CN110297140B - Fault prediction method and device of power distribution system - Google Patents

Fault prediction method and device of power distribution system Download PDF

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CN110297140B
CN110297140B CN201910574964.XA CN201910574964A CN110297140B CN 110297140 B CN110297140 B CN 110297140B CN 201910574964 A CN201910574964 A CN 201910574964A CN 110297140 B CN110297140 B CN 110297140B
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voltage
distribution system
power distribution
interval
fault prediction
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CN110297140A (en
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张佳为
赵玉飞
杨向东
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Beijing Machinery Equipment Research Institute
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
    • G01R31/086—Locating faults in cables, transmission lines, or networks according to type of conductors in power transmission or distribution networks, i.e. with interconnected conductors

Abstract

The invention relates to aA fault prediction method and a fault prediction device for a power distribution system belong to the technical field of fault prediction and solve the problem that the conventional prediction method cannot realize fault prediction based on historical data. The method comprises the following steps: collecting output voltage of power distribution system to form voltage sample set, calculating sample set mean value
Figure DDA0002111859360000012
And the variance S of the sample2Obtaining a confidence interval of the expected mu and the standard deviation sigma when the confidence level is 1-alpha; when a new voltage sample is collected, forming a new voltage sample set together with the voltage sample set at the previous moment, and calculating the confidence intervals of mu and sigma when the confidence level is 1-alpha under the new voltage sample set; repeating the above process to obtain continuous confidence intervals of μ and σ of several voltage sample sets, and taking the confidence intervals of μ and σ of the voltage sample sets if the confidence intervals are stable in the preset fluctuation range
Figure DDA0002111859360000011
σ2＝S2And obtaining a voltage output interval of the power distribution system in a normal working state, and realizing the fault prediction of the power distribution system according to the voltage output interval in the normal working state.

Description

Fault prediction method and device of power distribution system
Technical Field
The invention relates to the technical field of fault prediction, in particular to a fault prediction method and device of a power distribution system.
Background
The failure prediction is defined as that the electrical equipment is forecasted before failure by a technical means, and the failure prediction mechanism is that before the failure of the electrical equipment, partial internal systems or components of the electrical equipment deviate from a normal working range, although the operation of the system can be still ensured and the output in an index can be kept, as the operation time goes on, the deviation of the internal systems or components from the normal working range is more serious until the system fails. The failure prediction is to monitor the slight difference inside the system by technical means before the system failure, so as to achieve the purposes of early prediction, early preparation and early maintenance, and prevent the sudden system failure in the future.
The existing failure prediction means mostly adopt a mode of increasing the hardware arrangement of a sensor to perform data real-time interpretation on a plurality of parts which are possibly failed in a system, although the method improves the current situation that the whole electric system is used as a black box system to a certain extent, the system design and production cost is greatly increased, in addition, the local real-time data interpretation can ensure that the system fails to ensure the local failure of the system even if the system further fails in a larger range, and therefore the mode still cannot achieve the purposes of 'early prediction' and 'early maintenance'.
Through the above, the existing fault prediction has the limitation that more detection points are established in the electrical system, so that the signal acquisition range at the same moment is expanded, and the analysis and diagnosis are carried out through online monitoring essentially; the fault phenomena and factors around the events are emphasized, but the action process under the complex working condition is ignored, and the dynamic operation characteristics of the system cannot be adapted. In summary, the conventional method ignores the dynamic operation characteristic of the historical system output data to the system, and fails to realize the real fault prediction without comprehensively adopting a data processing means and the historical output data to analyze the operation state of the system.
Disclosure of Invention
In view of the above analysis, the present invention aims to provide a method and an apparatus for predicting faults of a power distribution system, so as to solve the problem that the existing prediction method does not comprehensively adopt a data processing means and historical output data to analyze the operation state of the system, and cannot realize the true fault prediction.
