639:
common to the three phases). When a group of customers sharing the neutral draw unequal phase currents, the common neutral wire carries the currents resulting from these imbalances. Electrical engineers try to design the three-phase power system for any one location so that the power drawn from each of three phases is the same, as far as possible at that site. Electrical engineers also try to arrange the distribution network so the loads are balanced as much as possible, since the same principles that apply to individual premises also apply to the wide-scale distribution system power. Hence, every effort is made by supply authorities to distribute the power drawn on each of the three phases over a large number of premises so that, on average, as nearly as possible a balanced load is seen at the point of supply.
2119:
3546:. This system was devised to avoid patent infringement. In this system, a generator was wound with a full-voltage single-phase winding intended for lighting loads and with a small fraction (usually 1/4 of the line voltage) winding that produced a voltage in quadrature with the main windings. The intention was to use this "power wire" additional winding to provide starting torque for induction motors, with the main winding providing power for lighting loads. After the expiration of the Westinghouse patents on symmetrical two-phase and three-phase power distribution systems, the monocyclic system fell out of use; it was difficult to analyze and did not last long enough for satisfactory energy metering to be developed.
1458:
496:
505:
2114:{\displaystyle {\begin{aligned}V_{12}&=V_{1}-V_{2}=(V_{\text{LN}}\angle 0^{\circ })-(V_{\text{LN}}\angle {-120}^{\circ })\\&={\sqrt {3}}V_{\text{LN}}\angle 30^{\circ }={\sqrt {3}}V_{1}\angle (\phi _{V_{1}}+30^{\circ }),\\V_{23}&=V_{2}-V_{3}=(V_{\text{LN}}\angle {-120}^{\circ })-(V_{\text{LN}}\angle 120^{\circ })\\&={\sqrt {3}}V_{\text{LN}}\angle {-90}^{\circ }={\sqrt {3}}V_{2}\angle (\phi _{V_{2}}+30^{\circ }),\\V_{31}&=V_{3}-V_{1}=(V_{\text{LN}}\angle 120^{\circ })-(V_{\text{LN}}\angle 0^{\circ })\\&={\sqrt {3}}V_{\text{LN}}\angle 150^{\circ }={\sqrt {3}}V_{3}\angle (\phi _{V_{3}}+30^{\circ }).\end{aligned}}}
213:
alternator is key in the history of electrification, as is the power transformer. These inventions enabled power to be transmitted by wires economically over considerable distances. Polyphase power enabled the use of water-power (via hydroelectric generating plants in large dams) in remote places, thereby allowing the mechanical energy of the falling water to be converted to electricity, which then could be fed to an electric motor at any location where mechanical work needed to be done. This versatility sparked the growth of power-transmission network grids on continents around the globe.
173:
3465:
transformers in parallel. Otherwise, the interconnection will behave like a short circuit, and excess current will flow. The direction of rotation of three-phase motors can be reversed by interchanging any two phases; it may be impractical or harmful to test a machine by momentarily energizing the motor to observe its rotation. Phase sequence of two sources can be verified by measuring voltage between pairs of terminals and observing that terminals with very low voltage between them will have the same phase, whereas pairs that show a higher voltage are on different phases.
307:
1445:
931:
435:), a three-phase supply with no neutral and the same phase-to-ground voltage and current capacity per phase can transmit three times as much power by using just 1.5 times as many wires (i.e., three instead of two). Thus, the ratio of capacity to conductor material is doubled. The ratio of capacity to conductor material increases to 3:1 with an ungrounded three-phase and center-grounded single-phase system (or 2.25:1 if both use grounds with the same gauge as the conductors). That leads to higher efficiency, lower weight, and cleaner waveforms.
619:
1271:
667:
2965:
34:
5357:
315:
643:
283:
5936:
3469:
instrument case. Another pattern uses a pair of lamps and an internal phase-shifting network to display the phase rotation. Another type of instrument can be connected to a de-energized three-phase motor and can detect the small voltages induced by residual magnetism, when the motor shaft is rotated by hand. A lamp or other indicator lights to show the sequence of voltages at the terminals for the given direction of shaft rotation.
3383:
2945:
2419:
1213:
6102:
674:" system used for mixed single-phase and three-phase loads on the same distribution system. Three-phase loads such as motors connect to L1, L2, and L3. Single-phase loads would be connected between L1 or L2 and neutral, or between L1 and L2. The L3 phase is 1.73 times the L1 or L2 voltage to neutral, so this leg is not used for single-phase loads.
2676:
2665:
2145:
949:
3317:
917:
3328:. A three-phase induction motor has a simple design, inherently high starting torque and high efficiency. Such motors are applied in industry for many applications. A three-phase motor is more compact and less costly than a single-phase motor of the same voltage class and rating, and single-phase AC motors above 10
3393:
In many
European countries electric stoves are usually designed for a three-phase feed with permanent connection. Individual heating units are often connected between phase and neutral to allow for connection to a single-phase circuit if three-phase is not available. Other usual three-phase loads in
4201:
In
Australia and New Zealand, active conductors can be any color except green/yellow, green, yellow, black, or light blue. Yellow is no longer permitted in the 2007 revision of wiring code ASNZS 3000. European color codes are used for all IEC or flex cables such as extension leads, appliance leads
592:
In an "open delta" or "V" system, only two transformers are used. A closed delta made of three single-phase transformers can operate as an open delta if one of the transformers has failed or needs to be removed. In open delta, each transformer must carry current for its respective phases as well as
418:
Wiring for three phases is typically identified by colors that vary by country and voltage. The phases must be connected in the correct order to achieve the intended direction of rotation of three-phase motors. For example, pumps and fans do not work as intended in reverse. Maintaining the identity
326:
of the same frequency and voltage amplitude relative to a common reference, but with a phase difference of one third of a cycle (i.e., 120 degrees out of phase) between each. The common reference is usually connected to ground and often to a current-carrying conductor called the neutral. Due to the
3464:
Verification of the phase sequence in a circuit is of considerable practical importance. Two sources of three-phase power must not be connected in parallel unless they have the same phase sequence, for example, when connecting a generator to an energized distribution network or when connecting two
699:
supply is sometimes used where one winding of a delta-connected transformer feeding the load is center-tapped and that center tap is grounded and connected as a neutral as shown in the second diagram. This setup produces three different voltages: If the voltage between the center tap (neutral) and
634:
A four-wire system with symmetrical voltages between phase and neutral is obtained when the neutral is connected to the "common star point" of all supply windings. In such a system, all three phases will have the same magnitude of voltage relative to the neutral. Other non-symmetrical systems have
442:
The phase currents tend to cancel out one another, summing to zero in the case of a linear balanced load, which allows a reduction of the size of the neutral conductor because it carries little or no current. With a balanced load, all the phase conductors carry the same current and so can have the
3413:
are used when three-phase equipment needs to be operated on a single-phase power source. They are used when three-phase power is not available or cost is not justifiable. Such converters may also allow the frequency to be varied, allowing speed control. Some railway locomotives use a single-phase
3191:
The currents returning from the customers' premises to the supply transformer all share the neutral wire. If the loads are evenly distributed on all three phases, the sum of the returning currents in the neutral wire is approximately zero. Any unbalanced phase loading on the secondary side of the
4276:
V high leg, the high leg (typically B phase) is always marked orange, commonly A phase is black and C phase is either red or blue. Local regulations may amend the N.E.C. The U.S. National
Electric Code has color requirements for grounded conductors, ground, and grounded-delta three-phase systems
707:
The reason for providing the delta connected supply is usually to power large motors requiring a rotating field. However, the premises concerned will also require the "normal" North
American 120 V supplies, two of which are derived (180 degrees "out of phase") between the "neutral" and
626:
There are two basic three-phase configurations: wye (Y) and delta (Δ). As shown in the diagram, a delta configuration requires only three wires for transmission, but a wye (star) configuration may have a fourth wire. The fourth wire, if present, is provided as a neutral and is normally
638:
The four-wire wye system is used when a mixture of single-phase and three-phase loads are to be served, such as mixed lighting and motor loads. An example of application is local distribution in Europe (and elsewhere), where each customer may be only fed from one phase and the neutral (which is
384:
In a three-phase system feeding a balanced and linear load, the sum of the instantaneous currents of the three conductors is zero. In other words, the current in each conductor is equal in magnitude to the sum of the currents in the other two, but with the opposite sign. The return path for the
212:
These alternators operated by creating systems of alternating currents displaced from one another in phase by definite amounts, and depended on rotating magnetic fields for their operation. The resulting source of polyphase power soon found widespread acceptance. The invention of the polyphase
3468:
Where the absolute phase identity is not required, phase rotation test instruments can be used to identify the rotation sequence with one observation. The phase rotation test instrument may contain a miniature three-phase motor, whose direction of rotation can be directly observed through the
388:
Constant power transfer is possible with any number of phases greater than one. However, two-phase systems do not have neutral-current cancellation and thus use conductors less efficiently, and more than three phases complicates infrastructure unnecessarily. Additionally, in some practical
331:
on any conductor reaches its peak at one third of a cycle after one of the other conductors and one third of a cycle before the remaining conductor. This phase delay gives constant power transfer to a balanced linear load. It also makes it possible to produce a rotating magnetic field in an
3122:
system and a corner-grounded delta system, single-phase loads may be connected across any two phases, or a load can be connected from phase to neutral. Distributing single-phase loads among the phases of a three-phase system balances the load and makes most economical use of conductors and
483:
4535:
We also stated one rationale for this three-phase system; namely, that a three-phase generator experiences a constant torque on its rotor as opposed to the pulsating torque that appears in a single- or two-phase machine, which is obviously preferable from a mechanical engineering
3402:. Homes in Europe have standardized on a nominal 230 V ±10% between any phase and ground. Most groups of houses are fed from a three-phase street transformer so that individual premises with above-average demand can be fed with a second or third phase connection.
3433:
A three-phase generator can be driven by a single-phase motor. This motor-generator combination can provide a frequency changer function as well as phase conversion, but requires two machines with all their expenses and losses. The motor-generator method can also form an
2940:{\displaystyle {\begin{aligned}I_{2}&={\sqrt {3}}I_{23}\angle (\phi _{I_{23}}-30^{\circ })={\sqrt {3}}I_{23}\angle (-120^{\circ }-\theta ),\\I_{3}&={\sqrt {3}}I_{31}\angle (\phi _{I_{31}}-30^{\circ })={\sqrt {3}}I_{31}\angle (120^{\circ }-\theta ),\end{aligned}}}
2465:
2414:{\displaystyle {\begin{aligned}I_{12}&={\frac {V_{12}}{|Z_{\Delta }|}}\angle (30^{\circ }-\theta ),\\I_{23}&={\frac {V_{23}}{|Z_{\Delta }|}}\angle (-90^{\circ }-\theta ),\\I_{31}&={\frac {V_{31}}{|Z_{\Delta }|}}\angle (150^{\circ }-\theta ),\end{aligned}}}
196:, which may be thought of as an alternating-current motor operating in reverse, so as to convert mechanical (rotating) power into electric power (as alternating current). On 11 March 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in
3552:
Have been built and tested for power transmission. Such transmission lines typically would use six or twelve phases. High-phase-order transmission lines allow transfer of slightly less than proportionately higher power through a given volume without the expense of a
1208:{\displaystyle {\begin{aligned}I_{1}&={\frac {V_{1}}{|Z_{\text{total}}|}}\angle (-\theta ),\\I_{2}&={\frac {V_{2}}{|Z_{\text{total}}|}}\angle (-120^{\circ }-\theta ),\\I_{3}&={\frac {V_{3}}{|Z_{\text{total}}|}}\angle (120^{\circ }-\theta ),\end{aligned}}}
3491:
Uses two AC voltages, with a 90-electrical-degree phase shift between them. Two-phase circuits may be wired with two pairs of conductors, or two wires may be combined, requiring only three wires for the circuit. Currents in the common conductor add to 1.4 times
3438:
when used in conjunction with a large flywheel and a battery-powered DC motor; such a combination will deliver nearly constant power compared to the temporary frequency drop experienced with a standby generator set gives until the standby generator kicks in.
3195:
If the supply neutral is broken, phase-to-neutral voltage is no longer maintained. Phases with higher relative loading will experience reduced voltage, and phases with lower relative loading will experience elevated voltage, up to the phase-to-phase voltage.
750:
3357:
may use a three-phase source to produce a six-pulse DC output. The output of such rectifiers is much smoother than rectified single phase and, unlike single-phase, does not drop to zero between pulses. Such rectifiers may be used for battery charging,
3425:
correction that produces balanced three-phase voltages. When properly designed, these rotary converters can allow satisfactory operation of a three-phase motor on a single-phase source. In such a device, the energy storage is performed by the
3301:
that are in-phase on all the supply phases. Consequently, such harmonic currents add in the neutral in a wye system (or in the grounded (zigzag) transformer in a delta system), which can cause the neutral current to exceed the phase current.
