CN110161375B - High-voltage direct-current transmission line calculation model based on distributed resistance parameters - Google Patents
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Abstract
The invention discloses a high-voltage direct-current transmission line calculation model based on distributed resistance parameters, which comprises the following steps of: firstly, acquiring a fault voltage signal and a current signal; decoupling to obtain a line mode component; calculating voltage and current line mode components along the direct current transmission line by using a distribution parameter line model considering the distribution resistance; fourthly, calculating the reverse traveling wave current along the direct current transmission line; and fifthly, calculating the modulus maximum value of the reverse wave current by adopting stationary wavelet transformation. After extracting the voltage and current values of the measuring points at the two ends of the line, the invention calculates the voltage and current linear mode component value along the direct current transmission line by using the line model considering the distributed resistance, calculates the reverse wave current value along the direct current transmission line according to the characteristics that the first reverse wave is not reflected, is not influenced by the frequency change of the reflection coefficient and has obvious fault characteristics, and finally calculates the mode maximum value of the reverse wave current by the stable wavelet transformation, thereby improving the accuracy of the calculation model of the transmission line.
Description
Technical Field
The invention relates to the technical field of power systems, in particular to a high-voltage direct-current power transmission line calculation model based on distributed resistance parameters.
Background
In recent years, high-voltage direct-current transmission projects in China are put into operation successively, and direct-current projects reach 36 items by 2020 according to planning, wherein the direct-current projects with voltage levels of +/-800 kV and above reach 16 items. The safe and stable operation of the high-voltage direct-current transmission project has important significance for ensuring the safety and reliability of the whole power grid. When a high-voltage direct-current transmission line breaks down, the fault reason needs to be quickly and accurately found out, and the fault position needs to be determined.
Because the high-voltage direct-current overhead transmission line extends hundreds to thousands of meters, the distribution parameter characteristic of the transmission line is obvious, the traditional centralized parameter model can not meet the requirement of fault location on the accuracy of the line model, the Bergeron model is widely applied to the fault location theoretical research because the Bergeron model has the characteristics of being capable of calculating any network transient process containing centralized parameter elements and distribution parameter elements, having high solving speed and basically meeting the requirement of precision, but because the resistance in the line is taken as a concentrated parameter and is connected in series at the two ends and the middle of the line, the model simplifies the line in an equivalent way and along with the continuous extension of the high-voltage direct-current transmission line, the fault location method based on the model can not be applied to actual engineering due to low precision.
Therefore, it is necessary to provide an improved calculation model for a high-voltage direct-current transmission line, so as to improve the accuracy of the line calculation model and further promote the practical process of the fault location method for the high-voltage direct-current transmission line.
Disclosure of Invention
The invention aims to solve the problem that the distance measurement error is increased due to inaccurate calculation model of the current high-voltage direct-current transmission line, and provides a calculation model of the high-voltage direct-current transmission line based on distributed resistance parameters.
In order to achieve the above object, the present invention comprises the steps of:
firstly, acquiring a fault voltage signal and a current signal;
decoupling to obtain voltage line mode components and current line mode components of measuring points at two ends of the line;
thirdly, calculating voltage line mode components and current line mode components along the direct current transmission line by using a distributed parameter line model considering distributed resistance;
fourthly, calculating the reverse traveling wave current along the direct current transmission line;
and fifthly, calculating the modulus maximum value of the reverse wave current by adopting stationary wavelet transformation.
Preferably, in the step (i), when the high-voltage direct-current transmission line has a fault, a fault voltage signal and a fault current signal of the high-voltage direct-current transmission line are respectively obtained from measurement points at two ends of the high-voltage direct-current transmission line.