The purpose of the invention is mainly realized by the following technical scheme:
a method of fault prediction for an electrical distribution system, comprising the steps of:
continuously collecting voltage sample X output by power distribution system1,X2,...,XnTo form a set of voltage samples that satisfy N (μ, σ)2) A distribution in which the expected μ and the standard deviation σ are unknowns;
calculating the voltage samplesMean value of the album
Figure BDA0002111859340000022
And variance S2Respectively obtaining confidence intervals of the expected mu and the standard deviation sigma when the confidence level is 1-alpha;
when a new voltage sample is collected, the new voltage sample set and the voltage sample set at the previous moment form a new voltage sample set, and the calculation steps are repeated to obtain a confidence interval of the expected mu and the standard deviation sigma when the confidence level of the new voltage sample set is 1-alpha;
repeating the new voltage sample collection and calculation process to obtain confidence intervals of the expected mu and the standard deviation sigma of the continuous voltage sample sets, and taking the confidence intervals of the expected mu and the standard deviation sigma of the continuous voltage sample sets when the confidence intervals are stable within a preset fluctuation range
Figure BDA0002111859340000021
σ2＝S2；
And determining a voltage output interval of the power distribution system in a normal working state according to the mu and the sigma, and realizing the fault prediction of the power distribution system according to the voltage output interval in the normal working state.
On the basis of the scheme, the invention is further improved as follows:
further, the confidence interval for the expected μ at a confidence level of 1- α is obtained by the following formula:
Figure BDA0002111859340000031
the confidence interval for μ at a confidence level of 1- α is then:
Figure BDA0002111859340000032
further, the confidence interval of the standard deviation σ at a confidence level of 1- α is obtained by the following formula:
Figure BDA0002111859340000033
the confidence interval for the standard deviation σ with a confidence level of 1- α is then:
Figure BDA0002111859340000034
further, it is determined that the confidence intervals of the expected μ and standard deviation σ for the successive sets of several voltage samples are each stable within a predetermined fluctuation range by:
confidence intervals of the expected mu and standard deviation sigma of the voltage sample sets respectively meet the condition that the deviation of the upper boundary value from the average value of the upper boundary is less than 0.1, and the deviation of the lower boundary value from the average value of the lower boundary is less than 0.1.
Further, a confidence level 1- α is set to 0.9.
Further, the voltage output interval of the power distribution system in the normal working state is determined by the following formula:
Figure BDA0002111859340000035
the interval of the output voltage x in the normal working state of the power distribution system is as follows: x is an element (mu-sigma. z)0.1/2,μ+σ·z0.1/2)。
Further, the fault prediction of the power distribution system is realized according to the voltage output interval in the normal working state, and the fault prediction comprises the following steps:
if the voltage output value of the power distribution system exceeds the voltage output interval in the normal working state, accumulating 100 voltage output values by taking the current voltage output value as a starting point, and calculating the average value of the 100 voltage output values
Figure BDA0002111859340000041
If it is
Figure BDA0002111859340000042
And if the voltage exceeds the voltage output interval of the power distribution system in the normal working state, judging that the power distribution system has a fault.
Further, or by implementing fault prediction for the power distribution system by:
after a voltage output interval of the power distribution system in a normal working state is determined, emptying the voltage sample set;
the voltage samples are collected again, each time one voltage sample is collected, a new voltage sample set is formed together with the voltage sample set at the previous moment, and the mean value of the sample sets is calculated
Figure BDA0002111859340000043
Sum variance S2(ii) a Mean of 100 groups per accumulation
Figure BDA0002111859340000045
And the variance S of the sample2Then, respectively calculate
Figure BDA0002111859340000044
And S2Average value of (2), average value of current calculation
Figure BDA0002111859340000046
Sample variance S2And respectively making differences with the average value, and if any difference value is greater than 0.2, judging that the power distribution system has faults.
The invention also discloses a fault prediction device of the power distribution system, and the system comprises: the device comprises a voltage acquisition module, a voltage processing module and a fault prediction module; wherein the content of the first and second substances,
the voltage acquisition module is used for acquiring the output voltage of the power distribution system;
the voltage processing module is used for executing the following operations to obtain a voltage output interval of the power distribution system in a normal working state:
continuously collecting voltage sample X output by power distribution system1,X2,...,XnTo form a set of voltage samples that satisfy N (μ, σ)2) A distribution wherein the desired μ and the standardThe difference sigma is an unknown quantity;
calculating a mean of the set of voltage samples
Figure BDA0002111859340000047
And variance S2Respectively obtaining confidence intervals of the expected mu and the standard deviation sigma when the confidence level is 1-alpha;
when a new voltage sample is collected, the new voltage sample set and the voltage sample set at the previous moment form a new voltage sample set, and the calculation steps are repeated to obtain a confidence interval of the expected mu and the standard deviation sigma when the confidence level of the new voltage sample set is 1-alpha;
repeating the new voltage sample collection and calculation process to obtain confidence intervals of the expected mu and the standard deviation sigma of the continuous voltage sample sets, and taking the confidence intervals of the expected mu and the standard deviation sigma of the continuous voltage sample sets when the confidence intervals are stable within a preset fluctuation range
Figure BDA0002111859340000051
σ ═ S; determining a voltage output interval of the power distribution system in a normal working state according to the mu and the sigma;
and the fault prediction module is used for realizing the fault prediction of the power distribution system according to the voltage output interval in the normal working state.
