CN103018632A - Small current grounding system single-phase ground fault line selection method based on fisher information - Google Patents

Abstract

The invention discloses a single-phase grounding fault line selection method for a small current grounding system based on Fisher information, comprising: S1, dividing discrete wavelet coefficients into a series of time windows; S2, packing data points in each time window into a state; S3. Construct a probability density function p _i based on the possibility of observing the system state in each time window; S4. Calculate Fisher information from the probability density function for each time window; S5. Select Fisher The line with the smallest information value is the faulty line. The present invention can effectively distinguish the faulty line from the non-faulty line under different grounding methods, and is not affected by the initial voltage phase angle, grounding resistance, and fault location, and can accurately locate the fault time; in short data, small amplitude, Under unfavorable conditions such as interference, it can effectively extract the characteristic information hidden in the signal sequence, and at the same time, it can quantitatively characterize the complexity of each signal sequence, which provides an effective means for the analysis of non-stationary signal sequences.

Description

Line selection method for single-phase grounding fault in small current grounding system based on Fischer information

technical field

The invention relates to the technical field of electric power system relay protection, in particular to a method for line selection for single-phase grounding faults in small current grounding systems based on Fisher information.

Background technique

Most of the neutral points of my country's medium and low voltage distribution network systems use indirect grounding, that is, small current grounding, and most of the faults are single-phase grounding faults. When a single-phase ground fault occurs, if the fault line is not cut off within the specified time, the fault will expand to two or more points to ground short circuit, thereby forming a phase-to-phase short circuit and even causing system overvoltage, which will damage the equipment and destroy the safe operation of the system. Therefore, it is necessary to Find the fault line and fault point as soon as possible and remove them; and fault line selection is an important prerequisite for accurately locating and eliminating single-phase ground faults in distribution networks.

In recent years, researchers at home and abroad have done a lot of work on this, and have studied a variety of fault line selection methods, which are mainly divided into two categories: line selection methods based on steady-state components and line selection methods based on transient components .

The former such as: zero-sequence current amplitude comparison method, zero-sequence current direction method, zero-sequence current active component method, negative-sequence current method, zero-sequence admittance method, harmonic method, etc. The advantage of this type of line selection method is that the steady-state component always exists during the operation with faults, and it is easy to extract; the disadvantage is that the steady-state current amplitude is small, and it is easily affected by grounding resistance, arc and unbalanced current of the current transformer. , its sensitivity is low, so the result of line selection is not as high as the accuracy of line selection using transient components. The patent "grounding line selection method, device and application system based on zero-sequence current active component" (patent number: 200910238392.4) is a line selection method based on steady-state quantities, and its principle is based on the ground conductance and arc suppression of the line There is resistance loss in the coil, and the fault current contains active components, and the active components of the fault line are larger than the non-fault lines and the direction is opposite to select the fault line. Its advantage is that it is not affected by the arc suppression coil; but because the active component in the fault current is very small and is affected by the unbalanced three-phase parameters of the line, the detection sensitivity is low and the reliability of line selection is not high. The injection signal method is also a kind of steady-state line selection method because it is limited to applications where the fault point is permanently grounded and the signal is relatively stable. The patent "Universal Small Current Grounding System Single-phase Grounding Line Selection and Positioning Device" (Patent No.: 93111309.1) and the patent "A Single-phase Grounding Line Selection Method for Small Grounding Current System" (Patent No. 200410024015.8) belong to this type of method. The advantage of the method is that it is not affected by the arc suppression coil, and does not require the installation of a zero-sequence current transformer (CT), and the location of the fault point of the overhead line can also be determined by detecting along the fault line with the detector; its disadvantage is that it needs to install signal injection In addition, the signal injection energy is limited by PT and cannot be too high; when the grounding resistance is large, the distributed capacitance of the non-fault line will shunt the injected signal and interfere with the correct line selection. For intermittent grounding, the injected signal changes discontinuously, affecting correct line selection. Compared with the above-mentioned line selection method based on steady-state quantity, the amplitude of transient current of small-current ground fault is several times to dozens of times that of the steady-state capacitive current to ground, and the value is between tens of A to hundreds of A, and Not affected by the arc suppression coil.

