RU2510514C1 - Reverse sequence current transducer - Google Patents

Abstract

FIELD: instrumentation.

SUBSTANCE: proposed transducer comprises the following main components: reverse sequence voltage filter, first and second differentiating inductive current inverters with their coils inductively coupled with current conductors of three-phase three-wire circuit and low-pass filter. Said reverse sequence voltage filter with output clips is composed of RC circuit including capacitors and trimmer resistors. Said filter is tuned so that in measurement of sine currents of direct sequence the voltage between said clips in steady state equals zero. Low-pass filter has complex-conjugated bands while peak of filter skirt corresponds to the source rated frequency. Filter suppresses higher harmonics to make said voltage between said clips in steady state, in fact, proportional to revere sequence current first harmonic.

EFFECT: higher selectivity and sensitivity of transducer at high content of higher harmonics.

2 cl, 5 dwg, 3 tbl

Description

The invention relates to means for measuring electrical quantities, in particular to means for measuring asymmetry in three-phase networks, in the presence of higher harmonics in the measured currents.

Known negative-sequence current transducers containing current transformers and reverse sequence current filters (see Atabekov G.I. Theoretical foundations of relay protection of high-voltage networks. - M., L .: Gosenergoizdat, 1957. - 344 pp. (Analog. - C .79-98, Fig.: 4-1, 4-3, 4-9 and 4-10, tables: 4-2 and 4-5.)

These analogues have two common disadvantages. The first and most important of these is the high mass, overall dimensions and cost of current transformers, which leads to the rare use of such reverse-sequence current transducers in relay protection devices. The second disadvantage is that the negative sequence current filters have a current that closes through the output terminals of these filters as the output signal. Such filters should work in a mode close to short circuit, that is, have a low load resistance. In this case, a current relay is usually used as the load. Modern relay protection solutions are based on digital technology. In this case, the analog signal of the measuring transducer is fed to a high-resistance input of the analog-to-digital converter. Therefore, to interface with an analog-to-digital converter, the output terminals of the reverse sequence current filters must be connected to the shunt, and the voltage taken from this shunt is fed to the input of the analog-to-digital converter. Obviously, when using a shunt, the quality factor, equal to the ratio of the total power at the input of the analog-to-digital converter to the total power of the same sequence at the input of the reverse sequence current filters, is extremely small. This conclusion indicates the irrational use of capacitors and resistors (or other elements) of which the filter is composed.

опережает фазное напряжение второго токопровода, и фильтр напряжения обратной последовательности, представляющий собой резисторно-конденсаторную цепь, подключенную к первому, второму и третьему входным зажимам, а также к первому и второму выходным зажимам этого фильтра, к первому и третьему входным зажимам которого подключены соответственно начало катушки первого и конец катушки второго дифференцирующих индукционных измерительных преобразователей тока, а конец катушки первого и начало катушки второго дифференцирующих индукционных измерительных преобразователей тока подключены ко второму входному зажиму этого фильтра, при этом между первым входным и первым выходным зажимами этого фильтра подключен первый конденсатор, между первым выходным и вторым входным зажимами фильтра - первый резистор, между вторым входным и вторым выходным зажимами фильтра - последовательное соединение второго конденсатора и второго резистора и между вторым выходным и третьим входным зажимами фильтра - третий резистор, причем при номинальном значении частоты трехфазной цепи, с которой связан указанный измерительный преобразователь, и при отключенной от выходных зажимов фильтра нагрузке ток участка резисторно-конденсаторной цепи, включенной между первым и вторым входными зажимами фильтра, опережает синусоидальную ЭДС катушки первого дифференцирующего индукционного измерительного преобразователя тока, подключеной между этими зажимами, на π/6, сопротивление второго конденсатора в $$\sqrt{3}$$

раз больше сопротивления третьего резистора, сопротивление второго резистора в $$\sqrt{3}$$

раз больше индуктивного сопротивления катушки второго дифференцирующего индукционного измерительного преобразователя тока, а емкостное сопротивление первого конденсатора равно сумме индуктивного сопротивления катушки первого дифференцирующего индукционного измерительного преобразователя тока и деленного на $$\sqrt{3}$$

сопротивления первого резистора (см. патент РФ №2426138, МПК G01R 29/16, 2011 г.).Also known is a negative-sequence current measuring transducer containing the first and second differentiating induction measuring current transducers having the same parameters of their coils, including the same mutual inductances, respectively, with the first and second current conductors of a three-phase circuit, and for the direct symmetrical component of sinusoidal voltages of this circuit, the phase voltage first conductor on $$\frac{2}{3}\pi$$

ahead of the phase voltage of the second current lead, and the negative sequence voltage filter, which is a resistor-capacitor circuit connected to the first, second and third input terminals, as well as to the first and second output terminals of this filter, to the first and third input terminals of which the beginning is connected coils of the first and the end of the coil of the second differentiating induction measuring current transducers, and the end of the coil of the first and the beginning of the coil of the second differentiating induction current measuring current transducers are connected to the second input terminal of this filter, while the first capacitor is connected between the first input and first output terminals of this filter, the first resistor is connected between the first output and second input terminals of the filter, and the serial connection of the second is connected between the second input and second output terminals of the filter a capacitor and a second resistor, and between the second output and third input terminals of the filter, a third resistor, and at a nominal frequency of a three-phase circuit with which the specified measuring transducer is occupied, and when the load is disconnected from the output terminals of the filter, the current of the resistor-capacitor circuit connected between the first and second input terminals of the filter is ahead of the sinusoidal EMF of the coil of the first differentiating induction current measuring transducer connected between these terminals by π / 6, the resistance of the second capacitor in $$\sqrt{3}$$

times the resistance of the third resistor, the resistance of the second resistor is $$\sqrt{3}$$

times the inductive resistance of the coil of the second differentiating induction current measuring transducer, and the capacitance of the first capacitor is equal to the sum of the inductive resistance of the coil of the first differentiating induction measuring current transducer and divided by $$\sqrt{3}$$

the resistance of the first resistor (see RF patent No. 2426138, IPC G01R 29/16, 2011).

The disadvantage of the prototype is that its selectivity and sensitivity decrease with increasing content of higher harmonics in the measured currents. Due to the presence of higher harmonics and in the absence of a negative sequence component in the first harmonics of the measured currents, the prototype output voltage is not equal to zero. If the amplitudes of the higher harmonics are small, then in order to eliminate false positives of the protection, it is necessary to reduce its sensitivity to the presence of a component of the reverse sequence in the first harmonics of the measured currents, which occurs, for example, when one phase of the circuit to which the prototype is connected is interrupted. At high amplitudes of higher harmonics, the selectivity of protection receiving information from the prototype cannot be ensured.

