CN113177043A - Single-phase electric meter phase judging method based on multiple linear regression - Google Patents

Single-phase electric meter phase judging method based on multiple linear regression Download PDF

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CN113177043A
CN113177043A CN202110573854.9A CN202110573854A CN113177043A CN 113177043 A CN113177043 A CN 113177043A CN 202110573854 A CN202110573854 A CN 202110573854A CN 113177043 A CN113177043 A CN 113177043A
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phase
electric meter
voltage
variables
judging
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董永乐
鲁继业
张理放
许飞宇
余佳
席佳
张帆
白露薇
毛永梅
殷超
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Inner Mongolia Electric Power Research Institute of Inner Mongolia Power Group Co Ltd
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    • G01R29/00—Arrangements for measuring or indicating electric quantities not covered by groups G01R19/00 - G01R27/00
    • G01R29/16—Measuring asymmetry of polyphase networks
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    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract

The invention discloses a phase-difference judging method of a single-phase electric meter based on multiple linear regression, which is characterized in that the voltage, the current and the current of the single-phase electric meter of a gateway are used as independent variables, the voltage measured by a single-phase electric meter of a user is used as a dependent variable, a phase-difference judging model of the single-phase electric meter based on the multiple linear regression is established, historical sample data is substituted into a phase-difference judging model formula (1) of the single-phase electric meter to obtain a regression equation formula (2), and the independent variable multiple collinearity inspection, the F inspection, the t inspection and the fitting goodness inspection are carried out on the formula (2).

Description

Single-phase electric meter phase judging method based on multiple linear regression
Technical Field
The invention belongs to the technical field of smart power grid districts, and particularly relates to a phase difference judgment method for a single-phase electric meter based on multiple linear regression.
Background
The current method for judging the phase of the single-phase electric meter is mainly divided into the following four types:
(1) based on a carrier wave. The method is suitable for occasions with the I-type concentrator, and requires that the concentrator and the electric meters have a carrier communication function and have higher requirements on signal processing.
(2) Based on cluster analysis. On the basis of the voltage time sequence, the connectivity of the electric meter is identified by utilizing K-means clustering with constraint, but the judging accuracy of the method fluctuates with months.
(3) Based on a correlation analysis. A method for identifying a distribution area by using correlation between voltage measurements of electric meters. The topological correctness of the distribution network geographic information system is verified based on the electric meter data, and the method is greatly influenced by the uncertainty of a line model.
(4) Integer programming is utilized. The method adopts 0-1 integer linear programming, and uses a branch and boundary search algorithm to carry out phase discrimination judgment, all electric meters under a transformer area need to participate in calculation at the same time, and the calculation amount expands rapidly along with the increase of the problem scale. The method of combining linear programming and quadratic programming is adopted to carry out phase-to-phase judgment, and the accuracy of the judgment result is influenced when the user data are similar.
Based on the phase information of the single-phase electric meter, the detection and judgment of the load imbalance can be carried out, and a basis is provided for accurate and effective load imbalance treatment. However, the current electricity consumption information management system does not contain phase information of the single-phase electric meters, and because the number of the user electric meters is large, the electricity consumption and wiring conditions are complex, the difficulty in establishing the phase information base of the single-phase electric meters by adopting a manual searching and confirming mode is high, and a method for automatically judging the phase of the single-phase electric meters needs to be researched.
Advanced measurement infrastructure (ami) has rapidly developed in recent years, and measurement information in a coverage system range can be provided by using a two-way communication system and an intelligent electric meter capable of recording detailed load information of a user. The analysis method based on the data of the intelligent electric meter opens up a new way for solving many practical problems by utilizing big data in the power industry. Due to the deployment and application of a large number of intelligent electric meters, an electric power company can obtain relatively comprehensive electricity consumption measurement data of the tail end of the power distribution network with high frequency, wide coverage and consistent time scale.
