# Autotransformers

## Basic principles

In a transformer, the primary and secondary windings with voltages U1 and U2 have currents I1 and I2 flowing in opposite directions. In an autotransformer, the connections make it possible to use part of the primary winding as a secondary and reduce the voltage in the secondary winding to U2 (see figure).
In this case, the primary winding itself includes a secondary and an additional part with voltage (U1 - U2). The current flowing in the common part of the autotransformer winding is the difference between the two currents (I2 - I1). Therefore, the common part of the winding can be made of a wire of a smaller cross-section, designed for the difference in currents (I2 - I1) instead of the total current I2.
On the other hand, the primary winding, which has a higher voltage, is, as it were, reduced to the series part of the autotransformer having n1 - n2 turns instead of the total number of turns n1. Consequently, the primary winding decreases in proportion to the value of (n1-n2) / n1, and the secondary in proportion to (I1-I2) / I2.
This allows for savings in active materials and dimensions.
Autotransformers are used in networks from low voltage, for example, in distribution networks of 110V and 220V, and up to very high voltages: 500 (525), 750 (787) and 1150 (1200) kV (in brackets - the highest operating voltage).
There are several types of autotransformers depending on their application:
♦ For communication between two systems of different voltages, possibly with voltage regulation;
♦ To regulate the voltage of the transformer over a wide range, while the secondary is low voltage, for example, in transformers supplying electric furnaces, rectifiers for electrolysis and (or) traction;
♦ For powering synchronous or asynchronous motors with reduced voltage when they are started.

## Equivalent dimensions

To compare transformers with different characteristics, such as power, winding voltage regulation, a two-winding equivalent is used. For a winding or part of a winding, the power is determined by the product of the maximum current and the maximum voltage under operating conditions. For the entire transformer, the two-winding equivalent will have a power equal to half the sum of the powers of all windings.
A transformer with two windings, without regulation and at constant voltage, has an equivalent power equal to the power of each of its coils. In the case of introduction of regulation in one of the windings and with the full required power on each branch, the equivalent double-winding power increases by the amount of power of the additional control winding.
For comparison of autotransformers and transformers, such concepts as "through" (Sap) and "typical" (St) power of an autotransformer are accepted.
Throughput power is the power transmitted by the autotransformer to the secondary network, typical power is the power of a two-winding transformer having the dimensions of this autotransformer.
The benefits that the autotransformer gives due to the alignment of the windings can be seen from the diagram in Fig. 6.1.

Thanks to the autotransformer connection, both windings are reduced in size in the same proportion, either by reducing the number of turns with the same wire cross-section, or by reducing the wire cross-section with the same number of turns. Such an autotransformer transmits the same power Snp as the original transformer having the same voltage ratio. However, the typical autotransformer power - the equivalent double-winding power St, which determines the physical dimensions, will correlate with the throughput power Snp as

From this it is seen that as k12 decreases, the value of p also decreases, tending to zero as k12 approaches unity. This is due to the fact that in the transformer all the energy is transformed from the primary winding into the secondary, while in the autotransformer only part of the total energy is transformed, and the other part is transferred directly from the system of one voltage to the system of another voltage without transformation.
The closer the voltage values of the two systems are, the greater the benefit is achieved with an autotransformer.
Most often, the values of the coefficient of profitability are in the range of 0.3-0.7.
Table 6.1 shows the values of the coefficients of profitability at various transformation ratios.

## Voltage regulation in autotransformers

Depending on the requirements for voltage regulation, different winding connection schemes are used.
Voltage regulation without excitation can be carried out in the same way as in a transformer, whereby the control turns or coils can be located either in the series winding when high voltage regulation is required, or in the common winding for medium voltage regulation, in which case the regulation is “coupled”. since the common winding is the MV winding and at the same time is part of the HV winding.
If necessary, voltage regulation under load is used in autotransformers.
The choice of the type and scheme of regulation depends on the conditions in the power system, from which the requirements for the autotransformer follow.
When choosing a control scheme, the consumption of materials, the possible design of the windings, including the control winding, the required characteristics of the switching device, overexcitation of the autotransformer, etc. are taken into account.
Depending on the voltage regulation conditions, different on-load voltage regulation schemes are used.
All applied circuits can be divided into three groups: control circuits on the HV side (Fig. 6.2), on the MV side (Fig. 6.3) and in the common neutral of the HV-MV (Fig. 6.4).
It is advisable to regulate in that winding, the voltage of which varies within wide limits. This should be taken into account when choosing a circuit - with regulation on the HV or MV side.

