CN101893674A - Pollution flashover index forecasting method for regional power grid - Google Patents

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

A kind of pollution flashover index forecasting method for regional power grid

Technical field

The invention belongs to the power transmission and distribution monitoring technical field, particularly a kind of pollution flashover index forecasting method for regional power grid.

Background technology

Electrical network is in operational process, because insulator surface generation pollution flashover has very adverse effect to electric power system, at present, Forecasting Methodology at the insulator surface pollution flashover has a lot, mainly concentrates on the prediction of prediction for the insulator surface equivalent salt deposit density, insulator contamination flashover voltage, and based on the pollution flashover prediction aspect of leakage current.

Wherein, the neural network prediction of equivalent salt density, the SVM prediction of pollution flashover voltage all is that these two parameters and the relation of the multidimensional nonlinear between the environment weather parameter of describing pollution flashover are carried out match with non-linear modeling method, this Forecasting Methodology at home and abroad all maintains the leading position, but these two kinds of methods still exist modeling object single, there is some difference between the forecast model of setting up and forecast function and the antifouling job requirement of electrical network, still can't in the pollution flashover control operational management of electrical network, obtain practical application, basic data based on the pollution flashover Forecasting Methodology of leakage current is abundant, method such as using artificial neural networks can obtain the fitting effect more approaching with the engineering actual specific on this basis, but the monitoring point of leakage current has a very limited distribution, and can't carry out comparatively comprehensively monitoring in real time and prediction to the pollution flashover state of electrical network.

Summary of the invention

At the deficiencies in the prior art, the invention provides a kind of pollution flashover index forecasting method for regional power grid.

A kind of pollution flashover index forecasting method for regional power grid of the present invention, step is as follows:

Step 1, application insulator surface equivalent salt density forecast model, real-time estimate equivalent salt density currency;

With the environmental parameter and the equivalent salt density history value isolated input sub-surface equivalent salt density forecast model of electrical network collection in worksite, the output of insulator surface equivalent salt density forecast model is real-time estimate equivalent salt density currency;

Step 2, application insulator contamination critical voltage forecast model, prediction pollution flashover critical voltage;

With the pollution flashover critical voltage forecast model of real-time estimate equivalent salt density currency and current collection environmental parameter isolated input, the output of the pollution flashover critical voltage forecast model of insulator is pollution flashover critical voltage predicted value;

Step 3, application pollution flashover classification prediction Early-warning Model, the sub-pollution flashover index of prediction line insulation;

With pollution flashover critical voltage predicted value input pollution flashover classification prediction Early-warning Model, the output of pollution flashover classification prediction Early-warning Model is the electrical network pollution flashover index of prediction;

Step 4, when the electrical network pollution flashover index is 0 and 5%, do not carry out the pollution flashover early warning; When the electrical network pollution flashover index is 20%, the early warning of issue pollution flashover III level; When the electrical network pollution flashover index was 50% and 85%, the pollution flashover probability of happening was issued the early warning of pollution flashover II level greater than 50%; When the electrical network pollution flashover index was 100%, the pollution flashover probability of happening was quite big, and this regional power grid at any time pollution flashover might take place, the early warning of issue pollution flashover I level.

The application of described insulator surface equivalent salt density forecast model, carry out as follows:

1) sets up multivariate equivalent salt density time series;

At Fixed Time Interval equivalent salt ciphertext data is measured, at a series of moment t ₁, t ₂..., t _nDiscrete ordered set { the x that obtains ₁, x ₂..., x _nBe called discrete equivalent salt density time series, abbreviate the equivalent salt density time series as;

Multivariate equivalent salt density time series is the multidimensional equivalent salt density time series that is made of equivalent salt density time series and the meteorologic parameter time series in the identical moment, is the form of expression by the multidimensional equivalent salt density nonlinear kinetics system that comprises the equivalent salt density time series;

M dimension equivalent salt density time series: X ₁, X ₂..., X _N, N represents number, wherein X constantly _i=(x _{1, i}, x _{2, i}..., x _{M, i}), promptly

$\left(\begin{array}{cccc}{x}_{\mathrm{1,1}}& x_{\mathrm{1,2}}...& x_{1,i}...& x_{1,N}\\ x_{\mathrm{2,1}}& x_{\mathrm{2,2}}...& x_{2,i}...& x_{2,N}\\ ...& & & \\ x_{M,1}& x_{M,2}...& x_{M,i}...& x_{M,N}\end{array}\right)$

In the formula, i=1,2 ..., N, x _{M, N}Represent that M variable is at the numerical value of n-hour, x _{M, i}Represent that M variable is at i numerical value constantly;

2) reconstruct multivariate equivalent salt density seasonal effect in time series phase space:

The point mutually of multivariate equivalent salt density time series phase space reconfiguration is:

$\left\{\begin{array}{c}{V}_n=(x_{1,n},x_{1,n-{\mathrm{\τ}}_1},...,x_{1,n-(m1-1){\mathrm{\τ}}_1},...,x_{M,n},x_{M,n-{\mathrm{\τ}}_M},...,x_{M,n-(m_M-1){\mathrm{\τ}}_M})\\ ...\\ V_i=(x_{1,i},x_{1,i-{\mathrm{\τ}}_1},...,x_{1,i-(m1-1){\mathrm{\τ}}_1},...,x_{M,i},x_{M,i-{\mathrm{\τ}}_M},...,x_{M,i-(m_M-1){\mathrm{\τ}}_M})\\ ...\\ V_N=(x_{1,N},x_{1,N-{\mathrm{\τ}}_1},...,x_{1,N-(m1-1){\mathrm{\τ}}_1},...,x_{M,N},x_{M,N-{\mathrm{\τ}}_M},...,x_{M,N-(m_M-1){\mathrm{\τ}}_M})\end{array}\right.$