The intelligent electric meter is used as a terminal device of the AMI, undertakes tasks of metering, collecting, uploading and the like of user electricity utilization data, and is a basis for realizing integration and calculation analysis of user electricity utilization information. The method can upload various metering information (such as electric energy, active power, reactive power, voltage, current and the like) according to preset time intervals (such as 5min, 15min and the like), the information can reflect the power consumption time section information of each node in the power supply network, the comprehensive embodiment of elements such as the topological structure, load, line loss and the like of the power supply network is realized, and a specific and describable incidence relation is provided mathematically, so that the phase relation of the single-phase electric meter can be judged through electric meter measuring data.
Disclosure of Invention
The invention provides a phase-class judging method of a single-phase electric meter based on multiple linear regression, which can solve the problem of judging the phase-class relation of the single-phase electric meter through electric meter measurement data.
In order to solve the technical problems, the invention adopts the following scheme: the phase-class judging method of the single-phase electric meter based on the multiple linear regression is characterized in that the voltage, the current and the current of the single-phase electric meter of a gateway are used as independent variables, the voltage measured by a single-phase electric meter of a user is used as a dependent variable, a phase-class judging model of the single-phase electric meter based on the multiple linear regression is established, and the phase-class judging model of the single-phase electric meter is as follows:
y＝β0+β1 x1+β2x2+…+βm xm+ε (1)；
wherein x is the independent variable, m is the number of independent variables, y is the dependent variable, β0Is a constant; β is a regression coefficient; ε represents a portion not determined by an argument as a random error term, ε to N (0, σ 2), the expected value of ε is 0, and the variance σ 2 is the same;
substituting the historical sample data into a formula (1), solving the estimators beta ^0, beta ^1, … and beta ^ m of beta 0, beta 1, beta 2, … and beta m by a least square method, and obtaining a regression equation as follows:
Figure BDA0003083626000000021
wherein the content of the first and second substances,
Figure BDA0003083626000000022
for equation fitting values, the independent variable multiple collinearity test, the F test, the t test, and the goodness-of-fit test are performed on equation (2).
According to the phase-difference judging method of the single-phase electric meter based on the multiple linear regression, the voltage and the current of the gateway electric meter are used as independent variables, the voltage measured by the user single-phase electric meter is used as a dependent variable, the multiple linear regression equation is established, the phase difference of the single-phase electric meter is judged by calculating the decision coefficient of the regression equation formed by the single-phase electric meter and each phase of the gateway electric meter, the problem of judging the phase-difference relation of the single-phase electric meter through electric meter measurement data can be solved, the reliability and the accuracy are high, and the accuracy can reach 100%.
The F-test (F-test), the most commonly used alias name, is called joint hypothesis test (English), and is also called variance ratio test, and variance homogeneity test. This is a mathematical concept with accurate definitions, examining the significance of the effect of all independent variables on the dependent variables as a whole.
the t test, also known as Student's t test, is mainly used for normal distribution with small sample content (e.g., n <30) and unknown total standard deviation sigma. the t test is to use the t distribution theory to deduce the probability of occurrence of difference, so as to compare whether the difference between two averages is significant or not. It is parallel to F test and chi fang test as three sampling distribution and test.
Preferably, in the independent variable multiple collinearity test, a common condition index and variance ratio are adopted for collinearity diagnosis, and when the condition index of a certain dimension is greater than or equal to 30 and the corresponding independent variable variance ratio is greater than 0.5, obvious collinearity exists among the independent variables; the method comprises the steps of specifically defining dimensions, condition indexes and variance ratios and judging criteria of multiple collinearity, selecting variables, controlling linear influence of other independent variables to analyze linear correlation of the independent variables and dependent variables in a system formed by multiple elements, calculating partial correlation coefficients of the independent variables and the dependent variables, eliminating the independent variables with small influence on the dependent variables according to the sizes of the independent variables, and keeping the independent variables with higher explanation degree on the dependent variables.
Preferably, in the F-test, the significance of the effect of all independent variables on the dependent variable as a whole is tested: if F is more than or equal to F alpha (m, n-m-1), wherein alpha is a significance level, and n is the number of samples, the regression effect is considered to be significant; otherwise, the regression effect is not obvious, and independent variables need to be searched again.
Wherein F ≧ F α (m, n-m-1), which is a standard F distribution expression, m is a degree of freedom independent variable, and F α refers to a change at a significance level relative to F.