### HV or MV side regulation

In addition to the above, these two control methods are equivalent, Fig. 6.2 shows some control schemes on the HV side. Scheme 6.2, b has the advantage over circuit 6.2, a, which makes it possible to use a switching device of the voltage class СН, i.e., it requires a switching device of a lower voltage class. Therefore, circuit 6.2, and can be used only in those cases when the voltages U1 and U2 are close to each other.

Reversing the adjusting winding in the 6.2 v circuit allows the regulation range to be doubled in comparison with the 6.2 b circuit.
Scheme fig. 6.2 g contains an additional booster transformer with its own magnetic circuit. The booster transformer can be located in the tank of the main autotransformer or outside it. Regulation is carried out in the main autotransformer.
The advantage of circuit 6.2, d is the ability to choose the most convenient one for regulating current and voltage in an auxiliary circuit containing a switching device. However, indirect regulation requires additional investment of materials and some increase in the overall dimensions of the autotransformer. Note that circuits 6.2, b and 6.2, c, regulating the voltage on the HV side, require adjustment equipment for the CH class.
In fig. 6.3. shows the voltage regulation circuits on the MV side. Scheme 6.3, b allows you to expand the control range by reversing. Scheme 6.3, c allows the use of low voltage control equipment.
The advantage of the 6.3, g circuit over the previous one is the constant value of the induction in the magnetic circuit of the booster transformer. This circuit can be used for longitudinal-lateral regulation on the MV side (i.e., simultaneous voltage regulation in magnitude and phase).

### Neutral voltage regulation

The method of voltage regulation in the neutral (Fig. 6.4.) Allows you to use an adjusting winding and a switching device for a voltage class significantly lower than the voltage U1 and U2, which is a great advantage of this method.
The disadvantage of this method is significant fluctuations in the magnetic induction during regulation, especially when the transformation ratio is less than two. Therefore, it is used in the case of a relatively small control range in autotransformers of a very high voltage class.
The use of indirect regulation in the neutral can significantly simplify the winding of the main autotransformer, especially when the booster transformer is placed in a separate tank.

### Comparison of control methods based on typical power

The previous sections provide a qualitative comparison of voltage regulation methods in autotransformers. Below is a comparison of the increase in the typical power of an autotransformer with regulation compared to the same transformer without regulation.
The typical power of an autotransformer will be called the half-sum of the powers of its windings
the power of the k-th winding, equal to the product of the maximum values of current and voltage in it; n is the number of windings.
The comparison is made with an autotransformer without regulation under load with a throughput power Snp for HV and MV windings connected according to an autotransformer circuit, and with a tertiary winding (LV), the power of which is equal to the typical power of the autotransformer.
The typical power of such a three-winding autotransformer will be St = 1.5 pSnp, where p is the autotransformer profitability factor, equal to p = 1-1 / k12, k12 is the transformation ratio between the HV and MV sides of the autotransformer, equal to the ratio of rated voltages.
In the presence of regulation under load, the power of the autotransformer increases, since new (regulating) windings appear and the power of the existing windings increases.
The typical power of an adjustable autotransformer is

Table 6.2 gives the values of the increase in the typical power ASt pcg when the regulation is introduced according to the diagrams in Fig. 6.2—6.4 for cases of symmetrical regulation ranges ± as a percentage of the corresponding voltage.
In this case, the throughput power is unchanged for all voltage levels.

For clarity in table 6.2. the values are indicated
From the data in Table 6.2. it can be seen, in particular, that indirect control methods lead to a doubling of the percentage increase in the typical power of the autotransformer in comparison with direct ones (for example, the circuit in Fig.6.2, d versus a, b and c, and also in Fig.6.3, c versus b), and in some cases they are even associated with an even greater expenditure of materials (for example, the diagram in Fig. 6.4, c versus a and b).

The use of schemes with reversal, doubling the control range, in some cases leads to additional investment of materials (scheme in Fig.6.3, b against a), and in others not (scheme in Fig.6.2, c versus a and b, as well as in Fig. . 6.4, b against a).

