﻿ Three-phase electric circuits

# Principle of three-phase elektricheskiy chains

Now alternating-current electrical energy is developed, transferred and distributed between separate current collectors in the system of three-phase chains.

Principle of connection of wires.

The system of three-phase chains call such set of electric circuits in which current collectors receive the power supply from the general three-phase generator.

The generator which has the winding consisting of three parts is called three-phase. Each part of this winding is called the phase. Therefore these generators also received the name three-phase. It should be noted that the term "phase" in electrical equipment has two values:

• in sense of the certain stage of batch oscillatory process;
• as name of the part of the alternating-current electric circuit (for example, part of the winding of the electrical machine).

Fig. 1. Scheme of the three-phase generator.

For explanation of the principle of operation of the three-phase generator we will address the model which is schematically represented in the figure 1. The model consists of the stator manufactured in the form of the steel ring, and the rotor - the permanent magnet. On the ring of the stator the three-phase winding with identical number of rounds in each phase is located. Phases of the winding are displaced in space one concerning another on the corner 120 °.
Let's imagine that the rotor of model of the generator is given to rotation with constant speed against the movement of the hour hand. Owing to the continuous movement of poles of the permanent magnet concerning stator winding conductors in each its phase EMF will be directed.

Applying the right-hand rule, it is possible to be convinced that the EMF induced in the winding phase by the North Pole of the rotating magnet will work in one direction, and induced by the South Pole - in another. Therefore, the EMF of the phase of the generator will be the variable.

Extreme points (clips) of each phase of the generator always mark: one extreme point of the phase is called the beginning, and another - the end. The beginnings of phases designate the Latin letters A, B, C, and their ends - according to X, Y, Z. Names give "beginning" and "end" of the phase, being guided by the following rule: positive EMF of the generator works in the direction from the end of the phase by its beginning.

EMF of the generator we will agree to consider positive if it is induced by the North Pole the rotating magnet. Then the marking of clips of the generator for the case of rotation of its rotor against the movement of the hour hand has to be such, as shown in the figure 1.

With the constant speed of rotation of poles of the rotor amplitude and frequency of the EMF created in stator winding phases remain invariable. However during every moment the size and the direction of action of EMF of one of phases differ from size and the direction of action of EMF of two other phases. It is explained by the space shift of phases. All phenomena in the second phase repeat the phenomena in the first phase, but with delay.

Fig. 2. Curves of instantaneous values of three-phase system of E.D.S.

They say that the EMF of the second phase lags behind in time the EMF of the first phase. They, for example, at different times reach the amplitude values. Really, the EMF greatest value, induced in any phase, will be while the center of the pole of the rotor passes the middle of this phase. In particular, for the instant corresponding to the rotor arrangement shown in the figure 1, the electromotive force of the first phase of the generator will be positive and maximum.

The EMF positive maximum value of the second phase will come later when the rotor turns on the corner 120 °. As for one turn of the bipolar rotor of the generator there is complete alternation of change of EMF, time T one turns is the period of change of EMF. It is obvious that the turn of the rotor on 120 ° requires time equal to one third of the period (T/3).

Therefore, all stages of change of EMF of the second phase step after the corresponding stages of change of EMF of the first phase on one third of the period. The same lag in alternation of EMF is observed in the third phase in relation to the second. Certainly that in relation to the first phase alternations of EMF of the third phase are made with delay on two thirds of the period (2/3 T).

Fig. 3. Scheme of the untied three-phase chain.

By giving of the corresponding form to poles of magnets it is possible to achieve change of EMF in time under the law close to sinusoidal.
Therefore, if change of EMF of the first phase of the generator happens under the law of the sine
e1 = Emsin? t,
that the law of change of EMF of the second phase can be written down by the formula
= I Eat with e2 sin? (t? T/3), and - the formula e3 = I Eat with the third sin? (t? 2/3 T).

Told illustrates the schedule of the figure 2.

Thus, it is possible to draw the following conclusion: at uniform rotation of poles of the rotor in all three phases of the generator the EMFs variables of identical frequency and amplitude which alternations on the relation are to each other made with delay for 1/3 periods are directed.

The three-phase generator is the power source of both single-phase, and three-phase electric devices. Single-phase current collectors, as we know, have two external clips. Lighting lamps, different household appliances, electrowelding machines, induction furnaces, electric motors with the single-phase winding concern them, for example.

Three-phase devices generally have six external clips. Each such device consists of three (usually identical) electric circuits which are called phases. Electric arc furnaces with three electrodes or electric motors with the three-phase winding can be examples of three-phase current collectors.

## Ways of connection of phases of the generator and current collector

The three-phase chain is called untied if each phase of the generator irrespective of others is connected by two wires to the current collector (fig. 3). The main lack of the untied three-phase chain is that from the generator to receivers it is necessary to apply six wires to transmission of energy. The number of wires can be reduced to four or even to three if to connect phases of the generator and current collectors among themselves in the corresponding way. In this case the three-phase chain is called the connected three-phase chain.

Fig. 4. The three-phase winding connected by the star: and - the scheme of connection, - the winding diagram.

Almost always put the connected three-phase chains as more perfect and economic into practice. There are two main ways of connection of phases of the generator and phases of receivers: wye and delta connection.
At connection of phases of the generator the star (fig. 4, a) all "ends" of phase windings of X, Y, Z connect in one generic point 0 called neutral or the origin of the generator.

In the figure 4, three phases of the generator in the form of coils which axes are displaced in space one concerning another on the corner 120 ° are schematically shown.
Tension between the beginning and the end of each phase of the generator is called phase tension, and between the beginnings of phases - linear.