Preferably, in the t test, the significance of the influence of each independent variable on the dependent variable is tested, if | t | ≧ t α/2(n-m-1), the influence of the independent variable is considered significant, otherwise, the influence is considered insignificant, and the variable is removed from the equation.
Preferably, in the goodness-of-fit test, a coefficient of determination R is calculated2Evaluating the goodness of fit of the regression equation to the observed values of the samples, namely:
Figure BDA0003083626000000031
wherein the content of the first and second substances,
Figure BDA0003083626000000032
yq、yˉrespectively an equation fitting value, an observed value and an average value of sample observed values of a sample q; r2And for determining coefficients, describing the proportion of the regression sum of squares to the total sum of squared deviations, wherein the value range is 0-1, the larger the numerical value is, the better the fitting between the regression equation and the sample is, calculating the determination coefficient of each regression equation, judging the degree of interpretation of the independent variable on the dependent variable according to the determination coefficient, and accordingly judging the phase of the single-phase electric meter.
Preferably, the method further comprises the following steps of power supply network topology and variable analysis:
(1) the power supply network topological structure is characterized in that in a 400V power supply network, a user ammeter is managed by taking a power supply station area as a unit, a three-phase gateway ammeter is arranged at a transformer outlet, and relatively complete electrical quantity parameters such as three-phase voltage, current, active power, reactive power, power factor, electric energy and the like are collected and recorded; the downstream single-phase electric meters of users are respectively connected with A, B, C three phases, and only the parameters of voltage, current, active power and active electric energy are measured and recorded;
(2) the analysis of the relation of the variables of the power supply network is based on the collection and recording of the types and the contents of the electric quantity information of the electric power automation equipment by various electric meters, the established multiple linear regression equation takes the voltage of the user single-phase electric meter as a dependent variable, and the voltage, the current and the power of each phase of the gateway electric meter and part or all of the current and the power parameters of the user single-phase electric meter as independent variables.
Preferably, the method further comprises the steps of constructing a collinearity diagnosis and a multiple linear regression equation:
a co-linear relation exists between the independent variable active power P and the current I, the co-linear relation cannot be directly used for electric meter phase judgment, the expression of the current I and the user electric meter voltage U is more in line with a linear regression equation, and a proper independent variable is selected by adopting a data analysis method according to actual conditions.
According to circuit theory, a co-linear relationship exists between the independent variable active power P and the current I, so that the independent variable active power P and the current I cannot be directly used for electric meter phase judgment, and the expression of the current I and the user electric meter voltage U is more consistent with the general form of a linear regression equation, but the conclusion is obtained under the condition of neglecting the reactive power Q on a line, and an appropriate independent variable needs to be selected by adopting a data analysis method according to actual conditions.
Preferably, the method further comprises an example analysis:
the method comprises the following steps of (1) carrying out sample analysis by adopting data collected by an electric meter, and showing that certain differences exist between the three-phase voltage amplitude and the variation trend of the gateway electric meter in an observation time period; the voltage amplitude variation trend of each single-phase electric meter is similar to the voltage amplitude variation trend of the corresponding phase of the gateway electric meter, obvious correlation exists between the voltage amplitude variation trend and the voltage amplitude variation trend, and a linear regression equation which takes the user voltage amplitude as a dependent variable and the voltage amplitude of the gateway electric meter as an independent variable is established to judge the phase of the single-phase electric meter;
analyzing by taking the phase judging process of the user electric meter A3 and the user electric meter B1 as an example, firstly, judging the phase according to the correlation of the voltage amplitude time sequence, respectively analyzing the correlation between the voltage amplitudes of the user electric meters A3 and B1 and the three-phase voltage amplitude of the gateway electric meter, and finding out that the following factors can influence the accuracy of the judging result by analyzing the self characteristics of the multiple linear regression method and the actual calculation result:
(1) the data acquisition synchronism of the gateway ammeter and each user ammeter is realized; at present, AMI cannot guarantee that data acquisition of each ammeter is strictly synchronous, and minute-level time errors often exist. Asynchronous data can influence the incidence relation among all variables, and further influence the correctness of a judgment result;
(2) changes in user load and line loss; the change of the user load can affect the line loss, so that the difference between the user and each phase of the summary table can be offset, and the uncertainty of the goodness of fit is increased;
(3) the number of data samples; if the data samples are too few, the judgment result has greater contingency, but the data samples are too many, the calculation amount is increased, and therefore, the appropriate sample data amount needs to be determined;
(4) unbalance degree of three-phase voltage of the gateway ammeter; if the three-phase voltage of the transformer area is basically balanced, the correlation difference between the user voltage and the three-phase voltage of the gateway ammeter is not obvious enough, and the accuracy of the judgment result is further influenced.