380:
because, although it is possible to design and implement asymmetric three-phase power systems (i.e., with unequal voltages or phase shifts), they are not used in practice because they lack the most important advantages of symmetric systems.
3350:
replays. It can be reduced by evenly spreading line frequency operated light sources across the three phases so that the illuminated area is lit from all three phases. This technique was applied successfully at the 2008 Beijing
Olympics.
3378:
may make the equivalent of six-phase full-wave rectification, twelve pulses per cycle, and this method is occasionally employed to reduce the cost of the filtering components, while improving the quality of the resulting DC.
610:) may be connected to allow ground fault currents to return from any phase to ground. Another variation is a "corner grounded" delta system, which is a closed delta that is grounded at one of the junctions of transformers.
4508:. [Excerpt taken from YMER 1941, häfte 2.Utgiven av Sällskapet för antropologi och geografi: Meddelande från Upsala univeristets geografiska institution, N:o 29, published by Esselte ab, Stockholm 1941 no. 135205]
716:
In the perfectly balanced case all three lines share equivalent loads. Examining the circuits, we can derive relationships between line voltage and current, and load voltage and current for wye- and delta-connected loads.
513:
Left image: elementary six-wire three-phase alternator with each phase using a separate pair of transmission wires. Right image: elementary three-wire three-phase alternator showing how the phases can share only three
3087:
Inspection of a phasor diagram, or conversion from phasor notation to complex notation, illuminates how the difference between two line-to-neutral voltages yields a line-to-line voltage that is greater by a factor of
4242:. (E.g. phase/neutral & earth, German: black/grey & red; France: green/red & white; Russia: red/grey & black; Switzerland: red/grey & yellow or yellow & red; Denmark: white/black & red.
934:
Three-phase AC generator connected as a wye or star source to a wye- or star-connected load. In the circuit shown, unbalanced currents will flow between the source and load through the ground, creating undesired
4224:
installers. About 7% to 10% of men cannot clearly distinguish between red and green, which is a particular concern in older schemes where red marks a live conductor and green marks protective earth or safety
662:
may supply 3 phases and neutral to each customer, but at a lower fuse rating, typically 40–63 A per phase, and "rotated" to avoid the effect that more load tends to be put on the first phase.
404:, the currents are usually well balanced. Transformers may be wired to have a four-wire secondary and a three-wire primary, while allowing unbalanced loads and the associated secondary-side neutral currents.
3599:), older standards or to no standard at all and may vary even within a single installation. For example, in the U.S. and Canada, different color codes are used for grounded (earthed) and ungrounded systems.
4813:
3563:
AC was historically used because it could be easily transformed to higher voltages for long distance transmission. However modern electronics can raise the voltage of DC with high efficiency, and DC lacks
3277:
When the currents on the three live wires of a three-phase system are not equal or are not at an exact 120° phase angle, the power loss is greater than for a perfectly balanced system. The method of
209:
for a three-phase electric motor design, application filed
October 12, 1887. Figure 13 of this patent shows that Tesla envisaged his three-phase motor being powered from the generator via six wires.
3186:
2660:{\displaystyle {\begin{aligned}I_{1}&=I_{12}-I_{31}=I_{12}-I_{12}\angle 120^{\circ }\\&={\sqrt {3}}I_{12}\angle (\phi _{I_{12}}-30^{\circ })={\sqrt {3}}I_{12}\angle (-\theta )\end{aligned}}}
1267:. Inductive and capacitive loads will cause current to either lag or lead the voltage. However, the relative phase angle between each pair of lines (1 to 2, 2 to 3, and 3 to 1) will still be −120°.
4867:
2681:
2470:
2150:
1463:
954:
755:
4251:
Note that while China officially uses phase 1: yellow, phase 2: green, phase 3: red, neutral: blue, ground: green/yellow, this is not strongly enforced and there is significant local variation.
1434:
4704:
586:
A "delta" (Δ) connected transformer winding is connected between phases of a three-phase system. A "wye" (Y) transformer connects each winding from a phase wire to a common neutral point.
912:{\displaystyle {\begin{aligned}V_{1}&=V_{\text{LN}}\angle 0^{\circ },\\V_{2}&=V_{\text{LN}}\angle {-120}^{\circ },\\V_{3}&=V_{\text{LN}}\angle {+120}^{\circ }.\end{aligned}}}
4925:
371:
4999:
678:
Based on wye (Y) and delta (Δ) connection. Generally, there are four different types of three-phase transformer winding connections for transmission and distribution purposes:
465:
from which most branch circuits will carry 120 V. Circuits designed for higher powered devices such as stoves, dryers, or outlets for electric vehicles carry 240 V.
290:
of the instantaneous voltages in a three-phase system in one cycle with time increasing to the right. The phase order is 1–2–3. This sequence repeats each cycle, and thus the
3528:, used a two-phase system, and some remnant two-phase distribution systems still exist, but three-phase systems have displaced the two-phase system for modern installations.
3446:
can be used to approximate a three-phase system in a static phase converter, but the voltage and phase angle of the additional phase may only be useful for certain loads.
3514:
4817:
593:
current for the third phase, therefore capacity is reduced to 87%. With one of three transformers missing and the remaining two at 87% efficiency, the capacity is 58% (
535:, one from each coil (or winding) of the generator. The windings are arranged such that the currents are at the same frequency but with the peaks and troughs of their
571:
After further voltage conversions in the transmission network, the voltage is finally transformed to the standard utilization before power is supplied to customers.
6119:
4721:
4503:
3332:(7.5 kW) are uncommon. Three-phase motors also vibrate less and hence last longer than single-phase motors of the same power used under the same conditions.
3126:
In a symmetrical three-phase four-wire wye system, the three phase conductors have the same voltage to the system neutral. The voltage between line conductors is
457:
However, most loads are single-phase. In North
America, single-family houses and individual apartments are supplied one phase from the power grid and use a
4874:
606:
Where a delta-fed system must be grounded for detection of stray current to ground or protection from surge voltages, a grounding transformer (usually a
4234:
In Europe, there still exist many installations with older colors but, since the early 1970s, all new installations use green/yellow earth according to
3587:
Conductors of a three-phase system are usually identified by a color code, to facilitate balanced loading and to assure the correct phase rotation for
4260:
Since 1975, the U.S. National
Electric Code has not specified coloring of phase conductors. It is common practice in many regions to identify 120/208
4103:
3311:
252:
a
Swedish patent on the same three-phase system. The possibility of transferring electrical power from a waterfall at a distance was explored at the
943:
The voltage seen by the load will depend on the load connection; for the wye case, connecting each load to a phase (line-to-neutral) voltages gives
6140:
2968:
A delta configuration and a corresponding phasor diagram of its currents. Phase voltages are equal to line voltages, and currents are calculated as
704:(100%), the voltage across the phase and anti-phase lines is 240 V (200%), and the neutral to "high leg" voltage is ≈ 208 V (173%).
646:
A delta-wye configuration across a transformer core (note that a practical transformer would usually have a different number of turns on each side)
4697:
4589:
94:
because it uses less conductor material to transmit a given amount of electrical power. Three-phase power is mainly used directly to power large
4848:
5208:
396:
wire. The neutral allows three separate single-phase supplies to be provided at a constant voltage and is commonly used for supplying multiple
3219:, however, LN load is imposed on one phase. A transformer manufacturer's page suggests that LN loading not exceed 5% of transformer capacity.
3516:) the current in the individual phases, so the common conductor must be larger. Two-phase and three-phase systems can be interconnected by a
4932:
302:, current, and power is offset from the others' by 120°, thus having all at equidistance. This symmetry can also be recreated in converters.
5881:
3110:, the impedance in the delta configuration must be 3 times what it would be in a wye configuration for the same power to be transferred.
75:
Three-phase electrical power was developed in the 1880s by several people. In three-phase power, the voltage on each wire is 120 degrees
6309:
6302:
453:
with a specified direction and constant magnitude, which simplifies the design of electric motors, as no starting circuit is required.
4113:
4108:
3095:. As a delta configuration connects a load across phases of a transformer, it delivers the line-to-line voltage difference, which is
1260:
The phase angle difference between voltage and current of each phase is not necessarily 0 and depends on the type of load impedance,
225:
20:
4958:
400:
loads. The connections are arranged so that, as far as possible in each group, equal power is drawn from each phase. Further up the
102:
and other heavy loads. Small loads often use only a two-wire single-phase circuit, which may be derived from a three-phase system.
3483:
Used when three-phase power is not available and allows double the normal utilization voltage to be supplied for high-power loads.
5031:
4220:
The international standard green-yellow marking of protective-earth conductors was introduced to reduce the risk of confusion by
3298:
419:
of phases is required if two sources could be connected at the same time. A direct connection between two different phases is a
6091:
5972:
4123:
6126:
5126:
5102:
4908:
4768:
4629:
4528:
4462:
4327:
3141:
6198:
5939:
5356:
720:
In a balanced system each line will produce equal voltage magnitudes at phase angles equally spaced from each other. With V
446:
Power transfer into a linear balanced load is constant, which, in motor/generator applications, helps to reduce vibrations.
318:
Three-phase transformer (Békéscsaba, Hungary): On the left are the primary wires, and on the right are the secondary wires.
37:
Three-phase transformer with four-wire output for 208Y/120 volt service: one wire for neutral, others for A, B and C phases
228:, where Dolivo-Dobrovolsky used the system to transmit electric power at the distance of 176 km (110 miles) with 75%
6366:
5778:
3102:
times greater than the line-to-neutral voltage delivered to a load in the wye configuration. As the power transferred is
631:
present above many transmission lines, which is solely for fault protection and does not carry current under normal use.
4728:
3430:(flywheel effect) of the rotating components. An external flywheel is sometimes found on one or both ends of the shaft.
1361:(KCL) to the neutral node, the three phase currents sum to the total current in the neutral line. In the balanced case:
936:
263:
fall at Hällsjön, Smedjebackens kommun, where a small iron work had been located, was selected. In 1893, a three-phase
134:. For example, for a 208/120-volt service, the line voltage is 208 volts, and the phase voltage is 120 volts.
5886:
5201:
4784:
1367:
79:
relative to each of the other wires. Because it is an AC system, it allows the voltages to be easily stepped up using
6280:
6232:
6162:
5506:
4684:
4486:
4402:
4380:
4359:
4277:
which result in one ungrounded leg having a higher voltage potential to ground than the other two ungrounded legs.
6356:
6172:
6054:
5669:
5594:
5465:
3818:
UK (before April 2006), Hong Kong (before April 2009), South Africa, Malaysia, Singapore (before
February 2011)
68:
employing three wires (or four including an optional neutral return wire) and is the most common method used by
5052:
343:
6371:
6213:
5841:
5773:
5763:
5639:
5539:
5194:
3339:
or space heating may be connected to three-phase systems. Electric lighting may also be similarly connected.
184:
Three phase power evolved out of electric motor development. In 1885, Galileo Ferraris was doing research on
468:
In Europe, three-phase power is normally delivered to the panelboard and further to higher powered devices.
6208:
6193:
6133:
5997:
5694:
5654:
5231:
3435:
477:
5921:
5916:
5634:
5609:
5599:
5575:
5570:
5276:
3569:
3557:(HVDC) converter at each end of the line. However, they require correspondingly more pieces of equipment.
3554:
3521:
3453:
565:
401:
397:
87:
61:
57:
3456:
use power electronic devices to synthesize a balanced three-phase supply from single-phase input power.
6361:
6224:
6049:
6024:
5965:
5836:
5524:
5301:
3478:
3294:
1358:
458:
150:
27:
4868:"Harmonics in Low Voltage Three-Phase Four-Wire Electric Distribution Systems and Filtering Solutions"
4596:
438:
Three-phase supplies have properties that make them desirable in electric power distribution systems:
6044:
5891:
5380:
5341:
4852:
3539:
504:
495:
241:
221:
1452:
In the delta circuit, loads are connected across the lines, and so loads see line-to-line voltages:
180:
developed by Italian physicist Galileo Ferraris. This was a two-phase motor and required four wires.
6218:
5866:
5674:
5614:
5271:
4575:
4561:
3486:
3449:
431:
As compared to a single-phase AC power supply that uses two current-carrying conductors (phase and
336:
and generate other phase arrangements using transformers (for instance, a two-phase system using a
4646:
6351:
6203:
5805:
5795:
5785:
5067:
3582:
3495:
539:
forms offset to provide three complementary currents with a phase separation of one-third cycle (
450:
185:
16:
Common electrical power generation, transmission and distribution method for alternating currents
6295:
5726:
5589:
5372:
5261:
4579:, Theo. Audel and Co., 2nd ed., 1917, vol. 4, Ch. 46: Alternating Currents, p. 1026, fig. 1261.
4565:, Theo. Audel and Co., 2nd ed., 1917, vol. 4, Ch. 46: Alternating Currents, p. 1026, fig. 1260.
