On the lowering ω 1>ω 2 ; U 1>U 2 ; To>1 ;

On the transitional ω 1 =ω 2 ; U 1=U 2 ; K=1.

Analysis of the transformer operation.

1. Idle mode

In this mode, the secondary winding is open. The switch is in position 1.The current consumed by the primary circuit is minimal and is called no-load current. The magnetic field around the primary winding is called the no-load magnetic field. This mode is harmless to the transformer.

2. Operation of the transformer in load mode

Turn the switch on position 2, while the transformer from the idle mode goes into the load mode. Current flows through the secondary winding I 2, whose magnetic flux, according to Lenz's law, is directed against the magnetic field of the primary winding Φ . As a result, the magnetic flux Φ at the first moment decreases, which causes a decrease in e. d.s. self-induction E 1 in the primary winding of the transformer. Since the applied voltage U 1 (mains, generator) remains unchanged, the electrical balance between voltage and e. d.s. self-induction is broken and there is an increase in current in the primary winding. An increase in current leads to an increase in magnetic flux, which in turn causes an increase in e. d.s. self-induction. This process continues until the electrical equilibrium between the applied voltage and e is restored. d.s. self-induction. But in this case, the current of the primary winding will be greater than at idle, i.e., the total magnetic flux of the primary and secondary windings of the transformer in load mode is equal to the magnetic flux of the primary winding in idle mode.

So, in the load mode, that is, when a secondary current appears, the primary current increases, a voltage drop is created in the secondary winding and the secondary voltage decreases. With a decrease in the load, i.e., with a decrease in the secondary current, the demagnetizing effect of the secondary winding decreases, the magnetic flux in the core at the first moment increases and e increases accordingly. d.s. self-induction E 1 . The electrical balance between U 1 and E 1 is disturbed, the current in the primary winding decreases, while there is a decrease in the magnetic flux and e. d.s. self-induction. This process continues until the temporarily disturbed electrical balance between U 1 and E 1 is restored, but at a lower current I 1 .

So, a decrease in current I 2 leads to a decrease in current I 1, the voltage drop in the secondary winding of the transformer decreases and the secondary voltage increases.

Any change in the secondary current causes a change in the primary current, aimed at maintaining a constant magnetic flux in the core of the transformer.

Now turn the switch on position 4.

The resistance of the secondary circuit will practically be equal to zero. The current of the secondary circuit will be maximum, the magnetic field of the secondary winding will be maximum. The magnetic field of the primary winding will decrease and become minimal, therefore, the inductive resistance of the primary winding will also become minimal. The current consumed by the primary circuit will increase to a maximum. This mode is called short circuit mode. This mode is dangerous for the transformer and the entire circuit. To protect against short circuits, fuses are installed in the primary or secondary circuit.

Can a transformer gain power?

The power developed in the primary circuit is equal to the product of U 1 * I 1 in the secondary circuit U 2 * I 2. The transformer does not give a gain in power, since any increase in voltage with the help of a transformer is accompanied by a corresponding decrease in current, i.e. how many times the transformer will increase the voltage so many times it will reduce the amount of current in the secondary circuit. In a step-down transformer, how many times the transformer will reduce the voltage by how many times it will increase the amount of current in the secondary circuit.

Transformer efficiency

Efficiency is the ratio of secondary power P 2 to primary P 1 (useful power to consumed) expressed in%.

For example, the efficiency of a transformer is 90%, which means that 90% of the energy received by the primary winding from the current source goes into the secondary winding and 10% is lost in the transformer at the active resistance of the transformer. The presence of losses leads to the fact that the power released in the load of the secondary winding of the transformer is always less than the power consumed by the primary winding.

Energy losses in a transformer consist of core losses and winding losses. Core losses include magnetic hysteresis loss and eddy current loss. Losses in the windings are due to the usual heating of the windings by current.

The efficiency of powerful stationary transformers is up to 99%. The efficiency of low-power transformers used in communication equipment is taken as 80%.

