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Power Systems Analysis
In power engineering, the power-flow study, 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 voltages, 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-scale physical models of ... [...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 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 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. 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 incandescent light bulb and the voltaic pile. Probably the greatest dis ... [...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 (''A''), angular frequency (''ω''), and initial phase (''θ'') are time-invariant. 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 situation in electrical networks powered by time varying current is the existence of multiple sinusoids all with the same frequency, but different amplitudes and phases. The only difference in their analytic representations is the complex amplitude (phasor). A linear combination of such functions can be represented as a linear com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reactive Power
Reactive may refer to: *Generally, capable of having a reaction (other) *An adjective abbreviation denoting a bowling ball coverstock made of reactive resin *Reactivity (chemistry) *Reactive mind *Reactive programming See also *Reactance (other) Reactance may refer to: * Electrical reactance In electrical circuits, reactance is the opposition presented to alternating current by inductance or capacitance. Greater reactance gives smaller current for the same applied voltage. Reactance is ... * Reactivity (other) {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Active Power
Active may refer to: Music * ''Active'' (album), a 1992 album by Casiopea * Active Records, a record label Ships * ''Active'' (ship), several commercial ships by that name * HMS ''Active'', the name of various ships of the British Royal Navy * USCS ''Active'', a US Coast Survey ship in commission from 1852 to 1861 * USCGC ''Active'', the name of various ships of the US Coast Guard * USRC ''Active'', the name of various ships of the US Revenue Cutter Service * USS ''Active'', the name of various ships of the US Navy Computers and electronics * Active Enterprises, a defunct video game developer * Sky Active, the brand name for interactive features on Sky Digital available in the UK and Ireland * Active (software), software used for open publishing by Indymedia; see Independent Media Center Sciences * Thermodynamic activity, measure of an effective concentration of a species in a mixture. * Activation, in chemistry the process whereby something is prepared for a su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holomorphic Embedding Load Flow Method
The Holomorphic Embedding Load-flow Method (HELM)HELM is a trademark of Gridquant Inc. is a solution method for the power-flow equations of electrical power systems. Its main features are that it is direct (that is, non-iterative) and that it mathematically guarantees a consistent selection of the correct operative branch of the multivalued problem, also signalling the condition of voltage collapse when there is no solution. These properties are relevant not only for the reliability of existing off-line and real-time applications, but also because they enable new types of analytical tools that would be impossible to build with existing iterative load-flow methods (due to their convergence problems). An example of this would be decision-support tools providing validated action plans in real time. The HELM load-flow algorithm was invented by Antonio Trias and has been granted two US Patents. A detailed description was presented at the 2012 IEEE PES General Meeting and subsequently ... [...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, and is similar to the Jacobi method. 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 The Gauss–Seidel method is an iterative technique for solving a square system of linear equations with unknown : A\mathbf x = \mathbf b . It is defined by the iteration L_* \mathbf^ = \mathbf - U \mathbf^, where \mathbf^ is the -th approximation or iteration of \mathbf,\,\mathbf^ is the next or -th it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Norm
In mathematics, a matrix norm is a vector norm in a vector space whose elements (vectors) are matrices (of given dimensions). Preliminaries Given a field K of either real or complex numbers, let K^ be the -vector space of matrices with m rows and n columns and entries in the field K. A matrix norm is a norm on K^. This article will always write such norms with double vertical bars (like so: \, A\, ). Thus, the matrix norm is a function \, \cdot\, : K^ \to \R that must satisfy the following properties: For all scalars \alpha \in K and matrices A, B \in K^, *\, A\, \ge 0 (''positive-valued'') *\, A\, = 0 \iff A=0_ (''definite'') *\left\, \alpha A\right\, =\left, \alpha\ \left\, A\right\, (''absolutely homogeneous'') *\, A+B\, \le \, A\, +\, B\, (''sub-additive'' or satisfying the ''triangle inequality'') The only feature distinguishing matrices from rearranged vectors is multiplication. Matrix norms are particularly useful if they are also sub-multiplicative: *\left\, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacobian Matrix And Determinant
In vector calculus, the Jacobian matrix (, ) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. When this matrix is square, that is, when the function takes the same number of variables as input as the number of vector components of its output, its determinant is referred to as the Jacobian determinant. Both the matrix and (if applicable) the determinant are often referred to simply as the Jacobian in literature. Suppose is a function such that each of its first-order partial derivatives exist on . This function takes a point as input and produces the vector as output. Then the Jacobian matrix of is defined to be an matrix, denoted by , whose th entry is \mathbf J_ = \frac, or explicitly :\mathbf J = \begin \dfrac & \cdots & \dfrac \end = \begin \nabla^ f_1 \\ \vdots \\ \nabla^ f_m \end = \begin \dfrac & \cdots & \dfrac\\ \vdots & \ddots & \vdots\\ \dfrac & \cdots ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series, when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally better as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ybus Matrix
In power engineering, nodal admittance matrix (or just admittance matrix) or Y Matrix or Ybus is an ''N x N'' matrix (mathematics), matrix describing a linear power system with ''N'' Bus (power engineering), buses. It represents the nodal admittance of the buses in a power system. In realistic systems which contain thousands of buses, the Y matrix is quite sparse. Each bus in a real power system is usually connected to only a few other buses through the electric power transmission, transmission lines. The Y Matrix is also one of the data requirements needed to formulate a power-flow study. Context Power engineering, Electric power transmission needs optimization in order to determine the necessary real and reactive power flows in a system for a given set of loads, as well as the voltages and currents in the system. Power flow studies are used not only to analyze current power flow situations, but also to plan ahead for anticipated disturbances to the system, such as the loss o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
