CN115640874A

CN115640874A - Transformer state prediction method based on improved grey model theory

Info

Publication number: CN115640874A
Application number: CN202211151451.6A
Authority: CN
Inventors: 池翔; 吴子衿; 汤蒙蒙; 杨辉; 杨苗; 陈小慧
Original assignee: State Grid Ningxia Electric Power Co Ltd
Current assignee: State Grid Ningxia Electric Power Co Ltd
Priority date: 2022-09-21
Filing date: 2022-09-21
Publication date: 2023-01-24

Abstract

The invention provides a transformer state prediction method based on an improved grey model theory, and belongs to the technical field of power transmission and transformation primary equipment state prediction. The method comprises the following steps: acquiring state data of the transformer changing along with time in a transformer insulation test to form a transformer state database; dividing all the state data in the transformer state database into a training set and a testing set; constructing an original sequence X of transformer states according to the training set ⁽⁰⁾ And further performing a summation process to obtain a summation sequence X ⁽¹⁾ (ii) a Optimization of parameter-a by CSO algorithm ₀ 、b ₀ And the initial correction term ε _k Obtaining a development coefficient-a, an ash action amount b and a correction term epsilon; optimizing the initial GM (1,1) model according to the optimized parameters-a, b and epsilon, resulting in an optimized GM (1,1) Model expression

Description

Transformer state prediction method based on improved grey model theory

Technical Field

The invention relates to the technical field of power transmission and transformation primary equipment state prediction, in particular to a transformer state prediction method based on an improved grey model theory.

Background

The power industry is closely related to all aspects of society, the power demand is increasing with the rapid development of economic level, and the scale of the power grid must be enlarged to meet the increase of the power demand. The current trend of grid size has slowly shifted from individual regional grids to interconnection of regional grids, thereby constructing large regional interconnected grids. Compared with a regional power grid, the regional interconnected large power grid has higher requirements on reliability, safety and the like. The power transformer is used as a junction for connecting a power receiving side, a power transmission side and a power consumer, and must be kept in normal operation all the time to ensure the safety and stability of the whole power system. When the power transformer is in an abnormal operation state or fails, the stable fluctuation of the whole power system is caused certainly, and therefore higher requirements are provided for the normal operation of the transformer compared with other power transmission and transformation equipment.

The evaluation of the running state of the power transformer is the basic content of the transformer state maintenance, the timely and accurate grasping of the running state of the power transformer is the premise of fault prediction of the transformer, reliable reference basis is provided for formulation of transformer operation and maintenance strategies, and a reasonable and scientific prediction scheme needs to be formulated to predict the state prediction of the power transformer so as to improve the transformer maintenance working efficiency and avoid damage to the transformer caused by blind maintenance.

Disclosure of Invention

In view of this, the invention provides a transformer state prediction method based on an improved gray model theory, which is used for predicting the transformer state and improving the transformer overhaul work efficiency.

The technical scheme adopted by the embodiment of the invention for solving the technical problem is as follows:

a transformer state prediction method based on an improved grey model theory comprises the following steps:

s11, acquiring state data of the transformer changing along with time in a transformer insulation test to form a transformer state database;

step S12, dividing all the state data in the transformer state database into a training set and a testing set;

s13, constructing an original sequence X of the transformer state according to the training set ⁽⁰⁾ And further performing a summation process to obtain a summation sequence X ⁽¹⁾ According to said once-accumulated sequence X ⁽¹⁾ For sequences with quasi-exponential law, the whitening differential equation of the initial GM (1,1) model is satisfied:

X ⁽⁰⁾ ＝(x ⁽⁰⁾ (1),x ⁽⁰⁾ (2),…x ⁽⁰⁾ (n))

X ⁽¹⁾ ＝(x ⁽¹⁾ (1),x ⁽¹⁾ (2),…x ⁽¹⁾ (n))

wherein, x (k)>e, k =1,2, … n, initial coefficient of development-a ₀ And initial ash contribution amount b ₀ Is solved by a least square method, and the initial edge value of the initial GM (1,1) model

Comprises the following steps:

step S14, optimizing parameter-a through CSO algorithm ₀ 、b ₀ And the initial correction term ε _k Is a system of developmentA number-a, a grey-acting quantity b and a correction term epsilon, wherein the initial correction term epsilon _k The expression of (a) is:

wherein the integral value

Is curve y = x ⁽¹⁾ (t) in the interval [ k-1,k]The area of a curved trapezoid surrounded by the t axis;

s15, optimizing the initial GM (1,1) model according to the optimized parameters-a, b and epsilon to obtain an optimized GM (1,1) model expression

And S16, verifying the optimized GM (1,1) model through the test set.

And S17, predicting the future state of the transformer based on the optimized GM (1,1) model.

Preferably, the state data includes an insulation resistance value or an oil dielectric loss tangent.

Preferably, the state data is insulation resistance value, the step S11 obtains state data of the transformer changing with time in the transformer insulation test, and the transformer state database is formed by:

acquiring the resistance value of the insulation resistor changing along with time;

and converting the resistance value of the insulation resistor into a reciprocal of the resistance value, and recording the reciprocal to the transformer state database.

