CN101546906A - Method for fault line selection of electric distribution network by using S transformation energy relative entropy - Google Patents

Abstract

The invention relates to a self-adaptive method for single-phase grounding fault line selection of an electric distribution network by using S transformation energy relative entropy. The method comprises the following steps: when the zero-sequence voltage instantaneous value of a bus is out of limit, starting a fault line selection device immediately; performing S transformation on zero-sequence current in 1/4 cycle after the fault of each line, and calculating transient energy under each frequency of the zero-sequence current of each line by using a complex matrix obtained by the S transformation; and calculating the S transformation energy relative entropy under each frequency of each line and solving the comprehensive S transformation energy relative entropy of each line by using the super-strong recognition capability of the relative entropy to slight differences between signals, and self-adaptively selecting out the fault line by comparing the size of the comprehensive S transformation energy relative entropy of each line under all frequencies. Theoretical analyses and a large number of emulations show that the method effectively avoids the influence caused by a CT saturation discontinuous angle on the line selection, and is applicable to the cable-wire mixed line, pure cable lines and pure aerial lines.

Description

Utilize the distribution network fault line selection method of S transformation energy relative entropy

Technical field:

The present invention relates to a kind of distribution network fault line selection method of the S of utilization transformation energy relative entropy, belong to the relay protection of power system technical field.

Background technology:

During resonant earthed system generation single phase ground fault, line voltage still symmetry and fault current is less, can continue to move 1～2h, helps improving the reliability of power supply.But be that non-fault phase-to-ground voltage raises, long-play can cause fault to expand as or multiple spot short circuit easily at 2; Arc grounding also can cause the total system overvoltage, and therefore the insulation of harm equipment and the safe operation of system must in time determine faulty line, fix a breakdown as early as possible.Yet the resonant earthed system grounding phenomenon is very complicated, and when single phase ground fault took place, because the compensating action of arc suppression coil, faulty line was all approaching on amplitude and phase place with the fault current that perfects circuit.

For addressing this problem, many scholars have carried out a large amount of research, proposed based on steady-state quantity selection method, based on the selection method and the signal injection method of transient state amount.Be subject to the influence of transition resistance and unstable arc based on the selection method of steady-state quantity, sensitivity is low, judges by accident easily; The method that the utilization of signal injection method is injected external signal to system is carried out route selection, but has significant disadvantages: 1. when high resistance ground, inject weak output signal and difficult the detection; 2. arc grounding time-harmonic wave content is abundant, injects pickup electrode and is vulnerable to disturb.3. the electric pressure of Shi Yonging lower (normally 10kV), operation and maintenance workload are bigger.During resonant earthed system generation single-phase earthing; fault phase capacitor discharge and the charging of non-fault phase electric capacity; produce the amplitude transient current bigger several times to tens times than steady-state value; highly sensitive and influenced by arc suppression coil little based on the selection method of transient state amount; but the route selection effect of existing method mostly can not be satisfactory; the protectiveness degree that mainly shows as route selection is little, and accuracy and reliability are lower.

Summary of the invention:

The objective of the invention is to overcome the deficiency of above-mentioned existing small current neutral grounding system selection method, inventing a kind of zero-sequence current in 1/4 cycle that utilizes after the fault analyzes, fully utilize the fault energy feature of each frequency, its route selection utilizes the distribution network fault line selection method of S transformation energy relative entropy accurately, reliably.The present invention has avoided the influence of the saturated interval angle of CT to the failure line selection accuracy; The influence of neutral point operational mode is less; When the short-term fault, can overcome the influence of sound long line capacitive earth current; Very strong noise resisting ability is arranged; Also correctly route selection when high resistance ground; Except that line selection apparatus started, whole route selection process did not need to use the bus residual voltage, and effectively having overcome voltage transformer progress of disease characteristic influences the route selection result.The present invention is a kind of distribution network fault line selection method that utilizes S transformation energy relative entropy that cable-wire mixed line, pure cable line and pure overhead transmission line all are suitable for.

