3-phase lancers. Triphasic lances. Zastosuvannya of the last payment
Federal Agency for Education GOU VPO "Ural State Technical University - UPI"
Electrical engineering: Triphasic electric lancers
Chief help
V.S. Proskuryakov, S.V. Sobolev, N.V. Khrulkova Department "Electrical Engineering and Electrotechnological Systems"
Yekaterinburg 2007
1. Basic understanding and purpose
How does a drop in voltage pour into the work of an electric motor?
As a result, the voltage on the end of the cable is less than the voltage on the bobbin of the cable. The drop in voltage can do it to the priority area on the level of the central dzherel of the livelihood of the house.
Recover the voltage drop at the cable
The axis is a theoretical formula for the expansion of the voltage drop at the cable.butt
Vіzmemo electrical cable 6 mm² for living stoves for cooking 32A, and a 30 m socket outlet on the wall. Working strum 32A. To solve this problem, increase the cross section power cable. Three-phase attachment, generator or receiver is made up of three single-phase blocks. There are two ways to install them three-phase circuits.
2. Otrimannya three-phase EPC system.
3. Ways to connect phases in triphasic lanceus.
4. The voltages of the three-phase dzherel.
5. Classification of primaries in triphasic lanceus.
6. Rozrahunok of the triphasic lancet at the beginning of the phases of the primach "Zirkoyu"
7. Neutral value
8. Triphasic lancet rozrahunok when catching phases of priming with "trikutnik"
Zirkopodіbne folding from neutral or without it - Delta-mounting. We also vikoristovuєmo terms zv'yazku zіrka and trikutnik zv'yazku. A mirror-like linkage of a triphasic primach. Leather from these priymachiv pratsyuє independently from others, as a bi vin was in single-phase. You can open up a strum, which will pass through the crisis.
In this mood, the folding is unbalanced. Not so, oskolki tse vector sum. The voltages and streams of the knot of the star from the neutral. Although the balances are accepted, the effective values of the strum and the voltage on the three phases are the same, then the strum at the neutral pole is equal to zero.
9. Pressure of the triphasic lanceug
Three-phase electric stake.
1. Basic understanding and purpose
Triphasic lancet - a collection of three electric lancets, in which
a source of energy.
Leather okremy lanceug, which enters before the triphasic lanceug, is usually called a phase.
In this way, the term "phase" can have two meanings in electrical engineering: the first is an argument of a sinusoidally minuscule value, the other is a part of the rich-phase system of electrical lances.
Simply put, in fig. Let's sweat the voltage drop in the lances and write it down. Medium three-phase cable 35 mm 2, 50 m live 400 V motor. The voltage drop on the cob of the line is in normal mode between 10 V phases. Like a drop in voltage on the terminals of the engine?
- Have a normal robot?
- Falling voltage for normal operation.
Triphasic lanciug є we call it a variant of rich-phase systems snake struma.
The broader width of the triphasic lancets is explained by a number of their advantages in the case of similar single-phase and other rich-phase lances:
ekonomіchnіst virobnіstva and transmission of energy is equal to single-phase lances;
the possibility of a simple elimination of a circular magnetic field, which wraps around, is necessary for a three-phase asynchronous motor;
It is transmitted that the three-phase line is balanced, and the messages are connected to one and the same point. What is the drop in voltage in the end of the line lighting?
- Voltage drop at the line.
- Falling voltage in any mono cables.
The value is below the maximum allowed by the standard. Three-phase values Balanced and unbalanced three-phase systems Three-phase systems of direct and reverse control. If, for example, the frequency is set to 50 Hz, then three phases are trimmed for 1/150 seconds per second. If three conductors are intermingled with streams of the same effective value, the system is considered to be balanced. In times electric socket The merging can be modeled with three voltage cables of the same amplitude, for example 230, which is effective in most European countries. sag with the skin phase, lie down in the tightness of the rest.
Possibility to use two operating voltages in one installation – phase and line.
The skin phase of a triphasic lancet can be standardly named:
first phase - phase "A"; another phase - phase "B"; the third phase is the "C" phase.
The ears of that end of the skin phase can also be standardized. Ears of the first, other and third phases are designated as A, B, C, and the last phases - X, Y, Z.
A three-phase strum allows you to solve problems with electricity, like a nearby single-phase strum. It is possible to show that a triphasic strum relieves mitigation without an impulse component, on the surface single-phase strumu, de mitteva tightness is a sinusoidal change of the subway frequency, superimposed on an uninterrupted warehouse.