Preferably, the step S14 optimizes the parameter-a by CSO algorithm ₀ 、b ₀ And the initial correction term ε _k And obtaining the development coefficient-a, the ash action amount b and the correction term epsilon comprises:

step S141, initializing variables, and determining the total number pop of chickens in the chicken group, the cock proportion, the hen proportion, the chick proportion, the space dimension dim, the total iteration number M and the relationship update iteration number G;

step S142, determining the objective function f (a, b, epsilon):

step S143, a weight vector w = (w) is set ₁ ,w ₂ ,w ₃ ) Wherein, let w ₁ 、w ₂ 、w ₃ At w _i ∈[0,1]Taking values within the range, and randomly generating pop space points as the roles of the chicken flocks;

step S144, calculating adaptive values of the space points, and sequentially determining individual types of the cocks, the hens and the chicks according to the cock proportion, the hen proportion and the chick proportion from small to large according to adaptive values, wherein an adaptive value function (w) is as follows:

wherein E is _w To generalize errors;

step S145, setting an initial weight vector, and enabling w ₁ ＝a ₀ 、w ₂ ＝b ₀ 、w ₃ ＝ε _k Starting an iterative operation based on the objective function f (a, b, epsilon);

step S146, respectively carrying out position updating iteration on the cock, the hen and the chicken, and calculating an adaptive value after the positions are updated;

step S147, when the iteration times t are multiples of G, the roles in the chicken flocks are redistributed;

step S14When t is>M, the iteration operation is ended, and w in the iteration process is selected ₁ Fitness, w ₂ Fitness, w ₃ Global optimum position w with fitness being the best fitness value _best ；

In step S149, let (a, b, ∈) = w _best To obtain a, b and epsilon.

Further, the invention provides a transformer state prediction method based on an improved grey model theory, which comprises the following steps:

s21, acquiring state data of the transformer changing along with time in a transformer insulation test to form a transformer state database;

s22, constructing an original sequence X of the transformer state according to the training set ⁽⁰⁾ ；

X ⁽⁰⁾ ＝(x ⁽⁰⁾ (1),x ⁽⁰⁾ (2),…x ⁽⁰⁾ (n))

Wherein x (k)>e，k＝1,2,…n；x ⁽⁰⁾ (k)

Step S23, based on transformation function, to the original sequence X ⁽⁰⁾ Data conversion is carried out to obtain a conversion original sequence Y ⁽⁰⁾ ：

Y ⁽⁰⁾ ＝(y ⁽⁰⁾ (1),y ⁽⁰⁾ (2),..y ⁽⁰⁾ (n))

Step S24, for the transformed original sequence Y ⁽⁰⁾ Performing a first accumulation process to obtain a first accumulation sequence Y ⁽¹⁾ ：

Y ⁽¹⁾ ＝(y ⁽¹⁾ (1),y ⁽¹⁾ (2),…y ⁽¹⁾ (n))

Step S25, according to the primary accumulation sequence Y ⁽¹⁾ For sequences with quasi-exponential law, the whitening differential equation of the initial GM (1,1) model is satisfied:

wherein the initial development coefficient-a and the initial gray action amount b are solved by least square method, and the initial margin of the initial GM (1,1) model

Step S26, through the initial correction term epsilon _k Correcting the initial edge value to obtain a corrected GM (1,1) model expression

And a data reduction expression:

wherein the integral value

Is curve m = y ⁽¹⁾ (t) in the interval [ k-1,k]The area of a curved trapezoid surrounded by the t axis;

step 27, the future state of the transformer is modeled based on the corrected GM (1,1).

Preferably, the state data is insulation resistance value, the step S21 obtains state data of the transformer changing with time in the transformer insulation test, and the step S constitutes a transformer state database including:

and converting the resistance value of the insulation resistor into a reciprocal of the resistance value, and inputting the reciprocal of the resistance value into the transformer state database.

Preferably, the transformation function is a logarithmic function, and the step S23 is to perform the transformation function on the original sequence X ⁽⁰⁾ Original sequence Y obtained by data transformation ⁽⁰⁾ Comprises the following steps:

Y ⁽⁰⁾ ＝(y ⁽⁰⁾ (1),y ⁽⁰⁾ (2),…y ⁽⁰⁾ (n))

wherein y = f (x (k)) = clnx (k) + d, c > max { x (k) | k =1,2, … n }, d ≧ 0, k =1,2, … n;

the data reduction expression in the step S26

Comprises the following steps:

preferably, the transformation function is a trigonometric function, and the step S23 is based on the transformation function to the original sequence X ⁽⁰⁾ Original sequence Y obtained by data transformation ⁽⁰⁾ Comprises the following steps:

Y ⁽⁰⁾ ＝(y ⁽⁰⁾ (1),y ⁽⁰⁾ (2),…y ⁽⁰⁾ (n))

wherein y = f (x) ^(k) )＝csc(x ^(k) )，

k＝1,2,..n；

The data reduction expression in the step S26

Comprises the following steps:

according to the technical scheme, the transformer state prediction based on the improved grey model theory provided by the embodiment of the inventionA method. The method comprises the following specific steps: acquiring state data of the transformer changing along with time in a transformer insulation test to form a transformer state database; dividing all state data in a transformer state database into a training set and a test set; constructing an original sequence X of transformer states from a training set ⁽⁰⁾ And further performing a summation process to obtain a summation sequence X ⁽¹⁾ (ii) a Optimization of parameter-a by CSO algorithm ₀ 、b ₀ And the initial correction term ε _k Obtaining a development coefficient-a, an ash action amount b and a correction term epsilon; optimizing an initial GM (1,1) model according to the optimized parameters-a, b and epsilon to obtain an optimized GM (1,1) model expression

The optimized GM (1,1) model is verified through a test set; predicting a future state of the transformer based on the optimized GM (1,1) model. The method and the device are used for predicting the state of the transformer and improving the overhauling working efficiency of the transformer so as to avoid damage to the transformer caused by blind overhauling.

Drawings

Fig. 1 is a first flowchart of a transformer state prediction method based on an improved gray model theory according to the present invention.

Fig. 2 is a second flowchart of the transformer state prediction method based on the improved gray model theory according to the present invention.

FIG. 3 is a diagram illustrating background errors.

FIG. 4 is a graph showing the variation of reciprocal insulation resistance with age.

Fig. 5 is a graph comparing the insulation resistance prediction result with the actual value.

Fig. 6 is a graph comparing the predicted result of the dielectric loss tangent of oil with the actual value.

Fig. 7 is a third flowchart of the transformer state prediction method based on the improved gray model theory according to the present invention.

Detailed Description

The technical scheme and the technical effect of the invention are further elaborated in the following by combining the drawings of the invention.

As shown in FIG. 1, the transformer state prediction method based on the improved grey model theory of the invention improves parameters in the grey prediction model through a chicken flock algorithm, and improves prediction accuracy. The method comprises the following steps:

s11, acquiring state data of the transformer changing along with time in a transformer insulation test to form a transformer state database; here, the state data includes the insulation resistance value and/or the oil dielectric loss factor, that is, the invention can predict the insulation resistance value and the oil dielectric loss factor of the transformer, and also can predict at the same time, it should be noted that the insulation resistance value needs to be calculated in a reciprocal manner, so the insulation resistance value in the transformer state database is actually the reciprocal of the resistance value;

step S12, dividing all state data in a transformer state database into a training set and a testing set;

s13, constructing an original sequence X of the transformer state according to the training set ⁽⁰⁾ ：

X ⁽⁰⁾ ＝(x ⁽⁰⁾ (1),x ⁽⁰⁾ (2),…x ⁽⁰⁾ (n)) (1.1)

And further carrying out primary accumulation processing to obtain a primary accumulation sequence X ⁽¹⁾ ：

X ⁽¹⁾ ＝(x ⁽¹⁾ (1),x ⁽¹⁾ (2),…x ⁽¹⁾ (n)) (1.2)

Wherein the content of the first and second substances,

look once cumulative sequence X ⁽¹⁾ For sequences with quasi-exponential law, from X ⁽¹⁾ An initial GM (1,1) model is established that satisfies the whitening differential equation:

wherein the initial coefficient of development-a ₀ And initial ash action amount b ₀ Is solved by the least square method, the initial edge value of the initial GM (1,1) model

Comprises the following steps:

by background value Z ⁽¹⁾ (k) In place of X ⁽¹⁾ (k) The basic form of the GM (1,1) model is obtained, with the gray differential equation expressed as:

x ⁽⁰⁾ (k)+a ₀ z ⁽¹⁾ (k)＝b ₀ (1.5)

note the book

For the parameter column, the formula (1.5) is converted into a matrix form

To obtain

The parameter solution is obtained by a least square method according to the original sequence;

obtaining the parameter a ₀ 、b ₀ After the value of (c), the differential equation is solved:

is also called the time response function, is

The time response sequence of the initial GM (1,1) model is

The reduction value is:

substituting k =2,3, …, n into the above formula to obtain an initial data fitting value; when k > n, a prediction for the future is obtained.

In addition, the initial correction term ε is given for the initial GM (1,1) model _k ：

In the interval [ k-1,k]For the GM (1,1) model

Integral calculation is carried out to obtain

Is simplified to obtain

Namely that

And formula (1.5) x ⁽⁰⁾ (k)+az ⁽¹⁾ (k) Comparison of = b, give

The background value of the original value is constructed as

The conventional background value is represented by the area of a trapezoid, and the integral value

Is curve y = x ⁽¹⁾ (t) in the interval [ k-1,k]The area of a curved trapezoid surrounded by the t axis. The error is shown in the shaded portion of figure 3, let

As can be seen from the lagrange median theorem,

wherein the integral value

Is curve y = x ⁽¹⁾ (t) in the interval [ k-1,k]The area of a curved trapezoid surrounded by the t axis; and x ⁽¹⁾ (ε) may be represented as x ⁽¹⁾ (ε)＝α _k x ⁽¹⁾ (k-1)+(1-α _k )x ⁽¹⁾ (k)，0<α _k <1, so the correct background value configuration is z ⁽¹⁾ (k)＝α _k x ⁽¹⁾ (k-1)+(1-α _k )x ⁽¹⁾ (k),0<α _k <1。