The present invention is a kind of to utilize the technical scheme of one-phase earthing failure in electric distribution network selection method of S transformation energy relative entropy as follows:

When bus residual voltage instantaneous value was out-of-limit, fault line selection device started immediately, gathered that the zero-sequence current in 1/4 cycle carries out the S conversion after each line fault, utilized the complex matrix of S conversion gained to calculate the energy of each circuit zero-sequence current under each frequency; In conjunction with relative entropy to nuance between signal superpower recognition capability, calculate each circuit under each frequency S transformation energy relative entropy and ask for the comprehensive S transformation energy relative entropy of every circuit, by comparing the comprehensive S transformation energy relative entropy size of each circuit under all frequencies, select faulty line adaptively, output route selection result instructs the power distribution network operational management.

The concrete steps of this method are as follows:

(1) as bus residual voltage instantaneous value u _n(t) greater than K _uU _n, fault line selection device starts immediately, notes the zero-sequence current of 1/4 each circuit of cycle after the fault, wherein K _uGeneral value is 0.15, U _nExpression bus rated voltage;

(2) according to following method to circuit i zero-sequence current fault after the sampled data in 1/4 cycle carry out the S conversion, obtain complex matrix S _i[m, n];

Circuit i zero-sequence current x _i[k] expression, k=0,1 ..., N-1, N are sampling number, i=0, and 1 ..., K, K are power distribution network circuit sum, x _iThe discrete representation form S of the S conversion of [k] _i[m, n] is:

$\begin{array}{cc}{S}_i[m,n]=\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{X}_i[n+k]e^{-2{\mathrm{\&pi;}}^2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A200910094432E00151.png"\; state="\{\{state\}\}">k</figure-callout>}}^2/n^2}{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A200910094432E00151.png"\; state="\{\{state\}\}">e</figure-callout>}}^j& n\&NotEqual;0\end{array}$

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

In the following formula

$\begin{array}{c}{X}_i\left[n\right]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{x}_i\left[k\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A200910094432E00151.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;kn}/N}\end{array}$

(3) according to following formula computational scheme i zero-sequence current in frequency f _nUnder transient state energy W _{I_n}

$\begin{array}{cc}{W}_{i\_n}=\underset{m}{\mathrm{\&Sigma;}}{\left[S_i(m,n)\right]}^2& i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K\end{array}$

(4) according to following formula calculated rate f _nFollowing system transient state energy and;

$\begin{array}{cc}{W}_n=\underset{i}{\mathrm{\&Sigma;}}\underset{m}{\mathrm{\&Sigma;}}{\left[S_i(m,n)\right]}^2& i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K\end{array}$

(5) ask for frequency f according to following formula _nThe transient state energy of following circuit i shared proportion, i.e. weight coefficient p in system's transient state energy under this frequency _{I_n}

$\begin{array}{cc}{p}_{i\_n}=\frac{W_{i\_n}}{W_n}& i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K\end{array}$

(6) according to the S transformation energy relative entropy M of the relative circuit l of following formula computational scheme i _Il

$M_{\mathrm{il}}=\underset{n}{\mathrm{\&Sigma;}}\left|p_{i\_n}\ln \frac{p_{i\_n}}{p_{l\_n}}\right|i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K;l=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K$

In the formula, p _{L_n}For in frequency f _nThe transient state energy of following circuit l shared proportion in system's transient state energy under this frequency;

(7) asking for circuit i according to following formula is M with respect to the comprehensive S transformation energy relative entropy of all the other each bar circuits _i

$M_i=\underset{l=1}{\overset{K}{\mathrm{\&Sigma;}}}(M_{\mathrm{il}}+M_{\mathrm{li}})i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K;l=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K$

In the formula, M _LiS transformation energy relative entropy for the relative circuit i of circuit l;

(8) failure line selection criterion: select comprehensive S transformation energy relative entropy maximum three, be respectively according to the size ordering: M _a, M _b, M _c, when satisfying M _aM _b+ M _cThe time, the M of comprehensive wavelet energy relative entropy maximum _aCorresponding circuit is a faulty line, otherwise, be judged to busbar fault.

