CN111579849B - Harmonic current distribution obtaining method and device - Google Patents

Harmonic current distribution obtaining method and device Download PDF

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CN111579849B
CN111579849B CN202010278810.9A CN202010278810A CN111579849B CN 111579849 B CN111579849 B CN 111579849B CN 202010278810 A CN202010278810 A CN 202010278810A CN 111579849 B CN111579849 B CN 111579849B
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pole
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CN111579849A (en
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樊丽娟
彭光强
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Maintenance and Test Center of Extra High Voltage Power Transmission Co
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Abstract

The invention discloses a harmonic current distribution acquisition method and a harmonic current distribution acquisition device, wherein the harmonic current distribution acquisition method comprises the steps of acquiring a bipolar line equivalent circuit, wherein the bipolar line equivalent circuit is used for being equivalent to a six-terminal network, specifying positive directions of line intra-pole current and earth intra-pole current of the bipolar line equivalent circuit, determining pole-to-ground voltage and pole intra-pole current, specifying symmetrical operation of the bipolar line equivalent circuit, determining symmetrical components of the pole-to-ground voltage and the pole intra-pole current, equating the bipolar line equivalent circuit to a four-terminal network according to the symmetrical components, and acquiring harmonic current distribution of a bipolar overhead line according to the four-terminal network. The invention has the beneficial effects that: aiming at the calculation of the harmonic current, the method provided by the invention can calculate the amplification mechanism of the harmonic current under the power frequency and has strong universality under the broadband.

Description

Harmonic current distribution obtaining method and device
Technical Field
The invention relates to the field of direct current transmission system safety, in particular to a harmonic current distribution obtaining method and device.
Background
As one of the most important components in high-voltage direct-current transmission, namely an overhead transmission line, long-distance transmission of electric energy can be realized. In addition, the overhead transmission line plays an indispensable role in electric energy transmission and trans-regional regulation between large trans-regional power grids. Because nonlinear elements such as large-scale power electronic equipment are widely applied to high-voltage direct-current transmission engineering, various harmonic waves are easily generated in the operation process of the system, if harmonic current is amplified when flowing through a direct-current circuit, overvoltage and overcurrent can be generated, direct-current protection action can be caused in serious conditions, and the operation condition of the HVDC system is deteriorated even power failure accidents are caused.
At present, direct current harmonic problem research is mainly focused on establishment of a converter harmonic model and harmonic instability caused by alternating current and direct current harmonic interaction, research and calculation are mainly performed on the generation reason, the amplification mechanism and the conduction condition of 50Hz harmonic current in a high-voltage direct current transmission system, a series of characteristics of the 50Hz harmonic current in the HVDC system are effectively analyzed, and the conclusion is poor in universality under wide frequency.
Disclosure of Invention
In order to solve the above problems, the present invention provides a method and an apparatus for obtaining harmonic current distribution, which mainly solve the problem that the existing converter harmonic model analysis method is not strong in universality under a wide frequency.
In order to solve the technical problems, the technical scheme of the invention is as follows:
a harmonic current distribution acquisition method includes the steps of,
acquiring a bipolar line equivalent circuit, wherein the bipolar line equivalent circuit is used for being equivalent to a six-terminal network; step two, defining positive directions of current in a line pole and current in the ground of the bipolar line equivalent circuit, determining voltage to earth and current in the pole, step three, defining symmetrical operation of the bipolar line equivalent circuit, and determining symmetrical components of the voltage to earth and the current in the pole, step four, equating the bipolar line equivalent circuit into a four-terminal network according to the symmetrical components, and step five, obtaining harmonic current distribution of the bipolar overhead line according to the four-terminal network.
The harmonic current distribution acquisition device comprises a first equivalent module, a first setting module, a second equivalent module and a harmonic current distribution acquisition module, wherein the first equivalent module is used for acquiring a bipolar line equivalent circuit which is equivalent to a six-terminal network; the first setting module is used for stipulating the positive directions of the current in the line pole and the current in the ground of the equivalent circuit of the bipolar line and determining the voltage of the pole to earth and the current in the pole, the second setting module is used for stipulating the symmetric operation of the equivalent circuit of the bipolar line and determining the symmetric components of the voltage of the pole to earth and the current in the pole, the second equivalent module is used for equating the equivalent circuit of the bipolar line into a four-terminal network according to the symmetric components, and the harmonic current distribution acquisition module is used for acquiring the harmonic current distribution of the bipolar overhead line according to the four-terminal network.