Step S14, optimizing parameter-a through CSO algorithm ₀ 、b ₀ And the initial correction term ε _k The method comprises the following steps of obtaining a development coefficient-a, an ash action amount b and a correction term epsilon:

step S142, determining the objective function f (a, b, epsilon):

step S143, sets a weight vector w = (w) ₁ ,w ₂ ,w ₃ ) Wherein, let w ₁ 、w ₂ 、w ₃ At w _i ∈[0,1]Taking values within the range, and randomly generating pop space points as the roles of the chicken flocks;

step S144, calculating adaptive values of all the space points, sorting and allocating roles according to the sizes of the adaptive values, sequentially determining the individual types of the cocks, the hens and the chicks according to the proportion of the cocks, the proportion of the hens and the proportion of the chicks from small to large according to the sequence of the adaptive values, wherein an adaptive value function (w) is as follows:

wherein, E _w To generalize errors;

the iterative formula for the cock is as follows:

in the formula (I), the compound is shown in the specification,

represents the j-dimension position value of the ith cock in the t iteration number, randn (0, sigma) ² ) Represents a compliance expectation of 0, varianceIs σ ² A random number that is too randomly distributed; f. of _i Denotes the fitness of the ith rooster, f _r The fitness of the r-th cock is shown, i is not equal to k, and epsilon is an infinite decimal number in order to avoid that the denominator is 0;

the iterative formula for hens is as follows:

C ₂ ＝exp(f _r2 -f _i ) (1.22)

rand is a random number with uniformly distributed intervals, r ₁ The chicken is a cock in the group of the ith hen; r is a radical of hydrogen ₂ Randomly selecting any individual from cock and hen in the whole chicken group ₁ ≠r ₂ ，C ₁ 、C ₂ Respectively representing the influence weight of the cock to which the ith hen belongs and other group cocks on the hen;

the iterative formula for chicks is as follows:

x _i,j ^t+1 ＝x _i,j ^t +FL*(x _m,j ^t -x _i,j ^t ) (1.23)

m represents the chicken mother of the ith chicken, FL is a following coefficient and generally takes a value in a specified interval [0,2 ].

Step S147, when the iteration times t are multiples of G, the roles in the chicken group are redistributed, namely the relationship in the group is reestablished;

step S148, when t is>M, the iteration operation is finished, and w in the iteration process is selected ₁ Fitness, w ₂ Fitness, w ₃ Global optimum position w with fitness being the best fitness value _best ；

In step S149, let (a, b, ∈) = w _best To obtain a, b and epsilon.

Step S15, according to optimizationOptimizing the initial GM (1,1) model by the post-parameters-a, b and epsilon to obtain an optimized GM (1,1) model expression

And S16, verifying the optimized GM (1,1) model through the test set.

As shown in fig. 2, further, the present invention provides a gray prediction model based on function transformation for predicting the future state of the transformer, and the prediction step includes:

s21, acquiring state data of the transformer changing along with time in a transformer insulation test to form a transformer state database; here, the state data includes the insulation resistance value or the oil dielectric loss factor, that is, the invention can predict the insulation resistance value and the oil dielectric loss factor of the transformer, it should be noted that the insulation resistance value needs to be calculated in a reciprocal manner, and therefore, the insulation resistance value in the transformer state database is actually the reciprocal of the resistance value;

X ⁽⁰⁾ ＝(x ⁽⁰⁾ (1),x ⁽⁰⁾ (2),…x ⁽⁰⁾ (n)) (2.1)

Wherein x (k) > e, k =1,2, … n;

step S23, based on the transformation function, the original sequence X ⁽⁰⁾ Carrying out data transformation to obtain a transformed original sequence Y ⁽⁰⁾ ：

Y ⁽⁰⁾ ＝(y ⁽⁰⁾ (1),y ⁽⁰⁾ (2),..y ⁽⁰⁾ (n)) (2.2)

Y ⁽¹⁾ ＝(y ⁽¹⁾ (1),y ⁽¹⁾ (2),…y ⁽¹⁾ (n)) (2.3)

Wherein, the first and the second end of the pipe are connected with each other,

k =1,2, … n, next to mean generation

Z ⁽¹⁾ ＝(z ⁽¹⁾ (1),z ⁽¹⁾ (2),…z ⁽¹⁾ (n)) (2.4)

Wherein the content of the first and second substances,

k＝1,2,…n；

step S25, according to the once accumulation sequence Y ⁽¹⁾ For sequences with quasi-exponential law, the whitening differential equation of the initial GM (1,1) model is satisfied:

gray differential equation for the GM (1,1) model:

y(k)+az ⁽¹⁾ (k)＝b (2.6)

GM (1,1) model y (k) + az ⁽¹⁾ (k) Time response sequence of = b

Least squares estimation of parameters a and b

Is composed of

Reverting to original data

And a data reduction expression:

wherein the integral value

Is curve m = y ⁽¹⁾ (t) in the interval [ k-1,k]Area correction term epsilon of curved trapezoid surrounded by t axis _k The specific derivation process of (a) is described with reference to the foregoing step S13;

step 27, based on the future state of the corrected GM (1,1) model transformer, if the input value is the oil dielectric loss factor, the output result is the fitting value and the predicted value of the oil dielectric loss factor; if the input value is the reciprocal of the insulation resistance, reciprocal reduction needs to be carried out on the output data to obtain a fitting value and a predicted value of the insulation resistance.

