CN101964515B - Method for converting boundary element by extra-high voltage direct current transmission line mode voltage S - Google Patents

Abstract

The invention discloses a method for converting a boundary element by an extra-high voltage direct current transmission line mode voltage S, comprising the following steps: when the direct current line is in fault, after a protective element is started, the line mode voltage is obtained by utilizing a phase mode transformational theory according to the two-pole direct current voltage detected on a protection installation part; a dispersion line mode voltage signal is selected to perform S conversion, wherein the sample sequence length is 200 points, and the conversion result is 101*200 time frequency complex matrix; mode calculation is performed on each element in the complex matrix; the high-frequency energy and the low-frequency energy of the line mode voltage are extracted according to the obtained mode matrix; the ratio of the high-frequency energy and the low-frequency energy of the line mode voltage is calculated; the faults in the cell and out of the cell are distinguished according to the ratio of the high-frequency energy and the low-frequency energy. A large amount of stimulated results prove that the method of the invention has better effect.

Description

The boundary element method of extra high voltage direct current transmission line line mode voltage S conversion

Technical field

The present invention relates to the Relay Protection Technology in Power System field, specifically a kind of extra high voltage direct current transmission line failure boundary element approach of utilizing line mode voltage S transform energy ratio.

Background technology

How to improve at present DC line Operation safety and reliability and become urgent problem, can make accurate judgment to DC line fault be the key of DC line protection.At present, extensively adopt in the world traveling-wave protection as the main protection of hvdc transmission line protection, its fast Non-unit protection be that Sudden Changing Rate, voltage traveling wave rate of change and curent change gradient according to voltage traveling wave is as criterion.It has the ultrahigh speed operating characteristics, is not subjected to that current transformer is saturated, the advantage such as system oscillation and long line distributed capacitance affect.But the related data according to domestic and international actual motion shows, but there is the impact because of line end smoothing reactor and DC filter in the DC line traveling-wave protection (mainly being provided by ABB and SIEMENS two companies) of using at present, causes voltage change ratio to reduce; Voltage quantities and topotype ripple are affected by fault distance; The problems such as direction row ripple rate of change is subjected to that transition resistance affects.Exactly because the existence of these influencing factors causes the tripping of existing direct current protecting device sometimes.

Summary of the invention

The objective of the invention is to overcome the deficiency of existing Non-unit protection, a kind of extra high voltage direct current transmission line failure boundary element approach of utilizing line mode voltage S transform energy ratio is provided.

DC transmission system comprises smoothing reactor and the DC filter at DC power transmission line and DC line two ends, smoothing reactor wherein and DC filter have consisted of " natural " border of DC power transmission line high frequency transient amount, and the edge frequency specificity analysis shows that there is significant feature difference in the high fdrequency component of line boundary internal and external fault signal, can propose accordingly to portray the criterion of internal fault external fault identification.

The present invention is based on the upper a kind of boundary element method that proposes of the single-ended ultrahigh speed protection philosophy of the DC power transmission line of utilizing the high fdrequency component feature (its theory diagram such as Fig. 1).

Specific implementation of the present invention is carried out according to the following steps:

(1) after DC line broke down, starting component started immediately.According to the two poles of the earth direct voltage, the employing Karenbauer transformation matrix that the protection installation place records, obtain line mode voltage u ₁:

u ₁＝(u ₊-u _-) (1)

In the formula, u ₊Be anodal direct voltage, u _-Be the negative pole direct current.

(2) the line mode voltage is carried out the S conversion, its sample frequency is 100kHz, and sample sequence length is 200 points, obtains 101 * 200 complex matrix through the S conversion:

$U\left[n\right]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}u\left[k\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000246299000032.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;kn}/N}---\left(2\right)$

$S[m,n]=\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}U[n+k]e^{-{2\mathrm{\&pi;}}^2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000246299000032.png"\; state="\{\{state\}\}">k</figure-callout>}}^2/n^2}{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HSA00000246299000032.png"\; state="\{\{state\}\}">e</figure-callout>}}^j,n\&NotEqual;0---\left(3\right)$

$S[m,n]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}u\left[k\right],n=0---\left(4\right)$

In the formula: u[k] be the individual discrete line mode voltage signaling point of the N that collects, k=0,1,1....N-1, N are sample sequence length.U[n] be u[k] Fourier transform.S[m, n] be multiple time-frequency matrix, it is listed as corresponding sampling time point, the row respective frequencies.