It is necessary to express the pulsation of tension, as it also manifests itself in mechanical tension, which is transmitted by the shaft of the generator of the squirt, and transforms into a pulsation of the mechanical moment, which to twist, which can lead to the collapse of the rest. In addition, three-phase generators work faster than their single-phase counterparts, and three-phase mode reduce the amount of cost per hour of online transportation of electricity.
The main elements of the triphasic lanzug є: three-phase generator that converts mechanical energy into electrical energy; power lines; priymachi (spozhivachі), yakі can be three-phase (for example, three-phase asynchronous motors), and single-phase (for example, heating lamps).
2. Introduction of the three-phase EPC system.
The main appointment. Three-phase values. System of three-phase values, chirp electrical voltage or strumiv, maybe described by equals. Three-phase system Balanced and unbalanced The system of three-phase values is called balanced, because three values, sinusoidal functions of an hour, have the same amplitude. It's easy to misunderstand what one's mood is. Potim yogo can be entered in the form.
To change the order of the phases, tobto. go from the direct order to the reverse order, and at the same time, it is necessary to say the order of the two phases. Triphasic rozpodil Triphasic rozpodil revenge 3 or 4 darts. Triphasic conductors in times of balanced tension, so that they maintain the same strum of the skin from three phases. It should be applied, for example, to three-phase electric motors. Neutral conductor, which is systematic, but often rozpodіlyaєetsya. If the attachments do not survive an identical strum on the skin phase, a superfluous strum is established, which neutral wire nіk allows you to evacuate, to increase the voltage of the rated voltage on the skin of the three layers of stress.
A three-phase generator creates three EPCs at the same time, however, according to the value, they are changed in phase by 1200.
The design of the three-phase EPC system is based on the principle of electromagnetic induction, which is the same for a three-phase generator. Three-phase generator is a synchronous electrical machine. The simplest design of such a generator is shown in Fig. 3.1.
Internal installations are often referred to as triphasic strum. Squirts of strum, contraction of the skin phase, as a whole, revitalize and change over time, electrical installation living house є, as a rule, asymmetric ambition how to make sure the connection is neutral. As if the rest is guilty of being unfair, the deacons of the lancers can take the load off, which is richly shifting them Rated voltage what are the serious consequences for connecting to a new appliance and the safety of their coristuvachiv.
Mathematically, we can mean. Vykoristovuyuchi complex numbers and zvazhayuchi on balancing rozpodіl, not yet written. Path of designation of peak voltage. Composite voltages are a system of three-phase voltages only and only if the system simple voltageє a balanced system.
Rice. 3.1. Scheme to add a three-phase generator
On the stator of 1 generator are placed three-phase winding 2. The skin phase of the three-phase winding of the stator є sukupnіstyu dekіlkoh kotushok s nоyu kіlkіstyu vitkіv, roztashovanih at the grooves of the stator. On fig. 3.1 the skin phase is mentally represented by one turn. The three phases of the stator winding of the generator are rotated side by side by 1/3 of the stake, tobto. magnetic axes of the phases rotated in the open space
Three warehouse voltages are equal to zero. As a result, the homopolar warehouse voltage between the phases will reach zero. Spivvіdnoshennia between single and warehouse tension. Fresnel's data Fresnel's diagram of simple and storage voltages, which are transmitted by a three-phase direct balanced system, is shown on the protile baby.
Those same stosuєtsya and indirect zbalansovanoy system. Also, in balancing a three-phase system, the effective value of simple and storage voltage is related to spivvіdnennyam. Triphasic adopters: three-phase primach consists of three dipoles, also called windings and phases. Since three dipoles may have the same impedance, the receiver must be balanced. Connection of a three-phase receiver: Three dipoles, which add up a three-phase receiver, are connected with 6 terminals, sound out of place, as shown in the small picture below.
2 3 π = 120°. The cobs of the phases are marked with the letters A, B and C, and the ends - X, Y, Z.
Rotor 3 of the generator is a permanent electromagnet, which is excited by a constant winding winding 4. The rotor creates a permanent magnetic field, the power lines of which are shown in Fig. 3.1 by a dotted line. Under an hour of operation of the generator, the magnetic field wraps around at once with the rotor.