Represent that M variable is τ in n-hour in time delay _MThe embedding dimension is m _MPhase space reconstruction in value;

Wherein n represents n constantly,

τ _iAnd m _iBe i seasonal effect in time series time delay and embedding dimension, the embedding dimension m=m of phase space reconstruction ₁+ m ₂+ ...+m _M, M is the seasonal effect in time series dimension;

Mutual information method is adopted in the selection of multivariate equivalent salt density seasonal effect in time series phase space reconfiguration parameter delay time T, and mutual information method is the time-delay that reaches for the first time hour with the mutual information time delay as phase space reconfiguration, by

Decision, R _Xx((i+1) τ) is the autocorrelation function of equivalent salt density time series time span for (i+1) τ, and τ is phase space reconfiguration parameter time delay; Embed dimension m by:

$E\left(m\right)=\frac{1}{N-\mathrm{m\τ}}\underset{i=1}{\overset{N-\mathrm{m\τ}}{\mathrm{\Σ}}}\mathrm{\α}(i,m)$

Decision, wherein:

$\mathrm{\α}(i,m)=\frac{\left|\right|X_i(m+1)-X_{n(i,m)}(m+1)\left|\right|}{\left|\right|X_i\left(m\right)-X_{n(i,m)}\left(m\right)\left|\right|}$

X _i(m+1) be the i point mutually in the equivalent salt density system phase space of (m+1) dimension reconstruct, (i is to make to put X mutually in m dimension equivalent salt density system phase space m) to n _{N (i, m)}(m) be to put X mutually _iThe integer of neighbor point (m), || || be the Euclidean distance on the equivalent salt density system phase space;

3) equivalent salt density time series determinacy check:

Adopt Li Ya spectrum promise husband index method to carry out the check of equivalent salt density seasonal effect in time series determinacy among the present invention, this index is the numerical representation method of the average index diverging rate of adjacent tracks in the phase space, sensitivity to initial state in order to the portrayal chaotic motion, this index conduct is along the long-term averaged result of track, be a kind of global feature, it is worth real number always;

Judge that equivalent salt density seasonal effect in time series nonlinear characteristic obtains by calculating largest Lyapunov exponent, this method is calculated the regression straight line slope by y (k) curve Be maximal index, wherein,

l _i(k) expression is to each calculates the Euclidean distance after k the discrete time to neighbor point in the equivalent salt density phase space of reconstruct, and M is the seasonal effect in time series dimension;

4) global prediction multivariate equivalent salt density time series:

According to Tai Kensi time-delay embedding theorems, as long as embed dimension m and delay time T is selected rationally, phase space reconstruction the track of embedded space just with the differomorphism meaning under equivalent salt density dynamical system equivalence, and have smooth mapping f:

Make: V _I+1=f (V _i), V _I+1The individual point mutually of i+1 in the expression phase space reconstruction is used the mapping of non-linear approach method structure

Come close approximation f, and make

Satisfy:

Minimum, wherein

M variable of expression expression is engraved in time delay when n be τ _MThe embedding dimension is m _MPhase space reconstruction in value, τ _MThe time delay of representing M variable, m _MThe embedding dimension of representing M variable;

5) utilize supporting vector machine model to find the solution multivariate equivalent salt density time series predicting model:

By finding the solution the Nonlinear Mapping in the forecast model

The close time series predicting model of certainty equivalents salt, and the Nonlinear Mapping that forecast model is tried to achieve

Under predicated error meet the demands, the support vector machine theory can solve Nonlinear Mapping in the equivalent salt density Forecast of Nonlinear Time Series model under the equivalent salt density data sample capacity situation less than normal effectively

The problem of finding the solution, the support vector machine method that is used for approaching equivalent salt density time series predicting model Nonlinear Mapping relation is a support vector regression;

If equivalent salt density system phase space is put the sample set of formation mutually: S={ (x _i, y _i), i=1,2 ..., M}, (x _i, y _i) represent the arbitrary point mutually in the phase space reconstruction, if an existence lineoid g (x)=＜wx 〉+b, w ∈ R ⁿ, b ∈ R, w, b represent vectorial parameter, in order to construct lineoid g (x), make: | y _i-g (x _i) |≤ε sets up, wherein,＜the expression inner product of vectors, and i=1,2 ..., M, M are equivalent salt density seasonal effect in time series dimension, then sample set S={ (x _i, y _i), i=1,2 ..., M} is the approximate collection of ε, has: |＜wx 〉+b-y _i|≤ε, promptly

I=1,2 ..., M;

Wherein,

For the point of S to lineoid f (x) apart from d _i, then have: I=1,2 ..., M, promptly the point in the S set to lineoid apart from maximal value is

Can obtain the best fit approximation lineoid of S set to the upper bound of lineoid distance by the point of maximization among the S, then the best fit approximation lineoid can be by the maximization formula

Obtain, therefore find the solution || w|| ²Minimization problem can obtain the best fit approximation lineoid of S set because the equivalent salt density system is a nonlinear system, must be with a Nonlinear Mapping