Higher harmonics are generated by electrical equipment, which includes elements with non-linear characteristics. In particular, such electrical equipment includes uncontrolled or controlled rectifiers, in the load circuit of which there is a sufficiently large inductive resistance. The phase input current of such rectifiers is an alternating sequence of pulses close in shape to a trapezoid. Only the leading and trailing edges of such a trapezoid are formed by segments of not sinuous lines, but of a sinusoid. Differentiating induction current transducers, measuring not currents but their derivatives, transform each trapezoid into two pulses, the length of which is equal to the duration of the leading and trailing edges of the trapezoid. The shape of the EMF pulses induced in the coils of the differentiating induction converters varies from close to triangular, when the thyristor control angle of the controlled rectifier is zero, to close to rectangular, when the control angle approaches π / 2. The duration of these pulses is only a few degrees. This form of these EMFs, which are fed to the inputs of the measuring transducer voltage of the negative sequence, is far from sinusoidal. Therefore, in the steady state, with complete symmetry of the measured input currents, the output voltage of the measuring transducer - prototype is not equal to zero.

The task to which the claimed technical solution is directed is to increase the selectivity and sensitivity of the measuring transducer current negative sequence with a high content of higher harmonics in the currents of this circuit.

The technical result that is achieved when solving the problem is expressed in the following: higher harmonics are suppressed in the output voltage of the measuring transducer of the current of negative sequence. In this case, such a converter reacts mainly to the first harmonics of the measured currents. With a symmetric system of these harmonics, when they are formed by components of only the direct sequence, the output voltage of the measuring transformer of the current of the negative sequence is negligible. If this system is asymmetrical, then the distortion in the shape of the output voltage of the measuring transducer under consideration is small, and this voltage is almost proportional to the first harmonic component of the negative sequence current for the system of currents measured by this transducer.

опережает фазное напряжение второго токопровода, и фильтр напряжения обратной последовательности, представляющий собой резисторно-конденсаторную цепь, подключенную к первому, второму и третьему входным зажимам, а также к первому и второму выходным зажимам этого фильтра, к первому и третьему входным зажимам которого подключены соответственно начало катушки первого и конец катушки второго дифференцирующих индукционных измерительных преобразователей тока, а конец катушки первого и начало катушки второго дифференцирующих индукционных измерительных преобразователей тока подключены ко второму входному зажиму этого фильтра, при этом между первым входным и первым выходным зажимами этого фильтра подключен первый конденсатор, между первым выходным и вторым входным зажимами фильтра - первый резистор, между вторым входным и вторым выходным зажимами фильтра - последовательное соединение второго конденсатора и второго резистора и между вторым выходным и третьим входным зажимами фильтра - третий резистор, причем при номинальном значении частоты трехфазной цепи, с которой связан указанный измерительный преобразователь, и при отключенной от выходных зажимов фильтра нагрузке ток участка резисторно-конденсаторной цепи, включенной между первым и вторым входными зажимами фильтра, опережает синусоидальную ЭДС катушки первого дифференцирующего индукционного измерительного преобразователя тока, подключеной между этими зажимами, на π/6, сопротивление второго конденсатора в $$\sqrt{3}$$

раз больше сопротивления третьего резистора, сопротивление второго резистора в $$\sqrt{3}$$

раз больше индуктивного сопротивления катушки второго дифференцирующего индукционного измерительного преобразователя тока, а емкостное сопротивление первого конденсатора равно сумме индуктивного сопротивления катушки первого дифференцирующего индукционного измерительного преобразователя тока и деленного на $$\sqrt{3}$$

сопротивления первого резистора, введен фильтр нижних частот, который имеет порядок не ниже второго, а максимум амплитудной частотной характеристики этого фильтра соответствует номинальной частоте источника, причем первый и второй входные зажимы указанного фильтра нижних частот подключены соответственно к первому и второму выходным зажимам упомянутого фильтра напряжения обратной последовательности, а выходные зажимы указанного фильтра нижних частот являются выходными зажимами измерительного преобразователя тока обратной последовательности.To solve the problem in a measuring transformer of current in the reverse sequence, containing the first and second differentiating induction measuring transducers of current having the same parameters of their coils, including the same mutual inductances, respectively, with the first and second conductors of a three-phase circuit, and for the direct symmetrical component of sinusoidal voltages of this circuit phase voltage of the first current lead on $$\frac{2}{3}\pi$$

ahead of the phase voltage of the second current lead, and the negative sequence voltage filter, which is a resistor-capacitor circuit connected to the first, second and third input terminals, as well as to the first and second output terminals of this filter, to the first and third input terminals of which the beginning is connected coils of the first and the end of the coil of the second differentiating induction measuring current transducers, and the end of the coil of the first and the beginning of the coil of the second differentiating induction current measuring current transducers are connected to the second input terminal of this filter, while the first capacitor is connected between the first input and first output terminals of this filter, the first resistor is connected between the first output and second input terminals of the filter, and the serial connection of the second is connected between the second input and second output terminals of the filter a capacitor and a second resistor, and between the second output and third input terminals of the filter, a third resistor, and at a nominal frequency of a three-phase circuit with which the specified measuring transducer is occupied, and when the load is disconnected from the output terminals of the filter, the current of the resistor-capacitor circuit connected between the first and second input terminals of the filter is ahead of the sinusoidal EMF of the coil of the first differentiating induction current measuring transducer connected between these terminals by π / 6, the resistance of the second capacitor in $$\sqrt{3}$$

times the resistance of the third resistor, the resistance of the second resistor is $$\sqrt{3}$$

times the inductive resistance of the coil of the second differentiating induction current measuring transducer, and the capacitance of the first capacitor is equal to the sum of the inductive resistance of the coil of the first differentiating induction measuring current transducer and divided by $$\sqrt{3}$$

the resistance of the first resistor, a low-pass filter is introduced, which is of the order of at least the second, and the maximum amplitude frequency response of this filter corresponds to the nominal frequency of the source, the first and second input terminals of the specified low-pass filter connected to the first and second output terminals of the said reverse voltage filter sequence, and the output terminals of the specified low-pass filter are the output terminals of the measuring transformer reverse current features.

In addition, the transfer function of the said low-pass filter is performed with double complex conjugate poles.

A comparative analysis of the features of the proposed solution and the characteristics of the analogue and prototype indicates its compliance with the criterion of "novelty."

In this case, the distinguishing features of the proposed technical solution perform the following functional tasks.

Signs: “... a low-pass filter has been introduced, which has an order of at least the second, ... and the first and second input terminals of the specified low-pass filter are connected respectively to the first and second output terminals of the reverse voltage filter, and the output terminals of the specified low-pass filter are output the clamps of the measuring transducer of the current of the negative sequence ”allows to reduce the harmonic coefficient of the output conjugation device compared with harmonic coefficient currents of three-phase protected circuit while fully compensating for the prototype inherent differentiating effect. This effect, which leads to an increase in the harmonic coefficient of the output voltage of the negative sequence voltage filter, is created by the action of both differentiating induction measuring current transducers and the first capacitor.

