# Three-phase alternating current

As a three-phase alternating current - by reference as a three-phase alternating voltage or short as three-phase denoted - is in electrical engineering , a form designated by polyphase alternating current, each of three alternating currents or alternating voltages of the same frequency is that to one another in their phase angles are shifted tight by 120 °.

Colloquially, three-phase alternating current is referred to as heavy current , which is incorrect.

The three-phase system is mainly used in the field of electrical energy technology for the transport and distribution of electrical energy in power grids . Examples of this are the national three-phase high-voltage transmission networks , low -voltage networks in the area of ​​local power supply or three-phase machines that are used to drive elevators or in electrically powered vehicles .

Compared to a single single-phase alternating current system, a symmetrical three- phase system halves the cost of materials for electrical lines with the same electrical power . Furthermore, three- phase AC transformers can be manufactured with a smaller core cross-section than single-phase transformers with the same power . The use of the three-phase system makes economic sense from a few kilowatts and is the reason for its importance in the field of electrical power engineering.

## Basics

Scheme of a three-phase generator. The rotating permanent magnet generates a three-phase system with the external conductor voltages U L1 , U L2 and U L3 in the coils by induction .

If three coils are arranged in a circle, each offset by 120 °, in a three-phase generator, three alternating voltages that are equally offset in time are produced when a rotating field rotates centrally . In the simplest case, this is done by a rotating permanent magnet . The alternating voltages reach their maximum deflection in time, offset by a third of a period one after the other. The time offset of the external conductor voltages is described by the phase shift angle . The three conductors are called outer conductors and are usually abbreviated as L1, L2 and L3. In the past, the term phase conductor with the abbreviations R , S and T was also used as a name for the outer conductor .

An important circuit in three-phase technology is the star connection with a center point that is connected to a neutral conductor  N. If the three outer conductors are evenly loaded, this carries no current; if the load is uneven, it carries a current, the size of which results from the addition of the instantaneous values ​​of the phase-shifted individual currents (not addition of the mean values!). Another important circuit is the delta connection , in which there is no neutral conductor.

In three-phase systems, the voltage between any two external conductors is referred to as a chained voltage , the voltage between the neutral conductor and any external conductor is referred to as star voltage . The rms values ​​of these voltages are related to each other via a fixed ratio, which is referred to as the chaining factor and which always has the value in three-phase systems . In the case of the voltages commonly used in low-voltage networks in Europe, the nominal value of the star voltage is 230 V, which means that between two external conductors there is a linked voltage of ${\ displaystyle {\ sqrt {3}}}$

${\ displaystyle 230 \, \ mathrm {V} \ cdot {\ sqrt {3}} \ approx 400 \, \ mathrm {V}}$

results. The voltages of three-phase systems are named according to DIN 40108 according to the effective value of the line-to-line voltage, for the low-voltage networks common in Europe, for example, as "400 V three-phase network".

Temporal progression of the tensions in a three-phase system

The time course of the various voltages is shown in the figure opposite. The three interlinked voltages are drawn with continuous lines and with an amplitude increased by the interlinking factor , the three star voltages are shown with dashed lines. In this illustration it can be seen that the star voltages are phase-shifted by 30 ° with respect to the linked voltages. This fact plays a role in the complex transformation ratio of three-phase transformers in the so-called vector group and in three-phase rectifiers in the 12-pulse circuit for the suppression of harmonics .

## Energy transfer

Three-phase transformer; blue: steel support profiles for the iron core , red:
windings encapsulated with cast resin insulation , black: cable connection of the windings for delta connection

Due to the material savings, three-phase systems are used almost exclusively in the context of three-phase high-voltage transmission (DHÜ) for energy transmission in power grids . Exceptions in some countries are traction current networks , which for historical reasons are built up as single-phase networks , and for connection between two points under special conditions high-voltage direct current transmission (HVDC). Three-phase current can be transformed between the various voltage levels in a technically simple manner and with a high degree of efficiency of over 99% in power grids using power transformers , usually designed as three-phase transformers in substations . In principle, three separate single-phase transformers could be used side by side in three-phase systems - one for each outer conductor. This is used in borderline cases, for example with large unbalanced loads or to reduce transport problems (weight, dimensions). Less material is used if a three-phase alternating current transformer with a three or five-leg iron core is used instead . By linking the magnetic fluxes of the three stellar currents, iron can be saved in the core. Furthermore, a three-phase transformer has lower iron losses than three single-phase transformers with the same total power, since the losses increase linearly with the iron core mass. A special circuit of two transformers, the Scott circuit , allows three-phase systems to be converted into two-phase systems or four-phase systems with the three-phase system being loaded as symmetrically as possible.