Has the advantages that:
1. aiming at the calculation of harmonic current, the method provided by the invention can calculate the amplification mechanism of the harmonic current under power frequency, and has strong universality under broadband (50-2500 Hz);
2. the invention provides a method for calculating harmonic current at each position of a direct current line, so that the conduction condition of the harmonic current in the direct current line can be analyzed, and certain reference function can be played for the selection of line models and harmonic suppression equipment in the early stage of related engineering.
Drawings
Fig. 1 is a flowchart of a harmonic current distribution acquisition method according to a first embodiment of the present invention;
fig. 2 is an equivalent six-terminal network of a bipolar overhead line according to a first embodiment of the present invention;
FIG. 3 is an equivalent circuit of a bipolar overhead line according to a first embodiment of the invention;
FIG. 4 is an equivalent four-terminal network of a "pole-pole" circuit according to a first embodiment of the present invention;
FIG. 5 is a comparison between a calculated value of harmonic current at the head end of the polar line 1 and a simulation result according to the first embodiment of the present invention;
FIG. 6 is a comparison between a calculated value of harmonic current at the end of the polar line 1 and a simulation result according to a first embodiment of the present invention;
fig. 7 is a comparison between a calculated value of harmonic current amplification factor at the end of the line 1 of the polar line and a simulation result according to the first embodiment of the present invention;
FIG. 8 is a diagram illustrating the harmonic current amplification applied to various parts of a 50-250Hz line;
FIG. 9 shows the harmonic current amplification applied to each part of 500-2500Hz line.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer and clearer, the following detailed description of the present invention is provided with reference to the accompanying drawings and detailed description. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention. It should be further noted that, for the convenience of description, only some but not all of the relevant aspects of the present invention are shown in the drawings.
Example one
As shown in fig. 1, the present embodiment proposes a harmonic current distribution acquisition method, including the steps of,
acquiring a bipolar line equivalent circuit, wherein the bipolar line equivalent circuit is used for being equivalent to a six-terminal network; step two, defining positive directions of current in a line pole and current in the ground of the bipolar line equivalent circuit, determining voltage to earth and current in the pole, step three, defining symmetrical operation of the bipolar line equivalent circuit, and determining symmetrical components of the voltage to earth and the current in the pole, step four, equating the bipolar line equivalent circuit into a four-terminal network according to the symmetrical components, and step five, obtaining harmonic current distribution of the bipolar overhead line according to the four-terminal network.
Aiming at the calculation of harmonic current, the method provided by the invention can calculate the amplification mechanism of the harmonic current under power frequency, and has strong universality under broadband (50-2500 Hz); the method for calculating the harmonic current at each position of the direct current line is provided, so that the conduction condition of the harmonic current in the direct current line can be analyzed, and certain reference function can be provided for the selection of line models and harmonic suppression equipment in the early stage of related engineering.
In the first step, the method for obtaining the equivalent circuit of the bipolar line includes that the converter station and the inverter station are both replaced by harmonic voltage sources, and the bipolar line can be equivalent to a six-terminal network, as shown in fig. 2. Assuming that for a certain harmonic, the voltage U at the beginning of the line is known 10 ＝-U 20 And the single-length parameter of the line can be obtained, namely the harmonic of the line two polar lines at the position x from the initial endWave current I 1 、I 2 . When determining bipolar line parameters, considering the asymmetric process, the sum of the currents in both poles is not zero for each harmonic, and some of the current will flow from ground.
In step two, the expression modes of the voltage to ground of the pole and the current in the pole are respectively as follows:
Figure BDA0002445799850000041
and
Figure BDA0002445799850000042
wherein, U 1 For polar line 1 to ground harmonic voltage, I 1 For polar 1 harmonic currents, U 2 For the polar line 2 to be connected to ground, I 2 For polar line 2 harmonic current, U 'is a voltage symmetric component, U "is a voltage asymmetric component, I' is a current symmetric component, and I" is a current asymmetric component. In FIG. 3, the positive direction of the current in the line pole and in the ground is specified, while the current I is 1 、I 2 And I 0 Harmonic currents, I, belonging to the process under investigation 1 、I 2 Flow through polar line 1 and polar lines 2, I 0 Flows through the ground. Under the action of the voltage 2U ', the current I' flows only in the line conductors of the "pole-pole" circuit. Under the action of the voltage U ", a current I" flows in the same direction in each pole and a current 2I "flows back through the ground. It should be noted that when the system operates symmetrically, the voltage of the bipolar line is symmetrical U 1 ＝-U 2 I.e. U' ═ U 1 U ″, is 0, so U 'and I' are defined as "symmetric components". The electromagnetic process in the line in the symmetric operation is only related to the parameters of a 'polar-polar' loop, and the current flowing in the earth is 0 at the moment, and the state is extremely similar to the calculation of the unit length distribution parameters of the monopole overhead line. Based on the theory, the calculation of loop parameters and harmonic currents in the symmetrical operation process is mainly discussed, and only the calculation of symmetrical components is involved in the process.