Based on the formulas given in Table 6.2, Fig. 6.5 the dependences of St.neper. On kp are plotted at p = ± 10 %. It follows from the graphs that the nature of the dependence is different for the control circuits on the HV and MV sides (curves 1–3) and in neutral (curves 4 and 5): in the first D5t-rcg circuits, it drops hyperbolically with an increase in kp, and with regulation in neutral - increases linearly.

This is due to the fact that when regulating on the HV or MV side, the absolute increase in the typical power does not depend on K12 and at a given value of p is a constant value. Therefore, the relative increase in the power St.neper. Decreases with an increase in kp, since at the same time the typical power of the autotransformer £ t.

In contrast to this, when regulating in neutral, the increase in the typical power D5t rcg also depends on K12, increasing with an increase in K12 faster than St.neper .. Therefore, for these schemes, the relative increase in the typical power AsT rcg increases with an increase in K12. The points of intersection of curves 1–3 with curves 4 and 5 (Fig. 6.5) determine the boundaries below which smaller investments of materials are required by circuits with regulation in the neutral, and above - circuits with regulation on the HV or MV side. In fig. 6.6 shows the dependence of St.p. on the regulation limits at K12 = 2. For all circuits, St.p. increases linearly with increasing p.

## Autotransformer short circuit voltage

The autotransformer connection scheme of the windings significantly affects the value of the short-circuit impedance. Indeed, if in the circuit in Fig. 6.1, b, we assume that the secondary side of the autotransformer is short-circuited, the primary voltage U1 will be applied not to the points of the AC, as in normal operation, but to the points AB. The ratio of the number of turns in the AB section to the total number of turns of the AC is just equal to the profitability coefficient p.
As a result, the short-circuit impedance of the autotransformer, referred to the throughput power of the autotransformer Snp, is only pz, where z is the impedance of the short-circuit in % of the 150/110 kV transformer formed by the AB and BC windings. This significantly affects the design of the autotransformer, since it is necessary to choose its dimensions so that its effective short-circuit resistance is sufficient to limit short-circuit currents for reasons of dynamic stability of the windings.
So, if for a transformer with power S with a gear ratio of 150/110 kV, the short-circuit currents (excluding the system resistance) should not exceed 12 times the rated current, then its resistance should be 8.3%.

If instead of a transformer we create an autotransformer with the same short-circuit current limitation in the windings and with the same short-circuit resistance value, then we must choose a transformer model with a capacity of St = 0.275 (here 0.27 is the coefficient of profitability for an autotransformer 150/110 kV ), but having a short-circuit resistance
In practice, this leads to a smaller cross-section, diameter and weight of the core and heavier windings than a transformer of a given typical power St with a resistance of the order of 10%.
At the same time, the ratio of masses and losses changes: the mass of electrical steel and no-load losses are significantly reduced, while the mass of copper and load losses are reduced to a lesser extent.
Due to this, it is easy to obtain a small value of the effective resistance, sufficient for reasons of dynamic stability of the windings in case of short circuits.

In general, there are two possible solutions [5]:
a) If we want the short-circuit current not to reach an excessively high value, we must increase the value of z, which corresponds to a very high value of zt due to the small value of p.

b) If we do not want to deviate too much from a balanced design, we should avoid large increases in zt and accept a sufficiently low z value with a low p value.

Usually a reasonable compromise is made between opposing requirements, as a result autotransformers have a relatively high short circuit resistance in relation to the typical power and a very low short circuit resistance in relation to the throughput power.

Therefore, relatively high short-circuit currents should be expected in autotransformers.
For example, below are the characteristics of real autotransformers:

1. Single-phase autotransformer with the following characteristics:

- rated three-phase power 250/250/50 MB • A;

- rated voltage 525: / 220: l / 3/35 kV;

- frequency 50 Hz;

- short-circuit resistance of the HV / MV windings related to the throughput capacity 250 MB • A - 12%;

- the coefficient of profitability p (525 - - 230) / 525 = 0.562;

- typical power of serial and common windings 250 x 0.562 - 140.5 MB • A;

- short-circuit resistance of HV / MV windings reduced to typical power 12 / 0.562 - 21.35%;

- typical power of a two-winding transformer = (140.5 + NO, 5 + 50) / 2 = = 165.5 MB • A.

Note that the 15-17% resistance is more typical for communication transformers.