Using the transient component to select the grounding line can overcome the shortcomings of low sensitivity and being affected by the arc suppression coil in the steady-state line selection method. The patent "a method and device for grounding line selection of small current grounding system" (patent number: 200910081958.7) and the patent "method for fault line selection of small current grounding system simulated after zero-mode current measurement" (patent number: 200810058173.3) are both A grounding line selection method based on transient components. However, the transient component attenuates quickly and is difficult to extract. If only the transient component is used for fault line selection, the line selection result will be inaccurate when the transient component is very small. In recent years, fault line selection methods based on modern signal processing have developed rapidly. The patent "Adaptive line selection method for single-phase ground fault in distribution network based on transient zero-sequence current" (Patent No.: 200710059830.1) is a line selection method based on wavelet transform. Its principle is to use wavelet to analyze ground fault transient signals , according to the relationship between the opposite phase and the maximum amplitude of the harmonics in the transient process, the line selection is made. The advantage of this type of method is that the sensitivity of wavelet analysis to singularities is used to make this type of line selection method more sensitive; the disadvantage is that the result of line selection is easily affected by interference signals.

The above methods are all based on various parameters of current zero-sequence components (current amplitude, phase, power, etc.) to give the results of line selection. However, when a single-phase ground fault occurs, the fault signal is generally very weak and the fault characteristics It is not obvious, which makes it difficult to obtain satisfactory results by conventional methods that only use information such as the magnitude and phase of the current. What is more critical is that after a small current grounding fault occurs, within 1 to 2 hours of faulty operation, the fault signal is not static. Some period signals reflect the fault characteristics and are suitable for line selection, and some period signal interference is not conducive to line selection. This also makes the actual application effect of the fault line selection method based on modern signal processing technology in recent years remains to be seen. Therefore, the problem of reliable identification of fault lines with single-phase ground faults in low-current grounding systems has not been satisfactorily resolved.

From the perspective of information theory, when a single-phase ground fault occurs in a small current grounding system, the fault signal contains a large amount of fault information, and the fault line information is far richer than the non-fault line information. Therefore, the key to the problem is how to make better use of these fault information, and find some generally applicable characteristic variables to characterize the fault line for the fault line selection problem of the small current grounding system. Fisher information is often used as an index to measure the sustainability of the ecosystem. It can keenly capture and describe the severity of sudden changes in the system. Inspired by it, it is applied to fault line selection. The faulty line is selected from the difference of the mutation degree of the faulty line, and a new way of thinking is used to solve the line selection problem of the single-phase grounding fault in the small current grounding system.

In view of this, it is necessary to provide a single-phase-to-ground fault line selection method for small current grounded systems based on Fisher information.

Contents of the invention

The invention proposes a method for line selection of a single-phase ground fault in a small current grounding system based on Fischer information, which effectively solves the problem of line selection for a single-phase ground fault in the small current grounding system.

In order to achieve the above object, the technical solutions provided by the implementation cases of the present invention are as follows:

A single-phase ground fault line selection method for small current grounding systems based on Fisher information, the method comprising:

S1, dividing the discrete wavelet coefficients into a series of time windows;

S2. Pack data points into states in each time window;

S3. Construct a probability density function p _i based on the possibility of observing the state of the system in each time window;

S4. Calculate Fischer information from the probability density function for each time window;

S5. Select the line with the smallest Fischer information value as the faulty line.

As a further improvement of the present invention, before the step S1, it also includes:

Signal preprocessing, the zero-sequence current signal of each line obtained by real-time sampling is subjected to wavelet decomposition in order to remove noise and separate fault features.