On the basis of the scheme, the invention is further improved as follows:
further, the failure prediction module performs the following operations to implement failure prediction:
if the voltage output value of the power distribution system exceeds the voltage output interval in the normal working state, accumulating 100 voltage output values by taking the current voltage output value as a starting point, and calculating the average value of the 100 voltage output values
Figure BDA0002111859340000052
If it is
Figure BDA0002111859340000053
Beyond the normal operation of the distribution systemJudging the power distribution system fault in a voltage output interval under the state; alternatively, the first and second electrodes may be,
after a voltage output interval of the power distribution system in a normal working state is determined, emptying the voltage sample set; the voltage samples are collected again, each time one voltage sample is collected, a new voltage sample set is formed together with the voltage sample set at the previous moment, and the mean value of the sample sets is calculated
Figure BDA0002111859340000054
Sum variance S2(ii) a Mean of 100 groups per accumulation
Figure BDA0002111859340000055
And the variance S of the sample2Then, respectively calculate
Figure BDA0002111859340000056
And S2Average value of (2), average value of current calculation
Figure BDA0002111859340000057
Sample variance S2And respectively making differences with the average value, and if any difference value is greater than 0.2, judging that the power distribution system has faults.
The invention has the following beneficial effects:
according to the fault prediction method of the power distribution system, the distribution characteristics met by the output voltage data of the power distribution system are obtained through analysis based on the output voltage data of the power distribution system, and fault prediction is achieved according to the distribution characteristics. According to the method, a probability analysis process is introduced into the fault prediction of the power distribution system, the operation state of the system can be analyzed by adopting a data processing means and historical output data, and the problem of the real fault prediction is realized. The method has a self-learning characteristic, and as data is increased, the power distribution system presents estimation convergence and estimation is more accurate, and the algorithm is to be popularized to other similar systems meeting normal distribution. The method embodiment and the device embodiment are based on the same principle, and the related parts can be referenced mutually, and the same technical effect can be achieved.
In the invention, the technical schemes can be combined with each other to realize more preferable combination schemes. Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.
FIG. 1 is a graph of a normal distribution;
FIG. 2 is a flow chart of a method for fault prediction in a power distribution system in accordance with an embodiment of the present invention;
FIG. 3 is a diagram of a power distribution system voltage sampling in accordance with an embodiment of the present invention;
FIG. 4 is a diagram of the mean value of the distribution system in the embodiment of the present invention
Figure BDA0002111859340000061
A change curve;
FIG. 5 shows the variance S in an embodiment of the present invention2A change curve;
FIG. 6 is a graph of expected μ confidence interval variation in an embodiment of the present invention
FIG. 7 shows the variance σ in an embodiment of the present invention2Confidence interval change curve.
Detailed Description
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate preferred embodiments of the invention and together with the description, serve to explain the principles of the invention and not to limit the scope of the invention.
