Summary of the invention
The objective of the invention is to solve the range error that circuit parameter uncertainty and both-end data asynchronism are brought in the direct current transmission line fault ranging process, the accuracy and the reliability of raising DC line fault range finding under metallic earthing and high resistance earthing fault situation, provide a kind of in conjunction with the fault traveling wave characteristic, dependence can be broken away from, and the direct current transmission line fault distance-finding method of double-end asynchronous and parameter self-adapting can be realized synchronous clock.
For reaching above-mentioned purpose, the present invention adopts following technical scheme: a kind of fault distance measuring time-domain method of direct current transmission line double-end asynchronous and parameter self-adapting, be characterized in, and comprise the steps:
The first step is with sample frequency f
_{s}Gather utmost point I, utmost point II DC line two ends M, the voltage of N, current instantaneous value u
_{MI}, i
_{NI}, u
_{MII}, i
_{MII}, u
_{NI}, u
_{NII}, i
_{NII}, i
_{NII}, convert line mode voltage, the line mould electric current u at M, N two ends to
_{m}, i
_{m}, u
_{n}, i
_{n}:
$\left\{\begin{array}{c}{u}_{m}=\sqrt{2}({u}_{\mathrm{mI}}-{u}_{\mathrm{mII}})\\ {i}_{m}=\sqrt{2}({i}_{\mathrm{mI}}-{i}_{\mathrm{mII}})\\ {u}_{n}=\sqrt{2}({u}_{\mathrm{nI}}-{u}_{\mathrm{nII}})\\ {i}_{n}=\sqrt{2}({i}_{\mathrm{nI}}-{i}_{\mathrm{nII}})\end{array}\right.$
Second step, window scope [t during specified data
_{Star}, t
_{Stop}], the line mode voltage travelling wave signal u when decomposing data in the window with multi-scale wavelet
_{m}And u
_{n}Carry out layering, and calculate the frequency content E of each layer
_{K}, in frequency domain scope 4～30kHz, choose E
_{K}Peaked frequency domain (experimental results show that the frequency range of 4～30kHz can avoid the influence of direct current and low frequency component on the one hand as the centre frequency of wave filter, can reduce the influence of line parameter circuit value frequency dependent characteristic on the other hand), to described line mode voltage, line mould current traveling wave signal u
_{m}, i
_{m}, u
_{n}, i
_{n}Filter, obtain band signal best in the fault analysis signal;
Wherein, t
_{Start}And t
_{Stop}The initial sum of window stops constantly when being respectively data,
t
_{stop}＝t
_{start}+3l/v
_{min}+t
_{rdn}
In the formula: l is the distance of DC line two ends M, N, v
_{Min}For the line mould of DC line is propagated the minimum value of velocity of wave, v
_{Min}=0.97～0.99c, c are the light velocity; t
_{Rdn}For calculating redundancy time, t
_{Rdn}=p Δ t
_{Cal}, p is a fault time domain observation equation number, the p＞actual number for the treatment of observed quantity, Δ t
_{Cal}Be interval computing time, Δ t
_{Cal}＞to the voltage of utmost point I or utmost point II DC line two ends M, N, current instantaneous value sampling time interval 10 times;
${E}_{K}=\frac{1}{{t}_{\mathrm{stop}}-{t}_{\mathrm{start}}}\sqrt{{\∫}_{t={t}_{\mathrm{start}}}^{{t}_{\mathrm{stop}}}{S}_{K}^{2}\left(t\right)\mathrm{dt}}$
In the formula: s
_{K}(t) be described line mode voltage travelling wave signal u
_{m}And u
_{n}The HFS of K layer signal after wavelet decomposition; The frequency band of described K layer correspondence is: f
_{s}/ 2
^{K+1}～f
_{s}/ 2
^{K}, centre frequency is 3f
_{s}/ 2
^{K+1}, bandwidth is f
_{s}/ 2
^{K+1}
In the 3rd step, set up fault time domain observation equation:
${f}_{\mathrm{Location}}(d,r,v{,Z}_{C},{t}_{\mathrm{\Δ}},t)=\frac{1}{2}{(1+\frac{\mathrm{rd}}{4{Z}_{C}})}^{2}[{u}_{m}(t-{t}_{\mathrm{\Δ}}+\frac{d}{v})-{i}_{m}(t-{t}_{\mathrm{\Δ}}+\frac{d}{v})({Z}_{C}+\frac{\mathrm{rd}}{4})]$
