CN103345578A - Electric transmission line traveling wave calculation method based on projection transformation - Google Patents

Electric transmission line traveling wave calculation method based on projection transformation Download PDF

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Publication number
CN103345578A
CN103345578A CN2013102618682A CN201310261868A CN103345578A CN 103345578 A CN103345578 A CN 103345578A CN 2013102618682 A CN2013102618682 A CN 2013102618682A CN 201310261868 A CN201310261868 A CN 201310261868A CN 103345578 A CN103345578 A CN 103345578A
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matrix
ripple
coefficient
propagator
line
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Inventor
漆柏林
安贵元
王少枫
王佩霞
赵喜全
马云飞
张军
郝志国
张保会
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Tianshui Power Supply Co Ltd Of Gansu Electric Power Corp
State Grid Corp of China SGCC
Xian Jiaotong University
State Grid Gansu Electric Power Co Ltd
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Tianshui Power Supply Co Ltd Of Gansu Electric Power Corp
State Grid Corp of China SGCC
Xian Jiaotong University
State Grid Gansu Electric Power Co Ltd
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Abstract

The invention discloses an electric transmission line traveling wave calculation method based on project transformation. The electric transmission line traveling wave calculation method comprises the following steps of calculating the coefficient of differential operator projecting on an orthogonal basis by means of the Gauss iteration method through selection of the coefficient of an orthogonal scaling function filter, obtaining an impedance matrix Z and an admittance matrix Y which form a line by means of a matrix H according to the sampling period and line distribution parameters, and calculating wave impedance, wave admittance, a forward propagation function, counter propagation function matrix in the line and the like according to the impedance matrix Z and the admittance matrix Y of the line and the length of the line. Therefore, the electric transmission line traveling wave calculation method based on projection transformation achieves the purpose that current traveling waves propagated from the opposite side can be accurately calculated by means of a line distribution parameter model under the conditions that the sampling frequency is lower and the propagating time of the line traveling waves is not integral multiple of a sampling interval, is small in calculation amount and suitable for real-time on-line calculation, and provides rapid and accurate calculation for current traveling wave differential protection.

Description

Transmission line travelling wave computing method based on projective transformation
Technical field
The present invention relates to power system automatic field, particularly, relate to a kind of transmission line travelling wave computing method based on projective transformation.
Background technology
At present, differential current protection is widely used in the protection of ultra-high-tension power transmission line, but since this protection philosophy based on Kirchhoff's theorem, therefore only be fit to than short-term road.For than long transmission line, because the influence of line distribution capacitance causes reliability and the sensitivity decline of differential current protection, even the situation of external area error malfunction appears.Utilize the distributed parameter model of circuit, utilize the differential protection philosophy of current traveling wave can fundamentally eliminate the influence of capacitance current.The present current traveling wave protection philosophy based on distribution parameter; what utilization calculated propagates into the current traveling wave of this side and the current traveling wave formation difference current row ripple of this side from the circuit offside; need the problem in the face of two aspects: the first needs higher sample frequency; be not suitable for the sample frequency of existing protective device, present protective device is generally weekly sample 12 points, or 32 points of phase at 16.It two is when the capable wave propagation time of circuit is not the integral multiple of sampling interval, needs complicated interpolation calculation.
The invention provides a kind of quick calculation method that offside is propagated the current traveling wave that comes that calculates, two problems above having solved.Namely utilize the circuit distributed parameter model, under low sample frequency, and the capable wave propagation time of circuit is not under the situation of sampling interval integral multiple, and the accurate Calculation offside is propagated the current traveling wave of coming, and calculated amount is little, is fit to real-time online and calculates.For realizing that the current traveling wave differential protection provides fast accurate computing method.
Summary of the invention
The objective of the invention is to, at the problems referred to above, a kind of transmission line travelling wave computing method based on projective transformation are proposed, to realize that low sample frequency or the capable wave propagation time of circuit are not under the situation of sampling interval integral multiple, the accurate Calculation offside is propagated the current traveling wave of coming, calculated amount is little, is fit to the advantage of calculating in real time.