Preferably, in the second step, because the high-voltage direct-current transmission line adopts a bipolar operation mode, electromagnetic coupling exists between two poles, and errors can be generated in the analysis of the subsequent steps based on the electromagnetic coupling, transient voltage signals and transient current signals in a period of time window before and after a fault are taken and subjected to phase-mode conversion decoupling, so that independent transient voltage line-mode components and transient current line-mode components are obtained;
u1representing high-band transient voltage line mode components, u, on the rectifying or inverting side0Representing the zero modulus component of the high-frequency band transient voltage on the rectifying side or the inverting side;
u+is represented by the formula1Transient voltage u of positive electrode line on same side_Is represented by the formula1The transient voltage of the cathode lines on the same side;
i1representing the transient current line mode component, i, on the rectifying or inverting side0Representing the zero modulus component of the transient current on the rectifying side or the inverting side;
i+is represented by1Transient current i of positive electrode line on the same side_Is represented by1The transient current of the cathode lines on the same side;
according to the formula, the method comprises the following steps of,
performing phase-mode conversion on the transient voltage of the positive electrode line at the rectifying side or the inverting side and the transient voltage of the negative electrode line at the rectifying side or the inverting side to respectively obtain a transient voltage line-mode component at the rectifying side or the inverting side and a transient voltage zero-mode component at the rectifying side or the inverting side;
according to the formula, the method comprises the following steps of,
and performing phase-mode conversion on the transient current of the positive pole line on the rectifying side or the inverting side and the transient current of the negative pole line on the rectifying side or the inverting side to respectively obtain a transient current line-mode component on the rectifying side or the inverting side and a transient current zero-mode component on the rectifying side or the inverting side.
Preferably, in the third step, the equivalent resistance, the inductance and the capacitance of a unit length in the high-voltage direct-current transmission line are regarded as a time domain model of distribution parameters, and a distributed voltage line mode component and a distributed current line mode component along the high-voltage direct-current transmission line are calculated.
Preferably, in the step (iv), the backward traveling wave is a traveling wave propagated from the fault point to the measurement points at the two ends of the dc transmission line, and the backward traveling wave current along the hvdc transmission line is calculated after the distributed voltage line mode component and the distributed current line mode component along the hvdc transmission line are calculated in the step (iii), and is obtained according to the following formula:
i+(t)、i-(t) is the forward wave of the current on the high voltage direct current transmission line, the reverse wave of the current on the high voltage direct current transmission line;
u1,i1respectively is the line mode component of the voltage distributed along the high voltage direct current transmission line and the line mode component of the current distributed along the high voltage direct current transmission line;
ZCis the wave impedance of the high voltage direct current transmission line body;
after the high-voltage direct-current transmission line breaks down, the fault traveling wave is transmitted from the fault point to two ends of the line, reflected after reaching the two ends of the line and transmitted to the fault point, so that the first reverse traveling wave after breaking down is not reflected, is not influenced by frequency change of a reflection coefficient, and has the characteristic of obvious fault characteristics.
Preferably, in the fifth step, after the reverse wave current along the HVDC transmission line is obtained by calculation, the mode maximum of the reverse wave current is calculated by adopting stationary wavelet transformation so as to conveniently find out the mutation point of the reverse wave current, and the stationary wavelet transformation does not generate a frequency mixing phenomenon in the scale reconstruction process and has an obvious singularity effect on the detection signal;
the stationary wavelet transform consists of two processes of decomposition and reconstruction, the decomposition process uses J times of iteration to make time series signal data x [ n ]](note as a)0) Transforming into wavelet coefficient set c (x [ n ]) distributed in j +1 wavelet scale])，c(x[n]) Can be expressed as:
c(x[n])＝[aj,bj,bj-1,L,b1]
time series signal data x [ n ]]The result of the wavelet transform of (c) is | wf (x) |, if x exists0∈x[n]And x is at x0In the neighborhood of (c), if the following equation holds, it is called | Wf (x)0) | is x [ n ]]Is transformed by a modulus maximum, x0Referred to as time series signal data x [ n ]]The calculation formula of the WMM point, namely the abrupt change point in the reverse wave current, of the abrupt change point of the reverse wave current is as follows:
|Wf(x)|≤|Wf(x0)|。
preferably, the distributed parameter power transmission line model is formed by infinite infinitesimal cascade, R, L, C is equivalent resistance, inductance and capacitance per unit length respectively by neglecting the line conductance, Δ x is the line infinitesimal length, l is the total length of the power transmission line, and the unit of l is km:
x is the distance between the point to be calculated and the initial end of the line, and the instantaneous voltage and current value expression of the point which is at the distance x from the end M of the line can be obtained by repeatedly calculating the space position of the point x-delta x and the previous point x:
calculating the distributed voltage and the distributed current along the high-voltage direct-current transmission line according to a formula (3), wherein: u. ofM,iM,uN,iN,ux,ixRespectively an M-end voltage instantaneous value, an M-end current instantaneous value, an N-end voltage instantaneous value, an N-end current instantaneous value, an x-point voltage instantaneous value and an x-point current instantaneous value of the circuit; u. of(i) M,i(i) MRespectively representing the i-order derivative of the sampling voltage at the M end to the time and the i-order derivative of the sampling current at the M end to the time, and time series signal data x [ n ] through wavelet decomposition]The different band components are separated into c (x n)]) In different scales, the above process is called multi-scale analysis, and the length of each wavelet scale of the stationary wavelet transform is equal to the length of decomposed signal x [ n ]]Has the same length and translation invariance and is suitable for time series divisionAnd (6) analyzing.
