CN110320436B - High-resistance grounding fault detection method for flexible direct-current power distribution network - Google Patents

High-resistance grounding fault detection method for flexible direct-current power distribution network Download PDF

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CN110320436B
CN110320436B CN201910632932.0A CN201910632932A CN110320436B CN 110320436 B CN110320436 B CN 110320436B CN 201910632932 A CN201910632932 A CN 201910632932A CN 110320436 B CN110320436 B CN 110320436B
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ground fault
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韦延方
王小丽
王鹏
曾志辉
王晓卫
杨明
宋振江
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Henan University of Technology
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Abstract

The invention discloses a high resistance grounding fault detection method for a flexible direct current power distribution network, which comprises the steps of firstly, extracting a characteristic modal component from transient zero-mode current by adopting a variational modal decomposition algorithm, and comparing and distinguishing a fault state and a normal state by adopting the characteristic modal component; secondly, calculating the Euclidean distance of the characteristic modal component, converting the Euclidean distance into gray scale, and calculating the mean value of the gray scale; and finally, converting the gray average value into a hexagonal cone space model by adopting a color relation classifier, and further judging the running state according to the hue, saturation and lightness values. Compared with the existing high-resistance fault diagnosis method, the fault detection method has the advantages of flexible reasoning model, high fault detection reliability, convenient embedding of the color relation classifier model into equipment, realization of real-time monitoring, overcoming of complexity in the fault detection process and improvement of calculation speed.

Description

High-resistance grounding fault detection method for flexible direct-current power distribution network
Technical Field
The invention belongs to the technical field of power grid fault detection, and particularly relates to a high-resistance grounding fault detection method for a flexible direct-current power distribution network.
Background
At present, the direct current distribution network is rapidly developed along with the diversity of energy sources used by a user side and the increase of load energy, and the investment of resources of a plurality of scholars and researchers also promotes the technology of the direct current distribution network to be mature. In order to solve the problem that investment cost is increased due to the requirement of a large number of power electronic converter equipment in the traditional alternating current power distribution network, a mature direct current power distribution network technology becomes the first choice of people in power distribution mode selection, and with the rapid development of the power electronic technology and the progress of the converter technology, the flexible direct current power distribution network system has the advantages of high power supply reliability, high electric energy quality, low investment cost, large future development potential and the like, so that the flexible direct current power distribution network system is independent of the power distribution mode selection.
Recently, the flexible direct current technology breaks through innovation continuously, but still has many problems to be solved by the common efforts of many scholars. The distribution network is densely distributed in human activity areas, the protection level is not high, the load capacity is continuously increased, and the fault rate is also increased year by year. When intermittent faults exist in the power distribution network, the direct current does not have zero crossing points due to the fact that the damping value of a direct current line is small, the fault arc is re-ignited after being extinguished, and the fault is difficult to cut due to the fact that the fault is high in self-healing capacity. On the other hand, high-resistance faults of the power distribution network are more, 2-5% of fault resistance belongs to the high-resistance faults, but direct current discharge time is short, discharge is completed almost within a few microseconds, fault data are difficult to obtain, and the fault data window is short, so that the existing fault protection measures cannot synchronously obtain effective fault information, and line protection fails. In addition, high resistance faults are many, signals of the high resistance faults and signals of the high resistance faults in normal working are difficult to distinguish, the difficulty of fault identification is increased, meanwhile, the high resistance faults are large in damage, the power distribution network is located in a human frequent activity area, and the problems of huge personal safety and power grid stability are easily caused. However, the flexible direct current high-resistance grounding fault research is very little, and the flexible direct current high-resistance grounding fault research is worth intensive research of researchers.
In order to solve the problem that fault characteristic signals are difficult to extract, the improved variational modal decomposition is adopted, so that modal aliasing and end effect phenomena which are easy to occur in empirical modal decomposition can be avoided, and compared with the set empirical modal decomposition, the problems that white noise needs to be artificially added and the frequency needs to be added are solved; compared with wavelet transformation and S transformation, extra function setting is not needed, the difficulty of feature extraction is reduced, and accurate signal extraction can be realized. For fault mode identification, a color relationship classifier is adopted, the obtained transient characteristic signal is converted into a hexagonal cone space model problem, small-resistance grounding, medium-resistance grounding and high-resistance grounding faults are distinguished by calculating hue, and the reliability of fault judgment is improved by saturation and brightness values. Aiming at the problems that the fault data window is short and the fault signal is difficult to obtain, the data sampled by the invention is completed within 2ms of the fault, the data acquisition is effective and quick, the color relation classifier does not need time limitation, and can be embedded into monitoring equipment to realize real-time monitoring, thereby being suitable for practical engineering application.