The advantage of this arrangement lies in the fact that it is possible to allow two clutches to be prepared with the same sizes, moreover, between two uninterrupted visnovkas, it is fast. Attachments may have three similar connections, most of which allow horizontal or vertical wiring. The number of lucky smugs is due to vicorist to reach the bag couplings: Z'ednannya star: the mirror-like windings are reached by the path of placing two terminal blocks in an offensive rank.
Three terminals that are left out will be connected to three-phase conductors. Three terminals, connected at the same time by two females, establish a point, as if we were changing in the neutral potential. This point is to blame, but it is connected to neutral, it has been dropped, as if the attachment does not have a balanced tension, for example, electric stove. For electrical machines, like, like and three-phase motors, may be balanced voltage, it is recommended not to connect the neutral. In the dawn zone, the linear and phase streams are the same.
When wrapping the rotor with a turbine with constant winding, the winding conductors of the stator winding with the power lines of the magnetic field are used. When this happens, a sinusoidal EPC is induced in the skin phase.
The value of EPC depends on the intensity of the magnetic field of the rotor and the number of turns in the winding.
The frequency of EPC is determined by the frequency of the wrapping of the rotor.
Then a phase cable is connected to the skin bar. Neutral cable not connected. At the tricot muff, it is necessary to spread the skin strum, which flows through the primaries. Kennelly's theorem. Tension, which is relieved by a triphasic primacy. Active force: Bouchereau's theorem imposes that the sum of forces equal to skin dipoles. .
For zbalansirovannyh priymachiv that kind of connection can be written. In sinusoidal mode, reactive tension is a noticeable part of the force that is given. Dipoles, which determine the impedance, the value of which is a purely visible number, may be zero active tensionі reactive tension, equal to the absolute value of their tightness. The tension is obvious: the tension, which is given, is accepted in the change mode, є by the addition of the rms value of the voltage on the dipole to the rms value electric struma that flows through the dipole.
Scatters of all phases of the stator winding are the same (mayut the same number of turns) and interchange with the same magnetic field of the rotor, which wraps, then the EPC of all phases may have the same amplitude E m and frequency ω.
2π | as the magnetic axis of the phases It is obvious that there is a tightness that is coming. Real tightness, which is given, is a module of apparent tightness. In other words, φ is the phase difference between the elastic and the strum. An alternative view of a three-phase generator of a zminny strum. Vіdsotok transmission of electricity. Three-phase transport saves cable and changes costs by joules: triphasic darts sufficient, since the phase zsuv between the skin phase is such that for a balanced system the sum of three strums is taken into account equal to zero і, also, the cream for saving the cable on large distances is taken as a bonus for the effect of joules. | space turn to | |||||||||||
120° cob phases їх ЕРС are drilled on the cut | 2π | ||||||||||||
We accept the cob phase of the EPC of phase A, which is equal to zero, so ψ eA = 0 Interest in the generation of electricity: the best generator of a squirrel strum: a three-phase generator of a squirt of a strumu from the very beginning was called the best compromise. More than 95% of electricity is generated by synchronous generators, electromechanical machines, which provide proportional wrapping. Qi machines are less expensive and may be better. Chim machine fast strumu, yakі zabezpechuyu napruga postіynogo struma Viraz delivered ї nabuvaє nabuvaє vglyadu. The turbine, through its inertia, wraps itself in a quasi-permanent mechanical fluidity, and at the same time at the skin moment it secures an identical tightness. Cіrіznіtі vіtuzhennostі prizvodіt to kolіvanі moment, scho to twist, іkі zdebіlіy vіdnayutsya іnіstіchnіstі transmission shaft і in kіntsemu p_іzku prіzvodi yogo ruynuvannya. | |||||||||||||
eA = Em sin ω t. | |||||||||||||
EPC phase V_dstaє vіd EPC phase A on | 2π | ||||||||||||
2π | Em sin(ω t − 120) . | ||||||||||||
eB = Em sin ω t− | |||||||||||||
2π | |||||||||||||
EPC phasing Z visible in EPC phasing on | |||||||||||||
4π | Em sin(ω t − 240) . | ||||||||||||
eС = Em sin ω t− | |||||||||||||
Chinne value of EPC of all phases is the same:
E | E | Em= E | ||||||
A three-phase symmetric EPC system can be represented by trigonometric functions, functions of a complex snake, graphs on clock diagrams, vectors on vector diagrams.