$+\frac{1}{2}{(1-\frac{\mathrm{rd}}{4{Z}_{C}})}^{2}[{u}_{m}(t-{t}_{\mathrm{\Δ}}-\frac{d}{v})-{i}_{m}(t-{t}_{\mathrm{\Δ}}-\frac{d}{v})({Z}_{C}-\frac{\mathrm{rd}}{4})]$
$-{\left(\frac{\mathrm{rd}}{4{Z}_{C}}\right)}^{2}{u}_{m}(t-{t}_{\mathrm{\Δ}})-\frac{\mathrm{rd}}{4}(1+\frac{\mathrm{rd}}{4{Z}_{C}})(1-\frac{\mathrm{rd}}{4{Z}_{C}}){i}_{m}(t-{t}_{\mathrm{\Δ}})---\left(1\right)$
$-\frac{1}{2}{(1+\frac{r(l-d)}{4{Z}_{C}})}^{2}[{u}_{n}(t+\frac{l-d}{v})-{i}_{n}(t+\frac{l-d}{v})({Z}_{C}+\frac{r(l-d)}{4})]$
$-\frac{1}{2}{(1-\frac{r(l-d)}{4{Z}_{C}})}^{2}[{u}_{n}(t-\frac{l-d}{v})-{i}_{n}(t-\frac{l-d}{v})({Z}_{C}-\frac{r(l-d)}{4})]$
$+{\left(\frac{r(l-d)}{4{Z}_{C}}\right)}^{2}{u}_{n}\left(t\right)+\frac{r(l-d)}{4}(1+\frac{r(l-d)}{4{Z}_{C}})(1-\frac{r(l-d)}{4{Z}_{C}}){i}_{n}\left(t\right)=0$
Wherein, l is that distance, the d of DC line two ends M, N are distance, the t of trouble spot apart from DC line M end
_{Δ}For DC line M, asynchronous mistiming of N two ends, r are that the line mould distributed resistance of DC line, the line mould that v is DC line are propagated velocity of wave, Z
_{C}Line modular character impedance for DC line;
Wherein, t
_{Δ}=t
_{M0}-t
_{N0}
In the formula, t
_{M0}For the reference of the M end data clock of DC line constantly, t
_{N0}Be the reference moment of DC line N end data clock;
Set up row wave property equation:
d＝(v
_{tw}Δt
_{f}+l)/2
Δt
_{f}＝T
_{fm}-T
_{fm}＝t
_{fm}-t
_{fn}+t
_{Δ}
In the formula, v
_{Tw}Be the capable wave-wave speed of described line mode voltage, Δ t
_{f}Be the capable ripple arrival DC line M of described line mode voltage, the mistiming at N two ends, T
_{Fm}And T
_{Fn}Be respectively fault initial line mode voltage row ripple and arrive the moment that DC line M holds and N holds; t
_{Fm}And t
_{Fn}Be respectively fault initial line mode voltage row ripple and arrive the moment at DC line M, N two ends with respect to each self-reference moment t
_{M0}, t
_{N0}Time;
The 4th step is to described line mode voltage travelling wave signal u
_{m}And u
_{n}Ask for modulus maximum constantly, it is arrived moment of DC line M end and N end as fault initial line mode voltage row ripple, and be made as the reference moment t of M, N two ends data clock the moment that fault initial line mode voltage row ripple arrives DC line M, N two ends respectively
_{M0}, t
_{N0}, t then
_{Fm}=t
_{Fn}=0, t
_{Δ}=Δ t
_{f}, promptly M, asynchronous mistiming of N two ends equal the mistiming that fault initial line mode voltage row ripple arrives the circuit two ends, according to row wave property equation, then:
t
_{Δ}＝Δt
_{f}＝(2d-l)/k
_{v}v (2)
Wherein, k
_{v}Ratio for travelling wave analysis line mould velocity of wave and time-domain analysis line mould velocity of wave;
In the 5th step,, get respectively and calculate t=t constantly formula (2) substitution formula (1)
_{1}, t
_{2}, t
_{3}..., t
_{P}, foundation comprises the described actual asynchronous fault Optimization of Time Domain of the both-end equation for the treatment of observed quantity:
$F(d,r,v,{Z}_{C})=\mathrm{min}\left[\underset{k=1}{\overset{P}{\mathrm{\Σ}}}\right|{f}_{\mathrm{Location}}(d,r,v,{Z}_{C},\frac{2d-l}{{k}_{v}v},{t}_{k})\left|\right]---\left(3\right)$
Formula (3) is carried out global optimizing find the solution, can realize the fault time domain range finding of direct current transmission line double-end asynchronous and parameter self-adapting;
Wherein, calculate t constantly
_{1}, t
_{2}..., t
_{k}..., t
_{p}For:
$\left\{\begin{array}{c}{t}_{1}={t}_{\mathrm{start}}+2l/{v}_{\mathrm{min}}\\ {t}_{p}={t}_{\mathrm{stop}}-l/{v}_{\mathrm{min}}\\ {t}_{2}={t}_{1}+({t}_{p}-{t}_{1})/p\\ \·\\ \·\\ \·\\ {t}_{k}={t}_{1}+(k-1)({t}_{p}-{t}_{1})/p\end{array}\right.$
In the formula, 1＜k＜p, k are natural number.