The sign "... the maximum amplitude frequency response of this filter corresponds to the nominal frequency of the source ..." allows you to reduce the sensitivity of the voltage transfer coefficient (the ratio of the output voltage modules to the input) of the low-pass filter to the frequency deviation of the three-phase circuit to which the negative-sequence current transducer is connected.

The sign of the main claim "... the maximum amplitude frequency response of this filter corresponds to the nominal frequency of the source ..." and the sign of the additional claim "... the transfer function of the said low-pass filter is performed with double complex conjugate poles" determines that it represents a cascade connection of two identical low-pass filters. Each of the filters can be made on the basis of one operational amplifier and has low-quality poles. The use of these two filters, in comparison with one low-pass filter of medium or high quality factor, provides the same suppression of the higher harmonics contained in its input voltage, but has three advantages. Firstly, the selection of filter capacitors and resistors is simplified, and the adjustment of the required filter parameters is facilitated. Secondly, the decrease in the output signal of the filter when the frequency deviation of its input voltage decreases. Thirdly, the time of transients in the filter is reduced.

The output low-pass filter can be digitally implemented as a microprocessor program. With an analog implementation, a filter can be passive or active based on an operational amplifier.

A passive filter is a quadrupole loaded on a resistor, consisting of reactors and capacitors. Such a filter, when used as part of the device under consideration, has the following disadvantages: the absence of industrially produced reactors with the required values of their inductances and rated currents, the deviation of the real values of the capacitance of the capacitors from their nominal values; the difficulty of setting the required parameters of the transfer function of such a filter.

Active filters, deprived of these drawbacks, replaced passive filters in all areas of electrical engineering, except for the use of filters in the output stages of power semiconductor converters. Active filters consist of resistors, capacitors, and operational amplifiers. Setting the required parameters of the filter transfer function is simplified by the fact that some filter resistors are variable. There are several options for active filter circuits: with single-loop or multi-loop feedback, with a signal to the inverting or non-inverting inputs of the operational amplifier.

It is best suited for use with a five-element negative sequence voltage filter that is suitable for two equivalent low-quality active low-pass filters, which consist of a minimum number of elements: one operational amplifier, three resistors and two capacitors. In the first of these options, the inverting input of the operational amplifier is used as a signal, and in the second version, a non-inverting input.

It is advisable to use recursive filters as a digital filter, in which the transfer functions are synthesized based on the transfer function of an analog prototype. Currently, the sampling frequency of digital filters is much higher than the frequency of the highest of the frequencies of significant harmonics of the input signal. Therefore, the frequency characteristics of the analog filter prototype and its corresponding digital filter, in the field of significant frequencies, are almost indistinguishable.

Below we will consider the operation of the proposed measuring transducer current negative sequence and related illustrative materials on an example in which the low-pass filter is made according to the first embodiment of the active low-quality low-pass filter.

The invention is illustrated by drawings, where figure 1 shows a schematic diagram of a measuring transducer current negative sequence, figure 2 is a schematic diagram of a low-pass filter. Figures 3 and 4 show oscillograms that characterize the operation of a three-phase bridge rectifier loaded on a direct current source, and a reverse sequence current measuring transducer that measures the input currents of the rectifier when a three-phase sinusoidal voltage source is connected to its input terminals. The oscillograms shown in Fig. 3 relate to the symmetric mode when all three input terminals of the rectifier are connected to an AC source, and Fig. 4 shows the oscillograms that occur when one of the input terminals of the rectifier is disconnected from the source. Figure 5 shows the amplitude frequency characteristics of the low-pass filter, forming the output stage of the measuring transducer current negative sequence.

The negative sequence current measuring transducer consists of a negative sequence voltage filter 1, the first 2 and second 3 differentiating induction measuring current transducers (DIIPT), as well as a low-pass filter 4. DIIPT 2 has a coil 5, and DIIPT 3 has a coil 6. Coils 5 and 6 are inductively connected to the conductors 7 and 8 of a three-phase three-wire circuit, respectively. For the direct symmetrical component of the voltages of this circuit, the phase voltage of the first current lead 7 (phase A) is 2 π / 3 ahead of the phase voltage of the second current lead 8 (phase B), and the latter is 2 π / 3 ahead of the phase voltage of the third current lead 9 (phase C). The negative sequence voltage filter (FNOP) is a resistor-capacitor circuit connected to the first 10, second 11 and third 12 input terminals, as well as to the first 13 and second 14 output terminals of filter 1, to which a low-pass filter 4 is connected.

A first capacitor 15 is connected between the first input 10 and the first output 13 terminals of the filter 1. A first resistor 16 is connected between the first output 13 and the second 11 input terminals of the filter 1. A serial connection of the second capacitor 17 is connected between the second input 11 and the second output 14 terminals of the filter 1 and the second resistor 18. Between the second output 14 and the third input 12 terminals of the filter 1, a third resistor 19 is connected. Since the capacitors 15 and 17 have standard capacitances, adjustable resistive elements 16, 18 and 19 are used resistors, that allows to establish the relation between the calculated resistance resistor-capacitor filter circuit 1.

The beginning of coil 5 of the first 2 DIIPT and the end of coil 6 of the second 3 DIIPT are connected respectively to the first 10 and third 12 input terminals of filter 1. The end of coil 5 of the first 2 DIIPT and the beginning of coil 6 of the second 3 DIIPT are connected to the second input terminal 11 of filter 1.

The output terminals 20 and 21 of the low-pass filter 4 are connected to the load 22 of the measuring transducer current negative sequence, for example the input circuit of an analog-to-digital Converter.

. Емкостное сопротивление Х₂ второго конденсатора 17 при угловой частоте ω₁ источника, а также сопротивления R₂ и R₃ второго 18 и третьего 19 резисторов и индуктивное сопротивление X_k катушек ДИИПТ связаны между собой следующими соотношениями: $$X_2=\sqrt{3}{R}_2$$

и $$R_3=\sqrt{3}{X}_k$$

.The parameters of the elements of the measuring transducer current negative sequence are interconnected by the following relationships. The mutual inductance M of the coil 5 with the conductive 7 is equal to the mutual inductance of the coil 6 with the conductive 8. The inductances L _{k of} these coils are also the same. For the angular frequency ω _{1 of the} source, which is equal to the angular frequency of the first harmonics of the current paths 7 and 8, the inductive resistances X _{k of the} coils 5 and 6 and their mutual inductive resistances X _m with the conductors 7 and 8 are respectively equal to _{k k} = ω ₁ L _k and X _m = ω ₁ M. The active resistances of coils 5 and 6 are negligible in comparison with the resistances of filter elements 1, and can be ignored. The capacitance X _{1 of the} first capacitor 15 at an angular frequency ω _{1 of the} source is connected with the resistance R _{1 of the} first resistor 16 and with the inductive resistance of the DIIPT coil by the formula: $$X_{\mathrm{one}}=R_{\mathrm{one}}/\sqrt{3}+X_k$$

. The capacitive resistance X _{2 of the} second capacitor 17 at an angular frequency ω _{1 of the} source, as well as the resistance R ₂ and R _{3 of the} second 18 and third 19 resistors and the inductive resistance X _{k of the} DIIPT coils are related by the following relationships: $${\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="00000065.png,00000068.png"\; state="\{\{state\}\}">X</figure-callout>}}_2=\sqrt{3}{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="00000065.png,00000068.png"\; state="\{\{state\}\}">R</figure-callout>}}_2$$

and $${\mathrm{<figure-callout\; id="3"\; label="R"\; filenames="00000065.png,00000068.png"\; state="\{\{state\}\}">R</figure-callout>}}_3=\sqrt{3}{X}_k$$

.