Disclosure of Invention
In order to achieve the purpose, the invention provides a high-resistance grounding fault detection method for a flexible direct current power distribution network, which is improved in that the method comprises the following steps:
step 1: extracting transient zero-mode current of the flexible direct-current power distribution network;
transient zero-mode current i0(t) is obtained by the following formula:
Figure GSB0000195665140000021
in the formula ip(t)、in(t) is the positive and negative currents of the flexible direct current distribution network respectively, and t represents time;
i0(t) the circulation directions of the positive electrode and the negative electrode are the same, and a loop is formed by passing through a grounding point; the structure of the direct current system zero mode network is related to the wiring mode of the transformer, the grounding mode of the neutral point and the grounding point position of the direct current system;
step 2: the method adopts a variational modal decomposition algorithm to extract characteristic modal components, and specifically comprises the following steps:
1) converting the transient zero-mode current signal i0(t) decomposition into K modal components uk(t) and each modal component is a finite bandwidth with a center frequency, the center frequency and finite bandwidth being continuously updated during the decomposition process, for uk(t) the single-sided spectrum of the signal can be obtained using the hilbert transform:
Figure GSB0000195665140000031
wherein K is a natural number, and K is 1, 2.,; δ (t) denotes a step function, uk(t) represents i0(t) decomposition into K modal components;
2) single-sided spectrum of signal multiplied by estimated center frequency
Figure GSB0000195665140000032
The following can be obtained:
Figure GSB0000195665140000033
3) computing
Figure GSB0000195665140000034
Square of gradient of (3) L2Norm to obtain each modal component uk(t) limited bandwidth, constructing a mathematical model of the variational modal constraints problem:
Figure GSB0000195665140000035
in the formula, δ represents a dirac distribution, { μ, represents a convolutionkIs the set of all modal components (μ) decomposed1，μ2，…，μk}，
Figure GSB0000195665140000036
Is the set of center frequencies of each modal component
Figure GSB0000195665140000037
Figure GSB0000195665140000041
Is a constraint condition of the reconstruction accuracy,
Figure GSB0000195665140000042
representing a gradient, | | | | represents a norm,
Figure GSB0000195665140000043
represents [ mu ]kThe sum of modal components;
4) the solution of the variational modal constraint problem specifically comprises the following steps:
a) introducing Lagrange multiplication operators and secondary punishment factors to the variational modal constraint problem to obtain an expanded Lagrange expression:
Figure GSB0000195665140000044
in the formula, alpha represents a secondary penalty factor, and lambda (t) represents a Lagrange multiplier;
b) solving by adopting an alternating direction multiplier algorithm to obtain K modal components;
analyzing K modal components, wherein the K modal components are related to a transient zero mode current signal i0(t) the modal component with the maximum correlation coefficient is used as the characteristic modal component, and different characteristics of a normal state and an abnormal state can be obtained, so that the normal state and the abnormal state of the flexible direct-current power distribution network can be distinguished: when the transient zero modulus and the high-frequency component do not exist in the characteristic modal component, judging that the system is in a normal state; when the transient zero modulus and the high-frequency component exist in the characteristic modal component, the system is judged to be in an abnormal operation state, so that a distinguishing criterion needs to be further established, and the following 4 states are further distinguished: small resistance earth fault, medium resistance earth fault, high resistance earth fault and load switching;
and step 3: calculating Euclidean distance of the characteristic modal components, and converting the Euclidean distance into gray level representation;