In summary, compared with the prior art, the berelong (Bergeron) model treats the line resistance as a centralized parameter and serially connects the line resistance at the two ends and the middle of the line, so that the line is equivalently simplified, and the error of the line distributed voltage and distributed current calculated by using the line distributed voltage and distributed current formula derived by the model is larger, and the invention has the advantages that: the distributed voltage and the distributed current along the high-voltage direct-current transmission line are calculated by using a line model considering the distributed resistance, then the reverse traveling wave current value along the direct-current transmission line is calculated according to the characteristic that the fault characteristic of the first reverse traveling wave which is not reflected is obvious, the modulus maximum value of the reverse traveling wave current is calculated by adopting the stationary wavelet transformation, the frequency mixing phenomenon cannot occur in the scale reconstruction process of the stationary wavelet transformation, and the singularity effect on the detection signal is obvious.
Drawings
Fig. 1 is a flowchart of improving accuracy of a calculation model of a power transmission line in the embodiment of the present invention;
fig. 2 is a diagram of a power transmission line model in which distributed resistances are taken into account in the embodiment of the present invention;
FIG. 3 is a diagram of a process of stationary wavelet transform in an embodiment of the present invention;
fig. 4 is a simulation diagram of the mode component decoupling of the fault voltage current line in the embodiment of the invention.
Detailed Description
To make the objects, technical solutions and advantages of the embodiments of the present invention clearer and more complete description of the technical solutions of the embodiments of the present invention will be given below with reference to the drawings of the embodiments of the present invention, it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments, and generally, components of the embodiments of the present invention described and illustrated in the drawings herein may be arranged and designed in various different configurations.
Therefore, the following detailed description of the embodiments of the present invention, provided in the accompanying drawings, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention, on the basis of which all other embodiments, obtained by a person skilled in the art without inventive step, fall within the scope of the invention.
Referring to the attached figure 1, the calculation model of the high-voltage direct-current transmission line based on the distributed resistance parameters comprises the following steps:
firstly, acquiring a fault voltage signal and a current signal;
decoupling to obtain voltage line mode components and current line mode components of measuring points at two ends of the line;
thirdly, calculating voltage line mode components and current line mode components along the direct current transmission line by using a distributed parameter line model considering distributed resistance;
fourthly, calculating the reverse traveling wave current along the direct current transmission line;
and fifthly, calculating the modulus maximum value of the reverse wave current by adopting stationary wavelet transformation.
In the first step, when the high-voltage direct-current transmission line has a fault, a fault voltage signal and a fault current signal of the high-voltage direct-current transmission line are respectively obtained from measuring points at two ends of the high-voltage direct-current transmission line, and the obtained fault voltage signal and the obtained fault current signal can directly obtain data through a voltmeter and an ammeter in a simulation experiment.
In the second step, because the high-voltage direct-current transmission line adopts a bipolar operation mode, electromagnetic coupling exists between two poles, and errors can be generated in the analysis of the subsequent steps based on the electromagnetic coupling, transient voltage signals and transient current signals in a period of time window before and after a fault are taken and subjected to phase-mode conversion decoupling, so that independent transient voltage line-mode components and transient current line-mode components are obtained.
