1 - primary winding; 2 - secondary winding; 3 - common axis of the windings and the core of the transformer; 4 - magnetic circuit; 5 - main scattering channel
Figure 2 - Leakage fluxes and concentric arrangement of transformer windings It is very difficult to directly measure the magnitude of scattering: the paths along which these flows can be closed are too diverse. Therefore, in practice, dissipation is evaluated by the effect it has on the voltage and currents in the windings. Obviously, leakage fluxes increase with increasing current flowing in the windings. It is also obvious that during normal operation of the transformer, the leakage flux is a relatively small fraction of the main flux Ф 0 . Indeed, the scattering flux is linked only to a part of the turns, the main flow is linked to all the turns. In addition, the scattering flux for most of the path is forced to pass through air, the magnetic permeability of which is taken as unity, i.e., it is hundreds of times less than the magnetic permeability of steel, along which the flow closes Ф 0 . All this is true both for normal operation and for the short circuit mode of the transformer. However, since the leakage fluxes are determined by the currents in the windings, and in the short-circuit mode, the currents increase hundreds of times, the fluxes F p increase by the same amount; at the same time, they significantly exceed the flux Ф 0 . Leakage fluxes induce in the self-induction emf windings E p1 and E p2 directed against the current. Counteraction, for example, emf E p2 can be considered as some additional resistance in the secondary winding circuit when it is short-circuited. This resistance is called reactive. For the secondary winding, the equation E 2 \u003d U 2 + I 2 r 2 + (-E p 2) is valid. In short circuit mode, U 2 \u003d 0 and the equation is converted as follows: E 2 \u003d I 2K r 2K + (-E p2K), or E 2 \u003d I 2K r 2K + I 2K x 2K, where the index "k" refers to resistances and currents in short circuit mode; I 2 K x 2 K - inductive voltage drop in short circuit mode, equal to the value of E p 2 K ; x 2 K - reactance of the secondary winding. Experience shows that, depending on the power of the transformer, the resistance x 2 is 5-10 times greater than r 2. Therefore, in reality, the current I 2 K is not 100, but only 10-20 times greater than the current I 2 during normal operation of the transformer (we neglect active resistance due to its small value). Consequently, in reality, the losses in the windings will increase not by a factor of 10,000, but only by a factor of 100-400; the temperature of the windings during the short circuit (a few seconds) will hardly reach 150-200 ° C and no serious damage will occur in the transformer during this short time. So, thanks to the dissipation, the transformer itself is able to protect itself from short-circuit currents. All the phenomena considered occur during a short circuit at the terminals (inputs) of the secondary winding (see points a and b in Figure 1). This is the emergency mode for most power transformers and, of course, it does not occur every day or even every year. During operation (15-20 years), a transformer can have only a few such severe short circuits. However, it must be designed and manufactured in such a way that they do not destroy it and cause an accident. It is necessary to clearly imagine the phenomena occurring in the transformer during a short circuit, to consciously assemble the most critical components of its design. In this regard, one of the most important characteristics of the transformer, the short-circuit voltage, plays a very significant role.
Transformer Short Circuit Experience
A short circuit test is a test of a transformer with a short circuit of the secondary winding and rated current primary winding. The scheme for conducting a short circuit test is shown in fig. 11.3. The experiment is carried out to determine the nominal value of the current of the secondary winding, the power losses in the wires and the voltage drop across the internal resistance of the transformer.
In the event of a short circuit in the secondary winding circuit, the current in it is limited only by the small internal resistance of this winding. Therefore, even at relatively small values of the EMF E2, the current I2 can reach dangerous values, cause overheating of the windings, destruction of the insulation and failure of the transformer. Considering this, the experiment starts at zero voltage at the input of the transformer, i.e. at . Then gradually increase the voltage of the primary winding to a value at which the current of the primary winding reaches the nominal value. In this case, the current of the secondary winding, measured by the ammeter A2, is taken equal to the nominal. The voltage is called the short circuit voltage.