In the foregoing step S23, the type of the transformation function may be a logarithmic function or a trigonometric function.

When the type of the transformation function is a logarithmic function, step S23 is to apply the transformation function to the original sequence X ⁽⁰⁾ Original sequence Y obtained by data transformation ⁽⁰⁾ Comprises the following steps:

Y ⁽⁰⁾ ＝(y ⁽⁰⁾ (1),y ⁽⁰⁾ (2),…y ⁽⁰⁾ (n)) (2.15)

y＝f(x(k))＝clnx(k)+d (2.16)

wherein c > max { x (k) | k =1,2, … n }, d ≧ 0, k =1,2, … n;

accordingly, in step S26, the expression of the GM (1,1) model is transformed based on the logarithmic function data according to equation (2.13)

Comprises the following steps:

when the type of the transformation function is a trigonometric function, step S23 is to apply the transformation function to the original sequence X ⁽⁰⁾ Original sequence Y obtained by data transformation ⁽⁰⁾ Comprises the following steps:

Y ⁽⁰⁾ ＝(y ⁽⁰⁾ (1),y ⁽⁰⁾ (2),…y ⁽⁰⁾ (n)) (2.18)

y＝f(x(k))＝csc(x(k)) (2.19)

wherein the content of the first and second substances,

k＝1,2,..n；

accordingly, in step S26, the expression of the GM (1,1) model is transformed based on trigonometric function data according to equation (2.13)

Comprises the following steps:

in the invention, the state data (DGA historical data and operation data) of the transformer can be obtained from an online monitoring system of a transformer substation, the change randomness of the concentration of the dissolved gas in oil is strong, and the change trend is not obvious under the influence of measurement errors, so that the change trend of the DGA data is better described, the change rule is more accurately explored, and the DGA data needs to be preprocessed firstly:

1) And noise data are eliminated, and the influence of measurement errors is reduced. A confidence level is defined, a confidence limit is determined, and errors exceeding the limit are rejected by considering it as an outlier. There are different methods for determining confidence, and three times the standard deviation is generally taken as confidence:

sample average of

Sample standard deviation of

If it is

The data is considered as noise data and is rejected.

2) And (5) smoothing the data. The method adopts a 'weighted moving average' smoothing processing method. The basic idea of weighting is to take a proper interval by taking a sample point as a center, and perform weighted average calculation on sample data in the interval, wherein the weight of data at the center is the largest, and the weight of data far away from the center is the smallest. The specific calculation formula of the five-point secondary smoothing method is as follows:

after the model is corrected, the prediction effect of the prediction model can be further evaluated for the corrected GM (1,1) model, and three evaluation modes, namely Mean Square Error (MSE), mean square error (RMSE), and Mean Absolute Percent Error (MAPE), are generally adopted:

1) Mean Square Error (MSE) is used as an evaluation criterion of prediction accuracy, and the calculation formula is

MSE＝MSE _Tr +MSE _Te (4.3)

2) The Root Mean Square Error (RMSE) is used as an evaluation standard of the prediction accuracy, and the calculation formula is as follows:

RMSE＝RMSE _Tr +RMSE _Te (4.6)

3) The Mean Absolute Percentage Error (MAPE) is used as an evaluation standard of prediction accuracy, and the calculation formula is as follows:

MAPE＝MAPE _Tr +MAPE _Te (4.9)

in the above formula, y _Tri 、x _Tri 、n _Tri Respectively representing the fitting value, actual value and sample number value, y, of the training data _Tei 、x _Tei 、n _Tei Respectively representing the fit value, actual value and sample number value of the test data. While MSE _Tr 、RMSE _Tr 、MAPE _Tr Reflecting the fitting error, MSE, of the training samples _Te 、RMSE _Te 、MAPE _Te Reflecting the extrapolation error of the test sample. And setting an error threshold value for evaluating the accuracy of the prediction model, and determining that the gray prediction model is feasible if the error threshold value is not exceeded.

Comprehensively considering all factors, the method selects the average absolute percentage error MAPE as the evaluation standard of the prediction model precision: MAPE _Tr Smaller means better fit performance; MAPE _Te Smaller means better extrapolation performance; a smaller MAPE means better prediction model performance.

The following are illustrated by way of example:

according to the method, by taking test data of a high-low ground winding, a sleeve insulation resistance and an oil medium loss factor of a 220kV main transformer of a certain transformer substation of a Yinchuan power grid as an example, the data of the first six years is taken as training data, the data of the last year is taken as test data, and an original GM (1,1) model, a GM (1,1) model based on logarithmic function data transformation, a GM (1,1) model based on trigonometric function and a GM (1,1) model based on chicken swarm algorithm parameter optimization are respectively subjected to fitting and extrapolation analysis.

