:"This article deals with the basic mathematics and principles of "three-phase" electricity. For information on where, how and why three-phase is used, see
three-phase electric power. "
electrical engineering, three-phase electric power systems have at least three conductors carrying voltage waveforms that are 2π/3 radians(120°,1/3 of a cycle in-phase) offset in time. In this article angles will be measured in radiansexcept where otherwise stated.
Also written as "
Variable setup and basic definitions
Let be the
instantaneous phaseof a signal of frequencyat time :
Using this, the waveforms for the three phases are
where is the peak voltage and the voltages on L1, L2 and L3 are measured relative to the neutral.
Generally, in electric power systems, the loads are distributed as evenly as is practical between the phases. It is usual practice to discuss a balanced system first and then describe the effects of unbalanced systems as deviations from the elementary case.
tar connected systems with neutral
This refers to a system with a resistive load between each phase and neutral.
Constant power transfer
An important property of three-phase power is that the power available to a resistive load, , is constant at all times.
To simplify the math, we define a nondimensionalized power for intermediate calculations,
Using angle subtraction formulae
Pythagorean trigonometric identity
Hence (substituting back):
since we have eliminated we can see that the total power does not vary with time. This is essential for keeping large generators and motors running smoothly.
No neutral current
For the case of equal loads on each of three phases, no net current flows in the neutral. The neutral current is the sum of the phase current.
We define a nondimensionalized current, .
Using angle subtraction formulae
tar connected systems without neutral
Since we have shown that the neutral current is zero we can see that removing the neutral core will have no effect on the circuit, provided the system is balanced. In reality such connections are generally used only when the load on the three phases is part of the same piece of equipment (for example a three-phase motor), as otherwise switching loads and slight imbalances would cause large voltage fluctuations.
Practical systems rarely have perfectly balanced loads, currents, voltages or impedances in all three phases. The analysis of unbalanced cases is greatly simplified by the use of the techniques of
symmetrical components. An unbalanced system is analyzed as the superposition of three balanced systems, each with the positive, negative or zero sequence of balanced voltages.
Revolving magnetic field
magnetic fieldof a three-phase motor.]
Any polyphase system, by virtue of the time displacement of the currents in the phases, makes it possible to easily generate a magnetic field that revolves at the line frequency. Such a revolving magnetic field makes polyphase
induction motorspossible. Indeed, where induction motors must run on single-phase power (such as is usually distributed in homes), the motor must contain some mechanism to produce a revolving field, otherwise the motor cannot generate any stand-still torqueand will not start. The field produced by a single-phase winding can provide energy to a motor already rotating, but without auxiliary mechanisms the motor will not accelerate from a stop when energized.
Visualization of the revolving magnetic field
As displayed in the image, when summarized, the three phase vectors of an ideal revolving magnetic field will form a circular pattern. In practical applications however, this may not always be the case. There can be technical malfunctions such as a missing phase, uneven phase voltage, or unbalanced loads without a neutral wire. This is unusual in the main grid, but sometimes happen on ships and other independent systems. It is also possible that the main grid is operating correctly, but that the phase voltages have been manipulated by an electronic motor control device. In these situations a vector visualization unit is used to display the actual form of the voltage-, current- and magnetic field vectors on a screen. For engineers this may be important information since any distortion from the ideal circular pattern will lead to vibrations, loss of power and risk for overload.
Conversion to other phase systems
Provided two voltage waveforms have at least some relative displacement on the time axis, other than a multiple of a half-cycle, any other polyphase set of voltages can be obtained by an array of passive
transformers. Such arrays will evenly balance the polyphase load between the phases of the source system. For example, balanced two-phase power can be obtained from a three-phase network by using two specially constructed transformers, with taps at 50% and 86.6% of the primary voltage. This "Scott T" connection produces a true two-phase system with 90° time difference between the phases. Another example is the generation of higher-phase-order systems for large rectifiersystems, to produce a smoother DC output and to reduce the harmoniccurrents in the supply.
When three-phase is needed but only single-phase is readily available from the utility company a
phase convertercan be used to generate three-phase power from the single phase supply.
* Stevenson, William D., Jr. (1975) "Elements of Power Systems Analysis", McGraw-Hill electrical and electronic engineering series, 3rd ed., New York: McGraw Hill, ISBN 0-07-061285-4
Charles Proteus Steinmetz
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Look at other dictionaries:
three-phase — three′ phase adj. elm of or pertaining to a circuit, system, or device that is energized by three electromotive forces that differ in phase by one third of a cycle, or 120° • Etymology: 1890–95 … From formal English to slang
three-phase — [thrē′fāz′] adj. Elec. powered by three equal AC voltages which are out of phase by one third of a cycle (120 degrees) … English World dictionary
three-phase — ˈ ̷ ̷| ̷ ̷ adjective : of, relating to, or operating by means of a combination of three circuits energized by alternating electromotive forces that differ in phase by one third of a cycle * * * /three fayz /, adj. Elect. 1. of or pertaining to a… … Useful english dictionary
three-phase — /three fayz /, adj. Elect. 1. of or pertaining to a circuit, system, or device that is energized by three electromotive forces that differ in phase by one third of a cycle or 120°. 2. having three phases. [1890 95] * * * … Universalium
three-phase — /ˈθri feɪz/ (say three fayz) adjective Electricity 1. denoting or relating to a circuit, system, or device which is energised by three voltage cycles which differ in phase by one third of a cycle, i.e., 120 degrees. 2. having three phases … Australian English dictionary
three-phase — adjective Date: 1892 of, relating to, or operating by means of a combination of three circuits energized by alternating electromotive forces that differ in phase by one third of a cycle … New Collegiate Dictionary
three-phase — Operating by means of combination of three alternating current circuits which differ in phase by one third of a cycle … Dictionary of automotive terms
three-phase — adjective relating to or denoting an electricity supply using three separate alternating components with phases differing by a third of a period … English new terms dictionary
three phase — high electrical flow which allows high performance … English contemporary dictionary
three-phase contact line — Three Phase Contact Line Линия трехфазного контакта Граничный контур (периметр основания капли) называется линией трехфазного контакта (ЛТК). Этот термин подчеркивает, что в смачивании участвуют три фазы: 1) твердое тело, 2) смачивающая… … Толковый англо-русский словарь по нанотехнологии. - М.