1. Winding

For the production of transformer windings, winding wires are used, they are copper and have insulation.

PE-wire enameled

PEL wire enameled varnish-resistant

Enamelled high-strength PEV-wire

PEL is designed for temperatures up to 90 0 , briefly 105 0 ; PEV up to 105 0, short-term up to 125 0

The windings are wound on a frame (plastic, textolite, getinaks, cardboard), there is also a frameless winding. The end of the winding wire must be fixed. The windings are wound in rows turn to turn. After each row, insulation is laid (a strip of capacitor or cable paper) so that there is no breakdown. The other end of the winding must also be fixed. After winding the first winding, better insulation is laid, for example, a strip of varnished cloth, then the next winding is wound. The windings are wound one on top of the other. Often, in the manufacture of transformers, the primary and secondary windings are divided into sections. In this case, the magnetic field of the primary winding better covers the secondary winding.

2. Cores

Cores are: rod, armor and toroidal.

For the production of cores, transformer steel of various grades is often used. The core is made of thin steel plates isolated from each other. As insulation, oxide (scale) is often used, which forms on the surface of the plates when they are heated during high temperature. If the core is made not from separate plates isolated from each other, but from two folded pieces, then the core will be heated by eddy currents. The eddy currents of the individual plates are small and, in general, the core heats up insignificantly. The core of the transformer must be well compressed so that it does not hum. The best way to compress is to compress with studs with nuts. Often, compression is applied with a staple that surrounds the core.

Transformer steel cores are poorly magnetized in weak magnetic fields. Therefore, at low audio frequencies Permalloy cores are used. Permalloy is an alloy of nickel, molybdenum, chromium, manganese, copper, silicon and iron.

Ferrite cores are used in high-frequency current circuits. Ferrite is a magnetodielectric, that is, a dielectric with magnetic properties. It is made from metal oxides in powder form mixed with resin or polystyrene.

Consists of two separate windings, called primary and secondary windings. An AC input voltage is applied to the primary winding and creates a changing magnetic field. This magnetic field interacts with the secondary winding, inducing an alternating current voltage (more precisely, EMF) in it. The voltage induced in the secondary winding has the same frequency as the input voltage, but its amplitude is determined by the ratio of the number of turns of the secondary and primary windings.

If the input voltage at the terminals of the primary winding = V1
output voltage at secondary terminals = V2
number of primary turns = T1
number of secondary turns = T2

then

In addition, I1/ I2 = T1/ T2, where I1 and I2 are the primary and secondary currents, respectively.

Coefficient of performance (COP) of the transformer

The above ratios assume that the transformer is 100% efficient, i.e. there is no power loss at all. Consequently,
Input power I1 V1 = Output power I2 V2.
In practice, transformers have an efficiency of about 96-99%. To increase the efficiency of the transformer, its primary and secondary windings are wound on the same magnetic core (Fig. 7.10).

step-up and step-down transformers

The step-up transformer produces at the output (in the secondary winding) more than high voltage than applied at the input (to the primary winding). For this, the number of turns of the secondary winding is made greater than the number of turns of the primary winding.
A step-down transformer produces less voltage at its output than at its input, since its secondary winding has fewer turns than the primary.

The transformer shown in fig. 7.11, has a load resistor r2 in the secondary winding circuit. The resistance r2 can be recalculated or, as they say, brought to the primary winding, that is, to the resistance of the transformer r1 from the side of the primary winding. The ratio r1/r2 is called the drag coefficient. This ratio can be calculated as follows. Since r1 = V1 / I1 and r2 = V2 / I2, then

Rice. 7.10. Transformer.

Rice. 7.11. Reduction factor
resistance

r1/ r2 = T12/ T22 = n2.

Rice. 7.12. Autotransformer.

Rice. 7.13. Autotransformer with multiple taps.