The x of point mutually in the equivalent salt density system phase space _iBe mapped to a higher dimensional space, in higher dimensional space, carry out linear regression then, owing to relate to the inner product operation of higher dimensional space in the optimizing process, for fear of inner product operation, with kernel function Ψ (x _i, x _I+1) the replacement inner product

Realize non-linear regression in the equivalent salt density system phase space, at this moment, the support vector regression problem on the equivalent salt density system phase space can be converted into following || w|| ²Optimization problem:

Wherein, i=1,2 ..., M, following formula are quadratic programming problem, its Lagrange function is:

$\left\{\begin{array}{c}\underset{\mathrm{\α},{\mathrm{\α}}^{*}}{\min }\frac{1}{2}\underset{i=1}{\overset{M}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)({{\mathrm{\α}}_{i+1}}^{*}-{\mathrm{\α}}_{i+1})\mathrm{\Ψ}(x_i,x_{i+1})+\mathrm{\ϵ}\underset{i=1}{\overset{M}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)-\underset{j=1}{\overset{M}{\mathrm{\Σ}}}{y}_j({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i),j=\mathrm{1,2},...,M\\ s.t.\underset{i=1}{\overset{M}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)=0,{\mathrm{\α}}_i\≥0,{\mathrm{\α}}_i^{*}\≥0,i=\mathrm{1,2},...,M\end{array}\right.$

Wherein, α _iWith

Be called as Lagrange multiplier, to any i=1,2 ..., M has equation

α _i〉=0,

Set up;

In carrying out equivalent salt density system phase space, during the Nonlinear Mapping approximation of function,, therefore introduce slack variable owing to inevitably have error between regression function of trying to achieve and the actual function:

ξ _i〉=0,

I=1,2 ..., M, ξ _iThe expression slack variable;

Being optimized for of this moment:

C is the punishment parameter in the formula, and c＞0;

Can get the Lagrange dual problem is:

$\left\{\begin{array}{c}\underset{\mathrm{\α},{\mathrm{\α}}^{*}}{\min }\frac{1}{2}\underset{i=1}{\overset{M}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)({{\mathrm{a\α}}_{i+1}}^{*}-{\mathrm{a\α}}_{i+1})\mathrm{\Ψ}(x_i,x_{i+1})+\mathrm{\ϵ}\underset{i=1}{\overset{M}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)-\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{y}_i({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)\\ s.t.\underset{i=1}{\overset{M}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)=0,{\mathrm{\α}}_i\≥c,{\mathrm{\α}}_i^{*}\≥0,i=\mathrm{1,2},...,M\end{array}\right.$

Following formula is as the prediction of insulator surface equivalent salt density;

Find the solution following formula get final product Nonlinear Mapping in the equivalent salt density system phase space

Regression function g (x), kernel function and y _iAs input quantity, can obtain next equivalent salt density value constantly, the penalty factor in parameter in the kernel function and the supporting vector machine model parameter is the Nonlinear Mapping that the decision support vector machine method is tried to achieve

The main factor of estimated performance adopts the cross validation method to carry out the selection of supporting vector machine model parameter.

The application of the pollution flashover critical voltage forecast model of described insulator, carry out as follows:

1) determining of pollution flashover critical voltage:

The data U that the pollution flashover critical voltage value selects for use the test of 50% pollution flashover voltage to obtain _50%, to equivalent salt density and meteorologic parameter and pollution flashover critical voltage value U _50%Between multidimensional nonlinear relation carry out the artificial neural network modeling, realize insulator contamination critical voltage U to known equivalent salt density and meteorologic parameter _50%Predict;

2) foundation of artificial nerve network model:

Adopt pollution flashover critical voltage prediction artificial nerve network model among the present invention based on the BP method;

Determine three layers of the input layer, hidden layer of pollution flashover critical voltage prediction BP artificial nerve network model and output layers;

Pollution flashover critical voltage prediction BP artificial nerve network model comprises input layer, hidden layer and output layer three-decker, and according to different artificial filthy experimental datas, hidden layer is respectively two-layer or three node layers are formed;

x ₁, x ₂..., x _nBe input layer, comprise equivalent salt density value, temperature, humidity, air pressure, wind speed and rainfall, h ₁, h ₂..., h _mBe hidden node, o is the output layer node, is insulator contamination critical voltage predicted value; V ₁, V ₂..., V _mBe the weights of input layer to hidden layer, W ₁, W ₂..., W _mFor hidden layer to the output layer weights, the training of pollution flashover critical voltage artificial nerve network model uses artificial withstand pollution test data as training data, the structure and parameter of whole network is optimized by training, the input layer dimension of network is n, the output dimension is that one dimension is the output of correlation predictive value, hidden layer cell dimension m optimizes definite in network training study, the predicted value of forecast model compares with the result of actual artificial withstand pollution test, and then network structure and weights are revised and perfect;

3) on the basis of artificial nerve network model, set up momentum term and the learning rate to the BP method carried out the self-adaptation adjustment:

For improving pollution flashover critical voltage prediction artificial neural network training speed, adjust momentum term of increase in the formula at weights, if represent the pollution flashover critical voltage to predict in the artificial neural network certain layer weight matrix with W, X represents certain layer of input vector, and the pollution flashover critical voltage prediction artificial neural network weights adjustment vector expression that then contains momentum term is:

Δ W (t)=η δ X+ α Δ W (t-1), letter representation meaning α is a momentum factor in the formula, establishes α ∈ (0,1), η is the learning rate of neural network, Δ W (t-1) is previous weights adjustment amount, and Δ W (t) is this weights adjustment amount, the adjustment experience before momentum term has reflected, adjustment constantly plays damping action for t, when rising and falling suddenly appears in the error curved surface, can reduce vibration trend, improve training speed;