4118:
3418:
3395:
3278:
142:
53:
4814:"The 3rd Harmonic Blocking Filter: A Well Established Approach to Harmonic Current Mitigation"
3769:
March 2004), Hong Kong (from July 2007), Singapore (from March 2009), Russia (since 2009; GOST
564:
At the power station, transformers change the voltage from generators to a level suitable for
6264:
6167:
6071:
5958:
5861:
5629:
5624:
5604:
3289:
With linear loads, the neutral only carries the current due to imbalance between the phases.
691:
wye (Y) – Delta (Δ) is used for step-down transformers, i.e., at the end of the transmission.
229:
172:
413:
392:
Three-phase systems may have a fourth wire, common in low-voltage distribution. This is the
5455:
5217:
4970:
3367:
3363:
525:
291:
217:
111:
4312:
2012 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES)
306:
8:
6248:
6240:
6188:
6157:
5826:
5659:
5559:
5534:
5487:
5296:
5286:
5251:
5119:
C22.1-15 – Canadian Electrical Code, Part I: Safety Standard for Electrical Installations
5095:
C22.1-15 – Canadian Electrical Code, Part I: Safety Standard for Electrical Installations
4986:
4873:. Texas A&M University Power Electronics and Power Quality Laboratory. Archived from
3517:
529:
337:
323:
233:
224:. His three-phase three-wire transmission system was displayed in 1891 in Germany at the
162:
83:
to high voltage for transmission and back down for distribution, giving high efficiency.
49:
4974:
1444:
86:
A three-wire three-phase circuit is usually more economical than an equivalent two-wire
6086:
5700:
5311:
5016:
4443:
Woodbank Communications Ltd.'s Electropaedia: "History of Batteries (and other things)"
4333:
3375:
3290:
607:
432:
393:
177:
3914:
Former USSR (Russia, Ukraine, Kazakhstan; before 2009), People's Republic of China (GB
930:
389:
generators and motors, two phases can result in a less smooth (pulsating) torque.
6376:
6287:
6256:
5851:
5731:
5336:
5163:
5122:
5098:
5048:
4904:
4764:
4680:
4625:
4524:
4482:
4458:
4398:
4376:
4355:
4323:
3343:
554:
295:
4418:
4337:
245:
154:
6315:
6014:
5800:
5741:
5445:
5440:
5417:
5326:
5266:
5181:
5155:
5076:
4978:
4756:
4315:
3535:
3127:
688:
Delta (Δ) – wye (Y) is used for step-up transformers, i.e., at generating stations,
618:
532:
146:
95:
65:
4147:
Many labelling systems exist for phases, some having additional meaning, such as:
4128:
2128:
is the phase shift for the first voltage, commonly taken to be 0°; in this case, Φ
589:
A single three-phase transformer can be used, or three single-phase transformers.
6272:
6034:
6019:
5831:
5790:
5768:
5649:
5619:
5584:
5544:
5346:
5065:
Brittain, J. E. (2007). "Electrical Engineering Hall of Fame: Charles F. Scott".
4926:"Sports Lighting – Design Considerations For The Beijing 2008 Olympic Games"
4758:
4619:
4308:"The analysis and development of controlled 3φ wavelet modulated AC-DC converter"
4221:
4211:
In Canada the high leg conductor in a high-leg delta system is always marked red.
3443:
3410:
237:
119:
99:
69:
574:
Most automotive alternators generate three-phase AC and rectify it to DC with a
274:
a distance of 15 km (10 miles), becoming the first commercial application.
6325:
5856:
5846:
5644:
5256:
4455:
Michael von Dolivo-Dobrowolsky und der Drehstrom. Geschichte der Elektrotechnik
4319:
4307:
4202:
etc. and are equally permitted for use in building wiring per AS/NZS 3000:2007.
3754:
3588:
3399:
3325:
3200:
3119:
1270:
737:
696:
671:
651:
333:
322:
In a symmetric three-phase power supply system, three conductors each carry an
189:
158:
115:
5080:
3777:
50462), Argentina, Ukraine, Belarus, Kazakhstan, South Korea (from Jan. 2021)
3316:
253:
6345:
6066:
6061:
5876:
5664:
5549:
5529:
5460:
5450:
5407:
5291:
5246:
5167:
3543:
3525:
666:
521:
420:
205:
5159:
2964:
1448:
Three-phase AC generator connected as a wye source to a delta-connected load
6320:
6007:
5981:
5896:
5871:
5736:
5705:
5519:
5321:
4982:
3422:
3359:
575:
376:
The symmetric three-phase systems described here are simply referred to as
166:
33:
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6002:
5721:
5689:
5482:
5470:
5390:
5316:
5306:
5236:
3565:
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3347:
2459:
by 120°. Calculating line currents by using KCL at each delta node gives
628:
314:
232:. In 1891 he also created a three-phase transformer and short-circuited (
80:
76:
4505:
Elektrifieringens utveckling i Sverige, en ekonomisk-geografisk översikt
642:
6330:
6039:
5684:
5679:
5492:
5475:
5331:
5186:
5121:(23rd ed.). Canadian Standards Association. 2015. Rule 24–208(c).
3329:
462:
271:
193:
4757:
J. Duncan Glover; Mulukutla S. Sarma; Thomas J. Overbye (April 2011).
4442:
282:
6029:
5400:
5395:
5281:
5241:
4959:"ACSL/Graphic Modeller Component Models for Electric Power Education"
4235:
3810:
3758:
3596:
3592:
3354:
627:
grounded. The three-wire and four-wire designations do not count the
540:
5047:
Steve Sentry, "Motor Control Fundamentals", Cengage Learning, 2012,
3414:
source to drive three-phase motors fed through an electronic drive.
5514:
5097:(23rd ed.). Canadian Standards Association. 2015. Rule 4–038.
700:
each of the top and bottom taps (phase and anti-phase) is 120
654:
may supply one phase and neutral at a high current (up to 100
287:
266:
4790:. Utility Technology Engineers-Consultants (UTEC). August 10, 2015
4268:
V (wye or delta) conductors as brown, orange, yellow. In a 120/240
3568:
which permits transmission wires to be lighter and cheaper and so
3382:
685:
Delta (Δ) – Delta (Δ) is used for large currents and low voltages,
385:
current in any phase conductor is the other two phase conductors.
5435:
5425:
5000:"British and European practices for domestic appliances compared"
3750:
3427:
3386:
659:
340:). The amplitude of the voltage difference between two phases is
328:
299:
192:. The research and his studies resulted in the development of an
123:
91:
4523:. Hoboken, New Jersey: John Wiley & Sons, Inc. p. 160.
922:
These voltages feed into either a wye- or delta-connected load.
5950:
5430:
3336:
3293:
and devices that utilize rectifier-capacitor front-end such as
655:
482:
3421:
is a three-phase motor with special starting arrangements and
130:. The voltage measured between any line and neutral is called
6101:
4647:"Three-Phase Power from Single-Phase Transformer Connections"
3192:
transformer will use the transformer capacity inefficiently.
682:
wye (Y) – wye (Y) is used for small current and high voltage,
558:
373:
times the amplitude of the voltage of the individual phases.
259:
197:
188:. Ferraris experimented with different types of asynchronous
19:
For a greater focus on the mathematics of this subject, see
5385:
4397:. Clifton Park, NY: Delmar, Cengage Learning. p. 411.
701:
536:
249:
4722:"Saving energy through load balancing and load scheduling"
3677:
Green/yellow-striped (installations prior to 1966: green)
3524:. Very early AC machines, notably the first generators at
3320:
Three-phase electric machine with rotating magnetic fields
6120:
The Inventions, Researches, and Writings of Nikola Tesla
3534:
An asymmetrical modified two-phase power system used by
5146:
Neidhofer, Gerhard (2007). "Early Three-Phase Power ".
4457:
VDE-Buchreihe, Volume 9, VDE VERLAG, Berlin Offenbach,
4264:
V (wye) conductors as black, red, and blue, and 277/480
3181:{\displaystyle V_{\text{LL}}={\sqrt {3}}V_{\text{LN}}.}
4957:
Pekarek, Steven; Skvarenina, Timothy (November 1998).
4476:
744:
the voltage between the line and the neutral we have:
4899:
Alexander, Charles K.; Sadiku, Matthew N. O. (2007).
3498:
3144:
2679:
2468:
2148:
1461:
1370:
952:
753:
346:
220:
and a three-phase electric motor in 1888 and studied
1288:
represents a phase voltage. Voltages are balanced as
613:
4838:
The boy electrician by J. W. Sims M.I.E.E. (p. 98).
3591:. Colors used may adhere to International Standard
1274:A phasor diagram for a wye configuration, in which
216:Mikhail Dolivo-Dobrovolsky developed a three-phase
6020:Alternating-current commutatorless induction motor
4752:
4750:
4748:
3508:
3342:Line frequency flicker in light is detrimental to
3180:
2939:
2659:
2413:
2113:
1428:
1207:
911:
365:
4956:
4104:Industrial and multiphase power plugs and sockets
3312:Industrial and multiphase power plugs and sockets
1429:{\displaystyle I_{1}+I_{2}+I_{3}=I_{\text{N}}=0.}
6343:
6141:My Inventions: The Autobiography of Nikola Tesla
4053:Alternate Practices (Delta with tapped winding)
5058:
5017:"Speeding-up Conventional Lines and Shinkansen"
4898:
4745:
4352:Elements of Power System Analysis Third Edition
4083:Green or Yellow/green-striped or no insulation
3297:, computers, office equipment and such produce
426:
3712:Green, perhaps yellow-striped, or uninsulated
3472:
3389:used in the past on electric stoves in Germany
3324:An important class of three-phase load is the
3135:times the phase conductor to neutral voltage:
528:converts mechanical power into a set of three
471:
5966:
5202:
4551:, 6th ed., Pitman, London, 1950, p. 268.
4306:Saleh, S. A.; Rahman, M. A. (25 March 2013).
3845:Green/yellow-striped (before c. 1970: green)
650:For domestic use, some countries such as the
310:Three-phase electric power transmission lines
240:. He designed the world's first three-phase
4624:(2nd ed.). McGraw-Hill. pp. 3–5.
4305:
298:of the power system. Ideally, each phase's
6310:The Man Who Invented the Twentieth Century
6303:Wizard: The Life and Times of Nikola Tesla
5973:
5959:
5209:
5195:
4677:Standard Handbook for Electrical Engineers
3203:provides phase-to-neutral relationship of
708:either of the center-tapped phase points.
581:
5145:
4613:
4611:
4609:
4590:"A New Design for Automotive Alternators"
4518:
4501:
4373:American Electricians' Handbook, 11th ed.
4114:Mathematics of three-phase electric power
4109:International Electrotechnical Exhibition
3335:Resistive heating loads such as electric
423:and leads to flow of unbalanced current.
226:International Electrotechnical Exhibition
21:Mathematics of three-phase electric power
5216:
5064:
4917:
4392:
4197:
4195:
4193:
4191:
3381:
3315:
2963:
1443:
1269:
1225:is the sum of line and load impedances (
929:
665:
658:) to one property, while others such as
641:
622:Wye (Y) and delta (Δ) circuits
617:
481:
366:{\displaystyle {\sqrt {3}}=1.732\ldots }
313:
305:
281:
171:
32:
4807:
4805:
4286:Must be the high leg, if it is present.
3572:gives lower losses over long distances.
3281:is used to analyze unbalanced systems.
6344:
6092:Tesla Electric Light and Manufacturing
4903:. New York: McGraw-Hill. p. 504.
4811:
4617:
4606:
4280:
4179:
4170:
4124:Three-phase AC railway electrification
3346:used in sports event broadcasting for
5954:
5190:
4644:
4638:
4477:Bergström och Nordlund, Lars (2002).
4371:Terrell Croft, Wilford Summers (ed),
4254:
4245:
4228:
4214:
4205:
4188:
4141:
3765:60445-2017), United Kingdom (since 31
3615:
3610:
3604:
3113:
1250:is the phase of the total impedance (
203:Two months later Nikola Tesla gained
6199:Tesla Science Center at Wardenclyffe
5024:Japan Railway & Transport Review
4802:
4763:. Cengage Learning. pp. 60–68.
4185:Also, earth, or grounding conductor.
3583:Electrical wiring § Colour code
3305:
925:
711:
3405:
3284:
3272:
2670:and similarly for each other line:
90:circuit at the same line-to-ground
13:
6100:
5887:Renewable energy commercialization
5139:
4865:
4760:Power System Analysis & Design
3982:
3657:
3374:, and for operation of DC motors.