The voltage value of the primary winding in the short circuit test is small and amounts to 5 ¸ 10% of the nominal value. Therefore, the effective value of the EMF of the secondary winding E2 is 2 ¸ 5%. In proportion to the value of the EMF, the magnetic flux decreases, and hence the power loss in the magnetic circuit - Pc. It follows from this that the readings of the wattmeter in the short circuit test practically determine only the losses in the wires Ppr, and 
(11.3)
We express the current I2K through the reduced current
We take into account that and also that 
.
Then we rewrite expression (11.3) as
(11.4)
where RK is the active resistance of the transformer in the short circuit mode, and
(11.5)
The value of the active resistance of the transformer allows you to calculate its inductive reactance 
When calculating accurately, it must be taken into account that RK depends on temperature. Therefore, the impedance of the transformer is determined reduced to a temperature of 750C, i.e.
.
Now it is easy to determine the voltage drop across the internal resistance of the transformer - ZK:
In practice, they use the given value of UK, as a percentage, denoting it with an asterisk, i.e. 
(11.6)
This value is given on the rating plate of the transformer.
Knowledge internal resistance transformer allows you to represent its equivalent circuit in the form of Fig. 11.4. The vector diagram corresponding to this scheme is shown in fig. 11.5.
The vector diagram allows you to determine the decrease in voltage at the output of the transformer D U due to the voltage drop across the complex resistance. The value of D U is defined as the distance between the straight line emerging from the points of the beginning and end of the vector and parallel to the x-axis. It can be seen from the diagram that this value is the sum of the legs of two right-angled triangles, the hypotenuses of which are and , and the acute angles are equal to j2.
That's why
In practice, the relative value of DU is used, in percent, indicated by an asterisk, i.e.
(11.7)
For high power transformers (SH> 1000 V×A), short circuit experience can be used to control the transformation ratio. For such transformers in the short circuit mode, the no-load current can be neglected, considering
That's why 
(11.8)
The last expression is more accurate, the greater the power of the transformer. However, it is not acceptable for low power transformers.
All transformers operate in two main modes: under load and at idle. However, another mode of operation is known, in which the mechanical forces and the leakage flux in the windings increase sharply. This mode is called transformer short circuit. This situation occurs when the primary winding receives power, when the secondary closes on its inputs. During the short circuit reactance occurs, while the current to the secondary winding continues to flow from the primary.
Then the current is given to the consumer, which is the secondary winding. Thus, the process of short-circuiting the transformer occurs.
The essence of the short circuit
In a closed section, a resistance arises, the value of which is much less than the load resistance. There is a sharp increase in primary and secondary currents, which can instantly burn the windings and completely destroy the transformer. However, this does not happen and the protection manages to disconnect it from the network. This is due to the fact that increased dissipations and fields of the transformer significantly reduce the impact of short-circuit currents, and also provide winding protection from electrodynamic and thermal loads. Therefore, even if there are losses in the windings, they simply do not have time to exert their negative impact.
Short circuit warning
During normal operation of the transformer, the value of electrodynamic forces has a minimum value. During the time, there is an increase in currents and efforts tenfold, creating a serious danger. As a result, windings can be deformed, their stability is lost, coils are bent, gaskets are crushed under the influence of axial forces.
In order to reduce electrodynamic forces, the windings are pressed in axially during assembly. This operation is performed repeatedly: first, when the windings are mounted and the upper beams are installed, and then, after the active part has dried. The second operation is of particular importance for reducing efforts, since poor quality pressing, under the action of a closure, may result in shearing or destruction of the coil. A serious danger is the coincidence of the self-resonance of the coil with the frequency present in the electrodynamic force. Resonance can cause forces that are completely harmless when normal mode work.
To improve the quality of the transformer, during assembly, you must immediately eliminate the possible shrinkage of the insulation, align all the heights, and ensure high-quality pressing. Subject to the necessary technological processes, a short circuit of the transformer may well do without serious consequences.
