CN116609610A - Single-phase earth fault phase selection method based on self-adaptive wavelet packet transformation - Google Patents
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Abstract
The invention relates to a phase selection method of a single-phase earth fault based on self-adaptive wavelet packet transformation, which is used for collecting three-phase current at a bus and calculating three-phase current abrupt change of one cycle before and after the fault; performing fast Fourier transform on the three-phase current abrupt change quantity to obtain a frequency component with the largest amplitude value; fixing the frequency component with the largest amplitude on a second frequency band to obtain the wavelet packet decomposition layer number of the three-phase current abrupt change, wherein the maximum value is the optimal decomposition layer number; and selecting a decomposition coefficient corresponding to the maximum characteristic frequency band energy to quantify the average gray correlation degree, wherein the phase corresponding to the minimum value of the average gray correlation degree is the fault phase. The invention has scientific and reasonable design, can dynamically update the wavelet packet decomposition layer number of the obtained three-phase current abrupt change under different single-phase grounding fault scenes, has high phase selection accuracy rate for high-resistance grounding faults and single-phase arc grounding faults, and has strong applicability and robustness and low calculation complexity.
Description
Technical Field
The invention belongs to the technical field of power distribution network fault analysis and signal processing, and particularly relates to a single-phase grounding fault phase selection method based on self-adaptive wavelet packet transformation.
Background
With the continuous development of the intelligent power distribution network, the occurrence probability of faults in the power distribution network is larger and larger, and if faults cannot be timely removed, the fault range is further expanded, so that the normal operation of the power distribution network is seriously influenced. In a distribution network with a neutral point grounded through an arc suppression coil, when a single-phase earth fault occurs, the arc suppression coil generates an inductive current, and the inductive current has a compensation function on the capacitance current to the ground of the fault point, so that the fault current is generally smaller. When a single-phase high-resistance ground fault occurs, the fault characteristic is not obvious, so that the possibility of phase selection errors exists in the existing phase selection method.
Single-phase earth faults are the most common fault types in operation of a power distribution network, and traditional single-phase earth fault phase selection methods can be classified into steady-state quantity-based and transient quantity-based methods from the viewpoint of fault data types. In faults with obvious transient quantity, the duration time of the transient process is long, so that the fault phase selection cannot be realized rapidly by a phase selection method based on steady-state quantity; in the high-resistance ground fault, the transient quantity-based method has the possibility of phase selection errors due to the fact that the transient quantity difference is not obvious. Therefore, the existing method still has the defects of low accuracy, low applicability and the like.
As the application of artificial intelligence algorithm in distribution network continues to be deep, the data processing method based on wavelet packet transformation is gradually used for phase selection when single-phase grounding fault occurs. However, conventional wavelet packet transforms typically fix the number of decomposition layers, resulting in over-or under-decomposition of the data in different failure scenarios, which is less applicable. There are also documents for improving the traditional wavelet packet transformation, presetting the range of the decomposition layer number and the data threshold value, and providing a self-adaptive wavelet packet transformation for traversing the decomposition layer number from top to bottom.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a single-phase grounding fault phase selection method based on adaptive wavelet packet transformation, which has small calculation amount, can rapidly identify fault phases, can accurately select phases under different fault scenes and has strong applicability.