As shown in FIG. 2, the low-pass filter 4 is an active second-order low-order filter with two-loop feedback, which contains an operational amplifier 23, a fourth 24, a fifth 25 and a sixth 26 resistors, as well as a third 27 and a fourth 28 capacitors. The input terminals of the filter 4 are the output terminals 13 and 14 of the negative sequence voltage filter 1. To the node 29 common to the input and output circuits of the operational amplifier 23, the first terminals of the resistors 24, 25, and 26 are connected, the second terminals of which are connected respectively to the input terminal 13 of the filter 1, the inverting terminal 30, and the output terminal 31 of the operational amplifier 23. The terminal 31 is connected also directly to the output terminal 20 of the low-pass filter 4, and to the inverting terminal 30 of the amplifier 23 through the fourth capacitor 28. The non-inverting terminal 32 of the amplifier 23 is connected to the input terminal 14 of the low-pass filter 4. The terminal 14 is also connected directly to the output terminal 21 of the low-pass filter 4, and to the common terminal 29 through the third capacitor 27. The first feedback loop of the operational amplifier 23 is formed by the fourth capacitor 28, and the second is the series connection of the fifth 25 and sixth 26 resistors.

The measuring transducer current negative sequence operates as follows.

и $$\frac{d{i}_{В}}{dt}$$

токов фаз А и В, проходящих по токопроводам 7 и 8. Рассмотрим случай, когда фазные токи и ЭДС, которые наводятся в катушках 5 и 6 ДИИПТ от действия этих токов, созданы подключением к источнику напряжения неискажающей нагрузки. При этом они имеют в установившемся режиме синусоидальную форму, а векторы ЭДС $${\underset{\_}{E}}_{А}$$

и $${\underset{\_}{E}}_{В}$$

, которые наводятся в катушках 5 и 6 ДИИПТ токами $${\underset{\_}{I}}_{А}$$

и $${\underset{\_}{I}}_{В}$$

, проходящими по токопроводам 7 и 8, определяются выражениямиThe instantaneous values of the EMF e _A and e _B , which are induced in coils 5 and 6 of the DIIPT, are equal to the products of the mutual inductance M and the derivatives with respect to time $$\frac{d{i}_{\mathrm{BUT}}}{dt}$$

and $$\frac{d{i}_{\mathrm{AT}}}{dt}$$

the currents of phases A and B passing through the conductors 7 and 8. Consider the case when the phase currents and EMF that are induced in the DIIPT coils 5 and 6 from the action of these currents are created by connecting a non-distorting load to the voltage source. Moreover, they have a steady state sinusoidal shape, and the EMF vectors $${\underset{\_}{E}}_{\mathrm{BUT}}$$

and $${\underset{\_}{E}}_{\mathrm{AT}}$$

, which are induced in coils 5 and 6 DIIPT currents $${\underset{\_}{I}}_{\mathrm{BUT}}$$

and $${\underset{\_}{I}}_{\mathrm{AT}}$$

passing through the conductors 7 and 8 are determined by the expressions

, $${\underset{\_}{E}}_{В}=-j{X}_m{\underset{\_}{I}}_{В},(1)$$

$${\underset{\_}{E}}_{\mathrm{BUT}}=j{X}_m{\underset{\_}{I}}_{\mathrm{BUT}}$$

, $${\underset{\_}{E}}_{\mathrm{AT}}=-j{X}_m{\underset{\_}{I}}_{\mathrm{AT}},(\mathrm{one})$$

по отношению к вектору $${\underset{\_}{I}}_{А}$$

в положительном направлении на угол π/2. Знак минус перед вторым выражением поставлен для учета того, что к входному зажиму 12 подключен конец, а не начало катушки 6, тогда как к входному зажиму 10 подключено начало катушки 5. Поэтому вектор $${\underset{\_}{E}}_{В}$$

повернут по отношению к вектору $${\underset{\_}{I}}_{В}$$

в отрицательном направлении на угол π/2.where j is the imaginary unit that indicates an additional rotation of the vector $${\underset{\_}{E}}_{\mathrm{BUT}}$$

in relation to the vector $${\underset{\_}{I}}_{\mathrm{BUT}}$$

in the positive direction by the angle π / 2. A minus sign in front of the second expression is taken to account for the fact that the end rather than the beginning of the coil 6 is connected to the input terminal 12, while the beginning of the coil 5 is connected to the input terminal 10. Therefore, the vector $${\underset{\_}{E}}_{\mathrm{AT}}$$

rotated relative to the vector $${\underset{\_}{I}}_{\mathrm{AT}}$$

in the negative direction by the angle π / 2.

и $${\underset{\_}{U}}_b$$

входных зажимов 10 и 12 фильтра 1, по отношению к зажиму 11, с учетом приведенных выше соотношений между параметрами фильтра 1, определяются выражениямиWhen analyzing the operation of the filter of negative voltage sequence 1, it is quite acceptable not to take into account the negligibly small values of the following quantities: the active resistances of the DIIPT coils and the input conductivity of the low-pass filter 4. At this voltage $${\underset{\_}{U}}_a$$

and $${\underset{\_}{U}}_{\mathrm{<figure-callout\; id="10"\; label="b\; input\; terminals"\; filenames="00000065.png,00000067.png"\; state="\{\{state\}\}"><figure-callout\; id="12"\; label="b\; input\; terminals"\; filenames="00000065.png"\; state="\{\{state\}\}">b\; </figure-callout></figure-callout>}}$$

input terminals 10 and 12 of the filter 1, with respect to the terminal 11, taking into account the above relations between the parameters of the filter 1, are determined by the expressions

$${\underset{\_}{U}}_a=\frac{\sqrt{3}}{2}{X}_m{\underset{\_}{I}}_{\mathrm{BUT}}\exp \left(\frac{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="00000065.png,00000068.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{2}+\frac{\pi }{6}\right),$$

$${\underset{\_}{U}}_b=\frac{\sqrt{3}}{2}{X}_m{\underset{\_}{I}}_{\mathrm{AT}}\exp \left(-\frac{\pi }{2}-\frac{\pi }{6}\right).(2)$$