First, the following description will be made of the related art used in the present embodiment:
N(μ,σ2): normal distribution with an expectation of μ and variance σ2；
Expected μ and mean of sample
Figure BDA00021118593400000714
The difference of (1): one total of X ═ X1,…,XnSample expectation
Figure BDA0002111859340000071
Since the total sample X has more elements, in practical application, one total sample (i.e. a set composed of partial total elements) is often used
Figure BDA0002111859340000072
Wherein X1,…,XiElements which are all total X, then mean
Figure BDA0002111859340000073
When the sample of the population approximates to the population X, the sample expects mu to approximate to the mean
Figure BDA0002111859340000074
And is
Figure BDA0002111859340000075
Unbiased estimation for μ;
sample variance S2And variance σ2The difference of (1): the variance of the population is the same as the expected mean
Figure BDA0002111859340000076
In practical applications, the total sample variance is often adopted
Figure BDA0002111859340000077
To approximate sigma2When the overall sample approaches the overall X, the sample variance S2Is approximated by the variance σ2And S is2Is σ2Unbiased estimation of (2);
unbiased estimation: unbiased estimation refers to that there is no system deviation between an estimator and a true value, only random deviation exists, and the value is the true value when the average value of all estimation values of the system is obtained. I.e. as long as the sample is sufficiently large, S2＝σ2，
Figure BDA0002111859340000078
Pivot amount: starting from a point estimate of μ, a function G (i.e., the pivot quantity in this text) is constructed with respect to μ
Figure BDA0002111859340000079
) The distribution of this function G is known and independent of μ. Amount of pivot in text
Figure BDA00021118593400000710
Obeying t distribution, and having no relation with mu, so that the confidence interval of mu can be obtained through the setting of the pivot quantity;
confidence interval: for an unknown parameter μ, if for a given constant α, (0 < α < 1), the upper limit is determined
Figure BDA00021118593400000711
And lower limitμSo that μ is in the interval
Figure BDA00021118593400000712
The probability of occurrence is 1-alpha, the interval
Figure BDA00021118593400000713
A confidence interval referred to as unknown parameter μ;
zα/2: represents a normal distribution N (0,1), μ ═ 0, σ2Given a confidence interval 1- α, the boundary values taken for sample X are shown in fig. 1. For a determined value of alpha, zα/2The value is a fixed value, can be obtained by table lookup, and can also be obtained by programming.
t (n): representing a t distribution with the number of samples n; chi shape2(n): χ representing number of samples n2Distributing;
t distribution, χ2The distributions are all converted to normal distributions in this patent, which is a well-known art in this field.
The embodiment of the invention discloses a fault prediction method and a fault prediction device for a power distribution system, and a flow chart is shown in fig. 2 and comprises the following steps:
a) continuously collecting voltage sample X output by power distribution system1,X2,...,XnTo form a set of voltage samples that satisfy N (μ, σ)2) A distribution in which the expected μ and the standard deviation σ are unknowns; setting a system confidence level 1-alpha to be 0.9;
calculating a mean of the set of voltage samples
Figure BDA0002111859340000081
And variance S2(ii) a Wherein the content of the first and second substances,
Figure BDA0002111859340000082
b) calculate the confidence interval for the expected μ at a confidence level of 1- α, due to the sample variance S2Is σ2Is estimated unbiased, so will
Figure BDA0002111859340000083
To
Figure BDA0002111859340000084
Due to the fact that
Figure BDA0002111859340000085
Get
Figure BDA0002111859340000086
As a pivot measure, get
Figure BDA0002111859340000087
Namely, it is
Figure BDA0002111859340000088
Then a confidence interval of 1-alpha for the desired μ confidence level is
Figure BDA0002111859340000089
T is t when n is more than 45α≈zαWherein z isαTo obey a normal distribution of N (0,1), the system calculates the system expected confidence interval from sample points N > 45, respectively, and therefore the above interval range can also be expressed as:
μ confidence lower limit interval:
Figure BDA0002111859340000091
upper μ confidence interval limit:
Figure BDA0002111859340000092
c) the confidence interval of the expected μ and standard deviation σ for a confidence level of 1- α is calculated, since
Figure BDA0002111859340000093
Get
Figure BDA0002111859340000094
As a pivot amount, then
Figure BDA0002111859340000095
Namely, it is
Figure BDA0002111859340000096
The confidence interval with a confidence level of 1-alpha is then
Figure BDA0002111859340000097
Since n is greater than 45
Figure BDA0002111859340000098
Wherein z isαIs positive obeying N (0,1)The state distribution, so the system calculates the system variance confidence interval after the sampling point n > 45, the calculation formula can also be expressed as:
σ confidence interval lower bound:
Figure BDA0002111859340000099
σ confidence interval upper bound:
Figure BDA00021118593400000910
d) collecting output voltage samples of the power distribution system in real time, repeating the steps b) and c) until 10 sample quantities are increased, respectively calculating the average values of upper and lower boundary values of a confidence interval, and when the difference between the upper boundary value corresponding to the mu confidence interval and the sigma confidence interval and the average value of the 10 upper boundary values is less than 0.1 and the difference between the lower boundary value and the average value of the 10 lower boundary values is less than 0.1, determining that the confidence interval of the mu and the sigma is stable,
Figure BDA0002111859340000101
can be identified as the desired μ of the distribution system output voltage; s can be regarded as the standard deviation sigma of the output voltage of the power distribution system;
e) due to the fact that
Figure BDA0002111859340000102
Push button
Figure BDA0002111859340000103
Determining high probability system outputs
Out of range (probability value set to 0.9), x e (μ - σ · z)0.1/2,μ+σ·z0.1/2) Wherein z is0.1/21.65, is the range value of the system output x, μ - σ · z0.1/2、μ+σ·z0.1/2Is the self-identifying boundary value of the system.
f) Predicting system fault information according to the following criteria; and if any one of the following two criteria is met, judging that the system monitors and alarms.