Analytical representation by trigonometric functions is induced in (3.1) - (3.3).
In a complex view, the EPC phases are represented by their complex values, which are:
j0 | ee | − j 120 | − j 2400 |
|||||
EA = Ee | E; EB | ; EC = Ee |
Graphs of mittevikh three-phase values symmetrical system The EPC on the clock diagram is shown in fig. 3.2. The stench is three sinusoids, zsunuti one at least one for 1/3 part of the period.
Rice. 3.2. Graphs of the mittiev of the value of the three-phase symmetric system EPC.
On the EPC vector diagram, the phases are represented by vectors of the same length, rotated one by one by 120 ° (Fig. 3.3).
Rice. 3.3. EPC vector diagram of three-phase symmetrical systems. (a – direct sequence of phases; b – reverse sequence of phases).
Since EPC induction in the stator windings may have the same amplitudes and phase failures, one alone at the same 120 ° cut, the three-phase EPC system is symmetrical.
It should be noted that the wiring of the phase EPC hours should be directly wrapped around the generator rotor along the three-phase stator winding. When wrapping the rotor behind the year hand, as shown in Fig. 3.1, a symmetrical three-phase EPC system can be directly drawn (A - B - C) (Fig. 3.3a). When wrapping the rotor with the opposite arrow, the EPC system is also symmetrical three-phase. The drafting of the phase EPCs will change at the hour. Such a drawing is called a return (A - C - B) (Fig. 3.3b).
It is important to check the numbering of phase EPCs when analyzing triphasic lancets and attachments. For example, the sequence of phases directly indicates the wrapping three-phase motors, etc. For a practical designation of the sequence of phases, special accessories are used - phase guides.
For ablutions in case of triphasic lances and their analyses, direct drawing of phasic EPCs of a triphasic dzherel is taken.
In the diagrams, the stator winding of the generator is shown, as shown in fig. 3.4a s of the accepted designations of the beginnings and ends of the phases.
On the substitution scheme, the three-phase dzherel is represented by three ideal dzherel EPC (Fig. 3.4b)
Rice. 3.4. Clever image of the generator winding stator.
For a mentally positive direct EPC in the skin phase, it is taken directly from the end of the phase to the cob.
3. Ways to connect the phases of a triphasic lance.
In order to induce a triphasic lancet to the skin phase of a triphasic dzherel, one phase of the triphasic intake is applied.
Fig. 3.5 Scheme of an unconnected three-phase lanzug.
Here, the three-phase dzherel is represented by three ideal dzherels EPC E&A, E&B, E&C. The three phases of the adopter are mentally ideal
elements with higher complex supports Z a, Z b, Z c. The skin phase of the priymach comes to the secondary phase of the dzherel, as shown in fig. 3.5. At whom three electric lances are established, structurally united by one three-phase dzherel, tobto. triphasic lanceug. In this lance, the three phases are combined only constructively and can be connected to each other by an electrical connection (electrically connected to each other). Such a lancet is called an incomprehensible triphasic lancet and practically does not vicorate.
In fact, three phases of a triphasic lancer are connected to each other (electrically connected).
Іsnuyut different ways connection of phases of three-phase dzherelta triphasic sleepers electricity. The most widened ones are "zirka" and "trikutnik". With this method, the phases of the dzherel and the phases of the slowing down phases in three-phase systems can be different. The phases of the dzherela sound like a “star”, the phases of the calm ones sound either a “star” or a “trikutnik”.
When the phases of the winding of the generator (or transformer) are connected, the “star” of їх kіntsi X, Y і Z is connected to one central point N, called the neutral point (or neutral) (Fig. 3.6). The ends of the phases of the adopters x, y, z also converge at one point n (neutral point of the adopter). Such a half is called "zirka".
Rice. 3.6. Scheme of joining the phases of the dzherel and priymach in the star.
Wire A-a, B-b and C-c, which connect the cob of the phases of the generator and the receiver, are called line wires (line wire A, line wire, line wire Z). Conduct N-n, which hits the point N of the generator with the point of acceptance, is called the neutral dart.
Here, as before, the skin phase is an electric lance, in which case the connections to the dual phase of the dzherel are used for the help of a neutral dart and one of the linear dart (dashed line in Fig. 3.6). However, on the view of an unconnected triphasic lance, the transmission lines have a smaller number of wires. The purpose of choosing one of the advantages of three-phase lances is the economy of energy transmission.