1) let the characteristic modal component under normal conditions be denoted as θ as the reference componentc(0)＝[u1(0)，u2(0)，...，un-1(0)，un(0)]The characteristic modal component of the small-resistance ground fault is represented by thetac(1)＝[u1(1)，u2(1)，...，un-1(1)，un(1)]The characteristic modal component of the medium resistance ground fault is represented by θc(2)＝[u1(2)，u2(2)，...，un-1(2)，un(2)]The characteristic modal component of the high resistance ground fault is represented as θc(3)＝[u1(3)，u2(3)，...，un-1(3)，un(3)]Subtracting the characteristic modal components of the small resistance ground fault, the medium resistance ground fault and the high resistance ground fault from the characteristic modal components under the normal condition to obtain the absolute value of the vector sum of the characteristic modal components as follows:
Δun(k)＝|un(0)-un(k)|，k＝1，2，3
in the formula un(0) Is a characteristic modal component in the normal condition, Δ un(1) Is the vector sum absolute value, Deltau, of the characteristic modal component of the small-resistance ground faultn(2) Is the vector sum absolute value, Deltau, of the characteristic modal component of the medium-impedance earth faultn(3) Is the absolute value of the vector sum of the high resistance ground fault characteristic modal components; n is a natural number greater than 0;
absolute value Delauu from the sum of characteristic modal component vectorsn(k) Obtaining the euclidean distance ed (k):
Figure GSB0000195665140000051
2) the euclidean distance ed (k) is expressed in grayscale ρ (k) as:
ρ(k)＝ξ-ξED(k)，k＝1，2，3
in the formula, xi is an identification coefficient, and xi takes the value of 5;
3) low resistance ground fault gray scale is expressed as ρSIF(t)＝[ρSIF(1)，ρSIF(2)，...，ρSIF(n)]The medium resistance ground fault gray scale is expressed as rhoMIF(t)＝[ρMIF(1)，ρMIF(2)，...，ρMIF(n)]The high resistance ground fault gray scale is expressed as ρHIF(t)＝[ρHIF(1)，ρHIF(2)，...，ρHIF(n)]The three variable expressions of the mean value of the small-resistance ground fault, the medium-resistance ground fault and the high-resistance ground fault are respectively as follows:
the mean value of the small resistance ground fault gray levels is:
Figure GSB0000195665140000052
the mean value of the gray levels of the medium-resistance ground faults is as follows:
Figure GSB0000195665140000061
the mean value of the high-resistance ground fault gray levels is:
Figure GSB0000195665140000062
4) taking the maximum value and the minimum value of the mean value of the gray levels of the small-resistance ground fault, the medium-resistance ground fault and the high-resistance ground fault, and setting the maximum value rho of the mean value of the gray levelsmaxWith a minimum value pminThe expressions for the two variables are:
ρmax＝max[ρaveSIF，ρaveMIF，ρaveHIF]
ρmin＝min[ρaveSIF，ρaveMIF，ρaveHIF]
subtracting the maximum value of the gray level average value from the minimum value of the gray level average value to obtain:
Δρ＝ρmax-ρmin，ρmin≠ρmax，ρmax≠0
and 4, step 4: constructing a red-green-blue space model for the obtained mean value of the small-resistance earth fault gray level, the mean value of the medium-resistance earth fault gray level and the mean value of the high-resistance earth fault gray level, converting the red-green-blue space model into a hexagonal pyramid space model for analysis, wherein a method based on the conversion of the red-green-blue space model and the hexagonal pyramid space model is called a color relation classifier, and the specific steps of the color relation classifier are as follows;
1) the red, green and blue space model expression obtained from step 3 is:
Figure GSB0000195665140000063
Figure GSB0000195665140000064
Figure GSB0000195665140000071
wherein r represents a red color value, g represents a green color value, and b represents a blue color value;
2) converting the red, green and blue space model into a hexagonal pyramid space model by adopting a color relation classifier, and obtaining:
Figure GSB0000195665140000072
V＝ρmax，
Figure GSB0000195665140000073
wherein H belongs to [0, 360], H represents hue, V represents lightness value, and S represents saturation;
based on this, the constructed distinguishing criterion 1 is: when S is more than 0.5 and less than 1, judging that the ground fault occurs; when S is more than or equal to 0.5 or less than or equal to 1, judging load switching, and distinguishing load switching and ground faults;
further, a distinguishing criterion 2 is constructed: distinguishing small resistance earth faults, medium resistance earth faults and high resistance earth faults; when S is more than 0.5 and less than 1 and the color displayed by the H value is blue, judging that high-resistance grounding fault occurs; when S is more than 0.5 and less than 1 and the color displayed by the H value is red, judging that the small resistance ground fault occurs; and when S is more than 0.5 and less than 1 and the color displayed by the H value is green, judging that the medium resistance grounding fault occurs.
