Ferroresonance in a voltage transformer: operating principle of a voltage stabilizer

Ferroresonance phenomena in electrical networks

The main factors that give rise to ferroresonance phenomena in electrical networks are elements of capacitive and inductive types.
They are capable of forming oscillatory circuits during switching periods. This effect is especially noticeable in power type transformers, linear booster transformers, shunt circuits and similar devices that are equipped with massive windings. This phenomenon comes in two types: resonance of currents and voltage.

Voltage ferroresonance is possible when there is inductance in the network, characterized by a nonlinear current-voltage property. This characteristic is characteristic of inductors, where the cores are made from ferromagnetic components. This is especially true for rectifiers from the NKF line. This negative phenomenon is caused by a small indicator of resistance of ohmic and inductive types in relation to power transformers.

What is ferroresonance

Ferroresonance is a phenomenon of a sharp increase in current, leading to overheating and damage to the converter and related electrical equipment.

The resonance that causes an accident is observed when an oscillatory circuit occurs with a series connection of the VT inductance and the network capacitance.

Why does it appear in transformers?

The phenomenon of resonance occurs when the neutral is ungrounded (isolated) together with an open-phase mode. With an isolated neutral, the network capacitance relative to the ground forms a series connection with the inductance of the ungrounded VT structure. An open-phase mode occurs when phases are partially switched on, during a phase break, or during an asymmetrical short circuit.

Ferroresonance in a voltage transformer

When a voltage transformer is connected to the network, series-combined LC circuits are formed in it, which are a resonant-type circuit. When an inductive element with a nonlinear current-voltage property is connected in series to a capacitive-type element, the voltage in this zone of the circuit is characterized as active-inductive.

After a certain time period, the voltage value on the inductive element becomes peak, the magnetic circuit is energized, and the voltage on the capacitive type component continues to increase. Ferroresonance in a voltage transformer occurs when the voltage of the inductance and capacitive element becomes equal.

The rapid transition of the applied voltage from the active-inductive type to the active-capacitive type is referred to as “phase reversal”. This effect is dangerous for electrical appliances.

Which transformers neutralize the effect of ferroresonance

To prevent sudden current overloads, protective voltage transformers are designed in conjunction with zero sequence transformers (ZPTs). Such specialized devices are called anti-resonance devices.

NAMIT-10-2

The equipment belongs to the TN type (N), A - anti-resonance (A), with natural oil cooling (M), for measuring circuits (I), three-phase (T), rated voltage 10 kV, version 2.

The measuring equipment consists of two units located in a common housing:

TNKI is a three-winding TN for insulation control;
TNP is a two-winding TNP that protects TNKI from accidents due to short circuits of individual phases. Photoresonance is compensated by the inductive reactance of the TNP in the primary circuit of the converter.

NAMI-10-95

Anti-resonance, oil, measuring equipment consists of:

three-phase three-rod direct (negative) sequence VT with an additional secondary winding;
single-phase two-rod TNP with a secondary winding connected in a closed delta circuit, which reduces the zero-sequence resistance of the device to the value of the leakage resistance.

NALI-SESH-6(10)

The NALI-SESH-6(10) equipment is represented by a cast (L) three-phase anti-resonance group of meters with a rated voltage of 6(10) kV.

The difference between the cast version and the oil version is its high fire and explosion safety, which makes it suitable for use in special conditions, for example at nuclear power plants.

NALI-SESH-6(10) is made using four active elements:

a block of three single-phase, two-pole, measuring TN NOL-SESH, each of which contains up to three secondary windings;
one TNP-SESH, which performs the function of protecting NOL-SESH from abrupt current transitions.

NALI-SESH-1

The equipment is made of single-phase TN with cast insulation type NOL-6(10) and TNP based on the operating principle and relay circuit of the NAMIT-10-2 device.

Ferroresonant stabilizers

Ferroresonance stabilizer
Ferroresonance rectifiers are not equipped with a built-in voltmeter, making it difficult to measure the output voltage of the network. You won't be able to adjust the voltage yourself. Ferroresonance type stabilizers partially distort real readings, the error is up to 12%.

Those who use such devices for a long time must remember that they are capable of emitting a magnetic field, which can disrupt the proper functioning of household electrical appliances. Stabilizers of this class are configured at the factory; they do not require any additional settings at home.

The influence of the stabilizer on technology

A ferroresonant voltage stabilizer, the operating principle of which is not simple, affects household appliances as follows:

Radio receiver - signal reception sensitivity can be reduced, the output power indicator is significantly reduced.
Music center - the output power of such equipment can be significantly reduced, erasing and recording new discs is significantly worse.
TV – when connected to a stabilizer, you can observe a significant decrease in the quality of the picture on TV, some colors are not transmitted correctly.

The electrical circuit of modern ferroresonant type normalizers has been improved, which allows them to withstand heavy loads. Such devices can guarantee precise regulation of the mains voltage. The adjustment procedure is performed by a transformer.

