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Alpha–beta Transformation
In electrical engineering, the alpha-beta (\alpha\beta\gamma) transformation (also known as the Clarke transformation) is a mathematical transformation employed to simplify the analysis of three-phase circuits. Conceptually it is similar to the dq0 transformation. One very useful application of the \alpha\beta\gamma transformation is the generation of the reference signal used for space vector modulation control of three-phase inverters. History In 1937 and 1938, Edith Clarke published papers with modified methods of calculations on unbalanced three-phase problems, that turned out to be particularly useful. Definition The \alpha\beta\gamma transform applied to three-phase currents, as used by Edith Clarke, is :i_(t) = Ti_(t) = \frac\begin 1 & -\frac & -\frac \\ 0 & \frac & -\frac \\ \frac & \frac & \frac \\ \end\begini_a(t)\\i_b(t)\\i_c(t)\end where i_(t) is a generic three-phase current sequence and i_(t) is the corresponding current sequence given by the transformation T. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transform (mathematics)
In mathematics, a transformation is a function ''f'', usually with some geometrical underpinning, that maps a set ''X'' to itself, i.e. . Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific affine transformations, such as rotations, reflections and translations. Partial transformations While it is common to use the term transformation for any function of a set into itself (especially in terms like "transformation semigroup" and similar), there exists an alternative form of terminological convention in which the term "transformation" is reserved only for bijections. When such a narrow notion of transformation is generalized to partial functions, then a partial transformation is a function ''f'': ''A'' → ''B'', where both ''A'' and ''B'' are subsets of some set ''X''. Algebraic structures The set of all transformations on a given base set, together with function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dq0 Transformation
The direct-quadrature-zero (DQZ or DQ0 or DQO, sometimes lowercase) transformation or zero-direct-quadrature (0DQ or ODQ, sometimes lowercase) transformation is a tensor that rotates the reference frame of a three-element vector or a three-by-three element matrix in an effort to simplify analysis. The DQZ transform is the product of the Clarke transform and the Park transform, first proposed in 1929 by Robert H. Park.R.H. Park ''Two Reaction Theory of Synchronous Machines'' AIEE Transactions 48:716–730 (1929). The DQZ transform is often used in the context of electrical engineering with three-phase circuits. The transform can be used to rotate the reference frames of AC waveforms such that they become DC signals. Simplified calculations can then be carried out on these DC quantities before performing the inverse transform to recover the actual three-phase AC results. As an example, the DQZ transform is often used in order to simplify the analysis of three-phase synchronous ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverter (electrical)
A power inverter, inverter or invertor is a power electronic device or circuitry that changes direct current (DC) to alternating current (AC). The resulting AC frequency obtained depends on the particular device employed. Inverters do the opposite of rectifiers which were originally large electromechanical devices converting AC to DC. The input voltage, output voltage and frequency, and overall power handling depend on the design of the specific device or circuitry. The inverter does not produce any power; the power is provided by the DC source. A power inverter can be entirely electronic or may be a combination of mechanical effects (such as a rotary apparatus) and electronic circuitry. Static inverters do not use moving parts in the conversion process. Power inverters are primarily used in electrical power applications where high currents and voltages are present; circuits that perform the same function for electronic signals, which usually have very low currents and vol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edith Clarke
Edith Clarke (February 10, 1883 – October 29, 1959) was the first woman to be professionally employed as an electrical engineer in the United States, and the first female professor of electrical engineering in the country. She was the first woman to deliver a paper at the American Institute of Electrical Engineers, the first female engineer whose professional standing was recognized by Tau Beta Pi, and the first woman named as a Fellow of the American Institute of Electrical Engineers. She specialized in electrical power system analysis and wrote ''Circuit Analysis of A-C Power Systems''. Early life and education One of nine children, Edith Clarke was born to lawyer John Ridgely Clarke and Susan Dorsey Owings on February 10, 1883, in Howard County, Maryland. After being orphaned at age 12, she was raised by an older sister. She used her inheritance to study mathematics and astronomy at Vassar College, where she graduated in 1908. After college, Clarke taught mathematics an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root Mean Square