The insulation resistance and oil dielectric loss data are shown in Table 1-1:

TABLE 1-1 insulation resistance and oil dielectric loss historical data

Firstly, insulation resistance is predicted:

and (3) taking the data of the previous 6 years in the table 1-1 as training sample data, training model parameters, taking the data of the 7 th year as prediction data, and verifying the fitting and extrapolation effects of the models. As described above, the insulation resistance is monotonically decreased, and the insulation resistance is first inverted. The reciprocal value of the insulation resistance after the treatment was changed with time as shown in fig. 4.

When the chicken swarm algorithm is used for determining the model parameters, the value range of the parameter a is determined as [0,1 ]]The value range of the ash action amount b is determined as [0,1 ]]The total number of chickens in the chicken group is 100, the number of the cocks is 15%, the number of the hens is 70%, the number of the chicks is 15%, the maximum iteration number M is 1000, and the individual relationship in the chicken group is updated once every 10 iterations. When the logarithmic function is used for data transformation of the original data, c is satisfied>max { x (k) | k =1,2,. N }, where c =1,d =0 is taken for simplicity of calculation. When the trigonometric function is used for carrying out data transformation on the original data, the requirement is met

k =1,2,3 … n.

And (3) performing grey model and improved method prediction on the data after the insulation resistance is subjected to reciprocal calculation, wherein the simulation result after reduction is shown in a table 1-2.

TABLE 1-2 simulation prediction results of insulation resistance

The comparison of the predicted value and the actual value of the insulation resistance by the GM (1,1) model and the improved method thereof is shown in FIG. 5.

As can be seen from tables 1-2 and FIG. 5, the prediction of the gray model on the insulation resistance is as follows, the fitting accuracy is between 3.15% and 4.94%, and the extrapolation accuracy is between 5.09% and 6.81%, wherein the fitting accuracy and the extrapolation accuracy of the CSOGM (1,1) model are the highest, and the prediction accuracy of the model is greatly improved by using the method of optimizing parameters by using the chicken swarm algorithm CSO.

Second, prediction of oil dielectric loss factor:

the oil dielectric loss data monotonically increases along with the increase of years and can be regarded as a quasi-smooth sequence, the oil dielectric loss data is directly used as original data to perform grey model prediction, and similarly, the data of the first 6 years is used as training data, and the data of the 7 th year is used as prediction data. Fitting and predictive analysis were performed with the original GM (1,1) model, the log function transform-based GM (1,1) model, the trigonometric function transform-based GM (1,1) model, and the CSOGM (1,1) model, respectively. The results of the predictive analysis are shown in tables 1-3. The comparison of the predicted value and the actual value of the oil dielectric loss factor by the GM (1,1) model and its improved method is shown in FIG. 6.

As can be seen from tables 1-3 and fig. 6, the gray model is used to predict the oil dielectric loss with relatively high accuracy in the monotonic increase transformation law, wherein the fitting error of the original GM (1,1) model is 2.51%, the extrapolation error is 3.67%, the relatively high accuracy can be achieved, the fitting error of the CSOGM (1,1) model is 2.21% at minimum, the extrapolation error is 2.05% at minimum, and the prediction effect of the CSOGM (1,1) model is the best. The two data-transformed GM (1,1) models are not very different from the original GM (1,1) model.

TABLE 1-3 simulation prediction results of oil dielectric loss factor

From the simulation calculation results of the insulation resistance and the oil dielectric loss factor, the following conclusion can be obtained:

(1) Compared with an original GM (1,1) model, the prediction precision of performing logarithm or trigonometric function data transformation on original data and then performing calculation by using the GM (1,1) model is improved, because the transformed data has reduced smooth ratio and compressed level ratio, the data characteristics described by a gray model are better met, and the reduction error is not amplified, so the prediction precision is higher;

(2) For sequences with more uniform growth, the fitting precision of the CSOGM model is not greatly improved compared with that of an original GM (1,1) model; for sequences that grow too rapidly, the fitting accuracy of the CSOGM model is significantly better than that of the GM (1,1) model. Because of the relatively uniform sequence for growth, the GM (1,1) model can achieve very high prediction accuracy; for sequences which grow too fast, the prediction accuracy of the GM (1,1) model is reduced, the parameter optimization of the CSOGM model shows superiority, and the prediction accuracy is improved.

Further, the foregoing step S23 transforms the original sequence X based on the transform function ⁽⁰⁾ Is Y ⁽⁰⁾ When the original data is transformed, the original sequence X is used to make the transformed data sequence more suitable for the modeling condition of the gray GM (1,1) model ⁽⁰⁾ The conditions of reducing the slip ratio, maintaining the non-negative concave-up characteristic, adjusting the step ratio compression and ensuring that the reduction error does not increase must be satisfied, and therefore, X can be judged in advance ⁽⁰⁾ Whether the above conditions are satisfied.

Defining an original sequence X = (X (1), X (2), … X (n)) as a system original behavior data sequence, X (k)>0,k =1,2, … n, the smooth ratio of the original sequence X is ρ (k), k =2,3, … n.