When the phases of the triphasic dzherel live with a tricot (Fig. 3.12), the end X of one phase closes with the ear of the other phase, the end Y of the other phase - with the ear of the third phase, the end of the third phase Z - with the ear of the first phase A. Ears A, B and Z of phases are connected for additional three wires to three phases of the primach, also using the "trikutnik" method.
Rice. 3.7. The scheme for connecting the phases of the dzherela and the primach at the trikutnik
Here, too, the skin phase is an electric lance, in which it is possible to connect to the second phase of the dzherel for the help of two linear wires (dotted line in Fig. 3.7). However, the transmission line has even fewer wires. The goal is to transfer electricity more economically.
With the method of calling the "tricutnik" of the phase of the primach, two symbols are called similarly to the linear darts, to which the phase is connected: phase "ab", phase "bc", phase "ca". The phase parameters are set
with different indices: Z ab ,Z bc ,Z ca
4. The voltages of the three-phase dzherel.
Three-phase dzherelo, connected by the "zirka" method, creating two three-phase voltage systems different sizes. At what point do the phases of the voltage differ line voltage.
Figure 3.8 shows the substitution scheme of a three-phase dzherel, connected by a "star" and connected to a power line.
Fig.3.8. Substitution scheme of a three-phase dzherel
Phase voltage U Ф - voltage between the cob and the end of the phase or between the linear drotom and the neutral (U & A, U & B, U & C). For mentally
positive direc- tions of the phase voltage take the direc- tions in the cob until the end of the phases.
Line voltage (U L) - voltage between line wires or between phase cobs (U & AB, U & BC, U & CA). Mentally positive
the straight lines of the line voltages are taken from a point that matches the first index, to a point that matches another index (that is, from a point with a higher high potential to a point with a lower one) (Fig. 3.8).
The development of rich-phase systems was zoomed in historically. Studies in this region were viklikanі vymogami vyrobnitstv, scho develop, and successes in the development of rich-phase systems have spliced evidence from the physics of electrical and magnetic phenomena.
The most important reason for the expansion of rich-phase electrical systems was the appearance of a magnetic field that turns around (G. Ferraris and N. Tesla, 1888). The first electric motors were two-phase, but they had low operating characteristics. The most rational and promising was the three-phase system, the main advantages of which will be considered further. A great contribution to the development of three-phase systems was made by the well-known Russian teaching-electrical engineer M.O.
Dzherelom three-phase voltage - a three-phase generator, on the stator of which (div. Fig. 1) a three-phase winding is placed. The phases of the coil windings are roztashovuyutsya in such a rank, so that their magnetic axes will be put out of the open space one at a time for eating. radium. On fig. 1 skin phase of the stator is mentally shown as one turn. Cobs of windings are considered to be great letters A, B, C, And kіntsi - apparently great x, y, z. EPC in the non-robust stator windings are induced as a result of a turn of their turns by a magnetic field, which creates a winding winding excitation of the rotor, which wraps around (in Fig. 1, the rotor is mentally imaged at a permanent magnet, which turns into practice at a low pressure). When the rotor is wrapped with equal swirl in the windings of the stator phases, sinusoidal EPCs are induced, which periodically change, however, the same frequency and amplitude, and then they are blown out of space, one in one in phase per rad. (Div. small 2).
Triphasic systems in Denmark have gained the greatest width. On the three-phase stream, there are a lot of large power plants and slow-moving ones, which are due to the low transcendence of the three-phase lances in front of the single-phase ones, the most important of them:
Economy of transmission of electric power is great;
The most economical, which satisfies the power of the industrial electric drive is an asynchronous motor with a short-circuited rotor;
Possibility of otrimannya for the help of non-robust windings of the magnetic field, what turns around, what is the basis of the synchronous robot asynchronous motors, as well as a number of other electrical appliances;
Vrivnovazhenist of symmetrical three-phase systems.
To see the most important dominance three-phase system, as will be brought further, let us understand the symmetry of the rich-phase system.
The EPC system (voltage, current flow) is called symmetrical as it is, there are m equals for the module of EPC vectors (voltage, strums, etc.), failures in phase, one at a time, one at a time. Zokrema vectordiagram for a symmetrical EPC system, which is similar to a three-phase sinusoidal system in fig. 2 is shown in fig. 3.
 |
|
| Fig.3 | Fig.4 |
W non-symmetric systems The greatest practical interest is to become a two-phase system with a 90-degree phase failure (div. Fig. 4).