But V1 / V2 = T1 / T2 = n and I2 / I1 = T1 / T2 = n, so

r1 / r2 = n2

For example, if the load resistance r2 \u003d 100 Ohm and the ratio of the number of turns of the windings (transformation ratio) T1 / T2 \u003d n \u003d 2: 1, then from the side of the primary winding the transformer can be considered as a resistor with a resistance of r1 \u003d 100 Ohm 22 \u003d 100 4 \u003d 400 Ohm.

A transformer may have a single winding with one tap from a portion of the turns of this winding, as shown in Fig. 7.12. Here T1 is the number of turns of the primary winding and T2 is the number of turns of the secondary winding. Voltages, currents, resistances and transformation ratio are determined by the same formulas that apply to a conventional transformer.
On fig. 7.13 shows another transformer with a single winding, in which several taps are made from this winding. All ratios for voltages, currents and resistances are still determined by the transformation ratio (V1/Va = T1/Ta, V1/Vb = T1/Tb, etc.).

On fig. 7.14 shows a transformer with a tap from the middle of its secondary winding. The output voltages Va and Vb are taken from the upper and lower halves of the secondary winding. The ratio of the input voltage (on the primary winding) to each of these output voltages is determined by the ratio of the number of turns, and

V1/Va = T1/Ta V1/Vb = T1/Tb

where T1, Ta and Tb are the number of turns of the primary, secondary a and secondary b windings, respectively. Since the tap is made from the middle of the secondary winding, the voltages Va and Vb are equal in amplitude. If the middle point is grounded, as in the circuit in fig. 7.14, then the output voltages taken from the two halves of the secondary winding are in antiphase.

Example

Let's turn to Fig. 7.15. (a) Calculate the voltage between terminals B and C of the transformer, (b) If there are 30 turns between terminals A and B, how many turns does the secondary winding of the transformer have?
Solution
a) VBC = VAD - VAB - VCD = 36V - 6V - 12V = 18V.
Number of turns between A and B
b) VAB / VAD == ---------------
Number of turns between A and D

Therefore, 6V/36V = 30/TAD, hence TAD = 30 36/6 = 180 turns.

Rice. 7.14. Transformer with a tap from the middle point of the secondary winding.

Rice. 7.15. VAD = 36V, VAB = bV,
VCD=12V.

Magnetic circuit

It is customary to say that in a magnetic circuit, a magnetic flux (or magnetic field), measured in Tesla, is created by a force called magnetomotive force (MMF). A magnetic circuit is usually compared to an electrical circuit, with magnetic flux being compared to current and magnetomotive force to electromotive force. Just like they say about the resistance R electrical circuit, we can talk about the magnetic resistance S of the magnetic value; these terms have the same meaning. For example, a soft magnetic material such as malleable iron has low magnetic resistance, i.e. low resistance to magnetic flux.

Magnetic permeability

The magnetic permeability of a material is a measure of how easily it can be magnetized. For example, malleable iron and other electromagnetic materials such as ferrites have high magnetic permeability. These materials are used in transformers, inductors, relays and ferrite antennas. In contrast, non-magnetic materials have very low magnetic permeability. Magnetic alloys such as silicon steel have the ability to remain magnetized in the absence of a magnetic field and are therefore used as permanent magnets in loudspeakers (dynamic heads), moving coil magnetoelectric meters, etc.

Shielding

Consider a hollow cylinder placed in a magnetic field (Fig. 7.16). If this cylinder is made of a material with low magnetic resistance (soft magnetic material), then the magnetic field will be concentrated in the walls of the cylinder, as shown in the figure, without falling into its inner region.

Rice. 7.16. Magnetic shielding.

Rice. 7.17. Electrostatic shielding in a transformer.