For achieving the above object, the technical solution used in the present invention is:
A kind of transmission line travelling wave computing method based on projective transformation may further comprise the steps:
Step 1: select quadrature scaling function filter coefficient
Figure 181698DEST_PATH_IMAGE002
Step 2: use the projection of Gauss's process of iteration computing differential operator in the coefficient of orthogonal basis
Figure 98838DEST_PATH_IMAGE004
:
Calculate the related coefficient of quadrature scaling function earlier
Figure 878576DEST_PATH_IMAGE006
:
Figure 336102DEST_PATH_IMAGE008
Recycling process of iteration computing differential operator projection coefficient draws
Figure 150474DEST_PATH_IMAGE004
That is:
Step 3: the differentiating operator projection coefficient that draws according to above-mentioned steps two Draw matrix H,
Step 4: draw impedance matrix Z and the admittance matrix Y that forms circuit according to sampling period and circuit distribution parameter;
Figure 999722DEST_PATH_IMAGE012
Figure 668601DEST_PATH_IMAGE014
Wherein, E is unit matrix, and Ts is sampling interval, the serial resistance value
Figure 724281DEST_PATH_IMAGE016
, the polyphone inductance value , the shunt conductance value
Figure 277940DEST_PATH_IMAGE020
With the shunt capacitance value
Figure 801325DEST_PATH_IMAGE022
Be respectively the circuit distribution parameter;
Step 5: draw line impedance matrix Z and admittance matrix Y and line length according to above-mentioned steps four, the wave impedance in the computational scheme, waveguide admittance, forward-propagating function, backpropagation Jacobian matrix;
Wherein, wave impedance matrix:
Figure 293486DEST_PATH_IMAGE024
, the waveguide admittance matrix: , the propagation parameter matrix:
Figure 374017DEST_PATH_IMAGE028
, and the ripple propagator matrix that moves ahead:
Figure 17488DEST_PATH_IMAGE030
, anti-capable ripple propagator matrix
Figure 414971DEST_PATH_IMAGE032
L is line length in the formula, wherein " SQRTM " calculates for the matrix extraction of square root, be that first linear transformation is diagonal matrix, the diagonal entry extraction of square root multiply by the transformation matrix inverse matrix more then, " EXPM " asks the nature exponent arithmetic for matrix, be that first linear transformation is diagonal matrix, diagonal entry is asked the nature index then, and then multiply by the transformation matrix inverse matrix;
Step 6: extract above-mentioned wave impedance matrix, waveguide admittance matrix, move ahead the propagator matrix and instead go the value of the middle row in the propagator matrix as wave impedance, waveguide admittance, propagator and the coefficient of propagator of instead going move ahead: be expressed as the wave impedance coefficient respectively
Figure 143893DEST_PATH_IMAGE034
, the waveguide admittance coefficient
Figure 285024DEST_PATH_IMAGE036
, the propagator coefficient moves ahead
Figure 783001DEST_PATH_IMAGE038
, anti-capable propagator coefficient
Figure 616965DEST_PATH_IMAGE040
Step 7: according to the wave impedance in the above-mentioned steps six, waveguide admittance, propagator and the ripple and instead go move ahead ripple and the ripple of instead going of ripple and voltage of moving ahead of electric current in the coefficient calculations circuit of propagator of instead going move ahead;
Wherein, the electric current ripple that moves ahead:
Figure 567604DEST_PATH_IMAGE042
,
The anti-capable current wave of electric current is:
Figure 450109DEST_PATH_IMAGE044
,
Wherein,
Figure 802593DEST_PATH_IMAGE046
Be the waveguide admittance coefficient of circuit, the discrete convolution of symbol " * " expression, M represents line scan pickup coil side, the other end of circuit is expressed as N,
The voltage ripple that moves ahead:
Figure 300134DEST_PATH_IMAGE048
,
The anti-capable ripple of voltage: ,
Step 8: calculate move ahead ripple and the anti-row ripple of move ahead ripple and anti-row ripple and voltage that offside is the electric current of N end according to move ahead ripple and the anti-row ripple of move ahead ripple and anti-row ripple and the voltage of the electric current of M end in the above-mentioned steps seven, its formula is as follows:
The ripple formula that moves ahead is:
Figure 158685DEST_PATH_IMAGE052
Anti-row ripple formula is:
Figure 693572DEST_PATH_IMAGE054
,
Wherein,
Figure 807021DEST_PATH_IMAGE056
, be the ripple propagation coefficient that moves ahead of circuit with distribution parameter,
Figure 732252DEST_PATH_IMAGE058
Be anti-row ripple propagation coefficient.
According to a preferred embodiment of the invention, in the described step 3: according to the differentiating operator projection coefficient
Figure DEST_PATH_IMAGE059
Draw matrix H, matrix H is specially: first behavior of matrix H
Figure DEST_PATH_IMAGE061
,
Figure DEST_PATH_IMAGE063
...,
Figure DEST_PATH_IMAGE065
, 0 ..., 0}, second behavior
Figure 18877DEST_PATH_IMAGE063
,
Figure DEST_PATH_IMAGE066
, ...,
Figure 427042DEST_PATH_IMAGE065
, 0 ..., 0}, namely the matrix H next line is moving to right of lastrow, is shown below:
。
According to a preferred embodiment of the invention, described matrix H is (2K+1) * (2K+1) rank matrixes, and is described
Figure DEST_PATH_IMAGE069
Be (2K+1) * (2K+1) rank unit matrix.
Technical scheme of the present invention has following beneficial effect:
Technical scheme of the present invention by utilizing the circuit distributed parameter model, has realized under low sample frequency, and the capable wave propagation time of circuit is not under the situation of sampling interval integral multiple, the accurate Calculation offside is propagated the current traveling wave of coming, and calculated amount is little, is fit to real-time online and calculates.For realizing that the current traveling wave differential protection provides fast accurate computation purpose.
Below by drawings and Examples, technical scheme of the present invention is described in further detail.
Description of drawings
Fig. 1 calculates wave impedance and propagator coefficient schematic flow sheet in the embodiment of the invention;
Fig. 2 is the embodiment of the invention schematic flow sheet of quick calculation method of skidding ripple of getting it right of falling into a trap;
Fig. 3 is concrete electric power station system connection diagram in the embodiment of the invention;
Fig. 4 a and Fig. 4 b sample frequency be the move ahead waveform synoptic diagram of ripple and anti-row ripple of 16 following Zou Countys of ripple electric field end weekly;
Fig. 5 a and Fig. 5 b are respectively account form in the employing the technical program among Fig. 4 a and Fig. 4 b obtain the moving ahead error synoptic diagram of ripple and anti-row ripple and move ahead ripple and the anti-row ripple that utilize EMTP to obtain;
Fig. 6 a and Fig. 6 b sample frequency be the move ahead waveform synoptic diagram of ripple and anti-row ripple of 32 following Zou Countys of ripple electric field end weekly;
Fig. 7 a and Fig. 7 b are respectively account form in the employing the technical program among Fig. 6 a and Fig. 6 b obtain the moving ahead error synoptic diagram of ripple and anti-row ripple and move ahead ripple and the anti-row ripple that utilize EMTP to obtain.
Embodiment
Below in conjunction with accompanying drawing the preferred embodiments of the present invention are described, should be appreciated that preferred embodiment described herein only is used for description and interpretation the present invention, and be not used in restriction the present invention.
As shown in Figure 1 and Figure 2, a kind of transmission line travelling wave computing method based on projective transformation may further comprise the steps:
Step 1: select quadrature scaling function filter coefficient
Figure 403350DEST_PATH_IMAGE070
Step 2: use the projection of Gauss's process of iteration computing differential operator in the coefficient of orthogonal basis :
Calculate the related coefficient of quadrature scaling function earlier
Figure DEST_PATH_IMAGE071
:
Figure 675249DEST_PATH_IMAGE008
Recycling process of iteration computing differential operator projection coefficient draws That is:
Figure DEST_PATH_IMAGE072
Step 3: the differentiating operator projection coefficient that draws according to above-mentioned steps two
Figure 827061DEST_PATH_IMAGE004
Draw matrix H,
Step 4: draw impedance matrix Z and the admittance matrix Y that forms circuit according to sampling period and circuit distribution parameter;
Figure DEST_PATH_IMAGE073
Figure DEST_PATH_IMAGE074
Wherein, E is unit matrix, and Ts is sampling interval, the serial resistance value
Figure 455489DEST_PATH_IMAGE016
, the polyphone inductance value
Figure 757157DEST_PATH_IMAGE018
, the shunt conductance value
Figure 117731DEST_PATH_IMAGE020
With the shunt capacitance value Be respectively the circuit distribution parameter;
Step 5: draw line impedance matrix Z and admittance matrix Y and line length according to step 4, the wave impedance in the computational scheme, waveguide admittance, forward-propagating function, backpropagation Jacobian matrix;
Wherein, wave impedance matrix:
Figure DEST_PATH_IMAGE075
, the waveguide admittance matrix:
Figure 435504DEST_PATH_IMAGE076
, the propagation parameter matrix: , and the ripple propagator matrix that moves ahead:
Figure 185471DEST_PATH_IMAGE030
, anti-capable ripple propagator matrix
Figure 794307DEST_PATH_IMAGE032
L is line length in the formula, wherein " SQRTM " calculates for the matrix extraction of square root, be that first linear transformation is diagonal matrix, diagonal entry extracts square root then, multiply by the inverse matrix of transformation matrix then, " EXPM " asks the nature exponent arithmetic for matrix, be that first linear transformation is diagonal matrix, diagonal entry is asked the nature index then, and then multiply by the inverse matrix of transformation matrix;
Step 6: extract wave impedance matrix, waveguide admittance matrix, move ahead the propagator matrix and instead go the value of the middle row in the propagator matrix as wave impedance, waveguide admittance, propagator and the coefficient of propagator of instead going move ahead: be expressed as the wave impedance coefficient respectively
Figure 967799DEST_PATH_IMAGE034
, the waveguide admittance coefficient , the propagator coefficient moves ahead , anti-capable propagator coefficient
Figure 104885DEST_PATH_IMAGE040
Step 7: according to the wave impedance in the step 6, waveguide admittance, propagator and the ripple and instead go move ahead ripple and the ripple of instead going of ripple and voltage of moving ahead of electric current in the coefficient calculations circuit of propagator of instead going move ahead;
Wherein, the electric current ripple that moves ahead: ,
The anti-capable current wave of electric current is: ,
Wherein,
Figure 882851DEST_PATH_IMAGE046
Be the waveguide admittance coefficient of circuit, the discrete convolution of symbol " * " expression, M represents line scan pickup coil side, the other end of circuit is expressed as N,
The voltage ripple that moves ahead:
Figure 466280DEST_PATH_IMAGE048
,
The anti-capable ripple of voltage: ,
Step 8: calculate move ahead ripple and the anti-row ripple of move ahead ripple and anti-row ripple and voltage that offside is the electric current of N end according to move ahead ripple and the anti-row ripple of move ahead ripple and anti-row ripple and the voltage of the electric current of M end in the step 7, its formula is as follows:
The ripple formula that moves ahead is:
Figure 715995DEST_PATH_IMAGE078
Anti-row ripple formula is:
Figure DEST_PATH_IMAGE079
,
Wherein,
Figure 265051DEST_PATH_IMAGE080
, be the ripple propagation coefficient that moves ahead of circuit with distribution parameter,
Figure 574809DEST_PATH_IMAGE081
Be anti-row ripple propagation coefficient.
Wherein in the step 3: according to the differentiating operator projection coefficient Draw matrix H, matrix H is specially: first behavior of matrix H
Figure 761257DEST_PATH_IMAGE066
,
Figure 601037DEST_PATH_IMAGE063
...,
Figure 81697DEST_PATH_IMAGE065
, 0 ..., 0}, second behavior
Figure 436455DEST_PATH_IMAGE063
,
Figure 293552DEST_PATH_IMAGE066
,
Figure 987839DEST_PATH_IMAGE063
...,
Figure 639400DEST_PATH_IMAGE065
, 0 ..., 0}, namely the matrix H next line is moving to right of lastrow, is shown below:
Figure 747033DEST_PATH_IMAGE067
。
Matrix H is (2K+1) * (2K+1) rank matrixes, and is described
Figure 142243DEST_PATH_IMAGE082
Be (2K+1) * (2K+1) rank unit matrix.
Its concrete computation process is as follows: the distribution parameter serial resistance value of circuit , the polyphone inductance value
Figure 345789DEST_PATH_IMAGE018
, the shunt conductance value
Figure 612822DEST_PATH_IMAGE020
With the shunt capacitance value
Figure 811722DEST_PATH_IMAGE022
Known, line length L is known, and sampling interval Ts is known,
Ask for surge impedance of a line (waveguide admittance) and row ripple propagator coefficient according to following method:
The first step: the projection coefficient of asking for differentiating operator
Figure 215022DEST_PATH_IMAGE084
At first select the filter coefficient of a tight quadrature scaling function that supports
Figure 536282DEST_PATH_IMAGE086
, suppose that filter length is M, given
Figure 290611DEST_PATH_IMAGE088
Initial value, carry out iterative according to following equation:
Figure 27623DEST_PATH_IMAGE090
（1）
Wherein,
Figure 551008DEST_PATH_IMAGE092
(2)
Second step: calculate wave impedance (waveguide admittance) and propagator matrix.The length K of wave impedance and propagator coefficient is set, and it is (2K+1) * (2K+1) rank matrix that the differentiating operator projection coefficient is constituted differentiating operator projection matrix H(H according to following form): the next line element is moving to right of lastrow element.
（3）
Form impedance Z and the admittance matrix Y of circuit then:
Figure 19216DEST_PATH_IMAGE095
（4a）
Figure 559918DEST_PATH_IMAGE097
（4b）
Wherein
Figure 203389DEST_PATH_IMAGE098
Be (2K+1) * (2K+1) rank unit matrix
Wave impedance or waveguide admittance matrix calculate according to following formula:
Figure 600873DEST_PATH_IMAGE100
（5a）
Figure DEST_PATH_IMAGE102
（5b）
" SQRTM " calculates for the matrix extraction of square root, i.e. first linear transformation is diagonal matrix, and diagonal entry extracts square root then, and then multiply by the transformation matrix inverse matrix.
The propagation parameter matrix:
Figure 329794DEST_PATH_IMAGE104
（6）
Ripple propagator and anti-row ripple propagator matrix (supposing that line length is L) move ahead:
Figure 972390DEST_PATH_IMAGE106
（7a）
Figure DEST_PATH_IMAGE108
（7b）
" EXPM " asks the nature exponent arithmetic for matrix, i.e. first linear transformation is diagonal matrix, and diagonal entry is asked the nature index then, multiply by the transformation matrix inverse matrix then.
The 3rd step: ask for wave impedance, waveguide admittance and propagator coefficient.Extract wave impedance, waveguide admittance, the propagator that moves ahead, instead go the value of the middle row (K is capable) in the propagator matrix as the coefficient of wave impedance, waveguide admittance, propagator:
（8a）
（8b）
Figure 38752DEST_PATH_IMAGE113
（8c）
Figure 254970DEST_PATH_IMAGE115
（8d）
(2) calculate the computing method real-time that propagate into the skidding ripple according to this skidding ripple.
Suppose that circuit one side is the M end, opposite side is the N end, the voltage and current that known M end is measured, move ahead ripple and the anti-row ripple of calculating N end.Circuit distribution parameter serial resistance value , the polyphone inductance value
Figure 489959DEST_PATH_IMAGE018
, the shunt conductance value With the shunt capacitance value
Figure 494825DEST_PATH_IMAGE022
All known.
The first step: ask for wave impedance (waveguide admittance), the propagator that moves ahead, anti-capable propagator coefficient according to the preceding method off-line.
Second step: form voltage traveling wave or current traveling wave:
The voltage and current that the M end is measured is respectively
Figure DEST_PATH_IMAGE118
With , then the current traveling wave that moves ahead of M side is:
Figure DEST_PATH_IMAGE122
（9a）
The anti-capable current wave of electric current is:
Figure DEST_PATH_IMAGE124
（9b）
Wherein,
Figure 995076DEST_PATH_IMAGE046
Be the waveguide admittance coefficient of circuit, the discrete convolution of symbol " * " expression.
If the formation voltage traveling wave, then formula is:
Figure DEST_PATH_IMAGE126
（10a）
Figure DEST_PATH_IMAGE128
（10b）
Wherein,
Figure DEST_PATH_IMAGE130
Be the surge impedance of a line coefficient, the discrete convolution of symbol " * " expression.
The 3rd step: according to move ahead ripple and the anti-row ripple of following formula online rapid calculation N side:
Propagate into the computing method of the capable ripple of N side from the M side:
Figure DEST_PATH_IMAGE132
（11a）
Figure DEST_PATH_IMAGE134
（11b）
Wherein,
Figure DEST_PATH_IMAGE136
, be the ripple propagation coefficient that moves ahead of circuit with distribution parameter,
Figure DEST_PATH_IMAGE138
Be anti-row ripple propagation coefficient.Calculated amount is very little, amounts to 2K+1 multiplication and 2K+1 sub-addition.
It is as shown in Figure 3 following to be with concrete transmission system that example describes below, and Shandong Power 500kV transmission system is propagated sample calculation to Zibo to Zou County circuit as the row ripple.Known conditions: the voltage and current that (1) Zibo side is measured; (2) sampling interval of Zibo side measuring voltage electric current; (3) circuit distribution parameter and length.
At 0.1 second constantly, behind station, Zibo (Zibo to Weifang circuit) exit generation in the other direction three-phase shortcircuit, electric current and voltage according to the measurement of Zibo side, move ahead ripple and the anti-row ripple that calculate the Zou County side (are the example explanation with the voltage traveling wave, the current traveling wave compute classes seemingly, different is that row ripple formation formula is different, and contrast equation (9a) is to formula (10b).
Line parameter circuit value such as following table:
Table 1: circuit distribution parameter
Figure DEST_PATH_IMAGE139
Line length for the validity of computing method is described, has increased line length for the 328km(physical length is 228km).
1. calculated off-line waveguide admittance coefficient, propagator coefficient, flow process as shown in Figure 1.
The first step: select a quadrature scaling function, this example is selected 4 rank Daubichies scaling functions, and its filter coefficient is:
Figure DEST_PATH_IMAGE141
={0.3258,1.0109,0.8922,-0.0396,-0.2645,0.0436, 0.0465, -0.0150}.
Filter length is that 8(k is from 0～7);
Second step: the projection coefficient of computing differential operator on this quadrature scaling function base.The filter coefficient length of quadrature scaling function is 8, then the differentiating operator projection coefficient
Figure DEST_PATH_IMAGE143
Length is 15( From-7 to 7).Elder generation's initialize iterates according to formula (1) then, obtains projection coefficient.
The 3rd step: select length K=8, form line impedance and admittance matrix Z and Y according to formula (3) and formula (4a), formula (4b).
The 4th step: as shown in table 2 to formula (8d) calculating wave impedance, propagator coefficient according to formula (5a).
The differentiating operator projection coefficient that table 2 is tried to achieve, wave impedance coefficient, the anti-capable ripple propagator coefficient of the ripple that moves ahead:
Figure DEST_PATH_IMAGE146
2. at move ahead ripple and the anti-row ripple of line computation N side
The first step: input wave impedance coefficient, the propagation coefficient that moves ahead, anti-capable propagation coefficient.
Second step: according to the voltage and current that Zibo side is measured, form move ahead ripple and the anti-row ripple of Zibo side according to formula 10a and formula 10b.
The 3rd step: move ahead ripple and the anti-row ripple that calculate the Zou County side according to formula (11a) and formula (11b).
Finish.
3. go ripple result of calculation
Under phases 16 point sampling frequency weekly, the result contrasts referring to Fig. 4 and Fig. 5.
Under phases 32 point sampling frequency weekly, the result contrasts referring to Fig. 6 and Fig. 7.
It should be noted that at last: the above only is the preferred embodiments of the present invention, be not limited to the present invention, although with reference to previous embodiment the present invention is had been described in detail, for a person skilled in the art, it still can be made amendment to the technical scheme that aforementioned each embodiment puts down in writing, and perhaps part technical characterictic wherein is equal to replacement.Within the spirit and principles in the present invention all, any modification of doing, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (3)

1. the transmission line travelling wave computing method based on projective transformation is characterized in that, may further comprise the steps:
Step 1: select quadrature scaling function filter coefficient
Figure 2013102618682100001DEST_PATH_IMAGE002
Step 2: use the projection of Gauss's process of iteration computing differential operator in the coefficient of orthogonal basis
Figure 2013102618682100001DEST_PATH_IMAGE004
:
Calculate the related coefficient of quadrature scaling function earlier
Figure 2013102618682100001DEST_PATH_IMAGE006
:
Recycling process of iteration computing differential operator projection coefficient draws
Figure DEST_PATH_IMAGE004A
That is:
Figure 2013102618682100001DEST_PATH_IMAGE010
Step 3: the differentiating operator projection coefficient that draws according to above-mentioned steps two
Figure DEST_PATH_IMAGE004AA
Draw matrix H,
Step 4: draw impedance matrix Z and the admittance matrix Y that forms circuit according to sampling period and circuit distribution parameter;
Figure 2013102618682100001DEST_PATH_IMAGE012
Figure 2013102618682100001DEST_PATH_IMAGE014
Wherein, E is unit matrix, and Ts is sampling interval, the serial resistance value
Figure 2013102618682100001DEST_PATH_IMAGE016
, the polyphone inductance value
Figure 2013102618682100001DEST_PATH_IMAGE018
, the shunt conductance value
Figure 2013102618682100001DEST_PATH_IMAGE020
With the shunt capacitance value Be respectively the circuit distribution parameter;
Step 5: draw line impedance matrix Z and admittance matrix Y and line length according to above-mentioned steps four, the wave impedance in the computational scheme, waveguide admittance, forward-propagating function, backpropagation Jacobian matrix;
Wherein, wave impedance matrix:
Figure 2013102618682100001DEST_PATH_IMAGE024
, the waveguide admittance matrix:
Figure 2013102618682100001DEST_PATH_IMAGE026
, the propagation parameter matrix:
Figure 2013102618682100001DEST_PATH_IMAGE028
, and the ripple propagator matrix that moves ahead:
Figure 2013102618682100001DEST_PATH_IMAGE030
, anti-capable ripple propagator matrix
Figure 2013102618682100001DEST_PATH_IMAGE032
L is line length in the formula, wherein " SQRTM " calculates for the matrix extraction of square root, be that first linear transformation is diagonal matrix, diagonal entry extracts square root then, multiply by the inverse matrix of transformation matrix then, " EXPM " asks the nature exponent arithmetic for matrix, be that first linear transformation is diagonal matrix, diagonal entry is asked the nature index then, multiply by the inverse matrix of transformation matrix then;
Step 6: extract above-mentioned wave impedance matrix, waveguide admittance matrix, move ahead the propagator matrix and instead go the value of the middle row in the propagator matrix as wave impedance, waveguide admittance, propagator and the coefficient of propagator of instead going move ahead: be expressed as the wave impedance coefficient respectively
Figure 2013102618682100001DEST_PATH_IMAGE034
, the waveguide admittance coefficient
Figure 2013102618682100001DEST_PATH_IMAGE036
, the propagator coefficient moves ahead
Figure 2013102618682100001DEST_PATH_IMAGE038
, anti-capable propagator coefficient
Figure 2013102618682100001DEST_PATH_IMAGE040
Step 7: according to the wave impedance in the above-mentioned steps six, waveguide admittance, propagator and the ripple and instead go move ahead ripple and the ripple of instead going of ripple and voltage of moving ahead of electric current in the coefficient calculations circuit of propagator of instead going move ahead;
Wherein, the electric current ripple that moves ahead: ,
The anti-capable current wave of electric current is:
Figure 2013102618682100001DEST_PATH_IMAGE044
,
Wherein, Be the waveguide admittance coefficient of circuit, the discrete convolution of symbol " * " expression, M represents line scan pickup coil side, the other end of circuit is expressed as N,
The voltage ripple that moves ahead:
Figure 2013102618682100001DEST_PATH_IMAGE048
,
The anti-capable ripple of voltage:
Figure 2013102618682100001DEST_PATH_IMAGE050
,
Step 8: calculate move ahead ripple and the anti-row ripple of move ahead ripple and anti-row ripple and voltage that offside is the electric current of N end according to move ahead ripple and the anti-row ripple of move ahead ripple and anti-row ripple and the voltage of the electric current of M end in the above-mentioned steps seven, its formula is as follows:
The ripple formula that moves ahead is:
Figure DEST_PATH_IMAGE052
Anti-row ripple formula is:
Figure DEST_PATH_IMAGE054
,
Wherein,
Figure DEST_PATH_IMAGE056
, be the ripple propagation coefficient that moves ahead of circuit with distribution parameter, Be anti-row ripple propagation coefficient.
2. the transmission line travelling wave computing method based on projective transformation according to claim 1 is characterized in that, in the described step 3: according to the differentiating operator projection coefficient
Figure DEST_PATH_IMAGE004AAA
Draw matrix H, matrix H is specially: first behavior of matrix H
Figure DEST_PATH_IMAGE060
, ...,
Figure DEST_PATH_IMAGE064
, 0 ..., 0}, second behavior
Figure DEST_PATH_IMAGE062A
,
Figure DEST_PATH_IMAGE060A
,
Figure DEST_PATH_IMAGE062AA
..., , 0 ..., 0}, namely the matrix H next line is moving to right of lastrow, is shown below:
Figure DEST_PATH_IMAGE068
。
3. the transmission line travelling wave computing method based on projective transformation according to claim 1 and 2 is characterized in that, described matrix H is (2K+1) * (2K+1) rank matrixes, and is described
Figure DEST_PATH_IMAGE070
Be (2K+1) * (2K+1) rank unit matrix.
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