650:
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.
2130:
3557:. 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.
1469:
507:
516:
2125:{\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}}}
224:
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.
184:
3476:
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.
318:
1456:
942:
446:), 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.
630:
1282:
678:
2976:
45:
5368:
326:
654:
294:
5947:
3480:
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.
3394:
2956:
2430:
1224:
6113:
685:" 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.
2687:
2676:
2156:
960:
3328:
928:
3339:. 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
3404:
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
4212:
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
603:
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
429:
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
337:
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
3475:
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
710:
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
645:
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
453:
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
3424:
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
3202:
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
4287:
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
718:
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
637:
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
649:
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
395:
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
223:
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
3479:
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
399:
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
342:
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
3133:
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
494:
4546:
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
3413:. 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.
3444:
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
2951:{\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}}}
2476:
2425:{\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}}}
207:, 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
3563:
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
1219:{\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}}}
3502:
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
3449:
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.
3206:
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.
761:
3368:
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,
3436:
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
3312:
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.
391:
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.
3361:
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.
3389:
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.
621:) 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.
4519:. [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]
727:
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.
524:
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
3098:
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
4253:. (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.
945:
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
4235:
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
673:
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.
415:, 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.
3610:), 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.
4824:
3574:
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
3288:
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
220:
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.
3197:
2671:{\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}}}
1278:. 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°.
4878:
2692:
2481:
2161:
1474:
965:
766:
4262:
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.
1445:
4715:
597:
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.
923:{\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}}}
4936:
382:
5010:
689:
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:
476:
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.
301:
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
3539:, 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.
3457:
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.
3525:
4828:
604:
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% (
546:, 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
582:
After further voltage conversions in the transmission network, the voltage is finally transformed to the standard utilization before power is supplied to customers.
6130:
4732:
4514:
3343:(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.
3137:
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
468:
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
4885:
617:
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
4245:
In Europe, there still exist many installations with older colors but, since the early 1970s, all new installations use green/yellow earth according to
3598:
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
4271:
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
4114:
3322:
263:
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
954:
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
6151:
2979:
A delta configuration and a corresponding phasor diagram of its currents. Phase voltages are equal to line voltages, and currents are calculated as
715:(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%).
657:
A delta-wye configuration across a transformer core (note that a practical transformer would usually have a different number of turns on each side)
4708:
4600:
105:
because it uses less conductor material to transmit a given amount of electrical power. Three-phase power is mainly used directly to power large
4859:
5219:
407:
wire. The neutral allows three separate single-phase supplies to be provided at a constant voltage and is commonly used for supplying multiple
3230:, however, LN load is imposed on one phase. A transformer manufacturer's page suggests that LN loading not exceed 5% of transformer capacity.
3527:) the current in the individual phases, so the common conductor must be larger. Two-phase and three-phase systems can be interconnected by a
4943:
313:, current, and power is offset from the others' by 120°, thus having all at equidistance. This symmetry can also be recreated in converters.
5892:
3121:, 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.
86:
Three-phase electrical power was developed in the 1880s by several people. In three-phase power, the voltage on each wire is 120 degrees
6320:
6313:
464:
with a specified direction and constant magnitude, which simplifies the design of electric motors, as no starting circuit is required.
4124:
4119:
3106:. As a delta configuration connects a load across phases of a transformer, it delivers the line-to-line voltage difference, which is
1271:
The phase angle difference between voltage and current of each phase is not necessarily 0 and depends on the type of load impedance,
236:
31:
4969:
411:
loads. The connections are arranged so that, as far as possible in each group, equal power is drawn from each phase. Further up the
113:
and other heavy loads. Small loads often use only a two-wire single-phase circuit, which may be derived from a three-phase system.
3494:
Used when three-phase power is not available and allows double the normal utilization voltage to be supplied for high-power loads.
5042:
4231:
The international standard green-yellow marking of protective-earth conductors was introduced to reduce the risk of confusion by
3309:
430:
of phases is required if two sources could be connected at the same time. A direct connection between two different phases is a
6102:
5983:
4134:
6137:
5137:
5113:
4919:
4779:
4640:
4539:
4473:
4338:
3152:
6209:
5950:
5367:
731:
In a balanced system each line will produce equal voltage magnitudes at phase angles equally spaced from each other. With V
457:
Power transfer into a linear balanced load is constant, which, in motor/generator applications, helps to reduce vibrations.
329:
Three-phase transformer (Békéscsaba, Hungary): On the left are the primary wires, and on the right are the secondary wires.
48:
Three-phase transformer with four-wire output for 208Y/120 volt service: one wire for neutral, others for A, B and C phases
239:, where Dolivo-Dobrovolsky used the system to transmit electric power at the distance of 176 km (110 miles) with 75%
6377:
5789:
3113:
times greater than the line-to-neutral voltage delivered to a load in the wye configuration. As the power transferred is
642:
present above many transmission lines, which is solely for fault protection and does not carry current under normal use.
4739:
3441:(flywheel effect) of the rotating components. An external flywheel is sometimes found on one or both ends of the shaft.
1372:(KCL) to the neutral node, the three phase currents sum to the total current in the neutral line. In the balanced case:
947:
274:
fall at Hällsjön, Smedjebackens kommun, where a small iron work had been located, was selected. In 1893, a three-phase
145:. For example, for a 208/120-volt service, the line voltage is 208 volts, and the phase voltage is 120 volts.
5897:
5212:
4795:
1378:
90:
relative to each of the other wires. Because it is an AC system, it allows the voltages to be easily stepped up using
6291:
6243:
6173:
5517:
4695:
4497:
4413:
4391:
4370:
4288:
which result in one ungrounded leg having a higher voltage potential to ground than the other two ungrounded legs.
6367:
6183:
6065:
5680:
5605:
5476:
3829:
UK (before April 2006), Hong Kong (before April 2009), South Africa, Malaysia, Singapore (before
February 2011)
79:
employing three wires (or four including an optional neutral return wire) and is the most common method used by
5063:
354:
6382:
6224:
5852:
5784:
5774:
5650:
5550:
5205:
3350:
or space heating may be connected to three-phase systems. Electric lighting may also be similarly connected.
195:
Three phase power evolved out of electric motor development. In 1885, Galileo Ferraris was doing research on
479:
In Europe, three-phase power is normally delivered to the panelboard and further to higher powered devices.
6219:
6204:
6144:
6008:
5705:
5665:
5242:
3446:
488:
5932:
5927:
5645:
5620:
5610:
5586:
5581:
5287:
3580:
3568:(HVDC) converter at each end of the line. However, they require correspondingly more pieces of equipment.
3565:
3532:
3464:
576:
412:
408:
98:
72:
68:
17:
3467:
use power electronic devices to synthesize a balanced three-phase supply from single-phase input power.
6372:
6235:
6060:
6035:
5976:
5847:
5535:
5312:
3489:
3305:
1369:
469:
161:
38:
4879:"Harmonics in Low Voltage Three-Phase Four-Wire Electric Distribution Systems and Filtering Solutions"
4607:
449:
Three-phase supplies have properties that make them desirable in electric power distribution systems:
6055:
5902:
5391:
5352:
4863:
3550:
515:
506:
252:
232:
1463:
In the delta circuit, loads are connected across the lines, and so loads see line-to-line voltages:
191:
developed by Italian physicist Galileo Ferraris. This was a two-phase motor and required four wires.
6229:
5877:
5685:
5625:
5282:
4586:
4572:
3497:
3460:
442:
As compared to a single-phase AC power supply that uses two current-carrying conductors (phase and
347:
and generate other phase arrangements using transformers (for instance, a two-phase system using a
4657:
6362:
6214:
5816:
5806:
5796:
5078:
3593:
3506:
550:
forms offset to provide three complementary currents with a phase separation of one-third cycle (
461:
196:
27:
Common electrical power generation, transmission and distribution method for alternating currents
6306:
5737:
5600:
5383:
5272:
4590:, Theo. Audel and Co., 2nd ed., 1917, vol. 4, Ch. 46: Alternating Currents, p. 1026, fig. 1261.
4576:, Theo. Audel and Co., 2nd ed., 1917, vol. 4, Ch. 46: Alternating Currents, p. 1026, fig. 1260.
4129:
3429:
3406:
3289:
153:
64:
4825:"The 3rd Harmonic Blocking Filter: A Well Established Approach to Harmonic Current Mitigation"
3780:
March 2004), Hong Kong (from July 2007), Singapore (from March 2009), Russia (since 2009; GOST
575:
At the power station, transformers change the voltage from generators to a level suitable for
6275:
6178:
6082:
5969:
5872:
5640:
5635:
5615:
3300:
With linear loads, the neutral only carries the current due to imbalance between the phases.
702:
wye (Y) – Delta (Δ) is used for step-down transformers, i.e., at the end of the transmission.
240:
183:
424:
403:
Three-phase systems may have a fourth wire, common in low-voltage distribution. This is the
5466:
5228:
4981:
3378:
3374:
536:
302:
228:
122:
4323:
2012 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES)
317:
8:
6259:
6251:
6199:
6168:
5837:
5670:
5570:
5545:
5498:
5307:
5297:
5262:
5130:
C22.1-15 – Canadian Electrical Code, Part I: Safety Standard for Electrical Installations
5106:
C22.1-15 – Canadian Electrical Code, Part I: Safety Standard for Electrical Installations
4997:
4884:. Texas A&M University Power Electronics and Power Quality Laboratory. Archived from
3528:
540:
348:
334:
244:
235:. His three-phase three-wire transmission system was displayed in 1891 in Germany at the
173:
94:
to high voltage for transmission and back down for distribution, giving high efficiency.
60:
4985:
1455:
97:
A three-wire three-phase circuit is usually more economical than an equivalent two-wire
6097:
5711:
5322:
5027:
4454:
Woodbank Communications Ltd.'s Electropaedia: "History of Batteries (and other things)"
4344:
3386:
3301:
618:
443:
404:
188:
3925:
Former USSR (Russia, Ukraine, Kazakhstan; before 2009), People's Republic of China (GB
941:
400:
generators and motors, two phases can result in a less smooth (pulsating) torque.
6387:
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6267:
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5742:
5347:
5174:
5133:
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4409:
4387:
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565:
306:
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256:
165:
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5752:
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5428:
5337:
5277:
5192:
5166:
5087:
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3546:
3138:
699:
Delta (Δ) – wye (Y) is used for step-up transformers, i.e., at generating stations,
629:
543:
157:
106:
76:
4158:
Many labelling systems exist for phases, some having additional meaning, such as:
4139:
2139:
is the phase shift for the first voltage, commonly taken to be 0°; in this case, Φ
600:
A single three-phase transformer can be used, or three single-phase transformers.