Mean of 100 groups per accumulation
Figure BDA0002111859340000104
And the variance S of the sample2Then, respectively calculate
Figure BDA0002111859340000105
And S2Average value of (2), average value of current calculation
Figure BDA0002111859340000106
Sample variance S2And respectively making differences with the average value, if any difference value is greater than 0.2, judging that an internal system of the power distribution system has an abnormal trend, and monitoring and alarming by the system.
Monitoring the output value of the system in real time, if the output value exceeds the self-identification boundary calculated in the step e), accumulating 100 output values by taking the output value as a starting point, and calculating the average value of the 100 output values
Figure BDA0002111859340000107
If it is
Figure BDA0002111859340000108
The system monitors for an alarm.
If the two criteria do not meet the conditions, judging that the current state of the system is normal, otherwise, judging that the power distribution system has a fault. Repeating steps a) to f) and continuously monitoring.
According to the fault prediction method of the power distribution system, the distribution characteristics met by the output voltage data of the power distribution system are obtained through analysis based on the output voltage data of the power distribution system, and fault prediction is achieved according to the distribution characteristics. According to the method, a probability analysis process is introduced into the fault prediction of the power distribution system, the operation state of the system can be analyzed by adopting a data processing means and historical output data, and the problem of the real fault prediction is realized. The method has a self-learning characteristic, and as data is increased, the power distribution system presents estimation convergence and estimation is more accurate, and the algorithm is to be popularized to other similar systems meeting normal distribution.
In another embodiment of the present invention, there is also provided a fault prediction apparatus of a power distribution system, the apparatus including: the device comprises a voltage acquisition module, a voltage processing module and a fault prediction module; the voltage acquisition module is used for acquiring the output voltage of the power distribution system; the voltage processing module is used for executing the following operations to obtain a voltage output interval of the power distribution system in a normal working state:
continuously collecting voltage sample X output by power distribution system1,X2,...,XnTo form a set of voltage samples that satisfy N (μ, σ)2) Distribution, wherein the desired μ and the variance σ2Is an unknown quantity;
calculating a mean of the set of voltage samples
Figure BDA0002111859340000112
And variance S2Respectively obtaining confidence intervals of the expected mu and the standard deviation sigma when the confidence level is 1-alpha;
when a new voltage sample is collected, the new voltage sample set and the voltage sample set at the previous moment form a new voltage sample set, and the calculation steps are repeated to obtain a confidence interval of the expected mu and the standard deviation sigma when the confidence level of the new voltage sample set is 1-alpha;
repeating the new voltage sample collection and calculation process to obtain confidence intervals of the expected mu and the standard deviation sigma of the continuous voltage sample sets, and taking the confidence intervals of the expected mu and the standard deviation sigma of the continuous voltage sample sets when the confidence intervals are stable within a preset fluctuation range
Figure BDA0002111859340000111
σ2＝S2(ii) a And according to the mu and the sigma2Determining a voltage output interval of the power distribution system in a normal working state; and the fault prediction module is used for realizing the fault prediction of the power distribution system according to the voltage output interval in the normal working state.
The specific implementation process of the device embodiment of the present invention may refer to the method embodiment described above, and this embodiment is not described herein again. Since the principle of the present embodiment is the same as that of the above method embodiment, the present system also has the corresponding technical effects of the above method embodiment.
The invention also carries out simulation analysis through the specific flow of monitoring the power distribution system. In the simulation results, fig. 3 shows the collection of the voltage output value of the power distribution system, and fig. 4 and 5 show the mean value of the voltage output of the power distribution system in the collection process
Figure BDA0002111859340000121
Variance S2The real-time calculation, the change curve graph is formed after a plurality of times of cyclic calculation, and the calculation process of each point in the curve corresponds to the step a) in the section 2.
