Why create an angle between current and voltage

Principle of electric generators

DC generator

A coil is supposed to rotate in a constant magnetic field, the stator field. It is also known as an armature or rotor. The coil ends are conductively connected to a collector. These are slip rings with current collectors resting on them, also called carbon brushes. The magnetic field can be provided by a permanent magnet. In large generators, electromagnets operated with direct current generate the magnetic field. The armature coils rotate within the pole pieces of the magnet. In power plants, the generators are driven by water power, gas or steam turbines. With the bicycle dynamo, it is the turning movement of the wheel that drives the armature. The generator principle also works when the magnetic field rotates and the voltage is induced in fixed field (stator) windings.

Whether the generator generates direct or alternating voltage is determined by the structure of the collector. In the DC machine there is a slip ring, which consists of two half rings isolated from each other per coil. The coil ends are each connected with a half ring. This results in a changeover switch, called a commutator, which reverses the polarity of the ends of the coil in relation to the current collector when changing. In the circuit, the current always flows in the same direction and the generator generates a pulsating DC voltage.

In the following video clip the right conductor loop should be viewed. It rotates counterclockwise in the static magnetic field from 0 ° to 180 °. The current flows through it to the front over the upper half of the slip ring. After 180 ° the upper carbon brush, the current collector, is no longer in contact with this slip ring. For the following 180 ° it is now connected to the formerly left conductor loop. The commutator has switched to the other half of the conductor loop, so that the current direction for the upper consumer remains unchanged.

The direction of the current can be determined using the right-hand rule. The hand is to be held in such a way that the magnetic field lines enter the open palm from north to south. The splayed thumb points in the direction of movement of the armature coil. The fingertips indicate the direction of the induced current.

An equivalent method uses the thumb, index and middle fingers of the right hand, which are spread apart standing perpendicular to each other. It is also called the UVW or generator rule. The thumb for the cause points in the direction of movement of the coil. The index finger for the mediation points in the direction of the magnetic field lines. The middle finger for the effect shows the direction of the current.


In this generator, an armature winding also rotates in a constant magnetic field. Their ends are connected to their own undivided slip ring in the collector. The conductor loop is no longer switched if it enters the south pole area after leaving the north pole area. The winding supplies a sinusoidal alternating voltage at its ends.

The video clip illustrates the principle of the alternating voltage generator. The rotation takes place for one period in 15 ° steps and then continuously. If the right leg of the conductor loop rotates counterclockwise from 0 ° through 90 ° to 180 °, the current in the upper part of the conductor flows from the back to the front. During this time, the outer ring has the more positive potential. For the following 180 ° it rotates past the south pole, while the other half of the ladder takes the way around the top. The current now flows through this coil section, which rotates from right to left, from back to front to the inner wiper ring, which now receives positive potential. In relation to the pantograph, the direction of the current has been reversed and with constant rotation, the current and voltage follow a sinusoidal curve.

Both types of generator can also be operated as a motor by applying the correct type of voltage to the armature.

Three-phase alternating current - alternator

The electricity companies provide us with electrical energy in the form of alternating voltage. In the power plant, voltage and current are generated according to the dynamo principle. In simplified terms, the alternating voltage generator consists of three stationary coils, the field windings, offset from one another by 120 °. A DC coil, the magnet armature, rotates in the center of the arrangement. This construction has two advantages. The magnetic field can be regulated and the armature coil's power supply comes from two undivided, thus low-wear slip rings. The AC voltage is picked up directly on the field windings.

From 1882 Nicola Tesla dealt with the generation of alternating voltage. In America in 1887 he built a two-phase alternating current machine, protected by a patent. On this basis, Friedrich August Haselwander built the three-phase generator in Germany in 1887. However, the patent applications he had submitted were not processed in a timely manner and so the use went to the AEG in 1889, where at the same time M. O. Doliwo-Dobrowolski was working on the generation of three-phase alternating current. The technically applicable solutions were available simultaneously in several countries around 1890. In Germany with AEG, in America with N. Tesla, in Switzerland Charles E. L. Brown and in Sweden Jonas Wenström developed practical solutions.