6283:
6045:
6030:
5842:
5801:
5779:
5660:
5630:
5595:
5555:
5357:
5076:
Brittain, J. E. (2007). "Electrical Engineering Hall of Fame: Charles F. Scott".
4937:"Sports Lighting – Design Considerations For The Beijing 2008 Olympic Games"
4769:
4630:
4319:"The analysis and development of controlled 3φ wavelet modulated AC-DC converter"
4232:
4222:
In Canada the high leg conductor in a high-leg delta system is always marked red.
3454:
3421:
248:
130:
110:
80:
585:
Most automotive alternators generate three-phase AC and rectify it to DC with a
285:
a distance of 15 km (10 miles), becoming the first commercial application.
6336:
5867:
5857:
5655:
5267:
4466:
Michael von Dolivo-Dobrowolsky und der Drehstrom. Geschichte der Elektrotechnik
4330:
4318:
4213:
etc. and are equally permitted for use in building wiring per AS/NZS 3000:2007.
3765:
3599:
3410:
3336:
3211:
3130:
1281:
748:
707:
682:
662:
344:
333:
In a symmetric three-phase power supply system, three conductors each carry an
200:
169:
126:
5091:
3788:
50462), Argentina, Ukraine, Belarus, Kazakhstan, South Korea (from Jan. 2021)
3327:
264:
6356:
6077:
6072:
5887:
5675:
5560:
5540:
5471:
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5418:
5302:
5257:
5178:
3554:
3536:
677:
532:
431:
216:
5170:
2975:
1459:
Three-phase AC generator connected as a wye source to a delta-connected load
6331:
6018:
5992:
5907:
5882:
5747:
5716:
5530:
5332:
4993:
3433:
3370:
586:
387:
The symmetric three-phase systems described here are simply referred to as
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by 120°. Calculating line currents by using KCL at each delta node gives
639:
325:
243:. In 1891 he also created a three-phase transformer and short-circuited (
91:
87:
4516:
Elektrifieringens utveckling i Sverige, en ekonomisk-geografisk översikt
653:
6341:
6050:
5695:
5690:
5503:
5486:
5342:
5197:
5132:(23rd ed.). Canadian Standards Association. 2015. Rule 24–208(c).
3340:
473:
282:
204:
4768:
J. Duncan Glover; Mulukutla S. Sarma; Thomas J. Overbye (April 2011).
4453:
293:
6040:
5411:
5406:
5292:
5252:
4970:"ACSL/Graphic Modeller Component Models for Electric Power Education"
4246:
3821:
3769:
3607:
3603:
3365:
638:
grounded. The three-wire and four-wire designations do not count the
551:
5058:
Steve Sentry, "Motor Control Fundamentals", Cengage Learning, 2012,
3425:
source to drive three-phase motors fed through an electronic drive.
5525:
5108:(23rd ed.). Canadian Standards Association. 2015. Rule 4–038.
711:
each of the top and bottom taps (phase and anti-phase) is 120
665:
may supply one phase and neutral at a high current (up to 100
298:
277:
4801:. Utility Technology Engineers-Consultants (UTEC). August 10, 2015
4279:
V (wye or delta) conductors as brown, orange, yellow. In a 120/240
3579:
which permits transmission wires to be lighter and cheaper and so
3393:
696:
Delta (Δ) – Delta (Δ) is used for large currents and low voltages,
396:
current in any phase conductor is the other two phase conductors.
5446:
5436:
5011:"British and European practices for domestic appliances compared"
3761:
3438:
3397:
670:
351:). The amplitude of the voltage difference between two phases is
339:
310:
203:. The research and his studies resulted in the development of an
134:
102:
4534:. Hoboken, New Jersey: John Wiley & Sons, Inc. p. 160.
933:
These voltages feed into either a wye- or delta-connected load.
5961:
5441:
3347:
3304:
and devices that utilize rectifier-capacitor front-end such as
666:
493:
3432:
is a three-phase motor with special starting arrangements and
141:. The voltage measured between any line and neutral is called
6112:
4658:"Three-Phase Power from Single-Phase Transformer Connections"
3203:
transformer will use the transformer capacity inefficiently.
693:
wye (Y) – wye (Y) is used for small current and high voltage,
569:
384:
times the amplitude of the voltage of the individual phases.
270:
208:
199:. Ferraris experimented with different types of asynchronous
30:
For a greater focus on the mathematics of this subject, see
5396:
4408:. Clifton Park, NY: Delmar, Cengage Learning. p. 411.
712:
547:
260:
4733:"Saving energy through load balancing and load scheduling"
3688:
Green/yellow-striped (installations prior to 1966: green)
3535:. Very early AC machines, notably the first generators at
3331:
Three-phase electric machine with rotating magnetic fields
6131:
The Inventions, Researches, and Writings of Nikola Tesla
3545:
An asymmetrical modified two-phase power system used by
5157:
Neidhofer, Gerhard (2007). "Early Three-Phase Power ".
4468:
VDE-Buchreihe, Volume 9, VDE VERLAG, Berlin Offenbach,
4275:
V (wye) conductors as black, red, and blue, and 277/480
3192:{\displaystyle V_{\text{LL}}={\sqrt {3}}V_{\text{LN}}.}
4968:
Pekarek, Steven; Skvarenina, Timothy (November 1998).
4487:
755:
the voltage between the line and the neutral we have:
4910:
Alexander, Charles K.; Sadiku, Matthew N. O. (2007).
3509:
3155:
2690:
2479:
2159:
1472:
1381:
963:
764:
357:
231:
and a three-phase electric motor in 1888 and studied
1299:
represents a phase voltage. Voltages are balanced as
624:
4849:
The boy electrician by J. W. Sims M.I.E.E. (p. 98).
3602:. Colors used may adhere to International Standard
1285:A phasor diagram for a wye configuration, in which
227:Mikhail Dolivo-Dobrovolsky developed a three-phase
6031:Alternating-current commutatorless induction motor
4763:
4761:
4759:
3519:
3353:Line frequency flicker in light is detrimental to
3191:
2950:
2670:
2424:
2124:
1439:
1218:
922:
376:
4967:
4115:Industrial and multiphase power plugs and sockets
3323:Industrial and multiphase power plugs and sockets
1440:{\displaystyle I_{1}+I_{2}+I_{3}=I_{\text{N}}=0.}
6354:
6152:My Inventions: The Autobiography of Nikola Tesla
4064:Alternate Practices (Delta with tapped winding)
5069:
5028:"Speeding-up Conventional Lines and Shinkansen"
4909:
4756:
4363:Elements of Power System Analysis Third Edition
4094:Green or Yellow/green-striped or no insulation
3308:, computers, office equipment and such produce
437:
3723:Green, perhaps yellow-striped, or uninsulated
3483:
3400:used in the past on electric stoves in Germany
3335:An important class of three-phase load is the
3146:times the phase conductor to neutral voltage:
539:converts mechanical power into a set of three
482:
5977:
5213:
4562:, 6th ed., Pitman, London, 1950, p. 268.
4317:Saleh, S. A.; Rahman, M. A. (25 March 2013).
3856:Green/yellow-striped (before c. 1970: green)
661:For domestic use, some countries such as the
321:Three-phase electric power transmission lines
251:. He designed the world's first three-phase
4635:(2nd ed.). McGraw-Hill. pp. 3–5.
4316:
309:of the power system. Ideally, each phase's
6321:The Man Who Invented the Twentieth Century
6314:Wizard: The Life and Times of Nikola Tesla
5984:
5970:
5220:
5206:
4688:Standard Handbook for Electrical Engineers
3214:provides phase-to-neutral relationship of
719:either of the center-tapped phase points.
592:
5156:
4624:
4622:
4620:
4601:"A New Design for Automotive Alternators"
4529:
4512:
4384:American Electricians' Handbook, 11th ed.
4125:Mathematics of three-phase electric power
4120:International Electrotechnical Exhibition
3346:Resistive heating loads such as electric
434:and leads to flow of unbalanced current.
237:International Electrotechnical Exhibition
32:Mathematics of three-phase electric power
5227:
5075:
4928:
4403:
4208:
4206:
4204:
4202:
3392:
3326:
2974:
1454:
1280:
1236:is the sum of line and load impedances (
940:
676:
669:) to one property, while others such as
652:
633:Wye (Y) and delta (Δ) circuits
628:
492:
377:{\displaystyle {\sqrt {3}}=1.732\ldots }
324:
316:
292:
182:
43:
4818:
4816:
4297:Must be the high leg, if it is present.
3583:gives lower losses over long distances.
3292:is used to analyze unbalanced systems.
14:
6355:
6103:Tesla Electric Light and Manufacturing
4914:. New York: McGraw-Hill. p. 504.
4822:
4628:
4617:
4291:
4190:
4181:
4135:Three-phase AC railway electrification
3357:used in sports event broadcasting for
5965:
5201:
4655:
4649:
4488:Bergström och Nordlund, Lars (2002).
4382:Terrell Croft, Wilford Summers (ed),
4265:
4256:
4239:
4225:
4216:
4199:
4152:
3776:60445-2017), United Kingdom (since 31
3626:
3621:
3615:
3124:
1261:is the phase of the total impedance (
214:Two months later Nikola Tesla gained
6210:Tesla Science Center at Wardenclyffe
5035:Japan Railway & Transport Review
4813:
4774:. Cengage Learning. pp. 60–68.
4196:Also, earth, or grounding conductor.
3594:Electrical wiring § Colour code
3316:
936:
722:
3416:
3295:
3283:
2681:and similarly for each other line:
101:circuit at the same line-to-ground
24:
6111:
5898:Renewable energy commercialization
5150:
4876:
4771:Power System Analysis & Design
3993:
3668:
3385:, and for operation of DC motors.
2916:
2857:
2788:
2729:
2649:
2590:
2550:
2449:Relative angles are preserved, so
2390:
2377:
2302:
2289:
2217:
2204:
2076:
2043:
2000:
1968:
1866:
1828:
1785:
1748:
1646:
1613:
1565:
1533:
1184:
1096:
1021:
895:
843:
796:
460:Three-phase systems can produce a
25:
6399:
6138:Colorado Springs Notes, 1899–1900
5186:
4912:Fundamentals of Electric Circuits
4632:Electrician's Calculations Manual
4606:. August 30, 2017. Archived from
4490:Ellära- Kretsteknik och fältteori
3965:Norway (before CENELEC adoption)
3645:Australia and New Zealand (AS/NZS
3067:The overall power transferred is
2965:is the phase of delta impedance (
2439:is the phase of delta impedance (
625:Three-wire and four-wire circuits
418:
5991:
5946:
5945:
5366:
5048:from the original on 2022-10-09.
4721:from the original on 2022-10-09.