In mathematics and its applications, the root mean square of a set of numbers x_i (abbreviated as RMS, or rms and denoted in formulas as either x_\mathrm or \mathrm_x) is defined as the square root of the mean square (the arithmetic mean of the squares) of the set. The RMS is also known as the quadratic mean (denoted M_2) and is a particular case of the generalized mean. The RMS of a continuously varying function (denoted f_\mathrm) can be defined in terms of an integral of the squares of the instantaneous values during a cycle. For alternating electric current, RMS is equal to the value of the constant direct current that would produce the same power dissipation in a resistive load. In estimation theory, the root-mean-square deviation of an estimator is a measure of the imperfection of the fit of the estimator to the data. Definition The RMS value of a set of values (or a continuous-time waveform) is the square root of the arithmetic mean of the squares of the values, or th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unitary Matrix
In linear algebra, a complex square matrix is unitary if its conjugate transpose is also its inverse, that is, if U^* U = UU^* = UU^ = I, where is the identity matrix. In physics, especially in quantum mechanics, the conjugate transpose is referred to as the Hermitian adjoint of a matrix and is denoted by a dagger (†), so the equation above is written U^\dagger U = UU^\dagger = I. The real analogue of a unitary matrix is an orthogonal matrix. Unitary matrices have significant importance in quantum mechanics because they preserve norms, and thus, probability amplitudes. Properties For any unitary matrix of finite size, the following hold: * Given two complex vectors and , multiplication by preserves their inner product; that is, . * is normal (U^* U = UU^*). * is diagonalizable; that is, is unitarily similar to a diagonal matrix, as a consequence of the spectral theorem. Thus, has a decomposition of the form U = VDV^*, where is unitary, and is diagonal and uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AlphaBeta Geometric Interpretation
Alphabeta were a group of Israeli singers who won the Eurovision Song Contest in 1978 with Izhar Cohen. The singers were Reuven Erez, Lisa Gold-Rubin, Nehama Shutan, Esther Tzuberi, and Itzhak Okev. The winning song was ''A-Ba-Ni-Bi''. Israel received five consecutive maximum 12 points during the voting, a Eurovision Song Contest record. The total score for the song was 157 points. When it became clear that Israel was going to win the contest, Jordan stopped its live broadcast on the pretext of technical difficulties. The viewing public was shown a picture of daffodils. A day later, Jordan presented the song from Belgium, which came in second, as the winning song. This victory entitled Israel to host the contest in Jerusalem in 1979. The head of the Israeli delegation, Rivka Michaeli, said that Cohen's song was sent to the contest because the other entries in the Israeli national competition were so bad. Nevertheless, Izhar Cohen was said to be confident that he would win. S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Y-Δ Transform
The Y-Δ transform, also written wye-delta and also known by many other names, is a mathematical technique to simplify the analysis of an electrical network. The name derives from the shapes of the circuit diagrams, which look respectively like the letter Y and the Greek capital letter Δ. This circuit transformation theory was published by Arthur Edwin Kennelly in 1899. It is widely used in analysis of three-phase electric power circuits. The Y-Δ transform can be considered a special case of the star-mesh transform for three resistors. In mathematics, the Y-Δ transform plays an important role in theory of circular planar graphs. Names The Y-Δ transform is known by a variety of other names, mostly based upon the two shapes involved, listed in either order. The Y, spelled out as wye, can also be called T or star; the Δ, spelled out as delta, can also be called triangle, Π (spelled out as pi), or mesh. Thus, common names for the transformation include wye-delta or delta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Field-oriented Control
Vector control, also called field-oriented control (FOC), is a variable-frequency drive (VFD) control method in which the stator currents of a three-phase AC or brushless DC electric motor are identified as two orthogonal components that can be visualized with a vector. One component defines the magnetic flux of the motor, the other the torque. The control system of the drive calculates the corresponding current component references from the flux and torque references given by the drive's speed control. Typically proportional-integral (PI) controllers are used to keep the measured current components at their reference values. The pulse-width modulation of the variable-frequency drive defines the transistor switching according to the stator voltage references that are the output of the PI current controllers. FOC is used to control AC synchronous and induction motors. It was originally developed for high-performance motor applications that are required to operate smoothly over ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