Operation principle of the present invention:

1, S transformation theory

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

$S(\mathrm{\&tau;},f)={\&Integral;}_{-\&infin;}^{\&infin;}x\left(t\right)w\left(\text{\&tau;-t,f}\right)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A200910094432E00151.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;ft}}\mathrm{dt}---\left(1\right)$

In the formula (1):

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

In formula (1) and the formula (2), (τ-t f) is Gauss's window to w; τ is the location parameter of control Gauss window at time shaft t; F is a frequency; J is an imaginary unit.

Traditional Fourier transform is made on formula (1) the right earlier, remake Fourier inversion, carry out substitution of variable at last and convert the S conversion function of the Fourier transform X (f) of signal x (t) to, that is:

$S(\mathrm{\&tau;},f)={\&Integral;}_{-\&infin;}^{\&infin;}X(v+f)e^{-\frac{2{\mathrm{\&pi;}}^2{v}^2}{f^2}}{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A200910094432E00151.png"\; state="\{\{state\}\}">e</figure-callout>}}^j\mathrm{dv}---\left(3\right)$

Formula (3), f ≠ 0.Like this, the S conversion just can utilize FFT to realize calculating fast.Can obtain the discrete representation form S[m of the S conversion of signal x (k) by formula (3), n] be:

$\begin{array}{cc}S[m,n]=\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}X[n+k]e^{-2{\mathrm{\&pi;}}^2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A200910094432E00151.png"\; state="\{\{state\}\}">k</figure-callout>}}^2/n^2}{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A200910094432E00151.png"\; state="\{\{state\}\}">e</figure-callout>}}^j& n\&NotEqual;0\end{array}---\left(4\right)$

$\begin{array}{cc}S[m,n]=\frac{1}{n}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}x\left[k\right]& n=0\end{array}---\left(5\right)$

Formula (4),

$\begin{array}{c}X\left[n\right]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}x\left[k\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A200910094432E00151.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;kn}/N}\end{array}---\left(6\right)$

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 (4), (5), and transformation results is a multiple time-frequency matrix, and note is made s-matrix, the corresponding sampling time point of its row, the row respective frequencies, the difference on the frequency Δ f between the adjacent lines is:

$\mathrm{\&Delta;f}=\frac{f_s}{N}---\left(7\right)$

Formula (7), f _sBe sample frequency, N is a sampling number.

The corresponding frequency f of n row _nFor:

$f_n=\frac{f_s}{N}n---\left(8\right)$

2, S transformation energy relative entropy

The one-phase earthing failure in electric distribution network network as shown in Figure 1.Figure 1 shows that a 110kV/35kV electric substation that 6 circuits are arranged, Z font transformer neutral point adopts LSJC-35 type current transformer by arc suppression coil series resistance ground connection.Circuit adopts overhead transmission line (L ₁, L ₃, L ₅), line-cable joint line (L ₄) and cable line (L ₂, L ₆), wherein, overhead transmission line adopts JS ₁The bar type, LGJ-70 type lead, span is 80m, cable line adopts YJV23-35/95 type cable.Among Fig. 1, T is a step-down transformer, and Tz is a grounding transformer, and K is a switch, and L is the arc suppression coil inductance, and R is the arc suppression coil series resistance, R _fBe earth fault transition resistance, i ₀₁, i ₀₄, i ₀₆Be respectively circuit L ₁, L ₄, L ₆Zero-sequence current.