и $${\underset{\_}{I}}_{В}$$

являются составляющими прямой последовательности, то ток фазы В отстает от тока фазы А на угол 2π/3, то есть $${\underset{\_}{I}}_{В}={\underset{\_}{I}}_{А}\exp (-2\pi /3)$$

. Тогда векторы обоих напряжений на зажимах 10 и 12 фильтра 1 равны между собой: $${\underset{\_}{U}}_a={\underset{\_}{U}}_b=\frac{\sqrt{3}}{2}{X}_m{\underset{\_}{I}}_{А}\exp \left(\frac{2\pi }{3}\right)$$

. При этом входное напряжение фильтра 4 нижних частот $${\underset{\_}{U}}_{ab}={\underset{\_}{U}}_a-{\underset{\_}{U}}_b$$

равно нулю. Естественно, что при этом и выходное напряжение фильтра 4 нижних частот также равно нулю.If the measured currents $${\underset{\_}{I}}_{\mathrm{BUT}}$$

and $${\underset{\_}{I}}_{\mathrm{AT}}$$

are components of a direct sequence, the phase B current lags behind the phase A current by an angle of 2π / 3, i.e. $${\underset{\_}{I}}_{\mathrm{AT}}={\underset{\_}{I}}_{\mathrm{BUT}}\exp (-2\pi /3)$$

. Then the vectors of both voltages at the terminals 10 and 12 of the filter 1 are equal to each other: $${\underset{\_}{U}}_a={\underset{\_}{U}}_b=\frac{\sqrt{3}}{2}{X}_m{\underset{\_}{I}}_{\mathrm{BUT}}\exp \left(\frac{2\pi }{3}\right)$$

. In this case, the input voltage of the low pass filter 4 $${\underset{\_}{U}}_{ab}={\underset{\_}{U}}_a-{\underset{\_}{U}}_b$$

equals zero. Naturally, in this case, the output voltage of the low-pass filter 4 is also equal to zero.

и $${\underset{\_}{I}}_{В}$$

являются составляющими обратной последовательности, ток фазы В опережает ток фазы А на угол 2π/3, то есть $${\underset{\_}{I}}_{В}={\underset{\_}{I}}_{А}\exp (2\pi /3)$$

. Тогда вектор напряжения на зажиме 12 фильтра 1 определяется выражением: $${\underset{\_}{U}}_b=\frac{\sqrt{3}}{2}{X}_m{\underset{\_}{I}}_{А}$$

. То есть векторы $${\underset{\_}{U}}_a$$

и $${\underset{\_}{U}}_b$$

имеют равные модули, а угол между ними составляет 2π/3. При этом модуль входного напряжения $${\underset{\_}{U}}_{ab}$$

фильтра 1 в $$\sqrt{3}/2$$

раз превосходит модули ЭДС катушек 5 и 6 ДИИПТ и составляет $$\frac{3}{2}{X}_m{I}_{А}$$

.Otherwise, when the measured currents $${\underset{\_}{I}}_{\mathrm{BUT}}$$

and $${\underset{\_}{I}}_{\mathrm{AT}}$$

are components of the reverse sequence, the phase B current is ahead of the phase A current by an angle of 2π / 3, i.e. $${\underset{\_}{I}}_{\mathrm{AT}}={\underset{\_}{I}}_{\mathrm{BUT}}\exp (2\pi /3)$$

. Then the voltage vector at the terminal 12 of the filter 1 is determined by the expression: $${\underset{\_}{U}}_b=\frac{\sqrt{3}}{2}{X}_m{\underset{\_}{I}}_{\mathrm{BUT}}$$

. I.e. vectors $${\underset{\_}{U}}_a$$

and $${\underset{\_}{U}}_b$$

have equal moduli, and the angle between them is 2π / 3. In this case, the input voltage module $${\underset{\_}{U}}_{ab}$$

1v filter $$\sqrt{3}/2$$

times superior to the EMF modules of coils 5 and 6 DIIPT and is $$\frac{3}{2}{X}_m{I}_{\mathrm{BUT}}$$

.

Thus, in the sinusoidal form of the currents of a three-phase three-wire system, the output voltages of the filter of the negative sequence voltage filter 1 and the low-pass filter 4 in the steady state differ from zero only if there are components of the negative sequence in the indicated currents, in particular, if there are currents in only two phases ( out of phase). During the transient process that occurs after a change in the forced component in the system of phase currents corresponding to a symmetrical non-distorting load, the output voltages of the negative sequence voltage filter 1 and the low-pass filter 4 are not equal to zero. These voltages practically reach zero during a time of the order of one or two periods of the source voltage after the practical completion of the specified transient in the system of phase currents.

Гармоники с номерами 6k+1 (седьмая, тринадцатая, девятнадцатая и т.д.) входят в составляющую прямой последовательности. А гармоники с номерами 6 k-1 (пятая, одиннадцатая, семнадцатая и т.д.) - в составляющую обратной последовательности.Currents in electric circuits that receive power from a source with sinusoidal voltages and contain non-linear elements differ from sinusoidal ones. Currents of power nonlinear three-phase circuits, as a rule, contain only odd higher harmonics. Moreover, in circuits without a neutral wire there are no harmonics that are multiples of three. Such circuits, in particular, include circuits with bridge semiconductor converters. The numbers n of the highest harmonics in such cases are determined by the formula: $$n=6k\mp \mathrm{one,}k=\mathrm{1,2,3}...$$

Harmonics with numbers 6k + 1 (seventh, thirteenth, nineteenth, etc.) are included in the direct sequence component. And harmonics with numbers 6 k-1 (fifth, eleventh, seventeenth, etc.) - into the component of the reverse sequence.

Each harmonic of currents with an effective value of I _n passing through current conductors 7 and 8 in coils 5 and 6 of the DIIPT induces an EMF whose effective value is I _n X _m n. Filters 1 voltage reverse sequence is usually performed with the involvement of an additional relationship between the parameters of its elements: R ₂ = X ₁ -X _k . Then the n-th harmonic of the output voltage of this filter, expressed in relative values (the EMF DIIPT I _n X _m n is taken as the base value), is determined by the formula

$$U_{ac}=\frac{\sqrt{3}n}{\sqrt{3}-j\left(\frac{\mathrm{one}+m}{n}-mn\right)}+\frac{\sqrt{3}(mn-j)\exp \left(\mp \frac{2\pi }{3}\right)}{\mathrm{one}+\sqrt{3}m-j\left(\frac{\sqrt{3}}{n}-mn\right)},m=X_k/{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="00000065.png,00000068.png"\; state="\{\{state\}\}">R</figure-callout>}}_2.(3)$$

The minus sign of the exponent argument corresponds to the harmonic numbers n = 6k + 1 (direct sequence), and the harmonics with the numbers n = 6k-1 (reverse sequence) correspond to the plus sign. For the first harmonic, the inductive resistance of the DIIPT coils is small: the parameter m does not exceed 0.1.