2905:
2846:
2777:
2718:
2638:
2579:
2539:
2438:Relative angles are preserved, so
2379:
2366:
2291:
2278:
2206:
2193:
2065:
2032:
1989:
1957:
1855:
1817:
1774:
1737:
1635:
1602:
1554:
1522:
1173:
1085:
1010:
884:
832:
785:
449:Three-phase systems can produce a
14:
6388:
6127:Colorado Springs Notes, 1899–1900
5175:
4901:Fundamentals of Electric Circuits
4621:Electrician's Calculations Manual
4595:. August 30, 2017. Archived from
4479:Ellära- Kretsteknik och fältteori
3954:Norway (before CENELEC adoption)
3634:Australia and New Zealand (AS/NZS
3056:The overall power transferred is
2954:is the phase of delta impedance (
2428:is the phase of delta impedance (
614:Three-wire and four-wire circuits
407:
5980:
5935:
5934:
5355:
5037:from the original on 2022-10-09.
4710:from the original on 2022-10-09.
4481:. Naturaläromedel. p. 283.
4354:, McGraw-Hill, New York (1975).
503:
494:
486:Animation of three-phase current
414:Electric machine § Sequence
270:system was used to transfer 400
126:between any two lines is called
5111:
5087:
5041:
5009:
4993:
4950:
4923:
4892:
4859:
4841:
4832:
4816:. IAEI Magazine. Archived from
4777:
4714:
4690:
4679:. 15th ed., McGraw-Hill, 2007,
4675:H. W. Beaty, D. G. Fink (ed.),
4669:
4645:Gibbs, J. B. (April 27, 1920).
4582:
4568:
4554:
4541:
4512:
4419:"AC Power History and Timeline"
4048:Bare Conductor (no insulation)
4018:Bare Conductor (no insulation)
1281:represents a line voltage, and
145:were independently invented by
6281:Nikola Tesla's Night of Terror
5148:IEEE Power and Energy Magazine
4963:IEEE Transactions on Education
4495:
4470:
4447:
4436:
4411:
4386:
4365:
4344:
4299:
3909:Green, perhaps yellow-striped
3877:Green, perhaps yellow-striped
3757:and others; since April 2004,
3646:60446 as approved by AS:3000)
3576:
2927:
2908:
2882:
2849:
2802:
2780:
2754:
2721:
2650:
2641:
2615:
2582:
2401:
2382:
2372:
2357:
2316:
2294:
2284:
2269:
2228:
2209:
2199:
2184:
2101:
2068:
2002:
1976:
1970:
1944:
1891:
1858:
1787:
1761:
1755:
1724:
1671:
1638:
1572:
1541:
1535:
1509:
1195:
1176:
1166:
1151:
1110:
1088:
1078:
1063:
1022:
1013:
1003:
988:
105:
1:
6233:Tesla – Lightning in His Hand
6214:Belgrade Nikola Tesla Airport
5882:Renewable Energy Certificates
5842:Cost of electricity by source
5764:Arc-fault circuit interrupter
5640:High-voltage shore connection
5182:AC Power History and Timeline
4931:. GE Lighting. Archived from
4519:von Meier, Alexandra (2006).
4292:
3744:Green perhaps yellow-striped
568:in order to minimize losses.
72:worldwide to transfer power.
6194:Nikola Tesla Memorial Center
6134:Fragments of Olympian Gossip
5897:Spark/Dark/Quark/Bark spread
5695:Transmission system operator
5655:Mains electricity by country
5232:Automatic generation control
3436:uninterruptible power supply
1439:
561:, depending on the country.
478:Mains electricity by country
427:Advantages and disadvantages
277:
7:
6055:Resonant inductive coupling
5922:List of electricity sectors
5917:Electric energy consumption
5635:High-voltage direct current
5610:Electric power transmission
5600:Electric power distribution
5277:Energy return on investment
5006:, volume 148, p. 691, 1965.
4096:
3570:high-voltage direct current
3555:high-voltage direct current
3538:around 1897, championed by
3509:{\displaystyle {\sqrt {2}}}
3473:Alternatives to three-phase
472:Generation and distribution
294:of the generator sets the
10:
6393:
6367:Inventions by Nikola Tesla
6225:The Secret of Nikola Tesla
6082:Three-phase electric power
6025:Tesla Experimental Station
5837:Carbon offsets and credits
5555:Three-phase electric power
4785:"What is "Stray Voltage"?"
4393:Brumbach, Michael (2014).
4350:William D. Stevenson, Jr.
4320:10.1109/PEDES.2012.6484282
3580:
3479:Split-phase electric power
3459:
3309:
3295:switch-mode power supplies
475:
411:
222:star and delta connections
151:Mikhail Dolivo-Dobrovolsky
137:
122:are called lines, and the
42:Three-phase electric power
28:Split-phase electric power
25:
18:
6181:
6150:
6111:
6098:
5988:
5930:
5905:
5892:Renewable Energy Payments
5815:
5752:
5714:
5568:
5505:
5416:
5381:Fossil fuel power station
5371:
5364:
5353:
5224:
5081:10.1109/JPROC.2006.892488
4502:Hjulström, Filip (1940).
4272:V delta system with a 208
4176:Also, grounded conductor.
4082:
4080:
4078:
4075:
4073:
4062:
4060:
4057:
4055:
4052:
4045:
4015:
3989:
3953:
3913:
3881:
3849:
3817:
3809:Older European (prior to
3808:
3748:
3681:
3633:
3628:
3625:
3622:
3607:
3540:Charles Proteus Steinmetz
3450:Variable-frequency drives
242:hydroelectric power plant
5675:Single-wire earth return
5615:Electrical busbar system
5272:Energy demand management
4576:Hawkins Electrical Guide
4562:Hawkins Electrical Guide
4135:
3549:High-phase-order systems
3487:Two-phase electric power
3454:digital phase converters
186:rotating magnetic fields
26:Not to be confused with
6204:IEEE Nikola Tesla Award
5806:Residual-current device
5796:Power system protection
5786:Generator interlock kit
5160:10.1109/MPE.2007.904752
5068:Proceedings of the IEEE
3394:the domestic field are
1359:Kirchhoff's current law
582:Transformer connections
451:rotating magnetic field
143:Polyphase power systems
6357:Electrical engineering
6296:Tesla: Man Out of Time
6105:
5590:Distributed generation
5262:Electric power quality
4983:10.1109/TE.1998.787374
4657:(17). McGraw-Hill: 673
4521:Electric Power Systems
4395:Industrial maintenance
4383:page 3-10 figure 3-23.
4119:Rotary phase converter
3985:yellow or uninsulated
3981:Yellow/green-striped;
3510:
3419:rotary phase converter
3396:tankless water heating
3390:
3321:
3279:symmetrical components
3259:was set as 100%, then
3182:
3084:
2941:
2661:
2415:
2115:
1449:
1430:
1354:
1353:(α = 0 in this case).
1209:
940:
913:
724:as our reference and V
675:
647:
623:
557:is typically 50 or 60
487:
367:
327:phase difference, the
319:
311:
303:
181:
54:electricity generation
48:) is a common type of
38:
6265:The Tesla World Light
6209:Tesla Satellite Award
6168:World Wireless System
6163:Westinghouse Electric
6104:
5862:Fossil fuel phase-out
5630:Electricity retailing
5625:Electrical substation
5605:Electric power system
4812:Lowenstein, Michael.
4618:Fowler, Nick (2011).
4549:Electrical Technology
3949:Green/yellow-striped
3813:, varied by country)
3804:Green/yellow-striped
3511:
3385:
3319:
3299:third-order harmonics
3183:
2967:
2942:
2662:
2416:
2116:
1447:
1431:
1298:= (1∠α − 1∠α + 120°)
1273:
1210:
937:stray ground voltages
933:
914:
670:A transformer for a "
669:
645:
621:
485:
368:
317:
309:
285:
175:
36:
6372:Three-phase AC power
5218:Electricity delivery
4375:, McGraw Hill, 1987
3496:
3368:electric arc furnace
3364:aluminium production
3248:≈ 100% × 1.73 = 173%
3142:
2677:
2466:
2146:
1459:
1368:
950:
751:
695:In North America, a
526:electrical generator
344:
292:rotational frequency
218:electrical generator
6283:" (2020 TV episode)
6249:Tower to the People
6189:Nikola Tesla Museum
6158:War of the currents
5827:Availability factor
5779:Sulfur hexafluoride
5660:Overhead power line
5560:Virtual power plant
5535:Induction generator
5488:Sustainable biofuel
5297:Home energy storage
5287:Grid energy storage
5252:Droop speed control
4975:1998ITEdu..41..348P
4820:on 8 September 2013
4453:Gerhard Neidhöfer:
3993:120, 208, or 240 V
3882:Chile – NCH 4/2003
3665:Dark blue, or grey
3518:Scott-T transformer
3376:Zigzag transformers
3291:Gas-discharge lamps
555:generator frequency
402:distribution system
378:three-phase systems
338:Scott-T transformer
324:alternating current
206:U.S. patent 381,968
169:in the late 1880s.
163:William Stanley Jr.
50:alternating current
6252:(2015 documentary)
6173:In popular culture
6106:
6087:Wardenclyffe Tower
6072:Tesla's oscillator
5701:Transmission tower
5312:Nameplate capacity
4423:Edison Tech Center
3918:50303-2002 Section
3616:Protective earth,
3506:
3391:
3362:processes such as
3344:high-speed cameras
3322:
3178:
3114:Single-phase loads
3085:
2937:
2935:
2657:
2655:
2411:
2409:
2136:= −240° or 120°.)
2111:
2109:
1450:
1426:
1355:
1205:
1203:
941:
909:
907:
676:
648:
624:
608:zigzag transformer
488:
459:split-phase system
363:
320:
312:
304:
244:in 1891. Inventor
182:
64:. It is a type of
39:
6362:Electrical wiring
6339:
6338:
5948:
5947:
5852:Environmental tax
5732:Cascading failure
5501:
5500:
5337:Utility frequency
5128:978-1-77139-718-6
5104:978-1-77139-718-6
4989:on June 26, 2003.
4910:978-0-07-297718-9
4849:"Federal pacific"
4770:978-1-111-42579-1
4687:, pp. 10–11.
4631:978-0-07-177017-0
4530:978-0-471-17859-0
4463:978-3-8007-3115-2
4329:978-1-4673-4508-8
4094:
4093:
3717:Isolated systems
3504:
3306:Three-phase loads
3229:≈ 1.73, defining
3172:
3163:
3152:
2893:
2834:
2765:
2706:
2626:
2567:
2377:
2289:
2204:
2053:
2029:
2020:
1986:
1954:
1843:
1814:
1805:
1771:
1734:
1623:
1599:
1590:
1551:
1519:
1417:
1171:
1162:
1083:
1074:
1008:
999:
926:Wye (or, star; Y)
881:
829:
782:
712:Balanced circuits
533:electric currents
352:
6384:
6219:New Yorker Hotel
6015:Polyphase system
5975:
5968:
5961:
5952:
5951:
5938:
5937:
5847:Energy subsidies
5801:Protective relay
5742:Rolling blackout
5369:
5368:
5359:
5327:Power-flow study
5267:Electrical fault
5211:
5204:
5197:
5188:
5187:
5171:
5133:
5132:
5115:
5109:
5108:
5091:
5085:
5084:
5062:
5056:
5045:
5039:
5038:
5036:
5030:: 58. Oct 2011.
5021:
5013:
5007:
5004:Electrical Times
4997:
4991:
4990:
4985:. Archived from
4954:
4948:
4947:
4945:
4943:
4938:on 28 April 2015
4937:
4930:
4921:
4915:
4914:
4896:
4890:
4889:
4887:
4885:
4879:
4872:
4866:Enjeti, Prasad.
4863:
4857:
4856:
4855:on May 30, 2012.
4851:. Archived from
4845:
4839:
4836:
4830:
4829:
4827:
4825:
4809:
4800:
4799:
4797:
4795:
4789:
4781:
4775:
4774:
4754:
4743:
4742:
4740:
4739:
4733:
4727:. Archived from
4726:
4718:
4712:
4711:
4709:
4702:
4694:
4688:
4673:
4667:
4666:
4664:
4662:
4642:
4636:
4635:
4615:
4604:
4603:
4601:
4594:
4586:
4580:
4572:
4566:
4558:
4552:
4545:
4539:
4538:
4516:
4510:
4509:
4499:
4493:
4492:
4474:
4468:
4451:
4445:
4440:
4434:
4433:
4431:
4429:
4415:
4409:
4408:
4390:
4384:
4369:
4363:
4348:
4342:
4341:
4314:. pp. 1–6.