Wherein
In formula (1), u1Representing the line-mode component u of the transient voltage on the rectifying or inverting side0Representing the zero modulus component of the transient voltage on the rectifying side or the inverting side;
u+is represented by the formula1Transient voltage u of positive electrode line on same side_Is represented by the formula1The transient voltage of the cathode lines on the same side;
i1representing the transient current line mode component, i, on the rectifying or inverting side0Representing the zero modulus component of the transient current on the rectifying side or the inverting side;
i+is represented by1Transient current i of positive electrode line on the same side_Is represented by1The transient current of the cathode lines on the same side;
in the formula (2), T is a matrix used in phase-mode conversion.
U is selected+、u_、i+、i_In time, it is necessary to ensure that the same side is selected for calculation, that is, u is selected1、u0、i1、i0In this case, the components on the rectification side and the components on the inversion side must be selected at the same time.
Referring to fig. 4, in the embodiment, decoupling simulation is performed by using the second step, in the decoupling simulation, taking a zault-wide fixed extra-high voltage direct current transmission system as an example, the value of the transition resistance is 50 Ω, the value of the fault position is 300km away from the rectification side, and the decoupling line mode component is simulated.
Referring to the attached figure 2, in the third step, the distributed parameter power transmission line model is formed by infinite infinitesimal cascade, in this embodiment, the conductance of the line is ignored, R, L, C are respectively equivalent resistance, inductance and capacitance per unit length, Δ x is the infinitesimal length of the line, l is the total length (unit: km) of the power transmission line, and the distributed voltage and the distributed current along the high-voltage direct-current power transmission line are calculated.
x is the distance between the point to be calculated and the initial end of the line, and the instantaneous voltage and current value expression of the point which is at the distance x from the end M of the line can be obtained by repeatedly calculating the space position of the point x-delta x and the previous point x:
wherein: u. ofM,iM,uN,iN,ux,ixRespectively an M-end voltage instantaneous value, an M-end current instantaneous value, an N-end voltage instantaneous value, an N-end current instantaneous value, an x-point voltage instantaneous value and an x-point current instantaneous value of the circuit; u. of(i) M,i(i) MRespectively representing the i-order derivative of the sampling voltage at the M end and the i-order derivative of the sampling current at the M end.
In order to eliminate the influence of electromagnetic coupling, and because the zero-mode traveling wave speed is greatly influenced by the actual environment and frequency, the attenuation is serious on the long-distance transmission line and the detection is not easy, in the embodiment, the line mode component calculation is adopted, namely u in the formula (3)M,iMRespectively rectifying u on the side of the flow in the step II1,i1Instead, uN,iNRespectively using step II to invert the u on the side of the inverter1,i1Instead.
In the fourth step, after the HVDC transmission line is out of order, the fault traveling wave is transmitted from the fault point to two end points of the line, and then is reflected and transmitted to the fault point, the traveling wave transmitted from the two end measuring points of the HVDC transmission line to the fault point is generally defined as a forward wave, the traveling wave transmitted from the fault point to the two end measuring points of the HVDC transmission line is defined as a backward wave, the distributed voltage and the distributed current line mode component along the HVDC transmission line obtained by the third step are calculated, and after the calculation, the forward traveling wave and the backward traveling wave current on the HVDC transmission line are calculated by the formula (4), after the HVDC transmission line is out of order, the fault traveling wave is transmitted from the fault point to the two end points of the line, and then is reflected and transmitted to the fault point, so the first backward traveling wave after the fault is not reflected, the method is not influenced by the frequency change of the reflection coefficient and has the characteristic of obvious fault characteristics.
In formula (4), i+(t)、i-(t) is the forward wave of the current on the high voltage direct current transmission line, the reverse wave of the current on the high voltage direct current transmission line;
u1,i1respectively is the line mode component of the voltage distributed along the high voltage direct current transmission line and the line mode component of the current distributed along the high voltage direct current transmission line;
ZCis the wave impedance of the high voltage direct current transmission line body.
The reflection coefficient is rho, rho is determined by wave impedance Z, the wave impedance is related to frequency, so the reflection coefficient is also related to frequency, and due to the influence of frequency change, the reflection coefficient is used for calculating the forward traveling wave, if the frequency change is not considered, the calculation error is greatly influenced, and if the frequency change is considered, a large amount of calculation is needed.