In step four, the step of equating the equivalent circuit of the bipolar line to a four-terminal network specifically includes: by "pole-pole" circuitsInstead of the bipolar line equivalent circuit. Due to U 10 ＝-U 20 Is provided with
Figure BDA0002445799850000051
Figure BDA0002445799850000052
I.e. only a symmetrical component is present in the circuit. Therefore, the original six-terminal network can be replaced by a pole-pole loop, so that the six-terminal network is equivalent to a four-terminal network, as shown in fig. 4, and the actual harmonic current can be calculated.
In step five, the harmonic current distribution of the bipolar overhead line is obtained by the following method:
to simplify the calculation, only the case where only the transmitting converter station generates harmonic voltages is deduced.
Solving symmetrical components of electric potentials at head and tail ends of line
Figure BDA0002445799850000053
U 10 For polar line 1 head-to-ground harmonic voltage, U 20 Is the 2 head to ground harmonic voltage of the polar line E' 0 For a symmetrical component of the head end potential, E l ' is the terminal potential symmetry component;
solving for input impedance Z 'of two-port network' BX Z 'tanh (γ' l) (2), where Z 'is a symmetrical component of the wave impedance of the line, γ' is a symmetrical component of the propagation coefficient of the line, and l is the line length;
according to the double-port network, the symmetrical components of the harmonic current at the first end and the terminal end of the line are respectively obtained according to the superposition principle
Figure BDA0002445799850000054
Wherein, I' 0 Is a head end harmonic current symmetric component; i' l Is the symmetrical component of the end harmonic current;
Figure BDA0002445799850000055
for the angle between the output impedance and the internal resistance of the converter station, when disregarding the output impedance,
Figure BDA0002445799850000056
solving the current of the head end and the tail end of the bipolar line
Figure BDA0002445799850000057
And
Figure BDA0002445799850000058
wherein, I 10 For the head end current of the polar line 1, I 20 Is the head end current of the polar line 2, I 1l For terminal currents of the polar lines 1, I 2l Is the current at the end of the polar line 2;
the bipolar line has a magnification of
Figure BDA0002445799850000061
Calculating harmonic current at each point on the line according to the transmission line equation
Figure BDA0002445799850000062
Wherein, U is the voltage on the uniform transmission line, I is the current on the uniform transmission line, R is the resistance of the long conductor of the unit transmission line, j is the imaginary number unit, omega is the angular velocity, L is the inductance of the long conductor of the unit transmission line, C is the capacitance between the two conductors on the long of the unit transmission line, G is the leakage inductance between the two conductors on the long of the unit transmission line, and x is the transmission line with any length;
push out
Figure BDA0002445799850000063
Gamma is the transmission line propagation coefficient;
to obtain
Figure BDA0002445799850000064
Wherein e is a natural constant;
in the formula (I), the compound is shown in the specification,
Figure BDA0002445799850000065
wherein, U 0 For line head-end harmonic electric voltages, I 0 Is the harmonic current at the head end of the line, and Z is the line wave impedance; a1 and A2 are the generation numbers of the simplified formulas, and have no practical significance, and are explained below;
are combined immediately
Figure BDA0002445799850000066
According to the formula (10), the harmonic current at any point on the line is
Figure BDA0002445799850000067
When x is 0, there is a line head end current
Figure BDA0002445799850000068
Obtaining the current at the tail end of the line:
Figure BDA0002445799850000071
then the symmetrical components of the current at any position on the line are:
Figure BDA0002445799850000072
wherein, U l For line end harmonic voltages, I l For line end harmonic currents, I x Is the harmonic current at the distance x of the line from the head end.
