Oldenbourg-Industrieverlag, 2541:

Central Station Engineers of the Westinghouse Electric Corporation,

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is the only facility that allows testing of multi-MW units (up to 7

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in 1891, AEG raised their standard frequency to 50 Hz in 1891.

44: 37:"ROCOF" redirects here. For the rate of occurrence of failures, see 2683:(Eleventh ed.). New York: McGraw-Hill. pp. 16–15, 16–16. 2391:"City of Coventry Single and Two Phase Generation and Distribution" 2300:

Electrical Transmission and Distribution Reference Book 4th Edition

1942:, with location-invariant frequency change per additional loading ( 1911:, and governors adjusted to counteract its value. The coefficient 3151: 3149: 2361: 2274:, Industry Applications Magazine, IEEE, Sep/Oct 2005, Pages 9–12, 2164: 2153: 2142: 1821:

refers to the difference between measured and desired values, and

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European Network of Transmission System Operators for Electricity

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Frequencies in use in 1946 (as well as 50 Hz and 60 Hz)

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50-Hz frequency: how the standard emerged from a European jungle

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Many different power frequencies were used in the 19th century.

101: 4036: 3272: 3001:, vol. 1, John Wiley and Sons, New York, 1948 pg. 189 2910:"Battery Storage: A Clean Alternative for Frequency Regulation" 2448:

Networks of Power: Electrification in Western Society 1880–1930

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of Hungary had standardized on 5000 alternations per minute (41

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Miller, Nicholas; Lew, Debra; Barnes, Steven (April 9, 2017).

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The waveform of 230 V and 50 Hz compared with 120 V and 60 Hz

3017:, pp. 48–49. Note that an older notation instead uses 2975:

Standard Handbook for Electrical Engineers, Eleventh Edition

1903:

refers to tie-line power. This instantaneous error is then

30:"60 cycles" redirects here. For the 1965 Canadian film, see 2891:

Grainger, John J.; Stevenson, William D. (1994).

2757:"National Grid: Real Time Frequency Data – Last 60 Minutes" 1655:

made time error correction mandatory in 2009. In 2011, The

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AEG, Oerlikon, and other manufacturers, eventual standard

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Many manufacturers, becoming "increasingly common" in 1897

27:

Frequency used on standard electricity grid in a given area

2017:{\displaystyle B={\frac {1}{2}}{\frac {dL}{df}}{\text{,}}} 1844:(ACE) associated with LFC at any moment in time is simply 1760:

automatically trigger on severe underfrequency (typically

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to follow the frequency signal. Indeed, a 2017 trial for

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to counteract frequency changes, typically within several

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General Electric at Portland Oregon for rotary converters

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now use the 50 Hz frequency tend to use 220–240

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that minimizes the magnitude of average frequency error,

1575:) is calculated at 08:00 each day in a control center in 728:

Though many theories exist, and quite a few entertaining

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The first applications of commercial electric power were

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Rate of Change of Frequency (ROCOF) withstand capability

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Entsoe Load Frequency Control and Performance, chapter D

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Westinghouse Niagara Falls 2-phase—for operating motors

871: Hz systems that in some cases ran for many years. 3225:

Advisory on Equipment Limits associated with High RoCoF

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of the frequency bias as defined here, and sometimes a

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Electrical Transmission and Distribution Reference Book

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power", into the minimized quantity. For a particular

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used by some clocks to accurately maintain their time.

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preserve the operation of at least part of the network

2450:, The Johns Hopkins University Press, Baltimore 1983 2051: 1972: 1850: 252: 2960:

Transmission and Distribution Electrical Engineering

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that restores the system frequency while respecting