The intelligent electric meter is a measuring terminal positioned at the tail end of a power grid, the coverage of AMI provides massive user side measuring data for power grid operation and management personnel, the data are fully utilized, the associated information among the data is mined, and various additional functions and value-added service functions can be realized.
The phase-to-phase judgment method of the single-phase electric meter based on the multiple linear regression is based on AMI measurement data in a 400V power supply network, utilizes the correlation between the measurement voltage of the user electric meter and the voltage of the electric meter at the gateway of the power supply station area, and adopts the multiple linear regression equation to describe the relationship between the measurement voltage and the voltage of the electric meter at the gateway of the power supply station area. The coefficient is determined by calculating and comparing linear regression equations respectively established for three phases of the user electric meter and the gateway electric meter, and the phase of the single-phase electric meter is judged.
The intelligent electric meter in the AMI can be internally programmed, and supports instant reading of electricity utilization information, voltage out-of-range detection, device interference and electricity stealing detection, remote connection and disconnection. When detecting the outage, smart electric meter can send back alarm information, provides very big convenience for fault detection and response. Other typical functions of the smart meter include providing bidirectional metering, supporting users with distributed power generation; providing voltage out-of-range detection and monitoring of power quality; remote programming setting and software upgrading can be carried out; support remote time synchronization; the load can be limited as required.
For each time there is an electricity meter measurement, the system satisfies a power flow equation where all end node voltages and powers are known, and the unknowns in the equation are the impedances (R and X) of the branches. Considering that the length and parameters of the system line are usually constant in a reasonable time period, the AMI system can provide a large amount of time sequence data, and ensure that the data of enough time intervals, i.e. enough equations, make the resistance and reactance values of each branch be solved. The large number of redundant equations enables the accuracy of the calculated resistance and reactance values to be guaranteed in an optimized manner.
The method has important significance in further carrying out applications such as accurate modeling of user side loads, analysis of user power utilization behaviors, judgment of user power supply abnormity, rapid power supply recovery, three-phase imbalance treatment and the like.
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The following further detailed description of embodiments of the invention is made with reference to the accompanying drawings:
fig. 1 is a 400V power supply topology.
Detailed Description
The invention relates to a phase-class judging method of a single-phase electric meter based on multiple linear regression, which is characterized in that the voltage and the current of a gateway electric meter and the current of the single-phase electric meter are used as independent variables, the voltage measured by a user single-phase electric meter is used as a dependent variable, a phase-class judging model of the single-phase electric meter based on the multiple linear regression is established, and the phase-class judging model of the single-phase electric meter is as follows:
y＝β0+β1 x1+β2x2+…+βm xm+ε (1)；
wherein x is the independent variable, m is the number of independent variables, y is the dependent variable, β0Is a constant; β is a regression coefficient; ε represents a portion not determined by an argument as a random error term, ε to N (0, σ 2), the expected value of ε is 0, and the variance σ 2 is all in phaseThe same is carried out;
substituting the historical sample data into a formula (1), solving the estimators beta ^0, beta ^1, … and beta ^ m of beta 0, beta 1, beta 2, … and beta m by a least square method, and obtaining a regression equation as follows:
Figure BDA0003083626000000061
wherein the content of the first and second substances,
Figure BDA0003083626000000062
for equation fitting values, the independent variable multiple collinearity test, the F test, the t test, and the goodness-of-fit test are performed on equation (2).