The invention solves the technical problems by the following technical proposal:
a single-phase grounding fault phase selection method based on adaptive wavelet packet transformation is characterized in that: the method comprises the following steps:
s1, acquiring three-phase current at a bus, and calculating three-phase current mutation quantity of one cycle before and after a fault occurs
When the power distribution network operates normally, the instantaneous value of the three-phase current is expressed as:
wherein: i.e kXC (t) (k=1, 2,) n, t=1, & gt, M, x=a, B, C) is the instantaneous value of the three-phase capacitive current to ground;
i kXL (t) is a three-phase load current;
C kX is a three-phase capacitance to ground;
e X is a three-phase power supply voltage;
u 0 is neutral point voltage;
when a single-phase earth fault occurs in the power distribution network, the instantaneous value of the three-phase current is expressed as:
wherein: i' kXL (t) is the load current after the fault occurs;
u' 0 is the neutral point offset voltage;
i f is fault point current;
assuming ideal conditions, the load current remains unchanged, i.e. i' kXL (t)＝i kXL (t), the three-phase current abrupt change is expressed as:
s2, obtaining the number of wavelet packet decomposition layers under different frequency values
The following formula holds for the first characteristic band of the j-th layer of the wavelet packet transform:
performing fast fourier transform on the three-phase current abrupt change to obtain a frequency component with the maximum amplitude of each phase, wherein the frequency value can be expressed as follows:x= { A, B, C }, according to the above, +.>The following must be satisfied:
transforming the above to obtain the relation of the decomposition layer number jIs not equal to:
from the above equation, the number of decomposition layers j is determined by l, and in order to minimize the number of decomposition layers to achieve the purpose of complexity reduction, l can be set to 2, i.e. the frequency component with the largest amplitude of three-phase current mutation is fixed on the 2 nd characteristic frequency band of decomposition of the j-th wavelet packet, since the sampling frequency is generally much larger thanThus (S)>The node sequence number of the characteristic frequency band is necessarily less than 2 j-1 And->The energy of the characteristic frequency band or the energy of the nodes nearby the characteristic frequency band is the largest in the full frequency band of the j layer in the normal case, so only the 2 nd characteristic frequency band to the 2 nd characteristic frequency band are calculated j-1 The energy of the individual characteristic frequency bands; in order to avoid the compensation effect of the neutral point on the power frequency capacitance current by the arc suppression coil in the arc suppression coil power distribution network, the frequency band of the power frequency component is generally in the 1 st frequency band, and the power frequency component is not calculated and compared;
three-phase current abrupt change amounts can be respectively calculated to obtain three decomposition layers, namely: j (j) X ＝[j A ,j B ,j C ]Finally, the number of decomposition layers of the self-adaptive wavelet packet of the three-phase current abrupt change is unified as follows: j=max (j) A ,j B ,j C )；
S3, calculating decomposition coefficients of wavelet packets of each phase of the j-th layer
According to the number of decomposition layers obtained in step S2, wavelet packet decomposition is used for the three-phase current abrupt change amount:
wherein:the j-th layerWavelet packet decomposition coefficients of l nodes;
wavelet packet decomposition coefficient for the 2l node of the (j+1) th layer;
wavelet packet decomposition coefficients for the (2l+1) th node of the (j+1) th layer;
h (p-2 q) and g (p-2 q) are low-pass and high-pass filter coefficients, respectively;
s4, calculating and obtaining a characteristic frequency band with the maximum energy ratio of the j th layer
After the wavelet packet decomposition coefficient of the j-th layer is obtained, solving the energy of the wavelet packet decomposition coefficient:
wherein: I.I l2 Performing arithmetic for l2 norms;
calculate the 2 nd characteristic band to 2 nd j-1 The energy of each characteristic frequency band is:
the energy duty cycle of each band can then be expressed as:
the repeated operation is carried out on the three-phase current mutation quantity, and the characteristic frequency band with the maximum energy occupation ratio is solved, so that three corresponding groups of wavelet packet decomposition coefficients can be obtained;
s5, calculating average gray correlation degree
After steps S1 to S4, it is assumed that the two-phase wavelet packet decomposition coefficients are: x (t) = [ x (1), x (2),..:
the absolute gray correlation of the X and Y phases can be written as:
epsilon was calculated for each of the three phases XY The average gray correlation of the three-phase current abrupt change values can be obtained as follows:
finally, the minimum value of three average gray correlation degrees is taken as follows:
thenThe corresponding phase is the failed phase.
The invention has the advantages and beneficial effects that:
1. the single-phase grounding fault phase selection method based on the self-adaptive wavelet packet transformation only needs to calculate and compare half of characteristic frequency band energy, has low calculation complexity and can reliably and quickly judge the fault phase;
2. the phase selection method of the single-phase grounding fault based on the self-adaptive wavelet packet transformation is correct in phase selection under the scenes of single-phase metallic grounding fault, single-phase high-resistance grounding fault, single-phase arc grounding fault and the like, and has high applicability;
3. the phase selection method of the single-phase grounding fault based on the self-adaptive wavelet packet transformation has good phase selection result and stronger robustness under the condition that different noise intensities exist in measured data.