Mathematical models of voltage transformers

When studying ferroresonance processes, mathematical models of TN play a key role. A voltage transformer of the NKF-500 type does not have structural steel in the magnetic core and can be modeled using a simple equivalent circuit shown in Fig. 1, a. The main characteristic of the VT in this case is its magnetization curve (Weber-amp characteristic). This characteristic was calculated based on the geometry of the magnetic core of the TN type NKF-500 and is shown in Fig. 1, b. In the diagram in Fig. 1, a: - VT flux linkage; i is the magnetizing current of the voltage transformer; R1 is the active resistance of the NKF-500 HV winding; R0 is an active resistance that models losses in the steel of the HP. In the mathematical model of the NAMI-500 type VT, it is necessary to take into account that in thick sheets of structural steel the electromagnetic field is displaced onto the surface of the sheets due to eddy currents (magnetic surface effect). The thickness of the structural steel plates is 6 mm. To take into account the surface effect, the sheet is divided into layers 0.5 mm thick (taking into account the symmetry of the sheet, there are only 6 layers). The magnetic flux in each layer is nonlinearly related to the field strength on the surface of the sheet.

Calculations of this dependence, as well as the dependence of active losses in each layer on the magnetic field strength, are carried out by numerically solving Maxwell’s equations using the finite element method in the FEMLAB package.

The dependence of the average induction in the sheet layers on the magnetic field strength on the sheet surface is shown in Fig. 2, a. When drawing up the magnetic equivalent circuit of the NAMI magnetic core, a sheet of structural steel, taking into account the division into layers, represents six parallel nonlinear magnetic resistances.

These resistances are 12 times less than the magnetic resistances of the layers, since there are six sheets of structural steel in the magnetic circuit in total and each is symmetrical relative to the middle (half a sheet is divided into layers).

The magnetic equivalent circuit of TN type NAMI-500 is shown in Fig. 2, b. The electrical equivalent circuit is shown in Fig. 2, c. In the diagram in Fig. 2, b: F1 - MMF of the HV VT winding; n1 — number of turns of the HV winding; 1 - total flux linkage in the magnetic circuit of the VT; ES - flux linkage in electrical steel; KS1KS6 - flux linkage in layers of structural steel sheet; RES, RKS1-RKS6 - magnetic resistance to flow, respectively, along electrical steel and across layers of structural steel sheet.

In the diagram in Fig. 2, in: nM - number of series-connected magnetic circuits in the NAMI500 cascade; RES0, RKS01-RKS06 - active resistances simulating losses in electrical steel and in layers of structural steel sheets; R1, L1 - active resistance and leakage inductance of the HV VT winding. From the dependencies in Fig. 2, but it can be seen that the magnetic field penetrates deep into the sheet of structural steel by only 1-1.5 mm.

Operating modes

The operating modes of stabilizers depend on a number of factors. The power indicator and the class of the device have a direct impact. The power characteristics of the device may be different; they must be selected taking into account the type of electrical equipment being connected.

The operating modes of the rectifier depend on the following types of load:

inductive;
active;
capacitive

Active loading in its pure form is extremely rare. It is necessary only in those circuits where the variable value of the device has no restrictions. Capacitive loads can only be used for those rectifiers that have low power.

History of ferroresonance

https://electricalschool.info/spravochnik/electroteh/1789-chto-takoe-ferrorezonans.html

In 1907, the French engineer Joseph Bethenot published an article “On resonance in transformers” (Sur le Transformateur à Rеsonance), where he first drew attention to the phenomenon of ferroresonance.

The term “ferroresonance” was introduced 13 years later by the Frenchman Paul Bouchereau, also an engineer and teacher of electrical engineering, who in 1920 described this phenomenon in his article entitled “The existence of two modes of ferroresonance

" Bouchereau analyzed the phenomenon of ferroresonance, and showed that there are two stable resonant frequencies in a circuit consisting of a capacitor, a resistor and a nonlinear inductance.

It is now known that the phenomenon of ferroresonance is associated with the nonlinearity of the inductive element in the circuit of the circuit in the electrical circuit is called ferroresonance. For nonlinear resonance to occur, it is necessary that the circuit necessarily contain:

1) nonlinear inductance and linear capacitance;

2) either nonlinear capacitance and linear inductance.

This work is specifically devoted to the first version of the circuit consisting of nonlinear inductance

and linear capacity.

Operating principle of ferroresonance stabilizers

The primary winding, which receives the input voltage, is located on the magnetic core. It has a large cross-section, which allows the core to be kept in an unsaturated state. At the input voltage forms magnetic fluxes.

The output voltage is generated at the terminals of the secondary winding. A load is connected to this winding, which is located on the core, has a small cross-section and is in a saturated state. In case of anomalies in the mains voltage and magnetic flux, its value is not actually modified, and the EMF indicator also remains unchanged. During an increase in the magnetic flux, some of it will be closed on the magnetic shunt.

The magnetic flux takes on a sinusoidal shape and, as it approaches the amplitude indicator, a separate section of it goes into saturation mode. The increase in magnetic flux stops. The flow through the magnetic shunt will be closed only when the magnetic flux is equal to the amplitude.

The presence of a capacitor allows the ferroresonant stabilizer to operate with an increased power coefficient. The stabilization indicator depends on the level of slope of the horizontal curve with respect to the abscissa. The slope of this area is significant, so it is impossible to achieve a high level of stabilization without auxiliary equipment.

Radiant energy in a transformer

In addition to the ferroresonance phenomena described in the book, there are undoubtedly other phenomena not mentioned in it. Our task is to identify them.

