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Slack Bus
In electrical power systems a slack bus (or swing bus), defined as a Vδ bus, is used to balance the active power , P, and reactive power , Q, in a system while performing load flow studies. The slack bus is used to provide for system losses by emitting or absorbing active and/or reactive power to and from the system. Load flow studies For power systems engineers, a load flow study explains the power system conditions at various intervals during operation. It aims to minimize the difference between the calculated and actual quantities. Here, the slack bus can contribute to the minimization by having an unconstrained real and reactive power input. P_i=P_-P_ \Delta P_i=P_i-P_ \Delta Q_i=Q_i-Q_ The use of a slack bus has an inherent disadvantage when dealing with uncertain input variables: the slack bus must absorb all uncertainties arising from the system and thus must have the widest possible nodal power distributions. Even moderate amounts of uncertainty in a large system ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Power
Electric power is the rate of transfer of electrical energy within a electric circuit, circuit. Its SI unit is the watt, the general unit of power (physics), power, defined as one joule per second. Standard prefixes apply to watts as with other SI units: thousands, millions and billions of watts are called kilowatts, megawatts and gigawatts respectively. In common parlance, electric power is the production and delivery of electrical energy, an essential public utility in much of the world. Electric power is usually produced by electric generators, but can also be supplied by sources such as Electric battery, electric batteries. It is usually supplied to businesses and homes (as domestic mains electricity) by the electric power industry through an electrical grid. Electric power can be delivered over long distances by electric power transmission, transmission lines and used for applications such as Electric motor, motion, Electric light, light or Electric heat, heat with high ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Flow Study
In power engineering, a power-flow study (also known as power-flow analysis or load-flow study) is a numerical analysis of the flow of electric power in an interconnected system. A power-flow study usually uses simplified notations such as a one-line diagram and per-unit system, and focuses on various aspects of AC power parameters, such as voltage, voltage angles, real power and reactive power. It analyzes the power systems in normal steady-state operation. Power-flow or load-flow studies are important for planning future expansion of power systems as well as in determining the best operation of existing systems. The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive power flowing in each line. Commercial power systems are usually too complex to allow for hand solution of the power flow. Special-purpose network analyzers were built between 1929 and the early 1960s to provide laboratory-s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phasor
In physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude and initial phase are time-invariant and whose angular frequency is fixed. It is related to a more general concept called analytic representation,Bracewell, Ron. ''The Fourier Transform and Its Applications''. McGraw-Hill, 1965. p269 which decomposes a sinusoid into the product of a complex constant and a factor depending on time and frequency. The complex constant, which depends on amplitude and phase, is known as a phasor, or complex amplitude, and (in older texts) sinor or even complexor. A common application is in the steady-state analysis of an electrical network powered by time varying current where all signals are assumed to be sinusoidal with a common frequency. Phasor representation allows the analyst to represent the amplitude and phase of the signal using a single complex number. The only difference in their analytic rep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauss Iterated Map
In mathematics, the Gauss map (also known as Gaussian mapChaos and nonlinear dynamics: an introduction for scientists and engineers, by Robert C. Hilborn, 2nd Ed., Oxford, Univ. Press, New York, 2004. or mouse map), is a nonlinear iterated map of the reals into a real interval given by the Gaussian function: : x_ = \exp(-\alpha x^2_n)+\beta, \, where ''α'' and ''β'' are real parameters. Named after Johann Carl Friedrich Gauss, the function maps the bell shaped Gaussian function similar to the logistic map. Properties In the parameter real space x_n can be chaotic. The map is also called the ''mouse map'' because its bifurcation diagram resembles a mouse A mouse (: mice) is a small rodent. Characteristically, mice are known to have a pointed snout, small rounded ears, a body-length scaly tail, and a high breeding rate. The best known mouse species is the common house mouse (''Mus musculus'' ... (see Figures). References Chaotic maps {{chaos-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauss–Seidel Method
In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel. Though it can be applied to any matrix with non-zero elements on the diagonals, convergence is only guaranteed if the matrix is either strictly diagonally dominant, or symmetric and positive definite. It was only mentioned in a private letter from Gauss to his student Gerling in 1823. A publication was not delivered before 1874 by Seidel. Description Let \mathbf A\mathbf x = \mathbf b be a square system of linear equations, where: \mathbf A = \begin a_ & a_ & \cdots & a_ \\ a_ & a_ & \cdots & a_ \\ \vdots & \vdots & \ddots & \vdots \\a_ & a_ & \cdots & a_ \end, \qquad \mathbf = \begin x_ \\ x_2 \\ \vdots \\ x_n \end , \qquad \mathbf = \begin b_ \\ b_2 \\ \vdots \\ b_n \end. When ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton–Raphson Method
In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a real-valued function , its derivative , and an initial guess for a root of . If satisfies certain assumptions and the initial guess is close, then x_ = x_0 - \frac is a better approximation of the root than . Geometrically, is the x-intercept of the tangent of the graph of at : that is, the improved guess, , is the unique root of the linear approximation of at the initial guess, . The process is repeated as x_ = x_n - \frac until a sufficiently precise value is reached. The number of correct digits roughly doubles with each step. This algorithm is first in the class of Householder's methods, and was succeeded by Halley's method. The method can also be extended to c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Engineering
Power engineering, also called power systems engineering, is a subfield of electrical engineering that deals with the generation, transmission, distribution, and utilization of electric power, and the electrical apparatus connected to such systems. Although much of the field is concerned with the problems of three-phase electric power, three-phase AC power – the standard for large-scale power transmission and distribution across the modern world – a significant fraction of the field is concerned with the conversion between rectifier, AC and DC power and the development of specialized power systems such as those used in aircraft or for electric railway networks. Power engineering draws the majority of its theoretical base from electrical engineering and mechanical engineering. History Pioneering years Electricity became a subject of scientific interest in the late 17th century. Over the next two centuries a number of important discoveries were made including the incandes ... [...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] |
Electric Power
Electric power is the rate of transfer of electrical energy within a electric circuit, circuit. Its SI unit is the watt, the general unit of power (physics), power, defined as one joule per second. Standard prefixes apply to watts as with other SI units: thousands, millions and billions of watts are called kilowatts, megawatts and gigawatts respectively. In common parlance, electric power is the production and delivery of electrical energy, an essential public utility in much of the world. Electric power is usually produced by electric generators, but can also be supplied by sources such as Electric battery, electric batteries. It is usually supplied to businesses and homes (as domestic mains electricity) by the electric power industry through an electrical grid. Electric power can be delivered over long distances by electric power transmission, transmission lines and used for applications such as Electric motor, motion, Electric light, light or Electric heat, heat with high ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