As a further improvement of the present invention, after the zero-sequence current signal is transformed by wavelet, the coefficient of the high-frequency component at time k at the j-th decomposition scale is cD _j (k), and the coefficient of the low-frequency component is cA _j (k). The frequency bandwidth range of the information contained in the signal components D _j (k) and A _j (k) obtained after branch reconstruction is

D _j (k):[2 ^-j f _s ,2 ^-(j-1) f _s ], A _j (k):[0,2 ^-j f _s ], j=1,2,...,J,

Among them, f _s is the sampling frequency of the signal, and J is the maximum decomposition scale.

As a further improvement of the present invention, the step S1 is specifically:

Assuming that on the jth layer, the discrete wavelet coefficients of the multiresolution analysis are D={d(k), k=1,...,N}, a sliding window is defined on the wavelet coefficients of this layer, and the window width is w∈N , the sliding factor is δ∈N, and the sliding window is:

W(m,w,δ)={d(k),k=1+m*δ,...,w+m*δ},

Where m=1, 2,...,M, M is the number of windows and satisfies M=(N-w)/δ.

As a further improvement of the present invention, the step S2 is specifically:

其中，Z_l={Z_l：|Z_l(i)-Z_l(j)|≤2*σ,i,j＝1,2,…w;i≠j}，σ为线路正常时的小波系数D的标准差。Divide all elements in the sliding window into L states, then the total number of elements in the window is equal to the sum of the number of elements in each state, that is

Among them, Z _l ={Z _l : |Z _l (i)-Z _l (j)|≤2*σ,i,j=1,2,…w;i≠j}, σ is the wavelet when the line is normal The standard deviation of the coefficient D.

As a further improvement of the present invention, the formula for calculating Fischer information from the probability density function in step S4 is: I≈4∑[q _i -q _i+1 ] ² , q _i and q _i+1 are i and The square root value of the probability density at i+1, I is the Fisher information.

The invention uses a dimensionless non-negative positive number as a single criterion to realize the line selection problem of a single-phase grounding fault in a small current grounding system. Has the following beneficial effects:

Under different grounding methods, it can effectively distinguish the faulty line from the non-faulty line, and is not affected by the initial phase angle of the voltage, grounding resistance, and fault location, and can accurately locate the fault moment;

Under unfavorable conditions such as short data, small amplitude, and interference, it can effectively extract the characteristic information hidden in the signal sequence, and at the same time quantitatively characterize the complexity of each signal sequence, providing an effective means for the analysis of non-stationary signal sequences.

Description of drawings

Fig. 1 is the schematic flow sheet of the method for line selection of a single-phase grounding fault in a small current grounding system based on Fischer information in the present invention;

Fig. 2 is the zero-sequence current waveform I01 of each line when the line L1 in the first embodiment of the present invention has a single-phase ground fault at a distance of 10km from the busbar, the time of fault occurrence is 0.02s, the grounding resistance is 200Ω, and the initial phase angle of the voltage is 0° ﹑Schematic diagram of I02﹑I03;

Figure 3 is a schematic diagram of the FI values of the faulty line L1 and the normal line L2 and L3 in Figure 2;

Fig. 4 is the zero-sequence current waveform I01 of each line when the line L1 in the first embodiment of the present invention has a single-phase ground fault at a distance of 20km from the busbar, the time of fault occurrence is 0.02s, the fault resistance is 20Ω, and the initial phase angle of the voltage is 180° ﹑Schematic diagram of I02﹑I03;

Fig. 5 is a schematic diagram of FI values of the faulty line L1 and the normal line L2 and L3 in Fig. 4 .

Detailed ways

The present invention will be described in detail below in conjunction with various embodiments shown in the drawings. However, these embodiments do not limit the present invention, and any structural, method, or functional changes made by those skilled in the art according to these embodiments are included in the protection scope of the present invention.

Referring to shown in Fig. 1, a kind of small current grounding system single-phase ground fault line selection method based on Fisher (fisher) information of the present invention comprises:

S1, dividing the discrete wavelet coefficients into a series of time windows;

S2. Pack data points into states in each time window;

S3. Construct a probability density function p _i based on the possibility of observing the state of the system in each time window;

S4. Calculate Fischer information from the probability density function for each time window;

S5. Select the line with the smallest Fischer information value as the faulty line.