As phase tension changes in time under the sinusoidal law, linear stresses will also change under the sinusoidal law. Let's agree for the positive direction of action of linear stresses to consider that direction when they work:

star: and - the scheme of connection, - the winding diagram

• from the clip A first phases to the clip B second phases;
• from the clip B second phases to the clip of the C third phase;
• from the clip of the C third phase to the clip A first phases.

Fig. 5. Four-wire three-phase circuit.

These three conditionally positive directions of action of linear stresses in the figure 4, are shown by shooters.
Calculations and measurements show that the operating value of linear stress of the generator which three phases are connected in the star is more than operating value of phase tension.

For transmission of energy from the generator connected by the star to single-phase or three-phase current collectors four wires are generally necessary. Three wires attach to the beginnings of phases of the generator (A, B, C). These wires are called line conductors. The fourth wire is connected to the neutral point (0) of the generator and call the neutral (zero) wire.

The three-phase chain with the neutral wire gives the chance to use two tension of the generator. Receivers in such chain can be turned on between line conductors on linear stress or between line conductors and the neutral wire on phase tension.

Fig. 6. Scheme of turning on of single-phase current collectors in four-wire network.

In the figure 5 the scheme of turning on of the current collectors expected the phase tension of the generator is shown. In this case phases of current collectors will have the generic point of connection - the neutral point 0’, and currents in line conductors (line currents) will be equal to currents in the corresponding phases of loading (phase currents).

Each phase of loading can be formed both by one current collector, and several current collectors included among themselves in parallel (fig. 6).
If phase currents and phase angles of these currents in relation to phase tension are identical, then such loading is called symmetric. If at least one of the specified conditions is not observed, then loading will be asymmetrical.

The symmetrical load can be created, for example, by glow lamps of identical power. Let's say that each phase of loading is formed by three identical lamps (fig. 7).
By direct measurements it is possible to be convinced that at inclusion of loading the star with the neutral wire tension on each phase of loading Uf will be less linear stress of Ul just as it was at inclusion the star of phases of windings of the generator.

Fig. 7. Scheme of connection of the symmetrical load star.

In practice three-phase chains with neutral wires at the tension were widely adopted
Ul = 380 V; Uf = 220 V
or
Ul = 220 V; Uf = 127 Century.

From the figure 7 it is visible that current in the line conductor (Il) is equal to current in the phase (If)
Il = If.

Current size at the symmetrical load is equal in the neutral wire to zero what it is possible to be convinced also by direct measurement of.

But if current in the neutral wire is absent, then why this wire is necessary?

For clarification of the role of the neutral wire we will do the following experience. Let's say that in each phase of loading there are about three identical lamps and to one voltmeter, and the neutral wire switched on the ampermeter (see fig. 7). When in each phase about three lamps are included, all of them are under the same tension and burn with identical heat, and current is equal in the neutral wire to zero.

Fig. 8. The scheme of lighting network of the house at connection of phases of loading the star.

Changing number of the included lamps in each phase of loading, we will be convinced that phase tension does not change (all lamps will burn with the former inclination), but in the neutral wire current will appear.
Let's disconnect the neutral wire from the origin of receivers and we will repeat all changes of loading in phases.

Now we will notice that bigger tension will fall on that phase which resistance is more than others that is where the smaller quantity of lamps is included. In this phase of the lamp will burn with the greatest heat and can even fuse. This results from the fact that in loading phases to big resistance there is also the bigger voltage drop.

Therefore, the neutral wire is necessary for alignment of phase tension of loading when resistance of these phases are different.

Thanks to the neutral wire each phase of loading is included on the phase tension of the generator which practically does not depend on the loading current size as internal voltage drop in the phase of the generator is insignificant. Therefore tension on each phase of loading will be almost invariable at changes of loading.

If resistance of phases of loading are equal in size and homogeneous, then the neutral wire is not necessary (fig. 7). The example of such loading are symmetric three-phase current collectors.

Usually lighting loading does not happen symmetric therefore without neutral wire it is not connected the star (fig. 8). Otherwise it would lead to nonuniform distribution of tension on loading phases: on one lamps tension would be higher normal and they could fuse, and others, on the contrary, would be under the lowered tension and would burn dimly.

For the same reason never put the safety lock in the neutral wire as burn-out of the safety lock can cause inadmissible the overstrain on separate phases of loading (see fig. 8).

Fig. 9. Three-wire three-phase chain.

If to include three phases of loading directly between line conductors, then we will receive such connection of phases of current collectors which is called delta connection (fig. 9).

Let's say that the first phase of loading R1 is included between the first and second line conductors, the second R2 - between the second and third wires, and the third R3 - between the third and first wires. Each line conductor is connected to two different phases of loading.

It is possible to connect the triangle any loadings. In the figure 10 it is given
such scheme.

Fig. 10. The scheme of lighting network of the house at connection of phases of loading the triangle.

Ul = Uf

This ratio remains also at the uneven load.

The line current at the symmetrical load of phases as show measurements, will be more phase current.
However it must be kept in mind that at asymmetrical loading of phases this ratio between currents is broken.

Fig. 11. The scheme of lighting network of the house at connection of phases of loading the triangle.

It is essentially possible to connect the triangle and generator phases, but usually it is not done. The matter is that for creation of the set linear stress each phase of the generator at delta connection has to be expected tension bigger, than in case of the wye. More high tension in the phase of the generator demands increase in number of rounds and reinforced insulation for the winding wire that increases the sizes and cost of the machine. For this reason phases of three-phase generators almost always connect the star.

Receivers of electrical energy irrespective of the way of connection of windings of the generator can be switched on by either the star, or the triangle. The choice of this or that way of connection is defined by the size of mains voltage and rated voltage of receivers.