In the independent variable multiple collinearity test, common condition indexes and variance ratios are adopted for collinearity diagnosis, and when the condition index of a certain dimension is greater than or equal to 30 and the corresponding independent variable variance ratio is greater than 0.5, obvious collinearity exists among the independent variables; the method comprises the steps of specifically defining dimensions, condition indexes and variance ratios and judging criteria of multiple collinearity, selecting variables, controlling linear influence of other independent variables to analyze linear correlation of the independent variables and dependent variables in a system formed by multiple elements, calculating partial correlation coefficients of the independent variables and the dependent variables, eliminating the independent variables with small influence on the dependent variables according to the sizes of the independent variables, and keeping the independent variables with higher explanation degree on the dependent variables.
In the F-test, the significance of the effect of all independent variables on the dependent variable as a whole is examined: if F is more than or equal to F alpha (m, n-m-1), wherein alpha is a significance level, and n is the number of samples, the regression effect is considered to be significant; otherwise, the regression effect is not obvious, and independent variables need to be searched again.
In the t test, the significance of the influence of each independent variable on the dependent variable is tested, if | t | ≧ t alpha/2 (n-m-1), the influence of the independent variable is considered to be significant, otherwise, the influence is considered to be insignificant, and the variable is removed from the equation. 5. The method as claimed in claim 1, wherein the goodness-of-fit test is performed by calculating a determination coefficient R2Evaluating the goodness of fit of the regression equation to the observed values of the samples, namely:
Figure BDA0003083626000000071
wherein the content of the first and second substances,
Figure BDA0003083626000000072
yq、yˉrespectively an equation fitting value, an observed value and an average value of sample observed values of a sample q; r2And for determining coefficients, describing the proportion of the regression sum of squares to the total sum of squared deviations, wherein the value range is 0-1, the larger the numerical value is, the better the fitting between the regression equation and the sample is, calculating the determination coefficient of each regression equation, judging the degree of interpretation of the independent variable on the dependent variable according to the determination coefficient, and accordingly judging the phase of the single-phase electric meter.
The method also comprises the following steps of power supply network topology structure and variable analysis:
(1) the power supply network topological structure is characterized in that in a 400V power supply network, a user ammeter is managed by taking a power supply station area as a unit, a three-phase gateway ammeter is arranged at a transformer outlet, and relatively complete electrical quantity parameters such as three-phase voltage, current, active power, reactive power, power factor, electric energy and the like are collected and recorded; the downstream single-phase electric meters of users are respectively connected with A, B, C three phases, and only the parameters of voltage, current, active power and active electric energy are measured and recorded;
(2) the analysis of the relation of the variables of the power supply network is based on the collection and recording of the types and the contents of the electric quantity information of the electric power automation equipment by various electric meters, the established multiple linear regression equation takes the voltage of the user single-phase electric meter as a dependent variable, and the voltage, the current and the power of each phase of the gateway electric meter and part or all of the current and the power parameters of the user single-phase electric meter as independent variables.
The method also comprises the following steps of collinearity diagnosis and multiple linear regression equation construction:
a co-linear relation exists between the independent variable active power P and the current I, the co-linear relation cannot be directly used for electric meter phase judgment, the expression of the current I and the user electric meter voltage U is more in line with a linear regression equation, and a proper independent variable is selected by adopting a data analysis method according to actual conditions.
The method also comprises the following steps of example analysis:
the method comprises the following steps of (1) carrying out sample analysis by adopting data collected by an electric meter, and showing that certain differences exist between the three-phase voltage amplitude and the variation trend of the gateway electric meter in an observation time period; the voltage amplitude variation trend of each single-phase electric meter is similar to the voltage amplitude variation trend of the corresponding phase of the gateway electric meter, obvious correlation exists between the voltage amplitude variation trend and the voltage amplitude variation trend, and a linear regression equation which takes the user voltage amplitude as a dependent variable and the voltage amplitude of the gateway electric meter as an independent variable is established to judge the phase of the single-phase electric meter;
analyzing by taking the phase judging process of the user electric meter A3 and the user electric meter B1 as an example, firstly, judging the phase according to the correlation of the voltage amplitude time sequence, respectively analyzing the correlation between the voltage amplitudes of the user electric meters A3 and B1 and the three-phase voltage amplitude of the gateway electric meter, and finding out that the following factors can influence the accuracy of the judging result by analyzing the self characteristics of the multiple linear regression method and the actual calculation result:
(1) the data acquisition synchronism of the gateway ammeter and each user ammeter is realized;
(2) changes in user load and line loss;
(3) the number of data samples;
(4) and unbalance degree of the three-phase voltage of the gateway ammeter.