Drawings
FIG. 1 is a line outgoing topological structure diagram of a power distribution network with a neutral point grounded through an arc suppression coil;
FIG. 2 is a graph showing the current distribution at the time of single-phase earth fault according to the present invention;
FIG. 3 is a graph of a three-phase current ramp amount spectrum of the present invention;
FIG. 4 is a diagram of a j-layer wavelet packet transform according to the present invention;
FIG. 5 is a diagram showing the number of decomposition levels according to the present invention;
FIG. 6 is a flow chart of a single phase ground fault phase selection process of the present invention;
fig. 7 is a graph of phase selection results for different noise intensities according to the present invention.
Detailed Description
The invention is further illustrated by the following examples, which are intended to be illustrative only and not limiting in any way.
A phase selection method of single-phase grounding fault based on self-adaptive wavelet packet transformation utilizes the fast Fourier transformation of three-phase current abrupt change to obtain the frequency component with the largest amplitude, and based on different fault scenes, the number of wavelet packet decomposition layers can be updated in real time. Under each fault scene, the maximum value is taken as the whole decomposition layer number after the three-phase wavelet packet decomposition layer number is obtained. If the smaller value of the three phases is taken, the frequency component with the largest amplitude of a certain phase falls in the 1 st frequency band, so that the frequency component is removed, and the phase selection accuracy is affected. Under the scenes of single-phase metallic faults, single-phase high-resistance grounding faults, single-phase arc grounding faults and the like, the phase selection results of the method are correct, and the average gray correlation degree difference of the three-phase current abrupt change amounts is obvious. After noise is added into the three-phase current mutation quantity, the phase selection results are correct, and good robustness is shown.
The appearance model of the power distribution network system with the neutral point passing through the arc suppression coil is shown in figure 1. The outgoing line consists of a cable and overhead line mixed line, and is divided into four outgoing lines L1, L2, L3 and L4, wherein one branch line exists in the L2 line. L2-1, L2-3 and L3-1 are overhead lines, and the rest lines are all cable lines. In addition, the high-voltage side and the low-voltage side of the transformer are 110kV/10.5kV, and the arc suppression coil and the Z-type transformer are connected in series at the bus. The experimental simulation of the present invention will be performed on the basis of this model.
The current distribution diagram when a single-phase ground fault occurs at the end of the line L1 is shown in fig. 2.
First, when the power distribution network is operating normally, the instantaneous value of the three-phase current can be expressed as:
wherein: i.e kXC (t) (k=1, 2,) n, t=1, & gt, M, x=a, B, C) is the instantaneous value of the three-phase capacitive current to ground;
i kXL (t) is a three-phase load current;
C kX is a three-phase capacitance to ground;
e X is the electromotive force of a three-phase power supply;
u 0 is the neutral point voltage.
When a single-phase earth fault occurs in the power distribution network, the above formula can be written as:
wherein: i' kXL (t) is the load current after the fault occurs;
u' 0 is the neutral point offset voltage;
i f is the fault point current.