When k is>k ₀ ，ρ(k)<Epsilon. Sequence X is called a smooth discrete sequence. The accumulated sequence generated by the smoothed discrete sequence is considered to have a quasi-exponential law. The non-negative transformation f (x (k)) satisfies rho _f (k)<The requirement for ρ (k) is f (x (k)) = x (k) g (k), where the sequence g (k) is non-negative and monotonically decreasing, ρ (k) _f (k) Is the transformed slenderness ratio.

The GM (1,1) model is a model describing data sequences with exponential regularity, when the smoothness ratio of the original data sequence satisfies the existence of epsilon<0.5, when k is>k ₀ ，ρ(k)<When epsilon, the original sequence is a quasi-smooth sequence, and the sequence generated by once accumulation meets the quasi-exponential law. The exponential law of the primary accumulation sequence is more pronounced as the smoothness ratio is smaller.

Defining the original sequence X as a non-negative sequence with a step ratio σ (k) = X (k)/X (k-1), k =2,3, … n with a step ratio deviation of

δ(k)＝|1-σ(k)|＝|1-x(k)/x(k-1)| (5.2)

If the non-negative transformation f (x (k)) = x (k) g (k) satisfies δ _f (k)<δ (k), then we call the transform f (x (k)) the stage ratio compression, where the transformed stage ratio bias is:

δ _f (k)＝|1-σ _f (k)|＝|1-f(x(k))/f(x(k-1))| (5.3)

g (k) is non-negative and strictly monotonically decreasing, X is an increasing sequence, and when the transformation f (X (k)) is an increasing function, f (X (k)) is a level ratio compression transformation; when the transformation f (x (k)) is a decreasing function, if satisfied

Then f (x (k)) is the step ratio compression transform.

When the system changes according to a good exponential law, the prediction accuracy of the gray model can achieve a high effect, but when the system increases too fast, the model still causes a large error. The continuous GM (1,1) model is required to develop the coefficient-a, and when-a is too large, the exponential growth is too rapid, resulting in a rapid increase in the error of the gray model. When-a is less than or equal to 0.3, the simulation precision can reach more than 98 percent; when-a is less than or equal to 0.5, the simulation precision can reach more than 95 percent; when-a >1, the simulation precision is lower than 70%; when-a >1.5, the simulation precision is lower than 50%; when-a >2, the gray model will have no predictive significance.

The step ratio σ (k) = x (k)/x (k-1) describes the growth speed of the data sequence, the growth speed is more obvious when the step ratio is larger, the growth speed is slower when the step ratio is smaller, the development coefficient-a is smaller, and the prediction accuracy is higher. Or from the perspective of the level ratio deviation, the level ratio deviation represents the growth rate, and the smaller the level ratio deviation is, the closer the level ratio is to 1, the higher the prediction accuracy is.

Defining the original sequence X as a non-negative sequence if satisfied

x(k+1)-x(k)>x(k)-x(k-1),k＝2,3,…n (5.5)

X is called a concave-up sequence, and vice versa. The GM (1,1) model simulates a data sequence with gray index law, and the reduced value sequence is a pure exponential sequence. Therefore, non-negative concave-up sequences are suitable for building GM (1,1) models. When data conversion is carried out, the influence of the concave-convex property needs to be considered, and the converted sequence is ensured to have non-negative concave-up characteristics. The effect of the reduction error must also be taken into account after the data changes.

Let y _i ＝f(x _i )，

For the fitted values of the GM (1,1) model,

for the reduced fitting value, the differential median theorem can be used

Xi is between x _i And

in the meantime. Then the reduction error is

Thus, compared to the fitting error of the transformed data column:

when | f' (ξ) | <1, the reduction error increases; when | f' (ξ) | =1, the reduction error is unchanged; when | f' (ξ) | >1, the reduction error decreases.

And analyzing the logarithm function sequence Y (k) after the transformation of the non-negative original sequence X according to the target of reducing the smooth ratio, keeping the non-negative concave-up characteristic, adjusting the level ratio compression and ensuring that the reduction error is not increased:

it can be seen that the function g (x) decreases strictly monotonically, p _f (k)<Rho (k), the logarithmic function sequence Y (k) satisfies the condition of improving the smoothness ratio; the step ratio deviation is delta (k) and the step ratio deviation of the transformed sequence is delta _f (k) Converting f (x (k)) into a level ratio compression conversion, and meeting the condition of adjusting the level ratio compression; due to c>max{x(k)|k＝1,2,…n}，

Therefore, the reduction error after the function transformation f (x (k)) is not amplified, and when x (k) is the concave-up function, f (x (k)) still maintains the concave-up characteristic.

The verification method of the trigonometric function sequence Y (k) after the transformation of the non-negative original sequence X is the same as the verification method.

In summary, when the original data is transformed, in order to make the transformed data sequence more conform to the modeling condition of the gray GM (1,1) model, the original sequence must satisfy the conditions of reducing the smooth ratio, maintaining the non-negative concave-up characteristic, adjusting the level ratio compression, and ensuring that the reduction error does not increase.

