CN113506033A - Distribution transformer gear discrimination method based on least square regression - Google Patents

Distribution transformer gear discrimination method based on least square regression Download PDF

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CN113506033A
CN113506033A CN202110854230.4A CN202110854230A CN113506033A CN 113506033 A CN113506033 A CN 113506033A CN 202110854230 A CN202110854230 A CN 202110854230A CN 113506033 A CN113506033 A CN 113506033A
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覃日升
段锐敏
姜訸
马红升
刑超
奚鑫泽
张建
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Electric Power Research Institute of Yunnan Power Grid Co Ltd
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Abstract

The application provides a distribution transformer gear distinguishing method based on least square regression, which comprises the following steps: acquiring distribution transformer voltage, and filling missing data in the distribution transformer voltage by using a Lagrange interpolation method to obtain target data; drawing a voltage curve by using the target data; performing least square regression on the voltage curve, and establishing a first equation; establishing a function of the parameters in the first equation, and calculating to obtain an expression of the parameters relative to the first equation to obtain a second equation; and calculating a least square voltage regression mean value according to a second equation, and filing by combining a distribution gear selection principle. According to the method, missing data are filled by using a Lagrange interpolation method, then least square regression straight lines are obtained by using distribution and transformation outlet voltages, and finally the least square regression mean value is calculated to match the gear. Experimental results show that the provided identification method can accurately carry out gear attribution and has certain reliability.

Description

Distribution transformer gear discrimination method based on least square regression
Technical Field
The application relates to the technical field of power system scheduling, in particular to a distribution transformer gear distinguishing method based on least square regression.
Background
In an electric power system, an electric distribution network distributes electric energy to various power consumers through various power distribution facilities, and a distribution transformer is a source of the electric distribution network and has a non-negligible influence on the electric distribution network. The quality of the electric energy output by the distribution transformer is influenced by a plurality of factors, including distribution transformer gears, distribution transformer connection groups, load rate and the like, the factors are scientifically analyzed, reasonable treatment measures are made, and the quality of the electric energy and the economical efficiency of power grid operation can be improved.
In recent years, as the number of users using electricity increases, the fluctuation of the electricity load becomes faster and faster, and the voltage fluctuation also increases. The voltage of users in some areas is low during peak period of electricity utilization, and the problem of low voltage in some areas is more prominent. Meanwhile, the gears of most distribution transformers are usually set once only by experience when being set, are always in the middle gear during operation, and are not adjusted according to the load change condition, so that the outlet voltage of the distribution transformer is unqualified, and the electric energy quality of a user is unqualified.
The distribution transformer gear can influence the state estimation result and the subsequent voltage stability analysis of the power distribution network, and is related to the judgment of a power grid dispatching person on the operation state of the power grid and the control capability of a dispatching center on the power grid. The distribution transformer is in reasonable gear operation, so that the energy loss of the distribution network can be further reduced, the voltage level of a user can be better maintained, and the electric energy quality is ensured.
At present, most of distribution transformers arranged in a distribution network are no-load voltage regulating devices, the adopted distribution transformer gear identification mode is mainly manual off-line verification, and verification is performed by using a verification device and on-line identification based on transformer windings. The manual check of the gear is carried out when the power is off, so that the process is busy, and time and labor are consumed. The electric shock risk exists when utilizing the calibration equipment to check up to can't guarantee measurement accuracy, the work load is huge, consumes the manpower. On-line identification based on windings is easy to generate interference when the transformer normally operates, and even the transformer can be damaged, so that power failure is caused. At present, gear identification of a distribution transformer is inaccurate, the gear identification is still influenced by voltage fluctuation, and gear attribution is inconvenient.
Disclosure of Invention
The application provides a distribution transformer gear distinguishing method based on least square regression to solve the problems that in the prior art, gear identification of a distribution transformer is inaccurate, the gear identification is still influenced by voltage fluctuation, and gear attribution is inconvenient.