Short circuit of the transformer in operation
Short circuits in electrical installations usually arise due to any malfunctions in the networks (with mechanical damage to the insulation, its electrical breakdown as a result of overvoltages, etc.) or due to erroneous actions of the operating personnel.
For a transformer, a short circuit is very dangerous, since very large currents are generated. When the terminals of the secondary winding are short-circuited, the load resistance Zн is practically equal to Zero and, therefore, the voltage at the terminals of the secondary winding U2 is also equal to zero. Thus, the voltage U1 applied to the primary winding will be balanced by the voltage drop in the impedances of the primary and secondary windings zK=Z1+Z2. The equivalent circuit for one phase of the transformer during a short circuit is shown in fig. 11, a.
Equilibrium equation e. d.s. the primary winding of the transformer in the event of a short circuit of the secondary winding will be written in the following form:
U1=Ikzk where Ik is the short circuit current.
On fig. 11b shows a vector diagram for one phase of a transformer during a short circuit. Short-circuit current vector Ik is directed vertically upwards. Parallel to the current vector, the vector of the voltage drop in the active resistance of the short circuit IkRk is directed. Turned relative to the current vector by - in the direction of advance (counterclockwise the voltage drop vector by inductive reactance insulation transformer
The geometric sum of the vectors IkRk will determine the vector of the voltage U1 applied to the primary winding, which is turned up relative to the short circuit current vector Ik in the direction of advance by the short circuit angle pk. This angle depends
on the ratio of the resistances xk and rk. The greater the inductive resistance xk and the smaller the active resistance rk, the greater will be the angle φ. Thus, the short circuit current of the transformer Ik=U1/zk
Since the voltage drop in the impedance of the transformer windings at rated current is 5-7% of the rated voltage, that is, the short circuit current will be greater than the rated current as many times as the rated voltage is greater than the voltage drop in the impedance of the windings at rated current.
The ratio Ik/In=100/uk is called the short-circuit current ratio, where Uk is the short-circuit voltage.
Therefore, the short-circuit current of the transformer is many times greater than the rated current. Here we meant the steady-state value of the short-circuit current of the transformer. Such a current, many times greater than the rated current, will flow in the transformer windings during the entire time of the short circuit, no matter how large it may be. However, at the moment of a short circuit, the multiplicity of the short circuit current may be even greater. Depending on the instantaneous value of the applied voltage, the instantaneous short-circuit current differs from the steady state by 2 times.
If the short circuit of the secondary winding of the transformer occurred at the moment when the instantaneous value of the voltage u is equal to the maximum value Uim, then the instantaneous short circuit current
In the event of a short circuit at the moment when the voltage is zero, the instantaneous short circuit current will be 2 times the steady current.
The short circuit current sharply increases the temperature of the winding, which threatens the integrity of the insulation. Losses in the wires of the transformer windings are proportional to the current to the second power. Therefore, in the case when the short-circuit current turns out to be, for example, 20 times greater than the rated current, the losses in the wires of the windings will be 400 times greater than at the rated current (if we do not take into account the increase in winding resistance from heating). The release of high power in the wires of the windings causes a sharp increase in their temperature, as a result of which the integrity of the insulation can be broken and the transformer can fail.
Therefore, all transformers are equipped with sufficiently fast protection, which turns off the transformer in case of a short circuit. If the time during which the transformer is in short circuit mode is short, its windings will not have time to heat up to a temperature dangerous for their insulation.
A short circuit of a transformer is very dangerous, as it can lead to its destruction. If currents flow in the same direction in two parallel wires, these wires are attracted to each other, and if the currents are directed in the opposite direction, the wires repel each other.
A transformer has many turns parallel to each other, each of which can be considered as a separate wire. In the turns of any one winding (primary or secondary) currents flow in the same direction, so that all turns of one winding are mutually attracted. The magnetizing forces of the primary and secondary windings are in the opposite direction, so the windings tend to repel each other.