Specifically, in order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the complete meter measurement information is shown in table 4. A simplified 400V power supply network topology is shown in figure 1.
Tables 1, 2 and 3 show the measured data per minute for the unidirectional electric meter, as follows:
numbering Single phase voltage Single phase current Total active power
01 229.4 6.457 1.468
02 229.4 6.457 1.468
03 229.8 1.084 0.212
04 229.8 1.084 0.212
05 229.7 1.082 0.212
06 229.8 1.08 0.211
07 229.8 0.885 0.175
08 229.7 0.876 0.173
09 229.7 0.877 0.173
10 229.6 0.877 0.173
11 229.6 0.877 0.173
12 229.5 0.873 0.173
13 229.4 0.874 0.173
14 229.8 0.876 0.173
15 229.7 0.873 0.173
16 229.7 0.873 0.173
17 229.7 0.873 0.173
18 229.7 0.873 0.173
19 229.6 0.88 0.174
20 229.6 0.881 0.174
21 229.7 0.88 0.174
22 229.4 0.873 0.173
23 229.4 0.873 0.173
24 229.4 0.873 0.173
25 229.4 0.873 0.173
26 229.4 0.873 0.173
27 229.4 0.873 0.173
28 229.4 0.873 0.173
29 229.7 0.712 0.095
30 229.7 0.712 0.095
TABLE 1 measurement data of unidirectional electric meter per minute
Numbering Single phase voltage Single phase current Total active power
01 229.4 6.457 1.468
02 229.4 6.457 1.468
03 229.8 1.084 0.212
04 229.8 1.084 0.212
05 229.7 1.082 0.212
06 229.8 1.08 0.211
07 229.8 0.885 0.175
08 229.7 0.876 0.173
09 229.7 0.877 0.173
10 229.6 0.877 0.173
11 229.6 0.877 0.173
12 229.5 0.873 0.173
13 229.4 0.874 0.173
14 229.8 0.876 0.173
15 229.7 0.873 0.173
16 229.7 0.873 0.173
17 229.7 0.873 0.173
18 229.7 0.873 0.173
19 229.6 0.88 0.174
20 229.6 0.881 0.174
21 229.7 0.88 0.174
22 229.4 0.873 0.173
23 229.4 0.873 0.173
24 229.4 0.873 0.173
25 229.4 0.873 0.173
26 229.4 0.873 0.173
27 229.4 0.873 0.173
28 229.4 0.873 0.173
29 229.7 0.712 0.095
30 229.7 0.712 0.095
TABLE 2 measurement data of unidirectional electric meter per minute
Numbering Single phase voltage Single phase current Total active power
01 229.4 6.457 1.468
02 229.4 6.457 1.468
03 229.8 1.084 0.212
04 229.8 1.084 0.212
05 229.7 1.082 0.212
06 229.8 1.08 0.211
07 229.8 0.885 0.175
08 229.7 0.876 0.173
09 229.7 0.877 0.173
10 229.6 0.877 0.173
11 229.6 0.877 0.173
12 229.5 0.873 0.173
13 229.4 0.874 0.173
14 229.8 0.876 0.173
15 229.7 0.873 0.173
16 229.7 0.873 0.173
17 229.7 0.873 0.173
18 229.7 0.873 0.173
19 229.6 0.88 0.174
20 229.6 0.881 0.174
21 229.7 0.88 0.174
22 229.4 0.873 0.173
23 229.4 0.873 0.173
24 229.4 0.873 0.173
25 229.4 0.873 0.173
26 229.4 0.873 0.173
27 229.4 0.873 0.173
28 229.4 0.873 0.173
29 229.7 0.712 0.095
30 229.7 0.712 0.095
TABLE 3 measurement data of unidirectional electric meter per minute
Wherein, the single column of data is de-duplicated according to the time stamp (the repetition time only keeps the first data); the timestamp of the single-column data loss corresponds to the voltage data filling 0; select 3 columns of voltage data: x is general table A phase, Y is sub table A phase, Z is sub table B phase, X is expected to be highly correlated with Y, and X is expected to be lowly correlated with Z; the above 3 columns of data are aligned with a time stamp.