Therefore, if any object is placed in this area, it will be protected (shielded) from the influence of the magnetic field in the surrounding space. This shielding, called magnetic shielding, is used to protect cathode ray tubes, moving coil magnetoelectric meters, dynamic loudspeakers, etc. from external magnetic fields.
Transformers sometimes use another type of shielding called electrostatic or electrical shielding. A shield of thin copper foil is placed between the primary and secondary windings of the transformer, as shown in Fig. 7.17. When such a screen is grounded, the effect of the capacitance between the windings, which occurs due to the potential difference between these windings, is greatly reduced. Electrostatic shielding is also used in coaxial cables and wherever conductors have different potentials and are in close proximity to each other.

This video talks about what a transformer is:

transformer called a static electromagnetic device that has two (or more) inductively coupled windings and is designed to convert one (primary) alternating current system into another (secondary) alternating current system through the phenomenon of electromagnetic induction.

In the general case, the secondary AC system can differ from the primary one in any parameters: voltage and current values, number of phases, voltage (current) waveform, frequency. The greatest application in electrical installations, as well as in energy transmission and distribution systems of electricity, are power transformers of general use, through which the values ​​​​of alternating voltage and current are changed. In this case, the number of phases, the shape of the voltage (current) curve and the frequency remain unchanged.

When considering the issues of this lecture, we will keep in mind power transformers for general use.

Consider the principle of operation of the simplest single-phase transformer. The simplest single-phase power transformer consists of a magnetic circuit (core) made of ferromagnetic material (usually sheet electrical steel) and two windings located on the cores of the magnetic circuit.

Why is the magnetic core of a transformer made of ferromagnetic material?

One of the windings, which is called primary, connected to an alternating current source for voltage U 1 . To another winding called secondary connected consumer Zн. The primary and secondary windings of the transformer do not have an electrical connection with each other, and the power from one winding to another is transmitted electromagnetically.

What is the purpose of a transformer core?

The magnetic circuit on which these windings are located serves to enhance the inductive coupling between the windings.

The action of the transformer is based on the phenomenon of electromagnetic induction (Fig. 2).

Rice. 2. Electromagnetic circuit of the transformer

When connecting the primary winding of the transformer to an alternating current network with voltage U 1 alternating current will flow through the winding i 1 , which will create a variable magnetic flux in the magnetic circuit F . The magnetic flux, penetrating the turns of the secondary winding, induces in it e 2 , which can be used to power the load. Closing in the magnetic circuit, this flux couples with both windings (primary and secondary) and induces an EMF in them:

In the primary EMF of self-induction:

In the secondary EMF of mutual induction:

When connecting the load Zn to the terminals of the secondary winding of the transformer under the action of EMF e 2 a current is created in the circuit of this winding i 2 , and the voltage U 2 is set at the terminals of the secondary winding.

Can a transformer run on direct current?

A transformer is an alternating current device. If its primary winding is connected to a direct current source, then the magnetic flux in the magnetic circuit of the transformer will be constant both in magnitude and in direction (dФ / dt \u003d 0), therefore, EMF of electromagnetic induction will not be induced in the transformer windings, and therefore, electricity from primary circuit will not be transferred to the secondary.

How is the problem of changing the voltage, for example, increasing it, on the secondary winding of the transformer solved?

The problem of increasing the voltage is solved as follows. Any turn of the transformer winding has the same voltage, if the number of turns on the secondary winding is increased compared to the primary winding, then the turns are connected in series, the voltage received on each of the turns will be summed up. Therefore, by increasing or decreasing the number of turns, it is possible to increase or decrease the voltage at the output of the transformer.

Since the primary and secondary windings of the transformer are pierced by the same magnetic flux F , expressions effective values EMF can be written as

where f - AC frequency; w 1 and w 2 - the number of turns of the primary and secondary windings.

Dividing one equality by another, we get an important parameter of the transformer - the transformation ratio:

where k - transformation coefficient.

If the circuit of the secondary winding of the transformer is open (idle), then the voltage at the terminals of the winding is equal to its EMF: U 2 = E 2 , and the power supply voltage is almost completely balanced by the EMF of the primary winding U 1 ≈ E 1 . Therefore, one can write that

Given the high efficiency of the transformer, it can be assumed that S 1 ≈ S 2 , where S 1 = U 1 I 1 - power consumed from the network; S 2 = U 2 I 2 - power delivered to the load.