2. Single-phase autotransformer:

- rated three-phase power 500/500/150 MB • A;

- rated voltage 500: J3 / 230: l / 3/35 kV;

- frequency 50 Hz;
- short-circuit resistance of the HV / MV windings related to the throughput capacity 500 MB • A - 11 %;

- the coefficient of profitability p (500 - - 230) / 500 = 0.54:

- typical power of serial and common windings St 250 x 0.54 = 270 MB • A;

- short-circuit resistance of HV / MV windings reduced to typical power 11 / 0.54 = 20.37%;

- typical three-phase power of a two-winding transformer St = (270 + 270 + + 150) / 2 = 345 MB • A.

## Modes of operation of autotransformers

### The location of the autotransformer windings

In a rod-type autotransformer, two burners are usually arranged in series in the radial direction from the core and have the same height (Fig. 6.7.). Autotransformer connection of windings in a three-phase system requires a star connection with a grounded neutral in order to avoid high potential hitting the terminals of the secondary windings due to their harmonic connection.

Therefore, systems connected via an autotransformer must be grounded.

We call "series winding" the winding between terminals A and Am in fig. 6.7 and "common winding" - a winding that is a common part of two systems, connected respectively between the terminals A and Am and neutral. Hence the high voltage side of the autotransformer consists of a common winding along with a series winding.

However, for brevity, the serial part is sometimes called "HV winding", and the common part is called "MV winding".

Typically, autotransformers have a tertiary winding. Depending on the mode of its operation, there are step-down and step-up autotransformers. In the first, the tertiary winding is located first at the magnetic rod, in the second - between the serial and common windings of the autotransformer (Fig. 6.8.).

### Modes of operation of autotransformers

Of greatest interest are the following basic modes [2]:

a) VN-CH and CH-VN modes are purely autotransformer modes. In these modes, in step-down autotransformers with PO (series winding) and RO (common winding) windings located side by side, the full rated power of the autotransformer can, as a rule, be transmitted. In step-up transformers with an LV winding located between the PO and RO windings, the throughput power in these modes has to be limited in some cases below the nominal in order to avoid excessively large additional losses in the structure due to the leakage magnetic flux. In these modes, short-circuit losses in step-down autotransformers can reach 60-70 % maximum.

b) HV-LV and LV-VN modes are purely transformer ones and allow the transmission of energy with a power equal to the typical power of the LV winding. In these modes, short-circuit losses are about 50% maximum.

c) Modes СН-НН and НН-СН allow to carry out transmission with power up to the typical power of the LV winding. These modes are purely transformer and cause short-circuit losses of 45-55% maximum (in step-down autotransformers).

d) Combined transformer-autotransformer modes VN — SN and simultaneously VN — NN, as well as SN — VN and simultaneously NN — VN. In these modes, the maximum short-circuit losses occur. The maximum allowable power is limited by the current in the series winding, which must not exceed its rated current. If there is no load on the LV side, then these modes are transformed into autotransformer VN-CH and CH-VN. With an increase in the load of the LV winding, the power on the MV side must accordingly decrease so that the series winding is not overloaded.

In fig. 6.9 shows the calculated values of the permissible load on the MV and LV side at the given values of coscp3 for the case coscp2 = 1. Indices 1, 2, 3 refer to the HV, MV and LV side, respectively. Curves in Fig. 6.9 are obtained from the condition of full load of the series winding, i.e. the current / j has a nominal value.

e) Combined transformer-autotransformer modes VN-CH and simultaneously NN-CH or CH-VN and simultaneously CH-NN. In these modes, the maximum power that can be supplied or removed from the MV side is limited by the current in the common winding. Let us assume that the common winding is fully loaded, i.e. the rated current flows through it. Under the condition cos (pi = 1 and the value of the profitability factor p = 0.5 (autotransformer 220/110 kV), the curves of Fig. 6.10 are plotted.

## Features of overvoltage in autotransformers

The presence of a direct electrical connection of the windings determines the features of impulse overvoltages in the windings of autotransformers.

The serial winding of the autotransformer can be subjected to impulse influences from both the HV linear end and the MV linear end.

When exposed to lightning impulses from the side of input A, the series winding of the autotransformer with respect to overvoltages acting on the longitudinal insulation, the so-called gradients (in coil windings, this is mainly the effect on the insulation between the coils), behaves like a HV transformer winding. This is due to two factors. First, the length of the series winding is usually quite large and the initial distribution of the impulse voltage, which determines the magnitude of the overvoltage in the winding, in the transformer and in the autotransformer does not differ much. Of course, we are talking about autotransformers having a sufficiently large transformation ratio, that is, the voltage ratios found in practice in power systems, shown in Table 6.1.