More specifically, the collection utmost point I in the described first step, utmost point II DC line two ends M, the voltage of N, current instantaneous value are meant with the fault traveling wave wave recording device that is installed in DC line M, N two ends and gather DC line two ends M, the voltage of N, current instantaneous value.
Sample frequency f in the described first step
_{s}Be 1MHz or 500kHz, this is a preferred version.
Wave filter in described second step is meant the Butterworth digital band-pass filter.
Described in described second step and the 5th step actual treat observed quantity be meant the trouble spot apart from the line modular character impedance of the line mould propagation velocity of wave of the line mould distributed resistance of the distance of DC line M end, DC line, DC line and DC line totally four treat observed quantity.
Described the 4th the step in to described line mode voltage travelling wave signal u
_{m}And u
_{n}Ask for modulus maximum constantly, be meant and adopt wavelet analysis detection signal singular point theory described line mode voltage travelling wave signal u
_{m}And u
_{n}Ask for modulus maximum constantly.
In described the 5th step formula (3) being carried out global optimizing finds the solution and is meant that utilizing particle swarm optimization algorithm that formula (3) is carried out global optimizing finds the solution.
The ratio k of travelling wave analysis line mould velocity of wave and time-domain analysis line mould velocity of wave in described the 4th step
_{v}Definite method be: (1) adopts LINE CONSTANTS program, according to the actual track parameter: the solid conductor internal diameter of transmission line of electricity, solid conductor external diameter, direct current resistance, horizontal range, suspension height, sag minimum altitude, split conductor number, heading spacing and lead angle, the line mould that calculates DC line is propagated the relation curve of velocity of wave and analysis frequency; (2), obtain described the 4th step employing wavelet analysis detection signal singular point theory to described line mode voltage travelling wave signal u according to described relation curve
_{m}And u
_{n}Ask for the line mould of analysis frequency range pairing DC line in curve that modulus maximum constantly adopted and propagate velocity of wave
And the E that chooses in described second step
_{K}The line mould of the DC line of peaked frequency domain correspondence is propagated velocity of wave v '; (3) can get as calculated
Because
And the value of v ' has certain scope, therefore the k that calculates
_{v}Certain scope is also arranged; This value is surveyed used frequency range and the required frequency range of time-domain analysis, then k as long as determined capable wave-wave head for a certain transmission line of electricity
_{v}The span of value not for some reason the barrier situation change and change, be a scope of determining, k
_{v}Optional value in its span all can reach and reduce row wave-wave speed v
_{Tw}The purpose of the influence that brings with the difference of propagating velocity of wave v.
The present invention with respect to the major advantage and the beneficial effect of prior art is: the fault distance measuring time-domain method of direct current transmission line double-end asynchronous and parameter self-adapting of the present invention, can be in conjunction with the row wave property, realization need not the asynchronous and adaptive direct current transmission line fault range finding of line parameter circuit value of both-end of synchronous clock, have higher transition resistance tolerance, can improve the accuracy and the reliability of DC line Two-terminal Fault Location effectively.
Embodiment
The present invention is described in further detail below in conjunction with embodiment and accompanying drawing, but embodiments of the present invention are not limited thereto.
Embodiment one
This example employing ± 500kV DC transmission system model, its transmission line of electricity total length is 936km, and wherein utmost point I circuit is the transmission line of electricity that breaks down, and utmost point II circuit is the transmission line of electricity of normal transmission of electricity, and the transmission line of electricity two ends are made as M end and N end respectively.The transmission line of electricity two ends adopt the fault traveling wave wave recording device to gather the voltage and current of M end and N end, and the data sampling frequency is 1MHz.