Further, in the present invention, the gray prediction model subjected to function transformation may be further optimized based on a chicken flock algorithm, that is, the gray prediction model shown in fig. 1 and fig. 2 and the related refining steps thereof are combined, specifically, the steps S21 to S26 and the steps S14 to S17 are combined, the accuracy of the gray prediction model based on exponential function and logarithmic function transformation is further improved with reference to fig. 7, and in the implementation process, the formula may be adaptively modified.

While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention.

Claims

1. A transformer state prediction method based on an improved grey model theory is characterized by comprising the following steps:

step S12, dividing all the state data in the transformer state database into a training set and a test set;

s13, constructing an original sequence X of the transformer state according to the training set ⁽⁰⁾ And further performing a summation process to obtain a summation sequence X ⁽¹⁾ According to said one-time accumulation sequence X ⁽¹⁾ For sequences with quasi-exponential law, the whitening differential equation of the initial GM (1,1) model is satisfied:

X ⁽⁰⁾ ＝(x ⁽⁰⁾ (1),x ⁽⁰⁾ (2),…x ⁽⁰⁾ (n))

X ⁽¹⁾ ＝(x ⁽¹⁾ (1),x ⁽¹⁾ (2),…x ⁽¹⁾ (n))

wherein the initial coefficient of development-a ₀ And initial ash action amount b ₀ Is solved by a least square method, and the initial edge value of the initial GM (1,1) model

Comprises the following steps:

step S14, optimizing parameter-a through CSO algorithm ₀ 、b ₀ And the initial correction term ε _k Obtaining a development coefficient-a, an ash action amount b and a correction term epsilon, wherein the initial correction term epsilon _k The expression of (a) is:

wherein the integral value

Step S16, verifying the optimized GM (1,1) model through the test set;

2. The method according to claim 1, wherein the state data comprises insulation resistance value or oil dielectric loss factor.

3. The method for predicting transformer state based on improved gray model theory as claimed in claim 2, wherein the state data is insulation resistance, the step S11 obtains the state data of the transformer in the transformer insulation test along with time, and the forming of the transformer state database comprises:

and converting the resistance value of the insulation resistor into a reciprocal of the resistance value, and recording the reciprocal of the resistance value to the transformer state database.

4. The method for predicting transformer state based on improved gray model theory as claimed in claim 3, wherein said step S14 optimizes parameter-a by CSO algorithm ₀ 、b ₀ And the initial correction term ε _k And obtaining the development coefficient-a, the ash action amount b and the correction term epsilon comprises:

step S142, determining the objective function f (a, b, epsilon):

wherein E is _w To generalize errors;

step S147, when the iteration times t are multiples of G, the roles in the chicken flock are redistributed;

In step S149, let (a, b, ∈) = w _best To obtain a, b and epsilon.

5. A transformer state prediction method based on an improved grey model theory is characterized by comprising the following steps:

step S21, acquiring state data of the transformer changing along with time in the transformer insulation test to form a transformer state database;

X ⁽⁰⁾ ＝(x ⁽⁰⁾ (1),x ⁽⁰⁾ (2),…x ⁽⁰⁾ (n))

Wherein x (k) > e, k =1,2, … n;

Y ⁽⁰⁾ ＝(y ⁽⁰⁾ (1),y ⁽⁰⁾ (2),..y ⁽⁰⁾ (n))

Y ⁽¹⁾ ＝(y ⁽¹⁾ (1),y ⁽¹⁾ (2),…y ⁽¹⁾ (n))

Step S25, according to the primary accumulation sequence Y ⁽¹⁾ For sequences with quasi-exponential regularity, the whitening differential equation of the initial GM (1,1) model is satisfied:

And a data reduction expression:

wherein the integral value

6. The method according to claim 5, wherein the state data comprises insulation resistance value or oil dielectric loss tangent.

7. The method for predicting transformer status according to claim 6, wherein the status data is insulation resistance, the step S21 obtains status data of the transformer in the transformer insulation test over time, and the forming of the transformer status database comprises:

8. The method for predicting transformer state based on improved gray model theory as claimed in claim 7, wherein said transformation function is a logarithmic function, and said step S23 is based on transformation function to said original sequence X ⁽⁰⁾ Original sequence Y obtained by data transformation ⁽⁰⁾ Comprises the following steps:

Y ⁽⁰⁾ ＝(y ⁽⁰⁾ (1),y ⁽⁰⁾ (2),…y ⁽⁰⁾ (n))

the data reduction expression in the step S26

Comprises the following steps:

9. the method for predicting transformer state based on improved gray model theory as claimed in claim 7, wherein said transformation function is a trigonometric function, and said step S23 is performed on said original sequence X based on the transformation function ⁽⁰⁾ Original sequence Y obtained by data transformation ⁽⁰⁾ Comprises the following steps:

Y ⁽⁰⁾ ＝(y ⁽⁰⁾ (1),y ⁽⁰⁾ (2),…y ⁽⁰⁾ (n))

wherein y = f (x) ^(k) )＝csc(x ^(k) )，

k＝1,2,..n；

The data reduction expression in the step S26

Comprises the following steps: