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Admittance Matrix
In power engineering, nodal admittance matrix (or just admittance matrix) or Y Matrix or Ybus is an ''N x N'' matrix describing a linear power system with ''N'' 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 transmission lines. The Y Matrix is also one of the data requirements needed to formulate a power-flow study. Context 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 of a transmission line to maintenance and repairs. The power flow study would determine whether ... [...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] |
3 Bus Network
3 (three) is a number, numeral and digit. It is the natural number following 2 and preceding 4, and is the smallest odd prime number and the only prime preceding a square number. It has religious or cultural significance in many societies. Evolution of the Arabic digit The use of three lines to denote the number 3 occurred in many writing systems, including some (like Roman and Chinese numerals) that are still in use. That was also the original representation of 3 in the Brahmic (Indian) numerical notation, its earliest forms aligned vertically. However, during the Gupta Empire the sign was modified by the addition of a curve on each line. The Nāgarī script rotated the lines clockwise, so they appeared horizontally, and ended each line with a short downward stroke on the right. In cursive script, the three strokes were eventually connected to form a glyph resembling a with an additional stroke at the bottom: ३. The Indian digits spread to the Caliphate in the 9th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zbus
Z Matrix or ''bus impedance matrix'' in computing is an important tool in power system analysis. Though, it is not frequently used in power flow study, unlike Ybus matrix, it is, however, an important tool in other power system studies like short circuit analysis or fault study. The Zbus matrix can be computed by matrix inversion of the Ybus matrix. Since the Ybus matrix is usually sparse, the explicit Zbus matrix would be dense and very memory intensive to handle directly. Context Electric power transmission needs optimization. Only Computer simulation allows the complex handling required. The ''Zbus'' matrix is a big tool in that box. Formulation Z Matrix can be formed by either inverting the Ybus matrix or by using Z bus building algorithm. The latter method is harder to implement but more practical and faster (''in terms of computer run time and number of floating-point operations per second'') for a relatively large system. Formulation: Z_ = ^ Because the Zbus is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nodal Analysis
In electric circuits analysis, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit in terms of the branch currents. In analyzing a circuit using Kirchhoff's circuit laws, one can either do nodal analysis using Kirchhoff's current law (KCL) or mesh analysis using Kirchhoff's voltage law (KVL). Nodal analysis writes an equation at each electrical node, requiring that the branch currents incident at a node must sum to zero. The branch currents are written in terms of the circuit node voltages. As a consequence, each branch constitutive relation must give current as a function of voltage; an admittance representation. For instance, for a resistor, Ibranch = Vbranch * G, where G (=1/R) is the admittance (conductance) of the resistor. Nodal analysis is possible when all the circuit elements' branch constitutive relations have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Admittance Parameters
Admittance parameters or Y-parameters (the elements of an admittance matrix or Y-matrix) are properties used in many areas of electrical engineering, such as power, electronics, and telecommunications. These parameters are used to describe the electrical behavior of linear electrical networks. They are also used to describe the small-signal ( linearized) response of non-linear networks. Y parameters are also known as short circuited admittance parameters. They are members of a family of similar parameters used in electronic engineering, other examples being: S-parameters, Z-parameters, H-parameters, T-parameters or ABCD-parameters. The Y-parameter matrix A Y-parameter matrix describes the behaviour of any linear electrical network that can be regarded as a black box with a number of ports. A ''port'' in this context is a pair of electrical terminals carrying equal and opposite currents into and out of the network, and having a particular voltage between them. The Y-matrix gives ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ohm's Law
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship: :I = \frac, where is the current through the conductor, ''V'' is the voltage measured ''across'' the conductor and ''R'' is the resistance of the conductor. More specifically, Ohm's law states that the ''R'' in this relation is constant, independent of the current. If the resistance is not constant, the previous equation cannot be called ''Ohm's law'', but it can still be used as a definition of static/DC resistance. Ohm's law is an empirical relation which accurately describes the conductivity of the vast majority of electrically conductive materials over many orders of magnitude of current. However some materials do not obey Ohm's law; these are called non-ohmic. The law was named after t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two Node Power Flow Diagram
2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures. Evolution Arabic digit The digit used in the modern Western world to represent the number 2 traces its roots back to the Indic Brahmic script, where "2" was written as two horizontal lines. The modern Chinese and Japanese languages (and Korean Hanja) still use this method. The Gupta script rotated the two lines 45 degrees, making them diagonal. The top line was sometimes also shortened and had its bottom end curve towards the center of the bottom line. In the Nagari script, the top line was written more like a curve connecting to the bottom line. In the Arabic Ghubar writing, the bottom line was completely vertical, and the digit looked like a dotless closing question mark. Restoring the bottom line to its original horizonta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Node Network
In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex). Node may refer to: In mathematics *Vertex (graph theory), a vertex in a mathematical graph *Vertex (geometry), a point where two or more curves, lines, or edges meet. *Node (autonomous system), behaviour for an ordinary differential equation near a critical point *Singular point of an algebraic variety, a type of singular point of a curve In science and engineering Astronomy *Orbital node, the points where an orbit crosses a plane of reference ** Lunar node, where the orbits of the sun and moon intersect ** Longitude of the ascending node, how orbital nodes are parameterized Biology *Lymph node, an immune system organ used to store white blood cells *Node of Ranvier, periodic gaps in the insulating myelin sheaths of myelinated axons *Sinoatrial node and atrioventricular node, specialized tissues in the heart responsible for initiating and coordinating the heartbeat *Primitive knot or pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric Matrix
In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, Because equal matrices have equal dimensions, only square matrices can be symmetric. The entries of a symmetric matrix are symmetric with respect to the main diagonal. So if a_ denotes the entry in the ith row and jth column then for all indices i and j. Every square diagonal matrix is symmetric, since all off-diagonal elements are zero. Similarly in characteristic different from 2, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative. In linear algebra, a real symmetric matrix represents a self-adjoint operator represented in an orthonormal basis over a real inner product space. The corresponding object for a complex inner product space is a Hermitian matrix with complex-valued entries, which is equal to its conjugate transpose. Therefore, in linear algebra over the complex numbers, it is often assumed that a symmetric matrix refe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
One-line Diagram
In power engineering, a single-line diagram (SLD), also sometimes called one-line diagram, is a simplest symbolic representation of an electric power system. A single line in the diagram typically corresponds to more than one physical conductor: in a direct current system the line includes the supply and return paths, in a three-phase system the line represents all three phases (the conductors are both supply and return due to the nature of the alternating current circuits). The one-line diagram has its largest application in power flow studies. Electrical elements such as circuit breakers, transformers, capacitors, bus bars, and conductors are shown by standardized schematic symbols. Instead of representing each of three phases with a separate line or terminal, only one conductor is represented. It is a form of block diagram graphically depicting the paths for power flow between entities of the system. Elements on the diagram do not represent the physical size or location ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a "-matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents composition of linear maps. Not all matrices are related to linear algebra. This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. ''This article focuses on matrices related to linear algebra, and, unle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kirchhoff's Circuit Laws
Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Clerk Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws. These laws can be applied in time and frequency domains and form the basis for network analysis. Both of Kirchhoff's laws can be understood as corollaries of Maxwell's equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits. Kirchhoff's current law This law, also called Kirchhoff's first law, or Kirchhoff's junction rule, states that, for any node (junction) in an electrical circuit, the sum of currents ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