The first step converts the voltage and current instantaneous value that utmost point I, utmost point II DC line M hold and N holds that collects to M, the line mode voltage at N two ends, electric current:
$\left\{\begin{array}{c}{u}_{m}=\sqrt{2}({u}_{\mathrm{mI}}-{u}_{\mathrm{mII}})\\ {i}_{m}=\sqrt{2}({i}_{\mathrm{mI}}-{i}_{\mathrm{mII}})\\ {u}_{n}=\sqrt{2}({u}_{\mathrm{nI}}-{u}_{\mathrm{nII}})\\ {i}_{n}=\sqrt{2}({i}_{\mathrm{nI}}-{i}_{\mathrm{nII}})\end{array}\right.$
Second step, window scope [t during specified data
_{Star}, t
_{Stop}], begin to calculate t from fault moment
_{Start}Get 0, v
_{Min}Determine according to 97% of the light velocity, get 2.91 * 10
^{5}Km/s, p gets 100, computing time interval of delta t
_{Cal}Get 0.03ms, greater than 10 times of the sampling interval of data, so calculate redundancy time t
_{Rdn}=p Δ t
_{Cal}=3ms, t
_{Stop}=t
_{Start}+ 3l/v
_{Min}+ t
_{Rdn}=12.65ms; Utilize multi-scale wavelet to decompose, during to data in the window signal carry out layering, sample frequency is 1MHz, 4～30KHz frequency range correspondence be the frequency domain scope of the 7th layer to the 5th layer high-frequency signal, this frequency range can be avoided the influence of direct current and low frequency component on the one hand, can reduce the influence of line parameter circuit value frequency dependent characteristic on the other hand, utilize formula
${E}_{K}=\frac{1}{{t}_{\mathrm{stop}}-{t}_{\mathrm{start}}}\sqrt{{\∫}_{t={t}_{\mathrm{start}}}^{{t}_{\mathrm{stop}}}{S}_{K}^{2}\left(t\right)\mathrm{dt}}$
The frequency content E of evaluation between from the 7th layer to the 5th layer
_{K}(if sample frequency is 500kHz, the frequency range of 4～30KHz correspondence is the frequency domain scope of the 6th layer to the 4th layer high-frequency signal, the frequency content between needing this moment to estimate from the 6th layer to the 4th layer.) choose E
_{K}Peaked frequency domain, i.e. f
_{s}/ 2
^{K+1}～f
_{s}/ 2
^{K}, as the logical frequency of band of Butterworth digital band-pass filter, to described line mode voltage, line mould current traveling wave signal u
_{m}, i
_{m}, u
_{n}, i
_{n}Filter, obtain band signal best in the fault analysis signal;
In the 3rd step, set up fault time domain observation equation:
${f}_{\mathrm{Location}}(d,r,v{,Z}_{C},{t}_{\mathrm{\Δ}},t)=\frac{1}{2}{(1+\frac{\mathrm{rd}}{4{Z}_{C}})}^{2}[{u}_{m}(t-{t}_{\mathrm{\Δ}}+\frac{d}{v})-{i}_{m}(t-{t}_{\mathrm{\Δ}}+\frac{d}{v})({Z}_{C}+\frac{\mathrm{rd}}{4})]$
$+\frac{1}{2}{(1-\frac{\mathrm{rd}}{4{Z}_{C}})}^{2}[{u}_{m}(t-{t}_{\mathrm{\Δ}}-\frac{d}{v})-{i}_{m}(t-{t}_{\mathrm{\Δ}}-\frac{d}{v})({Z}_{C}-\frac{\mathrm{rd}}{4})]$
$-{\left(\frac{\mathrm{rd}}{4{Z}_{C}}\right)}^{2}{u}_{m}(t-{t}_{\mathrm{\Δ}})-\frac{\mathrm{rd}}{4}(1+\frac{\mathrm{rd}}{4{Z}_{C}})(1-\frac{\mathrm{rd}}{4{Z}_{C}}){i}_{m}(t-{t}_{\mathrm{\Δ}})---\left(1\right)$
$-\frac{1}{2}{(1+\frac{r(l-d)}{4{Z}_{C}})}^{2}[{u}_{n}(t+\frac{l-d}{v})-{i}_{n}(t+\frac{l-d}{v})({Z}_{C}+\frac{r(l-d)}{4})]$
$-\frac{1}{2}{(1-\frac{r(l-d)}{4{Z}_{C}})}^{2}[{u}_{n}(t-\frac{l-d}{v})-{i}_{n}(t-\frac{l-d}{v})({Z}_{C}-\frac{r(l-d)}{4})]$
$+{\left(\frac{r(l-d)}{4{Z}_{C}}\right)}^{2}{u}_{n}\left(t\right)+\frac{r(l-d)}{4}(1+\frac{r(l-d)}{4{Z}_{C}})(1-\frac{r(l-d)}{4{Z}_{C}}){i}_{n}\left(t\right)=0$
Wherein, l is that distance, the d of DC line two ends M, N are distance, the t of trouble spot apart from DC line M end
_{Δ}For DC line M, asynchronous mistiming of N two ends, r are that the line mould distributed resistance of DC line, the line mould that v is DC line are propagated velocity of wave, Z
_{C}Line modular character impedance for DC line;
Wherein, t
_{Δ}=t
_{M0}-t
_{N0}
In the formula, t
_{M0}For the reference of the M end data clock of DC line constantly, t
_{N0}Be the reference moment of DC line N end data clock;
Set up row wave property equation:
d＝(v
_{tw}Δt