In contrast to direct current networks, alternating voltage networks and thus also three-phase systems can be operated as meshed networks or as a composite network , where several power generators feed in energy at different points in the network and electrical energy is withdrawn for the consumers at different points. All producers must work synchronously. The control of the power flows to avoid overloading individual lines takes place in meshed networks by setting the node voltages and influencing the reactive power via the phase position. For this purpose, there are step switches in the power transformers for voltage control, so-called phase shifter transformers or synchronous generators that work as phase shifters , and coils or capacitor banks for reactive power compensation for the reactive power flows. Since the end of the 1990s, power electronics have also been used to influence the power flow as part of the Flexible AC Transmission Systems (FACTS).

In direct voltage networks such as HVDC, there is no possibility of controlling the power flows in an interconnected network via a phase shift as with three-phase current. Therefore, high DC voltage can currently only be used for direct point-to-point connections. The advantage of high DC voltage for energy transmission is that the capacitive charging power does not play a role in long lines or underground cables. This is why HVDC point connections are mainly used for overhead lines over 750 km and for submarine cables from a few 10 km to a few 100 km in length.

## Rotating field

The three-phase alternating current offers a simple way of generating a uniform rotating field . This rotating field is used in three-phase machines for drives (motor operation) or to generate electrical energy (generator operation).

Three-phase machines are divided into

• Synchronous machines in which the rotor rotates at the same speed as the stator rotating field, and the
• Asynchronous machines in which the rotor has a speed different from the rotating field of the stator. The difference between the speeds of the rotor and the rotating field of the stator, specified as a percentage , is known as the slip .

By interchanging any two outer conductors, the direction of the rotating field in the three-phase system can be reversed, which is used to reverse the direction of three-phase motors in the reversing contactor circuit . The rotating field measuring device is used to measure the direction of the rotating field . In electrical energy networks, the rotating field is defined as clockwise .

Cutaway model of a three-phase asynchronous machine

Asynchronous machines with squirrel cage rotors are simple, robust, reliable, maintenance-free and economical. They don't have a commutator that can wear out and cause radio interference, and they are more reliable than single-phase AC motors . In the case of electrical machines, the connections are designated with the letters U , V and W , possibly extended by an index. The designations A , B and C are common in English-speaking countries .

In brushless DC motors , electronic circuits, the so-called converters , generate a three-phase current with a rotating field from the DC voltage supply.

To start of large AC motors circuits are like the star-delta circuit , starting transformer , soft start device or electronic inverter used.

## particularities

### Three-phase networks

In low - voltage networks and in high - voltage networks such as the 400 kV transport network level, the star point is rigidly earthed, in medium-voltage networks and on the 110 kV distribution network level, so-called deleted networks are common. The type of neutral point treatment plays a role in troubleshooting in three-phase systems .

Low-voltage networks are usually designed as four-wire systems with an earthed neutral conductor, also to facilitate the connection of single-phase loads. In the high voltage range three-wire systems are common. In the low-voltage range, various three -phase connectors are common, such as the CEE three-phase connector according to IEC 60309 or the Perilex three-phase connector in Germany and Austria or the T15 and T25 connector according to SEV 1011 in Switzerland .

A global list of single-phase connections in the lighting network can be found under the country overview of plug types, mains voltages and frequencies .

For active and reactive power measurement in three-phase systems are Aron two power meter required; In high-voltage areas such as substations, current and voltage converters are interposed for safe measurement.

### Balancing of single-phase loads

Circuit for balancing a single-phase load R

In the case of large single-phase consumers such as induction furnaces , to avoid unbalanced loads, it is necessary to distribute the power evenly over the three outer conductors of the three-phase system. This is done by adding reactances . The circuit shown in the picture should serve as an example; its middle node is not connected to the neutral conductor. The power that is converted in the effective resistance  R of the furnace should come about through currents that are the same size in each supply line and each in phase with the associated star voltage. The voltage across the resistor in this circuit is three times as high as a normal star voltage. The voltage across the reactances is as large as a triangular voltage. The reactances are

${\ displaystyle \ omega \ mathrm {L} = {\ frac {\ mathrm {1}} {\ omega \ mathrm {C}}} = {\ frac {\ mathrm {R}} {\ sqrt {3}}} }$

for the case that in the picture L 2 L 1 leads by 120 ° and L 3 L 1 lags by 120 °. Parasitic components such as inductance of the ohmic load or the resistance of the coil are not taken into account. The decisive disadvantage of these arrangements is that the values ​​of the components cannot be changed continuously during operation and thus load changes cannot be adapted.