Learning rate to the BP method in the modeling of pollution flashover critical voltage prediction artificial neural network carries out the self-adaptation adjustment, learning rate η ∈ (0,1) represents scale-up factor, establishes an initial learn rate, if through total error is increased, then this adjustment is invalid; If through total error is descended, then this is adjusted effectively;

4) on the basis of artificial nerve network model, introduce steepness factor, make the weights adjustment break away from the flat region:

In pollution flashover critical voltage prediction artificial nerve network model training process, introduce steepness factor, exist flat site on the error curved surface, it is that the pollution flashover critical voltage predicts that the neuron output of artificial neural network has entered the saturation region of transfer function that the weights adjustment enters the flat region representative, if after entering the flat region, manage to compress neuronic clean input, make its output and withdraw from the saturation region of transfer function, just can change the shape of error function, thereby make to adjust and break away from the flat region, specific practice is, in former transfer function, introduce a steepness factor ζ, make to be output as:

$o=\frac{1-e^{-\frac{\mathrm{net}}{\mathrm{\ξ}}}}{1+e^{-\frac{\mathrm{net}}{\mathrm{\ξ}}}}$

Wherein, net is the output valve of each node layer, when the d-o value is still big when finding Δ E approaching zero, promptly thinks to enter the flat region this seasonal ζ＞1; After withdrawing from the flat region, make ζ=1 again, when ζ＞1, the net coordinate has compressed doubly, the sensitive segment of the neuronic transfer function curve of pollution flashover critical voltage prediction artificial neural network is elongated, thereby makes the net value withdraw from saturation value, when ζ=1, transfer function restores to the original state, and less net value is had higher sensitivity;

Set up improved BP neural network prediction model, solution formula O (j)=f (net (j)) can obtain the pollution flashover critical voltage predicted value of insulator, j=1 wherein, 2, ..., l, l are the node number of output layer, the input summation of net (j) expression pollution flashover critical voltage prediction neuron j, f represents a kind of Nonlinear Mapping relation.

The application of described pollution flashover classification prediction Early-warning Model, carry out as follows:

Determine the pollution flashover index of insulator, the pollution flashover index forecast model passes through formula

Decision, wherein κ is a pollution flashover index; U _FFPredicted value for the pollution flashover critical voltage; U _OPBe working voltage, the predicted value of pollution flashover critical voltage is the input of this model, and κ is the output of this model, is the pollution flashover index of prediction.

Advantage of the present invention: proposed multivariate equivalent salt density seasonal effect in time series forecast model based on phase space reconfiguration, and it is found the solution with supporting vector machine model, solved at equivalent salt density data small sample and had forecasting problem under the noise situations, improved precision of prediction.

Description of drawings:

Fig. 1 (a) pollution flashover index forecasting method for regional power grid process flow diagram of the present invention;

Fig. 1 (b) the present invention uses the forecast model process flow diagram of insulator surface equivalent salt density;

Fig. 1 (c) the present invention uses the pollution flashover critical voltage forecast model process flow diagram of insulator;

Fig. 2 inventor artificial neural networks model figure;

Fig. 3 equivalent salt density of the present invention monitoring point equivalent salt density measured value and calculated value are relatively;

Fig. 4 pollution flashover critical voltage of the present invention measured value and calculated value comparison diagram;

Fig. 5 pollution flashover index prediction of the present invention Early-warning Model figure.

Embodiment:

A kind of pollution flashover index forecasting method for regional power grid of the present invention is illustrated with accompanying drawing in conjunction with the embodiments.

This method, step is as follows, shown in Fig. 1 (a):

Step 1, application insulator surface equivalent salt density forecast model, real-time estimate equivalent salt density currency;

With the environmental parameter and the equivalent salt density history value isolated input sub-surface equivalent salt density forecast model of electrical network collection in worksite, the output of insulator surface equivalent salt density forecast model is real-time estimate equivalent salt density currency;

Wherein the environmental parameter of collection in worksite comprises air speed value, temperature value, atmospheric pressure value, rainfall value, humidity value and equivalent salt density history value; The measurement data of wind speed, temperature, air pressure, rainfall amount, humidity and equivalent salt density history value constitute the equivalent salt density multivariate time series of a 6 DOF, and 20 different values constantly choosing the same time period of these six variablees constitute time series

Concrete parameter is formula as follows

$\left(\begin{array}{cccc}1.980& 2.017...& 2.583...& 1.679\\ 27.14& 26.170...& 18.048...& 14.798\\ ...& & & \\ 0.283& 0.0489...& 0.1061...& 0.1687\end{array}\right)$

In the following formula: the first behavior air speed value, unit is m/s; The second behavior temperature value, unit are ℃; The third line is an atmospheric pressure value, and unit is hPa; Fourth line is the rainfall value, and unit is mm; Fifth line is a rh value, and unit is %;

The close value of the 6th behavioral equivalence salt, unit is mg/cm ²

Step 2, application pollution flashover critical voltage forecast model, prediction pollution flashover critical voltage;

With the pollution flashover critical voltage forecast model of real-time estimate equivalent salt density currency and current collection environmental parameter isolated input, the output of the pollution flashover critical voltage forecast model of insulator is pollution flashover critical voltage predicted value;

Step 3, application pollution flashover classification prediction Early-warning Model, the sub-pollution flashover index of prediction line insulation;

With pollution flashover critical voltage predicted value input pollution flashover classification prediction Early-warning Model, the output of pollution flashover classification prediction Early-warning Model is the electrical network pollution flashover index of prediction;

Step 4, when the electrical network pollution flashover index is 0 and 5%, do not carry out the pollution flashover early warning; When the electrical network pollution flashover index is 20%, the early warning of issue pollution flashover III level; When the electrical network pollution flashover index was 50% and 85%, the pollution flashover probability of happening was issued the early warning of pollution flashover II level greater than 50%; When the electrical network pollution flashover index was 100%, the pollution flashover probability of happening was quite big, and this regional power grid at any time pollution flashover might take place, the early warning of issue pollution flashover I level, as shown in Figure 5.