4492:. Naturaläromedel. p. 283.
4365:, McGraw-Hill, New York (1975).
514:
505:
497:Animation of three-phase current
425:Electric machine § Sequence
281:system was used to transfer 400
137:between any two lines is called
5122:
5098:
5052:
5020:
5004:
4961:
4934:
4903:
4870:
4852:
4843:
4827:. IAEI Magazine. Archived from
4788:
4725:
4701:
4690:. 15th ed., McGraw-Hill, 2007,
4686:H. W. Beaty, D. G. Fink (ed.),
4680:
4656:Gibbs, J. B. (April 27, 1920).
4593:
4579:
4565:
4552:
4523:
4430:"AC Power History and Timeline"
4059:Bare Conductor (no insulation)
4029:Bare Conductor (no insulation)
1292:represents a line voltage, and
156:were independently invented by
6292:Nikola Tesla's Night of Terror
5159:IEEE Power and Energy Magazine
4974:IEEE Transactions on Education
4506:
4481:
4458:
4447:
4422:
4397:
4376:
4355:
4310:
3920:Green, perhaps yellow-striped
3888:Green, perhaps yellow-striped
3768:and others; since April 2004,
3657:60446 as approved by AS:3000)
3587:
2938:
2919:
2893:
2860:
2813:
2791:
2765:
2732:
2661:
2652:
2626:
2593:
2412:
2393:
2383:
2368:
2327:
2305:
2295:
2280:
2239:
2220:
2210:
2195:
2112:
2079:
2013:
1987:
1981:
1955:
1902:
1869:
1798:
1772:
1766:
1735:
1682:
1649:
1583:
1552:
1546:
1520:
1206:
1187:
1177:
1162:
1121:
1099:
1089:
1074:
1033:
1024:
1014:
999:
116:
13:
1:
6244:Tesla – Lightning in His Hand
6225:Belgrade Nikola Tesla Airport
5893:Renewable Energy Certificates
5853:Cost of electricity by source
5775:Arc-fault circuit interrupter
5651:High-voltage shore connection
5193:AC Power History and Timeline
4942:. GE Lighting. Archived from
4530:von Meier, Alexandra (2006).
4303:
3755:Green perhaps yellow-striped
579:in order to minimize losses.
83:worldwide to transfer power.
6205:Nikola Tesla Memorial Center
6145:Fragments of Olympian Gossip
5908:Spark/Dark/Quark/Bark spread
5706:Transmission system operator
5666:Mains electricity by country
5243:Automatic generation control
3447:uninterruptible power supply
1450:
572:, depending on the country.
489:Mains electricity by country
438:Advantages and disadvantages
288:
7:
6066:Resonant inductive coupling
5933:List of electricity sectors
5928:Electric energy consumption
5646:High-voltage direct current
5621:Electric power transmission
5611:Electric power distribution
5288:Energy return on investment
5017:, volume 148, p. 691, 1965.
4107:
3581:high-voltage direct current
3566:high-voltage direct current
3549:around 1897, championed by
3520:{\displaystyle {\sqrt {2}}}
3484:Alternatives to three-phase
483:Generation and distribution
305:of the generator sets the
10:
6404:
6378:Inventions by Nikola Tesla
6236:The Secret of Nikola Tesla
6093:Three-phase electric power
6036:Tesla Experimental Station
5848:Carbon offsets and credits
5566:Three-phase electric power
4796:"What is "Stray Voltage"?"
4404:Brumbach, Michael (2014).
4361:William D. Stevenson, Jr.
4331:10.1109/PEDES.2012.6484282
3591:
3490:Split-phase electric power
3470:
3320:
3306:switch-mode power supplies
486:
422:
233:star and delta connections
162:Mikhail Dolivo-Dobrovolsky
148:
133:are called lines, and the
53:Three-phase electric power
39:Split-phase electric power
36:
29:
6192:
6161:
6122:
6109:
5999:
5941:
5916:
5903:Renewable Energy Payments
5826:
5763:
5725:
5579:
5516:
5427:
5392:Fossil fuel power station
5382:
5375:
5364:
5235:
5092:10.1109/JPROC.2006.892488
4513:Hjulström, Filip (1940).
4283:V delta system with a 208
4187:Also, grounded conductor.
4093:
4091:
4089:
4086:
4084:
4073:
4071:
4068:
4066:
4063:
4056:
4026:
4000:
3964:
3924:
3892:
3860:
3828:
3820:Older European (prior to
3819:
3759:
3692:
3644:
3639:
3636:
3633:
3618:
3551:Charles Proteus Steinmetz
3461:Variable-frequency drives
253:hydroelectric power plant
5686:Single-wire earth return
5626:Electrical busbar system
5283:Energy demand management
4587:Hawkins Electrical Guide
4573:Hawkins Electrical Guide
4146:
3560:High-phase-order systems
3498:Two-phase electric power
3465:digital phase converters
197:rotating magnetic fields
37:Not to be confused with
6215:IEEE Nikola Tesla Award
5817:Residual-current device
5807:Power system protection
5797:Generator interlock kit
5171:10.1109/MPE.2007.904752
5079:Proceedings of the IEEE
3405:the domestic field are
1370:Kirchhoff's current law
593:Transformer connections
462:rotating magnetic field
154:Polyphase power systems
6368:Electrical engineering
6307:Tesla: Man Out of Time
6116:
5601:Distributed generation
5273:Electric power quality
4994:10.1109/TE.1998.787374
4668:(17). McGraw-Hill: 673
4532:Electric Power Systems
4406:Industrial maintenance
4394:page 3-10 figure 3-23.
4130:Rotary phase converter
3996:yellow or uninsulated
3992:Yellow/green-striped;
3521:
3430:rotary phase converter
3407:tankless water heating
3401:
3332:
3290:symmetrical components
3270:was set as 100%, then
3193:
3095:
2952:
2672:
2426:
2126:
1460:
1441:
1365:
1364:(α = 0 in this case).
1220:
951:
924:
735:as our reference and V
686:
658:
634:
568:is typically 50 or 60
498:
378:
338:phase difference, the
330:
322:
314:
192:
65:electricity generation
59:) is a common type of
49:
6276:The Tesla World Light
6220:Tesla Satellite Award
6179:World Wireless System
6174:Westinghouse Electric
6115:
5873:Fossil fuel phase-out
5641:Electricity retailing
5636:Electrical substation
5616:Electric power system
4823:Lowenstein, Michael.
4629:Fowler, Nick (2011).
4560:Electrical Technology
3960:Green/yellow-striped
3824:, varied by country)
3815:Green/yellow-striped
3522:
3396:
3330:
3310:third-order harmonics
3194:
2978:
2953:
2673:
2427:
2127:
1458:
1442:
1309:= (1∠α − 1∠α + 120°)
1284:
1221:
948:stray ground voltages
944:
925:
681:A transformer for a "
680:
656:
632:
496:
379:
328:
320:
296:
186:
47:
6383:Three-phase AC power
5229:Electricity delivery
4386:, McGraw Hill, 1987
3507:
3379:electric arc furnace
3375:aluminium production
3259:≈ 100% × 1.73 = 173%
3153:
2688:
2477:
2157:
1470:
1379:
961:
762:
706:In North America, a
537:electrical generator
355:
303:rotational frequency
229:electrical generator
6294:" (2020 TV episode)
6260:Tower to the People
6200:Nikola Tesla Museum
6169:War of the currents
5838:Availability factor
5790:Sulfur hexafluoride
5671:Overhead power line
5571:Virtual power plant
5546:Induction generator
5499:Sustainable biofuel
5308:Home energy storage
5298:Grid energy storage
5263:Droop speed control
4986:1998ITEdu..41..348P
4831:on 8 September 2013
4464:Gerhard Neidhöfer:
4004:120, 208, or 240 V
3893:Chile – NCH 4/2003
3676:Dark blue, or grey
3529:Scott-T transformer
3387:Zigzag transformers
3302:Gas-discharge lamps
566:generator frequency
413:distribution system
389:three-phase systems
349:Scott-T transformer
335:alternating current
217:U.S. patent 381,968
180:in the late 1880s.
174:William Stanley Jr.
61:alternating current
6263:(2015 documentary)
6184:In popular culture
6117:
6098:Wardenclyffe Tower
6083:Tesla's oscillator
5712:Transmission tower
5323:Nameplate capacity
4434:Edison Tech Center
3929:50303-2002 Section
3627:Protective earth,
3517:
3402:
3373:processes such as
3355:high-speed cameras
3333:
3189:
3125:Single-phase loads
3096:
2948:
2946:
2668:
2666:
2422:
2420:
2147:= −240° or 120°.)
2122:
2120:
1461:
1437:
1366:
1216:
1214:
952:
920:
918:
687:
659:
635:
619:zigzag transformer
499:
470:split-phase system
374:
331:
323:
315:
255:in 1891. Inventor
193:
75:. It is a type of
50:
6373:Electrical wiring
6350:
6349:
5959:
5958:
5863:Environmental tax
5743:Cascading failure
5512:
5511:
5348:Utility frequency
5139:978-1-77139-718-6
5115:978-1-77139-718-6
5000:on June 26, 2003.
4921:978-0-07-297718-9
4860:"Federal pacific"
4781:978-1-111-42579-1
4698:, pp. 10–11.
4642:978-0-07-177017-0
4541:978-0-471-17859-0
4474:978-3-8007-3115-2
4340:978-1-4673-4508-8
4105:
4104:
3728:Isolated systems
3515:
3317:Three-phase loads
3240:≈ 1.73, defining
3183:
3174:
3163:
2904:
2845:
2776:
2717:
2637:
2578:
2388:
2300:
2215:
2064:
2040:
2031:
1997:
1965:
1854:
1825:
1816:
1782:
1745:
1634:
1610:
1601:
1562:
1530:
1428:
1182:
1173:
1094:
1085:
1019:
1010:
937:Wye (or, star; Y)
892:
840:
793:
723:Balanced circuits
544:electric currents
363:
16:(Redirected from
6395:
6230:New Yorker Hotel
6026:Polyphase system
5986:
5979:
5972:
5963:
5962:
5949:
5948:
5858:Energy subsidies
5812:Protective relay
5753:Rolling blackout
5380:
5379:
5370:
5338:Power-flow study
5278:Electrical fault
5222:
5215:
5208:
5199:
5198:
5182:
5144:
5143:
5126:
5120:
5119:
5102:
5096:
5095:
5073:
5067:
5056:
5050:
5049:
5047:
5041:: 58. Oct 2011.