In order to verify the accuracy of the harmonic current distribution acquisition method, a series of simulation experiments are performed, and the method is divided into two parts:
1. harmonic current at the first and the last ends
In order to analyze the rationality of the harmonic current calculation method, simulation verification is carried out by combining certain high-voltage direct-current transmission engineering parameters and models on the basis of PSCAD/EMTDC electromagnetic transient simulation software.
Because the system is in a symmetrical operation state, harmonic currents flowing through the polar line 1 and the polar line 2 are equal in magnitude and same in direction, and therefore only the polar line 1 is analyzed.
Meanwhile, on a PSCAD/EMTDC simulation platform, simulation verification is carried out within the range of 50-2500Hz on the basis of a frequency-dependent phase domain model and with 50Hz as a step length, so that harmonic currents at the head end and the tail end of the corresponding frequency down pole line 1 can be obtained, and the result is shown as simulation values in FIGS. 5 and 6.
It can be found that the calculated values and the simulation results of the current at the head end and the tail end of the line keep high consistency on the trend of the waveform, which proves that the harmonic current calculating method provided by the invention has high accuracy. The calculated value and the simulation result have certain errors only at the wave crest, because the peak value of the current wave obtained by calculation mostly occurs when the frequency is not an integer, and the simulation verification results in the current when the frequency is an integer. In practical engineering, the harmonic waves of the corresponding order, which are amplified to the vicinity of the wave crest, should be filtered as much as possible.
Meanwhile, the amplification factor of the harmonic current at the tail end of the line is verified. On a PSCAD/EMTDC simulation platform, based on a frequency-dependent phase domain model, 100Hz is taken as a step length, and simulation verification is carried out within the range of 50-2500Hz, so that the harmonic current amplification factor of the corresponding frequency down pole line 1 can be obtained; and compared with the calculation results as shown in fig. 7.
It can be seen that the current amplification changes with frequency periodically to form peaks, and the peak value gradually decreases with increasing frequency. The calculated value of the current amplification factor and the simulated value have high consistency in numerical value, which proves that the harmonic current calculation method based on the distribution parameters of the direct current line adopted by the patent is reasonable and effective, and lays a foundation for the subsequent further research.
2. Verification of harmonic current amplification condition at each point of line
And further verifying the harmonic current at each point of the line based on the verification result of the harmonic currents at the first end and the last end. On a PSCAD/EMTDC simulation platform, based on a frequency-dependent phase domain model, with 20km as a step length, respectively verifying harmonic currents with frequencies of 50Hz-250Hz (the step length is 50Hz) and 500Hz-2500Hz (the step length is 500Hz), and obtaining the amplification conditions of the harmonic currents on polar lines 1 at corresponding frequencies and various positions of a line; and compared with the calculation results as shown in fig. 8 and 9.
It can be seen that at each verified frequency, the calculated value of the harmonic current amplification and the simulation result have high consistency in the trend of the waveform. Through calculation, the error between the harmonic current amplification value at each point obtained by calculation by the method and the simulation result is less than 8%, and the main reason of the error is that when the injection frequency is high, the harmonic current fluctuates by about 5%, which directly causes the error when the simulation result is read; errors due to readings are more pronounced when harmonic currents are smaller.
By selecting the step length with certain frequency and line length, the verification of the line harmonic current at different points of the same line under various frequencies is reasonable and representative, and the calculation method provided by the patent can be proved to be feasible and have higher accuracy. Under the broadband (50-2500Hz), the calculation method has universality on the calculation of the size, distribution and amplification condition of the harmonic current of the direct current line.
Example two
A harmonic current distribution acquisition device comprises a first equivalent module, a first setting module, a second equivalent module and a harmonic current distribution acquisition module, wherein the first equivalent module is used for acquiring a bipolar line equivalent circuit which is used for being equivalent to a six-terminal network; the first setting module is used for stipulating the positive directions of the current in the line pole and the current in the ground of the equivalent circuit of the bipolar line and determining the voltage of the pole to earth and the current in the pole, the second setting module is used for stipulating the symmetric operation of the equivalent circuit of the bipolar line and determining the symmetric components of the voltage of the pole to earth and the current in the pole, the second equivalent module is used for equating the equivalent circuit of the bipolar line into a four-terminal network according to the symmetric components, and the harmonic current distribution acquisition module is used for acquiring the harmonic current distribution of the bipolar overhead line according to the four-terminal network.