(3) each element in the multiple time-frequency matrix of the capable m row of the n+1 that obtains is asked mould, obtains modular matrix | S[m, n] |, its column vector represents signal amplitude-frequency characteristic at a time, its row vector representation signal time domain analysis under a certain frequency.

(4) ask low-and high-frequency energy summation in the whole time window according to following two formula:

${\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="HSA00000246299000021.png"\; state="\{\{state\}\}">E</figure-callout>}}_1=\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{n=6}{\overset{101}{\mathrm{\&Sigma;}}}\left|S\right[m,n\left]\right|---\left(5\right)$

${\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="HSA00000246299000032.png"\; state="\{\{state\}\}">E</figure-callout>}}_2=\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{n=2}{\overset{5}{\mathrm{\&Sigma;}}}\left|S\right[m,n\left]\right|---\left(6\right)$

In the formula: | S[m, n] | for each element in the s-matrix is asked the modular matrix that obtains behind the mould.E ₁Be high-frequency energy summation, E ₂Be the low frequency energy summation, m=1,2,3....N, N are time window length;

(5) obtain the ratio k of high-frequency energy and low frequency energy:

$k=\frac{E_1}{E_2}---\left(7\right)$

In the formula, E ₁High-frequency energy summation when whole in the window, E ₂Low frequency energy summation in the window when whole, k is the ratio of high-frequency energy in the time window of getting and low frequency energy;

(6) the examination criterion of internal fault external fault is external area error when k≤2, is troubles inside the sample space when k＞2.

Below be design principle of the present invention:

1. the single-ended ultrahigh speed protection philosophy of DC power transmission line

Existing hvdc transmission line protection (mainly being provided by ABB and SIEMENS two companies) is that electric current, the voltage traveling wave that utilizes instant of failure to transmit consists of, and is a kind of Non-unit protection of realizing its rapidity according to voltage traveling wave Sudden Changing Rate, voltage traveling wave rate of change and curent change gradient.But practical operating experiences shows: when DC line during through high resistive fault, the voltage change ratio of traveling-wave protection reduces, and causes sometimes the traveling-wave protection tripping.Utilize the single-ended ultrahigh speed protection philosophy of the DC power transmission line figure of transient state component feature as shown in Figure 1.Shown in the protection philosophy block diagram in, the high-voltage dc transmission electric protection is divided into several parts, therefore can overcome the shortcoming of the direct current protecting of existing use, this patent proposes a kind of method of new examination internal fault external fault based on this.

2. boundary element

The extra-high voltage DC transmission system structure chart as shown in Figure 2.Among Fig. 2, power transmission capacity is 5000MW, and the reactive compensation capacity of rectification side and inversion side is respectively 3000Mvar and 3040Mvar; Every utmost point convertor unit is composed in series by 2 12 pulse converters, and DC power transmission line is six-multiple conductor, and total length is taken as 1500km, adopts J.R.Marti frequency dependence model; The smoothing reactor of 400mH is equipped with in the circuit both sides; The M point is the protection installation place.

The present invention has creatively proposed to consist of its physical boundary with smoothing reactor and DC filter, and its amplitude-frequency characteristic is analyzed.As shown in Figure 3, u wherein ₁For distinguishing outer transient voltage, u ₂Be u ₁Fade to the voltage of DC line protection installation place through flank pass; B ₁, B ₂, B ₃, B ₄Be DC filter lightning arrester, D ₁Be smoothing reactor lightning arrester, D ₂Be DC bus arrester, the present invention is with lightning arrester B ₁, B ₂, B ₃, B ₄, D ₁, D ₂Be referred to as the border lightning arrester.B ₁, B ₂Rated voltage is 150kV, B ₃, B ₄Rated voltage is 75kV, D ₁, D ₂Rated voltage is 824kV.

Among Fig. 3, L=400mH, L ₁=39.09mH, L ₂=26.06mH, L ₃=19.545mH, L ₄=34.75mH, C ₁=0.9 μ F, C ₂=0.9 μ F, C ₃=1.8 μ F, C ₄=0.675 μ F.