Secondly, when considering gradient overvoltages on longitudinal insulation, a large capacitance to the ground of the input Аmplus, the characteristic impedance of the connected lines is equivalent to the grounding of this point.

The equivalent circuit for the effect of atmospheric overvoltages in this case looks as shown in Fig. 6.11.

This winding connection scheme is used when testing autotransformers with lightning impulses, since in this case it is the longitudinal insulation that determines the impulse strength.

In the case of a small coefficient, i.e. with close values of the voltages of the HV and MV bushings, the longitudinal insulation of the series winding will be subjected to very hard influences from both bushings. However, in practice, such a combination of voltages (see Table 6.1) does not occur in power systems.

In cases of disconnection of the input At from the network and when a full lightning impulse is applied to input A, voltage fluctuations in the windings, without creating high overvoltages on the longitudinal insulation, can cause unacceptably high voltages with respect to the ground at the input of Am.

The same situation can be in the reverse circuit, that is, an unacceptably high voltage at the open input A when acting on the input Am.

Table 6.3 shows a comparison of the potentials of the HV and MV linear ends of single-phase autotransformers and a transformer when one of them is exposed to a full lightning impulse. From these data it can be seen that when a full lightning impulse is applied to the input A (HV) at the input AT (CH), the potential reaches 750 x 0.25 = 187.5 kV in step-down transformers, and 750 x 0.68 = 510 kV in autotransformers , while the test voltage for 110 kV class is 480 kV (750 kV is the lightning impulse test voltage for 220 kV class.

When a full pink pulse is applied to input Аm (110 kV) at input А (220 kV), respectively, we obtain 480 x 1.17 = 561.6 kV in the transformer and 480 x 2.12 = 1051.6 kV in the transformer, which is also exceeds the test voltage with a full photic impulse for a class of 220 kV - 750 kV.

In the 500/230 kV autotransformer, the voltage at the Am inputs is 985.2 kV, and A - 1950 kV also exceeds the test voltage of these inputs.

Thus, in order to avoid breakdown of the insulation of autotransformers as a result of the impact of impulse overvoltages, the linear ends of the HV and MV in operation must be protected by the corresponding arresters, regardless of whether this input is connected to the line or not.

The maximum impacts on longitudinal insulation, in particular on inter-coil insulation, in transformers and in autotransformers practically do not differ both when exposed to a full lightning impulse, and when it is cut off. An exception is the area of the switching device (for switching without excitation), in which the difference can be significant. So in the above example of a 220/110 kV autotransformer, the maximum voltage value of a full lightning impulse was 34 % versus 19.5% in the transformer. This is due to the fact that with the same percentage of regulation, the number of turns off, referred to the number of turns of the series winding, turns out to be twice as large (at kp = 2) than that referred to the HV winding in the transformer.

For autotransformers with voltage regulation under load, the problem arises of ensuring sufficient electrical strength of the winding and switching device when they are located at the linear end of the MV winding, as in the circuits in Fig. 6.2 and 6.3.

In this case, the regulating winding and the switching device must withstand all the influences inherent in the MV winding class. In some cases, when the MV input voltage is high enough, for example 330 or 525 kV, this is difficult. Then it is necessary to resort to indirect methods of regulation, or to regulation in neutral.

Scheme fig. 6.2. in which the regulating winding is located at the linear end of the HV, is used only in special transformers with a HV voltage of not more than 35 kV. In this case, there are usually no difficulties in ensuring the impulse strength of the regulating winding and the switching device.

## Tertiary winding of the autotransformer

The tertiary winding of the autotransformer (LV winding) is usually delta-connected. In the autotransformer, the LV winding, connected according to the delta circuit, performs the same functions as in the transformer.

### Stabilization of phase-to-phase voltages with unbalanced load

If a single-phase load is connected between two phases, the current system on the primary side contains positive and negative sequence components, but no zero sequence components.

In the case of a single-phase load connected between phase and neutral, the winding currents contain a zero sequence component. Transformers with high zero-sequence resistance are more favorable for single-phase load.

For three-rod three-phase transformers, due to the mutual influence of the magnetic fluxes of the three rods, the conditions for a single-phase load are more favorable than, for example, for a group of single-phase transformers or five-rod transformers as well as for armored transformers.