In the first equivalent module, the bipolar line equivalent circuit is obtained by replacing the converter station and the inverter station with harmonic voltage sources.
In the first setting module, the expressions of the pole-to-ground voltage and the pole-in current are respectively as follows:
Figure BDA0002445799850000091
and
Figure BDA0002445799850000092
wherein, U 1 For polar line 1 to ground harmonic voltage, I 1 For polar 1 harmonic currents, U 2 For the polar line 2 to be connected to ground, I 2 For polar line 2 harmonic current, U 'is a voltage symmetric component, U "is a voltage asymmetric component, I' is a current symmetric component, and I" is a current asymmetric component.
In the second equivalent module, the equivalent of the bipolar line equivalent circuit to a four-terminal network specifically includes: the bipolar line equivalent circuit is replaced by a "pole-pole" circuit.
In the harmonic current distribution acquisition module, the harmonic current distribution of the bipolar overhead line is acquired by:
solving symmetrical components of electric potentials at head and tail ends of line
Figure BDA0002445799850000093
U 10 For polar line 1 head-to-ground harmonic voltage, U 20 Is the 2 head to ground harmonic voltage of the polar line E' 0 Being a head-end potential symmetrical component, E' l Is a terminal potential symmetric component;
solving for input impedance Z 'of two-port network' BX Z 'tanh (γ' l) (2), where Z 'is a symmetrical component of the wave impedance of the line, γ' is a symmetrical component of the propagation coefficient of the line, and l is the line length;
according to the double-port network, the symmetrical components of the harmonic current at the first end and the terminal end of the line are respectively obtained according to the superposition principle
Figure BDA0002445799850000101
Wherein, I' 0 Is a symmetrical component of the head end harmonic current; i' l Is a symmetrical component of the end harmonic current;
Figure BDA0002445799850000102
for the angle between the output impedance and the internal resistance of the converter station, when disregarding the output impedance,
Figure BDA0002445799850000103
solving the current of the head end and the tail end of the bipolar line
Figure BDA0002445799850000104
Wherein, I 10 For the head end current of the polar line 1, I 20 Is the head end current of the polar line 2, I 1l For terminal currents of the polar lines 1, I 2l Is the current at the end of the polar line 2;
the bipolar line has a magnification of
Figure BDA0002445799850000105
Calculating harmonic current at each point on the line according to the transmission line equation
Figure BDA0002445799850000106
Wherein, U is the voltage on the uniform transmission line, I is the current on the uniform transmission line, R is the resistance of the long conductor of the unit transmission line, j is the imaginary number unit, omega is the angular velocity, L is the inductance of the long conductor of the unit transmission line, C is the capacitance between the two conductors on the long of the unit transmission line, G is the leakage inductance between the two conductors on the long of the unit transmission line, and x is the transmission line with any length;
push out
Figure BDA0002445799850000107
Gamma is the transmission line propagation coefficient;
get U ═ A 1 e -γx +A 2 e γx (8) Wherein e is a natural constant;
in the formula (I), the compound is shown in the specification,
Figure BDA0002445799850000111
wherein, U 0 For line head-end harmonic electric voltages, I 0 Is the harmonic current at the head end of the line, and Z is the line wave impedance;
are combined immediately
Figure BDA0002445799850000112
According to the equation (10), the harmonic current at any point on the line is
Figure BDA0002445799850000113
When x is 0, there is a line head end current
Figure BDA0002445799850000114
Obtaining the current at the tail end of the line:
Figure BDA0002445799850000115
then the symmetrical components of the current at any position on the line are:
Figure BDA0002445799850000116
wherein, U l For line end harmonic voltages, I l For line end harmonic currents, I x Is the harmonic current at the distance x of the line from the head end.
The above embodiments are only for illustrating the technical concept and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and implement the present invention accordingly, and not to limit the protection scope of the present invention accordingly. All equivalent changes or modifications made in accordance with the spirit of the present disclosure are intended to be covered by the scope of the present disclosure.