The transfer function H (j ω) that now defines boundary element is:

$H\left(\mathrm{j\&omega;}\right)=\frac{Z_1\left(\mathrm{j\&omega;}\right)}{Z_1\left(\mathrm{j\&omega;}\right)+Z_2\left(\mathrm{j\&omega;}\right)}---\left(8\right)$

Z ₁(j ω) is the DC filter impedance, Z ₂(j ω) is the smoothing reactor impedance.Amplitude-frequency characteristic such as Fig. 4 of boundary element transfer function H (j ω).As can be seen from Figure 4: when f＜1000Hz, | H (j ω) | ≈ 0; When 1000Hz＜f＜2000Hz, H (j ω) spectrum curve has vibration, when f＞2000Hz, | H (j ω) |＞-30dB, the high fdrequency component that the visual field internal fault detects during than external area error high 30d so the present invention to select f＞2000Hz be high fdrequency component, f≤2000Hz is low frequency component.

3.S the basic theories of conversion

The S conversion is a kind of reversible local Time-Frequency Analysis Method, and its basic thought is the development to continuous wavelet transform and Short Time Fourier Transform.The S conversion s (τ, f) of signal x (t) is defined as follows:

$S(\mathrm{\&tau;},f)={\&Integral;}_{-\&infin;}^{\&infin;}x\left(t\right)w(\mathrm{\&tau;}-t,f)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000246299000032.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;ft}}\mathrm{dt}---\left(9\right)$

In the formula (9):

$w(\mathrm{\&tau;}-t,f)=\frac{\left|f\right|}{\sqrt{2\mathrm{\&pi;}}}{e}^{\left|\frac{-f^2{(\mathrm{\&tau;}-t)}^2}{2}\right|}---\left(10\right)$

In formula (9) and the formula (10), w (τ-t, f) is Gauss's window; τ is the location parameter of control Gauss window at time shaft t; F is frequency; J is imaginary unit.

Traditional Fourier transform is made first on formula (8) the right, remake Fourier inversion, carry out at last the function that substitution of variable converts the S conversion to the Fourier transform X (f) of signal x (t), that is:

$S(\mathrm{\&tau;},f)={\&Integral;}_{-\&infin;}^{\&infin;}X(v+f)e^{-\frac{{2\mathrm{\&pi;}}^2{v}^2}{f^2}}{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HSA00000246299000032.png"\; state="\{\{state\}\}">e</figure-callout>}}^j\mathrm{dv}---\left(11\right)$

In the formula (11), f ≠ 0.Like this, the S conversion just can utilize FFT to realize calculating fast.Can obtain signal x[k by formula (11)] the discrete representation form S[m of S conversion, n] be:

$X\left[n\right]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}x\left[k\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000246299000032.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;kn}/N}---\left(12\right)$

$S[m,n]=\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}X[n+k]e^{-{2\mathrm{\&pi;}}^2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000246299000032.png"\; state="\{\{state\}\}">k</figure-callout>}}^2/n^2}{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HSA00000246299000032.png"\; state="\{\{state\}\}">e</figure-callout>}}^j,n\&NotEqual;0---\left(13\right)$

$S[m,n]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}x\left[k\right],n=0---\left(14\right)$

So to N the discrete signal point x[k that collects] (k=0,1, ..., N-1) the S conversion is carried out in employing formula (11), (12), and transformation results is a multiple time-frequency matrix, is denoted as s-matrix, the corresponding sampling time point of its row, the row respective frequencies, the first row n=0 is corresponding to the DC component of signal, and the difference on the frequency Δ f between the adjacent lines is:

$\mathrm{\&Delta;f}=\frac{f_s}{N}---\left(15\right)$

In the formula (15), f _sBe sample frequency, N is sampling number.

The capable corresponding frequency f of n _nFor:

$f_n=\frac{f_s}{N}n---\left(16\right)$

4. in the district based on the S conversion, the examination of external area error

System shown in Figure 1 is at 150km place, distance protection installation place, and the plus earth fault occurs 0.5s, and line mode voltage waveform is shown in Fig. 5 (a); Time window length is chosen 2ms after the fault, and sample frequency is 100kHz.

Among the present invention, the line mode voltage is carried out the S conversion, sampled data length 200 points, conversion obtains 101 * 200 complex matrix through S.The corresponding DC component of n=1, the high fdrequency component of the utmost point wave voltage of n=101 respective frequencies 50kHz, side frequency be spaced apart 500Hz, s[m, n] column vector in the matrix represents signal amplitude-frequency characteristic at a time, the time domain of its row vector representation signal under a certain frequency distributes.

According to the amplitude-frequency characteristic of boundary element, selection n=5 is 2000Hz, as the boundary frequency of high fdrequency component and low frequency component.N＞5 are high fdrequency component, and n≤5 are low frequency component, each element is asked mould after, obtain again high-frequency energy and low frequency energy.

