Symmetrical components

﻿
Symmetrical components

In electrical engineering, the method of Symmetrical components is used to simplify analysis of unbalanced three phase power systems.

Description

Charles Legeyt Fortescue in a paper presented in 1918 ("Method of Symmetrical Co-Ordinates Applied to the Solution of Polyphase Networks") demonstrated that any set of N unbalanced polyphase quantities could be expressed as the sum of N symmetrical sets of balanced phasors. Only a single frequency component is represented by the phasors.

In a three-phase system, one set of phasors has the same phase sequence as the system under study (positive sequence - say ABC), the second set has the reverse phase sequence (negative sequence - BAC), and in the third set the phasors A, B and C are in phase with each other (zero sequence). Essentially, this method converts three unbalanced phases into three independent sources, which makes asymmetric fault analysis more tractable.

By expanding a one-line diagram to show the positive sequence, negative sequence and zero sequence impedances of generators and transformers and other devices, analysis of such unbalanced conditions as a single line to ground short-circuit fault is greatly simplified. The technique can also be extended to higher phase order systems.

Physically, in a three phase winding a positive sequence set of currents produces a normal rotating field, a negative sequence set produces a field with the opposite rotation, and the zero sequence set produces a field that oscillates but does not rotate. Since these effects can be detected physically, the mathematical tool became the basis for the design of protection relays, which used negative-sequence voltages and currents as a reliable indicator of fault conditions. Such relays may be used to trip circuit breakers or take other steps to protect electrical systems.

The analytical technique was adopted and advanced by engineers at General Electric and Westinghouse and after World War II it was an accepted method for asymmetric fault analysis.

The three-phase case

Symmetrical components are most commonly used for analysis of three-phase electrical power systems. If the phase quantities are expressed in phasor notation using complex numbers, a vector can be formed for the three phase quantities. For example, a vector for three phase voltages could be written as

and the three symmetrical components phasors arranged into a vector as

where the subscripts 0, 1, and 2 refer respectively to the zero, positive, and negative sequence components.

A phase rotation operator $alpha$ is defined to rotate a phasor vector forward by 120 degrees or $frac\left\{2 pi\right\}\left\{3\right\}$ radians. A matrix $A$ can be defined using this operator to transform the phase vector into symmetrical components.

$V_\left\{abc\right\} = A cdot V_s$

ee also

* Symmetry

References

* J. Lewis Blackburn "Symmetrical Components for Power Systems Engineering", Marcel Dekker, New York (1993). ISBN 0-8247-8767-6
* William D. Stevenson, Jr. "Elements of Power System Analysis Third Edition", McGraw-Hill, New York (1975). ISBN 0-07-061285-4.
* [http://www.ieee.org/organizations/pes/public/2004/nov/peshistory.html History article] from IEEE on early development of symmetrical components, retrieved May 12, 2005.
* Westinghouse Corporation, "Applied Protective Relaying", 1976, Westinghouse Corporation, no ISBN, Library of Congress card no. 76-8060 - a standard reference on electromechanical protection relays

Wikimedia Foundation. 2010.

Look at other dictionaries:

• Symmetrical Docking — is the name of a fictional combination system used in the Brave series of super robots. =Description=Symmetrical Docking is a system used by some mecha to combine with another. As the name suggests, each pair of mecha form one side of the new… …   Wikipedia

• symmetrical — I (Roget s IV) modif. Syn. balanced, well formed, shapely, proportional, well set; see also regular 3 . II (Roget s 3 Superthesaurus) a. balanced, even, uniform, corresponding, similar, matching, proportionate, harmonious, regular, parallel. ANT …   English dictionary for students

• Dqo transformation — Odq redirects here. For the professional association, see ODQ. Additional information needed In electrical engineering, direct–quadrature–zero (or dq0 or dqo) transformation or zero–direct–quadrature (or 0dq or odq) transformation is a… …   Wikipedia

• Charles Legeyt Fortescue — (1876–1936) was an electrical engineer. He was born in York Factory, in what is now Manitoba where the Hayes River enters Hudson Bay. He was the son of a Hudson s Bay Company fur trading factor and was among the first graduates of the Queen s… …   Wikipedia

• Asymmetric fault — In power engineering, specifically three phase power, an asymmetric or unbalanced fault is a fault which does not affect each of the three phases equally. This is in contrast to a symmetric fault, where each of the phases is affected equally. In… …   Wikipedia

• Component — may refer to: Usage Component may refer to: System components, the constituents of a system Electronic components, the constituents of electronic circuits Component ingredient, the main ingredient in a dish Component video, a type of analog video …   Wikipedia

• Scott-T transformer — A Scott T Transformer (also called a Scott Connection) is a type of circuit used to derive two phase (2 φ) current from a three phase (3 φ) source or vice versa. The Scott connection evenly distributes a balanced load between the phases of the… …   Wikipedia

• Alpha–beta transformation — In electrical engineering, the αβγ 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 dqo transformation. One very …   Wikipedia

• One-line diagram — A typical one line diagram with annotated power flows. Red boxes represent circuit breakers, grey lines represent three phase bus and interconnecting conductors, the orange circle represents an electric generator, the green spiral is an inductor …   Wikipedia

• Alternating current — (green curve). The horizontal axis measures time; the vertical, current or voltage. In alternating current (AC, also ac) the movement of electric charge periodically reverses direction. In direct current (DC, also dc), the flow of electric charge …   Wikipedia