861: Hz) for their products, so Ganz clients had 41 4096: 4070: 3987: 3897: 3834: 3796: 3650: 3587: 3498: 3453: 3446: 3306: 2124:). Testing of large thermal units is not possible. 1015:substations which convert the frequency; these are 2075: 2016: 1886: 277: 3046:5th Edition. Cengage Learning. 2012. pp. 663–664. 1257:Municipal power station, Frankfurt am Main, 1893 186:of the lamps; the effect is more pronounced with 2957:Bayliss, Colin; Hardy, Brian (14 October 2022). 2302:, Westinghouse Electric Corporation 1950, page 6 1609:, whenever the error exceeds 10 seconds for the 1290:Lauffen am Neckar, hydroelectric, 1891, to 1925 3244:North American Electric Reliability Corporation 3155: 3140: 2849:North American Electric Reliability Corporation 2842:"Time error correction and reliability (draft)" 1657:North American Electric Reliability Corporation 1567:, the deviation between network phase time and 922:(these were retrofitted to 60 Hz) and the 1516:exists for aircraft use of 400 Hz power. 1447:for railways, distributing single-phase AC at 92:. In large parts of the world this is 50 4048: 3284: 2973:Donald G. Fink and H. Wayne Beaty, 2468: 2466: 2464: 1318:St. James and Soho Electric Light Co. London 1166:Single-phase lighting systems, UK and Europe 8: 1174:Single-phase lighting system, UK and Europe 1035:Utility frequencies in North America in 1897 622:require regular maintenance and monitoring. 1887:{\displaystyle \Delta (P_{T}-Bf){\text{,}}} 1213:Single phase lighting, Germany, 1891, 1893 826:Newcastle-upon-Tyne Electric Supply Company 213:of the motor field. Though commutator-type 4055: 4041: 4033: 3450: 3291: 3277: 3269: 2985:, pp. 16‑15–16‑21 2681:Standard Handbook for Electrical Engineers 1788:Load-frequency control (LFC) is a type of 650:, providing reliability and cost savings. 2963:(4th ed.). Newnos. pp. 344–345. 2598:Recent Types of Dynamo-Electric Machinery 2339: 2337: 2335: 2333: 2065: 2060: 2052: 2050: 2009: 1989: 1979: 1971: 1879: 1861: 1849: 274: 259: 251: 3033:is included in the area control formula. 2412: 2410: 2236:The Evolution of Power-Line Frequencies 1340: 1151: 1038: 294: 3128: 3116: 3094: 3014: 2927:St. John, Jeff (19 January 2017). 2664:Electrical engineer's portable handbook 2291: 2024:and one region experienced a temporary 1797: 1724:-linked power supplies. However, such 1690:from the generator shaft, reducing the 1439:List of railway electrification systems 4078:Synchronous Motor and the Master Clock 3228:. General Electric International, Inc. 2596:Edwin J. Houston and Arthur Kennelly, 2345:The Technical Story of the Frequencies 1565:synchronous grid of Continental Europe 1333:60-cycle, or direct current supplies. 914:, the northern United States, and for 3254:On the load-frequency control problem 3056:Sterling, M. J. H. (1978). 2193:Electrical network frequency analysis 1547:and self-starting synchronous motor. 