According to principle of stacking, the fault power distribution network can be decomposed into normal operational system of being made up of three-phase voltage source and supply line and load and the fault component system that is made up of break down back fault point fault additional voltage source and circuit.The zero sequence energy function of definition circuit is:

$W_i\left(t\right)={\&Integral;}_0^t{u}_0\left(\mathrm{\&tau;}\right)i_{0i}\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;}i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K---\left(9\right)$

Formula (9), W _i(t) be the zero sequence energy function of i bar circuit after the fault; u ₀(t) be the bus residual voltage; i _0i(t) be the zero-sequence current of i bar circuit; K is a power distribution network circuit sum.

Under the normal condition, the magnetic flux density of current transformer (CT) iron core is lower, and the electric current that flows into energized circuit is very little, and secondary current is progress of disease primary current truly.When resonant earthed system generation single phase ground fault, contain abundant aperiodic of transient state component and higher harmonic components in the fault zero-sequence current, these components very easily cause the CT core sataration.The close saturated process that has of CT iron core magnetic, theory analysis and a large amount of emulation show that the saturated single phase ground fault that appears at usually of CT took place after 1/4 cycle.For avoiding the influence of the saturated interval angle of CT, select for use 1/4 cycle of fault zero-sequence current to analyze.Can get after the circuit i fault transient state energy W in 1/4 cycle according to formula (9) _iFor:

$W_i={\&Integral;}_0^{\frac{T}{4}}{u}_0\left(t\right)i_{0i}\left(t\right)\mathrm{dt}i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K---\left(10\right)$

Formula (10), T is a power frequency period.

The S mapping ensemble has suffered the advantage of Short Time Fourier Transform and wavelet transformation, has the time-frequency localization characteristic, can extract the feature of signal under each frequency effectively.Ignore the influence of public residual voltage, simultaneous formula (4), (5) and (10) definable circuit i zero-sequence current are in frequency f _nUnder transient state energy W _{I_n}For:

$\begin{array}{cc}{W}_{i\_n}=\underset{m}{\mathrm{\&Sigma;}}{\left[S_i(m,n)\right]}^2& i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K\end{array}---\left(11\right)$

In the formula (11), S _iThe discrete representation form of the S conversion that [m, n] calculates according to formula (4), (5) for circuit i zero-sequence current.

According to above-mentioned analysis, system shown in Figure 1 circuit L ₅Single phase ground fault takes place, 90 ° of fault switching angles, transition resistance 200 Ω calculate each bar circuit zero-sequence current in frequency f _nUnder transient state energy, the result is as shown in Figure 2.

As seen from Figure 2, during power distribution network generation single phase ground fault, the discharge of faulty line direct-to-ground capacitance perfects the line mutual-ground capacitor charging, faulty line with perfect circuit and have different charging and discharging circuit, so faulty line and perfect circuit and also be not quite similar in the Energy distribution of each Frequency point.Utilize the S conversion can amplify the energy response of a certain part, relative entropy can be used to measure the difference of two waveforms, and relative entropy is more little, illustrates that two different wave shapes are more little, and relative entropy is big more, illustrates that two different wave shapes are big more.Therefore calculating after each circuit zero-sequence current S conversion the energy of each Frequency point does relative entropy and can find small and very brief difference in each circuit zero-sequence current.

The transient state energy of all circuits on each frequency sued for peace respectively, can get frequency f _nFollowing system transient state energy and W _nFor:

$\begin{array}{cc}{W}_n=\underset{i}{\mathrm{\&Sigma;}}\underset{m}{\mathrm{\&Sigma;}}{\left[S_i(m,n)\right]}^2& i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K\end{array}---\left(12\right)$

Thus can be in frequency f _nThe transient state energy of following circuit i shared proportion, i.e. weight coefficient p in system's transient state energy under this frequency _{I_n}For:

$\begin{array}{cc}{p}_{i\_n}=\frac{W_{i\_n}}{W_n}& i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K\end{array}---\left(13\right)$

According to the relative entropy theory, the S transformation energy relative entropy M of the relative circuit l of definition circuit i _IlFor:

$M_{\mathrm{il}}=\underset{n}{\mathrm{\&Sigma;}}\left|p_{i\_n}\ln \frac{p_{i\_n}}{p_{l\_n}}\right|i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K;l=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K---\left(14\right)$

In the formula (14), p _{1_n}For in frequency f _nThe transient state energy of following circuit l shared proportion in system's transient state energy under this frequency.

