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126-524: 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 now use the 50 Hz frequency tend to use 220–240  V , 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

252-536: A d e E n e r g y   s u p p l i e d   p e r   s t a g e = U Δ V w Δ h {\displaystyle {\eta _{\mathrm {stage} }}={\frac {\mathrm {Work~done~on~blade} }{\mathrm {Energy~supplied~per~stage} }}={\frac {U\Delta V_{w}}{\Delta h}}} Where Δ h = h 2 − h 1 {\displaystyle \Delta h=h_{2}-h_{1}}

378-733: A bridge circuit . The cathode-ray oscilloscope works by amplifying the voltage and using it to deflect an electron beam from a straight path, so that the deflection of the beam is proportional to the voltage. A common voltage for flashlight batteries is 1.5 volts (DC). A common voltage for automobile batteries is 12 volts (DC). Common voltages supplied by power companies to consumers are 110 to 120 volts (AC) and 220 to 240 volts (AC). The voltage in electric power transmission lines used to distribute electricity from power stations can be several hundred times greater than consumer voltages, typically 110 to 1200 kV (AC). The voltage used in overhead lines to power railway locomotives

504-430: A generator ). On a macroscopic scale, a potential difference can be caused by electrochemical processes (e.g., cells and batteries), the pressure-induced piezoelectric effect , and the thermoelectric effect . Since it is the difference in electric potential, it is a physical scalar quantity . A voltmeter can be used to measure the voltage between two points in a system. Often a common reference potential such as

630-563: A quality near 90%. Non-condensing turbines are most widely used for process steam applications, in which the steam will be used for additional purposes after being exhausted from the turbine. The exhaust pressure is controlled by a regulating valve to suit the needs of the process steam pressure. These are commonly found at refineries, district heating units, pulp and paper plants, and desalination facilities where large amounts of low pressure process steam are needed. Reheat turbines are also used almost exclusively in electrical power plants. In

756-505: A static electric field , it corresponds to the work needed per unit of charge to move a positive test charge from the first point to the second point. In the International System of Units (SI), the derived unit for voltage is the volt (V) . The voltage between points can be caused by the build-up of electric charge (e.g., a capacitor ), and from an electromotive force (e.g., electromagnetic induction in

882-746: A 25 Hz power station exist in New Orleans for floodwater pumps. The 15 kV AC rail networks, used in Germany , Austria , Switzerland , Sweden , and Norway , still operate at 16 + 2 ⁄ 3  Hz or 16.7 Hz. 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 rotary converters 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

1008-683: A Heat Engine) was published in Berlin in 1903. A further book Dampf und Gas-Turbinen (English: Steam and Gas Turbines) was published in 1922. The Brown-Curtis turbine , an impulse type, which had been originally developed and patented by the U.S. company International Curtis Marine Turbine Company, was developed in the 1900s in conjunction with John Brown & Company . It was used in John Brown-engined merchant ships and warships, including liners and Royal Navy warships. The present day manufacturing industry for steam turbines consists of

1134-444: A common reduction gear, with a geared cruising turbine on one high-pressure turbine. The moving steam imparts both a tangential and axial thrust on the turbine shaft, but the axial thrust in a simple turbine is unopposed. To maintain the correct rotor position and balancing, this force must be counteracted by an opposing force. Thrust bearings can be used for the shaft bearings, the rotor can use dummy pistons, it can be double flow -

1260-400: A compound impulse turbine. The modern steam turbine was invented in 1884 by Charles Parsons , whose first model was connected to a dynamo that generated 7.5 kilowatts (10.1 hp) of electricity. The invention of Parsons' steam turbine made cheap and plentiful electricity possible and revolutionized marine transport and naval warfare. Parsons' design was a reaction type. His patent

1386-456: A generator. Tandem compound are used where two or more casings are directly coupled together to drive a single generator. A cross compound turbine arrangement features two or more shafts not in line driving two or more generators that often operate at different speeds. A cross compound turbine is typically used for many large applications. A typical 1930s-1960s naval installation is illustrated below; this shows high- and low-pressure turbines driving

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1512-523: 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 Lauffen-Frankfurt demonstration used 40 Hz to transmit power 175 km in 1891. A large interconnected 40 Hz network existed in north-east England (the Newcastle-upon-Tyne Electric Supply Company , NESCO) until

1638-495: A higher frequency. Electric power transmission over long lines favors lower frequencies. The effects of the distributed capacitance and inductance of the line are less at low frequency. 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 grid , providing reliability and cost savings. Many different power frequencies were used in

1764-665: A mechanical generator varies with the input force and output load experienced. Excess load withdraws rotational energy from the generator shaft, reducing the frequency of the generated current; excess force deposits rotational energy, increasing frequency. Automatic generation control (AGC) maintains scheduled frequency and interchange power flows by adjusting the generator governor to counteract frequency changes, typically within several decaseconds . Flywheel physics does not apply to inverter -connected solar farms or other DC -linked power supplies. However, such power plants or storage systems can be programmed to follow

1890-405: 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. Modern alternating-current grids use precise frequency control as an out-of-band signal to coordinate generators connected the network. The practice arose because the frequency of