1148:Utility frequencies in Europe to 1900 641:Synchronization (alternating current) 278:{\displaystyle N={\frac {120f}{P}}\,} 7: 3082: 3010: 2813:Federal Energy Regulatory Commission 2118:National Renewable Energy Laboratory 1686:experienced. Excess load withdraws 1670:use precise frequency control as an 1653:Federal Energy Regulatory Commission 1326:Single phase lighting, Germany 1897 1194:Single-phase lighting, Germany 1891 836:power station in the United States, 3184:"The hum that helps to fight crime" 1637:Frequency Monitoring Network (FNET) 1029:Higashi-Shimizu Frequency Converter 1011:regions contains four back-to-back 3969:Renewable energy commercialization 2613:Reference Data for Radio Engineers 2037:Rate of change of frequency (also 1851: 1265:Ganz customers, also Germany 1898 25: 3251:Bratton, Timothy Lee (May 1971). 3044:Power System Analysis and Design. 2298:A.C. Monteith, C.F. Wagner (ed), 1545:Warren Power Station Master Clock 838:Mechanicville Hydroelectric Plant 828:, NESCO) until the advent of the 4017: 4016: 3437: 2530:Central-Station Electric Service 1668:Modern alternating-current grids 1105:General Electric Lachine Rapids 668:Japan's utility frequencies are 3236:Balancing and Frequency Control 2977:, McGraw-Hill, New York, 1978, 2312:Wald, Matthew L. (2011-01-07). 822:Lauffen-Frankfurt demonstration 3260:(MSc thesis). Houston, Texas: 2876:. 25 June 2011. Archived from 2815:. May 21, 2009. Archived from 2717:"Manual Time Error Correction" 2478:IEEE Power and Energy Magazine 2419:Industry Applications Magazine 2128:Audible noise and interference 1876: 1854: 1232:Kilwangen generating station, 1069:General Electric single-phase 926:(until its 2006 closure) near 292:and P is the number of poles. 1: 3964:Renewable Energy Certificates 3924:Cost of electricity by source 3846:Arc-fault circuit interrupter 3722:High-voltage shore connection 3170:"Controllable Grid Interface" 3156:Miller, Lew & Barnes 2017 3141:Miller, Lew & Barnes 2017 613:Transmission and transformers 3979:Spark/Dark/Quark/Bark spread 3777:Transmission system operator 3737:Mains electricity by country 3314:Automatic generation control 2908:Lombardo, Tom (6 May 2016). 2582:(in Spanish). Archived from 2480:, July/August 2011 pp. 66–81 1966:). If the utility selected 1696:Automatic generation control 770:The first generators at the 694:design. Frequencies between 288:where f is the frequency in 106:mains electricity by country 4004:List of electricity sectors 3999:Electric energy consumption 3717:High-voltage direct current 3692:Electric power transmission 3682:Electric power distribution 3359:Energy return on investment 2610:H.T. Kohlhaas, ed. (1946). 2218:Network analyzer (AC power) 2176:Most countries chose their 2114:controllable grid interface 2033:Rate of change of frequency 1525:Time error correction (TEC) 1182:Single phase, Ferranti UK, 924:Rankine generating stations 629:Electric power transmission 126:Time error correction (TEC) 18:Time error correction (TEC) 4151: 3919:Carbon offsets and credits 3637:Three-phase electric power 2679:; Beaty, H. Wayne (1978). 