In this way, U 1 I 1 ≈ U 2 I 2 , where

The ratio of the currents of the secondary and primary windings is approximately equal to the transformation ratio, so the current I 2 how many times increases (decreases), how many times decreases (increases) U 2 .

in step-up transformers U 2 > U 1 , in decreasing U 2 < U 1 . Transformers have the property of reversibility, the same transformer can be used as step-up and step-down. But usually a transformer has a specific purpose: either it is step-up or step-down. The winding of a transformer connected to a network with a higher voltage is called a high voltage winding (HV); a winding connected to a lower voltage network - a low voltage winding (LV).

Why is high voltage used in power transmission?

The answer is simple - to reduce the heating losses of wires during transmission over long distances. Losses depend on the amount of current flowing and the diameter of the conductor, and not on the applied voltage.

Let's assume that from a power plant to a city located at a distance of 100 km from it, it is necessary to transmit electricity of 30 MW along one line. Due to the fact that the wires of the line have electrical resistance, the current heats them up. This heat is dissipated and cannot be used. The energy spent on heating is a loss.

It is impossible to reduce losses to zero. But they need to be limited. Therefore, the allowable losses are normalized, i.e. when calculating the cross sections of the line wires and choosing its voltage, it is assumed that the losses do not exceed, for example, 10% of the useful power transmitted over the line.

In our example, this is 0.1x30 MW = 3 MW.

If transformation is not applied, i.e., electricity is transmitted at a voltage of 220 V, then in order to reduce losses to a given value, the cross section of the wires would have to be increased to approximately 10 m 2. The diameter of such a "wire" exceeds 3 m, and the mass in the span is hundreds of tons.

Applying transformation, that is, increasing the voltage in the line, and then, reducing it near the location of consumers, they use another way to reduce losses: they reduce the current in the line.

What is the relationship between active power and current?

Losses in the transmission of electricity are proportional to the square of the current strength.

Indeed, when the voltage is doubled, the current is halved, and the losses are reduced by 4 times. If the voltage is increased by 100 times, then the losses will decrease by 100 2, i.e., by 10,000 times.

We illustrate this expression with the following example. The figure shows the energy transfer diagram (Fig. 3). A generator with a terminal voltage of 6.3 kV is connected to the primary winding of a step-up transformer. The voltage at the ends of the secondary winding is 110 kV.

Rice. 3. Power transmission scheme:

1 - generator; 2 - step-up transformer; 3 - power line;

4 - step-down transformer; 5 - consumer

At this voltage, energy is transferred along the transmission line. Let the transmitted power be 10,000 kW, there is no phase shift between current and voltage.

Since the powers in both windings are the same, the current in the primary winding is equal to, I \u003d P / U \u003d 10000 / 6.3 \u003d 1590 A, and in the secondary winding 10000/110 \u003d 91 A. The current in the line wires will have the same value transmission.

The principle of operation of a transformer can be demonstrated by the following educational film: "The principle of operation of a step-down transformer", "Heating water using a transformer."

Let's consolidate the material covered by answering the following questions.

The principle of operation of the transformer is based on ...

Ampère's law

Ohm's laws

Kirchhoff's laws

law of electromagnetic induction

If the number of turns of the primary winding of the transformer is w1=100, and the number of turns of the secondary winding is w2=20, determine the transformation ratio.

Not enough data to answer.

The effective value of the EMF induced in the transformer windings is determined by the formulas

Conclusion on the first question: The principle of operation of the transformer is based on the phenomenon of electromagnetic induction, therefore the transformer is an alternating current device. The voltage conversion in the transformer is carried out by changing the number of turns in the secondary winding. The main purpose of the transformer is to convert electricity of one voltage into electricity of another voltage in order to reduce capital investments in the construction and operation of power lines.