Calculating the mean value of the system in the above single step
Figure BDA0002111859340000122
Sample variance S2And then, respectively calculating confidence intervals of the expected mu and standard deviation sigma of the system according to b) and c), and obtaining a real-time calculation confidence interval change curve after multiple times of cyclic calculation.
Respectively judging the change conditions of the confidence interval of the expected mu and standard deviation sigma of the system according to d), wherein in the simulation process, the upper limit and the lower limit of the confidence interval calculated at the 1500 th collected data point meet the fluctuation requirement of d), and as shown in the stable confidence interval marked in figures 6 and 7, the mean value of the system calculated after the 1500 th collected data point can be considered to be
Figure BDA0002111859340000127
Sample variance S2Expected μ and variance σ of data samples for system output2As indicated by the labeled "estimated stable region" in fig. 4 and 5.
After the 1500 th data point is collected, calculating the mean value of the monitoring system in real time as described in e)
Figure BDA0002111859340000125
Sample variance S2Variation according to mean
Figure BDA0002111859340000123
Sample variance S2The power distribution system for making changes isAnd judging whether to carry out failure prediction alarm. In FIGS. 4 and 5, the system mean
Figure BDA0002111859340000124
Sample variance S2After the 1500 th sample point, the real-time calculated mean value
Figure BDA0002111859340000126
Sample variance S2All are in stable condition, and are free from fluctuation, so that the power distribution system is in a normal state, and can not break down in a long period of time in the later period.
Those skilled in the art will appreciate that all or part of the flow of the method implementing the above embodiments may be implemented by a computer program, which is stored in a computer readable storage medium, to instruct related hardware. The computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (8)

1. A method of fault prediction for an electrical distribution system, comprising the steps of:
continuously collecting voltage sample X output by power distribution system1,X2,...,XnTo form a set of voltage samples that satisfy N (μ, σ)2) A distribution in which μ and the standard deviation σ are expected as unknowns;
calculating a mean of the set of voltage samples
Figure FDA0002891574740000015
And variance S2Respectively obtaining confidence intervals of the expected mu and the standard deviation sigma when the confidence level is 1-alpha;
when a new voltage sample is collected, the new voltage sample set and the voltage sample set at the previous moment form a new voltage sample set, and the calculation steps are repeated to obtain a confidence interval of the expected mu and the standard deviation sigma when the confidence level of the new voltage sample set is 1-alpha;
repeating the new voltage sample collection and calculation process to obtain confidence intervals of the expected mu and the standard deviation sigma of the continuous voltage sample sets, and taking the confidence intervals of the expected mu and the standard deviation sigma of the continuous voltage sample sets when the confidence intervals are stable within a preset fluctuation range
Figure FDA0002891574740000011
σ2＝S2；
According to the mu and the sigma2Determining a voltage output interval of the power distribution system in a normal working state, and realizing fault prediction of the power distribution system according to the voltage output interval in the normal working state;
determining a voltage output interval of the power distribution system in a normal working state by the following formula:
Figure FDA0002891574740000012
the interval of the output voltage X in the normal operating state of the power distribution system is: x is an element (mu-sigma. z)0.1/2,μ+σ·z0.1/2)；
And realizing the fault prediction of the power distribution system according to the voltage output interval in the normal working state, wherein the fault prediction comprises the following steps:
if the voltage output value of the power distribution system exceeds the voltage output interval in the normal working state, accumulating 100 voltage output values by taking the current voltage output value as a starting point, and calculating the average value of the 100 voltage output values
Figure FDA0002891574740000013
If it is
Figure FDA0002891574740000014
And if the voltage exceeds the voltage output interval of the power distribution system in the normal working state, judging that the power distribution system has a fault.
2. The method of claim 1, wherein the confidence interval for the expected μ at a confidence level of 1- α is obtained by the following equation:
Figure FDA0002891574740000021
the confidence interval for μ at a confidence level of 1- α is then:
Figure FDA0002891574740000022
n represents the number of voltage samples.
3. The method of fault prediction for an electrical distribution system of claim 1 wherein the confidence interval for a standard deviation σ at a confidence level of 1- α is obtained by the following equation:
Figure FDA0002891574740000023
the confidence interval for the standard deviation σ with a confidence level of 1- α is then:
Figure FDA0002891574740000024
n represents the number of voltage samples.