2190: 2045:of the utility frequency ( 1728:or storage systems can be 1712:physics does not apply to 1651:In the United States, the 1494: Hz or 16.7 Hz. 1436: 989:Southern California Edison 968: Hz or 16.7 Hz. 901:Verband der Elektrotechnik 657: 638: 123: 82:wide area synchronous grid 36: 29: 4064:Electric clock technology 4012: 3974:Renewable Energy Payments 3463:Fossil fuel power station 3435: 3204:ENTSO-E (29 March 2017). 3042:Glover, Duncan J. et al. 2631: 2489:The Electricity Council, 2425:(6). IEEE: 8, 10, 12–14. 2089:variable renewable energy 2076:{\displaystyle {df}/{dt}} 1798:§ Frequency and load 1772:interconnection lines to 1573:International Atomic Time 1053:Wood arc-lighting dynamo 3757:Single-wire earth return 3697:Electrical busbar system 3354:Energy demand management 2213:Maximum demand indicator 2181:vertical synchronization 2093:inverter-based resources 1825:indicate time averages. 1553:1893 Chicago Worlds fair 758:to bring electricity to 3888:Residual-current device 3878:Power system protection 3868:Generator interlock kit 2775:www.dynamicdemand.co.uk 2100:protection devices and 1641:University of Tennessee 1619:Western Interconnection 1617:, or 2 seconds for the 1611:Eastern Interconnection 1445:traction power networks 1404:Italy, Libya (Tripoli) 934:rail networks, used in 916:railway electrification 76:of the oscillations of 4071:Powerline synchronized 3672:Distributed generation 3344:Electric power quality 2999:Power System Stability 2518:on September 23, 2005. 2173: 2162: 2151: 2085:synchronous generators 2077: 2018: 1905:numerically integrated 1888: 1784:Load-frequency control 1678:varies with the input 1536: 1478:traction powerstations 1282:Ganz Company, Hungary 1184:Deptford Power Station 1077:Stanley-Kelly Company 1061:Stanley-Kelly Company 987:In the United States, 745:Lauffen-Frankfurt link 676: 635:System interconnection 279: 58:(power) line frequency 49: 3944:Fossil fuel phase-out 3712:Electricity retailing 3707:Electrical substation 3687:Electric power system 3233:NERC (May 11, 2021). 2995:Edward Wilson Kimbark 2931:. Grid Optimization. 2894:Power system analysis 2744:Time Error Correction 2566:"Padrões brasileiros" 2314:"Hold That Megawatt!" 2171: 2160: 2149: 2078: 2019: 1889: 1738:accelerate a rotating 1615:Texas Interconnection 1534: 772:Niagara Falls project 751:Westinghouse Electric 667: 280: 169:incandescent lighting 47: 3300:Electricity delivery 3059:Power System Control 2822:on December 21, 2016 2270:Blalock, Thomas J., 2087:are replaced by the 2049: 1970: 1848: 1613:, 3 seconds for the 1543:'s invention of the 1129:Crocker-Wheeler for 760:Redlands, California 692:electrical generator 250: 3909:Availability factor 3861:Sulfur hexafluoride 3742:Overhead power line 3642:Virtual power plant 3617:Induction generator 3570:Sustainable biofuel 3379:Home energy storage 3369:Grid energy storage 3334:Droop speed control 3190:. 12 December 2012. 2564:Atitude Editorial. 2431:10.1109/2943.628099 2351:January -March 2007 2041:) is simply a time 1605:cycles per day. In 1422:British East Africa 954:, still operate at 776:alternating current 735:The German company 660:War of the currents 297: 192:mercury-vapor lamps 84:transmitted from a 78:alternating current 3783:Transmission tower 3394:Nameplate capacity 2880:on August 4, 2020. 