The correlation coefficient corel was calculated in excel.
The voltage mode of the household meter is as follows: u shapeai＝β0+β1U+β2I+β3Iai (4)；
Wherein beta is1U is the total voltage (A, B, C three-phase voltage), beta2I is the total current (A, B, C three-phase current), beta3IaiFor the household meter current, the formula needs to be respectively substituted into the formula (4) for calculation according to the data in the table 1, the table 2 and the table 3, and finally the data in the table 4 is obtained.
Figure BDA0003083626000000131
TABLE 4 measurement data of three-phase electric meter per minute in power supply area
The 400V power supply network is in a radial structure, the gateway electric meter and each single-phase electric meter are in an upstream-downstream relationship in a circuit, and a fixed and describable mathematical relationship exists between the electric quantities of the gateway electric meter and each single-phase electric meter. However, because important information such as network topology, power supply line parameters and the like cannot be obtained, and the electric meter can only provide measurement information of a certain time section but not a full time period, the objective mathematical relationship is difficult to directly describe.
The three-phase voltage of the low-voltage distribution transformer inevitably has a certain difference, and the difference of each phase voltage and load can cause the difference of each phase current, further causes the difference of loss on each phase circuit, so that the voltage of users with different phases and single phases can be distinguished under the general condition, and the voltage has the trend with the change of the voltage of a gateway table. Considering that strong correlation exists between the corresponding phasor measurement values of the single-phase electric meter and the gateway electric meter, the method has the condition for constructing a linear regression equation, and a multiple linear regression model can be adopted to describe the relationship between the variables.
The above-mentioned embodiments are further detailed to explain the objects, technical solutions and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only examples of the present invention, and are not intended to limit the present invention; any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (8)

1. A phase-class judging method of a single-phase electric meter based on multiple linear regression is characterized in that a phase-class judging model of the single-phase electric meter based on the multiple linear regression is established by taking voltage, current and current of a gateway electric meter as independent variables and voltage measured by a single-phase electric meter of a user as a dependent variable, wherein the phase-class judging model of the single-phase electric meter is as follows:
y＝β0+β1x1+β2x2+…+βmxm+ε (1)；
wherein x is the independent variable, m is the number of independent variables, y is the dependent variable, β0Is a constant; β is a regression coefficient; ε represents a portion not determined by an argument as a random error term, ε to N (0, σ 2), the expected value of ε is 0, and the variance σ 2 is the same;
the historical sample data is substituted into the formula (1), and the estimation quantities of beta 0, beta 1, beta 2, … and beta m are obtained by the least square method
Figure FDA0003083625990000011
The regression equation is obtained as:
Figure FDA0003083625990000012
wherein the content of the first and second substances,
Figure FDA0003083625990000013
for equation fitting values, the independent variable multiple collinearity test, the F test, the t test, and the goodness-of-fit test are performed on equation (2).
2. The method as claimed in claim 1, wherein in the independent variable multiple collinearity test, a collinearity diagnosis is performed by using a common condition index and variance ratio, and when the condition index of a certain dimension is greater than or equal to 30 and the corresponding independent variable variance ratio is greater than 0.5, it is indicated that there is an obvious collinearity between the independent variables; the method comprises the steps of specifically defining dimensions, condition indexes and variance ratios and judging criteria of multiple collinearity, selecting variables, controlling linear influence of other independent variables to analyze linear correlation of the independent variables and dependent variables in a system formed by multiple elements, calculating partial correlation coefficients of the independent variables and the dependent variables, eliminating the independent variables with small influence on the dependent variables according to the sizes of the independent variables, and keeping the independent variables with higher explanation degree on the dependent variables.
3. The multiple linear regression-based phase discrimination method for single-phase electric meters according to claim 1, wherein in the F-test, the significance of the influence of all independent variables on dependent variables as a whole is tested: if F is more than or equal to F alpha (m, n-m-1), wherein alpha is a significance level, and n is the number of samples, the regression effect is considered to be significant; otherwise, the regression effect is not obvious, and independent variables need to be searched again.