2016-408: A reheat turbine, steam flow exits from a high-pressure section of the turbine and is returned to the boiler where additional superheat is added. The steam then goes back into an intermediate pressure section of the turbine and continues its expansion. Using reheat in a cycle increases the work output from the turbine and also the expansion reaches conclusion before the steam condenses, thereby minimizing

2142-448: A row of moving blades, with multiple stages for compounding. This is also known as a Rateau turbine, after its inventor. A velocity-compounded impulse stage (invented by Curtis and also called a "Curtis wheel") is a row of fixed nozzles followed by two or more rows of moving blades alternating with rows of fixed blades. This divides the velocity drop across the stage into several smaller drops. A series of velocity-compounded impulse stages

2268-1371: A single stage impulse turbine). Therefore, the maximum value of stage efficiency is obtained by putting the value of U V 1 = 1 2 cos ⁡ α 1 {\displaystyle {\frac {U}{V_{1}}}={\frac {1}{2}}\cos \alpha _{1}} in the expression of η b {\displaystyle \eta _{b}} . We get: η b max = 2 ( ρ cos ⁡ α 1 − ρ 2 ) ( 1 + k c ) = 1 2 cos 2 ⁡ α 1 ( 1 + k c ) {\displaystyle {\eta _{b}}_{\text{max}}=2\left(\rho \cos \alpha _{1}-\rho ^{2}\right)(1+kc)={\frac {1}{2}}\cos ^{2}\alpha _{1}(1+kc)} . For equiangular blades, β 1 = β 2 {\displaystyle \beta _{1}=\beta _{2}} , therefore c = 1 {\displaystyle c=1} , and we get η b max = 1 2 cos 2 ⁡ α 1 ( 1 + k ) {\displaystyle {\eta _{b}}_{\text{max}}={\frac {1}{2}}\cos ^{2}\alpha _{1}(1+k)} . If

2394-500: A steam pressure drop and velocity increase as steam moves through the nozzles. Nozzles move due to both the impact of steam on them and the reaction due to the high-velocity steam at the exit. A turbine composed of moving nozzles alternating with fixed nozzles is called a reaction turbine or Parsons turbine . Except for low-power applications, turbine blades are arranged in multiple stages in series, called compounding , which greatly improves efficiency at low speeds. A reaction stage

2520-401: A valve, or left uncontrolled. Extracted steam results in a loss of power in the downstream stages of the turbine. Induction turbines introduce low pressure steam at an intermediate stage to produce additional power. These arrangements include single casing, tandem compound and cross compound turbines. Single casing units are the most basic style where a single casing and shaft are coupled to

2646-456: 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 steam turbines favored higher frequencies. The steadier rotation speed of high-speed machines allowed for satisfactory operation of commutators in rotary converters. The synchronous speed N in RPM is calculated using

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2772-423: A well-defined voltage between nodes in the circuit, since the electric force is not a conservative force in those cases. However, at lower frequencies when the electric and magnetic fields are not rapidly changing, this can be neglected (see electrostatic approximation ). The electric potential can be generalized to electrodynamics, so that differences in electric potential between points are well-defined even in

2898-399: Is a row of fixed nozzles followed by a row of moving nozzles. Multiple reaction stages divide the pressure drop between the steam inlet and exhaust into numerous small drops, resulting in a pressure-compounded turbine. Impulse stages may be either pressure-compounded, velocity-compounded, or pressure-velocity compounded. A pressure-compounded impulse stage is a row of fixed nozzles followed by

3024-468: Is a well-defined voltage across the inductor's terminals. This is the reason that measurements with a voltmeter across an inductor are often reasonably independent of the placement of the test leads. The volt (symbol: V ) is the derived unit for electric potential , voltage, and electromotive force . The volt is named in honour of the Italian physicist Alessandro Volta (1745–1827), who invented

3150-548: Is affected by thermodynamics. The quantity measured by a voltmeter is the negative of the difference of the electrochemical potential of electrons ( Fermi level ) divided by the electron charge and commonly referred to as the voltage difference, while the pure unadjusted electrostatic potential (not measurable with a voltmeter) is sometimes called Galvani potential . The terms "voltage" and "electric potential" are ambiguous in that, in practice, they can refer to either of these in different contexts. The term electromotive force

3276-547: Is appreciably less than V 2 {\displaystyle V_{2}} , we get Δ h ≈ 1 2 V 2 2 {\displaystyle {\Delta h}\approx {\frac {1}{2}}{V_{2}}^{2}} . Furthermore, stage efficiency is the product of blade efficiency and nozzle efficiency, or η stage = η b η N {\displaystyle \eta _{\text{stage}}=\eta _{b}\eta _{N}} . Nozzle efficiency

3402-427: Is between 12 kV and 50 kV (AC) or between 0.75 kV and 3 kV (DC). Inside a conductive material, the energy of an electron is affected not only by the average electric potential but also by the specific thermal and atomic environment that it is in. When a voltmeter is connected between two different types of metal, it measures not the electrostatic potential difference, but instead something else that

3528-555: Is calculated at 08:00 each day in a control center in Switzerland . 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  s / min × 60 min/ h × 24 h/ d = 4 320 000 cycles per day. In North America , whenever the error exceeds 10 seconds for the Eastern Interconnection , 3 seconds for