Compared with the prior art, the fault detection method has the advantages of flexible inference model, high fault detection reliability, convenient embedding of the color relation classifier model into equipment, realization of real-time monitoring, overcoming of complexity of the fault detection process and improvement of the calculation speed.
Drawings
FIG. 1 is a flow chart of the detection method of the present invention.
Detailed Description
The high-resistance grounding fault detection method based on the color relation classifier comprises the following implementation steps:
step 1: extracting transient zero-mode current of the flexible direct-current power distribution network;
transient zero-mode current i0(t) is obtained by the following formula:
Figure GSB0000195665140000081
in the formula ip(t)、in(t) is the positive and negative currents of the flexible direct current distribution network respectively, and t represents time;
i0(t) the circulation directions of the positive electrode and the negative electrode are the same, and a loop is formed by passing through a grounding point; the structure of the direct current system zero mode network is related to the wiring mode of the transformer, the grounding mode of the neutral point and the grounding point position of the direct current system;
step 2: the method adopts a variational modal decomposition algorithm to extract characteristic modal components, and specifically comprises the following steps:
1) converting the transient zero-mode current signal i0(t) decomposition into K modal components uk(t) and each modal component is a finite bandwidth with a center frequency, the center frequency and finite bandwidth being continuously updated during the decomposition process, for uk(t) the single-sided spectrum of the signal can be obtained using the hilbert transform:
Figure GSB0000195665140000082
wherein K is a natural number, and K is 1, 2.,; δ (t) denotes a step function, uk(t) represents i0(t) decomposition into K modal components;
2) single-sided spectrum of signal multiplied by estimated center frequency
Figure GSB0000195665140000083
The following can be obtained:
Figure GSB0000195665140000084
3) computing
Figure GSB0000195665140000091
Square of gradient of (3) L2Norm to obtain each modal component uk(t) limited bandwidth, constructing a mathematical model of the variational modal constraints problem:
Figure GSB0000195665140000092
in the formula, δ represents a dirac distribution, { μ, represents a convolutionkIs the set of all modal components (μ) decomposed1，μ2，…，μk}，
Figure GSB0000195665140000093
Is the set of center frequencies of each modal component
Figure GSB0000195665140000094
Figure GSB0000195665140000095
Is a constraint condition of the reconstruction accuracy,
Figure GSB0000195665140000099
representing a gradient, | | | | represents a norm,
Figure GSB0000195665140000096
represents [ mu ]kThe sum of modal components;
4) the solution of the variational modal constraint problem comprises a solution process and a secondary optimization process;
the solution of the variational modal constraint problem specifically comprises the following steps:
a) introducing Lagrange multiplication operators and secondary punishment factors to the variational modal constraint problem to obtain an expanded Lagrange expression:
Figure GSB0000195665140000097
in the formula, alpha represents a secondary penalty factor to ensure the reconstruction precision of the signal, and lambda (t) represents a Lagrange multiplication operator to strictly require constraint conditions;
b) adopting an alternating direction multiplier algorithm to solve optimization iteration to obtain a saddle point of the extended Lagrange expression, and specifically comprising the following steps:
initialization
Figure GSB0000195665140000098
{λ1And n;
executing a loop: n is n + 1;
③ all
Figure GSB0000195665140000101
Updating muk，
Figure GSB0000195665140000102
And λ, the three expressions are:
Figure GSB0000195665140000103
Figure GSB0000195665140000104
Figure GSB0000195665140000105
in the formula (I), the compound is shown in the specification,
Figure GSB0000195665140000106
are respectively muk(t)，λ(t)，
Figure GSB0000195665140000107
N is the number of optimization iterations;
fourthly, repeating the step III and the step III until the iteration stop condition
Figure GSB0000195665140000108
Stopping iteration to obtain K modal components;
analyzing K modal components, wherein the K modal components are related to a transient zero mode current signal i0(t) the modal component with the maximum correlation coefficient is used as the characteristic modal component, and different characteristics of a normal state and an abnormal state can be obtained, so that the normal state and the abnormal state of the flexible direct-current power distribution network can be distinguished: when the transient zero modulus and the high-frequency component do not exist in the characteristic modal component, judging that the system is in a normal state; when the transient zero modulus and the high-frequency component exist in the characteristic modal component, the system is judged to be in an abnormal operation state, so that a distinguishing criterion needs to be further established, and the following 4 states are further distinguished: small resistance earth fault, medium resistance earth fault, high resistance earth fault and load switching;
