On downgrading ω 1>ω 2 ; U 1>U 2 ; TO>1 ;

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

Analysis of 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 the 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 on the switch in position 2, in this case the transformer goes from idle mode to load mode. Current flows through the secondary winding I 2, the magnetic flux of which, 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 it 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 disrupted and the current in the primary winding increases. 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 electrical equilibrium is restored between the applied voltage and e. d.s. self-induction. But in this case, the current of the primary winding will be greater than during no-load mode, 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 no-load mode.

So, in load mode, i.e., when a secondary current appears, the primary current increases, a voltage drop is created in the secondary winding and the secondary voltage decreases. When the load decreases, i.e., when the secondary current decreases, the demagnetizing effect of the secondary winding decreases, the magnetic flux in the core at the first moment increases and, accordingly, e increases. d.s. self-induction E 1. The electrical balance between U 1 and E 1 is disrupted, the current in the primary winding decreases, and the magnetic flux and e.m. decrease. 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 transformer core.

Now let's turn on the switch position 4.

The resistance of the secondary circuit will be practically zero. The secondary circuit current 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 reactance of the primary winding will 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 U 1 * I 1 in the secondary circuit U 2 * I 2. The transformer does not provide any gain in power since any increase in voltage using a transformer is accompanied by a corresponding decrease in current, i.e. how many times will the transformer increase the voltage this is how many times it will reduce the current in the secondary circuit. In a step-down transformer, the number of times the transformer will reduce the voltage is the number of 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 power) 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 through 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 losses and eddy current losses. Losses in the windings are caused by the usual heating of the windings by current.

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

1.Windings

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

PE wire enameled

PEL wire, enameled, paint-resistant

High-strength enameled PEV wire

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

The windings are wound on a frame (plastic, textolite, getinax, cardboard), and there is also frameless winding. The end of the winding wire must be secured. The windings are wound in rows of turns to turn. After each row, insulation is laid (a strip of capacitor or cable paper) to prevent breakdown. The second end of the winding must also be secured. After winding the first winding, better insulation is laid, for example, a strip of varnished fabric, then the next winding is wound. The windings are wound one on top of the other. Often in the production 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

There are cores: rod, armor and toroidal.

Transformer steel of different grades is often used for the production of cores. The core is made of thin steel plates isolated from each other. Oxide (scale) is often used as insulation, which forms on the surface of the plates when they are heated at 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. Eddy currents of individual plates are small and, overall, the core heats up slightly. The transformer core must be well compressed so that it does not hum. The best compression method is using studs and nuts. Often compression is applied using a staple around 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, i.e. a dielectric with magnetic properties. It is made from metal oxides in powder form mixed with resin or polystyrene.

It consists of two separate windings called primary and secondary windings. The AC input voltage is applied to the primary winding and creates a varying 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 primary winding terminals = V1
output voltage at secondary terminals = V2
number of turns of the primary winding = T1
number of turns of the secondary winding = T2

That

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

Transformer efficiency (efficiency)

The above ratios assume that the transformer is 100% efficient, i.e. there is absolutely no power loss of any kind. Hence,
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

A step-up transformer produces at the output (in the secondary winding) more high voltage than applied at the input (to the primary winding). To do 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 the input because 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. Resistance r2 can be recalculated or, as they say, reduced to the primary winding, i.e., to the resistance of the transformer r1 from the side of the primary winding. The ratio r1/r2 is called the resistance reduction coefficient. This coefficient can be calculated as follows. Since r1 = V1 / I1 and r2 = V2 / I2, then

Rice. 7.10. Transformer.

Rice. 7.11. Reduction coefficient
resistance

r1/ r2 = Т12/ Т22 = n2.

Rice. 7.12. Autotransformer.

Rice. 7.13. Autotransformer with several taps.

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

r1 / r2 = n2

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

A transformer may have one single winding with one tap from part 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 ratios are determined by the same formulas that apply to a conventional transformer.
In Fig. Figure 7.13 shows another transformer with a single winding, in which several taps are made from this winding. All relationships for voltages, currents and resistances are still determined by the transformation ratio (V1/Va = T1/Ta, V1/Vb = T1/Tb, etc.).