The following video clip shows the principle of the three-phase alternating voltage generator. The amplitude values ​​correspond to our consumer-side mains voltages. The time diagrams of the individual phase voltages can be switched on and off. In the power plants, the generator coil sets are always combined to form a star connection. The three phase voltages L1, L2 and L3, phase-shifted by 120 °, are thus available at the coil ends or outer conductors against the common star point or neutral conductor N. The old conductor designations still valid on the network side are R, S, T. The three-phase network can be operated in two possible circuit types. In the star connection, three independent circuits are possible with one conductor each against the neutral conductor. In the delta connection, the connected load uses the three external conductor voltages at the same time without the neutral conductor.

The star connection

As can be seen in the video, the generator generates a sinusoidal phase voltage with every set of coils of the same color. This means that three independent consumer groups can be supplied. Three double lines are required to transmit and distribute the energy. With the same load on the three strings, the total current on the return lines has the value zero at all times. The return lines can be combined into one line, the neutral conductor N, at the star point. The result is the concatenation of the strings to form a star connection.

The graphic shows the vector diagrams of the star connection for currents and voltages. The three phase currents in the consumer circuit correspond to the three phase currents I1 ... I3. With symmetrical string loading, the sum of two string currents, as can be seen in the yellow pointer triangle of the currents, is equal to the negative value of the third string current. The currents cancel each other out at the star point.

The phase voltages U1 ... U3 form the yellow isosceles triangle with the neighboring voltages of the outer conductors ULL. The height shown divides the line voltage U12 in the middle. The angle φ in the right triangle is 30 °. This results in a concatenation factor of √3 for the conductor voltages among each other compared to the phase voltages L to N.

In the star connection, the currents of the phase conductors and phase currents are the same.
The conductor voltages L12, L23 and L31 are greater than the phase voltages by the concatenation factor √3.
With reference to the star point N, the voltages of the external conductors L1N, L2N and L3N are equal to the phase voltages.

The delta connection

Three consumer circuits can be switched between two external conductors without including the neutral conductor. This linkage with the circuits between L1-L2, L2-L3 and L3-L1 forms the delta connection of the three-phase system. The video teaching project shows that the useful voltage between two strings is also sinusoidal. It is greater by the concatenation factor √3 than the individual line voltage in the star connection. The power plant generators work in star connection. The power distribution between the substations is done by transformers in a delta connection. The energy distribution network therefore only needs three lines.

In the left part of the graphic you can see that in the delta connection the phase and phase voltages are the same. With symmetrical loading, the phase currents are the same. In the right part of the graphic, the current vectors IS1 ... IS3 are shifted so that they start at point 0. The phase angles of 120 ° between the phase currents are retained so that the sum of the phase currents is zero at all times. The external conductor current ILL forms the isosceles triangle 0-L2-L3 with 2 phase currents. The vertical from point 0 to ILL halves the height of the external current vector. Two right triangles are formed. The height halves the 120 ° angle between the legs, so the angle φ = 30 ° applies. With the help of the yellow triangle, the mathematical relationship between the phase current and the external conductor current can be derived. In the delta connection, the current linkage factor has the value √3.

In the delta connection, the voltages of the outer conductors and the phase voltages are the same.
The phase currents to each other are greater than the phase currents of each winding by the concatenation factor √3.

Current account

The performance of a three-phase system with symmetrical load is the same for the star and delta connection. It is calculated from the sum of the three line services. For the selected circuit, it can be determined by measuring the conductor voltage and the conductor current.

If the power consumption of a consumer in a star connection is compared with that in a delta connection, it can produce three times the power in a delta connection. Many drive machines in the three-phase network can be switched between star and delta. The machines start up with reduced load in a star connection. Compared to full load operation, only a third of the power is converted here. After the motors have reached their maximum speed, a switch is made to the delta connection so that full power is available.

Another chapter deals with the most important network types. There it is about the connection of the end consumer to the supply network without taking into account any energy transmission networks connected in between.