According to formula (14), definition circuit i is with respect to the comprehensive S transformation energy relative entropy M of all the other each bar circuits _iFor:

$M_i=\underset{l=1}{\overset{K}{\mathrm{\&Sigma;}}}(M_{\mathrm{il}}+M_{\mathrm{li}})i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K;l=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K---\left(15\right)$

In the formula (15), M _LiS transformation energy relative entropy for the relative circuit i of circuit l.

During power distribution network generation single phase ground fault, the comprehensive relative entropy of S transformation energy can react the difference of each circuit zero-sequence current.The comprehensive big more circuit of the relative entropy of S transformation energy, the difference of its zero-sequence current and all the other each circuit zero-sequence currents is big more; Otherwise, the comprehensive more little circuit of the relative entropy of S transformation energy, its zero-sequence current is close more with all the other each circuit zero-sequence currents.When bus generation single phase ground fault, each circuit zero-sequence current charging and discharging circuit is identical, so the comprehensive S transformation energy relative entropy value difference of each circuit zero-sequence current is different little.Can form the route selection criterion thus:

Select comprehensive S transformation energy relative entropy maximum three, be respectively according to the size ordering: M _a, M _b, M _c, when satisfying M _aM _b+ M _cThe time, the M of comprehensive wavelet energy relative entropy maximum _aCorresponding circuit is a faulty line, otherwise, be judged to busbar fault.M _aDuring for power distribution network generation single phase ground fault, the maximum of the comprehensive S transformation energy relative entropy of each circuit zero-sequence current, M _bDuring for power distribution network generation single phase ground fault, second largest value of the comprehensive S transformation energy relative entropy of each circuit zero-sequence current, M _cDuring for power distribution network generation single phase ground fault, the third-largest value of the comprehensive S transformation energy relative entropy of each circuit zero-sequence current.

The present invention compared with prior art has following advantage:

1, the present invention utilizes after the fault zero-sequence current in 1/4 cycle to analyze, and has avoided the influence of the saturated interval angle of CT to the failure line selection accuracy; Adopt S transformation energy relative entropy to realize route selection, fully utilized the fault energy feature of each frequency.

2, the present invention has stronger arc resistant grounded capacity; The influence of neutral point operational mode is less; When the short-term fault, can overcome the influence of sound long line capacitive earth current; Very strong noise resisting ability is arranged; Also correctly route selection during high resistance ground.

3, the present invention is except that line selection apparatus starts, and the route selection process does not need to use the bus residual voltage, has effectively overcome the influence of voltage transformer progress of disease characteristic to the route selection result.

Description of drawings:

The radial resonant earthed system of Fig. 1.

Fig. 2 circuit is at Energy distribution (a) the circuit L of each Frequency point ₁(b) circuit L ₂(c) circuit L ₃(d) circuit L ₄(e) circuit L ₅(f) circuit L ₆

Fig. 3 failure line selection algorithm flow chart.

The comprehensive S transformation energy relative entropy of each circuit of Fig. 4.

Embodiment:

Based on above-mentioned analysis, during power distribution network generation single phase ground fault, the zero-sequence current of 1/4 each circuit of cycle behind the record trouble can be realized perfect failure line selection algorithm by the comprehensive S transformation energy relative entropy that compares each circuit.The specific implementation flow process of failure line selection algorithm as shown in Figure 3.