The application provides a distribution transformer gear distinguishing method based on least square regression, which comprises the following steps:
acquiring distribution transformer voltage, and filling missing data in the distribution transformer voltage by using a Lagrange interpolation method to obtain target data;
drawing a voltage curve by using the target data;
performing least square regression on the voltage curve, and establishing a first equation;
establishing a function of the parameter in the first equation, and calculating to obtain an expression and a second equation of the parameter relative to the first equation;
calculating a least square voltage regression mean value according to the second equation, and filing by combining a distribution gear selection principle; the gear selection principle of the distribution transformer is as follows: i gear: shift range + 5%, voltage class 420V; II, grade: shift range + 2.5%, voltage level 410V; III stage: the gear range is 0%, and the voltage level is 400V; IV gear: the gear range is-2.5%, and the voltage level is 390V; v gear: the gear range is-5 percent, and the voltage level is 380V.
Optionally, the step of filling missing data in the distribution transformer voltage by using a lagrangian interpolation method to obtain target data includes:
establishing a polynomial function: (x)0,y0)，…，(xk,yk) Wherein x isjIs an independent variable, yjIs a dependent variable; due to any two x of polynomial functionsjIf different, the Lagrange interpolation polynomial can be expressed as:
Figure BDA0003183514630000021
and calculating missing data in the distribution voltage through a Lagrange difference polynomial, and combining the missing data with the distribution voltage to obtain target data.
Optionally, the voltage curve is subjected to least squares regression, and a first equation is set up as follows:
let the target data formed by the two variables be [ (x)1,y1),(x2,y2),...,(xi,yi)]Establishing a linear equation of the target data about the coordinate distribution of the x-y direct system; wherein the linear equation is a first equation and the expression is
Figure BDA0003183514630000022
Wherein, a0,a1Is any real number.
Optionally, the step of establishing a function of the parameter in the first equation, and calculating to obtain an expression of the parameter with respect to the first equation to obtain the second equation includes:
establishing a function of the parameters in the first equation
Figure BDA0003183514630000023
Wherein V is about a0,a1A function of two parameters;
substituting the function of the parameter into a first equation to obtain a formula 1; wherein, formula 1 is expressed as follows:
Figure BDA0003183514630000024
for a in the formula 10,a1Solving an extreme value by first-order partial derivative to obtain a formula 2; wherein, formula 2 is expressed as follows:
Figure BDA0003183514630000031
transforming the formula 2 by shifting terms to obtain a0,a1Two parameters with respect to xi,yiThe expression of (1); wherein the expression is as follows:
Figure BDA0003183514630000032
and substituting the expression into the first equation to obtain a second equation.
Optionally, the formula for calculating the least squares regression mean value according to the second equation is as follows:
Figure BDA0003183514630000033
wherein the content of the first and second substances,
Figure BDA0003183514630000034
it is meant that the voltage returns at each time,
Figure BDA0003183514630000035
refers to the mean value of the regressed voltage.
Optionally, the archiving in combination with the gear selection principle further includes archiving according to the voltage regression mean value; wherein the voltage regression mean values belong to I class [420,430), [410,420) II class, [400,410) III class, [390,400) IV class and [380- & 390) V class.
The application provides a distribution transformer gear distinguishing method based on least square regression, which comprises the following steps: acquiring distribution transformer voltage, and filling missing data in the distribution transformer voltage by using a Lagrange interpolation method to obtain target data; drawing a voltage curve by using the target data; performing least square regression on the voltage curve, and establishing a first equation; establishing a function of the parameter in the first equation, and calculating to obtain an expression and a second equation of the parameter relative to the first equation; and calculating a least square voltage regression mean value according to a second equation, and filing by combining a distribution gear selection principle. According to the method, missing data are filled by using a Lagrange interpolation method, then least square regression straight lines are obtained by using distribution and transformation outlet voltages, and finally the least square regression mean value is calculated to match the gear. Experimental results show that the provided identification method can accurately carry out gear attribution and has certain reliability.
The beneficial effect of this application is as follows:
(1) solving the problem of data loss of the distribution transformer voltage by using a Lagrange interpolation method;
(2) the least square regression of the distribution transformer voltage can eliminate the condition of over-high or over-low voltage, so that the voltage is distributed near a certain voltage gear, the gear identification is more accurate, and the influence of voltage fluctuation is avoided;
(3) and the gear attribution can be more conveniently carried out by calculating the voltage regression mean value and combining with the gear selection principle of the distribution transformer.
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In order to more clearly explain the technical solution of the present application, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious to those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a method for determining a gear of a distribution transformer based on least squares regression according to an embodiment of the present disclosure;
FIG. 2 is a diagram of a standard IEEE14 node system;
FIG. 3 is a comparison of the 24 point voltage curve before and after Lagrange interpolation in example 1;
FIG. 4 is a graph of the voltage curve at 24 th gear in example 1 and a least squares regression;
FIG. 5 is a graph of voltage at 24 th gear in example 1 and a least squares regression;
FIG. 6 shows the voltage curve at 24 th gear in example 1 and the least squares regression.
Detailed Description
Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following examples do not represent all embodiments consistent with the present application. But merely as exemplifications of systems and methods consistent with certain aspects of the application, as recited in the claims.
Referring to fig. 1, a schematic flow chart of a method for determining a gear of a distribution transformer based on least squares regression provided in the embodiment of the present application is shown.
The application provides a distribution transformer gear distinguishing method based on least square regression, which comprises the following steps:
s1: acquiring distribution transformer voltage, and filling missing data in the distribution transformer voltage by using a Lagrange interpolation method to obtain target data;
filling missing data in the distribution voltage by using a Lagrange interpolation method, and obtaining target data comprises the following steps:
establishing a polynomial function: (x)0,y0)，…，(xk,yk) Wherein x isjIs an independent variable, yjIs a dependent variable; due to any two x of polynomial functionsjIf different, the Lagrange interpolation polynomial can be expressed as:
Figure BDA0003183514630000041
and calculating missing data in the distribution voltage through a Lagrange difference polynomial, and combining the missing data with the distribution voltage to obtain target data.
S2: drawing a voltage curve by using the target data;
s3: performing least square regression on the voltage curve, and establishing a first equation;
performing least square regression on the voltage curve, and setting up a first equation as follows:
let the target data formed by the two variables be [ (x)1,y1),(x2,y2),...,(xi,yi)]Establishing a linear equation of the target data about the coordinate distribution of the x-y direct system; wherein the linear equation is a first equation and the expression is
Figure BDA0003183514630000042
Wherein, a0，a1Is any real number.
S4: establishing a function of the parameters in the first equation, and calculating to obtain an expression of the parameters relative to the first equation to obtain a second equation;
establishing a function of the parameters in the first equation
Figure BDA0003183514630000051
Wherein V is about a0，a1A function of two parameters;
substituting the function of the parameter into a first equation to obtain a formula 1; wherein, formula 1 is expressed as follows:
Figure BDA0003183514630000052
for a in the formula 10，a1Solving an extreme value by first-order partial derivative to obtain a formula 2; wherein, formula 2 is expressed as follows:
Figure BDA0003183514630000053
transforming the formula 2 by shifting terms to obtain a0，a1Two parameters with respect to xi，yiThe expression of (1); wherein the expression is as follows:
Figure BDA0003183514630000054
and substituting the expression into the first equation to obtain a second equation.
S5: calculating a least square voltage regression mean value according to the second equation, and filing by combining a distribution gear selection principle; the gear selection principle of the distribution transformer is as follows: i gear: shift range + 5%, voltage class 420V; II, grade: shift range + 2.5%, voltage level 410V; III stage: the gear range is 0%, and the voltage level is 400V; IV gear: the gear range is-2.5%, and the voltage level is 390V; v gear: the gear range is-5 percent, and the voltage level is 380V.
The formula for calculating the least squares regression mean of the voltages according to the second equation is:
Figure BDA0003183514630000055
wherein the content of the first and second substances,
Figure BDA0003183514630000056
it is meant that the voltage returns at each time,
Figure BDA0003183514630000057
refers to the mean value of the regressed voltage.
Specifically, the filing in combination with the gear selection principle of the distribution transformer further comprises filing according to the voltage regression mean value; wherein the voltage regression mean value belongs to I gear at [420,430), [410,420) II gear, [400,410) III gear, [390,400) IV gear and [380- & 390) V gear.
The application provides a distribution and transformation gear distinguishing method based on least square regression, which comprises three steps of distribution and transformation voltage preprocessing, voltage curve least square regression and gear attribution. Firstly, filling missing data by using a Lagrange interpolation method, then obtaining a least square regression line by using distribution outlet voltage, and finally calculating a least square regression mean value to match the gear.
Firstly, performing interpolation processing on a distribution transformation 24-point voltage curve by adopting a Lagrange method. A polynomial function is set: (x)0，y0)，...，(xk，yk) Wherein x isjIs an independent variable, yjIs a dependent variable; due to any two x of polynomial functionsjIf different, the Lagrange interpolation polynomial can be expressed as:
Figure BDA0003183514630000061
in practical application, when the distribution transform data is acquired, data measurement is incomplete due to reasons such as abnormality of a measuring device, and a 24-point curve cannot be formed, so that interpolation processing needs to be performed on the data, a lagrange interpolation method is commonly used for processing missing points, and the incompletely acquired data can be supplemented. Unknown data can be easily obtained by the least square method, and the sum of squares of errors between these obtained data and actual data is minimized.
And secondly, performing least square regression on the interpolated voltage curve. Least squares regression is defined as follows: let two variables form a data pair [ (x)1，y1)，(x2，y2)，...，(xi，yi)]The data are plotted in x-y coordinates and distributed near a straight line, and the expression of the straight line equation is:
Figure BDA0003183514630000062
the identification of distribution gear is based on voltage quantity, the voltage is time-varying data, and can be calculated by least square regression [ (t)1，u1)，(t2，u2)，...，(t24，u24)]Obtaining a straight line with the minimum sum of squares of errors between the actual dependent variable and the obtained data, wherein the regression straight line can eliminate the overhigh or overlow voltageSuch that the voltage is distributed around a certain voltage step.
Wherein a is0，a1Is any real number, the least square method is when the independent variable takes the value of xiDependent variable yiThe square of the difference between the predicted values and the actual dependent variable values is the minimum, and the sum of the squares of the differences between all the predicted values and the actual dependent variable values is the minimum for the whole regression equation. Therefore, the equation is established:
Figure BDA0003183514630000063
in formula (3) V is with respect to a0，a1The function of two parameters, substituting equation (2) for equation (3) can be obtained:
Figure BDA0003183514630000064
function V is respectively paired with a0，a1First order partial derivative extremum
Figure BDA0003183514630000065
The term of the equation (5) is transformed to obtain a0，a1Two parameters with respect to xi，yiIs described in (1).
Figure BDA0003183514630000066
And thirdly, performing least square regression on the 24-point voltage curve, calculating a mean value, and filing by combining a distribution gear selection principle. The gear selection principle of the distribution transformer is as follows: i gear: shift range + 5%, voltage class 420V; II, grade: shift range + 2.5%, voltage level 410V; III stage: the gear range is 0%, and the voltage level is 400V; IV gear: the gear range is-2.5%, and the voltage level is 390V; v gear: the gear range is-5%, and the voltage level is 380V; the regression voltage mean expression is as follows:
Figure BDA0003183514630000071
wherein the content of the first and second substances,
Figure BDA0003183514630000072
it is meant that the voltage returns at each time,
Figure BDA0003183514630000073
refers to the mean value of the regressed voltage.
The method for determining the gear position of the distribution transformer based on the least square regression is described below with reference to specific measured data.
Example 1:
the IEEE standard 14 node system simulation model is shown in fig. 2. The specific parameters are as follows: the voltage level is 10kV, the frequency is 50Hz, the transformer capacity is 10MW, and voltage curves of different gears of the distribution transformer are shown in figure 4.
The specific implementation steps are as follows:
(1) preprocessing the distribution voltage curve according to the step S1 in the specification, taking 24 points of data of each gear in one day to form the distribution voltage curve, and performing interpolation processing on the distribution voltage by adopting a Lagrange interpolation method. A comparison of the before and after interpolation is shown in FIG. 3.
(2) Performing least square regression on the data according to steps S2-S4 in the specification, taking five gear voltage, wherein the voltage fluctuation of each gear is large, if an error is generated by gear setting only by a peak value, performing least square regression on the 24-point voltage of each gear respectively, wherein the minimum value of the first gear regression voltage is 420.28V, and the maximum value is 423.08V; the minimum value of the second gear regression voltage is 412.57V, and the maximum value is 413.38V; the minimum value of the third-gear regression voltage is 402.00V, and the maximum value is 403.54V; the minimum value of the fourth gear regression voltage is 391.35V, and the maximum value is 391.95V; the minimum value of the fifth gear regression voltage is 379.04V, and the maximum value is 382.43V.
(3) According to the step S5 of the specification, averaging the least square regression straight line of the distribution and transformation voltage and performing gear attribution, wherein the regression average voltage of the first gear is 421.68V, and the attribution is the first gear; the second gear regression mean voltage is 412.98V, and the second gear regression mean voltage belongs to the second gear; the third gear regression mean voltage is 402.37V, and the attribution is the third gear; the fourth gear regression mean voltage is 391.65V, and the fourth gear regression mean voltage belongs to the fourth gear; the fifth gear regression mean voltage was 380.73V, and was assigned as fifth gear.
Example 2:
the IEEE standard 14 node system simulation model is shown in fig. 2. The specific parameters are as follows: the voltage level is 10kV, the frequency is 50Hz, the transformer capacity is 10MW, and voltage curves of different gears of the distribution transformer are shown in figure 5.
The specific implementation steps are as follows:
(1) preprocessing the distribution voltage curve according to the step S1 in the specification, taking 24 points of data of each gear in one day to form the distribution voltage curve, and performing interpolation processing on the distribution voltage by adopting a Lagrange interpolation method.
(2) Performing least square regression on the cleaned data according to steps S2-S4 in the specification, taking five gear voltages, and performing least square regression on the 24-point voltage of each gear respectively, wherein the minimum value of the first gear regression voltage is 418.56V, and the maximum value of the first gear regression voltage is 427.01V; the minimum value of the second gear regression voltage is 410.51V, and the maximum value is 422.14V; the minimum value of the third-gear regression voltage is 399.62V, and the maximum value is 403.93V; the minimum value of the fourth gear regression voltage is 387.04V, and the maximum value is 395.20V; the minimum value of the fifth gear regression voltage is 379.36V, and the maximum value is 381.33V.
(3) According to the step S5 of the specification, averaging the least square regression straight line of the distribution and transformation voltage and performing gear attribution, wherein the regression average voltage of the first gear is 422.79V, and the attribution is the first gear; the second gear regression mean voltage is 416.33V, and the second gear regression mean voltage belongs to the second gear; the third gear regression mean voltage is 401.78V, and the attribution is the third gear; the fourth gear regression mean voltage is 391.12V, and the fourth gear regression mean voltage belongs to the fourth gear; the fifth gear regression mean voltage was 380.34V, and was assigned as fifth gear.
Example 3:
the IEEE standard 14 node system simulation model is shown in fig. 2. The specific parameters are as follows: the voltage level is 10kV, the frequency is 50Hz, the transformer capacity is 10MW, and voltage curves of different gears of the distribution transformer are shown in figure 6.
The specific implementation steps are as follows:
(1) preprocessing the distribution voltage curve according to the step S1 in the specification, taking 24 points of data of each gear in one day to form the distribution voltage curve, and performing interpolation processing on the distribution voltage by adopting a Lagrange interpolation method.
(2) Performing least square regression on the cleaned data according to steps S2-S4 in the specification, taking five gear voltages, and performing least square regression on the 24-point voltage of each gear respectively, wherein the minimum value of the first gear regression voltage is 423.43V, and the maximum value of the first gear regression voltage is 424.95V; the minimum value of the second gear regression voltage is 408.63V, and the maximum value is 417.63V; the minimum value of the third-gear regression voltage is 400.79V, and the maximum value is 403.82V; the minimum value of the fourth gear regression voltage is 393.73V, and the maximum value is 394.97V; the minimum value of the fifth gear regression voltage is 381.12V, and the maximum value is 382.16V.
(3) According to the step S5 of the specification, averaging the least square regression straight line of the distribution and transformation voltage and performing gear attribution, wherein the regression average voltage of the first gear is 424.19V, and the attribution is the first gear; the second gear regression mean voltage is 413.13V, and the second gear regression mean voltage belongs to the second gear; the third gear regression mean voltage is 402.30V, and the attribution is the third gear; the fourth gear regression mean voltage is 394.35V, and the fourth gear regression mean voltage belongs to the fourth gear; the fifth gear regression mean voltage was 381.64V, and was assigned as fifth gear.
The application provides a distribution transformer gear distinguishing method based on least square regression, which comprises the following steps: acquiring distribution transformer voltage, and filling missing data in the distribution transformer voltage by using a Lagrange interpolation method to obtain target data; drawing a voltage curve by using the target data; performing least square regression on the voltage curve, and establishing a first equation; establishing a function of the parameters in the first equation, and calculating to obtain an expression of the parameters relative to the first equation to obtain a second equation; and calculating a least square voltage regression mean value according to the second equation, and filing by combining a distribution gear selection principle. According to the method, missing data are filled by using a Lagrange interpolation method, then least square regression straight lines are obtained by using distribution and transformation outlet voltages, and finally the least square regression mean value is calculated to match the gear. Experimental results show that the provided identification method can accurately carry out gear attribution and has certain reliability.

Claims (6)

1. A distribution transformer gear distinguishing method based on least square regression is characterized by comprising the following steps:
acquiring distribution transformer voltage, and filling missing data in the distribution transformer voltage by using a Lagrange interpolation method to obtain target data;
drawing a voltage curve by using the target data;
performing least square regression on the voltage curve, and establishing a first equation;
establishing a function of the parameter in the first equation, and calculating to obtain an expression and a second equation of the parameter relative to the first equation;
calculating a least square voltage regression mean value according to the second equation, and filing by combining a distribution gear selection principle; the gear selection principle of the distribution transformer is as follows: i gear: shift range + 5%, voltage class 420V; II, grade: shift range + 2.5%, voltage level 410V; III stage: the gear range is 0%, and the voltage level is 400V; IV gear: the gear range is-2.5%, and the voltage level is 390V; v gear: the gear range is-5 percent, and the voltage level is 380V.
2. The method for distinguishing the distribution transformer gear based on the least squares regression as claimed in claim 1, wherein the step of filling missing data in the distribution transformer voltage by using a lagrange interpolation method to obtain target data comprises:
establishing a polynomial function: (x)0,y0)，…，(xk,yk) Wherein x isjIs an independent variable, yjIs a dependent variable; due to any two x of polynomial functionsjIf different, the Lagrange interpolation polynomial can be expressed as:
Figure FDA0003183514620000011
and calculating missing data in the distribution voltage through a Lagrange difference polynomial, and combining the missing data with the distribution voltage to obtain target data.
3. The method for distinguishing the distribution transformer gear based on the least square regression is characterized in that the voltage curve is subjected to the least square regression, and the first equation is set up as follows:
let the target data formed by the two variables be [ (x)1,y1),(x2,y2),...,(xi,yi)]Establishing a linear equation of the target data about the coordinate distribution of the x-y direct system; wherein the linear equation is a first equation and the expression is
Figure FDA0003183514620000012
Wherein, a0,a1Is any real number.
4. The least squares regression-based gear shift level identification method for a distribution transformer according to claim 3, wherein the step of establishing a function of the parameters in the first equation and calculating an expression of the parameters with respect to the first equation and a second equation comprises:
establishing a function of the parameters in the first equation
Figure FDA0003183514620000013
Wherein V is about a0,a1A function of two parameters;
substituting the function of the parameter into a first equation to obtain a formula 1; wherein, formula 1 is expressed as follows:
Figure FDA0003183514620000014
for a in the formula 10,a1Solving an extreme value by first-order partial derivative to obtain a formula 2; wherein, formula 2 is expressed as follows:
Figure FDA0003183514620000015
transforming the formula 2 by shifting terms to obtain a0,a1Two parameters with respect to xi,yiThe expression of (1); wherein the expression is as follows:
Figure FDA0003183514620000021
and substituting the expression into the first equation to obtain a second equation.
5. The method for distinguishing the distribution transformer gear based on the least square regression is characterized in that the formula for calculating the least square voltage regression mean value according to the second equation is as follows:
Figure FDA0003183514620000022
wherein the content of the first and second substances,
Figure FDA0003183514620000023
it is meant that the voltage returns at each time,
Figure FDA0003183514620000024
refers to the mean value of the regressed voltage.
6. The least squares regression-based power distribution and transformation gear discrimination method according to any one of claims 1 to 5, wherein the filing in combination with the power distribution and transformation gear selection principle further comprises filing according to the voltage regression mean value; wherein the voltage regression mean values belong to I class [420,430), [410,420) II class, [400,410) III class, [390,400) IV class and [380- & 390) V class.
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