The total initial conditions of pollution flashover forecast model is a weather data, comprises historical record data and forecast, is output as the pollution flashover electric pressure, can make judgement to the pollution flashover occurrence risk according to the pollution flashover electric pressure.

The application of described insulator surface equivalent salt density forecast model is carried out as follows, shown in Fig. 1 (b):

1) sets up multivariate equivalent salt density time series;

Wherein the environmental parameter of collection in worksite comprises air speed value, temperature value, atmospheric pressure value, rainfall value, humidity value and equivalent salt density history value; The measurement data of wind speed, temperature, air pressure, rainfall amount, humidity and equivalent salt density history value constitute the equivalent salt density multivariate time series of a 6 DOF, and 20 different values constantly choosing the same time period of these six variablees constitute time series

Concrete parameter is formula as follows

$\left(\begin{array}{cccc}1.980& 2.017...& 2.583...& 1.679\\ 27.14& 26.170...& 18.048...& 14.798\\ ...& & & \\ 0.283& 0.0489...& 0.1061...& 0.1687\end{array}\right)$

In the following formula: the first behavior air speed value, unit is m/s; The second behavior temperature value, unit are ℃; The third line is an atmospheric pressure value, and unit is hPa; Fourth line is the rainfall value, and unit is mm; Fifth line is a rh value, and unit is %;

The close value of the 6th behavioral equivalence salt, unit is mg/cm ²

2) reconstruct multivariate equivalent salt density seasonal effect in time series phase space:

With delay time T=3 and embedding dimension m=6 equivalent salt density multivariate time series is carried out phase space reconfiguration, in the equivalent salt density phase space of reconstruct, put the training sample that constitutes equivalent salt density time series supporting vector machine model mutually with in the phase space all, set up supporting vector machine model, to the Nonlinear Mapping in the equivalent salt density time series global prediction model

Carry out match;

Whole training samples that constitute mutually in the phase space are:

$\left\{\begin{array}{c}{V}_n=(x_{1,n},x_{1,n-{\mathrm{\τ}}_1},...,x_{1,n-(m1-1){\mathrm{\τ}}_1},...,x_{M,n},x_{M,n-{\mathrm{\τ}}_M},...,x_{M,n-(m_M-1){\mathrm{\τ}}_M})\\ ...\\ V_i=(x_{1,i},x_{1,i-{\mathrm{\τ}}_1},...,x_{1,i-(m1-1){\mathrm{\τ}}_1},...,x_{M,i},x_{M,i-{\mathrm{\τ}}_M},...,x_{M,i-(m_M-1){\mathrm{\τ}}_M})\\ ...\\ V_N=(x_{1,N},x_{1,N-{\mathrm{\τ}}_1},...,x_{1,N-(m1-1){\mathrm{\τ}}_1},...,x_{M,N},x_{M,N-{\mathrm{\τ}}_M},...,x_{M,N-(m_M-1){\mathrm{\τ}}_M})\end{array}\right.$

Wherein add up to N=6 (n-(m-1) τ) mutually;

3) equivalent salt density time series determinacy check:

By the calculating maximum Lyapunov exponent of improving one's methods, the result approximates 0.047, and can be judged greater than zero by maximum Lyapunov exponent: the equivalent salt density time series is non-linear chaos time sequence;

4) global prediction multivariate equivalent salt density time series

Based on three above steps, having set up the multivariate equivalent salt density is time series global prediction model;

5) utilize supporting vector machine model to find the solution multivariate equivalent salt density time series predicting model

Put the supporting vector machine model training sample set capacity and the equivalent salt density nonlinear system characteristic of formation mutually according to equivalent salt density time series phase space reconstruction, use the crosscheck method, select supporting vector machine model kernel function and each parameter of model to be: kernel function is selected gaussian kernel function; Kernel function parameter γ=0.6; Punishment c=50; Insensitive loss function parameter ε=0.29;

Part equivalent salt density monitoring point equivalent salt density time series SVM prediction predicted results as shown in Figure 3, in the equivalent salt density forecast model of being set up, the error of equivalent salt density predicted value is controlled within 12% basically.