1, as bus residual voltage instantaneous value u _n(t) greater than K _uU _n, fault line selection device starts immediately, notes the zero-sequence current of 1/4 each circuit of cycle after the fault, wherein K _uGeneral value is 0.15, U _nExpression bus rated voltage;

2, utilize formula (4), (5), (6) to each circuit zero sequence current failure after the sampled data in 1/4 cycle carry out the S conversion, and calculate each bar circuit zero-sequence current in frequency f according to formula (11) _nUnder transient state energy W _{I_n}

3, according to formula (12) calculated rate f _nFollowing system transient state energy and, and ask for frequency f according to formula (13) _nThe following transient state energy of each circuit shared proportion, i.e. weight coefficient p in system's transient state energy under this frequency _{I_n}

4, according to the S transformation energy relative entropy M of the relative circuit l of formula (14) computational scheme i _Il, asking for circuit i according to formula (15) is M with respect to the comprehensive S transformation energy relative entropy of all the other each bar circuits _i

5, select three of comprehensive S transformation energy relative entropy maximum, be respectively according to the size ordering: M _a, M _b, M _c, when satisfying M _aM _b+ M _cThe time, the M of comprehensive wavelet energy relative entropy maximum _aCorresponding circuit is a faulty line, otherwise, be judged to busbar fault.

Embodiment:

Circuit L ₅Single phase ground fault, 90 ° of fault switching angles, transition resistance 200 Ω take place at distance bus 5km place.Zero-sequence current to 6 circuits in the T/4 after the fault of sampling acquisition carries out the S conversion, and the sample frequency of primary signal is 10kHz, and sample sequence length is 50 sampled points, obtains 6 50 * 26 complex matrix through the S conversion, and this matrix is asked mould.Ask for the S transformation energy relative entropy M of each bar circuit according to formula (11)～(14) _Il, 6 * 6 of formation S transformation energy relative entropy matrix M is thus:

$M=\left[\begin{array}{cccccc}{M}_{11}& M_{12}& M_{13}& M_{14}& M_{15}& M_{16}\\ M_{21}& M_{22}& M_{23}& M_{24}& M_{25}& M_{26}\\ M_{31}& M_{32}& M_{33}& M_{34}& M_{35}& M_{36}\\ M_{41}& M_{42}& M_{43}& M_{44}& M_{45}& M_{46}\\ M_{51}& M_{52}& M_{53}& M_{54}& M_{55}& M_{56}\\ M_{61}& M_{62}& M_{63}& M_{64}& M_{65}& M_{66}\end{array}\right]$

$=\left[\begin{array}{cccccc}0& 0.007& 0.002& 0.011& 0.013& 0.013\\ 2.359& 0& 1.182& 0.756& 1.623& 1.310\\ 0.054& 0.052& 0& 0.086& 0.126& 0.110\\ 27.363& 8.071& 18.591& 0& 6.133& 3.982\\ 975.161& 502.049& 727.622& 348.166& 0& 235.749\\ 109.936& 44.041& 83.306& 17.769& 10.082& 0\end{array}\right]$

In the following formula, M ₁₁For utilizing formula (14), work as i=1, the result who calculates during l=1 in like manner, can obtain other element in the matrix.

The S conversion complex energy relative entropy Mi that asks for each bar circuit according to formula (15) as shown in Figure 4.

M _i＝[1125.42 561.45 83.11 430.92 2807.22 516.29]

The individual arrangement according to size order of first three of S conversion complex energy relative entropy maximum is respectively: M ₅=2807.22, M ₁=1125.42, M ₂=561.45, therefore, M ₅M ₁+ M ₂Set up M ₅Corresponding circuit L ₅Be faulty line.

Select faulty line adaptively, output route selection result instructs the power distribution network operational management.Theory analysis and a large amount of emulation show that this method has effectively been avoided the influence of the saturated interval angle of CT to route selection, and for cable-wire mixed line, pure cable line and pure overhead transmission line, this method all is suitable for.