In the fifth step, after the reverse traveling wave current along the HVDC transmission line is obtained by calculation, the modular maximum value of the reverse traveling wave current is calculated by adopting the stationary wavelet transform in order to conveniently find out the abrupt change point of the reverse traveling wave current, the stationary wavelet transform does not generate a frequency mixing phenomenon in the scale reconstruction process, and the singularity effect on the detection signal is obvious.
Referring to FIG. 3, stationary wavelet transform is used to detect the abrupt change point in the inverted wave, i.e. the above-mentioned modulo maximum of the inverted wave current, and consists of decomposition and reconstruction, where the decomposition process iterates J times on the time series signal data x [ n ]](note as a)0) Transforming into wavelet coefficient set c (x [ n ]) distributed in j +1 wavelet scale])，c(x[n]) Can be represented by formula (5):
c(x[n])＝[aj,bj,bj-1,L,b1] (5)
wherein:
aj＝Hj-1[n]aj-1 (6)
bj＝Gj-1[n]aj-1 (7)
Hj[n]＝U0Hj-1[n] (8)
Gj[n]＝U0Gj-1[n] (9)
in formulae (5) to (9), the decomposition order J is 1, 2, …, J;
in formula (8), Hj[n]A wavelet low-pass decomposition filter of j level;
in formula (9), Gj[n]A high-pass decomposition filter of j stages;
in the formulae (8) and (9), U0Means to insert a zero after each coefficient of the filter, doubling the filter length;
in the formulae (6) and (7), ajIs the j-th order low frequency scale, bjIs the j-th level high frequency scale.
By wavelet decomposition, different frequency band components in time series signal data x [ n ] are separated into different scales in c (x [ n ]), and the above process is called multi-scale analysis.
The length of each wavelet scale of the stationary wavelet transform is the same as the length of the decomposed signal x [ n ], has translation invariance and is suitable for time series analysis.
Time series signal data x [ n ]]The result of the wavelet transform of (c) is | wf (x) |, if x exists0∈x[n]And x is at x0In the neighborhood of (2), if equation (10) is satisfied, | Wf (x)0) | is x [ n ]]Wavelet transform Modulus maximum (WMM), x0Referred to as time series signal data x [ n ]]I.e. a discontinuity in the counter wave.
|Wf(x)|≤|Wf(x0)| (10)
When the stationary wavelet transform is adopted, the value of J is selected according to the required decomposition series, and in this embodiment, the decomposition series J is 1, 2, …, J, so as to calculate the results of the equations (5) to (10) to be obtained, and obtain the inverse traveling wave current mutation point of the required series.
In summary, the present invention is not limited to the above-described embodiments. Numerous changes and modifications may be made by those skilled in the art without departing from the spirit and scope of the invention. The protection scope of the present invention shall be subject to the claims of the present invention.
Claims (3)
1. A high-voltage direct-current transmission line calculation model based on distributed resistance parameters is characterized by comprising the following steps:
firstly, acquiring a fault voltage signal and a current signal;
decoupling to obtain voltage line mode components and current line mode components of measuring points at two ends of the line;
calculating distributed voltage line mode components and distributed current line mode components along the high-voltage direct-current transmission line by using a distributed parameter line model considering distributed resistance, an equivalent resistance, an inductance and a capacitance in unit length in the high-voltage direct-current transmission line as a time domain model of distributed parameters, wherein the distributed parameter transmission line model is formed by infinite infinitesimal cascade connection, the line conductance is ignored, R, L, C is the equivalent resistance, the inductance and the capacitance in unit length respectively, delta x is the line infinitesimal length, l is the total length of the transmission line, and the unit of l is km:
x is the distance between the point to be calculated and the initial end of the line, and the instantaneous voltage and current value expression of the point which is at the distance x from the end M of the line can be obtained by repeatedly calculating the space position of the point x-delta x and the previous point x:
calculating the distributed voltage and the distributed current along the high-voltage direct-current transmission line according to a formula (3), wherein: u. ofM,iM,uN,iN,ux,ixRespectively an M-end voltage instantaneous value, an M-end current instantaneous value, an N-end voltage instantaneous value, an N-end current instantaneous value, an x-point voltage instantaneous value and an x-point current instantaneous value of the circuit; u. of(i) M,i(i) MRespectively representing the i-order derivative of the sampling voltage at the M end to the time and the i-order derivative of the sampling current at the M end to the time;
calculating the reverse traveling wave current along the direct current transmission line, wherein the reverse traveling wave is a traveling wave transmitted to the measuring points at two ends of the direct current transmission line from the fault point, calculating the reverse traveling wave current along the high-voltage direct current transmission line through the distributed voltage line mode component and the distributed current line mode component along the high-voltage direct current transmission line obtained by calculation in the step three, and obtaining the reverse traveling wave current according to the following formula:
i+(t)、i-(t) is the forward wave of the current on the high voltage direct current transmission line, the reverse wave of the current on the high voltage direct current transmission line;
u1,i1respectively is the line mode component of the voltage distributed along the high voltage direct current transmission line and the line mode component of the current distributed along the high voltage direct current transmission line;
ZCis the wave impedance of the high voltage direct current transmission line body;
after the reverse traveling wave current along the high-voltage direct-current transmission line is obtained through calculation, a mode maximum value of the reverse traveling wave current is calculated through smooth wavelet transformation in order to conveniently find out a catastrophe point of the reverse traveling wave current;
the stationary wavelet transform consists of two processes of decomposition and reconstruction, the decomposition process uses J times of iteration to make time series signal data x [ n ]](note as a)0) Transforming into wavelet coefficient set c (x [ n ]) distributed in j +1 wavelet scale])，c(x[n]) Can be expressed as:
c(x[n])＝[aj,bj,bj-1,L,b1]
time series signal data x [ n ]]The result of the wavelet transform of (c) is | wf (x) |, if x exists0∈x[n]And x is at x0In the neighborhood of (c), if the following equation holds, it is called | Wf (x)0) | is x [ n ]]Is transformed by a modulus maximum, x0Referred to as time series signal data x [ n ]]A WMM point ofNamely, the abrupt change point in the reverse traveling wave current, the calculation formula of the abrupt change point of the reverse traveling wave current is as follows:
|Wf(x)|≤|Wf(x0)|。
2. the calculation model of the HVDC transmission line based on the distributed resistance parameters of claim 1, wherein in step (i), when the HVDC transmission line fails, a fault voltage signal and a fault current signal of the HVDC transmission line are respectively obtained from measurement points at two ends of the HVDC transmission line.
3. The high-voltage direct current transmission line calculation model based on the distributed resistance parameters of claim 1, characterized in that in the second step, because the high-voltage direct current transmission line adopts a bipolar operation mode, electromagnetic coupling exists between two poles, and errors are generated in the analysis of the subsequent steps based on the electromagnetic coupling, so that transient voltage signals and transient current signals in a period of time window before and after a fault are taken and subjected to phase-mode conversion decoupling, and independent transient voltage line-mode components and transient current line-mode components are obtained;
u1representing the line-mode component u of the transient voltage on the rectifying or inverting side0Representing the zero modulus component of the transient voltage on the rectifying side or the inverting side;
u+is represented by the formula1Transient voltage u of positive electrode line on same side_Is represented by the formula1The transient voltage of the cathode lines on the same side;
i1representing the transient current line mode component, i, on the rectifying or inverting side0Representing the zero modulus component of the transient current on the rectifying side or the inverting side;
i+is represented by1Transient current i of positive electrode line on the same side-Is represented by1The transient current of the cathode lines on the same side;
according to the formula, the method comprises the following steps of,
performing phase-mode conversion on the transient voltage of the positive electrode line at the rectifying side or the inverting side and the transient voltage of the negative electrode line at the rectifying side or the inverting side to respectively obtain a transient voltage line-mode component at the rectifying side or the inverting side and a transient voltage zero-mode component at the rectifying side or the inverting side;
according to the formula, the method comprises the following steps of,
and performing phase-mode conversion on the transient current of the positive pole line on the rectifying side or the inverting side and the transient current of the negative pole line on the rectifying side or the inverting side to respectively obtain a transient current line-mode component on the rectifying side or the inverting side and a transient current zero-mode component on the rectifying side or the inverting side.
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| CN111551826A (en) * | 2020-06-18 | 2020-08-18 | 南京机电职业技术学院 | Reverse-traveling wave direct-current transmission line fault location method considering wave velocity change |
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