The application of the pollution flashover critical voltage forecast model of described insulator is carried out as follows, shown in Fig. 1 (c):

1) determining of pollution flashover critical voltage:

The data U that the pollution flashover critical voltage value selects for use the test of 50% pollution flashover voltage to obtain _50%, to equivalent salt density and meteorologic parameter and pollution flashover critical voltage value U _50%Between multidimensional nonlinear relation carry out the artificial neural network modeling, realize insulator contamination critical voltage U to known equivalent salt density and meteorologic parameter _50%Predict;

Wherein the data of pollution flashover voltage test acquisition are as follows:

The standardized value of air pressure	The standardized value of humidity	The standardized value of temperature	The standardized value of ESDD	U 50％Standardized value
					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

Standardized value is determined by following formula:

The U of i for obtaining _50%The number of data;

a _iBe the standardized value of a certain parameter, b _iBe arbitrary value of this parameter, b _MinBe the minimum value in this parameter all values, b _MaxBe the maximal value in this parameter all values; Select one group of data as test samples, other data are as the artificial neural network training sample;

2) at the artificial pollution test's data after handling, set up artificial nerve network model as accompanying drawing 2;

3) on the basis of artificial nerve network model, set up momentum term and the learning rate to the BP method carried out the self-adaptation adjustment:

With the standardized data in the step 1) is training sample, and setting network initial parameter value and network output error permissible value are trained network, after the network output error is less than permissible value, keep corresponding network architecture parameters;

4) on the basis of artificial nerve network model, introduce steepness factor, make the weights adjustment break away from the flat region, obtain pollution flashover critical voltage forecast model:

Part pollution flashover critical voltage forecast model predict the outcome with measured value more as shown in Figure 4, in the pollution flashover critical voltage forecast model of being set up, the error of pollution flashover critical voltage value is controlled at basically ± 6% within;

The application of described pollution flashover classification prediction Early-warning Model, carry out as follows:

The pollution flashover index forecast model passes through formula

Decision, wherein κ is a pollution flashover index; U _FFPredicted value for the pollution flashover critical voltage; U _OPBe working voltage.

Claims (4)

1. pollution flashover index forecasting method for regional power grid, it is characterized in that: step is as follows:

Step 1, application insulator surface equivalent salt density forecast model, real-time estimate equivalent salt density currency;

With the environmental parameter and the equivalent salt density history value isolated input sub-surface equivalent salt density forecast model of electrical network collection in worksite, the output of insulator surface equivalent salt density forecast model is real-time estimate equivalent salt density currency;

Step 2, application insulator contamination critical voltage forecast model, prediction pollution flashover critical voltage;

With the pollution flashover critical voltage forecast model of real-time estimate equivalent salt density currency and current collection environmental parameter isolated input, the output of the pollution flashover critical voltage forecast model of insulator is pollution flashover critical voltage predicted value;

Step 3, application pollution flashover classification prediction Early-warning Model, the sub-pollution flashover index of prediction line insulation;

With pollution flashover critical voltage predicted value input pollution flashover classification prediction Early-warning Model, the output of pollution flashover classification prediction Early-warning Model is the electrical network pollution flashover index of prediction;

Step 4, when the electrical network pollution flashover index is 0 and 5%, do not carry out the pollution flashover early warning; When the electrical network pollution flashover index is 20%, the early warning of issue pollution flashover III level; When the electrical network pollution flashover index was 50% and 85%, the pollution flashover probability of happening was issued the early warning of pollution flashover II level greater than 50%; When the electrical network pollution flashover index was 100%, the pollution flashover probability of happening was quite big, and this regional power grid at any time pollution flashover might take place, the early warning of issue pollution flashover I level.

2. by the described pollution flashover index forecasting method for regional power grid of claim 1, it is characterized in that: the application of described insulator surface equivalent salt density forecast model, carry out as follows:

1) sets up multivariate equivalent salt density time series;

At Fixed Time Interval equivalent salt ciphertext data is measured, at a series of moment t ₁, t ₂..., t _nDiscrete ordered set { the x that obtains ₁, x ₂..., x _nBe called discrete equivalent salt density time series, abbreviate the equivalent salt density time series as;

Multivariate equivalent salt density time series is the multidimensional equivalent salt density time series that is made of equivalent salt density time series and the meteorologic parameter time series in the identical moment, is the form of expression by the multidimensional equivalent salt density nonlinear kinetics system that comprises the equivalent salt density time series;

M dimension equivalent salt density time series: X ₁, X ₂..., X _N, N represents number, wherein X constantly _i=(x _{1, i}, x _{2, i}..., x _{M, i}), promptly

$\left(\begin{array}{cccc}{x}_{\mathrm{1,1}}& x_{\mathrm{1,2}}...& x_{1,i}...& x_{1,N}\\ x_{\mathrm{2,1}}& x_{\mathrm{2,2}}...& x_{2,i}...& x_{2,N}\\ ...& & & \\ x_{M,1}& x_{M,2}...& x_{M,i}...& x_{M,N}\end{array}\right)$

In the formula, i=1,2 ..., N, x _{M, N}Represent that M variable is at the numerical value of n-hour, x _{M, i}Represent that M variable is at i numerical value constantly;

2) reconstruct multivariate equivalent salt density seasonal effect in time series phase space;

The point mutually of multivariate equivalent salt density time series phase space reconfiguration is:

$\left\{\begin{array}{c}{V}_n=(x_{1,n},x_{1,n-{\mathrm{\τ}}_1},...,x_{1,n-(m1-1){\mathrm{\τ}}_1},...,x_{M,n},x_{M,n-{\mathrm{\τ}}_M},...,x_{M,n-(m_M-1){\mathrm{\τ}}_M})\\ ...\\ V_i=(x_{1,i},x_{1,i-{\mathrm{\τ}}_1},...,x_{1,i-(m1-1){\mathrm{\τ}}_1},...,x_{M,i},x_{M,i-{\mathrm{\τ}}_M},...,x_{M,i-(m_M-1){\mathrm{\τ}}_M})\\ ...\\ V_N=(x_{1,N},x_{1,N-{\mathrm{\τ}}_1},...,x_{1,N-(m1-1){\mathrm{\τ}}_1},...,x_{M,N},x_{M,N-{\mathrm{\τ}}_M},...,x_{M,N-(m_M-1){\mathrm{\τ}}_M})\end{array}\right.$

