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Admittance Matrix
In power engineering, nodal admittance matrix (or just admittance matrix) 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 admittance 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 nodal admittance matrix is used in the formulation of the power flow problem. Construction from a single line diagram The nodal admittance matrix of a power system is a form of Laplacian matrix of the nodal admittance diagram of the power system, which is derived by the application of Kirchhoff's laws to the admittance diagram of the power system. Starting from the single line diagram of a power system, the nodal admittance diagram is derived by: * replacing each line in the diagram with its equivalent admittance, and * converting all voltage sources to t ... [...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] |
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 and 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 c ... [...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 th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nodal Analysis
In electric circuit analysis, nodal analysis (also referred to as node-voltage analysis or the branch current method) is a method of determining the voltage between nodes (points where elements or branches connect) in an electrical circuit in terms of the branch currents. Nodal analysis is essentially a systematic application of Kirchhoff's current law (KCL) for circuit analysis. Similarly, mesh analysis is a systematic application of Kirchhoff's voltage law (KVL). Nodal analysis writes an equation at each electrical node specifying that the branch currents incident at a node must sum to zero (using KCL). 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 c ... [...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 engineering, power, electronic engineering, electronics, and telecommunications engineering, telecommunications. These parameters are used to describe the electrical behavior of linear electrical networks. They are also used to describe the small-signal (linearization, 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, Two port#Hybrid parameters (h-parameters), H-parameters, T-parameters or Two-port network#ABCD-parameters, 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 Port (circuit theory), ports. A ''po ... [...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 busbar, 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 analyzer (AC power), network analyzers were built between 1929 and the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermitian Matrix
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th row and -th column, for all indices and : A \text \quad \iff \quad a_ = \overline or in matrix form: A \text \quad \iff \quad A = \overline . Hermitian matrices can be understood as the complex extension of real symmetric matrices. If the conjugate transpose of a matrix A is denoted by A^\mathsf, then the Hermitian property can be written concisely as A \text \quad \iff \quad A = A^\mathsf Hermitian matrices are named after Charles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always having real eigenvalues. Other, equivalent notations in common use are A^\mathsf = A^\dagger = A^\ast, although in quantum mechanics, A^\ast typically means the complex conjugate onl ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ohm's Law
Ohm's law states that the electric current through a Electrical conductor, conductor between two Node (circuits), points is directly Proportionality (mathematics), proportional to the voltage across the two points. Introducing the constant of proportionality, the Electrical resistance, resistance, one arrives at the three mathematical equations used to describe this relationship: V = IR \quad \text\quad I = \frac \quad \text\quad R = \frac where is the current through the conductor, ''V'' is the voltage measured across the conductor and ''R'' is the electrical resistance, 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 Electrical resistance and conductance#Static and differential resistance, static/DC resistance. Ohm's law is an empirical law, empirical rel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (: matrices) is a rectangle, rectangular array or table of numbers, symbol (formal), symbols, or expression (mathematics), expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or 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 . Matrices are commonly used in linear algebra, where they represent linear maps. In geometry, matrices are widely used for specifying and representing geometric transformations (for example rotation (mathematics), rotations) and coordinate changes. In numerical analysis, many computational problems are solved by reducing them to a matrix computation, and this often involves computing with matrices of huge dimensions. Matrices are used in most areas of mathematics and scientific fields, either directly ... [...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 single-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 loca ... [...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 cur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