4. The method of claim 1, wherein the confidence intervals of the expected μ and standard deviation σ for the successive sets of voltage samples are determined to be stable within a predetermined fluctuation range by:
confidence intervals of the expected mu and standard deviation sigma of the voltage sample sets respectively meet the condition that the deviation of the upper boundary value from the average value of the upper boundary is less than 0.1, and the deviation of the lower boundary value from the average value of the lower boundary is less than 0.1.
5. The method of claim 1, wherein a confidence level of 1- α is set at 0.9.
6. The method of fault prediction of an electrical distribution system of claim 1, further comprising performing fault prediction of the electrical distribution system by:
after a voltage output interval of the power distribution system in a normal working state is determined, emptying the voltage sample set;
the voltage samples are collected again, each time one voltage sample is collected, a new voltage sample set is formed together with the voltage sample set at the previous moment, and the mean value of the sample sets is calculated
Figure FDA0002891574740000031
Sum variance S2(ii) a Mean of 100 groups per accumulation
Figure FDA0002891574740000032
And the variance S of the sample2Then, respectively calculate
Figure FDA0002891574740000033
And S2Average value of (2), average value of current calculation
Figure FDA0002891574740000034
Sample variance S2And respectively making differences with the average value, and if any difference value is greater than 0.2, judging that the power distribution system has faults.
7. A fault prediction device for an electrical distribution system, the system comprising: the device comprises a voltage acquisition module, a voltage processing module and a fault prediction module; wherein the content of the first and second substances,
the voltage acquisition module is used for acquiring the output voltage of the power distribution system;
the voltage processing module is used for executing the following operations to obtain a voltage output interval of the power distribution system in a normal working state:
continuously collecting voltage sample X output by power distribution system1,X2,...,XnTo form a set of voltage samples that satisfy N (μ, σ)2) A distribution in which μ and the standard deviation σ are expected as unknowns;
calculating a mean of the set of voltage samples
Figure FDA0002891574740000035
And variance S2Respectively obtaining confidence intervals of the expected mu and the standard deviation sigma when the confidence level is 1-alpha;
when a new voltage sample is collected, the new voltage sample set and the voltage sample set at the previous moment form a new voltage sample set, and the calculation steps are repeated to obtain a confidence interval of the expected mu and the standard deviation sigma when the confidence level of the new voltage sample set is 1-alpha;
repeating the new voltage sample collection and calculation process to obtain confidence intervals of the expected mu and the standard deviation sigma of the continuous voltage sample sets, and taking the confidence intervals of the expected mu and the standard deviation sigma of the continuous voltage sample sets when the confidence intervals are stable within a preset fluctuation range
Figure FDA0002891574740000036
σ2＝S2(ii) a And according to the mu and the sigma2Determining a voltage output interval of the power distribution system in a normal working state;
the fault prediction module is used for realizing the fault prediction of the power distribution system according to the voltage output interval in the normal working state;
determining a voltage output interval of the power distribution system in a normal working state by the following formula:
Figure FDA0002891574740000041
the interval of the output voltage X in the normal operating state of the power distribution system is: x is an element (mu-sigma. z)0.1/2,μ+σ·z0.1/2)；
And realizing the fault prediction of the power distribution system according to the voltage output interval in the normal working state, wherein the fault prediction comprises the following steps:
if the voltage output value of the power distribution system exceeds the voltage output interval in the normal working state, accumulating 100 voltage output values by taking the current voltage output value as a starting point, and calculating the average value of the 100 voltage output values
Figure FDA0002891574740000042
If it is
Figure FDA0002891574740000043
And if the voltage exceeds the voltage output interval of the power distribution system in the normal working state, judging that the power distribution system has a fault.
8. The fault prediction device of the power distribution system of claim 7, wherein the fault prediction module further performs the following operations to achieve fault prediction:
after a voltage output interval of the power distribution system in a normal working state is determined, emptying the voltage sample set; the voltage samples are collected again, each time one voltage sample is collected, a new voltage sample set is formed together with the voltage sample set at the previous moment, and the mean value of the sample sets is calculated
Figure FDA0002891574740000044
Sum variance S2(ii) a Mean of 100 groups per accumulation
Figure FDA0002891574740000045
And the variance S of the sample2Then, respectively calculate
Figure FDA0002891574740000046
And S2Average value of (2), average value of current calculation
Figure FDA0002891574740000047
Sample variance S2And respectively making differences with the average value, and if any difference value is greater than 0.2, judging that the power distribution system has faults.
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