Symmetrical Components
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Symmetrical Components
In electrical engineering, the method of symmetrical components simplifies analysis of unbalanced three-phase power systems under both normal and abnormal conditions. The basic idea is that an asymmetrical set of ''N'' phasors can be expressed as a linear combination of ''N'' symmetrical sets of phasors by means of a complex linear transformation. Fortescue's theorem (symmetrical components) is based on superposition principle, so it is applicable to linear power systems only, or to linear approximations of non-linear power systems. In the most common case of three-phase systems, the resulting "symmetrical" components are referred to as ''direct'' (or ''positive''), ''inverse'' (or ''negative'') and ''zero'' (or ''homopolar''). The analysis of power system is much simpler in the domain of symmetrical components, because the resulting equations are mutually linearly independent if the circuit itself is balanced. Description In 1918 Charles Legeyt Fortescue presented a paper which ...
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Electrical Engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the latter half of the 19th century after commercialization of the electric telegraph, the telephone, and electrical power generation, distribution, and use. Electrical engineering is now divided into a wide range of different fields, including computer engineering, systems engineering, power engineering, telecommunications, radio-frequency engineering, signal processing, instrumentation, photovoltaic cells, electronics, and optics and photonics. Many of these disciplines overlap with other engineering branches, spanning a huge number of specializations including hardware engineering, power electronics, electromagnetics and waves, microwave engineering, nanotechnology, electrochemistry, renewable energies, mechatronics/control, and electrical m ...
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Electrical Generator
In electricity generation, a generator is a device that converts motive power (mechanical energy) or fuel-based power (chemical energy) into electric power for use in an external circuit. Sources of mechanical energy include steam turbines, gas turbines, water turbines, internal combustion engines, wind turbines and even hand cranks. The first electromagnetic generator, the Faraday disk, was invented in 1831 by British scientist Michael Faraday. Generators provide nearly all of the power for electric power grids. In addition to electromechanical designs, photovoltaic and fuel cell powered generators utilize solar power and hydrogen-based fuels, respectively, to generate electrical output. The reverse conversion of electrical energy into mechanical energy is done by an electric motor, and motors and generators have many similarities. Many motors can be mechanically driven to generate electricity; frequently they make acceptable manual generators. Terminology Electromagnetic ...
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Harmonics (electrical Power)
In an electric power system, a harmonic of a voltage or current waveform is a sinusoidal wave whose frequency is an integer multiple of the fundamental frequency. Harmonic frequencies are produced by the action of non-linear loads such as rectifiers, discharge lighting, or saturated electric machines. They are a frequent cause of power quality problems and can result in increased equipment and conductor heating, misfiring in variable speed drives, and torque pulsations in motors and generators. Harmonics are usually classified by two different criteria: the type of signal (voltage or current), and the order of the harmonic (even, odd, triplen, or non-triplen odd); in a three-phase system, they can be further classified according to their phase sequence (positive, negative, zero). Current harmonics In a normal alternating current power system, the current varies sinusoidally at a specific frequency, usually 50 or 60 hertz. When a linear time-invariant electrical load is connected ...
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Discrete Fourier Transform
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence. The DFT is therefore said to be a frequency domain representation of the original input sequence. If the original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle. If the original sequence is one cycle of a periodic function, the DFT provides all the non-zero values of one DTFT cycle. The DFT is the most important discret ...
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Napoleon's Theorem
In geometry, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the lines connecting the centres of those equilateral triangles themselves form an equilateral triangle. The triangle thus formed is called the inner or outer ''Napoleon triangle''. The difference in the areas of the outer and inner Napoleon triangles equals the area of the original triangle. The theorem is often attributed to Napoleon Bonaparte (1769–1821). Some have suggested that it may date back to W. Rutherford's 1825 question published in ''The Ladies' Diary'', four years after the French emperor's death, but the result is covered in three questions set in an examination for a Gold Medal at the University of Dublin in October, 1820, whereas Napoleon died the following May. Proofs In the figure above, ABC is the original triangle. AZB, BXC, and CYA are equilateral triangles constructed on its sides' exteriors, and points L, ...
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Napoleon's Theorem
In geometry, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the lines connecting the centres of those equilateral triangles themselves form an equilateral triangle. The triangle thus formed is called the inner or outer ''Napoleon triangle''. The difference in the areas of the outer and inner Napoleon triangles equals the area of the original triangle. The theorem is often attributed to Napoleon Bonaparte (1769–1821). Some have suggested that it may date back to W. Rutherford's 1825 question published in ''The Ladies' Diary'', four years after the French emperor's death, but the result is covered in three questions set in an examination for a Gold Medal at the University of Dublin in October, 1820, whereas Napoleon died the following May. Proofs In the figure above, ABC is the original triangle. AZB, BXC, and CYA are equilateral triangles constructed on its sides' exteriors, and points L, ...