### Mathematical Methods

In three-phase systems, the methods of complex alternating current calculation are used. Graphic representations in phasor diagrams are used to include methods such as the symmetrical components for the treatment of asymmetrical three-phase systems. For rotating field machines and for describing the rotating field, the space vector representation and the vector control with transformations such as the Clarke and D / q transformation , which map the three axes into a complex plane with two axes, are important.

### Material savings

Conversion of a single-phase system into a symmetrical three-phase system with identical performance

A single-phase consumer such as a heating resistor requires two lines. If this heating resistor is divided into three heating resistors of equal size, each with three times the resistance and a third of the power, the total power remains the same, but the current per heating resistor is only a third and only requires a third of the original conductor cross-section. If the three supply voltages are out of phase with each other by 120 °, the currents on the common return conductor (neutral conductor) cancel each other out. This neutral conductor can therefore be omitted with symmetrical load distribution in a three-phase system. This means that the same total power can be transmitted at the same voltage with a total of only half the conductor cross-section and thus half the conductor material requirement. However, with three cables instead of two, the insulation effort is 50 percent higher, and the laying effort can also be higher.

The same consideration leads to a reduction in the core cross-section of three-phase transformers, a reduction in the use of materials for three-phase motors, etc.

The decisive step in saving the return conductor occurs with the transition from the single-phase to the symmetrical three-phase system. In the case of symmetrical phase systems with four or more phases, the total conductor cross-section required remains the same compared to three-phase systems, but the cost of insulation and laying increases further. Therefore, in the field of multi-phase systems in electrical power engineering, only systems with three phases are of greater importance.

As a practical example, electric cookers in private households that have a three-phase connection can serve. This serves to load all three outer conductors as evenly as possible because of the comparatively high electrical power of a stove compared to other household appliances. The heating elements in the stove, such as the hotplates and the oven, are single-phase 230-volt consumers that can be switched individually. Depending on the switching state, this results in asymmetrical loads of different strengths , which means that a neutral conductor connection is necessary. With a three-phase connection, however, this only carries a current that is at most as strong as the highest phase conductor current. If, on the other hand, all three external conductor connections of the electric cooker are fed from only one phase - this is possible because all consumers in the cooker are designed for only one phase - then the sum of the currents from the three external conductors flows through the neutral conductor.

## history

First synchronous machine from Haselwander with three-phase stator and four-pole rotor ( pole wheel )
Three-pole three-phase overhead line and Siemens three-phase motor car on the military railway near Berlin in 1903
Hellsjö power station 1895

The first mention of polyphase alternating current is associated with several names. The Italian Galileo Ferraris examined polyphase alternating currents in 1885. He defined the rotating field principle from the test results. Nikola Tesla had been dealing with the topic of multi-phase alternating currents since 1882 and constructed a two-phase alternating current motor in 1887 that was to introduce the three-phase network in America. The almost simultaneous developments by Galileo Ferraris and Nikola Tesla were protected by various patents, and legal disputes also arose. Charles Schenk Bradley independently patented ideas for various multi-phase systems in 1887 and 1888, but was unable to implement his ideas in practice.

The first three-phase synchronous generator was built in 1887 by the German inventor Friedrich August Haselwander , a patent application in the same year was initially rejected, but then recognized in 1889. However, large electrical companies, who recognized the importance of the invention, filed an objection against the granting of the patent and the amount in dispute for a legal dispute was estimated at 30 million marks, which Haselwander could not risk for itself. Haselwander worked as a senior engineer at Wilhelm Lahmeyer & Co in Frankfurt am Main and assigned his patent to the company. When AEG Lahmeyer took over in 1892, Haselwander lost his patent rights.

Independently of these events, Mikhail Ossipowitsch Doliwo-Dobrowolski worked at AEG in Germany in 1888 with three-phase alternating current and introduced the term "three-phase current" for it. The associated asynchronous motor, which he invented, was first delivered by AEG in early 1889. The first machines developed 2 to 3  HP . A motor from Haselwander built at the same time could not gain acceptance because its patents were revoked and its use was prohibited because it was feared that the telegraph lines would be disturbed.

The first power transmission with highly transformed three-phase alternating current took place in Germany in 1891 with the three-phase transmission Lauffen – Frankfurt as part of the international electrotechnical exhibition in 1891 in Frankfurt am Main . The test route lay between the cement works in Lauffen am Neckar and the exhibition in Frankfurt am Main, a distance of 175 km with a voltage of 15 kV and a transmitted power of around 173  kW . The system was designed by Doliwo-Dobrowolski and Oskar von Miller .