Assuming ideal conditions, the load current remains unchanged, i.e. i' kXL (t)＝i kXL (t), the three-phase current abrupt change can be expressed as:
after the three-phase current abrupt change is obtained, fast Fourier transformation is needed to be carried out on the three-phase current abrupt change to obtain a frequency component with the largest amplitude:x= { a, B, C }. As shown in fig. 3, a three-phase current jump spectrum chart when a single-phase arc ground fault occurs at each line end is shown in fig. 3 a) as a phase, fig. 3B) as a B phase, and fig. 3C) as a C phase. It can be seen from the figure that the frequency component with the greatest amplitude is concentrated between 200 and 500Hz except the power frequency component. Since the dc component is typically in a frequency band with the power frequency component, no comparison of the maximum amplitude is made. From FIG. 4, the frequency ++where the amplitude of the three-phase current abrupt change is maximum in any scene can be obtained>
FIG. 4 is a schematic diagram of a j-layer wavelet packet transform, where the following equation holds for the j-th layer of the characteristic frequency band of the wavelet packet transform:
in the case where l is unknown, according to the above equation,the following must be satisfied:
transforming the above to obtain the relation of the decomposition layer number jIs not equal to:
from the above equation, the size of the decomposition level j is determined by l. To minimize the number of decomposition layers for the purpose of complexity reduction, l may be set to 2, i.e., the frequency component with the largest amplitude of the three-phase current step-up is fixed on the 2 nd characteristic frequency band of the j-th layer wavelet packet decomposition. Thus, the above formula is further converted into:
in fig. 5, the hatched portion is a feasible region of the decomposition level j represented by equation 7. Wherein the value of the number of decomposition layers of each phase is the minimum positive integer in the formula 7, expressed as:
where ceil (·) is the rounding down symbol. In addition, three decomposition layer numbers, namely, three decomposition layer numbers, can be calculated respectively by three-phase current mutation amounts: j (j) X ＝[j A ,j B ,j C ]And finally, the number of the self-adaptive wavelet packet decomposition layers of the three-phase current abrupt change is as follows:
j＝max(j A ,j B ,j C ) (9)
furthermore, since the sampling frequency is generally much greaterThus (S)>The node sequence number of the characteristic frequency band is necessarily less than 2 j-1 . And (F)>The energy of the characteristic band or the energy of the nodes nearby is usually the largest in the full band of the j-th layer. Therefore, compared with the conventional phase selection method based on wavelet packet transformation and characteristic band energy, the method provided by the invention only needs to calculate the first step in FIG. 42 characteristic frequency bands to 2 nd j-1 The energy of the characteristic frequency band without calculating the 2 nd characteristic frequency band to the 2 nd characteristic frequency band j The energy of the characteristic frequency bands. In order to avoid the compensation effect of the neutral point on the power frequency capacitance current by the arc suppression coil in the arc suppression coil power distribution network, the frequency band of the power frequency component is generally in the 1 st frequency band, and calculation and comparison are not performed.
Then, the three-phase current abrupt change is decomposed by using a wavelet packet according to the obtained decomposition level j. The decomposition formula of the wavelet packet transform is as follows:
wherein,,wavelet packet decomposition coefficient for the jth level of the jth node,/for the jth level of the jth node>Wavelet packet decomposition coefficient of 2l node of (j+1) th layer,/>Wavelet packet decomposition coefficients for the (2l+1) th node of the (j+1) th layer. In addition, h (p-2 q) and g (p-2 q) are low-pass and high-pass filter coefficients, respectively. After the wavelet packet decomposition coefficients of the j-th layer nodes of the current abrupt change quantity of a certain phase are obtained, solving the energy of the wavelet packet decomposition coefficients:
wherein I l2 Is l 2 And (5) carrying out norm operation. At this time, the 2 nd characteristic band is calculated to 2 nd j-1 Energy of the individual characteristic bands:
the energy duty cycle of each band can then be expressed as:
and solving a characteristic frequency band with the maximum energy ratio:and (3) repeating the operation on the three-phase current abrupt change, so as to obtain three groups of wavelet packet decomposition coefficients corresponding to the maximum characteristic frequency band energy. After the wavelet packet decomposition coefficients of the respective phases are obtained, it is assumed that there are: x (t) = [ x (1), x (2),. The term x (M)]And y (t) = [ y (1), y (2),. The term, y (M)](M is the number of sampling points in the wavelet decomposition coefficients). The following formula can be defined:
the absolute gray correlation of the X and Y phases can be written as:
next, ε is calculated for each of the three phases XY The average gray correlation of the three-phase current abrupt change values can be obtained:
finally, the minimum value of three average gray correlation degrees is taken as follows:
wherein,,the corresponding phase is the failed phase.
After the fault phase is selected, a grounding arc suppression device in the power distribution network needs to perform switching-on operation. If the grounding switch is closed, the fault characteristic disappears, namely the transient fault, and the grounding switch can be reset; if the fault characteristics still exist after the grounding switch is switched on, the grounding switch is not reset, and the patrol personnel need to cut off the fault manually.