4303:
4287:
4284:
4278:
4275:
4271:
4267:
4263:
4258:
4252:
4249:
4243:
4239:
4232:
4226:
4218:
4212:
4209:
4203:
4199:
4186:
4183:
4177:
4174:
4168:
4166:
4162:
4158:
4154:
4150:
4145:
3984:
3921:
3917:
3776:
3772:
3768:
3764:
3659:
3645:
3641:
3638:3000:2007 Figure
3637:
3602:
3601:
3536:General Electric
3531:Monocyclic power
3522:Charles F. Scott
3515:
3513:
3512:
3507:
3505:
3500:
3444:autotransformers
3411:Phase converters
3406:Phase converters
3387:Three-phase plug
3285:Non-linear loads
3273:Unbalanced loads
3268:
3258:
3249:
3246:
3237:
3228:
3227:
3218:
3187:
3185:
3184:
3179:
3174:
3173:
3170:
3164:
3159:
3154:
3153:
3150:
3133:
3132:
3101:
3100:
3094:
3093:
2998:
2997:
2946:
2944:
2943:
2938:
2936:
2920:
2919:
2904:
2903:
2894:
2889:
2881:
2880:
2868:
2867:
2866:
2865:
2845:
2844:
2835:
2830:
2821:
2820:
2795:
2794:
2776:
2775:
2766:
2761:
2753:
2752:
2740:
2739:
2738:
2737:
2717:
2716:
2707:
2702:
2693:
2692:
2666:
2664:
2663:
2658:
2656:
2637:
2636:
2627:
2622:
2614:
2613:
2601:
2600:
2599:
2598:
2578:
2577:
2568:
2563:
2555:
2551:
2550:
2538:
2537:
2525:
2524:
2512:
2511:
2499:
2498:
2482:
2481:
2420:
2418:
2417:
2412:
2410:
2394:
2393:
2378:
2376:
2375:
2370:
2369:
2360:
2354:
2353:
2344:
2335:
2334:
2309:
2308:
2290:
2288:
2287:
2282:
2281:
2272:
2266:
2265:
2256:
2247:
2246:
2221:
2220:
2205:
2203:
2202:
2197:
2196:
2187:
2181:
2180:
2171:
2162:
2161:
2120:
2118:
2117:
2112:
2110:
2100:
2099:
2087:
2086:
2085:
2084:
2064:
2063:
2054:
2049:
2044:
2043:
2031:
2030:
2027:
2021:
2016:
2008:
2001:
2000:
1988:
1987:
1984:
1969:
1968:
1956:
1955:
1952:
1940:
1939:
1927:
1926:
1910:
1909:
1890:
1889:
1877:
1876:
1875:
1874:
1854:
1853:
1844:
1839:
1834:
1833:
1828:
1816:
1815:
1812:
1806:
1801:
1793:
1786:
1785:
1773:
1772:
1769:
1754:
1753:
1748:
1736:
1735:
1732:
1720:
1719:
1707:
1706:
1690:
1689:
1670:
1669:
1657:
1656:
1655:
1654:
1634:
1633:
1624:
1619:
1614:
1613:
1601:
1600:
1597:
1591:
1586:
1578:
1571:
1570:
1565:
1553:
1552:
1549:
1534:
1533:
1521:
1520:
1517:
1505:
1504:
1492:
1491:
1475:
1474:
1435:
1433:
1432:
1427:
1419:
1418:
1415:
1406:
1405:
1393:
1392:
1380:
1379:
1344:
1343:
1324:
1323:
1304:
1303:
1214:
1212:
1211:
1206:
1204:
1188:
1187:
1172:
1170:
1169:
1164:
1163:
1160:
1154:
1148:
1147:
1138:
1129:
1128:
1103:
1102:
1084:
1082:
1081:
1076:
1075:
1072:
1066:
1060:
1059:
1050:
1041:
1040:
1009:
1007:
1006:
1001:
1000:
997:
991:
985:
984:
975:
966:
965:
918:
916:
915:
910:
908:
901:
900:
895:
883:
882:
879:
866:
865:
849:
848:
843:
831:
830:
827:
814:
813:
797:
796:
784:
783:
780:
767:
766:
602:
601:
597:
550:
549:
545:
507:
498:
372:
370:
369:
364:
353:
348:
269:
262:
208:
147:Galileo Ferraris
96:induction motors
70:electrical grids
66:polyphase system
6392:
6391:
6387:
6386:
6385:
6383:
6382:
6381:
6342:
6341:
6340:
6335:
6321:SI derived unit
6273:The Current War
6177:
6146:
6107:
6096:
6035:Telegeodynamics
5990:
5984:
5979:
5949:
5944:
5926:
5910:
5908:
5901:
5832:Capacity factor
5820:
5818:
5811:
5791:Numerical relay
5769:Circuit breaker
5757:
5755:
5748:
5710:
5650:Load management
5620:Electrical grid
5585:Demand response
5578:
5573:
5564:
5545:Microgeneration
5497:
5412:
5360:
5351:
5347:Vehicle-to-grid
5220:
5215:
5178:
5142:
5140:Further reading
5137:
5136:
5129:
5117:
5116:
5112:
5105:
5093:
5092:
5088:
5063:
5059:
5046:
5042:
5034:
5019:
5015:
5014:
5010:
4998:
4994:
4955:
4951:
4941:
4939:
4935:
4928:
4922:
4918:
4911:
4897:
4893:
4883:
4881:
4880:on 13 June 2010
4877:
4870:
4864:
4860:
4847:
4846:
4842:
4837:
4833:
4823:
4821:
4810:
4803:
4793:
4791:
4787:
4783:
4782:
4778:
4771:
4755:
4746:
4737:
4735:
4731:
4724:
4720:
4719:
4715:
4707:
4700:
4696:
4695:
4691:
4674:
4670:
4660:
4658:
4643:
4639:
4632:
4616:
4607:
4599:
4592:
4588:
4587:
4583:
4573:
4569:
4559:
4555:
4546:
4542:
4531:
4517:
4513:
4500:
4496:
4489:
4475:
4471:
4452:
4448:
4441:
4437:
4427:
4425:
4417:
4416:
4412:
4405:
4391:
4387:
4370:
4366:
4349:
4345:
4330:
4304:
4300:
4295:
4290:
4285:
4281:
4273:
4269:
4265:
4261:
4259:
4255:
4250:
4246:
4237:
4233:
4229:
4219:
4215:
4210:
4206:
4200:
4189:
4184:
4180:
4175:
4171:
4164:
4160:
4156:
4152:
4148:
4146:
4142:
4138:
4133:
4099:
3919:
3915:
3774:
3770:
3766:
3762:
3737:White, or grey
3705:White, or grey
3670:Black, or blue
3643:
3639:
3635:
3617:
3612:
3585:
3579:
3499:
3497:
3494:
3493:
3475:
3462:
3442:Capacitors and
3408:
3400:storage heaters
3314:
3308:
3287:
3275:
3266:
3260:
3257:
3251:
3247:
3245:
3239:
3236:
3230:
3225:
3223:
3217:
3210:
3204:
3169:
3165:
3158:
3149:
3145:
3143:
3140:
3139:
3130:
3128:
3116:
3098:
3096:
3091:
3089:
3083:
3079:
3072:
3065:
3055:
3051:
3044:
3037:
3028:
3021:
3014:
3005:
2995:
2993:
2991:
2984:
2977:
2960:
2934:
2933:
2915:
2911:
2899:
2895:
2888:
2876:
2872:
2861:
2857:
2856:
2852:
2840:
2836:
2829:
2822:
2816:
2812:
2809:
2808:
2790:
2786:
2771:
2767:
2760:
2748:
2744:
2733:
2729:
2728:
2724:
2712:
2708:
2701:
2694:
2688:
2684:
2680:
2678:
2675:
2674:
2654:
2653:
2632:
2628:
2621:
2609:
2605:
2594:
2590:
2589:
2585:
2573:
2569:
2562:
2553:
2552:
2546:
2542:
2533:
2529:
2520:
2516:
2507:
2503:
2494:
2490:
2483:
2477:
2473:
2469:
2467:
2464:
2463:
2458:
2451:
2444:
2434:
2408:
2407:
2389:
2385:
2371:
2365:
2361:
2356:
2355:
2349:
2345:
2343:
2336:
2330:
2326:
2323:
2322:
2304:
2300:
2283:
2277:
2273:
2268:
2267:
2261:
2257:
2255:
2248:
2242:
2238:
2235:
2234:
2216:
2212:
2198:
2192:
2188:
2183:
2182:
2176:
2172:
2170:
2163:
2157:
2153:
2149:
2147:
2144:
2143:
2135:
2131:
2127:
2108:
2107:
2095:
2091:
2080:
2076:
2075:
2071:
2059:
2055:
2048:
2039:
2035:
2026:
2022:
2015:
2006:
2005:
1996:
1992:
1983:
1979:
1964:
1960:
1951:
1947:
1935:
1931:
1922:
1918:
1911:
1905:
1901:
1898:
1897:
1885:
1881:
1870:
1866:
1865:
1861:
1849:
1845:
1838:
1829:
1821:
1820:
1811:
1807:
1800:
1791:
1790:
1781:
1777:
1768:
1764:
1749:
1741:
1740:
1731:
1727:
1715:
1711:
1702:
1698:
1691:
1685:
1681:
1678:
1677:
1665:
1661:
1650:
1646:
1645:
1641:
1629:
1625:
1618:
1609:
1605:
1596:
1592:
1585:
1576:
1575:
1566:
1558:
1557:
1548:
1544:
1529:
1525:
1516:
1512:
1500:
1496:
1487:
1483:
1476:
1470:
1466:
1462:
1460:
1457:
1456:
1442:
1414:
1410:
1401:
1397:
1388:
1384:
1375:
1371:
1369:
1366:
1365:
1352:
1349:|∠α + 150°
1341:
1339:
1337:
1329:|∠α − 90°,
1321:
1319:
1317:
1309:|∠α + 30°,
1301:
1299:
1297:
1287:
1280:
1266:
1256:
1245:
1238:
1231:
1224:
1202:
1201:
1183:
1179:
1165:
1159:
1155:
1150:
1149:
1143:
1139:
1137:
1130:
1124:
1120:
1117:
1116:
1098:
1094:
1077:
1071:
1067:
1062:
1061:
1055:
1051:
1049:
1042:
1036:
1032:
1029:
1028:
1002:
996:
992:
987:
986:
980:
976:
974:
967:
961:
957:
953:
951:
948:
947:
928:
906:
905:
896:
888:
887:
878:
874:
867:
861:
857:
854:
853:
844:
836:
835:
826:
822:
815:
809:
805:
802:
801:
792:
788:
779:
775:
768:
762:
758:
754:
752:
749:
748:
743:
735:
731:
727:
723:
714:
616:
599:
595:
594:
584:
547:
543:
542:
518:
517:
516:
515:
510:
509:
508:
500:
499:
480:
474:
429:
416:
410:
347:
345:
342:
341:
280:
264:
257:
238:induction motor
204:
190:electric motors
140:
108:
100:electric motors
31:
24:
17:
12:
11:
5:
6390:
6380:
6379:
6374:
6369:
6364:
6359:
6354:
6352:Electric power
6337:
6336:
6334:
6333:
6328:
6323:
6318:
6313:
6306:
6299:
6292:
6284:
6277:
6269:
6261:
6253:
6245:
6237:
6229:
6221:
6216:
6211:
6206:
6201:
6196:
6191:
6185:
6183:
6179:
6178:
6176:
6175:
6170:
6165:
6160:
6154:
6152:
6148:
6147:
6145:
6144:
6137:
6130:
6123:
6115:
6113:
6109:
6108:
6099:
6097:
6095:
6094:
6089:
6084:
6079:
6074:
6069:
6064:
6059:
6058:
6057:
6052:
6050:Wireless power
6047:
6037:
6032:
6027:
6022:
6017:
6012:
6011:
6010:
6000:
5994:
5992:
5986:
5985:
5978:
5977:
5970:
5963:
5955:
5946:
5945:
5943:
5942:
5931:
5928:
5927:
5925:
5924:
5919:
5913:
5911:
5907:Statistics and
5906:
5903:
5902:
5900:
5899:
5894:
5889:
5884:
5879:
5874:
5869:
5864:
5859:
5857:Feed-in tariff
5854:
5849:
5844:
5839:
5834:
5829:
5823:
5821:
5816:
5813:
5812:
5810:
5809:
5803:
5798:
5793:
5788:
5783:
5782:
5781:
5776:
5766:
5760:
5758:
5753:
5750:
5749:
5747:
5746:
5745:
5744:
5734:
5729:
5724:
5718:
5716:
5712:
5711:
5709:
5708:
5703:
5698:
5692:
5687:
5682:
5677:
5672:
5667:
5662:
5657:
5652:
5647:
5645:Interconnector
5642:
5637:
5632:
5627:
5622:
5617:
5612:
5607:
5602:
5597:
5595:Dynamic demand
5592:
5587:
5581:
5579:
5569:
5566:
5565:
5563:
5562:
5557:
5552:
5547:
5542:
5537:
5532:
5527:
5525:Combined cycle
5522:
5517:
5511:
5509:
5503:
5502:
5499:
5498:
5496:
5495:
5490:
5485:
5480:
5479:
5478:
5473:
5468:
5463:
5458:
5448:
5443:
5438:
5433:
5428:
5422:
5420:
5414:
5413:
5411:
5410:
5405:
5404:
5403:
5398:
5393:
5388:
5377:
5375:
5366:
5362:
5361:
5354:
5352:
5350:
5349:
5344:
5339:
5334:
5329:
5324:
5319:
5314:
5309:
5304:
5302:Load-following
5299:
5294:
5289:
5284:
5279:
5274:
5269:
5264:
5259:
5257:Electric power
5254:
5249:
5244:
5239:
5234:
5228:
5226:
5222:
5221:
5214:
5213:
5206:
5199:
5191:
5185:
5184:
5177:
5176:External links
5174:
5173:
5172:
5141:
5138:
5135:
5134:
5127:
5110:
5103:
5086:
5075:(4): 836–839.