Claims (2)

1. A harmonic current distribution acquisition method is characterized by comprising the following steps,
acquiring a bipolar line equivalent circuit, wherein the bipolar line equivalent circuit is used for being equivalent to a six-terminal network; step two, defining positive directions of current in a line pole and current in the ground of the bipolar line equivalent circuit, determining voltage to earth and current in the pole, step three, defining symmetrical operation of the bipolar line equivalent circuit, and determining symmetrical components of the voltage to earth and the current in the pole, step four, equating the bipolar line equivalent circuit into a four-terminal network according to the symmetrical components, and step five, acquiring harmonic current distribution of the bipolar overhead line according to the four-terminal network;
in the first step, the method for obtaining the equivalent circuit of the bipolar line comprises the steps that the converter station and the inverter station are both replaced by harmonic voltage sources;
in step two, the expressions of the pole-to-ground voltage and the pole-to-medium current are respectively as follows:
Figure FDA0003780226170000011
and
Figure FDA0003780226170000012
wherein, U 1 For polar line 1 to ground harmonic voltage, I 1 For polar 1 harmonic currents, U 2 For the polar line 2 to be connected to ground, I 2 Is polar line 2 harmonic current, U 'is voltage symmetrical component, U' is voltage asymmetrical component, I 'is current symmetrical component, I' is current asymmetrical component;
in step four, the step of equating the equivalent circuit of the bipolar line to a four-terminal network specifically includes: replacing the bipolar line equivalent circuit with a "pole-pole" circuit;
in step five, the harmonic current distribution of the bipolar overhead line is obtained by the following method:
solving the head and tail end electricity of the linePotential symmetric component
Figure FDA0003780226170000013
U 10 For polar line 1 head-to-ground harmonic voltage, U 20 Is the 2 head to ground harmonic voltage of the polar line E' 0 Being a head-end potential symmetrical component, E' l Is a terminal potential symmetric component;
solving for input impedance Z 'of two-port network' BX Z 'tanh (γ' l) (2), where Z 'is a symmetrical component of the wave impedance of the line, γ' is a symmetrical component of the propagation coefficient of the line, and l is the line length;
according to the double-port network, the symmetrical components of the harmonic current at the first end and the terminal end of the line are respectively obtained according to the superposition principle
Figure FDA0003780226170000021
Figure FDA0003780226170000022
Wherein, I' 0 Is a head end harmonic current symmetric component; i' l Is a symmetrical component of the end harmonic current;
Figure FDA0003780226170000023
for the angle between the output impedance and the internal resistance of the converter station, when disregarding the output impedance,
Figure FDA0003780226170000024
solving the current of the head end and the tail end of the bipolar line
Figure FDA0003780226170000025
And
Figure FDA0003780226170000026
wherein, I 10 For the head end current of the polar line 1, I 20 For the head end current of the polar line 2, I 1l For terminal currents of the polar lines 1, I 2l Is the current at the end of the polar line 2;
the bipolar line has a magnification of
Figure FDA0003780226170000027
Calculating harmonic current at each point on the line according to the transmission line equation
Figure FDA0003780226170000028
Wherein, U is the voltage on the uniform transmission line, I is the current on the uniform transmission line, R is the resistance of the long conductor of the unit transmission line, j is the imaginary number unit, omega is the angular velocity, L is the inductance of the long conductor of the unit transmission line, C is the capacitance between the two conductors on the long conductor of the unit transmission line, G is the leakage inductance between the two conductors on the long conductor of the unit transmission line, and x is the transmission line with any length;
push out
Figure FDA0003780226170000029
Gamma is the transmission line propagation coefficient;
get U ═ A 1 e -γx +A 2 e γx (8) Wherein e is a natural constant;
in the formula (I), the compound is shown in the specification,
Figure FDA0003780226170000031
wherein, U 0 For line head-end harmonic voltages, I 0 Is the harmonic current at the head end of the line, and Z is the line wave impedance;
are combined immediately
Figure FDA0003780226170000032
According to the formula (10), the harmonic current at any point on the line is
Figure FDA0003780226170000033
When x is 0, there is a line head end current
Figure FDA0003780226170000034
Obtaining the harmonic current of the line at the distance x from the head end:
Figure FDA0003780226170000035
then the symmetrical components of the current at any position on the line are:
Figure FDA0003780226170000036
wherein, U l For line end harmonic voltages, I l For line end harmonic currents, I x Is the harmonic current at the distance x of the line from the head end.