${\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="HSA00000246299000021.png"\; state="\{\{state\}\}">E</figure-callout>}}_1=\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{n=6}{\overset{101}{\mathrm{\&Sigma;}}}\left|S\right[m,n\left]\right|---\left(17\right)$

${\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="HSA00000246299000032.png"\; state="\{\{state\}\}">E</figure-callout>}}_2=\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{n=2}{\overset{5}{\mathrm{\&Sigma;}}}\left|S\right[m,n\left]\right|---\left(18\right)$

In formula (17), (18), E ₁Be high-frequency energy, E ₂Be low frequency energy.

As can be seen from Figure 6: during external area error, owing to the attenuation of boundary element to high frequency, the high frequency content in the line mode voltage ripple that the protection installation place measures is relatively less.During troubles inside the sample space, high fdrequency component is not passed through boundary element, so high frequency content is much larger than low-frequency content

The maximum ratio k of definition high-frequency energy and low frequency energy:

$k=\frac{E_1}{E_2}---\left(19\right)$

Therefore, propose to distinguish interior, external area error criterion:

K≤2 are external area error (20a)

K＞2 are troubles inside the sample space (20b)

The present invention compared with prior art has following advantage:

1, this method sample frequency is 100kHz, and time window is 2ms, the impact of uncontrolled system, and delay protection is at Millisecond.

2, the method is to all correct identification of energy of the various fault types in the total track length scope.

3, this method robustness is good, and the performance of tolerance transition resistance is very strong, and interference-free impact has stronger practicality.

Description of drawings

Fig. 1 is the single-ended ultrahigh speed protection philosophy of direct current system transmission line block diagram, u among the figure ₁, i ₁Direct voltage and direct current for the acquisition of protection installation place.

Fig. 2 be cloud wide ± 800kV DC transmission system structure chart, F among the figure ₂, F ₃Be external area error, F ₁, F ₄Be troubles inside the sample space, M is the protection installation place.

Fig. 3 is the boundary element that smoothing reactor and DC filter consist of, U ₁For distinguishing outer transient voltage, U ₂Be U ₁Fade to the voltage of DC line protection installation place through flank pass; B ₁, B ₂, B ₃, B ₄Be the DC filter lightning arrester; D ₁Be smoothing reactor lightning arrester, D ₂Be DC bus arrester; L ₁, L ₂, L ₃, L ₄Be inductance element; C ₁, C ₂, C ₃, C ₄Be capacity cell.

Fig. 4 is the spectral characteristic figure of boundary element, and f is frequency, and Hz is the unit of frequency, and H (j ω) is the amplitude of frequency spectrum.

Fig. 5 is line mode voltage oscillogram, among the figure t/s be time/second, u/kV is voltage/kilovolt.Line mode voltage oscillogram when (a) being troubles inside the sample space; Line mode voltage oscillogram when (b) being external area error.

Fig. 6 is the energy profile of line mode voltage ripple of the present invention under different frequency, and n is frequency (n * Δ f=f _n), E _nBe the transient state energy of line mode voltage on each Frequency point.When (a) being troubles inside the sample space, the energy profile of line mode voltage under individual frequency; When (b) being external area error, the energy profile under each frequency of line mode voltage.

Fig. 7 be anodal monopolar grounding fault occurs in the district of the present invention, when earth resistance is respectively 0.1 Ω, 1 Ω, 10 Ω, 100 Ω; the distribution map of high-frequency energy and low frequency energy ratio; k＞2 o'clock are satisfied and are declared apart from requiring; k is the ratio of high fdrequency component and low frequency component among the figure; l/km is the distance of fault occurrence positions distance protection installation place, and unit is km.

Embodiment

Simulation model as shown in Figure 1, the plus earth fault occurs in 150km place, distance protection installation place, time window length is got 2ms, sample frequency is 100kHz.