Claims (2)

1, a kind of one-phase earthing failure in electric distribution network selection method that utilizes S transformation energy relative entropy, it is characterized in that: when bus residual voltage instantaneous value is out-of-limit, fault line selection device starts immediately, gather that the zero-sequence current in 1/4 cycle carries out the S conversion after each line fault, utilize the complex matrix of S conversion gained to calculate the energy of each circuit zero-sequence current under each frequency; In conjunction with relative entropy to nuance between signal superpower recognition capability, calculate each circuit under each frequency S transformation energy relative entropy and ask for the comprehensive S transformation energy relative entropy of every circuit, by comparing the comprehensive S transformation energy relative entropy size of each circuit under all frequencies, select faulty line adaptively, output route selection result instructs the power distribution network operational management.

2, the distribution netting twine-cable mixed line fault selection method that utilizes full range band wavelet energy relative entropy according to claim 1, the concrete steps of this method are as follows:

(1) as bus residual voltage instantaneous value u _n(t) greater than K _uU _n, fault line selection device starts immediately, notes the zero-sequence current of 1/4 each circuit of cycle after the fault, wherein K _uGeneral value is 0.15, U _nExpression bus rated voltage;

(2) according to following method to circuit i zero-sequence current fault after the sampled data in 1/4 cycle carry out the S conversion, obtain complex matrix S _i[m, n];

Circuit i zero-sequence current x _i[k] expression, k=0,1 ..., N-1, N are sampling number, i=0, and 1 ..., K, K are power distribution network circuit sum, x _iThe discrete representation form S of the S conversion of [k] _i[m, n] is:

$S_i[m,n]=\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{X}_i[n+k]e^{-2{\mathrm{\&pi;}}^2{k}^2/n^2}{e}^{j2\mathrm{\&pi;km}/N}$ n≠0

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

In the following formula

$X_i\left[n\right]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{x}_i\left[k\right]e^{-j2\mathrm{\&pi;kn}/N}$

(3) according to following formula computational scheme i zero-sequence current in frequency f _nUnder transient state energy W _{I_n}

$W_{i\_n}=\underset{m}{\mathrm{\&Sigma;}}{\left[S_i(m,n)\right]}^2$ i＝1，2，…，K

(4) according to following formula calculated rate f _nFollowing system transient state energy and;

$W_n=\underset{i}{\mathrm{\&Sigma;}}\underset{m}{\mathrm{\&Sigma;}}{\left[S_i(m,n)\right]}^2$ i＝1，2，…，K

(5) ask for frequency f according to following formula _nThe transient state energy of following circuit i shared proportion, i.e. weight coefficient p in system's transient state energy under this frequency _{I_n}

$p_{i\_n}=\frac{W_{i\_n}}{W_n}$ i＝1，2，…，K

(6) according to the S transformation energy relative entropy M of the relative circuit l of following formula computational scheme i _Il

$M_{\mathrm{il}}=\underset{n}{\mathrm{\&Sigma;}}\left|p_{i\_n}\ln \frac{p_{i\_n}}{p_{I\_n}}\right|$ i＝1，2，…，K；l＝1，2，…，K

In the formula, p _{1_n}For in frequency f _nThe transient state energy of following circuit 1 shared proportion in system's transient state energy under this frequency;

(7) asking for circuit i according to following formula is M with respect to the comprehensive S transformation energy relative entropy of all the other each bar circuits _i

$M_i=\underset{l=1}{\overset{K}{\mathrm{\&Sigma;}}}(M_{\mathrm{il}}+M_{\mathrm{li}})$ i＝1，2，…，K；l＝1，2，…，K

In the formula, M _LiS transformation energy relative entropy for circuit 1 relative circuit i;

(8) failure line selection criterion: select comprehensive S transformation energy relative entropy maximum three, be respectively according to the size ordering: M _a, M _b, M _c, when satisfying M _aM _b+ M _cThe time, the M of comprehensive wavelet energy relative entropy maximum _aCorresponding circuit is a faulty line, otherwise, be judged to busbar fault.

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