5057:
5040:
5008:
4992:
4949:
4916:
4909:
4891:
4858:
4840:
4831:
4801:
4776:
4769:
4744:
4713:
4689:
4668:
4637:
4630:
4605:
4602:on 2017-08-30.
4581:
4567:
4553:
4540:
4529:
4511:
4494:
4487:
4469:
4446:
4435:
4410:
4403:
4385:
4364:
4343:
4328:
4297:
4296:
4294:
4291:
4289:
4288:
4279:
4253:
4244:
4227:
4213:
4204:
4187:
4178:
4169:
4139:
4137:
4134:
4132:
4131:
4126:
4121:
4116:
4111:
4106:
4100:
4098:
4095:
4092:
4091:
4088:
4085:
4084:
4081:
4079:
4077:
4074:
4072:
4069:
4067:
4061:
4059:
4056:
4054:
4050:
4049:
4046:
4044:
4041:
4039:
4036:
4034:
4031:
4029:
4026:
4024:
4020:
4019:
4016:
4014:
4011:
4009:
4006:
4004:
4001:
3999:
3996:
3994:
3991:
3990:United States
3987:
3986:
3979:
3977:
3975:
3972:
3970:
3967:
3965:
3962:
3960:
3957:
3955:
3951:
3950:
3947:
3945:
3943:
3940:
3938:
3935:
3933:
3930:
3928:
3925:
3923:
3911:
3910:
3907:
3905:
3903:
3900:
3898:
3895:
3893:
3890:
3888:
3885:
3883:
3879:
3878:
3875:
3873:
3871:
3868:
3866:
3863:
3861:
3858:
3856:
3853:
3851:
3847:
3846:
3843:
3841:
3839:
3836:
3834:
3831:
3829:
3826:
3824:
3821:
3819:
3815:
3814:
3806:
3805:
3802:
3800:
3798:
3795:
3793:
3790:
3788:
3785:
3783:
3780:
3778:
3755:European Union
3746:
3745:
3742:
3740:
3738:
3735:
3733:
3730:
3728:
3725:
3723:
3720:
3718:
3714:
3713:
3710:
3708:
3706:
3703:
3701:
3698:
3696:
3693:
3691:
3688:
3686:
3683:
3679:
3678:
3675:
3673:
3671:
3668:
3666:
3663:
3661:
3654:
3652:
3651:Red, or brown
3649:
3647:
3631:
3630:
3627:
3624:
3620:
3619:
3614:
3609:
3606:
3578:
3575:
3574:
3573:
3561:
3558:
3550:
3547:
3532:
3529:
3520:, invented by
3503:
3489:
3484:
3481:
3474:
3471:
3461:
3458:
3407:
3404:
3326:electric motor
3307:
3304:
3286:
3283:
3274:
3271:
3264:
3255:
3243:
3238:as 100% gives
3234:
3215:
3208:
3201:high-leg delta
3189:
3188:
3177:
3168:
3162:
3157:
3148:
3123:transformers.
3120:high-leg delta
3115:
3112:
3082:
3081:
3077:
3070:
3063:
3057:
3054:
3053:
3049:
3042:
3035:
3030:
3026:
3019:
3012:
3007:
3003:
2989:
2982:
2975:
2969:
2958:
2950:where, again,
2948:
2947:
2932:
2929:
2926:
2923:
2918:
2914:
2910:
2907:
2902:
2898:
2892:
2887:
2884:
2879:
2875:
2871:
2864:
2860:
2855:
2851:
2848:
2843:
2839:
2833:
2828:
2825:
2823:
2819:
2815:
2811:
2810:
2807:
2804:
2801:
2798:
2793:
2789:
2785:
2782:
2779:
2774:
2770:
2764:
2759:
2756:
2751:
2747:
2743:
2736:
2732:
2727:
2723:
2720:
2715:
2711:
2705:
2700:
2697:
2695:
2691:
2687:
2683:
2682:
2668:
2667:
2652:
2649:
2646:
2643:
2640:
2635:
2631:
2625:
2620:
2617:
2612:
2608:
2604:
2597:
2593:
2588:
2584:
2581:
2576:
2572:
2566:
2561:
2558:
2556:
2554:
2549:
2545:
2541:
2536:
2532:
2528:
2523:
2519:
2515:
2510:
2506:
2502:
2497:
2493:
2489:
2486:
2484:
2480:
2476:
2472:
2471:
2456:
2449:
2442:
2432:
2422:
2421:
2406:
2403:
2400:
2397:
2392:
2388:
2384:
2381:
2374:
2368:
2364:
2359:
2352:
2348:
2342:
2339:
2337:
2333:
2329:
2325:
2324:
2321:
2318:
2315:
2312:
2307:
2303:
2299:
2296:
2293:
2286:
2280:
2276:
2271:
2264:
2260:
2254:
2251:
2249:
2245:
2241:
2237:
2236:
2233:
2230:
2227:
2224:
2219:
2215:
2211:
2208:
2201:
2195:
2191:
2186:
2179:
2175:
2169:
2166:
2164:
2160:
2156:
2152:
2151:
2133:
2129:
2125:
2122:
2121:
2106:
2103:
2098:
2094:
2090:
2083:
2079:
2074:
2070:
2067:
2062:
2058:
2052:
2047:
2042:
2038:
2034:
2025:
2019:
2014:
2011:
2009:
2007:
2004:
1999:
1995:
1991:
1982:
1978:
1975:
1972:
1967:
1963:
1959:
1950:
1946:
1943:
1938:
1934:
1930:
1925:
1921:
1917:
1914:
1912:
1908:
1904:
1900:
1899:
1896:
1893:
1888:
1884:
1880:
1873:
1869:
1864:
1860:
1857:
1852:
1848:
1842:
1837:
1832:
1827:
1824:
1819:
1810:
1804:
1799:
1796:
1794:
1792:
1789:
1784:
1780:
1776:
1767:
1763:
1760:
1757:
1752:
1747:
1744:
1739:
1730:
1726:
1723:
1718:
1714:
1710:
1705:
1701:
1697:
1694:
1692:
1688:
1684:
1680:
1679:
1676:
1673:
1668:
1664:
1660:
1653:
1649:
1644:
1640:
1637:
1632:
1628:
1622:
1617:
1612:
1608:
1604:
1595:
1589:
1584:
1581:
1579:
1577:
1574:
1569:
1564:
1561:
1556:
1547:
1543:
1540:
1537:
1532:
1528:
1524:
1515:
1511:
1508:
1503:
1499:
1495:
1490:
1486:
1482:
1479:
1477:
1473:
1469:
1465:
1464:
1441:
1438:
1437:
1436:
1425:
1422:
1413:
1409:
1404:
1400:
1396:
1391:
1387:
1383:
1378:
1374:
1351:
1350:
1335:
1330:
1315:
1310:
1295:
1289:
1285:
1278:
1264:
1254:
1243:
1236:
1229:
1222:
1216:
1215:
1200:
1197:
1194:
1191:
1186:
1182:
1178:
1175:
1168:
1158:
1153:
1146:
1142:
1136:
1133:
1131:
1127:
1123:
1119:
1118:
1115:
1112:
1109:
1106:
1101:
1097:
1093:
1090:
1087:
1080:
1070:
1065:
1058:
1054:
1048:
1045:
1043:
1039:
1035:
1031:
1030:
1027:
1024:
1021:
1018:
1015:
1012:
1005:
995:
990:
983:
979:
973:
970:
968:
964:
960:
956:
955:
927:
924:
920:
919:
904:
899:
894:
891:
886:
877:
873:
870:
868:
864:
860:
856:
855:
852:
847:
842:
839:
834:
825:
821:
818:
816:
812:
808:
804:
803:
800:
795:
791:
787:
778:
774:
771:
769:
765:
761:
757:
756:
741:
738:angle notation
733:
729:
725:
721:
713:
710:
697:high-leg delta
693:
692:
689:
686:
683:
672:high-leg delta
615:
612:
583:
580:
512:
511:
502:
501:
493:
492:
491:
490:
489:
473:
470:
455:
454:
447:
444:
428:
425:
409:
408:Phase sequence
406:
362:
359:
356:
351:
334:electric motor
279:
276:
246:Jonas Wenström
178:first AC motor
159:John Hopkinson
155:Jonas Wenström
139:
136:
116:voltage source
107:
104:
15:
9:
6:
4:
3:
2:
6389:
6378:
6375:
6373:
6370:
6368:
6365:
6363:
6360:
6358:
6355:
6353:
6350:
6349:
6347:
6332:
6329:
6327:
6324:
6322:
6319:
6317:
6314:
6312:
6311:
6307:
6305:
6304:
6300:
6298:
6297:
6293:
6290:
6289:
6285:
6282:
6278:
6275:
6274:
6270:
6267:
6266:
6262:
6259:
6258:
6254:
6251:
6250:
6246:
6243:
6242:
6238:
6235:
6234:
6230:
6227:
6226:
6222:
6220:
6217:
6215:
6212:
6210:
6207:
6205:
6202:
6200:
6197:
6195:
6192:
6190:
6187:
6186:
6184:
6180:
6174:
6171:
6169:
6166:
6164:
6161:
6159:
6156:
6155:
6153:
6149:
6143:
6142:
6138:
6135:
6131:
6129:
6128:
6124:
6122:
6121:
6117:
6116:
6114:
6110:
6103:
6093:
6090:
6088:
6085:
6083:
6080:
6078:
6075:
6073:
6070:
6068:
6067:Tesla turbine
6065:
6063:
6062:Radio control
6060:
6056:
6053:
6051:
6048:
6046:
6043:
6042:
6041:
6038:
6036:
6033:
6031:
6028:
6026:
6023:
6021:
6018:
6016:
6013:
6009:
6006:
6005:
6004:
6001:
5999:
5996:
5995:
5993:
5987:
5983:
5976:
5971:
5969:
5964:
5962:
5957:
5956:
5953:
5941:
5933:
5932:
5929:
5923:
5920:
5918:
5915:
5914:
5912:
5904:
5898:
5895:
5893:
5890:
5888:
5885:
5883:
5880:
5878:
5877:Pigouvian tax
5875:
5873:
5870:
5868:
5865:
5863:
5860:
5858:
5855:
5853:
5850:
5848:
5845:
5843:
5840:
5838:
5835:
5833:
5830:
5828:
5825:
5824:
5822:
5814:
5807:
5804:
5802:
5799:
5797:
5794:
5792:
5789:
5787:
5784:
5780:
5777:
5775:
5774:Earth-leakage
5772:
5771:
5770:
5767:
5765:
5762:
5761:
5759:
5751:
5743:
5740:
5739:
5738:
5735:
5733:
5730:
5728:
5725:
5723:
5720:
5719:
5717:
5715:Failure modes
5713:
5707:
5704:
5702:
5699:
5696:
5693:
5691:
5688:
5686:
5683:
5681:
5678:
5676:
5673:
5671:
5668:
5666:
5665:Power station
5663:
5661:
5658:
5656:
5653:
5651:
5648:
5646:
5643:
5641:
5638:
5636:
5633:
5631:
5628:
5626:
5623:
5621:
5618:
5616:
5613:
5611:
5608:
5606:
5603:
5601:
5598:
5596:
5593:
5591:
5588:
5586:
5583:
5582:
5580:
5577:
5572:
5567:
5561:
5558:
5556:
5553:
5551:
5550:Rankine cycle
5548:
5546:
5543:
5541:
5538:
5536:
5533:
5531:
5530:Cooling tower
5528:
5526:
5523:
5521:
5518:
5516:
5513:
5512:
5510:
5508:
5504:
5494:
5491:
5489:
5486:
5484:
5481:
5477:
5474:
5472:
5469:
5467:
5464:
5462:
5459:
5457:
5454:
5453:
5452:
5449:
5447:
5444:
5442:
5439:
5437:
5434:
5432:
5429:
5427:
5424:
5423:
5421:
5419:
5415:
5409:
5406:
5402:
5399:
5397:
5394:
5392:
5389:
5387:
5384:
5383:
5382:
5379:
5378:
5376:
5374:
5373:Non-renewable
5370:
5367:
5363:
5358:
5348:
5345:
5343:
5340:
5338:
5335:
5333:
5330:
5328:
5325:
5323:
5320:
5318:
5315:
5313:
5310:
5308:
5305:
5303:
5300:
5298:
5295:
5293:
5292:Grid strength
5290:
5288:
5285:
5283:
5280:
5278:
5275:
5273:
5270:
5268:
5265:
5263:
5260:
5258:
5255:
5253:
5250:
5248:
5247:Demand factor
5245:
5243:
5240:
5238:
5235:
5233:
5230:
5229:
5227:
5223:
5219:
5212:
5207:
5205:
5200:
5198:
5193:
5192:
5189:
5183:
5180:
5179:
5169:
5165:
5161:
5157:
5154:(5): 88–100.