2660:mainframe computer 2636:Elektrische Bahnen 2472:Gerhard Neidhofer 2379:cycles per second. 2174: 2163: 2152: 2073: 2014: 1884: 1842:area control error 1672:out-of-band signal 1663:Frequency and load 1537: 1240:Rome, Geneva 1900 1085:General Electric " 932:15 kV AC 842:frequency changers 830:National Grid (UK) 677: 295: 275: 96:, although in the 50: 4122: 4121: 4088:Synchronous motor 4083:Utility frequency 4030: 4029: 3934:Environmental tax 3814:Cascading failure 3583: 3582: 3419:Utility frequency 3119:, pp. 48–49. 2690:978-0-07-020974-9 2389:Gordon Woodward. 2208:Mains electricity 2169: 2158: 2147: 2097:inertial response 2012: 2007: 1987: 1933:. In the 1950s, 1907:to give the time 1882: 1758:protective relays 1688:rotational energy 1463:Mariazell Railway 1427: 1426: 1330: 1329: 1145: 1144: 1113:General Electric 973:rotary converters 604:mercury arc valve 600: 599: 326:RPM at 25 Hz 323:RPM at 40 Hz 320:RPM at 50 Hz 317:RPM at 60 Hz 272: 202:Rotating machines 196:fluorescent lamps 153:rotary converters 135:Operating factors 72:) is the nominal 54:utility frequency 16:(Redirected from 4142: 4057: 4050: 4043: 4034: 4020: 4019: 3929:Energy subsidies 3883:Protective relay 3824:Rolling blackout 3451: 3441: 3409:Power-flow study 3349:Electrical fault 3293: 3286: 3279: 3270: 3265: 3259: 3247: 3241: 3229: 3218: 3212: 3192: 3191: 3180: 3174: 3173: 3165: 3159: 3153: 3144: 3138: 3132: 3126: 3120: 3114: 3108: 3104: 3098: 3092: 3086: 3080: 3074: 3073: 3053: 3047: 3040: 3034: 3032: 3020: 3013:, p. 11 or 3008: 3002: 2992: 2986: 2971: 2965: 2964: 2954: 2948: 2947: 2945: 2943: 2924: 2918: 2917: 2905: 2899: 2898: 2888: 2882: 2881: 2866: 2860: 2859: 2857: 2855: 2846: 2838: 2832: 2831: 2829: 2827: 2821: 2810: 2802: 2796: 2795: 2792: 2790: 2785: 2779: 2778: 2771:"Dynamic Demand" 2767: 2761: 2760: 2753: 2747: 2741: 2735: 2734: 2732: 2730: 2721: 2713: 2707: 2701: 2695: 2694: 2673: 2667: 2653: 2647: 2646: 2633: 2627: 2621: 2620: 2618: 2607: 2601: 2594: 2588: 2587: 2576: 2570: 2569: 2561: 2555: 2552: 2546: 2539: 2533: 2526: 2520: 2519: 2508: 2502: 2487: 2481: 2470: 2459: 2444:Thomas P. Hughes 2441: 2435: 2434: 2414: 2405: 2404: 2402: 2396:. Archived from 2395: 2386: 2380: 2378: 2377: 2373: 2370: 2358: 2352: 2341: 2328: 2327: 2325: 2324: 2309: 2303: 2296: 2263:Rushmore, D.B., 2249: 2248: 2244: 2241: 2172:400 Hz power hum 2170: 2159: 2148: 2138:Magnetostriction 2082: 2080: 2079: 2074: 2072: 2064: 2059: 2023: 2021: 2020: 2015: 2013: 2010: 2008: 2006: 1998: 1990: 1988: 1980: 1965: 1964: 1962: 1961: 1955: 1952: 1914: 1902: 1893: 1891: 1890: 1885: 1883: 1880: 1866: 1865: 1839: 1820: 1816: 1812: 1811: 1790:integral control 1763: 1634: 1631: 1629: 1604: 1603: 1600: 1535:TEC availability 1493: 1492: 1488: 1485: 1460: 1459: 1455: 1452: 1369: 1368: 1364: 1341: 1315: 1314: 1310: 1279: 1278: 1274: 1254: 1253: 1249: 1152: 1039: 1025:Minami-Fukumitsu 967: 966: 962: 959: 870: 869: 865: 860: 859: 855: 817:General Electric 806: 805: 801: 798: 792: 791: 787: 784: 721: 720: 716: 