Further, before step S1, signal preprocessing is also included, and the zero-sequence current signals of each line obtained through real-time sampling are subjected to wavelet decomposition in order to remove noise and separate fault features.

Assume that after the zero-sequence current signal x(n) is transformed by wavelet, the coefficient of the high-frequency component at time k at the j-th decomposition scale is cD _j (k), and the coefficient of the low-frequency component is cA _j (k). After single-branch reconstruction The frequency bandwidth range of the information contained in the obtained signal components D _j (k) and A _j (k) is

D _j (k):[2 ^-j f _s ,2 ^-(j-1) f _s ], A _j (k):[0,2 ^-j f _s ], j=1,2,...,J,

Among them, f _s is the sampling frequency of the signal, and J is the maximum decomposition scale. In this embodiment, f _s is taken as 20kHz, db5 base wavelet is selected, and the data is decomposed by 5 layers of wavelet, that is, J is taken as 5.

Step S1 is specifically:

Assuming that on the jth layer, the discrete wavelet coefficients of the multiresolution analysis are D={d(k), k=1,...,N}, a sliding window is defined on the wavelet coefficients of this layer, and the window width is w∈N , the sliding factor is δ∈N, and the sliding window is as follows:

W(m,w,δ)={d(k),k=1+m*δ,…,w+m*δ},

Where m=1, 2,...,M, M is the number of windows and satisfies M=(N-w)/δ.

Step S2 is specifically:

Assuming that all elements in the sliding window can be divided into L states, then

$\mathrm{<span\; class="notranslate">\; Length</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; Length</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

Wherein, Z _l ={Z _l :|Z _l (i)-Z _l (j)|≤2*σ,i, j=1,2,...w; i≠j}.

The above formula shows that the total number of elements in the window is equal to the sum of the number of elements in each state. Where σ is the standard deviation of the wavelet coefficient D when the line is normal. According to the Chebyshev theorem, the above division principle can ensure that 89% of the data points in the window are in the same state regardless of the form of the probability distribution.

The formula for calculating Fischer information from the probability density function in step S4 is: I≈4∑[q _i -q _i+1 ] ² , q _i and q _i+1 are the probability densities at i and i+1 Square root value, I is Fisher information.

The Fischer information calculation formula is obtained by the following steps:

The Fischer information I for a single measurement of a variable is calculated as follows:

$\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&Integral;</span>\frac{\mathrm{<span\; class="notranslate">\; ds</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; dP</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; ds</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>$

Among them, P(s) is the probability density function (PDF), and s is a state variable;

Let q ² (s)=P(s), then the above formula becomes:

$\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; \&Integral;</span>\mathrm{<span\; class="notranslate">\; ds</span>}{<span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; dq</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; ds</span>}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>$

The approximate calculation formula of Fischer information can be obtained by replacing the differential in the above formula with the difference, and replacing the integral in the above formula with the sum:

I≈4∑[q _i -q _i+1 ] ² .

The present invention will be further described below in combination with specific embodiments.

Example 1: An example of line selection for a single-phase ground fault in a neutral point ungrounded system.

Assume that the three outgoing lines of the 35kv/10kv neutral point ungrounded system are L1, L2 and L3, and the positive sequence parameters of the line are R ₁ =0.484Ω/km, L ₁ =0.3454mH/km, C ₁ =0.0345μF/km, Zero sequence parameters R ₀ =1.16Ω/km, L ₀ =1.10362mH/km, C ₀ =0.0219μF/km, other parameters are the same as above.

Figure 2 shows the zero-sequence current waveforms I01, I02, and I03 of each line when a single-phase ground fault occurs on line L1 at a distance of 10km from the busbar. ; Figure 3 shows the FI value (that is, the Fischer information value) calculated by the above method for the zero-sequence current signal of each line.

Figure 4 shows the zero-sequence current waveforms I01, I02, and I03 of the three lines when a single-phase ground fault occurs on the line L1 at a distance of 20km from the busbar, the fault resistance is 20Ω, and the initial voltage angle is 180°; Figure 5 is calculated for the three lines FI value.