_{f}+l)/2
Δt
_{f}＝T
_{fm}-T
_{fn}＝t
_{fm}-t
_{fn}+t
_{Δ}
In the formula, v
_{Tw}Be the capable wave-wave speed of described line mode voltage, Δ t
_{f}Be the capable ripple arrival DC line M of described line mode voltage, the mistiming at N two ends, T
_{Fm}And T
_{Fn}Be respectively fault initial line mode voltage row ripple and arrive the moment that DC line M holds and N holds; t
_{Fm}And t
_{Fn}Be respectively fault initial line mode voltage row ripple and arrive the moment at DC line M, N two ends with respect to each self-reference moment t
_{M0}, t
_{N0}Time;
In the 4th step, adopt wavelet analysis detection signal singular point theory to above-mentioned line mode voltage travelling wave signal u
_{m}And u
_{n}Analyze, ask for described line mode voltage travelling wave signal u
_{m}And u
_{n}Modulus maximum constantly and is made as the moment that fault initial line mode voltage row ripple arrives DC line M, N two ends respectively reference the moment t of M, N two ends data clock
_{M0}, t
_{N0}, t then
_{Fm}=t
_{Fn}=0, t
_{Δ}=Δ t
_{f}, promptly M, asynchronous mistiming of N two ends equal the mistiming that fault initial line mode voltage row ripple arrives the circuit two ends, according to row wave property equation, then:
t
_{Δ}＝Δt
_{f}＝(2d-l)/k
_{v}v (2)
Wherein, k
_{v}Ratio for travelling wave analysis line mould velocity of wave and time-domain analysis line mould velocity of wave, according to the actual track parameter: the solid conductor internal diameter of transmission line of electricity, the solid conductor external diameter, direct current resistance, horizontal range, suspension height, the sag minimum altitude, the split conductor number, heading spacing and lead angle, the relation curve that utilizes LINECONSTANTS program computational scheme line mould to propagate velocity of wave and analysis frequency is determined, as shown in Figure 2 ± the 500kV curve is described relation curve, in time-domain analysis, the 5th layer to the 7th layer HFS of the corresponding wavelet decomposition of the frequency range of bandpass filter, sample frequency for 1MHz, the centre frequency scope is 5k to 20kHz, and corresponding velocity of wave scope is 2.963～2.966km/s; Above-mentioned employing wavelet analysis detection signal singular point theory is to described line mode voltage travelling wave signal u
_{m}And u
_{n}Ask for the analysis frequency range that modulus maximum is adopted constantly, centre frequency is about 250～500kHz, and corresponding row wave-wave speed is about 2.977km/s, so for this circuit, k
_{v}Span be: 1.004～1.0047, get 1.004 herein.
In the 5th step,, get a plurality of calculating t=t constantly with formula (2) substitution formula (1)
_{1}, t
_{2}, t
_{3}..., t
_{P}, foundation comprises fault distance, distributed resistance, propagation velocity of wave and characteristic impedance totally 4 the asynchronous fault Optimization of Time Domain of both-end equations for the treatment of observed quantity:
$F(d,r,v,{Z}_{C})=\mathrm{min}\left[\underset{k=1}{\overset{P}{\mathrm{\Σ}}}\right|{f}_{\mathrm{Location}}(d,r,v,{Z}_{C},\frac{2d-l}{{k}_{v}v},{t}_{k})\left|\right]---\left(3\right)$
Formula (3) is carried out global optimizing find the solution, can realize that line parameter circuit value is adaptive and need not the synchronous DC power transmission line time domain fault localization of GPS;
Wherein, calculate t constantly
_{1}, t
_{2}..., t
_{k}..., t
_{p}:
$\left\{\begin{array}{c}{t}_{1}={t}_{\mathrm{start}}+2l/{v}_{\mathrm{min}}=6.4\mathrm{ms}\\ {t}_{100}={t}_{\mathrm{stop}}-l/{v}_{\mathrm{min}}=9.4\mathrm{ms}\\ {t}_{2}={t}_{1}+({t}_{p}-{t}_{1})/p=6.43\mathrm{ms}\\ {t}_{3}={t}_{2}+({t}_{p}-{t}_{1})/p=6.46\mathrm{ms}\\ \·\\ \·\\ \·\end{array}\right.$
To optimizing equation (3), adopt PSO algorithm (particle swarm optimization algorithm) to find the solution.