5153:
5149:
5144:
5143:
5130:
5124:
5120:
5114:
5106:
5100:
5096:
5090:
5082:
5078:
5074:
5070:
5069:
5061:
5054:
5050:
5044:
5033:
5029:
5025:
5018:
5012:
5005:
5001:
4996:
4988:
4984:
4980:
4976:
4972:
4968:
4964:
4960:
4953:
4934:
4927:
4920:
4912:
4906:
4902:
4895:
4876:
4869:
4862:
4854:
4850:
4844:
4835:
4819:
4815:
4808:
4806:
4786:
4780:
4772:
4766:
4762:
4761:
4753:
4751:
4749:
4734:on 2014-09-11
4730:
4723:
4717:
4706:
4699:
4693:
4686:
4685:0-07-144146-8
4682:
4678:
4672:
4656:
4652:
4648:
4641:
4633:
4627:
4623:
4622:
4614:
4612:
4610:
4598:
4591:
4585:
4578:
4577:
4571:
4564:
4563:
4557:
4550:
4544:
4537:
4532:
4526:
4522:
4515:
4507:
4506:
4498:
4490:
4488:91-7536-330-5
4484:
4480:
4473:
4467:
4464:
4460:
4456:
4450:
4444:
4439:
4424:
4420:
4414:
4406:
4404:9781133131199
4400:
4396:
4389:
4382:
4381:0-07-013932-6
4378:
4374:
4368:
4361:
4360:0-07-061285-4
4357:
4353:
4347:
4339:
4335:
4331:
4325:
4321:
4317:
4313:
4309:
4302:
4298:
4283:
4257:
4248:
4241:
4231:
4223:
4217:
4208:
4198:
4196:
4194:
4192:
4182:
4173:
4144:
4140:
4130:
4129:Y-Δ transform
4127:
4125:
4122:
4120:
4117:
4115:
4112:
4110:
4107:
4105:
4102:
4101:
4089:
4087:
4086:
4070:
4068:
4066:
4051:
4047:
4042:
4040:
4037:
4035:
4032:
4030:
4027:
4025:
4023:277 or 480 V
4022:
4021:
4017:
4012:
4010:
4007:
4005:
4002:
4000:
3997:
3995:
3992:
3988:
3980:
3978:
3976:
3973:
3971:
3968:
3966:
3963:
3961:
3958:
3956:
3952:
3948:
3946:
3944:
3941:
3939:
3936:
3934:
3931:
3929:
3926:
3924:
3912:
3908:
3906:
3904:
3901:
3899:
3896:
3894:
3891:
3889:
3886:
3884:
3880:
3876:
3874:
3872:
3869:
3867:
3864:
3862:
3859:
3857:
3854:
3852:
3848:
3844:
3842:
3840:
3837:
3835:
3832:
3830:
3827:
3825:
3822:
3820:
3816:
3812:
3807:
3803:
3801:
3799:
3796:
3794:
3791:
3789:
3786:
3784:
3781:
3779:
3760:
3756:
3752:
3747:
3743:
3741:
3739:
3736:
3734:
3731:
3729:
3726:
3724:
3721:
3719:
3716:
3715:
3711:
3709:
3707:
3704:
3702:
3699:
3697:
3694:
3692:
3689:
3687:
3684:
3680:
3676:
3674:
3672:
3669:
3667:
3664:
3662:
3655:
3653:
3650:
3648:
3632:
3621:
3603:
3600:
3598:
3594:
3590:
3584:
3571:
3567:
3562:
3559:
3556:
3551:
3548:
3545:
3544:Elihu Thomson
3541:
3537:
3533:
3530:
3527:
3526:Niagara Falls
3523:
3519:
3501:
3490:
3488:
3485:
3482:
3480:
3477:
3476:
3470:
3466:
3457:
3455:
3451:
3447:
3445:
3440:
3437:
3431:
3429:
3424:
3420:
3415:
3412:
3403:
3401:
3397:
3388:
3384:
3380:
3377:
3373:
3369:
3365:
3361:
3356:
3352:
3349:
3345:
3340:
3338:
3333:
3331:
3327:
3318:
3313:
3303:
3300:
3296:
3292:
3282:
3280:
3270:
3263:
3254:
3242:
3233:
3220:
3214:
3207:
3202:
3197:
3193:
3175:
3166:
3160:
3155:
3146:
3138:
3137:
3136:
3134:
3124:
3121:
3111:
3109:
3105:
3075:
3069:
3062:
3059:
3058:
3048:
3041:
3034:
3031:
3025:
3018:
3011:
3008:
3002:
2988:
2981:
2974:
2971:
2970:
2966:
2962:
2957:
2953:
2930:
2924:
2921:
2916:
2912:
2900:
2896:
2890:
2885:
2877:
2873:
2869:
2862:
2858:
2853:
2841:
2837:
2831:
2826:
2824:
2817:
2813:
2805:
2799:
2796:
2791:
2787:
2783:
2772:
2768:
2762:
2757:
2749:
2745:
2741:
2734:
2730:
2725:
2713:
2709:
2703:
2698:
2696:
2689:
2685:
2673:
2672:
2671:
2647:
2644:
2633:
2629:
2623:
2618:
2610:
2606:
2602:
2595:
2591:
2586:
2574:
2570:
2564:
2559:
2557:
2547:
2543:
2534:
2530:
2526:
2521:
2517:
2513:
2508:
2504:
2500:
2495:
2491:
2487:
2485:
2478:
2474:
2462:
2461:
2460:
2455:
2448:
2441:
2436:
2431:
2427:
2404:
2398:
2395:
2390:
2386:
2362:
2350:
2346:
2340:
2338:
2331:
2327:
2319:
2313:
2310:
2305:
2301:
2297:
2274:
2262:
2258:
2252:
2250:
2243:
2239:
2231:
2225:
2222:
2217:
2213:
2189:
2177:
2173:
2167:
2165:
2158:
2154:
2142:
2141:
2140:
2137:
2132:= −120° and Φ
2104:
2096:
2092:
2088:
2081:
2077:
2072:
2060:
2056:
2050:
2045:
2040:
2036:
2023:
2017:
2012:
2010:
1997:
1993:
1980:
1973:
1965:
1961:
1948:
1941:
1936:
1932:
1928:
1923:
1919:
1915:
1913:
1906:
1902:
1894:
1886:
1882:
1878:
1871:
1867:
1862:
1850:
1846:
1840:
1835:
1830:
1825:
1822:
1808:
1802:
1797:
1795:
1782:
1778:
1765:
1758:
1750:
1745:
1742:
1728:
1721:
1716:
1712:
1708:
1703:
1699:
1695:
1693:
1686:
1682:
1674:
1666:
1662:
1658:
1651:
1647:
1642:
1630:
1626:
1620:
1615:
1610:
1606:
1593:
1587:
1582:
1580:
1567:
1562:
1559:
1545:
1538:
1530:
1526:
1513:
1506:
1501:
1497:
1493:
1488:
1484:
1480:
1478:
1471:
1467:
1455:
1454:
1453:
1446:
1423:
1420:
1411:
1407:
1402:
1398:
1394:
1389:
1385:
1381:
1376:
1372:
1364:
1363:
1362:
1360:
1348:
1345: |
1334:
1331:
1328:
1325: |
1314:
1311:
1308:
1305: |
1294:
1291:
1290:
1284:
1277:
1272:
1268:
1263:
1258:
1253:
1249:
1242:
1235:
1228:
1221:
1198:
1192:
1189:
1184:
1180:
1156:
1144:
1140:
1134:
1132:
1125:
1121:
1113:
1107:
1104:
1099:
1095:
1091:
1068:
1056:
1052:
1046:
1044:
1037:
1033:
1025:
1019:
1016:
993:
981:
977:
971:
969:
962:
958:
946:
945:
944:
938:
932:
923:
902:
897:
892:
889:
875:
871:
869:
862:
858:
850:
845:
840:
837:
823:
819:
817:
810:
806:
798:
793:
789:
776:
772:
770:
763:
759:
747:
746:
745:
739:
718:
709:
705:
703:
698:
690:
687:
684:
681:
680:
679:
673:
668:
664:
661:
657:
653:
644:
640:
636:
632:
630:
620:
611:
609:
604:
590:
587:
579:
577:
572:
569:
567:
562:
560:
556:
552:
538:
534:
531:
527:
523:
522:power station
506:
497:
484:
479:
469:
466:
464:
460:
452:
448:
445:
441:
440:
439:
436:
434:
424:
422:
421:short circuit
415:
405:
403:
399:
395:
390:
386:
382:
379:
374:
360:
357:
354:
349:
339:
335:
330:
325:
316:
308:
301:
297:
293:
289:
284:
275:
273:
268:
261:
255:
251:
247:
243:
239:
235:
234:squirrel-cage
231:
227:
223:
219:
214:
210:
207:
201:
199:
195:
191:
187:
179:
174:
170:
168:
164:
160:
156:
152:
148:
144:
135:
133:
132:phase voltage
129:
125:
121:
117:
113:
103:
101:
97:
93:
89:
84:
82:
78:
77:phase shifted
73:
71:
67:
63:
59:
55:
52:(AC) used in
51:
47:
44:(abbreviated
43:
35:
29:
22:
6326:Lunar crater
6308:
6301:
6294:
6286:
6271:
6263:
6255:
6247:
6241:The Prestige
6239:
6236:(2003 opera)
6231:
6223:
6139:
6125:
6118:
6081:
6008:plasma globe
5982:Nikola Tesla
5872:Net metering
5819:and policies
5737:Power outage
5706:Utility pole
5670:Pumped hydro
5576:distribution
5571:Transmission
5554:
5520:Cogeneration
5322:Power factor
5151:
5147:
5118:
5113:
5094:
5089:
5072:
5066:
5060:
5043:
5027:
5023:
5011:
5003:
4995:
4987:the original
4966:
4962:
4952:
4940:. Retrieved
4933:the original
4919:
4900:
4894:
4882:. Retrieved
4875:the original
4861:
4853:the original
4843:
4834:
4822:. Retrieved
4818:the original
4794:December 10,
4792:. Retrieved
4779:
4759:
4736:. Retrieved
4729:the original
4716:
4692:
4676:
4671:
4659:. Retrieved
4654:
4650:
4640:
4620:
4597:the original
4584:
4574:
4570:
4560:
4556:
4548:
4543:
4534:
4520:
4514:
4504:
4497:
4478:
4472:
4466:
4454:
4449:
4438:
4426:. Retrieved
4422:
4413:
4394:
4388:
4372:
4367:
4351:
4346:
4311:
4301:
4282:
4256:
4247:
4230:
4216:
4207:
4181:
4172:
4143:
4064:
3586:
3467:
3463:
3448:
3441:
3432:
3423:power factor
3416:
3409:
3398:systems and
3392:
3360:electrolysis
3353:
3341:
3334:
3323:
3288:
3276:
3261:
3252:
3240:
3231:
3221:
3212:
3205:
3198:
3194:
3190:
3125:
3118:Except in a
3117:
3107:
3103:
3086:
3073:
3067:
3060:
3046:
3039:
3032:
3023:
3016:
3009:
3000:
2986:
2979:
2972:
2955:
2951:
2949:
2669:
2453:
2446:
2439:
2437:
2429:
2425:
2423:
2138:
2123:
1451:
1357:By applying
1356:
1346:
1332:
1326:
1312:
1306:
1292:
1282:
1275:
1261:
1259:
1251:
1247:
1240:
1233:
1226:
1219:
1217:
942:
921:
719:
715:
706:
694:
677:
649:
637:
633:
625:
605:
591:
588:
585:
576:diode bridge
573:
570:
566:transmission
563:
519:
467:
456:
437:
430:
417:
398:single-phase
391:
387:
383:
377:
375:
321:
248:received in
215:
211:
202:
183:
167:Nikola Tesla
141:
131:
128:line voltage
127:
109:
88:single-phase
85:
81:transformers
74:
62:distribution
58:transmission
45:
41:
40:
6291:(2020 film)
6276:(2019 film)
6268:(2017 film)
6260:(2016 film)
6244:(2006 film)
6228:(1980 film)
6077:Tesla valve
6003:Plasma lamp
5867:Load factor
5722:Black start
5690:Transformer
5391:Natural gas
5342:Variability
5317:Peak demand
5307:Merit order
5237:Backfeeding
4942:18 December
4884:24 November
4824:24 November
4698:"Schneider"
4661:21 December
4547:Cotton, H,
4536:standpoint.