Example 2: An example of line selection for a single-phase ground fault in a neutral point grounded system through an arc suppression coil.

Table 1 lists the line selection results of the neutral point through the arc suppression coil grounding system under different fault conditions. When the arc suppression coil is grounded, the overcompensation method is adopted, and the compensation degree is 8%. Other parameters are the same as above.

Table 1: Line selection results of the neutral point through the arc suppression coil grounding system

It can be seen from the above embodiments that the present invention uses a dimensionless non-negative positive number as a single criterion to realize the problem of line selection for single-phase grounding faults in small current grounding systems. Compared with the prior art, it has the following advantages:

Under different grounding methods, it can effectively distinguish the faulty line from the non-faulty line, and is not affected by the initial phase angle of the voltage, grounding resistance, and fault location, and can accurately locate the fault time;

Under unfavorable conditions such as short data, small amplitude, and interference, it can effectively extract the characteristic information hidden in the signal sequence, and at the same time quantitatively characterize the complexity of each signal sequence, providing an effective means for the analysis of non-stationary signal sequences.

It should be understood that although this description is described according to implementation modes, not each implementation mode only contains an independent technical solution, and this description in the description is only for clarity, and those skilled in the art should take the description as a whole, and each The technical solutions in the embodiments can also be properly combined to form other embodiments that can be understood by those skilled in the art.

The series of detailed descriptions listed above are only specific descriptions for feasible implementations of the present invention, and they are not intended to limit the protection scope of the present invention. Any equivalent implementation or implementation that does not depart from the technical spirit of the present invention All changes should be included within the protection scope of the present invention.

Claims (6)

1. A single-phase grounding fault line selection method for small current grounding systems based on Fischer information, characterized in that, the method comprises: S1, dividing the discrete wavelet coefficients into a series of time windows; S2. Pack data points into states in each time window; S3. Construct a probability density function p _i based on the possibility of observing the state of the system in each time window; S4. Calculate Fischer information from the probability density function for each time window; S5. Select the line with the smallest Fischer information value as the faulty line. 2. The method according to claim 1, characterized in that before the step S1, it also includes: Signal preprocessing, the zero-sequence current signal of each line obtained by real-time sampling is subjected to wavelet decomposition in order to remove noise and separate fault features. 3. method according to claim 2, it is characterized in that, after described zero-sequence current signal is through wavelet transformation, the high-frequency component coefficient at k moment under j decomposition scale is cD _j (k), and low-frequency component coefficient is cA _j (k), the frequency bandwidth range of the information contained in the signal components D _j (k) and A _j (k) obtained after single branch reconstruction is D _j (k):[2 ^-j f _s ,2 ^-(j-1) f _s ], A _j (k):[0,2 ^-j f _s ], j=1,2,...,J, Among them, f _s is the sampling frequency of the signal, and J is the maximum decomposition scale. 4. The method according to claim 1, characterized in that, the step S1 is specifically: Assuming that on the jth layer, the discrete wavelet coefficients of the multiresolution analysis are D={d(k), k=1,...,N}, a sliding window is defined on the wavelet coefficients of this layer, and the window width is w∈N , the sliding factor is δ∈N, and the sliding window is: W(m,w,δ)={d(k),k=1+m*δ,...,w+m*δ}, Where m=1, 2,...,M, M is the number of windows and satisfies M=(N-w)/δ. 5. The method according to claim 4, characterized in that, the step S2 is specifically: Divide all elements in the sliding window into L states, then the total number of elements in the window is equal to the sum of the number of elements in each state, that is

Among them, Z _l ={Z _l :|Z _l (i)-Z _l (j)|≤2*σ,i, j=1,2,…w;i≠j}, σ is the wavelet when the line is normal The standard deviation of the coefficient D. 6. The method according to claim 1, characterized in that the formula for calculating Fischer information from the probability density function in the step S4 is: I≈4∑[q _i -q _i+1 ] ² , q _i , q _i+1 is the square root value of the probability density at i and i+1, and I is the Fisher information.

Images