713: 707: 706: 702: 699: 675: 671: 570: 569: 565: 558: 557: 553: 546: 545: 541: 338: 337: 333: 313: 312: 308: 298: 284: 282: 281: 276: 273: 268: 260: 190:, and the later 62:American English 21: 4150: 4149: 4145: 4144: 4143: 4141: 4140: 4139: 4125: 4124: 4123: 4118: 4092: 4066: 4061: 4031: 4026: 4008: 3992: 3990: 3983: 3914:Capacity factor 3902: 3900: 3893: 3873:Numerical relay 3851:Circuit breaker 3839: 3837: 3830: 3792: 3732:Load management 3702:Electrical grid 3667:Demand response 3660: 3655: 3646: 3627:Microgeneration 3579: 3494: 3442: 3433: 3429:Vehicle-to-grid 3302: 3297: 3262:Rice University 3257: 3250: 3239: 3232: 3221: 3210: 3203: 3200: 3195: 3182: 3181: 3177: 3167: 3166: 3162: 3158:, p. 2-16. 3154: 3147: 3143:, p. 3-17. 3139: 3135: 3131:, pp. 3–4. 3127: 3123: 3115: 3111: 3105: 3101: 3097:, pp. 4–5. 3093: 3089: 3081: 3077: 3070: 3055: 3054: 3050: 3041: 3037: 3030: 3027:unit conversion 3018: 3009: 3005: 2993: 2989: 2972: 2968: 2956: 2955: 2951: 2941: 2939: 2926: 2925: 2921: 2914:Engineering.com 2907: 2906: 2902: 2890: 2889: 2885: 2868: 2867: 2863: 2853: 2851: 2844: 2840: 2839: 2835: 2825: 2823: 2819: 2808: 2804: 2803: 2799: 2787: 2786: 2782: 2769: 2768: 2764: 2755: 2754: 2750: 2742: 2738: 2728: 2726: 2719: 2715: 2714: 2710: 2702: 2698: 2691: 2677:Fink, Donald G. 2675: 2674: 2670: 2654: 2650: 2629: 2628: 2624: 2616: 2609: 2608: 2604: 2595: 2591: 2578: 2577: 2573: 2563: 2562: 2558: 2554:Hughes as above 2553: 2549: 2540: 2536: 2528:Samuel Insull, 2527: 2523: 2510: 2509: 2505: 2488: 2484: 2471: 2462: 2442: 2438: 2416: 2415: 2408: 2400: 2393: 2388: 2387: 2383: 2375: 2371: 2368: 2366: 2359: 2355: 2342: 2331: 2322: 2320: 2311: 2310: 2306: 2297: 2293: 2289: 2246: 2242: 2239: 2237: 2234:Furfari, F.A., 2231: 2229:Further reading 2204: 2195: 2186:AC/DC receivers 2165: 2161:60 Hz power hum 2154: 2150:50 Hz power hum 2143: 2130: 2047: 2046: 2035: 1999: 1991: 1968: 1967: 1956: 1953: 1947: 1946: 1944: 1943: 1931:post-war period 1917:on the order of 1912: 1900: 1895: 1857: 1846: 1845: 1837: 1818: 1814: 1806: 1805: 1786: 1761: 1750:interconnection 1665: 1649: 1630:.mainsfrequency 1626: 1601: 1598: 1596: 1527: 1522: 1500: 1490: 1486: 1483: 1481: 1457: 1453: 1450: 1448: 1441: 1435: 1366: 1362: 1361: 1312: 1308: 1307: 1276: 1272: 1271: 1251: 1247: 1246: 1131:calcium carbide 998:Decreto-Lei 852 992:volts in 1914. 978:static inverter 964: 960: 957: 955: 920:Sir Adam Beck 1 882:Standardization 877: 875:Standardization 867: 863: 862: 857: 853: 852: 813: 803: 799: 796: 794: 789: 785: 782: 780: 768: 718: 714: 711: 709: 704: 700: 697: 695: 673: 669: 662: 656: 643: 637: 615: 567: 563: 562: 555: 551: 550: 543: 539: 538: 335: 331: 330: 310: 306: 305: 261: 248: 247: 226:electric motors 221:induction motor 204: 177:electric motors 165: 137: 128: 122: 120:Electric clocks 70:British English 66:mains frequency 42: 35: 28: 23: 22: 15: 12: 11: 5: 4148: 4146: 4138: 4137: 4135:Electric power 4127: 4126: 4120: 4119: 4117: 4116: 4111: 4106: 4100: 4098: 4094: 4093: 4091: 4090: 4085: 4080: 4074: 4072: 4068: 4067: 4062: 4060: 4059: 4052: 4045: 4037: 4028: 