4428:January 24,
4222:color blind
4065:(High-Leg)
3964:White/grey
3761:, later IEC
3642:3.2, or IEC
3577:Color codes
3566:skin effect
3372:steelmaking
3348:slow-motion
635:been used.
629:ground wire
286:Normalized
254:Grängesberg
106:Terminology
6346:Categories
6040:Tesla coil
5991:inventions
5989:Career and
5909:production
5754:Protective
5685:Super grid
5680:Smart grid
5507:Generation
5441:Geothermal
5332:Repowering
5053:1133709176
4969:(4): 348.
4924:Hui, Sun.
4738:2014-08-03
4293:References
4149:H1, H2, H3
3685:Mandatory
3581:See also:
3355:Rectifiers
3310:See also:
476:See also:
463:panelboard
443:same size.
412:See also:
272:horsepower
230:efficiency
194:alternator
114:between a
112:conductors
6030:Teleforce
5817:Economics
5540:Micro CHP
5418:Renewable
5401:Petroleum
5396:Oil shale
5282:Grid code
5242:Base load
5168:1540-7977
5055:, page 70
3942:Sky blue
3811:IEC 60446
3759:IEC 60446
3749:European
3611:Neutral,
3597:IEC 60445
3593:IEC 60446
2925:θ
2922:−
2917:∘
2906:∠
2878:∘
2870:−
2854:ϕ
2847:∠
2800:θ
2797:−
2792:∘
2784:−
2778:∠
2750:∘
2742:−
2726:ϕ
2719:∠
2648:θ
2645:−
2639:∠
2611:∘
2603:−
2587:ϕ
2580:∠
2548:∘
2540:∠
2527:−
2501:−
2399:θ
2396:−
2391:∘
2380:∠
2367:Δ
2314:θ
2311:−
2306:∘
2298:−
2292:∠
2279:Δ
2226:θ
2223:−
2218:∘
2207:∠
2194:Δ
2139:Further:
2097:∘
2073:ϕ
2066:∠
2041:∘
2033:∠
1998:∘
1990:∠
1974:−
1966:∘
1958:∠
1929:−
1887:∘
1863:ϕ
1856:∠
1831:∘
1823:−
1818:∠
1783:∘
1775:∠
1759:−
1751:∘
1743:−
1738:∠
1709:−
1667:∘
1643:ϕ
1636:∠
1611:∘
1603:∠
1568:∘
1560:−
1555:∠
1539:−
1531:∘
1523:∠
1494:−
1440:Delta (Δ)
1193:θ
1190:−
1185:∘
1174:∠
1108:θ
1105:−
1100:∘
1092:−
1086:∠
1020:θ
1017:−
1011:∠
898:∘
885:∠
846:∘
838:−
833:∠
794:∘
786:∠
732:lagging V
728:lagging V
603:of 87%).
361:…
296:frequency
288:waveforms
278:Principle
265:9.5
256:mine. A
6377:AC power
6331:Asteroid
6112:Writings
5940:Category
5727:Brownout
5515:AC power
5225:Concepts
5032:Archived
4705:Archived
4338:32935308
4097:See also
3922:15.2.2)
3605:Country
3370:used in
3366:and the
736:, using
541:120° or
258:45
98:, other
6182:Related
6045:history
5998:Patents
5756:devices
5466:Thermal
5461:Osmotic
5456:Current
5436:Biomass
5426:Biofuel
5408:Nuclear
5365:Sources
4971:Bibcode
4225:ground.
4165:R, Y, B
4161:U, V, W
4157:R, S, T
4153:A, B, C
4063:Orange
4038:Yellow
4033:Orange
3927:Yellow
3860:Yellow
3828:Yellow
3751:CENELEC
3732:Yellow
3722:Orange
3682:Canada
3660:yellow
3656:White;
3608:Phases
3595:(later
3460:Testing
3428:inertia
3337:boilers
3267:≈ 57.7%
3224:√
3129:√
3097:√
3090:√
2999:
2994:√
1340:√
1320:√
1300:√
1246:), and
740:, and V
660:Germany
598:⁄
553:). The
551:radians
546:⁄
520:At the
461:to the
433:neutral
394:neutral
329:voltage
300:voltage
138:History
124:voltage
92:voltage
5451:Marine
5431:Biogas
5166:
5125:
5101:
5051:
4907:
4767:
4683:
4628:
4527:
4485:
4461:
4401:
4379:
4362:, p. 2
4358:
4336:
4326:
4274:
4270:
4266:
4262:
4238:
4076:White
4058:Black
4028:Brown
4013:White
3998:Black
3969:Brown
3959:Black
3932:Green
3920:
3916:
3902:White
3892:Black
3870:Black
3850:India
3838:Black
3787:Black
3782:Brown
3775:
3771:
3767:
3763:
3727:Brown
3695:Black
3644:
3640:
3636:
3589:motors
3222:Since
3006:∠−30°,
2424:where
1218:where
514:wires.
165:, and
118:and a
60:, and
6288:Tesla
6257:Tesla
6151:Other
5808:(GFI)
5697:(TSO)
5483:Solar
5471:Tidal
5446:Hydro
5035:(PDF)
5020:(PDF)
4936:(PDF)
4929:(PDF)
4878:(PDF)
4871:(PDF)
4788:(PDF)
4732:(PDF)
4725:(PDF)
4708:(PDF)
4701:(PDF)
4651:Power
4600:(PDF)
4593:(PDF)
4334:S2CID
4240:60446
4136:Notes
4090:Blue
4043:Gray
4008:Blue
3983:prev.
3974:Blue
3887:Blue
3865:Blue
3833:Blue
3797:Blue
3792:Grey
3700:Blue
3658:prev.
3250:. If
3078:phase
3071:phase
2452:lags
2445:lags
1255:total
1230:total
1223:total
1161:total
1073:total
998:total
524:, an
358:1.732
198:Turin
6316:Boat
5574:and
5493:Wind
5476:Wave
5386:Coal
5164:ISSN
5123:ISBN
5099:ISBN
5049:ISBN
4944:2012
4905:ISBN
4886:2012
4826:2012
4796:2023
4765:ISBN
4681:ISBN
4663:2012
4626:ISBN
4525:ISBN
4483:ISBN
4459:ISBN
4430:2022
4399:ISBN
4377:ISBN
4356:ISBN
4324:ISBN
4071:Red
4003:Red
3937:Red
3897:Red
3855:Red
3823:Red
3690:Red
3542:and
3452:and
3211:= 2
537:wave
250:1890
176:The
120:load
110:The
5156:doi
5077:doi
4979:doi
4316:doi
4236:IEC
3629:L3
3626:L2
3623:L1
3618:PE
3066:= 3
2961:).
2913:120
2788:120
2544:120
2435:).
2387:150
2037:150
1962:120
1779:120
1746:120
1563:120
1257:).
1181:120
1096:120
893:120
841:120
6348::
5162:.
5150:.
5073:95
5071:.
5028:58
5026:.
5022:.
5002:,
4977:.
4967:41
4965:.
4961:.
4804:^
4747:^
4703:.
4655:51
4653:.
4649:.
4608:^
4533:.
4421:.
4332:.
4322:.
4310:.
4190:^
4163:;
4159:;
4155:;
4151:;
3613:N
3560:DC
3417:A
3330:hp
3269:.
3265:LN
3256:LL
3244:LL
3235:LN
3216:LN
3209:LL
3199:A
3171:LN
3151:LL
3064:3Φ
3050:bc
3045:−
3043:ca
3038:=
3027:ab
3022:−
3020:bc
3015:=
3004:ab
2992:=
2990:ca
2985:−
2983:ab
2978:=
2901:31
2874:30
2863:31
2842:31
2773:23
2746:30
2735:23
2714:23
2634:12
2607:30
2596:12
2575:12
2535:12
2522:12
2509:31
2496:12
2457:12
2450:23
2443:31
2351:31
2332:31
2302:90
2263:23
2244:23
2214:30
2178:12
2159:12
2134:v3
2130:v2
2126:v1
2124:(Φ
2093:30
2028:LN
1985:LN
1953:LN
1907:31
1883:30
1826:90
1813:LN
1770:LN
1733:LN
1687:23
1663:30
1607:30
1598:LN
1550:LN
1518:LN
1472:12
1424:0.
1338:=
1336:ca
1318:=
1316:bc
1296:ab
1286:an
1279:ab
1239:+
1237:LN
1232:=
880:LN
828:LN
781:LN
742:LN
652:UK
578:.
559:Hz
544:2π
530:AC
267:kV
236:)
200:.
161:,
157:,
153:,
149:,
56:,
46:3ϕ
6279:"
6136:"
6132:"
5974:e
5967:t
5960:v
5210:e
5203:t
5196:v
5170:.
5158::
5152:5
5131:.
5107:.
5083:.
5079::
4981::
4973::
4946:.
4913:.
4888:.
4828:.
4798:.
4773:.
4741:.
4665:.
4634:.
4491:.
4465:.
4432:.
4407:.
4340:.
4318::
4167:.
3773:R
3753:(
3502:2
3492:(
3262:V
3253:V
3241:V
3232:V
3226:3
3213:V
3206:V
3176:.
3167:V
3161:3
3156:=
3147:V
3131:3
3108:Z
3106:/
3104:V
3099:3
3092:3
3080:.
3076:*
3074:I
3068:V
3061:S
3052:.
3047:I
3040:I
3036:c
3033:I
3029:,
3024:I
3017:I
3013:b
3010:I
3001:I
2996:3
2987:I
2980:I
2976:a
2973:I
2959:Δ
2956:Z
2952:θ
2931:,
2928:)
2909:(
2897:I
2891:3
2886:=
2883:)
2859:I
2850:(
2838:I
2832:3
2827:=
2818:3
2814:I
2806:,
2803:)
2781:(
2769:I
2763:3
2758:=
2755:)
2731:I
2722:(
2710:I
2704:3
2699:=
2690:2
2686:I
2651:)
2642:(
2630:I
2624:3
2619:=
2616:)
2592:I
2583:(
2571:I
2565:3
2560:=
2531:I
2518:I
2514:=
2505:I
2492:I
2488:=
2479:1
2475:I
2454:I
2447:I
2440:I
2433:Δ
2430:Z
2426:θ
2405:,
2402:)
2383:(
2373:|
2363:Z
2358:|
2347:V
2341:=
2328:I
2320:,
2317:)
2295:(
2285:|
2275:Z
2270:|
2259:V
2253:=
2240:I
2232:,
2229:)
2210:(
2200:|
2190:Z
2185:|
2174:V
2168:=
2155:I
2105:.
2102:)
2089:+
2082:3
2078:V
2069:(
2061:3
2057:V
2051:3
2046:=
2024:V
2018:3
2013:=
2003:)
1994:0
1981:V
1977:(
1971:)
1949:V
1945:(
1942:=
1937:1
1933:V
1924:3
1920:V
1916:=
1903:V
1895:,
1892:)
1879:+
1872:2
1868:V
1859:(
1851:2
1847:V
1841:3
1836:=
1809:V
1803:3
1798:=
1788:)
1766:V
1762:(
1756:)
1729:V
1725:(
1722:=
1717:3
1713:V
1704:2
1700:V
1696:=
1683:V
1675:,
1672:)
1659:+
1652:1
1648:V
1639:(
1631:1
1627:V
1621:3
1616:=
1594:V
1588:3
1583:=
1573:)
1546:V
1542:(
1536:)
1527:0
1514:V
1510:(
1507:=
1502:2
1498:V
1489:1
1485:V
1481:=
1468:V
1421:=
1416:N
1412:I
1408:=
1403:3
1399:I
1395:+
1390:2
1386:I
1382:+
1377:1
1373:I
1347:V
1342:3
1333:V
1327:V
1322:3
1313:V
1307:V
1302:3
1293:V
1283:V
1276:V
1265:y
1262:Z
1252:Z
1248:θ
1244:Y
1241:Z
1234:Z
1227:Z
1220:Z
1199:,
1196:)
1177:(
1167:|
1157:Z
1152:|
1145:3
1141:V
1135:=
1126:3
1122:I
1114:,
1111:)
1089:(
1079:|
1069:Z
1064:|
1057:2
1053:V
1047:=
1038:2
1034:I
1026:,
1023:)
1014:(
1004:|
994:Z
989:|
982:1
978:V
972:=
963:1
959:I
939:.
903:.
890:+
876:V
872:=
863:3
859:V
851:,
824:V
820:=
811:2
807:V
799:,
790:0
777:V
773:=
764:1
760:V
734:1
730:2
726:3
722:1
702:V
656:A
600:3
596:2
548:3
355:=
350:3
260:m
30:.
23:.
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