At the transmission line of electricity diverse location metallic earthing fault and high resistance earthing fault are set respectively, the range finding of various faults the results are shown in table 1, as seen, adopts method disclosed by the invention to carry out fault localization, and error is little, accuracy rate is high.
Table 1
10 |
9.923 |
2.9726 |
-3.0820 |
-0.077 |
10.118 |
2.9749 |
-3.0783 |
0.118 |
100 |
100.332 |
2.9700 |
-2.4759 |
0.332 |
100.640 |
2.9705 |
-2.434 |
0.640 |
200 |
199.520 |
2.9724 |
-1.8065 |
-0.480 |
200.404 |
2.9724 |
-1.8001 |
0.404 |
300 |
300.189 |
2.9730 |
-1.1289 |
0.189 |
300.251 |
2.9722 |
-1.1288 |
0.251 |
400 |
399.886 |
2.9728 |
-0.4583 |
-0.114 |
400.267 |
2.9714 |
-0.4559 |
0.267 |
536 |
535.951 |
2.9711 |
0.4574 |
-0.049 |
535.884 |
2.9717 |
0.4569 |
-0.116 |
636 |
635.770 |
2.9725 |
1.1288 |
-0.230 |
635.808 |
2.9728 |
1.1289 |
-0.192 |
736 |
736.460 |
2.9726 |
1.8062 |
0.460 |
735.654 |
2.9717 |
1.8014 |
-0.346 |
836 |
835.803 |
2.9724 |
2.4748 |
-0.197 |
835.769 |
2.9718 |
2.4751 |
-0.231 |
926 |
926.255 |
2.9723 |
3.0836 |
0.255 |
925.385 |
2.9713 |
3.0787 |
-0.615 |
936 |
935.880 |
2.9759 |
3.1445 |
-0.120 |
935.223 |
2.9709 |
3.1453 |
-0.777 |
Embodiment two
This example employing ± 800kV DC transmission system model, its transmission line of electricity total length is 1438km, and wherein utmost point I circuit is the transmission line of electricity that breaks down, and utmost point II circuit is the transmission line of electricity of normal transmission of electricity, and the circuit two ends are made as M end and N end respectively.The circuit two ends adopt the fault traveling wave wave recording device to gather the voltage and current of M end and N end, and the data sampling frequency is 1MHz.
The first step converts the voltage and current instantaneous value that utmost point I, utmost point II DC line M hold and N holds that collects to M, the line mode voltage at N two ends, electric current:
$\left\{\begin{array}{c}{u}_{m}=\sqrt{2}({u}_{\mathrm{mI}}-{u}_{\mathrm{mII}})\\ {i}_{m}=\sqrt{2}({i}_{\mathrm{mI}}-{i}_{\mathrm{mII}})\\ {u}_{n}=\sqrt{2}({u}_{\mathrm{nI}}-{u}_{\mathrm{nII}})\\ {i}_{n}=\sqrt{2}({i}_{\mathrm{nI}}-{i}_{\mathrm{nII}})\end{array}\right.$
Second step, window scope [t during specified data
_{Star}, t
_{Stop}], begin to calculate t from fault moment
_{Start}Get 0, v
_{Min}Determine according to 97% of the light velocity, get 2.91 * 10
^{5}Km/s, p gets 100, Δ t
_{Cal}Get 0.03ms, greater than 10 times of the sampling interval of data, so calculate redundancy time t
_{Rdn}=p Δ t
_{Cal}=3ms, t
_{Stop}=t
_{Start}+ 3l/v
_{Min}+ t
_{Rdn}=17.82ms; Utilize multi-scale wavelet to decompose, during to data in the window signal carry out layering, sample frequency is 1MHz, the frequency range of 4～30KHz correspondence is the frequency domain scope of the 7th layer to the 5th layer high-frequency signal, this frequency range can be avoided the influence of direct current and low frequency component on the one hand, can reduce the influence of line parameter circuit value frequency dependent characteristic on the other hand, utilize formula
${E}_{K}=\frac{1}{{t}_{\mathrm{stop}}-{t}_{\mathrm{start}}}\sqrt{{\∫}_{t={t}_{\mathrm{start}}}^{{t}_{\mathrm{stop}}}{S}_{K}^{2}\left(t\right)\mathrm{dt}}$
The frequency content E of evaluation between from the 7th layer to the 5th layer