In summary, in the distribution network with the neutral point grounded through the arc suppression coil, the phase flow path of the single-phase ground fault selection based on the adaptive wavelet packet transformation is shown in fig. 6. When a single-phase earth fault occurs in the system, firstly, three-phase current abrupt change is obtained, and is adapted to fast Fourier transform for spectrum analysis, so that frequency components with maximum amplitude values of the three-phase current abrupt change of each phase are obtained, the frequency values are substituted into a frequency band segmentation formula of wavelet packet transform, and the number j of decomposition layers of each phase is solved A ,j B And j C After the overall optimal decomposition layer number j is obtained, wavelet packet coefficient decomposition is performed. Except that the 1 st frequency band is removed, calculate the 2 nd frequency band 2 in the j-th layer j-1 And searching the energy of each frequency band, searching the frequency band with the maximum energy ratio, taking the corresponding wavelet packet coefficient, and calculating the average gray correlation degree. Finally, the phase corresponding to the minimum value is the fault phase.
Simulation verification
The power distribution network topological structure shown in the figure 1 is built in PSCAD/ETDMC, the grade of a main transformer is 110/10.5kV, a fault phase is set to be a C phase, the sampling frequency is set to be 20kHz, a wavelet basis function uses db6', and fault points are respectively arranged at the tail ends of L1-1, L2-1, L4-1 and L4-2. The fault types are single-phase ground faults through fixed resistance values and single-phase arc ground faults. The transition resistances of the single-phase ground faults through fixed resistance values are respectively set to be 0.01, 10, 100, 1000, 3000 and 5000 omega.
And (3) verifying the accuracy and the effectiveness of the method:
as shown in table 1, the phase selection validity and accuracy of the proposed method were verified. Wherein R is f Is the transition resistance.
Phase selection for the procedure presented in Table 1
As can be seen from table 1, for line L1-1, when a single-phase metallic ground fault and a single-phase arc ground fault occur, the number of decomposition layers is calculated to be 6, while the other fault scenarios are 7; for line L2-1, when a single-phase arc ground fault occurs, the number of decomposition layers is calculated to be 6, and other fault scenarios are 7. Simulation results show that the method provided by the invention can update the decomposition layer number of wavelet packet transformation in real time according to different fault scenes, and has strong applicability.
In addition, for two lines, the method is correct in phase selection, and the average gray correlation degree difference between the sound phase and the fault phase is obvious, so that the effectiveness and the accuracy of fault phase selection are shown.
Robustness verification:
as shown in fig. 7, the robustness verification of the proposed method of the invention. In actual operation of the power distribution network, the collected data is affected by synchronization problems, precision of measuring instruments and the like, certain errors exist, and the anti-noise performance, namely robustness, of the method is required to be verified. Because of the fuzzy fault characteristics in the system when the high-resistance ground fault occurs, the existing phase selection method is generally difficult to completely select the phase correctly. Therefore, gaussian white noise with the intensities of 5, 10 and 20dB is added into the obtained three-phase current abrupt change so as to verify the phase selection accuracy of the method during high-resistance ground faults.
In FIG. 7, single-phase high-resistance ground faults are respectively arranged at the tail ends of the lines L4-1 and L4-2, and transition resistances are respectively arranged at 3000 and 5000 omega, so that the phase selection results of the proposed method are correct under different noise intensities. It can be seen that when the noise intensity is 5dB, the average gray correlation difference between the sound phase and the faulty phase is reduced, but the actual faulty phase can still be judged. The method provided by the invention has stronger robustness.
Although the embodiments of the present invention and the accompanying drawings have been disclosed for illustrative purposes, those skilled in the art will appreciate that: various substitutions, changes and modifications are possible without departing from the spirit and scope of the invention and the appended claims, and therefore the scope of the invention is not limited to the embodiments and the disclosure of the drawings.