and step 3: calculating Euclidean distance of the characteristic modal components, and converting the Euclidean distance into gray level representation;
1) let the characteristic modal component under normal conditions be denoted as θ as the reference componentc(0)＝[u1(0)，u2(0)，...，un-1(0)，un(0)]The characteristic modal component of the small-resistance ground fault is represented by thetac(1)＝[u1(1)，u2(1)，...，un-1(1)，un(1)]The characteristic modal component of the medium resistance ground fault is represented by θc(2)＝[u1(2)，u2(2)，...，un-1(2)，un(2)]The characteristic modal component of the high resistance ground fault is represented as θc(3)＝[u1(3)，u2(3)，...，un-1(3)，un(3)]Subtracting the characteristic modal components of the small resistance ground fault, the medium resistance ground fault and the high resistance ground fault from the characteristic modal components under the normal condition to obtain the absolute value of the vector sum of the characteristic modal components as follows:
Δun(k)＝|un(0)-un(k)|，k＝1，2，3
in the formula un(0) Is a characteristic modal component in the normal condition, Δ un(1) Is the vector sum absolute value, Deltau, of the characteristic modal component of the small-resistance ground faultn(2) Is the vector sum absolute value, Deltau, of the characteristic modal component of the medium-impedance earth faultn(3) Is the absolute value of the vector sum of the high resistance ground fault characteristic modal components; n is a natural number greater than 0;
absolute value Delauu from the sum of characteristic modal component vectorsn(k) Obtaining the euclidean distance ed (k):
Figure GSB0000195665140000111
2) the euclidean distance ed (k) is expressed in grayscale ρ (k) as:
ρ(k)＝ξ-ξED(k)，k＝1，2，3
in the formula, xi is an identification coefficient, and xi takes the value of 5;
3) low resistance ground fault gray scale is expressed as ρSIF(t)＝[ρSIF(1)，ρSIF(2)，...，ρSIF(n)]The medium resistance ground fault gray scale is expressed as rhoMIF(t)＝[ρMIF(1)，ρMIF(2)，...，ρMIF(n)]The high resistance ground fault gray scale is expressed as ρHIF(t)＝[ρHIF(1)，ρHIF(2)，...，ρHIF(n)]The three variable expressions of the mean value of the small-resistance ground fault, the medium-resistance ground fault and the high-resistance ground fault are respectively as follows:
the mean value of the small resistance ground fault gray levels is:
Figure GSB0000195665140000121
the mean value of the gray levels of the medium-resistance ground faults is as follows:
Figure GSB0000195665140000122
the mean value of the high-resistance ground fault gray levels is:
Figure GSB0000195665140000123
4) taking the maximum value and the minimum value of the mean value of the gray levels of the small-resistance ground fault, the medium-resistance ground fault and the high-resistance ground fault, and setting the maximum value rho of the mean value of the gray levelsmaxWith a minimum value pminThe expressions for the two variables are:
ρmax＝max[ρaveSIF，ρaveMIF，ρaveHIF]
ρmin＝min[ρaveSIF，ρaveMIF，ρaveHIF]
subtracting the maximum value of the gray level average value from the minimum value of the gray level average value to obtain:
Δρ＝ρmax-ρmin.ρmin≠ρmax，ρmax≠0
and 4, step 4: constructing a red-green-blue space model for the obtained mean value of the small-resistance earth fault gray level, the mean value of the medium-resistance earth fault gray level and the mean value of the high-resistance earth fault gray level, converting the red-green-blue space model into a hexagonal pyramid space model for analysis, wherein a method based on the conversion of the red-green-blue space model and the hexagonal pyramid space model is called a color relation classifier, and the specific steps of the color relation classifier are as follows;
1) the red, green and blue space model expression obtained from step 3 is:
Figure GSB0000195665140000124
Figure GSB0000195665140000131
Figure GSB0000195665140000132
wherein r represents a red color value, g represents a green color value, and b represents a blue color value;
2) converting the red, green and blue space model into a hexagonal pyramid space model by adopting a color relation classifier, and obtaining:
Figure GSB0000195665140000133
V＝ρmax，
Figure GSB0000195665140000134
wherein H belongs to [0, 360], H represents hue, V represents lightness value, and S represents saturation;
based on this, the constructed distinguishing criterion 1 is: when S is more than 0.5 and less than 1, judging that the ground fault occurs; when S is more than or equal to 0.5 or less than or equal to 1, judging load switching, and distinguishing load switching and ground faults;
further, a distinguishing criterion 2 is constructed: distinguishing small resistance earth faults, medium resistance earth faults and high resistance earth faults; when S is more than 0.5 and less than 1 and the color displayed by the H value is blue, judging that high-resistance grounding fault occurs; when S is more than 0.5 and less than 1 and the color displayed by the H value is red, judging that the small resistance ground fault occurs; and when S is more than 0.5 and less than 1 and the color displayed by the H value is green, judging that the medium resistance grounding fault occurs.