(1) after DC line broke down, starting component started immediately, according to formula:

u ₁＝(u ₊-u _-) (1)

Obtain line mode voltage u ₁, line mode voltage waveform is shown in Fig. 5 (a);

(2) according to formula

$S[m,n]=\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}U[n+k]e^{-{2\mathrm{\&pi;}}^2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000246299000032.png"\; state="\{\{state\}\}">k</figure-callout>}}^2/n^2}{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HSA00000246299000032.png"\; state="\{\{state\}\}">e</figure-callout>}}^j,n\&NotEqual;0---\left(3\right)$

$S[m,n]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}u\left[k\right],n=0---\left(4\right)$

The line mode voltage is carried out the S conversion, obtain 101 * 200 complex matrix;

(3) each element in the complex matrix is asked mould, according to the amplitude-frequency characteristic of boundary element, selection n=5 is 2000Hz, as the boundary frequency of high fdrequency component and low frequency component.N＞5 are high fdrequency component, and n≤5 are low frequency component, according to formula

${\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="HSA00000246299000021.png"\; state="\{\{state\}\}">E</figure-callout>}}_1=\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{n=6}{\overset{101}{\mathrm{\&Sigma;}}}\left|S\right[m,n\left]\right|---\left(5\right)$

${\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="HSA00000246299000032.png"\; state="\{\{state\}\}">E</figure-callout>}}_2=\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{n=2}{\overset{5}{\mathrm{\&Sigma;}}}\left|S\right[m,n\left]\right|---\left(6\right)$

Obtain fault interior high-frequency energy summation and the low frequency energy summation of rear whole time window occurs.

(4) obtain the ratio k of high-frequency energy and low frequency energy:

$k=\frac{E_1}{{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="HSA00000246299000032.png"\; state="\{\{state\}\}">E</figure-callout>}}_2}=4.36---\left(8\right)$

Satisfy and declare apart from k＞2 (formula (20b)), judge that this fault is troubles inside the sample space.

Among the present invention different fault distances, different earth resistances have been carried out simulating, verifying, obtained the ratio k of line mode voltage high-frequency energy and low frequency energy, the result is as shown in the table.

Claims (1)

1. the internal fault external fault discriminating method based on extra high voltage direct current transmission line line mode voltage S conversion consists of boundary element by smoothing reactor and DC filter, it is characterized in that carrying out according to the following steps:

(1) after DC line breaks down, according to the two poles of the earth direct voltage, the employing Karenbauer transformation matrix that the protection installation place records, obtains line mode voltage u ₁:

u ₁＝(u ₊-u _-) (1)

In the formula, u ₊Be anodal direct voltage, u _-Be the negative pole direct current;

(2) the line mode voltage is carried out the S conversion, its sample frequency is 100kHz, and sample sequence length is 200 points, obtains 101 * 200 complex matrix through the S conversion:

$U\left[n\right]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}u\left[k\right]e^{-j2\mathrm{\&pi;kn}/N}---\left(2\right)$

$S[m,n]=\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}U[n+k]e^{-2{\mathrm{\&pi;}}^2{k}^2/n^2}{e}^{j2\mathrm{\&pi;km}/N},n\&NotEqual;0---\left(3\right)$

$S[m,n]\frac{1}{N}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}u\left[k\right]\begin{array}{cc}& n=0\end{array}---\left(4\right)$

In the formula: u[k] be the N that collects discrete line mode voltage signaling point, k=0,1,2....N-1, N are sample sequence length, U[n] be u[k] Fourier transform, S[m, n] be multiple time-frequency matrix, the corresponding sampling time point of its row is gone respective frequencies;

(3) each element in the multiple time-frequency matrix of the capable m row of the n+1 that obtains is asked mould, obtains modular matrix | S[m, n] |, its column vector represents signal amplitude-frequency characteristic at a time, its row vector representation signal time domain analysis under a certain frequency;

(4) ask low-and high-frequency energy summation in the whole time window according to following two formula:

$E_1=\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{n=6}{\overset{101}{\mathrm{\&Sigma;}}}\left|S\right[m,n\left]\right|---\left(5\right)$

$E_2=\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{n=2}{\overset{5}{\mathrm{\&Sigma;}}}\left|S\right[m,n\left]\right|---\left(6\right)$

In the formula: | S[m, n] | for each element in the s-matrix is asked the modular matrix that obtains behind the mould, E ₁Be high-frequency energy summation, E ₂Be the low frequency energy summation, m=1,2,3....N, N are time window length;

(5) obtain the ratio k of high-frequency energy and low frequency energy:

$k=\frac{E_1}{E_2}---\left(7\right)$

In the formula, E ₁High-frequency energy summation when whole in the window, E ₂Low frequency energy summation in the window when whole, k is the ratio of high-frequency energy in the time window of getting and low frequency energy;

(6) the examination criterion of internal fault external fault is external area error when k≤2, is troubles inside the sample space when k＞2.

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