4. The method for judging the phase of the single-phase electric meter based on the multiple linear regression is characterized in that in the t test, the significance of each independent variable on the influence of a dependent variable is tested, if | t | ≧ t alpha/2 (n-m-1), the influence of the independent variable is considered to be significant, otherwise, the influence is considered to be insignificant, and the variable is removed from an equation.
5. The method as claimed in claim 1, wherein the goodness-of-fit test is performed by calculating a determination coefficient R2Evaluating the goodness of fit of the regression equation to the observed values of the samples, namely:
Figure FDA0003083625990000021
wherein the content of the first and second substances,
Figure FDA0003083625990000022
yq、y-respectively an equation fitting value, an observed value and an average value of sample observed values of a sample q; r2And for determining coefficients, describing the proportion of the regression sum of squares to the total sum of squared deviations, wherein the value range is 0-1, the larger the numerical value is, the better the fitting between the regression equation and the sample is, calculating the determination coefficient of each regression equation, judging the degree of interpretation of the independent variable on the dependent variable according to the determination coefficient, and accordingly judging the phase of the single-phase electric meter.
6. The method for judging the phase of the single-phase electric meter based on the multiple linear regression as claimed in claim 1, wherein the method further comprises the following steps of analyzing the topology structure and variables of the power supply network:
(1) the power supply network topological structure is characterized in that in a 400V power supply network, a user ammeter is managed by taking a power supply station area as a unit, a three-phase gateway ammeter is arranged at a transformer outlet, and relatively complete electrical quantity parameters such as three-phase voltage, current, active power, reactive power, power factor, electric energy and the like are collected and recorded; the downstream single-phase electric meters of users are respectively connected with A, B, C three phases, and only the parameters of voltage, current, active power and active electric energy are measured and recorded;
(2) the analysis of the relation of the variables of the power supply network is based on the collection and recording of the types and the contents of the electric quantity information of the electric power automation equipment by various electric meters, the established multiple linear regression equation takes the voltage of the user single-phase electric meter as a dependent variable, and the voltage, the current and the power of each phase of the gateway electric meter and part or all of the current and the power parameters of the user single-phase electric meter as independent variables.
7. The method for judging the phase of the single-phase electric meter based on the multiple linear regression as claimed in claim 1, wherein the method further comprises the steps of colinear diagnosis and multiple linear regression equation construction:
a co-linear relation exists between the independent variable active power P and the current I, the co-linear relation cannot be directly used for electric meter phase judgment, the expression of the current I and the user electric meter voltage U is more in line with a linear regression equation, and a proper independent variable is selected by adopting a data analysis method according to actual conditions.
8. The method for judging the phase of the single-phase electric meter based on the multiple linear regression as claimed in claim 1, further comprising the following steps of:
the method comprises the following steps of (1) carrying out sample analysis by adopting data collected by an electric meter, and showing that certain differences exist between the three-phase voltage amplitude and the variation trend of the gateway electric meter in an observation time period; the voltage amplitude variation trend of each single-phase electric meter is similar to the voltage amplitude variation trend of the corresponding phase of the gateway electric meter, obvious correlation exists between the voltage amplitude variation trend and the voltage amplitude variation trend, and a linear regression equation which takes the user voltage amplitude as a dependent variable and the voltage amplitude of the gateway electric meter as an independent variable is established to judge the phase of the single-phase electric meter;
analyzing by taking the phase judging process of the user electric meter A3 and the user electric meter B1 as an example, firstly, judging the phase according to the correlation of the voltage amplitude time sequence, respectively analyzing the correlation between the voltage amplitudes of the user electric meters A3 and B1 and the three-phase voltage amplitude of the gateway electric meter, and finding out that the following factors can influence the accuracy of the judging result by analyzing the self characteristics of the multiple linear regression method and the actual calculation result:
(1) the data acquisition synchronism of the gateway ammeter and each user ammeter is realized;
(2) changes in user load and line loss;
(3) the number of data samples;
(4) and unbalance degree of the three-phase voltage of the gateway ammeter.
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