Without a tertiary winding (Fig. 6.12), the current flowing in uncompensated phases is purely magnetizing, and saturation leads to distortion of phase voltages, displacement of the neutral and heating of the tank walls due to distortion of the leakage flux. By introducing a triangle of tertiary refining, the balance of ampere turns in the phases is achieved and these phenomena are eliminated (Fig. 6.13).

In any case, a 10% single-phase load of three-phase nominal power, connected between the line terminal of the phases and the neutral, can be obtained from a three-rod transformer without excessive neutral displacement.

Rice. 6.13. Distribution of currents with a single-phase load in a transformer with a star-star connection and in an autotransformer with a tertiary winding connected in a delta.

### Suppression of the third and multiple harmonics

With neutral grounded, the third harmonic is present in the no-load current. The third harmonics and multiples of it interfere with nearby low-voltage cables, especially telephone lines that are not shielded.

In the case of an isolated neutral, harmonics appear in the voltage and flux, causing the neutral to shift.

The tertiary winding triangle suppresses these phenomena.

The use of magnetically oriented steel for the manufacture of the magnetic system reduces the no-load current to a minimum value. At the same time, the negative effect of harmonics is not very noticeable.

### Reducing zero sequence resistance

Delta connection is used to reduce the zero sequence resistance of star-to-star transformers and therefore the system resistance. The consequence of this is the stabilization of the neutral, both with single-phase faults and with an asymmetrical load between phase and neutral, as well as a decrease in the system grounding factor and possible currents of single-phase short circuits.1

For a system with an effectively grounded neutral, the grounding factor does not exceed 1.4.

7.3.1. Resistance of the zero sequence from the side of the star-connected winding with a grounded neutral, with an open secondary winding
The following cases are possible: There is no delta winding:

1.1. A group of single-phase transformers. Since all the magnetizing flux

can flow in the core, the zero sequence resistance when the secondary winding is open is equal to the positive sequence resistance, i.e. is equal to the resistance of magnetization and can be taken equal to infinity. At the same time, there is no current in the tank.

1.2. Three-phase three-rod transformer.

The grounding factor is the ratio of the operating frequency voltage between the healthy phase and ground in a single-phase fault to the voltage of this phase before the fault.

The magnetizing fluxes are the same in all three rods. Therefore, the flux must be closed outside the magnetic circuit in an environment with low magnetic conductivity. As a result, the zero sequence resistance is relatively low. However, with an open secondary winding, it still turns out to be 5-10 times greater than the short-circuit resistance between the windings. This is due to the influence of the tank on the magnetic conductivity outside the magnetic circuit, and, consequently, on the zero sequence resistance.

The tank can be thought of as a short-circuited winding. At low voltage, the tank is a highly permeable medium for the leakage flux, and the value of the zero sequence resistance turns out to be voltage dependent.

1.3. Three-phase five-rod transformer.

In a five-rod transformer, the side rods that do not carry the windings can serve as a path for closing the flow of the rods. Therefore, the zero sequence resistance will be high. Up to a voltage of about 30% nominal (depending on the design), it is equal to the magnetizing resistance.

At higher voltage saturation of the lateral jug occurs and the resistance decreases. The dependence of current on voltage will correspond to the magnetization curve. At rated voltage, the side rods and yokes are fully saturated, and the zero sequence resistance will be approximately the same as in case 1.2.

2. With a delta-connected tertiary winding.

2.1. A group of single-phase transformers.

The zero sequence resistance with an open secondary winding is the same as the short-circuit resistance between the considered winding and the tertiary windings, since the triangle of the tertiary windings for the zero sequence currents is similar to the short-circuiting of these windings. There is no current in the walls of the tank.

2.2. Three-phase, three-sided transformer.

The tank acts like a delta-connected outer winding and the resistance can be determined using stray field calculation methods.

The effect of the tank somewhat reduces the zero-sequence resistance in comparison with the short-circuit resistance of the excited winding and the delta-connected winding. 2.3. Three-phase five-rod transformer.

Up to a voltage slightly above the 30% nominal zero sequence resistance, the no-load resistance is equal to the short-circuit resistance between the winding in question and the delta winding. At a voltage close to the nominal, a current appears in the tank, and the resistance can be determined as in 2.2.