4027: 4025: 4024: 4013: 4010: 4009: 4007: 4006: 4001: 3995: 3993: 3989:Statistics and 3988: 3985: 3984: 3982: 3981: 3976: 3971: 3966: 3961: 3956: 3951: 3946: 3941: 3939:Feed-in tariff 3936: 3931: 3926: 3921: 3916: 3911: 3905: 3903: 3898: 3895: 3894: 3892: 3891: 3885: 3880: 3875: 3870: 3865: 3864: 3863: 3858: 3848: 3842: 3840: 3835: 3832: 3831: 3829: 3828: 3827: 3826: 3816: 3811: 3806: 3800: 3798: 3794: 3793: 3791: 3790: 3785: 3780: 3774: 3769: 3764: 3759: 3754: 3749: 3744: 3739: 3734: 3729: 3727:Interconnector 3724: 3719: 3714: 3709: 3704: 3699: 3694: 3689: 3684: 3679: 3677:Dynamic demand 3674: 3669: 3663: 3661: 3651: 3648: 3647: 3645: 3644: 3639: 3634: 3629: 3624: 3619: 3614: 3609: 3607:Combined cycle 3604: 3599: 3593: 3591: 3585: 3584: 3581: 3580: 3578: 3577: 3572: 3567: 3562: 3561: 3560: 3555: 3550: 3545: 3540: 3530: 3525: 3520: 3515: 3510: 3504: 3502: 3496: 3495: 3493: 3492: 3487: 3486: 3485: 3480: 3475: 3470: 3459: 3457: 3448: 3444: 3443: 3436: 3434: 3432: 3431: 3426: 3421: 3416: 3411: 3406: 3401: 3396: 3391: 3386: 3384:Load-following 3381: 3376: 3371: 3366: 3361: 3356: 3351: 3346: 3341: 3339:Electric power 3336: 3331: 3326: 3321: 3316: 3310: 3308: 3304: 3303: 3298: 3296: 3295: 3288: 3281: 3273: 3267: 3266: 3248: 3230: 3219: 3199: 3196: 3194: 3193: 3175: 3160: 3145: 3133: 3121: 3109: 3099: 3087: 3075: 3068: 3048: 3035: 3003: 2987: 2966: 2949: 2937:Wood Mackenzie 2919: 2900: 2883: 2861: 2833: 2797: 2780: 2762: 2748: 2736: 2708: 2696: 2689: 2668: 2648: 2622: 2602: 2589: 2586:on 2009-12-13. 2571: 2556: 2547: 2534: 2521: 2512:"News in DOTD" 2503: 2482: 2460: 2436: 2406: 2403:on 2007-10-31. 2381: 2353: 2329: 2304: 2290: 2288: 2285: 2284: 2283: 2268: 2261: 2230: 2227: 2226: 2225: 2220: 2215: 2210: 2203: 2200: 2191:Main article: 2129: 2126: 2071: 2068: 2063: 2058: 2055: 2034: 2031: 2005: 2002: 1997: 1994: 1986: 1983: 1978: 1975: 1898: 1878: 1875: 1872: 1869: 1864: 1860: 1856: 1853: 1834:frequency bias 1817:is frequency, 1800:establishes a 1785: 1782: 1762:0.5–2 Hz 1664: 1661: 1648: 1647:US regulations 1645: 1587:× 60 min/ 1526: 1523: 1521: 1518: 1504:computer power 1499: 1496: 1437:Main article: 1434: 1431: 1425: 1424: 1418: 1414: 1413: 1410: 1406: 1405: 1402: 1398: 1397: 1394: 1390: 1389: 1386: 1382: 1381: 1378: 1374: 1373: 1370: 1357: 1356: 1353: 1349: 1348: 1345: 1328: 1327: 1324: 1320: 1319: 1316: 1303: 1302: 1296: 1292: 1291: 1288: 1284: 1283: 1280: 1267: 1266: 1263: 1259: 1258: 1255: 1242: 1241: 1238: 1234: 1233: 1227: 1223: 1222: 1219: 1215: 1214: 1211: 1207: 1206: 1200: 1196: 1195: 1192: 1188: 1187: 1180: 1176: 1175: 1172: 1168: 1167: 1164: 1160: 1159: 1156: 1143: 1142: 1139: 1135: 1134: 1127: 1123: 1122: 1119: 1115: 1114: 1111: 1107: 1106: 1103: 1099: 1098: 1095: 1091: 1090: 1083: 1079: 1078: 1075: 1071: 1070: 1067: 1063: 1062: 1059: 1055: 1054: 1051: 1047: 1046: 1043: 876: 873: 812: 809: 767: 764: 655: 652: 639:Main article: 636: 633: 614: 611: 598: 597: 594: 591: 588: 585: 582: 579: 575: 574: 571: 559: 547: 535: 532: 529: 525: 524: 521: 518: 515: 512: 509: 506: 502: 501: 498: 495: 492: 489: 486: 483: 479: 