All symmetrical tri- and m-phase (m>3) systems, as well as two-phase systems investment. Tse means that in the last phases of the mitteva, the tension of the pulse (div. Fig. 5, a), changing not only the value for an hour of one period, but in the total depression, the sign, the total mitteva of all phases is filled with a constant value of the stretch of the sinus period of the sinus (div. Fig. 5, b).
Timeliness is more important than practical value. Yakby sumarna mitteva the tension throbbed, then on the shaft between the turbine and the generator there was a pulsating moment. Such a change in mechanical innovation would be shkidbilosly used on power generating installations, a short term of service. Qi w mirkuvannya can be seen and up to rich-phase electric motors.
If the symmetry is destroyed (Tesla's two-phase system, due to its specificity, is not accepted to respect), then the vrіvnovazhenіst is also destroyed. That's why it's hard to follow him in the energy sector, so that the generator's voltage becomes symmetrical.
Circuit diagrams for three-phase systems
A three-phase generator (transformer) may have three windings, however, for the number of turns, but also develop EPC, phase failures by 1200. It would be possible to reverse the system, in which phase the generator windings would not be galvanically connected one to one. Tse is so called awkward system. And here the skin phase of the generator must be connected with two wires, tobto. mother of the six-wire line, which is non-economical. In connection with cym, similar systems did not take away a wide zastosuvannya in practice.
To change the number of rods, the phase lines of the generator are galvanically connected to each other. Distinguish two kinds of z'ednan: at the sirkuі at the trickster. At your own discretion, when connected to the mirror, the system can be three-і chotiriprovidny.
Z'ednannya at the zirku
On fig. 6, a three-phase system is induced when the generator phases are connected and driven into the star. Here the darts AA', BB' and CC' are linear darts.
Linear the wire is called, which connects the cob of the phases of the generator winding and the primach. Krapka, at some end of the phases, they grow up at the deep vuzol, they are called neutral(in Fig. 6, N and N' are apparently neutral points of the generator and the bias).
The conductor that connects the neutral points of the generator and the receiver is called neutral(In Fig. 6, the indications are dotted). A three-phase system when connected to the mirror without a neutral drotu is called triprovidny, with a neutral dart - chotiriprovidny.
All quantities that are seen before the phases sound phase change, to the line - linear. As can be seen from the diagram in Fig. 6, when entering into the mirror linear streams and dovnyuyut vіdpovіdnim phase strums. For the presence of a neutral dart strum at a neutral dart 
. Yakscho system phase streams is symmetrical, then . Since the yakbi symmetry of the strum is guaranteed, then the neutral wire is not needed. As will be shown further, the neutral conductor ensures the improvement of the symmetry of the voltage on the vane while the asymmetry of the vane itself.
(The first phase is close to zero), it is possible to phase failure of the linear stresses along the extension to the center axis, and their modules are visible to (4). So for linear voltages and in the tricoutnik prot_katime strum short hum. Also, for a tricoutnik, it is necessary to strictly trim the order of the phases: the cob of one phase starts with the end of the other.
The scheme for connecting the phases of the generator and the primach into the trikutnik is shown in fig. nine.
It is obvious that when connected to the tricot, the linear voltages are equal to the corresponding phases. According to the first law of Kirchhoff, the connection between linear and phase strumas is marked by spontaneity
Similarly, it is possible to visualize linear streams through phase strums generators.
On fig. 10 shows a vector diagram of a symmetrical system of linear and phase streams. Її analysis shows that the symmetry of the strum
| . | (5) |
At the end, it is significant that the Crimean days “zirka - zirka” and “tricutnik - tricutnik” in practice are also zastosovuyutsya schemes “zirka - trikutnik” and “tricutnik - zirka”.
Literature
- foundations theory of lanzugiv: Navch. for universities / G.V.Zeveke, P.A.Ionkin, A.V.Netushil, S.V.Strakhov. -5th species., Rev. -M.: Vishcha school, 1989. -528s.
- Bezsonov L.A. Theoretical foundations electrical engineering: Electrical stake. Navch. for students of electrical engineering, energy and industrial specialties of universities. -7th view., Rev. that dod. -M.: Vishch. school, 1978. -528s.