. При m=0,05 этот предел равен 33,8, а при m=0,05 он снижается до 16,5.Table 1 shows the relative values of the output voltage of filter 1 calculated by formula (3) for higher harmonics from the fifth to nineteenth. These values are given for two values of the parameter m: 0.05 and 0.1. For all harmonics included in the direct sequence of currents (seventh, thirteenth, etc.), the output voltage of filter 1 is not equal to zero, as for the first harmonic. For the seventh harmonic at m = 0.05, the relative value of this voltage is 5.3, and at m = 0.1 it is 5.0. The indicated values are less than for the previous fifth harmonic, which is part of the reverse sequence. For harmonic numbers greater than seven, the relative value of the output voltage of filter 1 increases with increasing number, without showing the influence of whether the harmonic belongs to the sequence: direct or inverse. For m = 0.05 and n≥7, the voltage value U _{ac is} approximately equal to the harmonic number n, and for m = 0.1 it is slightly less than this estimate. Based on formula (3), an expression is found that determines the modulus limit of the relative value of the output voltage of filter 1 when n tends to infinity: $$\frac{\sqrt{3}}{m}\sqrt{\mathrm{one}-m+{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="00000065.png,00000068.png"\; state="\{\{state\}\}">m</figure-callout>}}^2}$$

. For m = 0.05, this limit is 33.8, and for m = 0.05 it decreases to 16.5.

Table 1 Dependences of the relative value of the output voltage of filter 1 on the number of higher harmonics n 5 7 eleven 13 17 19 m = 0.05 6.2 5.3 11.7 13,4 16,4 17.7 U _ac m = 0.1 6.0 5,0 10.3 11.3 12.8 13,4

Thus, the shape of the output voltage of the prototype is distorted much more than the shape of the currents measured by it. This property of the prototype is the reason for its indicated drawback, which is manifested in a decrease in the selectivity and sensitivity of the measuring transducer current negative sequence with an increase in the content of higher harmonics in the measured currents.

ток фазы А и на тот же угол опережает ток фазы С. Вершины импульсов фазных входных токов выпрямителя (фиг.3,а) - это отрезки выходного тока, а передний и задний фронты этих импульсов являются отрезками синусоид. Длительность указанных импульсов, в радианах, равна $$\frac{2}{3}\pi +\gamma$$

, где γ - угол коммутации, в течение которого ток проводят не два, а три вентиля выпрямителя. В рассматриваемом случае γ=0,506 радиана (29 градусов). Соответствующее углу γ время коммутации равно 1,6 мс.When the shape of the currents of a three-phase circuit is close to trapezoidal, the selectivity of the prototype measuring transducer may be completely absent, which is confirmed by the following example. Figure 3, a shows the input currents of an uncontrolled rectifier connected to a three-phase sinusoidal voltage source. The amplitude of this voltage is 145 V. The inductance of the load circuit of the rectifier smoothes its output current. When analyzing the operation of such a rectifier, it is usually assumed that there are no ripples in the output current. In this case, the output circuit of the rectifier can be replaced by a constant current source. In the example, the current of this source is 35 A. The phase input currents of the rectifier form a symmetrical system: the phase B current lags by an angle $$\frac{2}{3}\pi$$

the current of phase A and by the same angle is ahead of the current of phase C. The vertices of the pulses of the phase input rectifier currents (Fig. 3, a) are segments of the output current, and the leading and trailing edges of these pulses are segments of sinusoids. The duration of these pulses, in radians, is equal to $$\frac{2}{3}\pi +\gamma$$

, where γ is the switching angle during which the current is conducted not by two, but by three rectifier valves. In the case under consideration, γ = 0.506 radians (29 degrees). The switching time corresponding to the angle γ is 1.6 ms.

The EMF waveforms shown in Fig. 3b, which are induced in the coils of phase 5 A (upper graph) and phase 6 B (lower graph), have the form of pulse sequences close in shape to triangular. The amplitude of these pulses is 25.7 V, and their angular duration is γ. If the currents measured by DIIPT had a sinusoidal shape, then with an amplitude of these currents equal to 35 A, the amplitude of the sinusoidal EMF of the DIIPT coils would be 7 V.

As the oscillogram shown in Fig. 3c shows, the output voltage of the filter 1 is not equal to zero, as it should be for a direct sequence of currents of the first harmonic. The higher harmonics of these currents were manifested in the output voltage, which changes its polarity 10 times during one source period (0.02 s). This fact indicates that its fifth harmonic is most pronounced in the indicated voltage. The maximum maximum of the absolute value of this voltage is 17.7 V. If the output terminals 13 and 14 were the output terminals of the entire measuring transformer of the current in the reverse sequence, then the protection relay connected to these terminals worked, as if there was an asymmetry in the measured current system. Such a relay would be false. It reflects not the asymmetry of the system of measured currents, but the presence of higher harmonics currents in it.

The difference between the waveforms shown in Fig. 4 from those discussed above is due to the fact that these waveforms relate to the case when the circuit connecting the output terminal of phase C to the corresponding input terminal of the rectifier is broken. For oppositely directed input currents of phases A and B, the instantaneous absolute values are equal to each other (Fig. 4, a). These currents change their direction after half the period of the three-phase source. During the switching time (2.3 ms), the current changes not by 35 A, as in Fig. 3, but, but by 70 A. Because of this, the switching angle y is larger than in Fig. 3, a, and is 0.723 radian (41.4 degrees). The amplitude of the EMF pulses shown in Fig. 4, b, which are induced in the coils of phase 5 A (upper graph) and phase 6 B (lower graph), is 35.8 V.

As the oscillogram shown in Fig. 4c shows, the highest maximum of the absolute value of the output voltage of filter 1 is 20.2 V. The higher harmonics of these currents are manifested in the output voltage, which changes 6 times during one source period (0.02 s) its polarity. The shape of the output voltage of the filter 1 shows that the presence of the first harmonic is clearly manifested in this voltage.

To eliminate false positives when measuring currents with significant shape distortion, a low-pass filter 4 is connected between the output terminals 13 and 14 of the filter 1 and the output terminals of the entire inverse sequence current transducer, as shown in FIG.