2. A harmonic current distribution acquisition device is characterized by comprising a first equivalent module, a first setting module, a second equivalent module and a harmonic current distribution acquisition module, wherein the first equivalent module is used for acquiring a bipolar line equivalent circuit which is equivalent to a six-terminal network; the first setting module is used for specifying positive directions of line intra-pole current and ground-to-ground current of the bipolar line equivalent circuit and determining pole-to-ground voltage and pole-to-ground current, the second setting module is used for specifying symmetric operation of the bipolar line equivalent circuit and determining symmetric components of the pole-to-ground voltage and the pole-to-ground current, the second equivalent module is used for enabling the bipolar line equivalent circuit to be equivalent to a four-terminal network according to the symmetric components, and the harmonic current distribution acquisition module is used for acquiring harmonic current distribution of the bipolar overhead line according to the four-terminal network;
in the first equivalent module, the bipolar line equivalent circuit is obtained by replacing a converter station and an inverter station with harmonic voltage sources;
in the first setting module, the expressions of the pole-to-ground voltage and the pole-in current are respectively as follows:
Figure FDA0003780226170000041
and
Figure FDA0003780226170000042
wherein, U 1 For polar line 1 to ground harmonic voltage, I 1 For polar 1 harmonic currents, U 2 For the polar line 2 to be connected to ground, I 2 Is polar line 2 harmonic current, U 'is voltage symmetrical component, U' is voltage asymmetrical component, I 'is current symmetrical component, I' is current asymmetrical component;
in the second equivalent module, the equivalent of the bipolar line equivalent circuit to a four-terminal network specifically includes: replacing the bipolar line equivalent circuit with a "pole-pole" circuit;
in the harmonic current distribution acquisition module, the harmonic current distribution of the bipolar overhead line is acquired by:
solving symmetrical components of electric potentials at head and tail ends of line
Figure FDA0003780226170000043
U 10 For polar line 1 head-to-ground harmonic voltage, U 20 Is head-to-ground harmonic voltage of polar line 2' 0 Is a head end potential symmetric component, E' l Is a terminal potential symmetric component;
solving for input impedance Z 'of two-port network' BX Z 'tanh (γ' l) (2), where Z 'is a symmetrical component of the wave impedance of the line, γ' is a symmetrical component of the propagation coefficient of the line, and l is the line length;
according to the double-port network, the symmetrical components of the harmonic current at the first end and the terminal end of the line are respectively obtained according to the superposition principle
Figure FDA0003780226170000044
Figure FDA0003780226170000045
Wherein, I' 0 Is a head end harmonic current symmetric component; i' l Is a symmetrical component of the end harmonic current;
Figure FDA0003780226170000051
for the angle between the output impedance and the internal resistance of the converter station, when disregarding the output impedance,
Figure FDA0003780226170000052
solving the current of the head end and the tail end of the bipolar line
Figure FDA0003780226170000053
And
Figure FDA0003780226170000054
wherein, I 10 For the head end current of the polar line 1, I 20 For the head end current of the polar line 2, I 1l For terminal currents of the polar lines 1, I 2l Is the current at the end of the polar line 2;
the bipolar line has a magnification of
Figure FDA0003780226170000055
Calculating harmonic current at each point on the line according to the transmission line equation
Figure FDA0003780226170000056
Wherein U is the voltage on the uniform transmission line, I is the current on the uniform transmission line, R is the resistance of the long conductor of the unit transmission line, j is the imaginary number unit, omega is the angular velocity, L is the inductance of the long conductor of the unit transmission line, and C is the capacitance between the two conductors on the long conductor of the unit transmission lineG is leakage inductance between two conductors in unit transmission line length, and x is a transmission line with any length;
is pushed out
Figure FDA0003780226170000057
Gamma is the transmission line propagation coefficient;
get U ═ A 1 e -γx +A 2 e γx (8) Wherein e is a natural constant;
in the formula (I), the compound is shown in the specification,
Figure FDA0003780226170000058
wherein, U 0 For line head end harmonic voltage, I 0 Is the harmonic current at the head end of the line, and Z is the line wave impedance;
are combined immediately
Figure FDA0003780226170000061
According to the equation (10), the harmonic current at any point on the line is
Figure FDA0003780226170000062
When x is 0, there is a line head end current
Figure FDA0003780226170000063
Obtaining the harmonic current of the line at the distance x from the head end:
Figure FDA0003780226170000064
then the symmetrical components of the current at any position on the line are:
Figure FDA0003780226170000065
wherein, U l For line end harmonic voltages, I l For line end harmonic currents, I x Is the harmonic current at the distance x of the line from the head end.
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