The mechanical forces acting on the windings depend on the design of the windings, the placement of the turns, and the currents flowing in the windings. In concentric symmetrical windings, the forces F acting on the windings are directed perpendicular to the axis of the coils; in disk alternating windings, the forces are directed parallel to the axis of the coils
Since the forces acting on wires with current depend on the product of currents, the forces F acting on the windings of transformers during a short circuit will be many times greater than the forces that occur at rated load. Under the action of very large mechanical forces, the transformer windings are deformed to such an extent that the insulation can be broken and their electrical strength is sharply reduced. The design of the windings must be designed for such a mechanical strength that would withstand the forces arising at the first moment from instantaneous short-circuit currents.
The short-circuit mode of a transformer is such a mode when the terminals of the secondary winding are closed by a current conductor with a resistance equal to zero (ZH = 0). A short circuit of the transformer under operating conditions creates an emergency mode, since the secondary current, and therefore the primary one, increases several tens of times compared to the nominal one. Therefore, in circuits with transformers, protection is provided that, in the event of a short circuit, automatically turns off the transformer.
Under laboratory conditions, it is possible to carry out a test short circuit of the transformer, in which the terminals of the secondary winding are short-circuited, and such a voltage Uk is applied to the primary, at which the current in the primary winding does not exceed the nominal value (Ik is the characteristic of the transformer indicated in the passport.
In this way (%):
where U1nom is the rated primary voltage.
The short circuit voltage depends on higher voltage windings of the transformer. So, for example, at the highest voltage of 6-10 kV uK = 5.5%, at 35 kV uK = 6.5÷7.5%, at 110 kV uK = 10.5%, etc. As can be seen, with increasing the rated higher voltage increases the short-circuit voltage of the transformer.
When the voltage Uk is 5-10% of the rated primary voltage, the magnetizing current (no-load current) decreases by 10-20 times or even more significantly. Therefore, in the short circuit mode, it is considered that
The main magnetic flux Ф also decreases by 10-20 times, and the leakage fluxes of the windings become commensurate with the main flux.
Since in the event of a short circuit of the secondary winding of the transformer, the voltage at its terminals U2 = 0, the equation e. d.s. for her takes the form
and the voltage equation for the transformer is written as
This equation corresponds to the equivalent circuit of the transformer shown in fig. one.
The vector diagram of a transformer during a short circuit corresponding to the equation and diagram of fig. 1 is shown in fig. 2. Short circuit voltage has active and reactive components. The angle φk between the vectors of these voltages and currents depends on the ratio between the active and reactive inductive components of the transformer resistance.
Rice. 1. Transformer equivalent circuit in case of short circuit
Rice. 2. Vector diagram of a transformer in a short circuit
For transformers with a rated power of 5-50 kVA XK/RK = 1 ÷ 2; with a rated power of 6300 kVA or more XK/RK = 10 or more. Therefore, it is believed that for high power transformers UK = Ukr, and the impedance ZK = Hk.
short circuit experience.
This experiment, like the open circuit test, is carried out to determine the parameters of the transformer. A circuit is assembled (Fig. 3), in which the secondary winding is short-circuited by a metal jumper or conductor with a resistance close to zero. A voltage Uk is applied to the primary winding, at which the current in it is equal to nominal value I1nom.
Rice. 3. Transformer short circuit experience diagram
According to the measurement data, following parameters transformer.
Short circuit voltage
where UK is the voltage measured by the voltmeter at I1, = I1nom. In short-circuit mode, UK is very small, so no-load losses are hundreds of times less than at rated voltage. Thus, we can assume that Рpo = 0 and the power measured by the wattmeter is the power loss Рpc due to the active resistance of the transformer windings.
At current I1, = I1nom get rated power losses for winding heating Rpk.nom, which are called electrical losses or short circuit losses.
From the voltage equation for the transformer, as well as from the equivalent circuit (see Fig. 1), we obtain
where ZK is the impedance of the transformer.