, где постоянная времени Т равна произведению сопротивления резистора на емкость конденсатора этого фильтра. Исследования показывают, что для рассмотренных в примере токов трапецеидальной формы, такой фильтр не обеспечивает достаточное подавление высших гармонических составляющих в выходном напряжении фильтра 1. Так при постоянной времени $$Т=1/{\omega }_1$$

выходное напряжение фильтра нижних частот становится более сглаженным, по сравнению с показанной на фиг.3, в осциллограммой. Но максимальная амплитуда этого напряжения остается достаточно большой: она составляет 2,2 В. Аналогичным образом изменилась и форма выходного напряжения фильтра 1 при отключении от входа выпрямителя фазы С. Максимальная амплитуда выходного напряжения фильтра нижних частот снизилась до 6,7 В. Близость максимальных амплитудных значений у выходного напряжения фильтра нижних частот при симметричной системе измеряемых токов (2,2 В) и при обрыве одной фазы (6,7 В) Позволяет сделать следующий вывод. Селективность и чувствительность измерительного преобразователя тока обратной последовательности с фильтром нижних частот первого порядка при трапецеидальной форме измеряемых токов явно недостаточны.The simplest low-pass filter is a first-order RC filter. It includes a capacitor, which is connected to the output terminals of the filter 1 through a resistor. Capacitor terminals are the output terminals of the entire negative sequence current transducer. The amplitude frequency response of such a filter is determined by the expression: $$\mathrm{one}/\sqrt{\mathrm{one}+{\omega }^2{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="00000065.png,00000068.png"\; state="\{\{state\}\}">T</figure-callout>}}^2}$$

where the time constant T is equal to the product of the resistance of the resistor and the capacitance of this filter. Studies show that for the trapezoidal currents considered in the example, such a filter does not provide sufficient suppression of the higher harmonic components in the output voltage of filter 1. So with a time constant $$T=\mathrm{one}/{\omega }_{\mathrm{one}}$$

the output voltage of the low-pass filter becomes smoother, compared with that shown in figure 3, in the waveform. But the maximum amplitude of this voltage remains quite large: it is 2.2 V. The shape of the output voltage of filter 1 also changed in the same way when disconnecting phase C from the input of the rectifier. The maximum amplitude of the output voltage of the low-pass filter decreased to 6.7 V. The proximity of the maximum amplitude values at the output voltage of the low-pass filter with a symmetrical system of measured currents (2.2 V) and when one phase breaks (6.7 V) Allows you to make the following conclusion. The selectivity and sensitivity of the measuring transducer of the reverse sequence current with a first-order low-pass filter with a trapezoidal shape of the measured currents is clearly insufficient.

The frequency transfer function of the second-order low-pass filter 4 has the form

$$W(j\overline{\omega })=\frac{b}{\mathrm{one}+j{a}_{\mathrm{one}}\overline{\omega }-a_2{\overline{\omega }}^2},$$

$$\overline{\omega }=\frac{\omega }{{\omega }_{\mathrm{one}}},(\mathrm{four})$$

- относительное значение угловой частоты, которое для номинальной частоты источника равно единице, ω - текущее значение угловой частоты, ω₁ - угловая частота первой гармоники или номинальная угловая частота источника, от действия которого образованы измеряемые токи, а b, а₁ и а₂ - коэффициенты нормированной передаточной функции фильтра 4 нижних частот. Из (4) можно получить передаточную функцию путем замены $$j\overline{\omega }$$

на $$\overline{s}$$

- приведенный к номинальной угловой частоте аргумент изображения функций времени с помощью преобразования Лапласа.Where $$\overline{\omega }$$

is the relative value of the angular frequency, which is equal to unity for the nominal frequency of the source, ω is the current value of the angular frequency, ω ₁ is the angular frequency of the first harmonic or the nominal angular frequency of the source, from the action of which measured currents are generated, and b, a ₁ and a ₂ - the coefficients of the normalized transfer function of the low pass filter 4. From (4), one can obtain the transfer function by replacing $$j\overline{\omega }$$

on $$\overline{s}$$

- the argument of the image of time functions reduced to the nominal angular frequency using the Laplace transform.

. Выполнение требования о наличии максимума амплитудной частотной характеристики фильтра 4 на частоте источника позволяет минимизировать те отклонения коэффициента передачи через фильтр 4 напряжения первой гармоники, которые вызваны отличием частоты источника от номинальной. При определении параметров фильтра 4 целесообразно выполнять еще одно требование: максимум амплитудной частотной характеристики равен единице. Тогда первая гармоника напряжения, подаваемого на вход фильтра 4, проходит через него без изменения своего действующего значения. При соблюдении обоих указанных требований любые два коэффициента частотной передаточной функции (4) могут быть выражены через третий. В частности, коэффициенты b и а₁ выражаются через коэффициент а₂ According to the claims, the amplitude frequency response of the filter 4 at the source frequency has a maximum. Therefore, the poles of the transfer function are complex conjugate. In this case, the Q factor of the pole (the ratio of half the pole module to the module of its real part) exceeds 0.5. For the accepted form (4) of recording the frequency transfer function, the quality factor of the pole is determined by the formula $$q=\sqrt{a_2}/a_{\mathrm{one}}$$

. Fulfillment of the requirement that there is a maximum in the amplitude frequency response of filter 4 at the source frequency allows to minimize those deviations of the transmission coefficient through the filter 4 of the first harmonic voltage that are caused by the difference between the source frequency and the nominal one. When determining the parameters of the filter 4, it is advisable to fulfill one more requirement: the maximum amplitude frequency response is equal to unity. Then the first harmonic of the voltage supplied to the input of the filter 4 passes through it without changing its effective value. Subject to both of these requirements, any two coefficients of the frequency transfer function (4) can be expressed in terms of the third. In particular, the coefficients b and a ₁ are expressed in terms of the coefficient a ₂

$$b=\sqrt{\mathrm{one}-a_2^2},$$

$$a_{\mathrm{one}}=\sqrt{2a_2(\mathrm{one}-a_2)}.(5)$$

The circuit implementation of second-order analog filters built on the basis of operational amplifiers depends on the value of the quality factor of the pole. Low-Q filters (q≤2) filters, which, in addition to the operational amplifier, include two capacitors and three resistors, are most simplicity. Such a filter can be performed according to the circuit shown in figure 2. The composition of mid-Q (q≤20) filters are additionally introduced two more resistors. The most complex are high-quality (q> 20) filters: they are built on the basis of two or three operational amplifiers.