Claims (1)
1. A single-phase grounding fault phase selection method based on adaptive wavelet packet transformation is characterized in that: the method comprises the following steps:
s1, acquiring three-phase current at a bus, and calculating three-phase current mutation quantity of one cycle before and after a fault occurs
When the power distribution network operates normally, the instantaneous value of the three-phase current is expressed as:
wherein: i.e kXC (t) (k=1, 2,) n, t=1, & gt, M, x=a, B, C) is the instantaneous value of the three-phase capacitive current to ground;
i kXL (t) is a three-phase load current;
C kX is a three-phase capacitance to ground;
e X is a three-phase power supply voltage;
u 0 is neutral point voltage;
when a single-phase earth fault occurs in the power distribution network, the instantaneous value of the three-phase current is expressed as:
wherein: i' kXL (t) is the load current after the fault occurs;
u' 0 is the neutral point offset voltage;
i f is fault point current;
assuming ideal conditions, the load current remains unchanged, i.e. i' kXL (t)＝i kXL (t), the three-phase current abrupt change is expressed as:
s2, obtaining the number of wavelet packet decomposition layers under different frequency values
The following formula holds for the first characteristic band of the j-th layer of the wavelet packet transform:
performing fast fourier transform on the three-phase current abrupt change to obtain a frequency component with the maximum amplitude of each phase, wherein the frequency value can be expressed as follows:x= { A, B, C }, according to the above, +.>The following must be satisfied:
transforming the above to obtain the relation of the decomposition layer number jIs not equal to:
from the above equation, the number of decomposition layers j is determined by l, and in order to minimize the number of decomposition layers to achieve the purpose of complexity reduction, l can be set to 2, i.e. the frequency component with the largest amplitude of three-phase current mutation is fixed on the 2 nd characteristic frequency band of decomposition of the j-th wavelet packet, since the sampling frequency is generally much larger thanThus (S)>The node sequence number of the characteristic frequency band is necessarily less than 2 j-1 And->The energy of the characteristic frequency band or the energy of the nodes nearby the characteristic frequency band is the largest in the full frequency band of the j layer in the normal case, so only the 2 nd characteristic frequency band to the 2 nd characteristic frequency band are calculated j-1 The energy of the individual characteristic frequency bands; in order to avoid the compensation effect of the neutral point on the power frequency capacitance current by the arc suppression coil in the arc suppression coil power distribution network, the frequency band of the power frequency component is generally in the 1 st frequency band, and the power frequency component is not calculated and compared;
three-phase current abrupt change amounts can be respectively calculated to obtain three decomposition layers, namely: j (j) X ＝[j A ,j B ,j C ]Finally, the number of decomposition layers of the self-adaptive wavelet packet of the three-phase current abrupt change is unified as follows: j=max (j) A ,j B ,j C )；
S3, calculating decomposition coefficients of wavelet packets of each phase of the j-th layer
According to the number of decomposition layers obtained in step S2, wavelet packet decomposition is used for the three-phase current abrupt change amount:
wherein: d, d l j Wavelet packet decomposition coefficient for the j-th layer of the first node;
wavelet packet decomposition coefficient for the 2l node of the (j+1) th layer;
wavelet packet decomposition coefficients for the (2l+1) th node of the (j+1) th layer;
h (p-2 q) and g (p-2 q) are low-pass and high-pass filter coefficients, respectively;
s4, calculating and obtaining a characteristic frequency band with the maximum energy ratio of the j th layer
After the wavelet packet decomposition coefficient of the j-th layer is obtained, solving the energy of the wavelet packet decomposition coefficient:
wherein: I.I l2 Performing arithmetic for l2 norms;
calculate the 2 nd characteristic band to 2 nd j-1 The energy of each characteristic frequency band is:
the energy duty cycle of each band can then be expressed as:
the repeated operation is carried out on the three-phase current mutation quantity, and the characteristic frequency band with the maximum energy occupation ratio is solved, so that three corresponding groups of wavelet packet decomposition coefficients can be obtained;
s5, calculating average gray correlation degree
After steps S1 to S4, it is assumed that the two-phase wavelet packet decomposition coefficients are: x (t) = [ x (1), x (2),..:
the absolute gray correlation of the X and Y phases can be written as:
epsilon was calculated for each of the three phases XY The average gray correlation of the three-phase current abrupt change values can be obtained as follows:
finally, the minimum value of three average gray correlation degrees is taken as follows:
thenThe corresponding phase is the failed phase.
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| CN117110797A (en) * | 2023-10-23 | 2023-11-24 | 武汉格蓝若智能技术股份有限公司 | Multi-criterion-based single-phase earth fault positioning method and device for power distribution network |
| CN117110797B (en) * | 2023-10-23 | 2024-01-12 | 武汉格蓝若智能技术股份有限公司 | Multi-criterion-based single-phase earth fault positioning method and device for power distribution network |
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