Represent that M variable is τ in n-hour in time delay _MThe embedding dimension is m _MPhase space reconstruction in value;

Wherein n represents n constantly,

τ _iAnd m _iBe i seasonal effect in time series time delay and embedding dimension, the embedding dimension m=m of phase space reconstruction ₁+ m ₂+ ...+m _M, M is the seasonal effect in time series dimension;

Mutual information method is adopted in the selection of multivariate equivalent salt density seasonal effect in time series phase space reconfiguration parameter delay time T, and mutual information method is the time-delay that reaches for the first time hour with the mutual information time delay as phase space reconfiguration, by

Decision, R _Xx((i+1) τ) is the autocorrelation function of equivalent salt density time series time span for (i+1) τ, and τ is phase space reconfiguration parameter time delay; Embed dimension m by:

$E\left(m\right)=\frac{1}{N-\mathrm{m\τ}}\underset{i=1}{\overset{N-\mathrm{m\τ}}{\mathrm{\Σ}}}\mathrm{\α}(i,m)$

Decision, wherein:

$\mathrm{\α}(i,m)=\frac{\left|\right|X_i(m+1)-X_{n(i,m)}(m+1)\left|\right|}{\left|\right|X_i\left(m\right)-X_{n(i,m)}\left(m\right)\left|\right|}$

X _i(m+1) be the i point mutually in the equivalent salt density system phase space of (m+1) dimension reconstruct, (i is to make to put X mutually in m dimension equivalent salt density system phase space m) to n _{N (i, m)}(m) be to put X mutually _iThe integer of neighbor point (m), || || be the Euclidean distance on the equivalent salt density system phase space;

3) equivalent salt density time series determinacy check;

Adopt Li Ya spectrum promise husband index method to carry out the check of equivalent salt density seasonal effect in time series determinacy among the present invention, this index is the numerical representation method of the average index diverging rate of adjacent tracks in the phase space, sensitivity to initial state in order to the portrayal chaotic motion, this index conduct is along the long-term averaged result of track, be a kind of global feature, it is worth real number always;

Judge that equivalent salt density seasonal effect in time series nonlinear characteristic obtains by calculating largest Lyapunov exponent, this method is calculated the regression straight line slope by y (k) curve

Be maximal index, wherein,

l _i(k) expression is to each calculates the Euclidean distance after k the discrete time to neighbor point in the equivalent salt density phase space of reconstruct, and M is the seasonal effect in time series dimension;

4) global prediction multivariate equivalent salt density time series;

According to Tai Kensi time-delay embedding theorems, as long as embed dimension m and delay time T is selected rationally, phase space reconstruction the track of embedded space just with the differomorphism meaning under equivalent salt density dynamical system equivalence, and have smooth mapping f:

Make: V _I+1=f (V _i), V _I+1The individual point mutually of i+1 in the expression phase space reconstruction is used the mapping of non-linear approach method structure

Come close approximation f, and make

Satisfy:

Minimum, wherein

M variable of expression expression is engraved in time delay when n be τ _MThe embedding dimension is m _MPhase space reconstruction in value, τ _MThe time delay of representing M variable, m _MThe embedding dimension of representing M variable;

5) utilize supporting vector machine model to find the solution multivariate equivalent salt density time series predicting model;

By finding the solution the Nonlinear Mapping in the forecast model

The close time series predicting model of certainty equivalents salt, and the Nonlinear Mapping that forecast model is tried to achieve

Under predicated error meet the demands, the support vector machine theory can solve Nonlinear Mapping in the equivalent salt density Forecast of Nonlinear Time Series model under the equivalent salt density data sample capacity situation less than normal effectively

The problem of finding the solution, the support vector machine method that is used for approaching equivalent salt density time series predicting model Nonlinear Mapping relation is a support vector regression;

If equivalent salt density system phase space is put the sample set of formation mutually: S={ (x _i, y _i), i=1,2 ..., M}, (x _i, y _i) represent the arbitrary point mutually in the phase space reconstruction, if an existence lineoid g (x)=＜wx 〉+b, w ∈ R ⁿ, b ∈ R, w, b represent vectorial parameter, in order to construct lineoid g (x), make: | y _i-g (x _i) |≤ε sets up, wherein,＜the expression inner product of vectors, and i=1,2 ..., M, M are equivalent salt density seasonal effect in time series dimension, then sample set S={ (x _i, y _i), i=1,2 ..., M} is the approximate collection of ε, has: |＜wx 〉+b-y _i|≤ε, promptly

I=1,2 ..., M;

Wherein,

For the point of S to lineoid f (x) apart from d _i, then have: I=1,2 ..., M, promptly the point in the S set to lineoid apart from maximal value is

Can obtain the best fit approximation lineoid of S set to the upper bound of lineoid distance by the point of maximization among the S, then the best fit approximation lineoid can be by the maximization formula Obtain, therefore find the solution || w|| ²Minimization problem can obtain the best fit approximation lineoid of S set because the equivalent salt density system is a nonlinear system, must be with a Nonlinear Mapping

The x of point mutually in the equivalent salt density system phase space _iBe mapped to a higher dimensional space, in higher dimensional space, carry out linear regression then, owing to relate to the inner product operation of higher dimensional space in the optimizing process, for fear of inner product operation, with kernel function Ψ (x _i, x _I+1) the replacement inner product