478: 475: 472: 469: 466: 463: 460: 456: 455: 452: 449: 446: 443: 440: 437: 433: 432: 429: 426: 423: 420: 417: 414: 410: 409: 406: 403: 400: 397: 394: 391: 387: 386: 383: 380: 377: 374: 371: 368: 364: 363: 360: 357: 354: 351: 348: 345: 341: 340: 327: 324: 321: 318: 315: 302: 286: 285: 271: 267: 264: 258: 255: 237:steam turbines 203: 200: 164: 161: 157:direct current 155:for producing 136: 133: 124:Main article: 121: 118: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 4147: 4136: 4133: 4132: 4130: 4115: 4112: 4110: 4107: 4105: 4102: 4101: 4099: 4095: 4089: 4086: 4084: 4081: 4079: 4076: 4075: 4073: 4069: 4065: 4058: 4053: 4051: 4046: 4044: 4039: 4038: 4035: 4023: 4015: 4014: 4011: 4005: 4002: 4000: 3997: 3996: 3994: 3986: 3980: 3977: 3975: 3972: 3970: 3967: 3965: 3962: 3960: 3959:Pigouvian tax 3957: 3955: 3952: 3950: 3947: 3945: 3942: 3940: 3937: 3935: 3932: 3930: 3927: 3925: 3922: 3920: 3917: 3915: 3912: 3910: 3907: 3906: 3904: 3896: 3889: 3886: 3884: 3881: 3879: 3876: 3874: 3871: 3869: 3866: 3862: 3859: 3857: 3856:Earth-leakage 3854: 3853: 3852: 3849: 3847: 3844: 3843: 3841: 3833: 3825: 3822: 3821: 3820: 3817: 3815: 3812: 3810: 3807: 3805: 3802: 3801: 3799: 3797:Failure modes 3795: 3789: 3786: 3784: 3781: 3778: 3775: 3773: 3770: 3768: 3765: 3763: 3760: 3758: 3755: 3753: 3750: 3748: 3747:Power station 3745: 3743: 3740: 3738: 3735: 3733: 3730: 3728: 3725: 3723: 3720: 3718: 3715: 3713: 3710: 3708: 3705: 3703: 3700: 3698: 3695: 3693: 3690: 3688: 3685: 3683: 3680: 3678: 3675: 3673: 3670: 3668: 3665: 3664: 3662: 3659: 3654: 3649: 3643: 3640: 3638: 3635: 3633: 3632:Rankine cycle 3630: 3628: 3625: 3623: 3620: 3618: 3615: 3613: 3612:Cooling tower 3610: 3608: 3605: 3603: 3600: 3598: 3595: 3594: 3592: 3590: 3586: 3576: 3573: 3571: 3568: 3566: 3563: 3559: 3556: 3554: 3551: 3549: 3546: 3544: 3541: 3539: 3536: 3535: 3534: 3531: 3529: 3526: 3524: 3521: 3519: 3516: 3514: 3511: 3509: 3506: 3505: 3503: 3501: 3497: 3491: 3488: 3484: 3481: 3479: 3476: 3474: 3471: 3469: 3466: 3465: 3464: 3461: 3460: 3458: 3456: 3455:Non-renewable 3452: 3449: 3445: 3440: 3430: 3427: 3425: 3422: 3420: 3417: 3415: 3412: 3410: 3407: 3405: 3402: 3400: 3397: 3395: 3392: 3390: 3387: 3385: 3382: 3380: 3377: 3375: 3374:Grid strength 3372: 3370: 3367: 3365: 3362: 3360: 3357: 3355: 3352: 3350: 3347: 3345: 3342: 3340: 3337: 3335: 3332: 3330: 3329:Demand factor 3327: 3325: 3322: 3320: 3317: 3315: 3312: 3311: 3309: 3305: 3301: 3294: 3289: 3287: 3282: 3280: 3275: 3274: 3271: 3263: 3256: 3255: 3249: 3245: 3238: 3237: 3231: 3227: 3226: 3220: 3216: 3209: 3208: 3202: 3201: 3197: 3189: 3185: 3179: 3176: 3171: 3164: 3161: 3157: 3152: 3150: 3146: 3142: 3137: 3134: 3130: 3125: 3122: 3118: 3113: 3110: 3103: 3100: 3096: 3091: 3088: 3085:, p. 20. 3084: 3079: 3076: 3071: 3069:0-906048-01-X 3065: 3061: 3060: 3052: 3049: 3045: 3039: 3036: 3028: 3024: 3016: 3012: 3007: 3004: 3000: 2996: 2991: 2988: 2984: 2983:0-07-020974-X 2980: 2976: 2970: 2967: 2962: 2961: 2953: 2950: 2938: 2934: 2930: 2923: 2920: 2915: 2911: 2904: 2901: 2896: 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