7.4. Connecting reactive power sources or supplying local networks
It is also possible to supply energy to the HV and MV network when the generator is connected to the LV winding. In this case, it is convenient to place the winding between the concentrators of the serial and common winding of the autotransformer.

A low value of the short-circuit resistance between the main windings of the autotransformer and the LV winding can lead to high values of the short-circuit current in this winding. In addition, the LV winding is exposed to high single-phase short-circuit currents. Therefore, it is often necessary to increase the electrodynamic strength of the tertiary winding or to increase its short-circuit resistance.

The presence of a tertiary winding with a power of 1/3 S, where S is the throughput of the transformer, increases its cost by about 10 %.

For autotransformers, the increase in cost depending on voltages can reach 50 % [4].

Therefore, if there are no requirements for connecting LV energy sources, the need for a tertiary winding, taking into account paragraphs. 7.1 to 7.3 is determined by the system conditions and the design of the transformer.

Typically, a three-phase, three-rod transformer, whose power does not exceed several tens of MB • A, can be manufactured without a delta winding.

The same analysis of all conditions is necessary for the autotransformer, if, for reasons of economy, one strives to determine the possibility of abandoning the tertiary winding.

Autotransformers without a tertiary winding work both in Europe and America, and in Russia.

With a favorable ratio of primary and secondary voltages, an autotransformer has significant advantages over a transformer with the same voltage ratio and the same throughput power. The autotransformer has a smaller mass, dimensions, no-load and load losses, magnetizing current and short-circuit resistance.

As you know, the linear dimensions of the transformer are proportional to its power to the power of 0.25 (S0.025), and the volume and mass - to the power of 0.75 (S0.75), all other things being equal.

Thus, the lower the typical power in comparison with the throughput, the smaller the dimensions, weight and losses of the autotransformer. So with a typical power that is half the throughput, the mass loss and no-load current of the autotransformer will be 10% less than that of a transformer of the same throughput. By reducing losses, the efficiency is increased.

Reducing the short-circuit resistance makes it possible to reduce the voltage drop during the operation of the autotransformer.

The reduced weight and dimensions of the autotransformer create more favorable conditions for its delivery to the installation site. If it is necessary to transform a very high power, for example, when connecting two very powerful power systems, only an autotransformer can be manufactured within the transport restrictions in terms of weight and overall dimensions, that is, in one transport unit.

The presence of a galvanic connection of the windings in the autotransformer results in certain disadvantages.

As a rule, the windings of the autotransformer are connected in a star with a grounded neutral. Other connections are theoretically possible, but are associated with certain inconveniences and therefore are rarely used. The neutral grounding mode of both systems must be the same: solid ground or resistance grounding. In this case, the resistance value should be such that unacceptable voltages do not arise at the MV inputs of healthy phases when one phase is short to ground in the HV system.

This danger increases as the voltage difference between the two systems increases. For the same reason, autotransformers are not used in systems with a grounded neutral.

High potentials of lightning overvoltages at the idle input of the autotransformer when an overvoltage wave is applied to another input makes it necessary to install arresters on the inputs, which are not disconnected when the line connected to this input is disconnected.

The series winding of an autotransformer and its longitudinal insulation can be subject to very severe lightning effects when the voltage values of the two systems are close. However, in practice, such combinations of voltages do not exist.

The regulating winding, when regulating in the HV or MV line, is subjected to all the influences normalized for the line input. Sometimes it is difficult to ensure the dielectric strength of the insulation of the regulating winding and the switching device, especially for extra-high voltage MV (class 525 kV and above).

The short-circuit resistance of the autotransformer is relatively low, which is the reason for the more severe effects of short-circuit currents. Special measures have to be taken to increase the short-circuit resistance.

Ensuring strength in single-phase faults requires special attention. The presence of the LV winding (tertiary winding) requires ensuring its dynamic strength, for example, by increasing the zero sequence resistance (resistance in the neutral or in the triangle) [4].

8.3. Conditions for the use of autotransformers

Compared to conventional transformers of the same parameters, autotransformers are smaller, but require certain conditions that limit their use in power systems.

Disregarding special applications where no alternative is available, autotransformers should be selected after careful consideration of all operating conditions.

In general, the decision to use autotransformers can be made under the following conditions [4]:

- system with grounded neutral;

- the system has a limited short-circuit power:

- favorable situation with overvoltage;

- transformation ratio close to unity (0.5-2);

S.D.Lizunov A.K. Lokhanin "Power transformers"

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