5032:
5024:
5018:
5015:Electrical Times
5008:
5002:
5001:
4996:. Archived from
4965:
4959:
4958:
4956:
4954:
4949:on 28 April 2015
4948:
4941:
4932:
4926:
4925:
4907:
4901:
4900:
4898:
4896:
4890:
4883:
4877:Enjeti, Prasad.
4874:
4868:
4867:
4866:on May 30, 2012.
4862:. Archived from
4856:
4850:
4847:
4841:
4840:
4838:
4836:
4820:
4811:
4810:
4808:
4806:
4800:
4792:
4786:
4785:
4765:
4754:
4753:
4751:
4750:
4744:
4738:. Archived from
4737:
4729:
4723:
4722:
4720:
4713:
4705:
4699:
4684:
4678:
4677:
4675:
4673:
4653:
4647:
4646:
4626:
4615:
4614:
4612:
4605:
4597:
4591:
4583:
4577:
4569:
4563:
4556:
4550:
4549:
4527:
4521:
4520:
4510:
4504:
4503:
4485:
4479:
4462:
4456:
4451:
4445:
4444:
4442:
4440:
4426:
4420:
4419:
4401:
4395:
4380:
4374:
4359:
4353:
4352:
4325:. pp. 1–6.
4314:
4298:
4295:
4289:
4286:
4282:
4278:
4274:
4269:
4263:
4260:
4254:
4250:
4243:
4237:
4229:
4223:
4220:
4214:
4210:
4197:
4194:
4188:
4185:
4179:
4177:
4173:
4169:
4165:
4161:
4156:
3995:
3932:
3928:
3787:
3783:
3779:
3775:
3670:
3656:
3652:
3649:3000:2007 Figure
3648:
3613:
3612:
3547:General Electric
3542:Monocyclic power
3533:Charles F. Scott
3526:
3524:
3523:
3518:
3516:
3511:
3455:autotransformers
3422:Phase converters
3417:Phase converters
3398:Three-phase plug
3296:Non-linear loads
3284:Unbalanced loads
3279:
3269:
3260:
3257:
3248:
3239:
3238:
3229:
3198:
3196:
3195:
3190:
3185:
3184:
3181:
3175:
3170:
3165:
3164:
3161:
3144:
3143:
3112:
3111:
3105:
3104:
3009:
3008:
2957:
2955:
2954:
2949:
2947:
2931:
2930:
2915:
2914:
2905:
2900:
2892:
2891:
2879:
2878:
2877:
2876:
2856:
2855:
2846:
2841:
2832:
2831:
2806:
2805:
2787:
2786:
2777:
2772:
2764:
2763:
2751:
2750:
2749:
2748:
2728:
2727:
2718:
2713:
2704:
2703:
2677:
2675:
2674:
2669:
2667:
2648:
2647:
2638:
2633:
2625:
2624:
2612:
2611:
2610:
2609:
2589:
2588:
2579:
2574:
2566:
2562:
2561:
2549:
2548:
2536:
2535:
2523:
2522:
2510:
2509:
2493:
2492:
2431:
2429:
2428:
2423:
2421:
2405:
2404:
2389:
2387:
2386:
2381:
2380:
2371:
2365:
2364:
2355:
2346:
2345:
2320:
2319:
2301:
2299:
2298:
2293:
2292:
2283:
2277:
2276:
2267:
2258:
2257:
2232:
2231:
2216:
2214:
2213:
2208:
2207:
2198:
2192:
2191:
2182:
2173:
2172:
2131:
2129:
2128:
2123:
2121:
2111:
2110:
2098:
2097:
2096:
2095:
2075:
2074:
2065:
2060:
2055:
2054:
2042:
2041:
2038:
2032:
2027:
2019:
2012:
2011:
1999:
1998:
1995:
1980:
1979:
1967:
1966:
1963:
1951:
1950:
1938:
1937:
1921:
1920:
1901:
1900:
1888:
1887:
1886:
1885:
1865:
1864:
1855:
1850:
1845:
1844:
1839:
1827:
1826:
1823:
1817:
1812:
1804:
1797:
1796:
1784:
1783:
1780:
1765:
1764:
1759:
1747:
1746:
1743:
1731:
1730:
1718:
1717:
1701:
1700:
1681:
1680:
1668:
1667:
1666:
1665:
1645:
1644:
1635:
1630:
1625:
1624:
1612:
1611:
1608:
1602:
1597:
1589:
1582:
1581:
1576:
1564:
1563:
1560:
1545:
1544:
1532:
1531:
1528:
1516:
1515:
1503:
1502:
1486:
1485:
1446:
1444:
1443:
1438:
1430:
1429:
1426:
1417:
1416:
1404:
1403:
1391:
1390:
1355:
1354:
1335:
1334:
1315:
1314:
1225:
1223:
1222:
1217:
1215:
1199:
1198:
1183:
1181:
1180:
1175:
1174:
1171:
1165:
1159:
1158:
1149:
1140:
1139:
1114:
1113:
1095:
1093:
1092:
1087:
1086:
1083:
1077:
1071:
1070:
1061:
1052:
1051:
1020:
1018:
1017:
1012:
1011:
1008:
1002:
996:
995:
986:
977:
976:
929:
927:
926:
921:
919:
912:
911:
906:
894:
893:
890:
877:
876:
860:
859:
854:
842:
841:
838:
825:
824:
808:
807:
795:
794:
791:
778:
777:
613:
612:
608:
561:
560:
556:
518:
509:
383:
381:
380:
375:
364:
359:
280:
273:
219:
158:Galileo Ferraris
107:induction motors
81:electrical grids
77:polyphase system
21:
6403:
6402:
6398:
6397:
6396:
6394:
6393:
6392:
6353:
6352:
6351:
6346:
6332:SI derived unit
6284:The Current War
6188:
6157:
6118:
6107:
6046:Telegeodynamics
6001:
5995:
5990:
5960:
5955:
5937:
5921:
5919:
5912:
5843:Capacity factor
5831:
5829:
5822:
5802:Numerical relay
5780:Circuit breaker
5768:
5766:
5759:
5721:
5661:Load management
5631:Electrical grid
5596:Demand response
5589:
5584:
5575:
5556:Microgeneration
5508:
5423:
5371:
5362:
5358:Vehicle-to-grid
5231:
5226:
5189:
5153:
5151:Further reading
5148:
5147:
5140:
5128:
5127:
5123:
5116:
5104:
5103:
5099:
5074:
5070:
5057:
5053:
5045:
5030:
5026:
5025:
5021:
5009:
5005:
4966:
4962:
4952:
4950:
4946:
4939:
4933:
4929:
4922:
4908:
4904:
4894:
4892:
4891:on 13 June 2010
4888:
4881:
4875:
4871:
4858:
4857:
4853:
4848:
4844:
4834:
4832:
4821:
4814:
4804:
4802:
4798:
4794:
4793:
4789:
4782:
4766:
4757:
4748:
4746:
4742:
4735:
4731:
4730:
4726:
4718:
4711:
4707:
4706:
4702:
4685:
4681:
4671:
4669:
4654:
4650:
4643:
4627:
4618:
4610:
4603:
4599:
4598:
4594:
4584:
4580:
4570:
4566:
4557:
4553:
4542:
4528:
4524:
4511:
4507:
4500:
4486:
4482:
4463:
4459:
4452:
4448:
4438:
4436:
4428:
4427:
4423:
4416:
4402:
4398:
4381:
4377:
4360:
4356:
4341:
4315:
4311:
4306:
4301:
4296:
4292:
4284:
4280:
4276:
4272:
4270:
4266:
4261:
4257:
4248:
4244:
4240:
4230:
4226:
4221:
4217:
4211:
4200:
4195:
4191:
4186:
4182:
4175:
4171:
4167:
4163:
4159:
4157:
4153:
4149:
4144:
4110:
3930:
3926:
3785:
3781:
3777:
3773:
3748:White, or grey
3716:White, or grey
3681:Black, or blue
3654:
3650:
3646:
3628:
3623:
3596:
3590:
3510:
3508:
3505:
3504:
3486:
3473:
3453:Capacitors and
3419:
3411:storage heaters
3325:
3319:
3298:
3286:
3277:
3271:
3268:
3262:
3258:
3256:
3250:
3247:
3241:
3236:
3234:
3228:
3221:
3215:
3180:
3176:
3169:
3160:
3156:
3154:
3151:
3150:
3141:
3139:
3127:
3109:
3107:
3102:
3100:
3094:
3090:
3083:
3076:
3066:
3062:
3055:
3048:
3039:
3032:
3025:
3016:
3006:
3004:
3002:
2995:
2988:
2971:
2945:
2944:
2926:
2922:
2910:
2906:
2899:
2887:
2883:
2872:
2868:
2867:
2863:
2851:
2847:
2840:
2833:
2827:
2823:
2820:
2819:
2801:
2797:
2782:
2778:
2771:
2759:
2755:
2744:
2740:
2739:
2735:
2723:
2719:
2712:
2705:
2699:
2695:
2691:
2689:
2686:
2685:
2665:
2664:
2643:
2639:
2632:
2620:
2616:
2605:
2601:
2600:
2596:
2584:
2580:
2573:
2564:
2563:
2557:
2553:
2544:
2540:
2531:
2527:
2518:
2514:
2505:
2501:
2494:
2488:
2484:
2480:
2478:
2475:
2474:
2469:
2462:
2455:
2445:
2419:
2418:
2400:
2396:
2382:
2376:
2372:
2367:
2366:
2360:
2356:
2354:
2347:
2341:
2337:
2334:
2333:
2315:
2311:
2294:
2288:
2284:
2279:
2278:
2272:
2268:
2266:
2259:
2253:
2249:
2246:
2245:
2227:
2223:
2209:
2203:
2199:
2194:
2193:
2187:
2183:
2181:
2174:
2168:
2164:
2160:
2158:
2155:
2154:
2146:
2142:
2138:
2119:
2118:
2106:
2102:
2091:
2087:
2086:
2082:
2070:
2066:
2059:
2050:
2046:
2037:
2033:
2026:
2017:
2016:
2007:
2003:
1994:
1990:
1975:
1971:
1962:
1958:
1946:
1942:
1933:
1929:
1922:
1916:
1912:
1909:
1908:
1896:
1892:
1881:
1877:
1876:
1872:
1860:
1856:
1849:
1840:
1832:
1831:
1822:
1818:
1811:
1802:
1801:
1792:
1788:
1779:
1775:
1760:
1752:
1751:
1742:
1738:
1726:
1722:
1713:
1709:
1702:
1696:
1692:
1689:
1688:
1676:
1672:
1661:
1657:
1656:
1652:
1640:
1636:
1629:
1620:
1616:
1607:
1603:
1596:
1587:
1586:
1577:
1569:
1568:
1559:
1555:
1540:
1536:
1527:
1523:
1511:
1507:
1498:
1494:
1487:
1481:
1477:
1473:
1471:
1468:
1467:
1453:
1425:
1421:
1412:
1408:
1399:
1395:
1386:
1382:
1380:
1377:
1376:
1363:
1360:|∠α + 150°
1352:
1350:
1348:
1340:|∠α − 90°,
1332:
1330:
1328:
1320:|∠α + 30°,
1312:
1310:
1308:
1298:
1291:
1277:
1267:
1256:
1249:
1242:
1235:
1213:
1212:
1194:
1190:
1176:
1170:
1166:
1161:
1160:
1154:
1150:
1148:
1141:
1135:
1131:
1128:
1127:
1109:
1105:
1088:
1082:
1078:
1073:
1072:
1066:
1062:
1060:
1053:
1047:
1043:
1040:
1039:
1013:
1007:
1003:
998:
997:
991:
987:
985:
978:
972:
968:
964:
962:
959:
958:
939:
917:
916:
907:
899:
898:
889:
885:
878:
872:
868:
865:
864:
855:
847:
846:
837:
833:
826:
820:
816:
813:
812:
803:
799:
790:
786:
779:
773:
769:
765:
763:
760:
759:
754:
746:
742:
738:
734:
725:
627:
610:
606:
605:
595:
558:
554:
553:
529:
528:
527:
526:
521:
520:
519:
511:
510:
491:
485:
440:
427:
421:
358:
356:
353:
352:
291:
275:
268:
249:induction motor
215:
201:electric motors
151:
119:
111:electric motors
42:
35:
28:
23:
22:
15:
12:
11:
5:
6401:
6391:
6390:
6385:
6380:
6375:
6370:
6365:
6363:Electric power
6348:
6347:
6345:
6344:
6339:
6334:
6329:
6324:
6317:
6310:
6303:
6295:
6288:
6280:
6272:
6264:
6256:
6248:
6240:
6232:
6227:
6222:
6217:
6212:
6207:
6202:
6196:
6194:
6190:
6189:
6187:
6186:
6181:
6176:
6171:
6165:
6163:
6159:
6158:
6156:
6155:
6148:
6141:
6134:
6126:
6124:
6120:
6119:
6110:
6108:
6106:
6105:
6100:
6095:
6090:
6085:
6080:
6075:
6070:
6069:
6068:
6063:
6061:Wireless power
6058:
6048:
6043:
6038:
6033:
6028:
6023:
6022:
6021:
6011:
6005:
6003:
5997:
5996:
5989:
5988:
5981:
5974:
5966:
5957:
5956:
5954:
5953:
5942:
5939:
5938:
5936:
5935:
5930:
5924:
5922:
5918:Statistics and
5917:
5914:
5913:
5911:
5910:
5905:
5900:
5895:
5890:
5885:
5880:
5875:
5870:
5868:Feed-in tariff
5865:
5860:
5855:
5850:
5845:
5840:
5834:
5832:
5827:
5824:
5823:
5821:
5820:
5814:
5809:
5804:
5799:
5794:
5793:
5792:
5787:
5777:
5771:
5769:
5764:
5761:
5760:
5758:
5757:
5756:
5755:
5745:
5740:
5735:
5729:
5727:
5723:
5722:
5720:
5719:
5714:
5709:
5703:
5698:
5693:
5688:
5683:
5678:
5673:
5668:
5663:
5658:
5656:Interconnector
5653:
5648:
5643:
5638:
5633:
5628:
5623:
5618:
5613:
5608:
5606:Dynamic demand
5603:
5598:
5592:
5590:
5580:
5577:
5576:
5574:
5573:
5568:
5563:
5558:
5553:
5548:
5543:
5538:
5536:Combined cycle
5533:
5528:
5522:
5520:
5514:
5513:
5510:
5509:
5507:
5506:
5501:
5496:
5491:
5490:
5489:
5484:
5479:
5474:
5469:
5459:
5454:
5449:
5444:
5439:
5433:
5431:
5425:
5424:
5422:
5421:
5416:
5415:
5414:
5409:
5404:
5399:
5388:
5386:
5377:
5373:
5372:
5365:
5363:
5361:
5360:
5355:
5350:
5345:
5340:
5335:
5330:
5325:
5320:
5315:
5313:Load-following
5310:
5305:
5300:
5295:
5290:
5285:
5280:
5275:
5270:
5268:Electric power
5265:
5260:
5255:
5250:
5245:
5239:
5237:
5233:
5232:
5225:
5224:
5217:
5210:
5202:
5196:
5195:
5188:
5187:External links
5185:
5184:
5183:
5152:
5149:
5146:
5145:
5138:
5121:
5114:
5097:
5086:(4): 836–839.
5068:
5051:
5019:
5003:
4960:
4927:
4920:
4902:
4869:
4851:
4842:
4812:
4787:
4780:
4755:
4724:
4700:
4679:
4648:
4641:
4616:
4613:on 2017-08-30.
4592:
4578:
4564:
4551:
4540:
4522:
4505:
4498:
4480:
4457:
4446:
4421:
4414:
4396:
4375:
4354:
4339:
4308:
4307:
4305:
4302:
4300:
4299:
4290:
4264:
4255:
4238:
4224:
4215:
4198:
4189:
4180:
4150:
4148:
4145:
4143:
4142:
4137:
4132:
4127:
4122:
4117:
4111:
4109:
4106:
4103:
4102:
4099:
4096:
4095:
4092:
4090:
4088:
4085:
4083:
4080:
4078:
4072:
4070:
4067:
4065:
4061:
4060:
4057:
4055:
4052:
4050:
4047:
4045:
4042:
4040:
4037:
4035:
4031:
4030:
4027:
4025:
4022:
4020:
4017:
4015:
4012:
4010:
4007:
4005:
4002:
4001:United States
3998:
3997:
3990:
3988:
3986:
3983:
3981:
3978:
3976:
3973:
3971:
3968:
3966:
3962:
3961:
3958:
3956:
3954:
3951:
3949:
3946:
3944:
3941:
3939:
3936:
3934:
3922:
3921:
3918:
3916:
3914:
3911:
3909:
3906:
3904:
3901:
3899:
3896:
3894:
3890:
3889:
3886:
3884:
3882:
3879:
3877:
3874:
3872:
3869:
3867:
3864:
3862:
3858:
3857:
3854:
3852:
3850:
3847:
3845:
3842:
3840:
3837:
3835:
3832:
3830:
3826:
3825:
3817:
3816:
3813:
3811:
3809:
3806:
3804:
3801:
3799:
3796:
3794:
3791:
3789:
3766:European Union
3757:
3756:
3753:
3751:
3749:
3746:
3744:
3741:
3739:
3736:
3734:
3731:
3729:
3725:
3724:
3721:
3719:
3717:
3714:
3712:
3709:
3707:
3704:
3702:
3699:
3697:
3694:
3690:
3689:
3686:
3684:
3682:
3679:
3677:
3674:
3672:
3665:
3663:
3662:Red, or brown
3660:
3658:
3642:
3641:
3638:
3635:
3631:
3630:
3625:
3620:
3617:
3589:
3586:
3585:
3584:
3572:
3569:
3561:
3558:
3543:
3540:
3531:, invented by
3514:
3500:
3495:
3492:
3485:
3482:
3472:
3469:
3418:
3415:
3337:electric motor
3318:
3315:
3297:
3294:
3285:
3282:
3275:
3266:
3254:
3249:as 100% gives
3245:
3226:
3219:
3212:high-leg delta
3200:
3199:
3188:
3179:
3173:
3168:
3159:
3134:transformers.
3131:high-leg delta
3126:
3123:
3093:
3092:
3088:
3081:
3074:
3068:
3065:
3064:
3060:
3053:
3046:
3041:
3037:
3030:
3023:
3018:
3014:
3000:
2993:
2986:
2980:
2969:
2961:where, again,
2959:
2958:
2943:
2940:
2937:
2934:
2929:
2925:
2921:
2918:
2913:
2909:
2903:
2898:
2895:
2890:
2886:
2882:
2875:
2871:
2866:
2862:
2859:
2854:
2850:
2844:
2839:
2836:
2834:
2830:
2826:
2822:
2821:
2818:
2815:
2812:
2809:
2804:
2800:
2796:
2793:
2790:
2785:
2781:
2775:
2770:
2767:
2762:
2758:
2754:
2747:
2743:
2738:
2734:
2731:
2726:
2722:
2716:
2711:
2708:
2706:
2702:
2698:
2694:
2693:
2679:
2678:
2663:
2660:
2657:
2654:
2651:
2646:
2642:
2636:
2631:
2628:
2623:
2619:
2615:
2608:
2604:
2599:
2595:
2592:
2587:
2583:
2577:
2572:
2569:
2567:
2565:
2560:
2556:
2552:
2547:
2543:
2539:
2534:
2530:
2526:
2521:
2517:
2513:
2508:
2504:
2500:
2497:
2495:
2491:
2487:
2483:
2482:
2467:
2460:
2453:
2443:
2433:
2432:
2417:
2414:
2411:
2408:
2403:
2399:
2395:
2392:
2385:
2379:
2375:
2370:
2363:
2359:
2353:
2350:
2348:
2344:
2340:
2336:
2335:
2332:
2329:
2326:
2323:
2318:
2314:
2310:
2307:
2304:
2297:
2291:
2287:
2282:
2275:
2271:
2265:
2262:
2260:
2256:
2252:
2248:
2247:
2244:
2241:
2238:
2235:
2230:
2226:
2222:
2219:
2212:
2206:
2202:
2197:
2190:
2186:
2180:
2177:
2175:
2171:
2167:
2163:
2162:
2144:
2140:
2136:
2133:
2132:
2117:
2114:
2109:
2105:
2101:
2094:
2090:
2085:
2081:
2078:
2073:
2069:
2063:
2058:
2053:
2049:
2045:
2036:
2030:
2025:
2022:
2020:
2018:
2015:
2010:
2006:
2002:
1993:
1989:
1986:
1983:
1978:
1974:
1970:
1961:
1957:
1954:
1949:
1945:
1941:
1936:
1932:
1928:
1925:
1923:
1919:
1915:
1911:
1910:
1907:
1904:
1899:
1895:
1891:
1884:
1880:
1875:
1871:
1868:
1863:
1859:
1853:
1848:
1843:
1838:
1835:
1830:
1821:
1815:
1810:
1807:
1805:
1803:
1800:
1795:
1791:
1787:
1778:
1774:
1771:
1768:
1763:
1758:
1755:
1750:
1741:
1737:
1734:
1729:
1725:
1721:
1716:
1712:
1708:
1705:
1703:
1699:
1695:
1691:
1690:
1687:
1684:
1679:
1675:
1671:
1664:
1660:
1655:
1651:
1648:
1643:
1639:
1633:
1628:
1623:
1619:
1615:
1606:
1600:
1595:
1592:
1590:
1588:
1585:
1580:
1575:
1572:
1567:
1558:
1554:
1551:
1548:
1543:
1539:
1535:
1526:
1522:
1519:
1514:
1510:
1506:
1501:
1497:
1493:
1490:
1488:
1484:
1480:
1476:
1475:
1452:
1449:
1448:
1447:
1436:
1433:
1424:
1420:
1415:
1411:
1407:
1402:
1398:
1394:
1389:
1385:
1362:
1361:
1346:
1341:
1326:
1321:
1306:
1300:
1296:
1289:
1275:
1265:
1254:
1247:
1240:
1233:
1227:
1226:
1211:
1208:
1205:
1202:
1197:
1193:
1189:
1186:
1179:
1169:
1164:
1157:
1153:
1147:
1144:
1142:
1138:
1134:
1130:
1129:
1126:
1123:
1120:
1117:
1112:
1108:
1104:
1101:
1098:
1091:
1081:
1076:
1069:
1065:
1059:
1056:
1054:
1050:
1046:
1042:
1041:
1038:
1035:
1032:
1029:
1026:
1023:
1016:
1006:
1001:
994:
990:
984:
981:
979:
975:
971:
967:
966:
938:
935:
931:
930:
915:
910:
905:
902:
897:
888:
884:
881:
879:
875:
871:
867:
866:
863:
858:
853:
850:
845:
836:
832:
829:
827:
823:
819:
815:
814:
811:
806:
802:
798:
789:
785:
782:
780:
776:
772:
768:
767:
752:
749:angle notation
744:
740:
736:
732:
724:
721:
708:high-leg delta
704:
703:
700:
697:
694:
683:high-leg delta
626:
623:
594:
591:
523:
522:
513:
512:
504:
503:
502:
501:
500:
484:
481:
466:
465:
458:
455:
439:
436:
420:
419:Phase sequence
417:
373:
370:
367:
362:
345:electric motor
290:
287:
257:Jonas Wenström
189:first AC motor
170:John Hopkinson
166:Jonas Wenström
150:
147:
127:voltage source
118:
115:
26:
9:
6:
4:
3:
2:
6400:
6389:
6386:
6384:
6381:
6379:
6376:
6374:
6371:
6369:
6366:
6364:
6361:
6360:
6358:
6343:
6340:
6338:
6335:
6333:
6330:
6328:
6325:
6323:
6322:
6318:
6316:
6315:
6311:
6309:
6308:
6304:
6301:
6300:
6296:
6293:
6289:
6286:
6285:
6281:
6278:
6277:
6273:
6270:
6269:
6265:
6262:
6261:
6257:
6254:
6253:
6249:
6246:
6245:
6241:
6238:
6237:
6233:
6231:
6228:
6226:
6223:
6221:
6218:
6216:
6213:
6211:
6208:
6206:
6203:
6201:
6198:
6197:
6195:
6191:
6185:
6182:
6180:
6177:
6175:
6172:
6170:
6167:
6166:
6164:
6160:
6154:
6153:
6149:
6146:
6142:
6140:
6139:
6135:
6133:
6132:
6128:
6127:
6125:
6121:
6114:
6104:
6101:
6099:
6096:
6094:
6091:
6089:
6086:
6084:
6081:
6079:
6078:Tesla turbine
6076:
6074:
6073:Radio control
6071:
6067:
6064:
6062:
6059:
6057:
6054:
6053:
6052:
6049:
6047:
6044:
6042:
6039:
6037:
6034:
6032:
6029:
6027:
6024:
6020:
6017:
6016:
6015:
6012:
6010:
6007:
6006:
6004:
5998:
5994:
5987:
5982:
5980:
5975:
5973:
5968:
5967:
5964:
5952:
5944:
5943:
5940:
5934:
5931:
5929:
5926:
5925:
5923:
5915:
5909:
5906:
5904:
5901:
5899:
5896:
5894:
5891:
5889:
5888:Pigouvian tax
5886:
5884:
5881:
5879:
5876:
5874:
5871:
5869:
5866:
5864:
5861:
5859:
5856:
5854:
5851:
5849:
5846:
5844:
5841:
5839:
5836:
5835:
5833:
5825:
5818:
5815:
5813:
5810:
5808:
5805:
5803:
5800:
5798:
5795:
5791:
5788:
5786:
5785:Earth-leakage
5783:
5782:
5781:
5778:
5776:
5773:
5772:
5770:
5762:
5754:
5751:
5750:
5749:
5746:
5744:
5741:
5739:
5736:
5734:
5731:
5730:
5728:
5726:Failure modes
5724:
5718:
5715:
5713:
5710:
5707:
5704:
5702:
5699:
5697:
5694:
5692:
5689:
5687:
5684:
5682:
5679:
5677:
5676:Power station
5674:
5672:
5669:
5667:
5664:
5662:
5659:
5657:
5654:
5652:
5649:
5647:
5644:
5642:
5639:
5637:
5634:
5632:
5629:
5627:
5624:
5622:
5619:
5617:
5614:
5612:
5609:
5607:
5604:
5602:
5599:
5597:
5594:
5593:
5591:
5588:
5583:
5578:
5572:
5569:
5567:
5564:
5562:
5561:Rankine cycle
5559:
5557:
5554:
5552:
5549:
5547:
5544:
5542:
5541:Cooling tower
5539:
5537:
5534:
5532:
5529:
5527:
5524:
5523:
5521:
5519:
5515:
5505:
5502:
5500:
5497:
5495:
5492:
5488:
5485:
5483:
5480:
5478:
5475:
5473:
5470:
5468:
5465:
5464:
5463:
5460:
5458:
5455:
5453:
5450:
5448:
5445:
5443:
5440:
5438:
5435:
5434:
5432:
5430:
5426:
5420:
5417:
5413:
5410:
5408:
5405:
5403:
5400:
5398:
5395:
5394:
5393:
5390:
5389:
5387:
5385:
5384:Non-renewable
5381:
5378:
5374:
5369:
5359:
5356:
5354:
5351:
5349:
5346:
5344:
5341:
5339:
5336:
5334:
5331:
5329:
5326:
5324:
5321:
5319:
5316:
5314:
5311:
5309:
5306:
5304:
5303:Grid strength
5301:
5299:
5296:
5294:
5291:
5289:
5286:
5284:
5281:
5279:
5276:
5274:
5271:
5269:
5266:
5264:
5261:
5259:
5258:Demand factor
5256:
5254:
5251:
5249:
5246:
5244:
5241:
5240:
5238:
5234:
5230:
5223:
5218:
5216:
5211:
5209:
5204:
5203:
5200:
5194:
5191:
5190:
5180:
5176:
5172:
5168:
5165:(5): 88–100.
5164:
5160:
5155:
5154:
5141:
5135:
5131:
5125:
5117:
5111:
5107:
5101:
5093:
5089:
5085:
5081:
5080:
5072:
5065:
5061:
5055:
5044:
5040:
5036:
5029:
5023:
5016:
5012:
5007:
4999:
4995:
4991:
4987:
4983:
4979:
4975:
4971:
4964:
4945:
4938:
4931:
4923:
4917:
4913:
4906:
4887:
4880:
4873:
4865:
4861:
4855:
4846:
4830:
4826:
4819:
4817:
4797:
4791:
4783:
4777:
4773:
4772:
4764:
4762:
4760:
4745:on 2014-09-11
4741:
4734:
4728:
4717:
4710:
4704:
4697:
4696:0-07-144146-8
4693:
4689:
4683:
4667:
4663:
4659:
4652:
4644:
4638:
4634:
4633:
4625:
4623:
4621:
4609:
4602:
4596:
4589:
4588:
4582:
4575:
4574:
4568:
4561:
4555:
4548:
4543:
4537:
4533:
4526:
4518:
4517:
4509:
4501:
4499:91-7536-330-5
4495:
4491:
4484:
4478:
4475:
4471:
4467:
4461:
4455:
4450:
4435:
4431:
4425:
4417:
4415:9781133131199
4411:
4407:
4400:
4393:
4392:0-07-013932-6
4389:
4385:
4379:
4372:
4371:0-07-061285-4
4368:
4364:
4358:
4350:
4346:
4342:
4336:
4332:
4328:
4324:
4320:
4313:
4309:
4294:
4268:
4259:
4252:
4242:
4234:
4228:
4219:
4209:
4207:
4205:
4203:
4193:
4184:
4155:
4151:
4141:
4140:Y-Δ transform
4138:
4136:
4133:
4131:
4128:
4126:
4123:
4121:
4118:
4116:
4113:
4112:
4100:
4098:
4097:
4081:
4079:
4077:
4062:
4058:
4053:
4051:
4048:
4046:
4043:
4041:
4038:
4036:
4034:277 or 480 V
4033:
4032:
4028:
4023:
4021:
4018:
4016:
4013:
4011:
4008:
4006:
4003:
3999:
3991:
3989:
3987:
3984:
3982:
3979:
3977:
3974:
3972:
3969:
3967:
3963:
3959:
3957:
3955:
3952:
3950:
3947:
3945:
3942:
3940:
3937:
3935:
3923:
3919:
3917:
3915:
3912:
3910:
3907:
3905:
3902:
3900:
3897:
3895:
3891:
3887:
3885:
3883:
3880:
3878:
3875:
3873:
3870:
3868:
3865:
3863:
3859:
3855:
3853:
3851:
3848:
3846:
3843:
3841:
3838:
3836:
3833:
3831:
3827:
3823:
3818:
3814:
3812:
3810:
3807:
3805:
3802:
3800:
3797:
3795:
3792:
3790:
3771:
3767:
3763:
3758:
3754:
3752:
3750:
3747:
3745:
3742:
3740:
3737:
3735:
3732:
3730:
3727:
3726:
3722:
3720:
3718:
3715:
3713:
3710:
3708:
3705:
3703:
3700:
3698:
3695:
3691:
3687:
3685:
3683:
3680:
3678:
3675:
3673:
3666:
3664:
3661:
3659:
3643:
3632:
3614:
3611:
3609:
3605:
3601:
3595:
3582:
3578:
3573:
3570:
3567:
3562:
3559:
3556:
3555:Elihu Thomson
3552:
3548:
3544:
3541:
3538:
3537:Niagara Falls
3534:
3530:
3512:
3501:
3499:
3496:
3493:
3491:
3488:
3487:
3481:
3477:
3468:
3466:
3462:
3458:
3456:
3451:
3448:
3442:
3440:
3435:
3431:
3426:
3423:
3414:
3412:
3408:
3399:
3395:
3391:
3388:
3384:
3380:
3376:
3372:
3367:
3363:
3360:
3356:
3351:
3349:
3344:
3342:
3338:
3329:
3324:
3314:
3311:
3307:
3303:
3293:
3291:
3281:
3274:
3265:
3253:
3244:
3231:
3225:
3218:
3213:
3208:
3204:
3186:
3177:
3171:
3166:
3157:
3149:
3148:
3147:
3145:
3135:
3132:
3122:
3120:
3116:
3086:
3080:
3073:
3070:
3069:
3059:
3052:
3045:
3042:
3036:
3029:
3022:
3019:
3013:
2999:
2992:
2985:
2982:
2981:
2977:
2973:
2968:
2964:
2941:
2935:
2932:
2927:
2923:
2911:
2907:
2901:
2896:
2888:
2884:
2880:
2873:
2869:
2864:
2852:
2848:
2842:
2837:
2835:
2828:
2824:
2816:
2810:
2807:
2802:
2798:
2794:
2783:
2779:
2773:
2768:
2760:
2756:
2752:
2745:
2741:
2736:
2724:
2720:
2714:
2709:
2707:
2700:
2696:
2684:
2683:
2682:
2658:
2655:
2644:
2640:
2634:
2629:
2621:
2617:
2613:
2606:
2602:
2597:
2585:
2581:
2575:
2570:
2568:
2558:
2554:
2545:
2541:
2537:
2532:
2528:
2524:
2519:
2515:
2511:
2506:
2502:
2498:
2496:
2489:
2485:
2473:
2472:
2471:
2466:
2459:
2452:
2447:
2442:
2438:
2415:
2409:
2406:
2401:
2397:
2373:
2361:
2357:
2351:
2349:
2342:
2338:
2330:
2324:
2321:
2316:
2312:
2308:
2285:
2273:
2269:
2263:
2261:
2254:
2250:
2242:
2236:
2233:
2228:
2224:
2200:
2188:
2184:
2178:
2176:
2169:
2165:
2153:
2152:
2151:
2148:
2143:= −120° and Φ
2115:
2107:
2103:
2099:
2092:
2088:
2083:
2071:
2067:
2061:
2056:
2051:
2047:
2034:
2028:
2023:
2021:
2008:
2004:
1991:
1984:
1976:
1972:
1959:
1952:
1947:
1943:
1939:
1934:
1930:
1926:
1924:
1917:
1913:
1905:
1897:
1893:
1889:
1882:
1878:
1873:
1861:
1857:
1851:
1846:
1841:
1836:
1833:
1819:
1813:
1808:
1806:
1793:
1789:
1776:
1769:
1761:
1756:
1753:
1739:
1732:
1727:
1723:
1719:
1714:
1710:
1706:
1704:
1697:
1693:
1685:
1677:
1673:
1669:
1662:
1658:
1653:
1641:
1637:
1631:
1626:
1621:
1617:
1604:
1598:
1593:
1591:
1578:
1573:
1570:
1556:
1549:
1541:
1537:
1524:
1517:
1512:
1508:
1504:
1499:
1495:
1491:
1489:
1482:
1478:
1466:
1465:
1464:
1457:
1434:
1431:
1422:
1418:
1413:
1409:
1405:
1400:
1396:
1392:
1387:
1383:
1375:
1374:
1373:
1371:
1359:
1356: |
1345:
1342:
1339:
1336: |
1325:
1322:
1319:
1316: |
1305:
1302:
1301:
1295:
1288:
1283:
1279:
1274:
1269:
1264:
1260:
1253:
1246:
1239:
1232:
1209:
1203:
1200:
1195:
1191:
1167:
1155:
1151:
1145:
1143:
1136:
1132:
1124:
1118:
1115:
1110:
1106:
1102:
1079:
1067:
1063:
1057:
1055:
1048:
1044:
1036:
1030:
1027:
1004:
992:
988:
982:
980:
973:
969:
957:
956:
955:
949:
943:
934:
913:
908:
903:
900:
886:
882:
880:
873:
869:
861:
856:
851:
848:
834:
830:
828:
821:
817:
809:
804:
800:
787:
783:
781:
774:
770:
758:
757:
756:
750:
729:
720:
716:
714:
709:
701:
698:
695:
692:
691:
690:
684:
679:
675:
672:
668:
664:
655:
651:
647:
643:
641:
631:
622:
620:
615:
601:
598:
590:
588:
583:
580:
578:
573:
571:
567:
563:
549:
545:
542:
538:
534:
533:power station
517:
508:
495:
490:
480:
477:
475:
471:
463:
459:
456:
452:
451:
450:
447:
445:
435:
433:
432:short circuit
426:
416:
414:
410:
406:
401:
397:
393:
390:
385:
371:
368:
365:
360:
350:
346:
341:
336:
327:
319:
312:
308:
304:
300:
295:
286:
284:
279:
272:
266:
262:
258:
254:
250:
246:
245:squirrel-cage
242:
238:
234:
230:
225:
221:
218:
212:
210:
206:
202:
198:
190:
185:
181:
179:
175:
171:
167:
163:
159:
155:
146:
144:
143:phase voltage
140:
136:
132:
128:
124:
114:
112:
108:
104:
100:
95:
93:
89:
88:phase shifted
84:
82:
78:
74:
70:
66:
63:(AC) used in
62:
58:
55:(abbreviated
54:
46:
40:
33:
19:
6337:Lunar crater
6319:
6312:
6305:
6297:
6282:
6274:
6266:
6258:
6252:The Prestige
6250:
6247:(2003 opera)
6242:
6234:
6150:
6136:
6129:
6092:
6019:plasma globe
5993:Nikola Tesla
5883:Net metering
5830:and policies
5748:Power outage
5717:Utility pole
5681:Pumped hydro
5587:distribution
5582:Transmission
5565:
5531:Cogeneration
5333:Power factor
5162:
5158:
5129:
5124:
5105:
5100:
5083:
5077:
5071:
5054:
5038:
5034:
5022:
5014:
5006:
4998:the original
4977:
4973:
4963:
4951:. Retrieved
4944:the original
4930:
4911:
4905:
4893:. Retrieved
4886:the original
4872:
4864:the original
4854:
4845:
4833:. Retrieved
4829:the original
4805:December 10,
4803:. Retrieved
4790:
4770:
4747:. Retrieved
4740:the original
4727:
4703:
4687:
4682:
4670:. Retrieved
4665:
4661:
4651:
4631:
4608:the original
4595:
4585:
4581:
4571:
4567:
4559:
4554:
4545:
4531:
4525:
4515:
4508:
4489:
4483:
4477:
4465:
4460:
4449:
4437:. Retrieved
4433:
4424:
4405:
4399:
4383:
4378:
4362:
4357:
4322:
4312:
4293:
4267:
4258:
4241:
4227:
4218:
4192:
4183:
4154:
4075:
3597:
3478:
3474:
3459:
3452:
3443:
3434:power factor
3427:
3420:
3409:systems and
3403:
3371:electrolysis
3364:
3352:
3345:
3334:
3299:
3287:
3272:
3263:
3251:
3242:
3232:
3223:
3216:
3209:
3205:
3201:
3136:
3129:Except in a
3128:
3118:
3114:
3097:
3084:
3078:
3071:
3057:
3050:
3043:
3034:
3027:
3020:
3011:
2997:
2990:
2983:
2966:
2962:
2960:
2680:
2464:
2457:
2450:
2448:
2440:
2436:
2434:
2149:
2134:
1462:
1368:By applying
1367:
1357:
1343:
1337:
1323:
1317:
1303:
1293:
1286:
1272:
1270:
1262:
1258:
1251:
1244:
1237:
1230:
1228:
953:
932:
730:
726:
717:
705:
688:
660:
648:
644:
636:
616:
602:
599:
596:
587:diode bridge
584:
581:
577:transmission
574:
530:
478:
467:
448:
441:
428:
409:single-phase
402:
398:
394:
388:
386:
332:
259:received in
226:
222:
213:
194:
178:Nikola Tesla
152:
142:
139:line voltage
138:
120:
99:single-phase
96:
92:transformers
85:
73:distribution
69:transmission
56:
52:
51:
6302:(2020 film)
6287:(2019 film)
6279:(2017 film)
6271:(2016 film)
6255:(2006 film)
6239:(1980 film)
6088:Tesla valve
6014:Plasma lamp
5878:Load factor
5733:Black start
5701:Transformer
5402:Natural gas
5353:Variability
5328:Peak demand
5318:Merit order
5248:Backfeeding
4953:18 December
4895:24 November
4835:24 November
4709:"Schneider"
4672:21 December
4558:Cotton, H,
4547:standpoint.
4439:January 24,
4233:color blind
4076:(High-Leg)
3975:White/grey
3772:, later IEC
3653:3.2, or IEC
3588:Color codes
3577:skin effect
3383:steelmaking
3359:slow-motion
646:been used.
640:ground wire
297:Normalized
265:Grängesberg
117:Terminology
18:Three phase
6357:Categories
6051:Tesla coil
6002:inventions
6000:Career and
5920:production
5765:Protective
5696:Super grid
5691:Smart grid
5518:Generation
5452:Geothermal
5343:Repowering
5064:1133709176
4980:(4): 348.
4935:Hui, Sun.
4749:2014-08-03
4304:References
4160:H1, H2, H3
3696:Mandatory
3592:See also:
3366:Rectifiers
3321:See also:
487:See also:
474:panelboard
454:same size.
423:See also:
283:horsepower
241:efficiency
205:alternator
125:between a
123:conductors
6041:Teleforce
5828:Economics
5551:Micro CHP
5429:Renewable
5412:Petroleum
5407:Oil shale
5293:Grid code
5253:Base load
5179:1540-7977
5066:, page 70
3953:Sky blue
3822:IEC 60446
3770:IEC 60446
3760:European
3622:Neutral,
3608:IEC 60445
3604:IEC 60446
2936:θ
2933:−
2928:∘
2917:∠
2889:∘
2881:−
2865:ϕ
2858:∠
2811:θ
2808:−
2803:∘
2795:−
2789:∠
2761:∘
2753:−
2737:ϕ
2730:∠
2659:θ
2656:−
2650:∠
2622:∘
2614:−
2598:ϕ
2591:∠
2559:∘
2551:∠
2538:−
2512:−
2410:θ
2407:−
2402:∘
2391:∠
2378:Δ
2325:θ
2322:−
2317:∘
2309:−
2303:∠
2290:Δ
2237:θ
2234:−
2229:∘
2218:∠
2205:Δ
2150:Further:
2108:∘
2084:ϕ
2077:∠
2052:∘
2044:∠
2009:∘
2001:∠
1985:−
1977:∘
1969:∠
1940:−
1898:∘
1874:ϕ
1867:∠
1842:∘
1834:−
1829:∠
1794:∘
1786:∠
1770:−
1762:∘
1754:−
1749:∠
1720:−
1678:∘
1654:ϕ
1647:∠
1622:∘
1614:∠
1579:∘
1571:−
1566:∠
1550:−
1542:∘
1534:∠
1505:−
1451:Delta (Δ)
1204:θ
1201:−
1196:∘
1185:∠
1119:θ
1116:−
1111:∘
1103:−
1097:∠
1031:θ
1028:−
1022:∠
909:∘
896:∠
857:∘
849:−
844:∠
805:∘
797:∠
743:lagging V
739:lagging V
614:of 87%).