In Fig. Figure 7.14 shows a transformer with a tap from the middle of its secondary winding. The output voltages Va and Vb are removed 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 removed 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 30 turns are wound between terminals A and B, how many turns does the secondary winding of the transformer have?
Solution
a) VBC = VAD – VAB – VCD = 36 V – 6 V – 12 V = 18 V.
Number of turns between A and B
b) VAB / VAD == ---------------
Number of turns between A and D

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

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

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

Magnetic circuit

It is commonly said that in a magnetic circuit, the magnetic flux (or magnetic field), measured in teslas, is created by a force called magnetomotive force (MMF). A magnetic circuit is usually compared to an electrical circuit, with magnetic flux compared to current and magnetomotive force to electromotive force. Just like they talk about resistance R electrical circuit, we can talk about the magnetic resistance S of the magnetic value; these concepts have a similar meaning. For example, a soft magnetic material such as ductile iron has low magnetic reluctance, that is, low resistance to magnetic flux.

Magnetic permeability

The magnetic permeability of a material is a measure of its ease of magnetization. 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 maintain a magnetized state in the absence of a magnetic field and are therefore used as permanent magnets in loudspeakers, 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 entering its internal area.

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, loudspeaker drivers, etc. from external magnetic fields.
Transformers sometimes use another type of shielding called electrostatic or electrical shielding. A thin copper foil screen is placed between the primary and secondary windings of the transformer, as shown in Fig. 7.17. When such a screen is grounded, the influence of capacitance between the windings, which arises due to the potential difference between these windings, is greatly reduced. Electrostatic shielding is also used in coaxial cables and anywhere where conductors have different potentials and are in close proximity to each other.

This video explains what a transformer is:

Transformer is a static electromagnetic device having two (or more) inductively coupled windings and designed to transform, through the phenomenon of electromagnetic induction, one (primary) alternating current system into another (secondary) alternating current system.

In general, the secondary AC system may differ from the primary in any parameters: voltage and current values, number of phases, shape of the voltage (current) curve, frequency. The greatest use in electrical installations, as well as in energy transmission and distribution systems, are general purpose power transformers, 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 in this lecture, we will keep in mind power transformers for general use.

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

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

One of the windings, called primary, connected to an alternating current source at voltage U 1. To another winding called secondary consumer Zn is connected. The primary and secondary windings of a transformer have no electrical connection with each other, and power is transferred from one winding to the other electromagnetically.

What is the purpose of a transformer magnetic circuit?

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

The operation 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 begin to flow through the winding i 1 , which will create an alternating 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 influence 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 operate 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 core of the transformer will be constant both in magnitude and direction (dФ/dt = 0), therefore, the EMF of electromagnetic induction will not be induced in the windings of the transformer, and therefore, electric energy from the 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 a transformer solved?

The problem of increasing 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 obtained on each of the turns will be summed. Therefore, by increasing or decreasing the number of turns, you can increase or decrease the voltage at the transformer output.

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

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

Dividing one equality by the other, we obtain 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 (no-load mode), then the voltage at the terminals of the winding is equal to its EMF: U 2 = E 2 , and the voltage of the power source is almost completely balanced by the EMF of the primary winding U 1 ≈ E 1 . Therefore, we can write that

Considering the high efficiency of the transformer, we can assume that S 1 ≈ S 2 , Where S 1 = U 1 I 1 - power consumed from the network; S 2 = U 2 I 2 - power supplied to the load.

Thus, 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, therefore the current I 2 the number of times it increases (decreases) and the number of times it decreases (increases) U 2 .

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

Why is high voltage used when transmitting electricity?

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

Let us assume that from a power plant to a city located 100 km away from it, it is necessary to transmit 30 MW of electricity along one line. Because the line wires have electrical resistance, the current heats them up. This heat is dissipated and cannot be used. The energy expended on heating represents loss.

It is impossible to reduce losses to zero. But it is necessary to limit them. Therefore, permissible losses are normalized, i.e. When calculating the cross-section of the line wires and choosing its voltage, it is assumed that losses do not exceed, for example, 10% of the useful power transmitted along the line.

In our example it is 0.1x30 MW = 3 MW.

If transformation is not used, that is, 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 per span is hundreds of tons.

By using 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?

Electricity transmission losses are proportional to the square of the current.

Indeed, when the voltage is doubled, the current is reduced by half, and 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.

Let us illustrate this expression with the following example. The figure shows a diagram of energy transfer (Fig. 3). A generator, the terminal voltage of which is 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. Electricity transmission diagram:

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=P/U=10000/6.3 = 1590 A, and in the secondary winding 10000/110 = 91 A. The current in the line wires will have the same value transfers.

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 operating principle of the transformer is based on...

Ampere'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.

There is not enough data to answer.

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

Conclusion on the first question: The principle of operation of a transformer is based on the phenomenon of electromagnetic induction, therefore the transformer is an alternating current device. Voltage conversion in a transformer is carried out by changing the number of turns in the secondary winding. The main purpose of a 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.