Given the quality factor of the pole, you can find the coefficient a ₂

$$a_2=\mathrm{one}-\frac{\mathrm{one}}{2{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="00000065.png,00000068.png"\; state="\{\{state\}\}">q</figure-callout>}}^2}.(6)$$

(штриховая линия), и в данных, которые помещены в таблицу 2. В ней приведены значения этих амплитудных частотных характеристик, соответствующие номерам гармоник с 1 по 13.Then, according to formulas (5), the remaining two coefficients of the transfer function of the low-pass filter 4 are calculated. The higher the Q factor of the pole q, the stronger the higher harmonics are suppressed. This result is clearly visible in figure 5, which shows the amplitude frequency characteristics of the low-pass filters at q = 2 (solid line) and $$q=\mathrm{four}/3$$

(dashed line), and in the data that are placed in table 2. It shows the values of these amplitude frequency characteristics corresponding to the harmonic numbers 1 to 13.

table 2 Dependences of the relative value of the output voltage of the second-order filter 4 on the number of higher harmonics n 0.95 one 1.05 5 7 eleven 13 k q = 4/3 0,995 1,0 0,994 0,040 0,020 0.0081 0.0058 q = 2 0.985 1,0 0.983 0,023 0.012 0.0046 0.0033

But with increasing q, the following negative consequences are more and more apparent. Firstly, the required accuracy of installation of the calculated parameters of the resistors and capacitors of the filter increases, the procedure for setting the set values of the module and the quality factor of the poles of the transfer function of the filter is complicated. Secondly, the decrease in the filter transmission coefficient at the first harmonic of the source is caused by the deviation of the frequency of this harmonic from the nominal value. In autonomous electric power systems, such as ship systems, the frequency deviation in static modes is allowed within ± 5% of the nominal. In table 2, these boundaries correspond to the values of n: 0.95 and 1.05. It can be seen that for low-Q filters, the corresponding decrease in the transmission coefficient is small: it does not exceed 1.7%. But for medium-quality filters, with q = 20, this decrease goes beyond the acceptable range: it reaches 56%. Thirdly, in proportion to the quality factor, the time of transients in the filter increases. At q = 2, it is equal to the duration of three periods of source voltage (0.06 s for a frequency of 50 Hz), and at q = 20 it reaches thirty of these periods (0.6 s for a frequency of 50 Hz). Such large values of the transient time when using medium-Q filters require the introduction of no less values of the time delay when the protection is activated. Such a decrease in the speed of protection should be avoided, and for this reason, abandon the use of medium and high quality filters.

For the considered example with the measurement of trapezoidal currents, it is sufficient to use a low-Q filter with the highest figure of merit: q = 2. Figure 3, c shows the input voltage of the low-pass filter 4 when measuring symmetrical trapezoidal currents, and figure 3, d shows its output voltage. The use of filter 4 made it possible to reduce the maximum amplitude of the output voltage of the reverse current transducer by 59 times: from 17.7 V to 0.3 V. Figure 4, shows the input voltage of the low-pass filter 4 when measuring trapezoidal currents in a dangling phase system C, and figure 4, g - its output voltage. Filter 4 reduced the maximum amplitude of the output voltage of the reverse current transducer by 3.5 times: from 20.2 V to 5.8 V. Moreover, the shape of the output voltage of filter 4 became almost sinusoidal. Thus, the use of a second-order low-Q filter with a q factor of q = 2 ensures high selectivity of the measuring transducer of the current in the reverse sequence when measuring trapezoidal currents: the output voltage of the transducer increases by 19 times when one phase is cut off.

The selectivity of such a filter may be insufficient when measuring currents with a greater distortion of the shape of the measured currents than in the considered example. In particular, these may be the input currents of the thyristor converter at a thyristor control angle close to π / 2. In this case, the switching angle is reduced several times, compared with the considered example. The pulse shape of the EMF of the DIIPT coils becomes close to rectangular. The amplitudes of these pulses, the maximums of the extreme values of the output voltage of the filter 1, and the amplitudes of the higher harmonics in this voltage increase significantly. The amplitude values of the output voltages of the low-pass filter 4, made as a low-Q filter with a quality factor of q = 2, become symmetric with a symmetrical system of currents and with a break in one phase.

показана в таблице 3,а график его амплитудной частотной характеристики изображен на фиг.5 пунктирной линией.In such cases, instead of using medium-quality or high-quality filters with the inherent disadvantages listed above, a fourth-order filter should be used, having two pairs of low-quality complex conjugate poles. The dependence of the gain of such a filter on the frequency at $$q=\mathrm{four}/3$$

shown in table 3, and a graph of its amplitude frequency response is shown in figure 5 by a dashed line.

Table 3 The dependence of the relative value of the output voltage of the fourth-order filter 4 at q = 4/3 on the number of higher harmonics n 0.95 one 1.05 5 7 eleven 13 k 0.99 1,0 0.99 0.0016 0,00041 0.000065 0.000033

It can be seen that the output voltage of the first harmonic decreases by only 1%, with a deviation of its frequency from the nominal by ± 5%. The fifth harmonic, which is largest in amplitude, decreases approximately 625 times (25 times compared to a second-order filter with the same poles). The transition time in the fourth-order filter 4 at q = 4/3 is practically the same as for the second-order filter with the same poles: it is about three periods of the source frequency (0.06 s).

Thus, a measuring transducer equipped with a fourth-order low-pass filter with double low-Q poles is capable of detecting the first harmonic of the reverse sequence currents for any highly distorted currents encountered in practice.

Claims (2)

1. A negative-sequence current measuring transducer containing the first and second differentiating induction measuring current transducers having the same parameters of their coils, including the same mutual inductances, respectively, with the first and second current conductors of a three-phase circuit, and for the direct symmetrical component of sinusoidal voltages of this circuit, the phase voltage first conductor on

ahead of the phase voltage of the second current lead, and the negative sequence voltage filter, which is a resistor-capacitor circuit connected to the first, second and third input terminals, as well as to the first and second output terminals of this filter, to the first and third input terminals of which the beginning is connected coils of the first and the end of the coil of the second differentiating induction measuring current transducers, and the end of the coil of the first and the beginning of the coil of the second differentiating induction current measuring current transducers are connected to the second input terminal of this filter, while the first capacitor is connected between the first input and first output terminals of this filter, the first resistor is connected between the first output and second input terminals of the filter, and the serial connection of the second is connected between the second input and second output terminals of the filter a capacitor and a second resistor, and between the second output and third input terminals of the filter, a third resistor, and at a nominal frequency of a three-phase circuit with which the specified measuring transducer is occupied, and when the load is disconnected from the output terminals of the filter, the current of the resistor-capacitor circuit connected between the first and second input terminals of the filter is ahead of the sinusoidal EMF of the coil of the first differentiating induction measuring current transducer connected between these terminals by π / 6, second capacitor resistance

times the resistance of the third resistor, the resistance of the second resistor is

times the inductive resistance of the coil of the second differentiating induction current measuring transducer, and the capacitance of the first capacitor is equal to the sum of the inductive resistance of the coil of the first differentiating induction measuring current transducer and divided by

the resistance of the first resistor, characterized in that a low-pass filter is introduced, which has an order of at least the second, and the maximum amplitude frequency response of this filter corresponds to the nominal frequency of the source, and the first and second input terminals of the specified low-pass filter are connected to the first and second output terminals, respectively said negative sequence voltage filter, and the output terminals of said low-pass filter are output terminals of the transmitter reverse sequence current. 2. The measuring transducer according to claim 1, characterized in that the transfer function of said low-pass filter is performed with double complex conjugate poles.

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