372:…
307:frequency
299:waveforms
289:Principle
276:9.5
267:mine. A
6388:AC power
6342:Asteroid
6123:Writings
5951:Category
5738:Brownout
5526:AC power
5236:Concepts
5043:Archived
4716:Archived
4349:32935308
4108:See also
3933:15.2.2)
3616:Country
3381:used in
3377:and the
747:, using
552:120° or
269:45
109:, other
6193:Related
6056:history
6009:Patents
5767:devices
5477:Thermal
5472:Osmotic
5467:Current
5447:Biomass
5437:Biofuel
5419:Nuclear
5376:Sources
4982:Bibcode
4236:ground.
4176:R, Y, B
4172:U, V, W
4168:R, S, T
4164:A, B, C
4074:Orange
4049:Yellow
4044:Orange
3938:Yellow
3871:Yellow
3839:Yellow
3762:CENELEC
3743:Yellow
3733:Orange
3693:Canada
3671:yellow
3667:White;
3619:Phases
3606:(later
3471:Testing
3439:inertia
3348:boilers
3278:≈ 57.7%
3235:√
3140:√
3108:√
3101:√
3010:
3005:√
1351:√
1331:√
1311:√
1257:), and
751:, and V
671:Germany
609:⁄
564:). The
562:radians
557:⁄
531:At the
472:to the
444:neutral
405:neutral
340:voltage
311:voltage
149:History
135:voltage
103:voltage
5462:Marine
5442:Biogas
5177:
5136:
5112:
5062:
4918:
4778:
4694:
4639:
4538:
4496:
4472:
4412:
4390:
4373:, p. 2
4369:
4347:
4337:
4285:
4281:
4277:
4273:
4249:
4087:White
4069:Black
4039:Brown
4024:White
4009:Black
3980:Brown
3970:Black
3943:Green
3931:
3927:
3913:White
3903:Black
3881:Black
3861:India
3849:Black
3798:Black
3793:Brown
3786:
3782:
3778:
3774:
3738:Brown
3706:Black
3655:
3651:
3647:
3600:motors
3233:Since
3017:∠−30°,
2435:where
1229:where
525:wires.
176:, and
129:and a
71:, and
6299:Tesla
6268:Tesla
6162:Other
5819:(GFI)
5708:(TSO)
5494:Solar
5482:Tidal
5457:Hydro
5046:(PDF)
5031:(PDF)
4947:(PDF)
4940:(PDF)
4889:(PDF)
4882:(PDF)
4799:(PDF)
4743:(PDF)
4736:(PDF)
4719:(PDF)
4712:(PDF)
4662:Power
4611:(PDF)
4604:(PDF)
4345:S2CID
4251:60446
4147:Notes
4101:Blue
4054:Gray
4019:Blue
3994:prev.
3985:Blue
3898:Blue
3876:Blue
3844:Blue
3808:Blue
3803:Grey
3711:Blue
3669:prev.
3261:. If
3089:phase
3082:phase
2463:lags
2456:lags
1266:total
1241:total
1234:total
1172:total
1084:total
1009:total
535:, an
369:1.732
209:Turin
6327:Boat
5585:and
5504:Wind
5487:Wave
5397:Coal
5175:ISSN
5134:ISBN
5110:ISBN
5060:ISBN
4955:2012
4916:ISBN
4897:2012
4837:2012
4807:2023
4776:ISBN
4692:ISBN
4674:2012
4637:ISBN
4536:ISBN
4494:ISBN
4470:ISBN
4441:2022
4410:ISBN
4388:ISBN
4367:ISBN
4335:ISBN
4082:Red
4014:Red
3948:Red
3908:Red
3866:Red
3834:Red
3701:Red
3553:and
3463:and
3222:= 2
548:wave
261:1890
187:The
131:load
121:The
5167:doi
5088:doi
4990:doi
4327:doi
4247:IEC
3640:L3
3637:L2
3634:L1
3629:PE
3077:= 3
2972:).
2924:120
2799:120
2555:120
2446:).
2398:150
2048:150
1973:120
1790:120
1757:120
1574:120
1268:).
1192:120
1107:120
904:120
852:120
6359::
5173:.
5161:.
5084:95
5082:.
5039:58
5037:.
5033:.
5013:,
4988:.
4978:41
4976:.
4972:.
4815:^
4758:^
4714:.
4666:51
4664:.
4660:.
4619:^
4544:.
4432:.
4343:.
4333:.
4321:.
4201:^
4174:;
4170:;
4166:;
4162:;
3624:N
3571:DC
3428:A
3341:hp
3280:.
3276:LN
3267:LL
3255:LL
3246:LN
3227:LN
3220:LL
3210:A
3182:LN
3162:LL
3075:3Φ
3061:bc
3056:−
3054:ca
3049:=
3038:ab
3033:−
3031:bc
3026:=
3015:ab
3003:=
3001:ca
2996:−
2994:ab
2989:=
2912:31
2885:30
2874:31
2853:31
2784:23
2757:30
2746:23
2725:23
2645:12
2618:30
2607:12
2586:12
2546:12
2533:12
2520:31
2507:12
2468:12
2461:23
2454:31
2362:31
2343:31
2313:90
2274:23
2255:23
2225:30
2189:12
2170:12
2145:v3
2141:v2
2137:v1
2135:(Φ
2104:30
2039:LN
1996:LN
1964:LN
1918:31
1894:30
1837:90
1824:LN
1781:LN
1744:LN
1698:23
1674:30
1618:30
1609:LN
1561:LN
1529:LN
1483:12
1435:0.
1349:=
1347:ca
1329:=
1327:bc
1307:ab
1297:an
1290:ab
1250:+
1248:LN
1243:=
891:LN
839:LN
792:LN
753:LN
663:UK
589:.
570:Hz
555:2π
541:AC
278:kV
247:)
211:.
172:,
168:,
164:,
160:,
67:,
57:3ϕ
6290:"
6147:"
6143:"
5985:e
5978:t
5971:v
5221:e
5214:t
5207:v
5181:.
5169::
5163:5
5142:.
5118:.
5094:.
5090::
4992::
4984::
4957:.
4924:.
4899:.
4839:.
4809:.
4784:.
4752:.
4676:.
4645:.
4502:.
4476:.
4443:.
4418:.
4351:.
4329::
4178:.
3784:R
3764:(
3513:2
3503:(
3273:V
3264:V
3252:V
3243:V
3237:3
3224:V
3217:V
3187:.
3178:V
3172:3
3167:=
3158:V
3142:3
3119:Z
3117:/
3115:V
3110:3
3103:3
3091:.
3087:*
3085:I
3079:V
3072:S
3063:.
3058:I
3051:I
3047:c
3044:I
3040:,
3035:I
3028:I
3024:b
3021:I
3012:I
3007:3
2998:I
2991:I
2987:a
2984:I
2970:Δ
2967:Z
2963:θ
2942:,
2939:)
2920:(
2908:I
2902:3
2897:=
2894:)
2870:I
2861:(
2849:I
2843:3
2838:=
2829:3
2825:I
2817:,
2814:)
2792:(
2780:I
2774:3
2769:=
2766:)
2742:I
2733:(
2721:I
2715:3
2710:=
2701:2
2697:I
2662:)
2653:(
2641:I
2635:3
2630:=
2627:)
2603:I
2594:(
2582:I
2576:3
2571:=
2542:I
2529:I
2525:=
2516:I
2503:I
2499:=
2490:1
2486:I
2465:I
2458:I
2451:I
2444:Δ
2441:Z
2437:θ
2416:,
2413:)
2394:(
2384:|
2374:Z
2369:|
2358:V
2352:=
2339:I
2331:,
2328:)
2306:(
2296:|
2286:Z
2281:|
2270:V
2264:=
2251:I
2243:,
2240:)
2221:(
2211:|
2201:Z
2196:|
2185:V
2179:=
2166:I
2116:.
2113:)
2100:+
2093:3
2089:V
2080:(
2072:3
2068:V
2062:3
2057:=
2035:V
2029:3
2024:=
2014:)
2005:0
1992:V
1988:(
1982:)
1960:V
1956:(
1953:=
1948:1
1944:V
1935:3
1931:V
1927:=
1914:V
1906:,
1903:)
1890:+
1883:2
1879:V
1870:(
1862:2
1858:V
1852:3
1847:=
1820:V
1814:3
1809:=
1799:)
1777:V
1773:(
1767:)
1740:V
1736:(
1733:=
1728:3
1724:V
1715:2
1711:V
1707:=
1694:V
1686:,
1683:)
1670:+
1663:1
1659:V
1650:(
1642:1
1638:V
1632:3
1627:=
1605:V
1599:3
1594:=
1584:)
1557:V
1553:(
1547:)
1538:0
1525:V
1521:(
1518:=
1513:2
1509:V
1500:1
1496:V
1492:=
1479:V
1432:=
1427:N
1423:I
1419:=
1414:3
1410:I
1406:+
1401:2
1397:I
1393:+
1388:1
1384:I
1358:V
1353:3
1344:V
1338:V
1333:3
1324:V
1318:V
1313:3
1304:V
1294:V
1287:V
1276:y
1273:Z
1263:Z
1259:θ
1255:Y
1252:Z
1245:Z
1238:Z
1231:Z
1210:,
1207:)
1188:(
1178:|
1168:Z
1163:|
1156:3
1152:V
1146:=
1137:3
1133:I
1125:,
1122:)
1100:(
1090:|
1080:Z
1075:|
1068:2
1064:V
1058:=
1049:2
1045:I
1037:,
1034:)
1025:(
1015:|
1005:Z
1000:|
993:1
989:V
983:=
974:1
970:I
950:.
914:.
901:+
887:V
883:=
874:3
870:V
862:,
835:V
831:=
822:2
818:V
810:,
801:0
788:V
784:=
775:1
771:V
745:1
741:2
737:3
733:1
713:V
667:A
611:3
607:2
559:3
366:=
361:3
271:m
41:.
34:.
20:)
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