Claims (1)

1. A high-resistance grounding fault detection method for a flexible direct-current power distribution network is characterized by comprising the following steps:
step 1: extracting transient zero-mode current of the flexible direct-current power distribution network;
transient zero-mode current i0(t) is obtained by the following formula:
Figure FSB0000195665130000011
in the formula ip(t)、in(t) is the positive and negative currents of the flexible direct current distribution network respectively, and t represents time;
i0(t) the circulation directions of the positive electrode and the negative electrode are the same, and a loop is formed by passing through a grounding point; the structure of the zero-mode network of the DC system and the wiring mode of the transformer,The grounding mode of the neutral point is related to the grounding point position of the direct current system;
step 2: the method adopts a variational modal decomposition algorithm to extract characteristic modal components, and specifically comprises the following steps:
1) converting the transient zero-mode current signal i0(t) decomposition into K modal components uk(t) and each modal component is a finite bandwidth with a center frequency, the center frequency and finite bandwidth being continuously updated during the decomposition process, for uk(t) the single-sided spectrum of the signal can be obtained using the hilbert transform:
Figure FSB0000195665130000012
wherein K is a natural number, and K is 1, 2.,; δ (t) denotes a step function, uk(t) represents i0(t) decomposition into K modal components;
2) single-sided spectrum of signal multiplied by estimated center frequency
Figure FSB0000195665130000013
The following can be obtained:
Figure FSB0000195665130000014
3) computing
Figure FSB0000195665130000021
Square of gradient of (3) L2Norm to obtain each modal component uk(t) limited bandwidth, constructing a mathematical model of the variational modal constraints problem:
Figure FSB0000195665130000022
in the formula, δ represents a dirac distribution, { μ, represents a convolutionkIs the set of all modal components (μ) decomposed1，μ2，…，μk}，
Figure FSB0000195665130000023
Is the set of center frequencies of each modal component
Figure FSB0000195665130000024
Figure FSB0000195665130000025
Is a constraint condition of the reconstruction accuracy,
Figure FSB0000195665130000026
representing a gradient, | | | | represents a norm,
Figure FSB0000195665130000027
represents [ mu ]kThe sum of modal components;
4) the solution of the variational modal constraint problem specifically comprises the following steps:
a) introducing Lagrange multiplication operators and secondary punishment factors to the variational modal constraint problem to obtain an expanded Lagrange expression:
Figure FSB0000195665130000028
in the formula, alpha represents a secondary penalty factor, and lambda (t) represents a Lagrange multiplier;
b) solving by adopting an alternating direction multiplier algorithm to obtain K modal components;
analyzing K modal components, wherein the K modal components are related to a transient zero mode current signal i0(t) the modal component with the maximum correlation coefficient is used as the characteristic modal component, and different characteristics of a normal state and an abnormal state can be obtained, so that the normal state and the abnormal state of the flexible direct-current power distribution network can be distinguished: when the transient zero modulus and the high-frequency component do not exist in the characteristic modal component, judging that the system is in a normal state; when transient zero modulus exists in characteristic modal component and high frequency component existsIf the system is judged to be in an abnormal operation state, therefore, a distinguishing criterion needs to be further established to further distinguish the following 4 states: small resistance earth fault, medium resistance earth fault, high resistance earth fault and load switching;
and step 3: calculating Euclidean distance of the characteristic modal components, and converting the Euclidean distance into gray level representation;
1) let the characteristic modal component under normal conditions be denoted as θ as the reference componentc(0)＝[u1(0)，u2(0)，...，un-1(0)，un(0)]The characteristic modal component of the small-resistance ground fault is represented by thetac(1)＝[u1(1)，u2(1)，...，un-1(1)，un(1)]The characteristic modal component of the medium resistance ground fault is represented by θc(2)＝[u1(2)，u2(2)，...，un-1(2)，un(2)]The characteristic modal component of the high resistance ground fault is represented as θc(3)＝[u1(3)，u2(3)，...，un-1(3)，un(3)]Subtracting the characteristic modal components of the small resistance ground fault, the medium resistance ground fault and the high resistance ground fault from the characteristic modal components under the normal condition to obtain the absolute value of the vector sum of the characteristic modal components as follows:
Δun(k)＝|un(0)-un(k)|，k＝1，2，3
in the formula un(0) Is a characteristic modal component in the normal condition, Δ un(1) Is the vector sum absolute value, Deltau, of the characteristic modal component of the small-resistance ground faultn(2) Is the vector sum absolute value, Deltau, of the characteristic modal component of the medium-impedance earth faultn(3) Is the absolute value of the vector sum of the high resistance ground fault characteristic modal components; n is a natural number greater than 0;
absolute value Delauu from the sum of characteristic modal component vectorsn(k) Obtaining the euclidean distance ed (k):
Figure FSB0000195665130000031
2) the euclidean distance ed (k) is expressed in grayscale ρ (k) as:
ρ(k)＝ξ-ξED(k)，k＝1，2，3
in the formula, xi is an identification coefficient, and xi takes the value of 5;
3) low resistance ground fault gray scale is expressed as ρSIF(t)＝[ρSIF(1)，ρSIF(2)，...，ρSIF(n)]The medium resistance ground fault gray scale is expressed as rhoMIF(t)＝[ρMIF(1)，ρMIF(2)，...，ρMIF(n)]The high resistance ground fault gray scale is expressed as ρHIF(t)＝[ρHIF(1)，ρHIF(2)，...，ρHIF(n)]The three variable expressions of the mean value of the small-resistance ground fault, the medium-resistance ground fault and the high-resistance ground fault are respectively as follows:
the mean value of the small resistance ground fault gray levels is:
Figure FSB0000195665130000041
the mean value of the gray levels of the medium-resistance ground faults is as follows:
Figure FSB0000195665130000042
the mean value of the high-resistance ground fault gray levels is:
Figure FSB0000195665130000043
4) taking the maximum value and the minimum value of the mean value of the gray levels of the small-resistance ground fault, the medium-resistance ground fault and the high-resistance ground fault, and setting the maximum value rho of the mean value of the gray levelsmaxWith a minimum value pminThe expressions for the two variables are:
ρmax＝max[ρaveSIF，ρaveMIF，ρaveHIF]
ρmin＝min[ρaveSIF，ρaveMIF，ρaveHIF]
subtracting the maximum value of the gray level average value from the minimum value of the gray level average value to obtain:
Δρ＝ρmax-ρmin，ρmin≠ρmax，ρmax≠0
and 4, step 4: constructing a red-green-blue space model for the obtained mean value of the small-resistance earth fault gray level, the mean value of the medium-resistance earth fault gray level and the mean value of the high-resistance earth fault gray level, converting the red-green-blue space model into a hexagonal pyramid space model for analysis, wherein a method based on the conversion of the red-green-blue space model and the hexagonal pyramid space model is called a color relation classifier, and the specific steps of the color relation classifier are as follows;
1) the red, green and blue space model expression obtained from step 3 is:
Figure FSB0000195665130000051
wherein r represents a red color value, g represents a green color value, and b represents a blue color value;
2) converting the red, green and blue space model into a hexagonal pyramid space model by adopting a color relation classifier, and obtaining:
Figure FSB0000195665130000052
Figure FSB0000195665130000053
wherein H belongs to [0, 360], H represents hue, V represents lightness value, and S represents saturation;
based on this, the constructed distinguishing criterion 1 is: when S is more than 0.5 and less than 1, judging that the ground fault occurs; when S is more than or equal to 0.5 or less than or equal to 1, judging load switching, and distinguishing load switching and ground faults;
further, a distinguishing criterion 2 is constructed: distinguishing small resistance earth faults, medium resistance earth faults and high resistance earth faults; when S is more than 0.5 and less than 1 and the color displayed by the H value is blue, judging that high-resistance grounding fault occurs; when S is more than 0.5 and less than 1 and the color displayed by the H value is red, judging that the small resistance ground fault occurs; and when S is more than 0.5 and less than 1 and the color displayed by the H value is green, judging that the medium resistance grounding fault occurs.
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