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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. T ... [...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 that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the latter half of the 19th century after the commercialization of the electric telegraph, the telephone, and electrical power generation, distribution, and use. Electrical engineering is 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, Electromagnetism, electromagnetics and waves, microwave engineering, nanotechnology, electrochemistry, renewable energies, mechatronics/control ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transform (mathematics)
In mathematics, a transformation, transform, or self-map 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 ... [...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 (AC) 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 several people. In three-phase power, the voltage on each wire is 120 degrees phase shifted relative to each of the other wires. Because it is 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 dire ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dq0 Transformation
The direct-quadrature-zero (DQZ, DQ0 or DQO, sometimes lowercase) or Park transformation (named after Robert H. Park) 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 transformation is equivalent to the product of the Clarke transformation and a Rotation matrix, rotation. The Park transformation is often used in the context of electrical engineering with Three-phase electric power, three-phase circuits. The transformation can be used to rotate the reference frames of Alternating current, AC waveforms such that they become Direct current, DC signals. Simplified calculations can then be carried out on these DC quantities before performing the inverse transformation to recover the actual three-phase AC results. As an example, the Park transformation is often used in order to simplify the analysis of three-phase Synchronous motor, synchronous machines or to simplify calculations for the con ... [...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 maybe 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 an American engineer and academic. She 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, the oldest engineering honor society and the second oldest collegiate honor society in the United States; 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 Ellicott City, Maryland. After being orphaned at age 12, she was raised by an older sister. She us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root Mean Square
In mathematics, the root mean square (abbrev. RMS, or rms) of a set of values is the square root of the set's mean square. Given a set x_i, its RMS is denoted as either x_\mathrm or \mathrm_x. The RMS is also known as the quadratic mean (denoted M_2), a special case of the generalized mean. The RMS of a continuous function is denoted f_\mathrm and can be defined in terms of an integral of the square of the function. In estimation theory, the root-mean-square deviation of an estimator measures how far the estimator strays from 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 the square of the function that defines the continuous waveform. In the case of a set of ''n'' values \, the RMS is : x_\text = \sqrt. The corresponding formula for a continuous function (or waveform) ''f''(''t'') defined over the interval T_1 \le t \le T_2 is : f_\text = \sqrt , and the R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unitary Matrix
In linear algebra, an invertible complex square matrix is unitary if its matrix inverse equals its conjugate transpose , that is, if U^* U = 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. A complex matrix is special unitary if it is unitary and its matrix determinant equals . For real numbers, the 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AlphaBeta Geometric Interpretation
"A-Ba-Ni-Bi" (; bet-language language game for the word ''aní'', meaning "I" in Hebrew) is a song recorded by Israeli group Izhar Cohen and the Alphabeta, with music composed by Nurit Hirsh and Hebrew lyrics written by Ehud Manor. It in the Eurovision Song Contest 1978 held in Paris, winning the contest. Background Conception "A-Ba-Ni-Bi" was composed by Nurit Hirsh with lyrics by Ehud Manor, a duo who had collaborated frequently in writing Israeli Eurovision entries, including the country's debut "Ey Sham". It is an up-tempo disco number, heralding a move towards this style of performance in later years. In addition to the version fully in Hebrew, Izhar Cohen and the Alphabeta recorded a version with English and Hebrew lyrics. The Alphabeta was a group of singers composed by two men, Reuven Erez and Itzhak Okev, and three women, Lisa Gold-Rubin, Nehama Shutan, and Esther Tzuberi. The song deals with the way in which children relate to love. Cohen sings that, growing up, " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetrical Components
In electrical engineering, the method of symmetrical components simplifies the 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 the 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Control (motor)
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 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 PI controller, 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 alternating current, AC synchronous machine, synchronous and induction motors. It was originally developed for high-performance motor applications that are required ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
