CN101893674A - Pollution flashover index forecasting method for regional power grid - Google Patents
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Abstract
The invention relates to a pollution flashover index forecasting method for a regional power grid, belonging to the technical field of transmission and distribution monitoring. The method of the invention comprises the following steps: (1) forecasting the current value of the equivalent salt deposit density in real time by an insulator surface equivalent salt deposit density forecasting model; (2) forecasting pollution flashover critical voltage by an insulator pollution flashover critical voltage forecasting model; (3) forecasting the insulator pollution flashover index of the power grid by a pollution flashover graded forecasting and prewarning model; and (4) judging the state. The invention has the advantages of providing a multivariable equivalent salt deposit density time sequence forecasting model based on phase space reconstruction, solving by a supporting vector machine model, solving the forecasting problem under the conditions of small sample of equivalent salt deposit density data and noise, and improving the forecasting prediction.
Description
Technical Field
The invention belongs to the technical field of power transmission and distribution monitoring, and particularly relates to a regional power grid pollution flashover index prediction method.
Background
In the operation process of a power grid, as the pollution flashover on the surface of an insulator has adverse effect on a power supply system, at present, a plurality of prediction methods for the pollution flashover on the surface of the insulator are provided, and the prediction methods mainly focus on the aspects of prediction of equivalent salt deposit density on the surface of the insulator, prediction of pollution flashover voltage of the insulator and pollution flashover prediction based on leakage current.
Wherein, the neural network prediction of equivalent salt deposit density and the support vector machine prediction of pollution flashover voltage are to fit the multidimensional nonlinear relation between the two parameters describing pollution flashover and environmental meteorological parameters by a nonlinear modeling method, the prediction method is in the leading position at home and abroad, however, the two methods still have single modeling object, certain difference exists between the established prediction model and the prediction function thereof and the antifouling work requirement of the power grid, the method can not be practically applied to the pollution flashover prevention operation management of the power grid, the pollution flashover prediction method based on leakage current has rich basic data, on the basis, the method of applying the artificial neural network and the like can obtain the fitting effect which is closer to the actual engineering, however, the distribution range of the monitoring points of the leakage current is limited, and the pollution flashover state of the power grid cannot be comprehensively monitored and predicted in real time.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a regional power grid pollution flashover index prediction method.
The invention discloses a regional power grid pollution flashover index prediction method, which comprises the following steps:
inputting the environmental parameters and the equivalent salt deposit density historical values collected on the site of the power grid into an insulator surface equivalent salt deposit density prediction model, wherein the output of the insulator surface equivalent salt deposit density prediction model is the current value of the real-time predicted equivalent salt deposit density;
inputting the current value of the real-time predicted equivalent salt deposit density and the current collected environmental parameters into a pollution flashover critical voltage prediction model of the insulator, wherein the output of the pollution flashover critical voltage prediction model of the insulator is a pollution flashover critical voltage prediction value;
inputting the pollution flashover critical voltage predicted value into a pollution flashover grading prediction early warning model, wherein the output of the pollution flashover grading prediction early warning model is a predicted power grid pollution flashover index;
The application of the insulator surface equivalent salt deposit density prediction model is carried out according to the following steps:
1) establishing a multivariable equivalent salt deposit density time sequence;
the equivalent salt deposit density data is measured at regular time intervals and at a series of moments t1，t2，...，tnResulting discrete ordered set { x1，x2，...，xnThe time sequence is called discrete equivalent salt deposit density time sequence, and is called the equivalent salt deposit density time sequence for short;
the multivariable equivalent salt deposit density time sequence is a multidimensional equivalent salt density time sequence which is composed of an equivalent salt density time sequence and a meteorological parameter time sequence in the same moment and is a representation form of a multidimensional equivalent salt density nonlinear dynamics system comprising the equivalent salt density time sequence;
m-dimensional equivalent salt deposit density time series: x1，X2，...，XNN stands for the number of moments, where Xi＝(x1，i，x2，i，...，xM，i) I.e. by
Wherein i is 1, 2M，NRepresenting the value of the Mth variable at time N, xM，iThe value of the Mth variable at the moment i is shown;
2) reconstructing the phase space of the multivariate equivalent salt deposit time series:
the phase points of the multivariate equivalent salt deposit density time sequence phase space reconstruction are as follows:
denotes that the Mth variable is delayed by tau at time NMEmbedding dimension mMThe reconstructed phase space of (a);
where n denotes the time of the nth time instant,
τiand miFor the delay time and the embedding dimension of the ith time series, the embedding dimension m of the reconstructed phase space is m1+m2+...+mMM is the dimension of the time series;
the phase space reconstruction parameter delay time tau of the multivariable equivalent salt deposit density time sequence is selected by adopting a mutual information method, the mutual information method takes the delay when the mutual information reaches the minimum for the first time as the delay time of the phase space reconstruction, and the method comprises the following steps of
Determination of Rxx((i +1) τ) is an autocorrelation function with an equivalent salt deposit time series time span of (i +1) τ, τ being the phase space reconstruction parameter delay time; the embedding dimension m is defined by:
determining, wherein:
Xi(m +1) is the ith phase point in the (m +1) -dimensional reconstructed iso-salt deposit system phase space, and n (i, m) is the phase point X in the m-dimensional iso-salt deposit system phase spacen(i，m)(m) is the phase point Xi(m) nearest integer, | | · | |, is the euclidean distance over the equivalent salt deposit system phase space;
3) and (3) testing the certainty of the equivalent salt deposit density time series:
in the invention, a Lyapunov exponent method is adopted to carry out deterministic test on an equivalent salt deposit time sequence, the exponent is a numerical representation of the average exponent divergence rate of adjacent orbits in a phase space and is used for depicting the initial state sensitivity of chaotic motion, and the exponent is an integral characteristic as a long-term average result along the orbits and is always real;
the non-linear characteristic of the equivalent salt deposit density time sequence is judged by calculating the maximum Lyapunov exponent, and the method calculates the slope of the regression line of the y (k) curveIs the maximum index, wherein,
li(k) representing each pair of nearest points in the reconstructed equivalent salt dense-phase space, and calculating Euclidean distances after k discrete times, wherein M is the dimension of a time sequence;
4) global prediction multivariable equivalent salt deposit time series:
according to the Thanksgiving time-delay embedding theorem, as long as the embedding dimension m and the delay time tau are reasonably selected, the track of the reconstructed phase space in the embedding space is equivalent to an equivalent salt deposit kinetic system in the differential homoembryo sense, and a smooth mapping f exists:
such that: vi+1＝f(Vi)，Vi+1Representing the (i +1) th phase point in the reconstruction phase space, and applying a nonlinear approximation method to construct a mapping
To approximate f and make
Satisfies the following conditions:
at a minimum, wherein
The expression indicates that the Mth variable is delayed by tau at the time nMEmbedding dimension mMTo reconstruct the value in phase space, τMDenotes the delay time of the Mth variable, MMAn embedding dimension representing an Mth variable;
5) solving a multivariate equivalent salt deposit density time sequence prediction model by using a support vector machine model:
by solving non-linear mappings in the prediction model
Determining an equivalent salt deposit density time series prediction model and mapping the prediction model on the obtained nonlinear
The lower prediction error meets the requirement, and the support vector machine theory can effectively solve the problem of nonlinear mapping in the equivalent salt deposit density nonlinear time sequence prediction model under the condition that the equivalent salt deposit density data sample capacity is small
The support vector machine method for approximating the non-linear mapping relationship in the equivalent salt deposit density time series prediction model is support vector regression;
a sample set formed by phase space phase points of an equivalent salt density system is set as follows: s { (x)i，yi)，i＝1，2，...，M}，(xi，yi) Representing any phase point in the reconstructed phase space, if there is one hyperplane g (x) ═ g<w·x>+b，w∈RnB ∈ R, w, b denote vector parameters, in order to construct a hyperplane g (x), such that: | yi-g(xi) If | ≦ ε, wherein,<·>representing the vector inner product, i { (x) }, 1, 2, M being the dimension of the equivalent salt-dense time series, then the sample set S { (x)i，yi) 1, 2, M is an approximate set of epsilon, with: non-viable cells<w·x>+b-yi|≤Epsilon, i.e.
i＝1，2，...，M；
Wherein,
distance d from point of S to hyperplane f (x)iThen, there are:1, 2, M, i.e. the maximum distance of a point in the set S to the hyperplane is
The optimal approximation hyperplane of set S can be obtained by maximizing the upper bound of the point-to-hyperplane distance in S, and the optimal approximation hyperplane can be obtained by a maximization formula
Get, thus solve | | w | | non-woven phosphor2The optimal approximate hyperplane of the set S can be obtained by the minimization problem, and a nonlinear mapping is needed because the equivalent salt deposit density system is a nonlinear system
Dividing phase point x in equivalent salt deposit density system phase spaceiMapping to a high-dimensional space, and performing linear regression in the high-dimensional space, wherein a kernel function psi (x) is used to avoid inner product operation due to the inner product operation of the high-dimensional space involved in the optimization processi，xi+1) Substitute for inner product
To realize the non-linear regression in the equivalent salt density system phase space, at this time, the problem of the support vector regression in the equivalent salt density system phase space can be converted into | | w | | computationally2Optimizing the problem:
where, i ═ 1, 2., M, the above equation is a quadratic programming problem, and its Lagrange function is:
wherein alpha isiAnd
known as lagrange multipliers, there is an equation for any i 1, 2
αi≥0，
If true;
when the nonlinear mapping function approximation in the equivalent salt density system phase space is carried out, because the obtained regression function and the actual function have inevitable errors, a relaxation variable is introduced:
ξi≥0，
i＝1，2，...，M，ξirepresents a relaxation variable;
the optimization at this time is as follows:
wherein c is a penalty parameter, and c is more than 0;
the Lagrange dual problem can be found as:
the above formula is used for predicting the equivalent salt deposit density of the surface of the insulator;
solving the above formula to obtain the non-linear mapping in the phase space of the equivalent salt deposit density system
The regression function g (x), the kernel function and yiThe equivalent salt deposit density value at the next moment can be obtained as input quantity, and the parameters in the kernel function and the penalty factors in the model parameters of the support vector machine are nonlinear mappings obtained by a method for determining the support vector machine
The most main factor of the predictive performance is the selection of the support vector machine model parameters by adopting a cross-validation method.
The application of the pollution flashover critical voltage prediction model of the insulator is carried out according to the following steps:
1) determination of pollution flashover threshold voltage:
the pollution flashover critical voltage value is the data U obtained by a 50% pollution flashover voltage test50％Equivalent salt deposit density, meteorological parameters and pollution flashover critical voltage value U50％The multi-dimensional nonlinear relation between the three-dimensional parameters is subjected to artificial neural network modeling, and the insulator pollution flashover critical voltage U with known equivalent salt deposit density and meteorological parameters is realized50％Carrying out prediction;
2) establishing an artificial neural network model:
the invention adopts a pollution flashover critical voltage prediction artificial neural network model based on a BP method;
determining three layers of an input layer, a hidden layer and an output layer of a pollution flashover critical voltage prediction BP artificial neural network model;
the pollution flashover critical voltage prediction BP artificial neural network model comprises an input layer, a hidden layer and an output layer, wherein the hidden layer is composed of two or three layers of nodes according to different artificial pollution experimental data;
x1，x2，...，xnis an input layer node, including equivalent salt density value, temperature, humidity, air pressure, wind speed and rainfall, h1，h2，...，hmIs a hidden layer node, o is an output layer node, and is a predicted value of the pollution flashover critical voltage of the insulator; v1，V2，...，VmIs the weight from the input layer to the hidden layer, W1，W2，...，WmThe method comprises the following steps that a weight value from a hidden layer to an output layer is obtained, artificial pollution voltage withstand test data are used as training data for training of an artificial neural network model of pollution flashover critical voltage, the structure and parameters of the whole network are optimized through training, the dimension of an input layer of the network is n, the output dimension is one dimension, namely the output of a relevant predicted value, the hidden layer unit dimension m is determined in an optimized mode in network training learning, the predicted value of a prediction model is compared with the result of an actual artificial pollution voltage withstand test, and then the network structure and the weight value are corrected and perfected;
3) adding momentum items on the basis of the artificial neural network model and adaptively adjusting the learning rate of the BP method:
in order to improve the training speed of the artificial neural network for predicting the pollution flashover critical voltage, a momentum item is added in a weight value adjusting formula, if W represents a weight value matrix of a certain layer in the artificial neural network for predicting the pollution flashover critical voltage and X represents an input vector of the certain layer, the expression of the weight value adjusting vector of the artificial neural network for predicting the pollution flashover critical voltage containing the momentum item is as follows:
Δ W (t) ═ η δ X + α Δ W (t-1), where the letter in the formula means α is a momentum coefficient, and α ∈ (0, 1) is set, η is the learning rate of the neural network, Δ W (t-1) is the previous weight adjustment amount, Δ W (t) is the current weight adjustment amount, the momentum term reflects the previous adjustment experience, and plays a role in damping the adjustment at time t, when the error surface suddenly fluctuates, the oscillation trend can be reduced, and the training speed can be increased;
self-adaptive adjustment is carried out on the learning rate of the BP method in the artificial neural network modeling of pollution flashover critical voltage prediction, the learning rate eta belongs to (0, 1) to represent a proportionality coefficient, an initial learning rate is set, and if the total error is increased after one-time weight adjustment, the adjustment is invalid; if the total error is reduced after the weight is adjusted once, the adjustment is effective;
4) introducing a gradient factor on the basis of the artificial neural network model to enable weight adjustment to be separated from a flat area:
introducing a gradient factor in the process of training an artificial neural network model for predicting the pollution flashover critical voltage, wherein a flat area exists on an error curved surface, weight adjustment entering the flat area represents that the output of neurons of the artificial neural network for predicting the pollution flashover critical voltage enters a saturated area of a transfer function, if the net input of the neurons is compressed after the neurons enter the flat area, the net input of the neurons is output and exits the saturated area of the transfer function, the shape of the error function can be changed, and the adjustment is separated from the flat area, specifically, introducing a gradient factor zeta in an original transfer function to ensure that the output is:
wherein net is the output value of each layer of nodes, when the delta E is close to zero and the d-o value is still larger, the node is considered to enter a flat area, and the zeta is larger than 1; when zeta > 1, the net coordinate is compressed by times, the sensitive segment of the transfer function curve of the neuron of the artificial neural network predicted by the pollution flashover critical voltage is lengthened, so that the net value is withdrawn from the saturation value, and when zeta equals 1, the transfer function is recovered to the original state, so that the sensitivity is higher for smaller net values;
an improved BP artificial neural network prediction model is established, a formula O (j) f (net (j)) is solved, and then a pollution flashover critical voltage prediction value of the insulator can be obtained, wherein j (1, 2.. the sum of the input of a pollution flashover critical voltage prediction neuron j is represented by l, the number of nodes of an output layer is represented by net (j), and f represents a nonlinear mapping relation.
The application of the pollution flashover grading prediction early warning model is carried out according to the following steps:
determining pollution flashover index of the insulator, and predicting the pollution flashover index by a formula
Determining, wherein κ is a pollution flashover index; u shapeFFThe predicted value of the pollution flashover critical voltage is; u shapeOPThe predicted value of the pollution flashover critical voltage is the input of the model, and kappa is the output of the model, namely the predicted pollution flashover index.
The invention has the advantages that: a multivariate equivalent salt deposit density time sequence prediction model based on phase space reconstruction is provided, and a support vector machine model is used for solving the multivariate equivalent salt deposit density time sequence prediction model, so that the prediction problem under the conditions of small samples of equivalent salt deposit density data and noise is solved, and the prediction precision is improved.
Description of the drawings:
FIG. 1(a) is a flow chart of a regional power grid pollution flashover index prediction method of the present invention;
FIG. 1(b) is a flow chart of a prediction model for applying equivalent salt deposit density on the surface of an insulator according to the present invention;
FIG. 1(c) is a flow chart of a pollution flashover critical voltage prediction model of the insulator of the present invention;
FIG. 2 is a diagram of an artificial neural network model of the present invention;
FIG. 3 is a comparison of the equivalent salt deposit density measurement values and calculated values for the equivalent salt deposit density monitoring points of the present invention;
FIG. 4 is a graph comparing the measured and calculated values of the contamination flash threshold voltage of the present invention;
FIG. 5 is a model diagram of the pollution flashover index prediction and early warning.
The specific implementation mode is as follows:
the invention discloses a regional power grid pollution flashover index prediction method which is described by combining an embodiment and an attached drawing.
The method comprises the following steps as shown in figure 1 (a):
inputting the environmental parameters and the equivalent salt deposit density historical values collected on the site of the power grid into an insulator surface equivalent salt deposit density prediction model, wherein the output of the insulator surface equivalent salt deposit density prediction model is the current value of the real-time predicted equivalent salt deposit density;
the environment parameters collected on site comprise a wind speed value, a temperature value, an air pressure value, a rain amount value, a humidity value and an equivalent salt deposit density historical value; the measured data of wind speed, temperature, air pressure, rainfall and humidity and the historical value of equivalent salt deposit form a six-dimensional equivalent salt deposit multivariable time sequence, and 20 different time values of the same time period of the six variables are selected to form the time sequence
The specific parameters are shown in the following formula
In the above formula: the first is the wind speed value in m/s; a second behavior temperature value in units of; the third row is the barometric pressure value in hPa; the fourth line is the rainfall value, in mm; the fifth element is the relative humidity value in%;
sixth line is the equivalent salt density in mg/cm2。
inputting the current value of the real-time predicted equivalent salt deposit density and the current collected environmental parameters into a pollution flashover critical voltage prediction model of the insulator, wherein the output of the pollution flashover critical voltage prediction model of the insulator is a pollution flashover critical voltage prediction value;
inputting the pollution flashover critical voltage predicted value into a pollution flashover grading prediction early warning model, wherein the output of the pollution flashover grading prediction early warning model is a predicted power grid pollution flashover index;
The total input conditions of the pollution flashover prediction model are meteorological data, including historical data and forecasts, the output is pollution flashover voltage grade, and the pollution flashover risk can be judged according to the pollution flashover voltage grade.
The application of the insulator surface equivalent salt deposit density prediction model is carried out according to the following steps, as shown in FIG. 1 (b):
1) establishing a multivariable equivalent salt deposit density time sequence;
the environment parameters collected on site comprise a wind speed value, a temperature value, an air pressure value, a rain amount value, a humidity value and an equivalent salt deposit density historical value; the measured data of wind speed, temperature, air pressure, rainfall and humidity and the historical value of equivalent salt deposit form a six-dimensional equivalent salt deposit multivariable time sequence, and 20 different time values of the same time period of the six variables are selected to form the time sequence
The specific parameters are shown in the following formula
In the above formula: the first is the wind speed value in m/s; a second behavior temperature value in units of; the third row is the barometric pressure value in hPa; the fourth line is the rainfall value, in mm; the fifth element is the relative humidity value in%;
sixth line is the equivalent salt density in mg/cm2。
2) Reconstructing the phase space of the multivariate equivalent salt deposit time series:
performing phase space reconstruction by using a salt density multivariable time sequence with equivalent value of delay time tau 3 and embedding dimension m 6, forming a training sample of an equivalent salt density time sequence support vector machine model by using all phase points in the phase space in a reconstructed equivalent salt dense phase space, establishing the support vector machine model, and performing nonlinear mapping in an equivalent salt density time sequence global prediction model
Fitting is carried out;
the training samples composed of all the phase points in the phase space are:
wherein the total number of phase points is N ═ 6(N- (m-1) τ);
3) and (3) testing the certainty of the equivalent salt deposit density time series:
calculating the maximum Lyapunov index by an improved method, wherein the result is approximately equal to 0.047, and the maximum Lyapunov index is larger than zero to judge that: the equivalent salt deposit density time sequence is a nonlinear chaotic time sequence;
4) global prediction multivariable equivalent salt deposit density time series
Based on the three steps, a multivariate equivalent salt deposit density time sequence global prediction model is established;
5) multivariate equivalent salt deposit density time sequence prediction model solved by using support vector machine model
According to the capacity of a training sample set of a support vector machine model formed by reconstructing phase space phase points of an equivalent salt density time sequence and the characteristics of an equivalent salt density nonlinear system, a cross-checking method is applied, and the kernel function of the support vector machine model and the parameters of the model are selected as follows: selecting a Gaussian kernel function by the kernel function; the kernel function parameter gamma is 0.6; penalty c is 50; the insensitive loss function parameter epsilon is 0.29;
the prediction result of the prediction model of the support vector machine of the equivalent salt deposit time sequence of the partial equivalent salt deposit monitoring points is shown in figure 3, and the error of the equivalent salt deposit prediction value in the established equivalent salt deposit prediction model is basically controlled within 12%.
The application of the pollution flashover critical voltage prediction model of the insulator is performed according to the following steps, as shown in fig. 1 (c):
1) determination of pollution flashover threshold voltage:
the pollution flashover critical voltage value is the data U obtained by a 50% pollution flashover voltage test50％Equivalent salt deposit density, meteorological parameters and pollution flashover critical voltage value U50％Between the twoCarrying out artificial neural network modeling on the relation to realize the pollution flashover critical voltage U of the insulator with known equivalent salt deposit density and meteorological parameters50％Carrying out prediction;
the data obtained from the pollution flashover voltage test are as follows:
| normalized value of air pressure | Normalized value of humidity | Normalized value of temperature | Normalized value of ESDD | U50％Normalized value of |
| 0.3913 | 0.8780 | 0.5354 | 0.4900 | 0.3070 |
| 0.8669 | 0.8785 | 0.6283 | 0.1580 | 0.6580 |
| 0.4332 | 0.7560 | 0.4486 | 0.0800 | 0.6588 |
| 0.6100 | 0.6918 | 0.6514 | 0.6360 | 0.2343 |
The normalized value is determined by the following equation:
aias a normalized value of a certain parameter, biAt any value of the parameter, bminIs the minimum of all values of the parameter, bmaxIs the maximum value of all the values of the parameter; selecting a group of data as a test sample, and using other data as a training sample of the artificial neural network;
2) aiming at the processed artificial pollution test data, establishing an artificial neural network model shown in the attached figure 2;
3) adding momentum items on the basis of the artificial neural network model and adaptively adjusting the learning rate of the BP method:
setting an initial value of a network parameter and an allowable value of a network output error by taking the standardized data in the step 1) as a training sample, training the network, and keeping a corresponding network structure parameter after the network output error is smaller than the allowable value;
4) introducing a gradient factor on the basis of an artificial neural network model to enable weight adjustment to be separated from a flat area, and obtaining a pollution flashover critical voltage prediction model:
comparing the prediction result with the measured value of the partial pollution flashover critical voltage prediction model as shown in fig. 4, the error of the pollution flashover critical voltage value in the established pollution flashover critical voltage prediction model is basically controlled within ± 6%;
the application of the pollution flashover grading prediction early warning model is carried out according to the following steps:
pollution flashover index prediction model passing formula
Determining, wherein κ is a pollution flashover index; u shapeFFThe predicted value of the pollution flashover critical voltage is; u shapeOPIs the operating voltage.
Claims (4)
1. A regional power grid pollution flashover index prediction method is characterized by comprising the following steps: the method comprises the following steps:
step 1, applying an equivalent salt deposit density prediction model on the surface of an insulator to predict the current value of the equivalent salt deposit density in real time;
inputting the environmental parameters and the equivalent salt deposit density historical values collected on the site of the power grid into an insulator surface equivalent salt deposit density prediction model, wherein the output of the insulator surface equivalent salt deposit density prediction model is the current value of the real-time predicted equivalent salt deposit density;
step 2, applying an insulator pollution flashover critical voltage prediction model to predict pollution flashover critical voltage;
inputting the current value of the real-time predicted equivalent salt deposit density and the current collected environmental parameters into a pollution flashover critical voltage prediction model of the insulator, wherein the output of the pollution flashover critical voltage prediction model of the insulator is a pollution flashover critical voltage prediction value;
step 3, applying a pollution flashover grading prediction early warning model to predict a pollution flashover index of the power grid insulator;
inputting the pollution flashover critical voltage predicted value into a pollution flashover grading prediction early warning model, wherein the output of the pollution flashover grading prediction early warning model is a predicted power grid pollution flashover index;
step 4, when the pollution flashover index of the power grid is 0% and 5%, carrying out no pollution flashover early warning; when the pollution flashover index of the power grid is 20%, issuing a pollution flashover grade III early warning; when the pollution flashover index of the power grid is 50% and 85%, the pollution flashover occurrence probability is greater than 50%, and a pollution flashover II-level early warning is issued; when the pollution flashover index of the power grid is 100%, the pollution flashover occurrence probability is quite large, pollution flashover is likely to occur in the regional power grid at any time, and a pollution flashover I-level early warning is issued.
2. The regional power grid pollution flashover index prediction method according to claim 1, characterized in that: the application of the insulator surface equivalent salt deposit density prediction model is carried out according to the following steps:
1) establishing a multivariable equivalent salt deposit density time sequence;
the equivalent salt deposit density data is measured at regular time intervals and at a series of moments t1，t2，...，tnResulting discrete ordered set { x1，x2，...，xnThe time sequence is called discrete equivalent salt deposit density time sequence, and is called the equivalent salt deposit density time sequence for short;
the multivariable equivalent salt deposit density time sequence is a multidimensional equivalent salt density time sequence which is composed of an equivalent salt density time sequence and a meteorological parameter time sequence in the same moment and is a representation form of a multidimensional equivalent salt density nonlinear dynamics system comprising the equivalent salt density time sequence;
m-dimensional equivalent salt deposit density time series: x1，X2，...，XNN stands for the number of moments, where Xi＝(x1，i，x2，i，...，xM，i) I.e. by
Wherein i is 1, 2M，NRepresenting the value of the Mth variable at time N, xM，iThe value of the Mth variable at the moment i is shown;
2) reconstructing a phase space of a multivariable equivalent salt deposit density time sequence;
the phase points of the multivariate equivalent salt deposit density time sequence phase space reconstruction are as follows:
where n denotes the time of the nth time instant,
τiand miFor the delay time and the embedding dimension of the ith time series, the embedding dimension m of the reconstructed phase space is m1+m2+...+mMM is the dimension of the time series;
the phase space reconstruction parameter delay time tau of the multivariable equivalent salt deposit density time sequence is selected by adopting a mutual information method, the mutual information method takes the delay when the mutual information reaches the minimum for the first time as the delay time of the phase space reconstruction, and the method comprises the following steps of
Determination of Rxx((i +1) τ) is an autocorrelation function with an equivalent salt deposit time series time span of (i +1) τ, τ being the phase space reconstruction parameter delay time; the embedding dimension m is defined by:
determining, wherein:
Xi(m +1) is the ith phase point in the (m +1) -dimensional reconstructed iso-salt deposit system phase space, and n (i, m) is the phase point X in the m-dimensional iso-salt deposit system phase spacen(i，m)(m) is the phase point Xi(m) nearest integer, | | · | |, is the euclidean distance over the equivalent salt deposit system phase space;
3) testing the certainty of the equivalent salt deposit density time sequence;
in the invention, a Lyapunov exponent method is adopted to carry out deterministic test on an equivalent salt deposit time sequence, the exponent is a numerical representation of the average exponent divergence rate of adjacent orbits in a phase space and is used for depicting the initial state sensitivity of chaotic motion, and the exponent is an integral characteristic as a long-term average result along the orbits and is always real;
the non-linear characteristic of the equivalent salt deposit density time sequence is judged by calculating the maximum Lyapunov exponent, and the method calculates the slope of the regression line of the y (k) curve
Is the maximum index, wherein,
li(k) representing each pair of nearest points in the reconstructed equivalent salt dense-phase space, and calculating Euclidean distances after k discrete times, wherein M is the dimension of a time sequence;
4) globally predicting a multivariable equivalent salt deposit density time sequence;
according to the Thanksgiving time-delay embedding theorem, as long as the embedding dimension m and the delay time tau are reasonably selected, the track of the reconstructed phase space in the embedding space is equivalent to an equivalent salt deposit kinetic system in the differential homoembryo sense, and a smooth mapping f exists:
such that: vi+1＝f(Vi)，Vi+1Representing the (i +1) th phase point in the reconstruction phase space, and applying a nonlinear approximation method to construct a mapping
To approximate f and make
Satisfies the following conditions:
at a minimum, wherein
The expression indicates that the Mth variable is delayed by tau at the time nMEmbedding dimension mMTo reconstruct the value in phase space, τMDenotes the delay time of the Mth variable, MMAn embedding dimension representing an Mth variable;
5) solving a multivariate equivalent salt deposit density time sequence prediction model by using a support vector machine model;
by solving non-linear mappings in the prediction model
Determining an equivalent salt deposit density time series prediction model and mapping the prediction model on the obtained nonlinear
The lower prediction error meets the requirement, and the support vector machine theory can effectively solve the problem of nonlinear mapping in the equivalent salt deposit density nonlinear time sequence prediction model under the condition that the equivalent salt deposit density data sample capacity is small
The support vector machine method for approximating the non-linear mapping relationship in the equivalent salt deposit density time series prediction model is support vector regression;
a sample set formed by phase space phase points of an equivalent salt density system is set as follows: s { (x)i，yi)，i＝1，2，...，M}，(xi，yi) Representing any phase point in the reconstructed phase space, if there is one hyperplane g (x) ═ g<w·x>+b，w∈RnB ∈ R, w, b denote vector parameters, in order to construct a hyperplane g (x), such that: | yi-g(xi) If | ≦ ε, wherein,<·>denotes the vector inner product, i 1, 2Dimension of the salt time series, then the sample set S { (x)i，yi) 1, 2, M is an approximate set of epsilon, with: non-viable cells<w·x>+b-yiI.e. less than or equal to epsilon
i＝1，2，...，M；
Wherein,
distance d from point of S to hyperplane f (x)iThen, there are:1, 2, M, i.e. the maximum distance of a point in the set S to the hyperplane is
The optimal approximation hyperplane of set S can be obtained by maximizing the upper bound of the point-to-hyperplane distance in S, and the optimal approximation hyperplane can be obtained by a maximization formulaGet, thus solve | | w | | non-woven phosphor2The optimal approximate hyperplane of the set S can be obtained by the minimization problem, and a nonlinear mapping is needed because the equivalent salt deposit density system is a nonlinear system
Dividing phase point x in equivalent salt deposit density system phase spaceiMapping to a high-dimensional space, and performing linear regression in the high-dimensional space, wherein a kernel function psi (x) is used to avoid inner product operation due to the inner product operation of the high-dimensional space involved in the optimization processi，xi+1) Substitute for inner product
To realize the non-linear regression in the phase space of the equivalent salt deposit density system, at the moment, the equivalent salt deposit density systemThe problem of support vector regression in unified phase space can be converted into | | w | | luminance as follows2Optimizing the problem:
where, i ═ 1, 2., M, the above equation is a quadratic programming problem, and its Lagrange function is:
wherein alpha isiAnd
known as lagrange multipliers, there is an equation for any i 1, 2αi≥0，
If true;
when the nonlinear mapping function approximation in the equivalent salt density system phase space is carried out, because the obtained regression function and the actual function have inevitable errors, a relaxation variable is introduced:
ξi≥0，
i＝1，2，...，M，ξirepresents a relaxation variable;
the optimization at this time is as follows:
wherein c is a penalty parameter, and c is more than 0;
the Lagrange dual problem can be found as:
the above formula is used for predicting the equivalent salt deposit density of the surface of the insulator;
solving the above formula to obtain the non-linear mapping in the phase space of the equivalent salt deposit density system
The regression function g (x), the kernel function and yiThe equivalent salt deposit density value at the next moment can be obtained as input quantity, and the parameters in the kernel function and the penalty factors in the model parameters of the support vector machine are nonlinear mappings obtained by a method for determining the support vector machine
The most main factor of the predictive performance is the selection of the support vector machine model parameters by adopting a cross-validation method.
3. The regional power grid pollution flashover index prediction method according to claim 1, characterized in that: the application of the pollution flashover critical voltage prediction model of the insulator is carried out according to the following steps:
1) determining a pollution flashover critical voltage;
the pollution flashover critical voltage value is the data U obtained by a 50% pollution flashover voltage test50％Equivalent salt deposit density, meteorological parameters and pollution flashover critical voltage value U50％The multi-dimensional nonlinear relation between the three-dimensional parameters is subjected to artificial neural network modeling, and the insulator pollution flashover critical voltage U with known equivalent salt deposit density and meteorological parameters is realized50％Carrying out prediction;
2) establishing an artificial neural network model;
the invention adopts a pollution flashover critical voltage prediction artificial neural network model based on a BP method;
determining three layers of an input layer, a hidden layer and an output layer of a pollution flashover critical voltage prediction BP artificial neural network model;
the pollution flashover critical voltage prediction BP artificial neural network model comprises an input layer, a hidden layer and an output layer, wherein the hidden layer is composed of two or three layers of nodes according to different artificial pollution experimental data;
x1，x2，...，xnis an input layer node, including equivalent salt density value, temperature, humidity, air pressure, wind speed and rainfall, h1，h2，...，hmIs a hidden layer node, o is an output layer node, and is a predicted value of the pollution flashover critical voltage of the insulator; v1，V2，...，VmIs the weight from the input layer to the hidden layer, W1，W2，...，WmThe method comprises the following steps that a weight value from a hidden layer to an output layer is obtained, artificial pollution voltage withstand test data are used as training data for training of an artificial neural network model of pollution flashover critical voltage, the structure and parameters of the whole network are optimized through training, the dimension of an input layer of the network is n, the output dimension is one dimension, namely the output of a relevant predicted value, the hidden layer unit dimension m is determined in an optimized mode in network training learning, the predicted value of a prediction model is compared with the result of an actual artificial pollution voltage withstand test, and then the network structure and the weight value are corrected and perfected;
3) adding momentum items on the basis of the artificial neural network model and adaptively adjusting the learning rate of the BP method;
in order to improve the training speed of the artificial neural network for predicting the pollution flashover critical voltage, a momentum item is added in a weight value adjusting formula, if W represents a weight value matrix of a certain layer in the artificial neural network for predicting the pollution flashover critical voltage and X represents an input vector of the certain layer, the expression of the weight value adjusting vector of the artificial neural network for predicting the pollution flashover critical voltage containing the momentum item is as follows:
Δ W (t) ═ η δ X + α Δ W (t-1), where the letter in the formula means α is a momentum coefficient, and α ∈ (0, 1) is set, η is the learning rate of the neural network, Δ W (t-1) is the previous weight adjustment amount, Δ W (t) is the current weight adjustment amount, the momentum term reflects the previous adjustment experience, and plays a role in damping the adjustment at time t, when the error surface suddenly fluctuates, the oscillation trend can be reduced, and the training speed can be increased;
self-adaptive adjustment is carried out on the learning rate of the BP method in the artificial neural network modeling of pollution flashover critical voltage prediction, the learning rate eta belongs to (0, 1) to represent a proportionality coefficient, an initial learning rate is set, and if the total error is increased after one-time weight adjustment, the adjustment is invalid; if the total error is reduced after the weight is adjusted once, the adjustment is effective;
4) introducing a gradient factor on the basis of the artificial neural network model to enable weight adjustment to be separated from a flat area;
introducing a gradient factor in the process of training an artificial neural network model for predicting the pollution flashover critical voltage, wherein a flat area exists on an error curved surface, weight adjustment entering the flat area represents that the output of neurons of the artificial neural network for predicting the pollution flashover critical voltage enters a saturated area of a transfer function, if the net input of the neurons is compressed after the neurons enter the flat area, the net input of the neurons is output and exits the saturated area of the transfer function, the shape of the error function can be changed, and the adjustment is separated from the flat area, specifically, introducing a gradient factor zeta in an original transfer function to ensure that the output is:
wherein net is the output value of each layer of nodes, when the delta E is close to zero and the d-o value is still larger, the node is considered to enter a flat area, and the zeta is larger than 1; when zeta > 1, the net coordinate is compressed by times, the sensitive segment of the transfer function curve of the neuron of the artificial neural network predicted by the pollution flashover critical voltage is lengthened, so that the net value is withdrawn from the saturation value, and when zeta equals 1, the transfer function is recovered to the original state, so that the sensitivity is higher for smaller net values;
an improved BP artificial neural network prediction model is established, a formula O (j) f (net (j)) is solved, and then a pollution flashover critical voltage prediction value of the insulator can be obtained, wherein j (1, 2.. the sum of the input of a pollution flashover critical voltage prediction neuron j is represented by l, the number of nodes of an output layer is represented by net (j), and f represents a nonlinear mapping relation.
4. The regional power grid pollution flashover index prediction method according to claim 1, characterized in that: the application of the pollution flashover grading prediction early warning model is carried out according to the following steps:
determining pollution flashover index of the insulator, and predicting the pollution flashover index by a formula
Determining, wherein κ is a pollution flashover index; u shapeFFThe predicted value of the pollution flashover critical voltage is; u shapeOPThe predicted value of the pollution flashover critical voltage is the input of the model, and kappa is the output of the model, namely the predicted pollution flashover index.
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