At the beginning of my video “Addition No. 2 to the video: How a capacitor works in an alternating current circuit”

, available at the link

I have already given the text of the article “How to create your own creative laboratory.” So on page 5 of this test the following is written:

or her:

In the video, I will not be able to convey the subjective feeling in the hand from the twitching of a magnet located next to a configured operating transformer, but it is possible to show the presence of a radiant next to the transformer using an objective sensor. The sensor is a Sidorovich magnet, on behalf of the one who first made and used it.

Let's watch video fragment No. 3:

I am sure that physics professors will have to work hard to explain the phenomenon of rotation of this sensor, given that, according to theory, the entire magnetic flux should be inside the transformer core.

The transformer itself emits strong longitudinal waves, which can be detected by a scalar wave receiver.

Let's watch video fragment No. 4:

This concludes our preliminary acquaintance with ferroresonance. There are other interesting studies ahead, but before I finish filming this video, I want to touch on one more important point.

Advantages and disadvantages

Among the key advantages of ferroresonant rectifiers are:

resistance to overloads;
wide range of operational values;
speed of adjustment;
the current takes the form of a sine;
high leveling accuracy.

But with all these advantages, devices of this class also have their disadvantages:

The quality of operation depends on the load indicator.
During operation, external electromagnetic interference is generated.
Unstable operation at low loads.
High weight and size indicators.
Noise occurs during operation.

Most modern models do not have such disadvantages, but they are distinguished by their considerable cost, sometimes higher than the price of a UPS. Also, the devices are not equipped with a voltmeter, which makes it impossible to adjust them.

ESIS Electrical systems and networks

Ferroresonance in networks

with isolated neutral

Ph.D. tech. Sciences Polyakov V.S.

1.
Analysis of the causes of equipment damage in networks
with isolated neutral

A significant number of equipment damages in networks with an isolated neutral are caused by ferroresonance, since this phenomenon causes overvoltages or overcurrents for which the equipment is not designed and from which it is not protected. In addition, ferroresonance occurs more often than other types of influences, and is especially dangerous because the duration of its existence is unlimited.

Ferroresonance is a resonance in a circuit containing at least one ferromagnetic element.

Ferromagnetic elements in electrical networks are power transformers, arc suppression reactors, current and voltage measuring transformers, electric motors, that is, all devices that have a coil with a ferromagnetic (steel) core. A special feature of a coil with a ferromagnetic core is the nonlinear dependence of current on voltage (flux).

Under normal conditions, in such a circuit there are no conditions for the excitation of resonance, that is, undamped oscillations. However, when acting on a ferromagnetic element, leading to saturation of the core, a smooth change in the inductance of this element occurs, which creates the possibility of resonance between the inductance and capacitance.

Moreover, if in the network equivalent circuit the capacitance and inductance are connected in series with an alternating voltage source, then voltage resonance occurs, accompanied by a significant increase in voltage on the capacitance and on all network elements electrically connected to this capacitance. In this case, they talk about ferroresonant overvoltages.

If the capacitance and inductance of a ferromagnetic element are connected in parallel with an alternating voltage source, then a current resonance occurs, accompanied by a significant increase in the inductance and capacitance of the network. In this case, they talk about ferroresonant supercurrents.

as, for example, in open-phase modes. If capacitance and nonlinear inductance are mentioned in the failure reviews, damage to voltage transformers, electric motors, complete outdoor switchgears (KRUN), nonlinear surge arresters (OSL) and valve arresters. It is believed that these damages occur due to the occurrence of internal overvoltages.

Sufficient grounds for such qualification is the absence of compensating devices in the network, where their installation is necessary in accordance with the requirements of the Rules of Technical Operation (RTE) [1], in the presence of an arc fault or simply any single-phase short circuit to ground in the initial stage of damage development. Such a simplified approach does not allow us to identify the true causes of equipment damage and, therefore, to develop effective measures to prevent such cases. In some cases, damage is qualified due to the occurrence of internal overvoltages in conditions where their occurrence is generally impossible, for example, when events begin with a phase-to-phase short circuit (SC). True, the development of such damage is accompanied by the closure of large air gaps, not only in complete switchgears, where all insulating gaps are reduced, but also in closed switchgears of a conventional design with sufficiently large insulating distances, which creates the impression of exposure to high-multiplicity overvoltages. In fact, the closing of such large air gaps is caused by the effect of phase-to-phase short-circuit current on defective contact connections.

1.1. Development of damage in the presence of a defective

contact connection

The presence of a defective contact connection in a switchgear or switchgear can lead to the closure of large air gaps when this contact connection is exposed to phase-to-phase short circuit current. When exposed to short-circuit current in any contact connection, the contact pads melt. When calculating and designing detachable contact connections, this phenomenon is considered as positive, since melting of the contact pads leads to welding of the contact connection, and thereby to a decrease in its contact resistance.

Rice. 1. Diagram of the development of damage to a defective contact connection under the influence of short-circuit currents, accompanied by melting of the contact pads and dynamic forces acting on the molten metal of the contact.

However, a decrease in the total area of contact pads or contact pressure leads to an increase in the contact resistance of the contact connection, an increase in the amount of heat released during the flow of short-circuit current and the volume of molten metal. This molten metal, as well as the busbars through which the short-circuit current flows, is subject to powerful electrodynamic forces, which leads to the splashing of the molten metal into the interphase space and the closing of large air gaps in the area of the defective contact connection. Since the operating time of the relay protections that disconnect the supply transformer is quite long, amounting to one or more seconds, the occurrence of a phase-to-phase short circuit in the switchgear leads to a large amount of equipment damage, which makes it difficult to identify the root cause of the incident. It is possible to identify the original source of such damage by localizing the damage only in the area where the air gap is blocked due to metal splashing out of the contact connection. To do this, it is necessary to perform two measures: coating the switchgear insulation with a hydrophobic paste, which prevents the insulation from overlapping due to arc combustion products deposited on its surface, and accelerating the action of relay protection, for example, with a logical busbar protection device that turns off the input circuit breaker in the event of any overlap in the switchgear. It was in this way that it was possible to identify the cause of the annual overlaps in KRUN-10 kV substation No. 20 of Lenenergo in 1979. At this substation, copper lugs were soldered with tin-zinc solder to the aluminum cable cores. When exposed to short-circuit currents, this solder melted and splashed into the interphase space, which led to the blocking of air gaps about 60 cm long. After replacing all solder tips with crimped ones, the damage completely stopped. It should be noted that in all eight 10 kV sections of this substation, the single-phase ground fault current ranges from 150 to 200 A and that there is no compensation, however, eliminating the true cause of the overlap led to reliable operation of the equipment even in the absence of compensation for capacitive currents. Similar observations are available for other substations of Lenenergo and other power systems.

Indirect confirmation of the version about defective contacts as the root cause of damage can be a post-accident examination of contact connections of undamaged sections of the substation. Thus, at the South Lipetskenergo substation in 1991, damage occurred to several 6 kV switchgear cells when outgoing cables were damaged by a third party, accompanied by a phase-to-phase short circuit, which was qualified due to the occurrence of overvoltages. In the same year, when examining contact connections with a thermal imager at this substation, overheating of the plug-in contacts up to 160 °C was detected at currents less than the rated one. During a short circuit at such a connection, melting of the contacts with subsequent blocking of the air gaps is inevitable.

If, during the investigation of the damage, it is established that at the beginning of the events a two- or three-phase short circuit occurred on one of the network elements, then the occurrence of overvoltages as a cause of further development of the damage is unlikely, since the short circuit introduces the greatest possible attenuation into the zero-sequence circuit of the network in which it occurs development of resonant oscillations or accumulation of charges on the capacitance of network phases, which eliminates the development of overvoltages. It is more likely that damage will develop according to the scheme considered, and in this case it is necessary to take measures to improve the condition of the contact connections, rather than measures to protect against overvoltages.

1.2. Development of damage in non-full-phase modes

According to domestic and foreign studies, as well as operating experience, in networks with an isolated neutral, the occurrence of overvoltages is most often associated with open-phase modes. What is meant here is that the open-phase mode is not only an obvious break in the phase wire or a blown fuse, but also those cases when the disconnection of an unloaded step-down transformer or electric motor occurs by a switching device with non-simultaneous disconnection of all three phases. If the non-simultaneity of the shutdown is 0.04 s (2 periods of frequency 50 Hz) or more, then during this time overvoltages of dangerous magnitude have time to develop. In open-phase modes, ferroresonant overvoltages occur that exceed the insulation level of electric motors. They are dangerous for arresters with shunt resistances and arresters, as well as for voltage transformers due to their duration, since they last as long as the open-phase mode exists [2]. Their danger also lies in the fact that in open-phase modes the presence or absence of compensation does not affect the probability of occurrence and the level of overvoltages [3-5], while the installation of protective devices on the busbars is useless, since overvoltages occur in the phase section separated from the busbars ( after phase failure).

The open-phase mode leads to ferroresonant conversion of single-phase voltage to three-phase. The direction of phase rotation can be either forward or reverse. The establishment of direct phase rotation leads to a long-term increase in voltage to (2.2 - 2.3) × U f

and causes the VT fuses to blow.
In reverse alternation, the phase is reversed and one of the phase voltages increases to (3.8 - 4.2) ×U f
, and lightly loaded consumer motors begin to rotate in the opposite direction; in this case, damage occurs to the arresters with shunt resistances, surge arresters and voltage transformers.

It should be noted that the nature and levels of overvoltages during ferroresonance of step-down transformers and spontaneous displacement of the neutral are absolutely similar, both in terms of overvoltage values equal to 3.8 ×U f

and
4.0 ×U f
in one case, and equal to
2.2 ×U f
and
2.0 ×U f
for the second type of overvoltage, and for the resulting network damage. That is, we are talking about the same phenomenon, called by different terms. The term “ferroresonance of step-down transformers” should be considered more correct, as it corresponds to a real physical phenomenon.

1.3. Development of TN damage during FRP

Every year in the country's power systems, according to ORGRES estimates, up to 6-8% of the number of installed transformers in networks with an isolated neutral are damaged. Damage occurs when a voltage transformer is exposed to an intermittent arc in cases where the ignition and extinguishing of the arc occurs once per period or less frequently, or when a regular arc occurs with ignition once per period at a voltage of only one polarity. Damage to VTs from the effects of ferroresonant overvoltages occurs after almost every case of formation of a circuit leading to excitation of the FRP. VT damage occurs even in the presence of active resistances included in the open delta circuit.

An analysis of the causes of damage to the VT shows that the VT is a fairly reliable device and is not damaged for any reason other than exposure to modes for which it is not designed. This mode is the long-term flow of currents through the primary winding of a voltage transformer, the value of which significantly exceeds the value of the current maximum permissible for the thermal stability of the winding insulation. It has been established that such currents arise during ferroresonance processes (FRP) in the circuit formed under certain modes of the network in which the VT is installed. The occurrence of FRP becomes possible due to phenomena that cause saturation of the steel of the VT magnetic circuit. This leads to a smooth change in the inductance of the VT winding and, with a favorable ratio of the parameters of the capacitances of the network elements connected in series and in parallel with the VT, an FRP occurs.

2. Conditions for the occurrence and existence of ferroresonance

processes in circuits with voltage transformers

In circuits with voltage transformers (VT), the possibility of the occurrence and existence of a ferroresonant process (FRP) is determined by the following three conditions:

1st condition

The value of network equivalent capacitance (NECA) must be within the limits determined by the limits of change in the inductance of the voltage transformer, i.e.

£ SEKV
£ (1)
where Lxx is the no-load inductance xx, H;

LS – saturation inductance, H;

w – angular frequency of network voltage, 1/s

The excitation of the FRP is associated with a nonlinear change in the inductance of the VT. Moreover, the smooth change in inductance that begins occurs until resonance conditions arise w ×L=1/ w ×C

(such as in a circuit with linear inductance), which leads to a steady-state PDF. This is obvious because A PDF with the same voltage transformer occurs in circuits with different equivalent capacitances.

Considering the processes of magnetization of the steel core of a VT, it is possible to determine the limits of change in the inductance of a VT: the maximum value of inductance is equal to the inductance XX

and can be calculated taking into account the fact that the relative magnetic permeability has a maximum value and is equal to
m max = 25000
, and the inductance of the VT takes on its maximum value when it reaches saturation, after which it remains unchanged and equal to the inductance of the VT winding without a magnetic core, because
the relative magnetic permeability of steel at saturation is close to unity. True, as studies have shown [13], the inductance of a transformer never reaches the value of the inductance of a winding without a magnetic core, but exceeds it by 30-50%, which is explained by the following: with a winding flux linkage of 2.0 × Y n,
a significant part of the flux inside the winding goes through the air , leaving the magnetic circuit.

The magnetic circuit flux is only (1.3 – 1.4)
× Y n
. If this flux were evenly distributed throughout the magnetic circuit, it would saturate it completely, and the dynamic magnetic permeability would drop to unity. In reality, the flux is unevenly distributed, and individual parts of the magnetic circuit remain incompletely saturated. Therefore, the average magnetic permeability of steel increases slightly, which increases the saturation inductance by 1.3-1.4 times.

Taking into account the increase in inductance due to incomplete saturation by 1.3 times, a formula was obtained for calculating the saturation inductance of a VT:

(2)

where w is the number of turns of the primary winding;

d – average winding diameter, m;

a – winding height, m;

Ka, K – winding shape coefficients taken according to table. 6.2, 6. and 6.6

reference book [16] ;

m0 – magnetic permeability of air.

Inductance XX

let's determine from

Lxx=
(3)

Ixx= lk
× , (4)
_____________

where Zk=Ö(w×Ls)2 + R2ВН, and Ls is the saturation inductance according to (2), we obtain an expression for calculating the inductance хх

L xx
= 100 × (5)
This calculation of the values of the XX
(L xx )
and saturation inductance (Ls) for the ZNOM-35 TN and the limits for changing the equivalent network capacitance according to (I), at which it is possible to excite the FRP are as follows: Lxx = 1330 H ; Cmin= 7.6 nF or Ic min= 0.05 A; Ls= 75H, Cmax = 6300 nF or Ic max= 4A.

That is, with a network capacity of 4.0 A or more per one VT type ZNOM-35, FRP does not occur.

2nd condition

To excite the PDF in a circuit with parameters that meet condition (1), an event is necessary that leads to a change in the inductance of the VT. Such an event in a network with an isolated neutral is the disconnection of an arc metal fault to ground, in which the voltage at the VT changes abruptly from Ul to Uph.

When the voltage on a VT changes abruptly, a residual flux corresponding to the voltage value before the jump (Yrest) is maintained in its magnetic circuit, on which an alternating flux from the voltage established after the jump (Yset) is superimposed. This is clearly visible in Fig. 9. After the circuit is turned off, at the moment the voltage on phase A after the transient process is set to almost equal to Ul (1.71 × Uph), and the flow of the same phase of the VT increases from the value Yl before the circuit is turned off to the value (Yl + Yph) after the circuit is turned off. The current of the primary winding of the VT increases sharply, which corresponds to the saturation mode of the VT.

The FRP will be excited in a circuit with resonant parameters after a voltage surge if the total flux in the magnetic circuit of the VT turns out to be greater than the flux of the initial saturation of the magnetic circuit ( Y initial saturation
), since this causes saturation of the magnetic circuit and a smooth change in the inductance of the VT:
Y rest
+ Y set ³ Y start us (6)
Dependence of flow on current Y= f

(I) TN there is no point of sharp transition from the
XX
to the saturation section, the so-called “knee”. However, analysis of this dependence shows that when the induction in the magnetic circuit is 1.65 T, which corresponds to the maximum induction (BmaxN = 1.1×BN = 1.1×1.5 = 1.65 T), this dependence has a clearly defined linear character. Therefore, the flux in the magnetic circuit with an induction of BmaxN = 1.65 T can be taken as the initial saturation flux Yinit.us = Y1.65. Then the second condition for the excitation and existence of the PDF (6) can be written in the following form

Y ost
+ Y mouth ³ Y 1.65 (7)
The magnitude of the flow is related to the voltage on the VT by the relation

U m
= 4.44 × f × g m , (8)
with induction

Y
= P s × N × V s × 10 -4 , (9)
where Ps is the cross-section of the magnetic core, cm2;

N – number of winding turns,

The results of calculations according to (8) and (9) of the ZNOM-35 kV type are given in Table 1.

Table 1

Calculated values of flux in the magnetic circuit of the VT

No.	Flow, Sun	NTMI-6	STMI -10	ZNOM-35
1	Yf	16	26	92
2	Yl	27	45	157
3	(Yl + Yf)	43	71	249
4	Y1.65	32	56	256

From the analysis of the data in Table 1, it follows that in 6 and 10 kV networks, the total flux after a voltage jump from linear to phase exceeds the initial saturation flux, and ferroresonance occurs even when the metallic ground fault is disconnected at the nominal voltage level in the network.

And in a 35 kV network, when the metallic fault is turned off and at the rated voltage value, the FRP does not occur. At the same time, when the network voltage is 5% higher than the nominal one, the second condition for excitation of the FRP is also met in the 35 kV network ( Y l + Y f = 261 ×B ×C >
Y 1.65 = 256 ×B ×C)
. This coincides with operating experience and explains the fact that not every deviation of a metallic ground fault in a 35 kV network is accompanied by excitation of the FRP. It should be noted that the calculation was performed for the case when the ground fault is disconnected at the moment of maximum flux, which creates the best conditions for excitation of the PDF. If the shutdown occurs when the flow value is close to 0, then the FRP does not occur. Network operational personnel came to this conclusion empirically and use it as one of the methods for suppressing the FRP: if, when disconnecting a metal fault to the ground, an FRP occurs, then the operator turns on the connection with the short circuit again, and then turns it off, and so on until the next time disabling the FRP will not occur.

The second condition allows us to determine what change in magnetization characteristics Y= f

(i) The VT must be produced so that the FRP in networks with an isolated neutral is not excited at all. In this case, the magnetic circuit of the VT should be designed so that with induction BN = 1.5 T, the voltage on the VT would not be (for a network with an isolated neutral), but 1.8 times greater. This means that the product Ps×W1 (the cross-section of the magnetic core Ps by the number of turns of the primary winding W1) that determines the calculation of the voltage transformer should be 1.8 times larger. Leaving one of the parameters, for example, the number of turns W, unchanged, it is necessary to increase the cross-section of the rod Ps by 1.8 times.

It is possible to change two parameters Ps and W, which is determined by the minimum cost of manufacturing such a HP.

In a network with an isolated neutral, taking into account possible fluctuations in the network voltage, the VT must be calculated so that

U n
= 1.15 × (U l + U f ) @ 1.8 × U l (10)
From this it follows that the FRP will not occur in a network with a VT, the magnetization characteristics of which are calculated based on the nominal induction = 0, 9 Tesla, not BN = 1.5 Tesla, as is now common.

By the way, the NAMI-10 type VT, recommended to replace the NTMI-10 type VT [17], is designed this way. This VT has a winding of phase “B”, connected to the phase wire and ground, designed for long-term application of linear voltage (the duration of the metallic fault is not limited, arc fault – 8 hours) and for a full test voltage of 4×Ul=42 kV for a network with an insulated neutral . For the NTMI-10 transformer, the duration of operation at linear voltage is limited to four hours, and the test voltage is only 30% higher than linear. True, a decrease in the nominal induction led to an increase in the cross-section of the magnetic circuit and, accordingly, an increase in the mass of the voltage transformer to 110 kg.

3rd condition

The 3rd condition can be formulated as follows:

“The amount of energy entering the ferroresonant circuit with each change in the parameter (VT inductance) must be greater than the amount of losses in it.

FRP refers to parametric processes, since it occurs when conditions are created (first and second) for changing one of the circuit parameters - the VT inductance, which changes stepwise from the inductance xx Lxx to the saturation inductance Ls. Parametric resonance has been studied quite fully. It is known that with a sudden increase in inductance, the energy of the circuit increases by an amount of 0.5 × (Lxx-Ls) × I2c, a decrease in inductance does not cause a change in the supply of electromagnetic energy of the circuit, since no work is spent on this change.

The frequency of free current oscillations in a parametric circuit is equal to:

______________

= (1/LC) – (R/2L)2
(11)
This natural frequency is determined solely by the parameters L, C, and R of the circuit. If the active resistance is small compared to the characteristic impedance of the circuit, then with sufficient accuracy

____

f = 1 / L/C (12)

In this circuit, the natural frequency depends only on the inductance and capacitance of the circuit and coincides with its resonant frequency.

As the active resistance increases, the relative value of the second term under the root in expression (11) increases and the natural frequency decreases, that is, the free current oscillations become slower. When the active resistance reaches the value

____

R=2 L/C (13)

the natural frequency becomes zero, the oscillations stop and the free current decreases according to an aperiodic law, and in this case the occurrence of resonant oscillations is impossible. Introducing into the circuit attenuation equivalent to the attenuation introduced by the critical resistance prevents the excitation of the FRP. The value of the resistor required to suppress the PDF can be calculated using (13), however, the presence of a nonlinear dependence L = f

(i) complicates calculations and requires the use of a computer.

Let us simplify (13) using the fact that with FRP the equality of the inductive and capacitive conductances of the circuit remains valid, as with resonance in a linear circuit, which makes it possible to express the inductance of a VT through the equivalent capacitance of the circuit, which remains constant, that is, does not depend on the voltage value or current, as is the case for VT inductance. Then

L=1/ w 2 C, and R nf =2/ w C eq
(14)
Relationship (14) is the mathematical expression of the third condition for the existence of the PDF. The values of critical resistances corresponding to the limits of change in the resonating capacitance according to the 1st condition for ZNOM-35 are equal to: Rmax = 835 kOhm; Rmin= 47 kOhm.

A certain value of the critical resistance makes it possible to estimate the value of the losses necessary to suppress the PDF, through attenuation in the circuit or through the value of the active component of the ground fault current.

Let us compare the obtained values of critical resistance, active current and attenuation according to (14) with the criterion for reducing arc overvoltages, first developed by Petersen back in 1918 [8]. Formula for choosing an overvoltage limiting resistance according to Petersen:

I a = (0.4….1.0) × I s (15)

R n = (1.0…..2.5)/ w × C eq (16)

Let us express the critical value of attenuation and active current for the network through its zero-sequence resistance and capacitance according to (13):

cr = 1/R×wC = 0.5, because Rcr = 2/wC;

cr = Ia/Ic = 0.5, because IAcr = 0.5×Ic

As you can see, the compared values practically coincide, and we can conclude that protecting the network from FRP with critical resistance according to (14) allows you to simultaneously protect it from arc overvoltages.

At the same time, the results obtained make it possible to explain the cases when, in a network with resonant characteristics based on the ratio of the capacitance and inductance parameters of the VT, FRP is not always possible. This is due to the fact that the network’s own attenuation at the time of the experiment or during a short circuit in the network is equal to or exceeds the critical value of 0.5, and this is a quite probable state of the network. Hence the conclusion follows: before conducting an experiment to assess the effectiveness of protective measures, it is necessary to evaluate the real value of the network attenuation, correlate it with the value critical for it, and only if these values differ significantly (by an order of magnitude or more), can the results obtained be considered reliable.

The third condition (13) allows the simplest calculation to assess the sufficiency of the attenuation introduced in one way or another into the circuit to suppress the PDF, that is, to assess the effectiveness of any protective measure. There is a widely known proposal to include a 25 Ohm resistor [9] in an open delta circuit, which turned out to be ineffective. This is explained by the fact that the resistor value is selected from the long-term permissible power of the VT to which the resistor is connected and is 400 VA:

rW = U2W/P = 1002/400 = 25 Ohm; (Uw= 100 V; P = 400 W)

Such attenuation can suppress the FRP only at a very small value of the equivalent network capacitance. Let's recalculate the value rW = 25 Ohm, taking it as critical, into the value of the equivalent network capacitance, for which it will be an effective means of suppressing the FRP. For example, for TN type ZNOM-35

R1= rW × K2tr = 25 × 3502 = 3.06 × 106 Ohm

Seq = 2/wR1 = 2.1 nF or Ic = 0.013 A

As you can see, introducing attenuation with a 25 Ohm resistor by connecting it to an open delta VT circuit is effective only with very small network capacitances (Ic 0.013 A). At the same time, it is known from operating experience that most often VTs are damaged by FRP in a network with Ic = 0.8 - 1.0 A per set of VTs. To suppress the FRP in such a network, it would be necessary to include a resistor rW = 0.33 Ohm in the open delta circuit, which would introduce a load on the VT P = 3.3 kW and is unacceptable (the maximum power of the VT is 1200 VA).

In general, the amount of attenuation introduced into the circuit by connecting resistors to the secondary winding of a VT is limited by the maximum power of the VT, which is no more than 1200 VA, which in some cases turns out to be insufficient.

The required amount of attenuation can be introduced by connecting resistors to the primary circuit. So, in a network with an isolated neutral, it is most effective to connect a resistor to the neutral of the network, for example, to the neutral of a power supply transformer.

Determining the optimal parameters of a discharge device capable of protecting network devices from the effects of adverse factors accompanying almost all studied types of faults with a single-phase ground fault must be carried out based on the following requirements:

1. The discharge device must withstand the operating voltage of the network for a long time and meet the requirements of the PUE.

2. Connecting a discharge device should only minimally change the network neutral mode, that is, it should not significantly increase the ground fault current.

3. The discharge of the network capacity through this discharge device must occur in a time less than half the period of the industrial frequency ( £ 0.01 s).

4. The attenuation introduced by the equivalent resistance of the discharge device into the circuit formed by the network must be no less than the attenuation introduced by the resistance equal to the critical resistance for a given circuit.

The discharge or suppression device selected according to these conditions corresponds to the critical resistance for the protected network. In this case, the value of the resistor selected in accordance with the third condition (13) is optimal. As shown above, in addition to suppressing the FRP, such a resistor also prevents the occurrence of arc overvoltages. The same resistor manages to discharge the network even in the most unfavorable mode of an arc fault to ground, when the arc closes once per period and is actually a rectifier, which leads to overexcitation of the inductive elements of the network with direct current.

A resistor connected to the neutral of the network will discharge its capacitance in a time less than a half-cycle, that is, it prevents the adverse effects of this type of arc

(
= RC eq = 2C eq / w C eq = 2/ w @ 1/150 0.01sec).
The resistor selected according to (13) practically does not change the network neutral mode, since it increases the ground fault current by only 11%

_______ ____________ _____

I =
Ö (I2 k +I2 c ) = Ö (0.5 × I c ) 2 + I2c = 1.25 × I c 1.11 × I c
An additional positive factor of grounding the neutral through active resistance is to improve the operating conditions of relay protection from ground faults due to the appearance of a stable active component in the ground fault current [10]. This method of protecting networks with an isolated neutral is recommended by the symposium [11], in addition, a similar technical solution is used to protect MV networks of thermal and nuclear power plants [12].

Technical requirements for protective resistors for ZES are given in Appendix 1.

Conclusions on section 2

2.1. Three conditions for the excitation and existence of a PDF in a circuit with a VT make it possible to analytically, without resorting to solving a system of nonlinear equations on a computer, evaluate the possibility of the emergence and existence of a PDF in networks with an isolated neutral.

2.2. To prevent FRP in networks with an isolated VT neutral, Un=1.8Ul must be calculated, which corresponds to a decrease in the nominal induction from BN=1.5 T to BN=0.9 T.

2.3. The most effective means of protecting network insulation from arc overvoltages should be considered to be grounding the neutral through an active resistance, the optimal value of which is equal to the critical resistance, selected according to the third condition (13).

2.4. Connecting resistors to the secondary winding of a VT in order to introduce the necessary attenuation is ineffective, since the amount of attenuation introduced is limited by the maximum power of the VT, and in most cases is not sufficient to suppress the FRP.

Bibliography

1. Rules for the technical operation of power plants and networks. Ed., 13th, revised. and additional M.: Energy, 1977 (USSR Ministry of Energy). – 288 p.

2. Alekseev V.G., Zikherman M.Kh. Ferroresonance in networks 6 – 10 kV. – Electric stations, 1978, No. 1, p. 63 – 65.

3. Petrov O.A. Neutral displacement during phase-by-phase shutdowns and phase breaks in a compensated network. – Electric stations, 1972, No. 9, p. 557 – 61.

4. Khalilov F.Kh. Once again about arc overvoltages in distribution networks 6 - 35 kV. – Industrial Energy, 1985, No. 2, p. 35 – 37.

5. Khalilov F.Kh. Switching overvoltages in networks 6 – 10 kV. – Industrial Energy, 19855, No. 11, p. 37 – 41.

6. Kalantarov N.L., Tseytlin L.A. Calculation of inductances. Reference book, 3rd ed., revised. and additional L.; Energoatomizdat.1966, p. 288

7. Decision No. E-Z/87 of the Main Technical Directorate of the USSR Ministry of Energy dated 02.25.87. On the replacement of instrument transformers NTMI-10. M.: Soyuztekhenergo

8. Petersen W. Suppression of arcing grounds through neutral resistors and lightning arresters E.TZ, 39, 1918, 341.

9. Explanations to the decision of the Main Technical Directorate No. E-18/72 “On the protection of electrical installations with a voltage of 3-35 kV from internal overvoltages.” M.: ORGRES / Express Information, ser. Operation of power system equipment, 1974, No. 31/159

10. Polyakov V.S. About the neutral mode of networks with voltage 6-35 kV. On Sat. Abstracts of reports of the symposium “Theoretical and Electrophysical problems of increasing the reliability and durability of insulation of networks with isolated and resonantly grounded neutral”. Tallinn, 1989

11. Decision of the symposium “Theoretical and electrophysical problems of increasing the reliability and durability of insulation of networks with isolated and resonantly grounded neutral” Tallinn, April 18-19, 1989 TPI

12. On protection against ground faults of the 6.3 kV network for the auxiliary needs of thermal power plants and nuclear power plants. Directive No. 2799-E 09.29.86. M.: Atomteploelektroproekt, GUKS Ministry of Energy of the USSR.

13. Belyakov N.N., Zakherman M.Kh. Study of the characteristics of magnetized ultra-high voltage power transformers. Proceedings of VNIEE. Issue XXXIV. M.: Energy, No. 3, p.46-58

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The design of rectifiers is constantly being modernized, the quality of their circuits is improving, which allows them to withstand significant ferroresonant overvoltages. Modern models are distinguished by their high level of performance, accuracy of adjustment and long service life. The modes are set by the power characteristics of the device and its type.

The main condition for choosing a ferroresonant stabilizer is its connection location. Usually it is installed at the entrance of the electrical network to the premises or near household appliances. If a rectifier is installed for all equipment, it is necessary to select devices with a high power level and connect them immediately behind the distribution panel.

DIY ferroresonant voltage stabilizer

The ferroresonant circuit is the simplest for DIY production. Its operation is based on the magnetic resonance effect.

The design of a fairly powerful ferroresonant type rectifier can be assembled from three elements:

primary choke;
secondary throttle;
capacitor.

However, the simplicity of this option is accompanied by a whole set of inconveniences. A powerful normalizer made using a ferroresonant circuit turns out to be massive, bulky and heavy.