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Three-phase Electric Power
Three-phase electric power (abbreviated 3φ) is a common type of alternating current used in electricity generation, transmission, and distribution. It is a type of polyphase system employing three wires (or four including an optional neutral return wire) and is the most common method used by electrical grids worldwide to transfer power. Three-phase electrical power was developed in the 1880s by multiple people. Three-phase power works by the voltage and currents being 120 degrees out of phase on the three wires. As an AC system it allows the voltages to be easily stepped up using transformers to high voltage for transmission, and back down for distribution, giving high efficiency. A three-wire three-phase circuit is usually more economical than an equivalent two-wire single-phase circuit at the same line to ground voltage because it uses less conductor material to transmit a given amount of electrical power. Three-phase power is mainly used directly to power large induction ...
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World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing military alliances: the Allies and the Axis powers. World War II was a total war that directly involved more than 100 million personnel from more than 30 countries. The major participants in the war threw their entire economic, industrial, and scientific capabilities behind the war effort, blurring the distinction between civilian and military resources. Aircraft played a major role in the conflict, enabling the strategic bombing of population centres and deploying the only two nuclear weapons ever used in war. World War II was by far the deadliest conflict in human history; it resulted in 70 to 85 million fatalities, mostly among civilians. Tens of millions died due to genocides (including the Holocaust), starvation, ma ...
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Westinghouse Electric Corporation
The Westinghouse Electric Corporation was an American manufacturing company founded in 1886 by George Westinghouse. It was originally named "Westinghouse Electric & Manufacturing Company" and was renamed "Westinghouse Electric Corporation" in 1945. The company acquired the CBS television network in 1995 and was renamed "CBS Corporation" until being acquired by Viacom in 1999, a merger completed in April 2000. The CBS Corporation name was later reused for one of the two companies resulting from the split of Viacom in 2006. The Westinghouse trademarks are owned by Westinghouse Electric Corporation, and were previously part of Westinghouse Licensing Corporation. The nuclear power business, Westinghouse Electric Company, was spun off from the Westinghouse Electric Corporation in 1999. History Westinghouse Electric was founded by George Westinghouse in Pittsburgh, Pennsylvania, on January 8, 1886. The firm became active in developing electric infrastructure throughout the U ...
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General Electric
General Electric Company (GE) is an American multinational conglomerate founded in 1892, and incorporated in New York state and headquartered in Boston. The company operated in sectors including healthcare, aviation, power, renewable energy, digital industry, additive manufacturing and venture capital and finance, but has since divested from several areas, now primarily consisting of the first four segments. In 2020, GE ranked among the Fortune 500 as the 33rd largest firm in the United States by gross revenue. In 2011, GE ranked among the Fortune 20 as the 14th most profitable company, but later very severely underperformed the market (by about 75%) as its profitability collapsed. Two employees of GE – Irving Langmuir (1932) and Ivar Giaever (1973) – have been awarded the Nobel Prize. On November 9, 2021, the company announced it would divide itself into three investment-grade public companies. On July 18, 2022, GE unveiled the brand names of the companies it will ...
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Circuit Breaker
A circuit breaker is an electrical safety device designed to protect an electrical circuit from damage caused by an overcurrent or short circuit. Its basic function is to interrupt current flow to protect equipment and to prevent the risk of fire. Unlike a fuse, which operates once and then must be replaced, a circuit breaker can be reset (either manually or automatically) to resume normal operation. Circuit breakers are made in varying sizes, from small devices that protect low-current circuits or individual household appliances, to large switchgear designed to protect high voltage circuits feeding an entire city. The generic function of a circuit breaker, or fuse, as an automatic means of removing power from a faulty system, is often abbreviated as OCPD (Over Current Protection Device). Origins An early form of circuit breaker was described by Thomas Edison in an 1879 patent application, although his commercial power distribution system used fuses. Its purpose was to pro ...
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Protective Relay
In electrical engineering, a protective relay is a relay device designed to trip a circuit breaker when a fault is detected. The first protective relays were electromagnetic devices, relying on coils operating on moving parts to provide detection of abnormal operating conditions such as over-current, overvoltage, reverse power flow, over-frequency, and under-frequency. Microprocessor-based solid-state digital protection relays now emulate the original devices, as well as providing types of protection and supervision impractical with electromechanical relays. Electromechanical relays provide only rudimentary indication of the location and origin of a fault. In many cases a single microprocessor relay provides functions that would take two or more electromechanical devices. By combining several functions in one case, numerical relays also save capital cost and maintenance cost over electromechanical relays. However, due to their very long life span, tens of thousands of these "sil ...
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