_{K}(if sample frequency is 500kHz, the frequency range of 4～30KHz correspondence is the frequency domain scope of the 6th layer to the 4th layer high-frequency signal, the frequency content between needing this moment to estimate from the 6th layer to the 4th layer.) choose E
_{K}Peaked frequency domain, i.e. f
_{s}/ 2
^{K+1}～f
_{s}/ 2
^{K}, as the logical frequency of band of Butterworth digital band-pass filter, to described line mode voltage, line mould current traveling wave signal u
_{m}, i
_{m}, u
_{n}, i
_{n}Filter, obtain band signal best in the fault analysis signal;
In the 3rd step, set up fault time domain observation equation:
${f}_{\mathrm{Location}}(d,r,v{,Z}_{C},{t}_{\mathrm{\Δ}},t)=\frac{1}{2}{(1+\frac{\mathrm{rd}}{4{Z}_{C}})}^{2}[{u}_{m}(t-{t}_{\mathrm{\Δ}}+\frac{d}{v})-{i}_{m}(t-{t}_{\mathrm{\Δ}}+\frac{d}{v})({Z}_{C}+\frac{\mathrm{rd}}{4})]$
$+\frac{1}{2}{(1-\frac{\mathrm{rd}}{4{Z}_{C}})}^{2}[{u}_{m}(t-{t}_{\mathrm{\Δ}}-\frac{d}{v})-{i}_{m}(t-{t}_{\mathrm{\Δ}}-\frac{d}{v})({Z}_{C}-\frac{\mathrm{rd}}{4})]$
$-{\left(\frac{\mathrm{rd}}{4{Z}_{C}}\right)}^{2}{u}_{m}(t-{t}_{\mathrm{\Δ}})-\frac{\mathrm{rd}}{4}(1+\frac{\mathrm{rd}}{4{Z}_{C}})(1-\frac{\mathrm{rd}}{4{Z}_{C}}){i}_{m}(t-{t}_{\mathrm{\Δ}})---\left(1\right)$
$-\frac{1}{2}{(1+\frac{r(l-d)}{4{Z}_{C}})}^{2}[{u}_{n}(t+\frac{l-d}{v})-{i}_{n}(t+\frac{l-d}{v})({Z}_{C}+\frac{r(l-d)}{4})]$
$-\frac{1}{2}{(1-\frac{r(l-d)}{4{Z}_{C}})}^{2}[{u}_{n}(t-\frac{l-d}{v})-{i}_{n}(t-\frac{l-d}{v})({Z}_{C}-\frac{r(l-d)}{4})]$
$+{\left(\frac{r(l-d)}{4{Z}_{C}}\right)}^{2}{u}_{n}\left(t\right)+\frac{r(l-d)}{4}(1+\frac{r(l-d)}{4{Z}_{C}})(1-\frac{r(l-d)}{4{Z}_{C}}){i}_{n}\left(t\right)=0$
Wherein, l is that distance, the d of DC line two ends M, N are distance, the t of trouble spot apart from DC line M end
_{Δ}For DC line M, asynchronous mistiming of N two ends, r are that the line mould distributed resistance of DC line, the line mould that v is DC line are propagated velocity of wave, Z
_{C}Line modular character impedance for DC line;
Wherein, t
_{Δ}=t
_{M0}-t
_{N0}
In the formula, t
_{M0}For the reference of the M end data clock of DC line constantly, t
_{N0}Be the reference moment of DC line N end data clock;
Set up row wave property equation:
d＝(v
_{tw}Δt
_{f}+l)/2
Δt
_{f}＝T
_{fm}-T
_{fn}＝t
_{fm}-t
_{fn}+t
_{Δ}
In the formula, v
_{Tw}Be the capable wave-wave speed of described line mode voltage, Δ t
_{f}Be the capable ripple arrival DC line M of described line mode voltage, the mistiming at N two ends, T
_{Fm}And T
_{Fn}Be respectively fault initial line mode voltage row ripple and arrive the moment that DC line M holds and N holds; t
_{Fm}And t
_{Fn}Be respectively fault initial line mode voltage row ripple and arrive the moment at DC line M, N two ends with respect to each self-reference moment t
_{M0}, t
_{N0}Time;
In the 4th step, adopt wavelet analysis detection signal singular point theory to above-mentioned line mode voltage travelling wave signal u
_{m}And u
_{n}Analyze, ask for described line mode voltage travelling wave signal u
_{m}And u
_{n}Modulus maximum constantly and is made as the moment that fault initial line mode voltage row ripple arrives DC line M, N two ends respectively reference the moment t of M, N two ends data clock
_{M0}, t
_{N0}, then be t
_{Fm}=t
_{Fn}=0, t
_{Δ}=Δ t
_{f}, M, asynchronous mistiming of N two ends equal the mistiming that fault initial line mode voltage row ripple arrives the circuit two ends, according to row wave property equation, then:
t
_{Δ}＝Δt
_{f}＝(2d-l)/k
_{v}v (2)
Wherein, k
_{v}Ratio for travelling wave analysis line mould velocity of wave and time-domain analysis line mould velocity of wave, according to the actual track parameter: the solid conductor internal diameter of transmission line of electricity, the solid conductor external diameter, direct current resistance, horizontal range, suspension height, the sag minimum altitude, the split conductor number, heading spacing and lead angle, the relation curve that utilizes LINECONSTANTS program computational scheme line mould to propagate velocity of wave and frequency is determined, as shown in Figure 2 ± the 800kV curve is described relation curve, in time-domain analysis, the 5th layer to the 7th layer HFS of the corresponding wavelet decomposition of the frequency range of bandpass filter, sample frequency for 1MHz, the centre frequency scope is 5k to 20kHz, and corresponding velocity of wave scope is 2.958～2.961km/s; Above-mentioned employing wavelet analysis detection signal singular point theory is to described line mode voltage travelling wave signal u
_{m}And u
_{n}Ask for the analysis frequency range that modulus maximum is adopted constantly, centre frequency is about 250～500kHz, and corresponding row wave-wave speed is about 2.966km/s, so for this circuit, k
_{v}Span be: 1.0017～1.0027, get 1.002 herein.
In the 5th step,, get a plurality of calculating t=t constantly with formula (2) substitution formula (1)
_{1}, t
_{2}, t
_{3}..., t
_{P}, foundation comprises fault distance, distributed resistance, propagation velocity of wave and characteristic impedance totally 4 the asynchronous fault Optimization of Time Domain of both-end equations for the treatment of observed quantity:
$F(d,r,v,{Z}_{C})=\mathrm{min}\left[\underset{k=1}{\overset{P}{\mathrm{\Σ}}}\right|{f}_{\mathrm{Location}}(d,r,v,{Z}_{C},\frac{2d-l}{{k}_{v}v},{t}_{k})\left|\right]---\left(3\right)$
Formula (3) is carried out global optimizing find the solution, can realize that line parameter circuit value is adaptive and need not the synchronous DC power transmission line time domain fault localization of GPS;
Wherein, calculate t constantly
_{1}, t
_{2}..., t
_{k}..., t
_{p}:
$\left\{\begin{array}{c}{t}_{1}={t}_{\mathrm{start}}+2l/{v}_{\mathrm{min}}=9.9\mathrm{ms}\\ {t}_{100}={t}_{\mathrm{stop}}-l/{v}_{\mathrm{min}}=12.9\mathrm{ms}\\ {t}_{2}={t}_{1}+({t}_{p}-{t}_{1})/p=9.93\mathrm{ms}\\ {t}_{3}={t}_{2}+({t}_{p}-{t}_{1})/p=9.96\mathrm{ms}\\ \·\\ \·\\ \·\end{array}\right.$
To optimizing equation (3), adopt PSO algorithm (particle swarm optimization algorithm) to find the solution.
At the circuit diverse location metallic earthing fault and high resistance earthing fault are set respectively, the range finding of various faults the results are shown in table 2, as seen, adopts method disclosed by the invention to carry out fault localization, and error is little, accuracy rate is high.
Table 2
The foregoing description is a preferred implementation of the present invention; but embodiments of the present invention are not restricted to the described embodiments; other any do not deviate from change, the modification done under spirit of the present invention and the principle, substitutes, combination, simplify; all should be the substitute mode of equivalence, be included within protection scope of the present invention.