Under the direction of Ernst Danielson , chief designer at Allmänna Svenska Elektriska Aktiebolaget (ASEA) in Västerås , the first commercial application was carried out two years after the test in Germany in Sweden, between Lake Hellsjön and the mining area of ​​Grängesberg in Bergslagen, twelve kilometers away , Dalarna . The voltage there was 9.5 kV and the power transmitted was almost 220 kW. Previously the area was mechanically by means of art linkage been supplied with operating power.

In the old Rheinfelden hydropower plant, which went into operation on the German-Swiss border in the Rhine in 1898, three-phase alternating current with a frequency of 50 Hz was generated on an industrial scale for the first time worldwide . This frequency is the network frequency in many countries today . The Budapest machine works Ganz & Cie had a 1.5 kilometer long test railway line built on the Altofen Danube Island in 1899 under the chief designer Kálmán Kandó and in 1900 the factory railway of the ammunition factory Wöllersdorf near Wiener Neustadt for operation with 3 kV.

From 1899 the study society for electric rapid transit (St.ES) researched the electric train operation at high speed. For this purpose, the military railway near Berlin was provided with a three-pole overhead line for three-phase operation . At the height of the tests in 1904, an AEG three-phase motor car reached the record speed of 210 kilometers per hour.

The railway company Rete Adriatica (RA) opened the Veltlinbahn in 1902 , the first high-voltage electrified main railway line in the world. For this, Ganz & Cie also supplied the 3 kV and 15.6 Hz supply and the associated locomotives. This "Trifase" system was later extended to all of northern Italy and existed under the Ferrovie dello Stato until 1976. The three-phase drive was only able to establish itself in railways in the following decades when the power electronics in the form of frequency converters made it possible to use three-phase current of variable frequency in the vehicle to generate from the single-phase traction current.

## literature

Textbooks:

• Adolf J. Schwab: Electrical energy systems - generation, transport, transmission and distribution of electrical energy . Springer, 2006, ISBN 3-540-29664-6 .
• Adalbert Prechtl: Lectures on the basics of electrical engineering . tape 2 . Springer, Vienna 1995, ISBN 3-211-82685-8 , chap. 25 .

Historical development:

• Gerhard Neidhöfer: Michael von Dolivo-Dobrowolsky and the three-phase current (=  history of electrical engineering . Volume 19 ). 2nd Edition. VDE Verlag, 2008, ISBN 978-3-8007-3115-2 .

## Web links

Commons : Three phase alternating current  - collection of pictures, videos and audio files
Wiktionary: Heavy current  - explanations of meanings, word origins, synonyms, translations

## Individual evidence

1. DIN 40108: 2003-06 "Electricity systems - terms, quantities, symbols" Section 3.3.2.3 Three-phase system, three-phase electricity system , multi-phase electricity system with the number of phases m = 3.
2. In Germany, up to the year 2000, the VDE regulations used the terms heavy current or heavy current system for all single or multi-phase systems up to 1000 V that did not come under the category of low voltage (colloquially low current ). In more recent VDE regulations, systems up to 1000 V are referred to as low-voltage systems. Since then, the term power systems has only been used in standards for systems from 1 kV nominal voltage. The building industry standard DIN 276 continues to use the term heavy current systems for all electrical systems that are not exclusively used for signal transmission . In Switzerland, in accordance with Art. 2 EleG, in contrast to low-voltage systems, high- voltage systems are viewed as "those in which currents are used or occur that may be dangerous for people or property."
3. ^ Transfer I: current systems, three-phase current . (PDF; 122 kB) University of Stuttgart, Institute for Power Electronics and Electrical Drives.
4. VDE 0100, Part 550, 1988-04, Section 4.7 "Three-phase plug devices must be connected in such a way that a clockwise rotating field results when the sockets are viewed clockwise from the front."
5. ^ Gerhard Neidhöfer: Early Three-Phase Power , 2007, IEEE Power Engineering Society, Online ( Memento from December 11, 2012 in the Internet Archive )
6. About the first power transmission with three-phase alternating current at the Tekniska museet ( Memento from February 4, 2007 in the Internet Archive )
7. ^ Danielson, Ernst . In: Bernhard Meijer, Theodor Westrin (ed.): Nordisk familjebok konversationslexikon och realencyklopedi . 2nd Edition. tape 5 : Cestius-Degas . Nordisk familjeboks förlag, Stockholm 1906, Sp. 1258 (Swedish, runeberg.org ).
8. ^