3654-458: Is called a pressure-velocity compounded turbine. By 1905, when steam turbines were coming into use on fast ships (such as HMS  Dreadnought ) and in land-based power applications, it had been determined that it was desirable to use one or more Curtis wheels at the beginning of a multi-stage turbine (where the steam pressure is highest), followed by reaction stages. This was more efficient with high-pressure steam due to reduced leakage between

3780-436: Is composed of different regions of composition. A uniform dispersion of the gamma-prime phase – a combination of nickel, aluminum, and titanium – promotes the strength and creep resistance of the blade due to the microstructure. Refractory elements such as rhenium and ruthenium can be added to the alloy to improve creep strength. The addition of these elements reduces the diffusion of the gamma prime phase, thus preserving

3906-422: Is connected to the casing and one set of rotating blades is connected to the shaft. The sets intermesh with certain minimum clearances, with the size and configuration of sets varying to efficiently exploit the expansion of steam at each stage. An impulse turbine has fixed nozzles that orient the steam flow into high speed jets. These jets contain significant kinetic energy, which is converted into shaft rotation by

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4032-436: Is considered to be an isentropic process , or constant entropy process, in which the entropy of the steam entering the turbine is equal to the entropy of the steam leaving the turbine. No steam turbine is truly isentropic, however, with typical isentropic efficiencies ranging from 20 to 90% based on the application of the turbine. The interior of a turbine comprises several sets of blades or buckets . One set of stationary blades

4158-407: 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 require regular maintenance and monitoring. 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

4284-474: Is given by η N = V 2 2 2 ( h 1 − h 2 ) {\displaystyle \eta _{N}={\frac {{V_{2}}^{2}}{2\left(h_{1}-h_{2}\right)}}} , where the enthalpy (in J/Kg) of steam at the entrance of the nozzle is h 1 {\displaystyle h_{1}} and the enthalpy of steam at

4410-454: Is little certitude in the details of the history of 60 Hz vs. 50 Hz. The German company AEG (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 monopoly and their standard spread to the rest of Europe. After observing flicker of lamps operated by the 40 Hz power transmitted by

4536-594: Is not a priority in astern turbines, so only a few stages are used to save cost. A major challenge facing turbine design was reducing the creep experienced by the blades. Because of the high temperatures and high stresses of operation, steam turbine materials become damaged through these mechanisms. As temperatures are increased in an effort to improve turbine efficiency, creep becomes significant. To limit creep, thermal coatings and superalloys with solid-solution strengthening and grain boundary strengthening are used in blade designs. Protective coatings are used to reduce

4662-410: 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 flicker of the lamps; the effect is more pronounced with arc lamps , and the later mercury-vapor lamps and fluorescent lamps . Open arc lamps made an audible buzz on alternating current, leading to experiments with high-frequency alternators to raise

4788-444: Is the angular velocity of the turbine, then the blade speed is U = ω r {\displaystyle U=\omega r} . The power developed is then W = m ˙ U ( Δ V w ) {\displaystyle W={\dot {m}}U(\Delta V_{w})} . Blade efficiency ( η b {\displaystyle {\eta _{b}}} ) can be defined as

4914-530: Is the intensity of the electric field. In this case, the voltage increase from point A to point B is equal to the work done per unit charge, against the electric field, to move the charge from A to B without causing any acceleration. Mathematically, this is expressed as the line integral of the electric field along that path. In electrostatics, this line integral is independent of the path taken. Under this definition, any circuit where there are time-varying magnetic fields, such as AC circuits , will not have

5040-480: Is the only utility frequency shown for that region. Other power frequencies are still used. Germany, Austria, Switzerland, Sweden, and Norway use traction power networks for railways, distributing single-phase AC at 16 + 2 ⁄ 3  Hz or 16.7 Hz. A frequency of 25 Hz is used for the Austrian Mariazell Railway , as well as Amtrak and SEPTA 's traction power systems in

5166-421: Is the specific enthalpy drop of steam in the nozzle. By the first law of thermodynamics : h 1 + 1 2 V 1 2 = h 2 + 1 2 V 2 2 {\displaystyle h_{1}+{\frac {1}{2}}{V_{1}}^{2}=h_{2}+{\frac {1}{2}}{V_{2}}^{2}} Assuming that V 1 {\displaystyle V_{1}}

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5292-450: Is the sum of the voltage between A and B and the voltage between B and C . The various voltages in a circuit can be computed using Kirchhoff's circuit laws . When talking about alternating current (AC) there is a difference between instantaneous voltage and average voltage. Instantaneous voltages can be added for direct current (DC) and AC, but average voltages can be meaningfully added only when they apply to signals that all have

5418-478: Is the voltage that can be directly measured with a voltmeter. The Galvani potential that exists in structures with junctions of dissimilar materials is also work per charge but cannot be measured with a voltmeter in the external circuit (see § Galvani potential vs. electrochemical potential ). Voltage is defined so that negatively charged objects are pulled towards higher voltages, while positively charged objects are pulled towards lower voltages. Therefore,

5544-787: The Higashi-Shimizu Frequency Converter . Utility frequencies in North America in 1897 Utility frequencies in Europe to 1900 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, 60-cycle, or direct current supplies. Frequencies in use in 1946 (as well as 50 Hz and 60 Hz) Where regions are marked (*), this

5670-506: The Lauffen-Frankfurt link in 1891, AEG raised their standard frequency to 50 Hz in 1891. Westinghouse Electric 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 that frequency

5796-692: The Texas Interconnection , or 2 seconds for the Western Interconnection , 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. 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

5922-498: The Warren Power Station Master Clock and self-starting synchronous motor. Nikola Tesla demonstrated the concept of clocks synchronized by line frequency at the 1893 Chicago Worlds fair . The Hammond Organ 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. Today, AC power network operators regulate

6048-528: The control volume is equal to the net time change of angular momentum flux through the control volume. The swirling fluid enters the control volume at radius r 1 {\displaystyle r_{1}} with tangential velocity V w 1 {\displaystyle V_{w1}} and leaves at radius r 2 {\displaystyle r_{2}} with tangential velocity V w 2 {\displaystyle V_{w2}} . A velocity triangle paves

6174-403: The conventional current in a wire or resistor always flows from higher voltage to lower voltage. Historically, voltage has been referred to using terms like "tension" and "pressure". Even today, the term "tension" is still used, for example within the phrase " high tension " (HT) which is commonly used in thermionic valve ( vacuum tube ) based and automotive electronics. In electrostatics ,

6300-409: The fatigue resistance, strength, and creep resistance. Turbine types include condensing, non-condensing, reheat, extracting and induction. Condensing turbines are most commonly found in electrical power plants. These turbines receive steam from a boiler and exhaust it to a condenser . The exhausted steam is at a pressure well below atmospheric, and is in a partially condensed state, typically of

6426-480: The ground of the system is used as one of the points. In this case, voltage is often mentioned at a point without completely mentioning the other measurement point. A voltage can be associated with either a source of energy or the loss, dissipation, or storage of energy. The SI unit of work per unit charge is the joule per coulomb , where 1 volt = 1 joule (of work) per 1 coulomb of charge. The old SI definition for volt used power and current ; starting in 1990,

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6552-533: The quantum Hall and Josephson effect were used, and in 2019 physical constants were given defined values for the definition of all SI units. Voltage is denoted symbolically by Δ V {\displaystyle \Delta V} , simplified V , especially in English -speaking countries. Internationally, the symbol U is standardized. It is used, for instance, in the context of Ohm's or Kirchhoff's circuit laws . The electrochemical potential

6678-430: The voltaic pile , possibly the first chemical battery . A simple analogy for an electric circuit is water flowing in a closed circuit of pipework , driven by a mechanical pump . This can be called a "water circuit". The potential difference between two points corresponds to the pressure difference between two points. If the pump creates a pressure difference between two points, then water flowing from one point to

6804-523: The 1914 edition of the standard. Remnant installations at other frequencies persisted until well after the Second World War. 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 Ontario , Quebec , the northern United States, and for railway electrification . In

6930-581: 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 Sir Adam Beck 1 (these were retrofitted to 60 Hz) and the Rankine generating stations (until its 2006 closure) near Niagara Falls to provide power for large industrial customers who did not want to replace existing equipment; and some 25 Hz motors and

7056-414: The 19th century. Very early isolated AC generating schemes used arbitrary frequencies based on convenience for steam engine , water turbine , and electrical generator design. Frequencies between 16 + 2 ⁄ 3  Hz and 133 + 1 ⁄ 3  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

7182-682: The 1st century by Hero of Alexandria in Roman Egypt . In 1551, Taqi al-Din in Ottoman Egypt described a steam turbine with the practical application of rotating a spit . Steam turbines were also described by the Italian Giovanni Branca (1629) and John Wilkins in England (1648). The devices described by Taqi al-Din and Wilkins are today known as steam jacks . In 1672, an impulse turbine -driven small toy car

7308-575: The Au Sable Electric Company used 30 Hz at transmission voltages up to 110,000 volts in 1914. 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, Decreto-Lei 852 , intended to bring the whole country under 50 Hz within eight years. The law did not work, and in

7434-495: The United States in 2022 was by the use of steam turbines. Technical challenges include rotor imbalance , vibration , bearing wear , and uneven expansion (various forms of thermal shock ). In large installations, even the sturdiest turbine will shake itself apart if operated out of trim. The first device that may be classified as a reaction steam turbine was little more than a toy, the classic Aeolipile , described in

7560-443: The United States. Other AC railway systems are energized at the local commercial power frequency, 50 Hz or 60 Hz. Traction power may be derived from commercial power supplies by frequency converters, or in some cases may be produced by dedicated traction powerstations . 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

7686-618: The Westinghouse company objected that this would be undesirable for lighting and suggested 33 + 1 ⁄ 3  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. A General Electric study concluded that 40 Hz would have been

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7812-609: The Westinghouse standard. The first generators at the Niagara Falls project , built by Westinghouse in 1895, were 25 Hz, because the turbine speed had already been set before alternating current 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 16 + 2 ⁄ 3  Hz power suitable for heavy commutator-type motors, but

7938-1070: The advent of the National Grid (UK) in the late 1920s, and projects in Italy used 42 Hz. The oldest continuously operating commercial hydroelectric power station in the United States, Mechanicville Hydroelectric Plant , still produces electric power at 40 Hz and supplies power to the local 60 Hz transmission system through frequency changers . 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. The Ganz Company of Hungary had standardized on 5000 alternations per minute (41 2 ⁄ 3  Hz) for their products, so Ganz clients had 41 2 ⁄ 3  Hz systems that in some cases ran for many years. In

8064-1370: The blade speed to the absolute steam velocity at the inlet is termed the blade speed ratio ρ = U V 1 {\displaystyle \rho ={\frac {U}{V_{1}}}} . η b {\displaystyle \eta _{b}} is maximum when d η b d ρ = 0 {\displaystyle {\frac {d\eta _{b}}{d\rho }}=0} or, d d ρ ( 2 cos ⁡ α 1 − ρ 2 ( 1 + k c ) ) = 0 {\displaystyle {\frac {d}{d\rho }}\left(2{\cos \alpha _{1}-\rho ^{2}}(1+kc)\right)=0} . That implies ρ = 1 2 cos ⁡ α 1 {\displaystyle \rho ={\frac {1}{2}}\cos \alpha _{1}} and therefore U V 1 = 1 2 cos ⁡ α 1 {\displaystyle {\frac {U}{V_{1}}}={\frac {1}{2}}\cos \alpha _{1}} . Now ρ o p t = U V 1 = 1 2 cos ⁡ α 1 {\displaystyle \rho _{opt}={\frac {U}{V_{1}}}={\frac {1}{2}}\cos \alpha _{1}} (for

8190-410: The bucket-like shaped rotor blades, as the steam jet changes direction. A pressure drop occurs across only the stationary blades, with a net increase in steam velocity across the stage. As the steam flows through the nozzle its pressure falls from inlet pressure to the exit pressure (atmospheric pressure or, more usually, the condenser vacuum). Due to this high ratio of expansion of steam, the steam leaves

8316-553: 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 importance. The best frequency is a compromise among competing requirements. In the late 19th century, designers would pick a relatively high frequency for systems featuring transformers and arc lights , so as to economize on transformer materials and to reduce visible flickering of

8442-413: The circuit are not negligible, then their effects can be modelled by adding mutual inductance elements. In the case of a physical inductor though, the ideal lumped representation is often accurate. This is because the external fields of inductors are generally negligible, especially if the inductor has a closed magnetic path . If external fields are negligible, we find that is path-independent, and there

8568-432: The correct voltage, but using the original train network frequency like 16 + 2 ⁄ 3  Hz or 16.7 Hz. Power frequencies as high as 400 Hz are used in aircraft, spacecraft, submarines, server rooms for computer power , 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

8694-629: The cosines of the blade angles at the outlet and inlet can be taken and denoted c = cos ⁡ β 2 cos ⁡ β 1 {\displaystyle c={\frac {\cos \beta _{2}}{\cos \beta _{1}}}} . The ratio of steam velocities relative to the rotor speed at the outlet to the inlet of the blade is defined by the friction coefficient k = V r 2 V r 1 {\displaystyle k={\frac {V_{r2}}{V_{r1}}}} . k < 1 {\displaystyle k<1} and depicts

8820-464: The customer's equipment. 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 turbine . 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

8946-458: 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 maintained at a nominal value within a few hundred parts per million. In the synchronous grid of Continental Europe , the deviation between network phase time and UTC (based on International Atomic Time )

9072-431: The device with respect to a common reference point (or ground ). The voltage drop is the difference between the two readings. Two points in an electric circuit that are connected by an ideal conductor without resistance and not within a changing magnetic field have a voltage of zero. Any two points with the same potential may be connected by a conductor and no current will flow between them. The voltage between A and C

9198-427: 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 Lei 4.454 was declared in 1964. Brazil underwent a frequency conversion program to 60 Hz that was not completed until 1978. In Mexico, areas operating on 50 Hz grid were converted during the 1970s, uniting the country under 60 Hz. In Japan,

9324-427: 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). Standardization allowed international trade in electrical equipment. Much later, the use of standard frequencies allowed interconnection of power grids. It

9450-402: The economics of electricity production, since system load was more uniform during the course of a day. The first applications of commercial electric power were incandescent lighting and commutator -type electric motors . 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. If an incandescent lamp

9576-446: The electric field in the region exterior to each component is conservative, and voltages between nodes in the circuit are well-defined, where as long as the path of integration does not pass through the inside of any component. The above is the same formula used in electrostatics. This integral, with the path of integration being along the test leads, is what a voltmeter will actually measure. If uncontained magnetic fields throughout

9702-428: The electric field, rather than to differences in electric potential. In this case, the voltage rise along some path P {\displaystyle {\mathcal {P}}} from r A {\displaystyle \mathbf {r} _{A}} to r B {\displaystyle \mathbf {r} _{B}} is given by: However, in this case the "voltage" between two points depends on

9828-502: The erosion of the blades in last rows. In most of the cases, maximum number of reheats employed in a cycle is 2 as the cost of super-heating the steam negates the increase in the work output from turbine. Extracting type turbines are common in all applications. In an extracting type turbine, steam is released from various stages of the turbine, and used for industrial process needs or sent to boiler feedwater heaters to improve overall cycle efficiency. Extraction flows may be controlled with

9954-1038: The exit of the nozzle is h 2 {\displaystyle h_{2}} . Δ V w = V w 1 − ( − V w 2 ) = V w 1 + V w 2 = V r 1 cos ⁡ β 1 + V r 2 cos ⁡ β 2 = V r 1 cos ⁡ β 1 ( 1 + V r 2 cos ⁡ β 2 V r 1 cos ⁡ β 1 ) {\displaystyle {\begin{aligned}\Delta V_{w}&=V_{w1}-\left(-V_{w2}\right)\\&=V_{w1}+V_{w2}\\&=V_{r1}\cos \beta _{1}+V_{r2}\cos \beta _{2}\\&=V_{r1}\cos \beta _{1}\left(1+{\frac {V_{r2}\cos \beta _{2}}{V_{r1}\cos \beta _{1}}}\right)\end{aligned}}} The ratio of

10080-454: The following companies: Steam turbines are made in a variety of sizes ranging from small <0.75 kW (<1 hp) units (rare) used as mechanical drives for pumps, compressors and other shaft driven equipment, to 1,500 MW (2,000,000 hp) turbines used to generate electricity. There are several classifications for modern steam turbines. Turbine blades are of two basic types, blades and nozzles . Blades move entirely due to

10206-543: The formula, where f is the frequency in hertz and P is the number of poles. Direct-current power was not entirely displaced by alternating current and was useful in railway and electrochemical processes. Prior to the development of mercury arc valve rectifiers , rotary converters were used to produce DC power from AC. Like other commutator-type machines, these worked better with lower frequencies. With AC, transformers can be used to step down high transmission voltages to lower customer utilization voltage. The transformer

10332-399: The frequency signal. Indeed, a 2017 trial for CAISO discovered that solar plants could respond to the signal faster than traditional generators, because they did not need to accelerate a rotating mass. Voltage Voltage , also known as (electrical) potential difference , electric pressure , or electric tension is the difference in electric potential between two points. In

10458-417: The friction due to the blade surface is neglected then η b max = cos 2 ⁡ α 1 {\displaystyle {\eta _{b}}_{\text{max}}=\cos ^{2}\alpha _{1}} . In the reaction turbine , the rotor blades themselves are arranged to form convergent nozzles . This type of turbine makes use of the reaction force produced as

10584-409: The generating capacity of a unit was scaled up by about 10,000 times, and the total output from turbo-generators constructed by his firm C. A. Parsons and Company and by their licensees, for land purposes alone, had exceeded thirty million horse-power. Other variations of turbines have been developed that work effectively with steam. The de Laval turbine (invented by Gustaf de Laval ) accelerated

10710-419: The impact of steam on them and their profiles do not converge. This results in a steam velocity drop and essentially no pressure drop as steam moves through the blades. A turbine composed of blades alternating with fixed nozzles is called an impulse turbine , Curtis turbine , Rateau turbine , or Brown-Curtis turbine . Nozzles appear similar to blades, but their profiles converge near the exit. This results in

10836-414: The inductance of transmission lines, making power transmission difficult. Consequently, 400 Hz power systems are usually confined to a building or vehicle. Transformers , 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

10962-409: The kinetic energy supplied to the moving blades (m). Or, E {\displaystyle E} = enthalpy drop over the fixed blades, Δ h f {\displaystyle \Delta h_{f}} + enthalpy drop over the moving blades, Δ h m {\displaystyle \Delta h_{m}} . The effect of expansion of steam over the moving blades

11088-445: The lamps, but would pick a lower frequency for systems with long transmission lines or feeding primarily motor loads or rotary converters for producing direct current . 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

11214-642: The loss in the relative velocity due to friction as the steam flows around the blades ( k = 1 {\displaystyle k=1} for smooth blades). η b = 2 U Δ V w V 1 2 = 2 U V 1 ( cos ⁡ α 1 − U V 1 ) ( 1 + k c ) {\displaystyle \eta _{b}={\frac {2U\Delta V_{w}}{{V_{1}}^{2}}}={\frac {2U}{V_{1}}}\left(\cos \alpha _{1}-{\frac {U}{V_{1}}}\right)(1+kc)} The ratio of

11340-439: 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 current, and the rotation speed; so, a given standard speed limits the choice of frequency (and the reverse). Once AC electric motors became common, it was important to standardize frequency for compatibility with

11466-463: The middle) before exiting at low pressure, almost certainly to a condenser . The condenser provides a vacuum that maximizes the energy extracted from the steam, and condenses the steam into feedwater to be returned to the boilers. On the left are several additional reaction stages (on two large rotors) that rotate the turbine in reverse for astern operation, with steam admitted by a separate throttle. Since ships are rarely operated in reverse, efficiency

11592-404: The nozzle with a very high velocity. The steam leaving the moving blades has a large portion of the maximum velocity of the steam when leaving the nozzle. The loss of energy due to this higher exit velocity is commonly called the carry over velocity or leaving loss. The law of moment of momentum states that the sum of the moments of external forces acting on a fluid which is temporarily occupying

11718-418: The observed potential difference at the terminals of an electrochemical cell when it was open circuit must exactly balance the emf of the cell so that no current flowed. Steam turbine A steam turbine or steam turbine engine is a machine or heat engine that extracts thermal energy from pressurized steam and uses it to do mechanical work on a rotating output shaft. Its modern manifestation

11844-459: The other and no apparent desire for complete worldwide standardization. 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 used by some clocks to accurately maintain their time. Several factors influence

11970-407: The other will be able to do work, such as driving a turbine . Similarly, work can be done by an electric current driven by the potential difference provided by a battery . For example, the voltage provided by a sufficiently-charged automobile battery can "push" a large current through the windings of an automobile's starter motor . If the pump is not working, it produces no pressure difference, and

12096-424: The path taken. In circuit analysis and electrical engineering , lumped element models are used to represent and analyze circuits. These elements are idealized and self-contained circuit elements used to model physical components. When using a lumped element model, it is assumed that the effects of changing magnetic fields produced by the circuit are suitably contained to each element. Under these assumptions,

12222-430: The points across which the voltage is measured. When using a voltmeter to measure voltage, one electrical lead of the voltmeter must be connected to the first point, one to the second point. A common use of the term "voltage" is in describing the voltage dropped across an electrical device (such as a resistor). The voltage drop across the device can be understood as the difference between measurements at each terminal of

12348-414: The presence of time-varying fields. However, unlike in electrostatics, the electric field can no longer be expressed only in terms of the electric potential. Furthermore, the potential is no longer uniquely determined up to a constant, and can take significantly different forms depending on the choice of gauge . In this general case, some authors use the word "voltage" to refer to the line integral of

12474-444: The ratio of the work done on the blades to kinetic energy supplied to the fluid, and is given by A stage of an impulse turbine consists of a nozzle set and a moving wheel. The stage efficiency defines a relationship between enthalpy drop in the nozzle and work done in the stage. η s t a g e = W o r k   d o n e   o n   b l

12600-415: The same frequency and phase. Instruments for measuring voltages include the voltmeter , the potentiometer , and the oscilloscope . Analog voltmeters , such as moving-coil instruments, work by measuring the current through a fixed resistor, which, according to Ohm's law , is proportional to the voltage across the resistor. The potentiometer works by balancing the unknown voltage against a known voltage in

12726-404: 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 MIL-STD-704 exists for aircraft use of 400 Hz power. Regulation of power system frequency for timekeeping accuracy was not commonplace until after 1916 with Henry Warren 's invention of

12852-509: 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 have simplified these designs, but the installed base at 25 Hz was too large to be economically opposed. In the United States, Southern California Edison 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

12978-486: The sound above the range of human hearing. Commutator -type motors do not operate well on high-frequency AC, because the rapid changes of current are opposed by the inductance of the motor field. Though commutator-type universal motors are common in AC household appliances and power tools, they are small motors, less than 1 kW. The induction motor was found to work well on frequencies around 50 to 60 Hz, but with

13104-423: The standard frequency system via a rotary converter or static inverter 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. 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

13230-400: The stator and decelerating through the rotor, with no net change in steam velocity across the stage but with a decrease in both pressure and temperature, reflecting the work performed in the driving of the rotor. Energy input to the blades in a stage: E = Δ h {\displaystyle E=\Delta h} is equal to the kinetic energy supplied to the fixed blades (f) +

13356-399: The steam accelerates through the nozzles formed by the stator. Steam is directed onto the rotor by the fixed vanes of the stator . It leaves the stator as a jet that fills the entire circumference of the rotor. The steam then changes direction and increases its speed relative to the speed of the blades. A pressure drop occurs across both the stator and the rotor, with steam accelerating through

13482-444: The steam enters in the middle of the shaft and exits at both ends, or a combination of any of these. In a double flow rotor, the blades in each half face opposite ways, so that the axial forces negate each other but the tangential forces act together. This design of rotor is also called two-flow , double-axial-flow , or double-exhaust . This arrangement is common in low-pressure casings of a compound turbine. An ideal steam turbine

13608-400: The steam to full speed before running it against a turbine blade. De Laval's impulse turbine is simpler and less expensive and does not need to be pressure-proof. It can operate with any pressure of steam, but is considerably less efficient. Auguste Rateau developed a pressure compounded impulse turbine using the de Laval principle as early as 1896, obtained a US patent in 1903, and applied

13734-765: The synchronous grid of Continental Europe is available on websites such as www .mainsfrequency .com . The Frequency Monitoring Network (FNET) at the University of Tennessee 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. In the United States, the Federal Energy Regulatory Commission made time error correction mandatory in 2009. In 2011, The North American Electric Reliability Corporation (NERC) discussed

13860-574: The thermal damage and to limit oxidation . These coatings are often stabilized zirconium dioxide -based ceramics. Using a thermal protective coating limits the temperature exposure of the nickel superalloy. This reduces the creep mechanisms experienced in the blade. Oxidation coatings limit efficiency losses caused by a buildup on the outside of the blades, which is especially important in the high-temperature environment. The nickel-based blades are alloyed with aluminum and titanium to improve strength and creep resistance. The microstructure of these alloys

13986-470: The turbine rotor and the casing. This is illustrated in the drawing of the German 1905 AEG marine steam turbine. The steam from the boilers enters from the right at high pressure through a throttle , controlled manually by an operator (in this case a sailor known as the throttleman). It passes through five Curtis wheels and numerous reaction stages (the small blades at the edges of the two large rotors in

14112-742: The turbine to a French torpedo boat in 1904. He taught at the École des mines de Saint-Étienne for a decade until 1897, and later founded a successful company that was incorporated into the Alstom firm after his death. One of the founders of the modern theory of steam and gas turbines was Aurel Stodola , a Slovak physicist and engineer and professor at the Swiss Polytechnical Institute (now ETH ) in Zurich. His work Die Dampfturbinen und ihre Aussichten als Wärmekraftmaschinen (English: The Steam Turbine and its prospective use as

14238-401: The turbine will not rotate. Likewise, if the automobile's battery is very weak or "dead" (or "flat"), then it will not turn the starter motor. The hydraulic analogy is a useful way of understanding many electrical concepts. In such a system, the work done to move water is equal to the " pressure drop" (compare p.d.) multiplied by the volume of water moved. Similarly, in an electrical circuit,

14364-457: The use of multiple stages in the expansion of the steam, which results in a closer approach to the ideal reversible expansion process. Because the turbine generates rotary motion , it can be coupled to a generator to harness its motion into electricity. Such turbogenerators are the core of thermal power stations which can be fueled by fossil fuels , nuclear fuels , geothermal , or solar energy . About 42% of all electricity generation in

14490-548: The voltage increase from point r A {\displaystyle \mathbf {r} _{A}} to some point r B {\displaystyle \mathbf {r} _{B}} is given by the change in electrostatic potential V {\textstyle V} from r A {\displaystyle \mathbf {r} _{A}} to r B {\displaystyle \mathbf {r} _{B}} . By definition, this is: where E {\displaystyle \mathbf {E} }

14616-731: The way for a better understanding of the relationship between the various velocities. In the adjacent figure we have: Then by the law of moment of momentum, the torque on the fluid is given by: For an impulse steam turbine: r 2 = r 1 = r {\displaystyle r_{2}=r_{1}=r} . Therefore, the tangential force on the blades is F u = m ˙ ( V w 1 − V w 2 ) {\displaystyle F_{u}={\dot {m}}\left(V_{w1}-V_{w2}\right)} . The work done per unit time or power developed: W = T ω {\displaystyle W=T\omega } . When ω

14742-545: 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 regions contains four back-to-back HVDC substations which convert the frequency; these are Shin Shinano , Sakuma Dam , Minami-Fukumitsu , and

14868-465: The work done to move electrons or other charge carriers is equal to "electrical pressure difference" multiplied by the quantity of electrical charges moved. In relation to "flow", the larger the "pressure difference" between two points (potential difference or water pressure difference), the greater the flow between them (electric current or water flow). (See " electric power ".) Specifying a voltage measurement requires explicit or implicit specification of

14994-489: 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 Mill Creek to bring electricity to Redlands, California using 50 Hz, but changed to 60 Hz a year later to maintain market share with

15120-404: Was completely established only after World War II . By about 1900, European manufacturers had mostly standardized on 50 Hz for new installations. The German Verband der Elektrotechnik (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

15246-473: Was designed by Ferdinand Verbiest . A more modern version of this car was produced some time in the late 18th century by an unknown German mechanic. In 1775 at Soho James Watt designed a reaction turbine that was put to work there. In 1807, Polikarp Zalesov designed and constructed an impulse turbine, using it for the fire pump operation. In 1827 the Frenchmen Real and Pichon patented and constructed

15372-617: Was first used by Volta in a letter to Giovanni Aldini in 1798, and first appeared in a published paper in 1801 in Annales de chimie et de physique . Volta meant by this a force that was not an electrostatic force, specifically, an electrochemical force. The term was taken up by Michael Faraday in connection with electromagnetic induction in the 1820s. However, a clear definition of voltage and method of measuring it had not been developed at this time. Volta distinguished electromotive force (emf) from tension (potential difference):

15498-404: Was in use until 1906. The proliferation of frequencies grew out of the rapid development of electrical machines in the period 1880 through 1900. 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. Though many theories exist, and quite a few entertaining urban legends , there

15624-483: Was invented by Charles Parsons in 1884. Fabrication of a modern steam turbine involves advanced metalwork to form high-grade steel alloys into precision parts using technologies that first became available in the 20th century; continued advances in durability and efficiency of steam turbines remains central to the energy economics of the 21st century. The steam turbine is a form of heat engine that derives much of its improvement in thermodynamic efficiency from

15750-477: Was licensed and the turbine scaled up shortly after by an American, George Westinghouse . The Parsons turbine also turned out to be easy to scale up. Parsons had the satisfaction of seeing his invention adopted for all major world power stations, and the size of generators had increased from his first 7.5 kilowatts (10.1 hp) set up to units of 50,000 kilowatts (67,000 hp) capacity. Within Parsons' lifetime,

15876-473: Was not until after World War II – with the advent of affordable electrical consumer goods – that more uniform standards were enacted. 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 National Grid starting in 1926 compelled the standardization of frequencies among the many interconnected electrical service providers. The 50 Hz standard

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