Realize non-linear regression in the equivalent salt density system phase space, at this moment, the support vector regression problem on the equivalent salt density system phase space can be converted into following || w|| ²Optimization problem:

Wherein, i=1,2 ..., M, following formula are quadratic programming problem, its Lagrange function is:

$\left\{\begin{array}{c}\underset{\mathrm{\α},{\mathrm{\α}}^{*}}{\min }\frac{1}{2}\underset{i=1}{\overset{M}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)({{\mathrm{\α}}_{i+1}}^{*}-{\mathrm{\α}}_{i+1})\mathrm{\Ψ}(x_i,x_{i+1})+\mathrm{\ϵ}\underset{i=1}{\overset{M}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)-\underset{j=1}{\overset{M}{\mathrm{\Σ}}}{y}_j({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i),j=\mathrm{1,2},...,M\\ s.t.\underset{i=1}{\overset{M}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)=0,{\mathrm{\α}}_i\≥0,{\mathrm{\α}}_i^{*}\≥0,i=\mathrm{1,2},...,M\end{array}\right.$

Wherein, α _iWith

Be called as Lagrange multiplier, to any i=1,2 ..., M has equation α _i〉=0,

Set up;

In carrying out equivalent salt density system phase space, during the Nonlinear Mapping approximation of function,, therefore introduce slack variable owing to inevitably have error between regression function of trying to achieve and the actual function:

ξ _i〉=0,

I=1,2 ..., M, ξ _iThe expression slack variable;

Being optimized for of this moment:

C is the punishment parameter in the formula, and c＞0;

Can get the Lagrange dual problem is:

$\left\{\begin{array}{c}\underset{\mathrm{\α},{\mathrm{\α}}^{*}}{\min }\frac{1}{2}\underset{i=1}{\overset{M}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)({a_{i+1}}^{*}-a_{i+1})\mathrm{\Ψ}(x_i,x_{i+1})+\mathrm{\ϵ}\underset{i=1}{\overset{M}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)-\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{y}_i({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)\\ s.t.\underset{i=1}{\overset{M}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)=0,{\mathrm{\α}}_i\≥c,{\mathrm{\α}}_i^{*}\≥0,i=\mathrm{1,2},...,M\end{array}\right.$

Following formula is as the prediction of insulator surface equivalent salt density;

Find the solution following formula get final product Nonlinear Mapping in the equivalent salt density system phase space

Regression function g (x), kernel function and y _iAs input quantity, can obtain next equivalent salt density value constantly, the penalty factor in parameter in the kernel function and the supporting vector machine model parameter is the Nonlinear Mapping that the decision support vector machine method is tried to achieve

The main factor of estimated performance adopts the cross validation method to carry out the selection of supporting vector machine model parameter.

3. by the described pollution flashover index forecasting method for regional power grid of claim 1, it is characterized in that: the application of the pollution flashover critical voltage forecast model of described insulator, carry out as follows:

1) the pollution flashover critical voltage determines;

The data U that the pollution flashover critical voltage value selects for use the test of 50% pollution flashover voltage to obtain _50%, to equivalent salt density and meteorologic parameter and pollution flashover critical voltage value U _50%Between multidimensional nonlinear relation carry out the artificial neural network modeling, realize insulator contamination critical voltage U to known equivalent salt density and meteorologic parameter _50%Predict;

2) foundation of artificial nerve network model;

Adopt pollution flashover critical voltage prediction artificial nerve network model among the present invention based on the BP method;

Determine three layers of the input layer, hidden layer of pollution flashover critical voltage prediction BP artificial nerve network model and output layers;

Pollution flashover critical voltage prediction BP artificial nerve network model comprises input layer, hidden layer and output layer three-decker, and according to different artificial filthy experimental datas, hidden layer is respectively two-layer or three node layers are formed;

x ₁, x ₂..., x _nBe input layer, comprise equivalent salt density value, temperature, humidity, air pressure, wind speed and rainfall, h ₁, h ₂..., h _mBe hidden node, o is the output layer node, is insulator contamination critical voltage predicted value; V ₁, V ₂..., V _mBe the weights of input layer to hidden layer, W ₁, W ₂..., W _mFor hidden layer to the output layer weights, the training of pollution flashover critical voltage artificial nerve network model uses artificial withstand pollution test data as training data, the structure and parameter of whole network is optimized by training, the input layer dimension of network is n, the output dimension is that one dimension is the output of correlation predictive value, hidden layer cell dimension m optimizes definite in network training study, the predicted value of forecast model compares with the result of actual artificial withstand pollution test, and then network structure and weights are revised and perfect;

3) on the basis of artificial nerve network model, set up momentum term and the learning rate to the BP method carried out the self-adaptation adjustment;

For improving pollution flashover critical voltage prediction artificial neural network training speed, adjust momentum term of increase in the formula at weights, if represent the pollution flashover critical voltage to predict in the artificial neural network certain layer weight matrix with W, X represents certain layer of input vector, and the pollution flashover critical voltage prediction artificial neural network weights adjustment vector expression that then contains momentum term is:

Δ W (t)=η δ X+ α Δ W (t-1), letter representation meaning α is a momentum factor in the formula, establishes α ∈ (0,1), η is the learning rate of neural network, Δ W (t-1) is previous weights adjustment amount, and Δ W (t) is this weights adjustment amount, the adjustment experience before momentum term has reflected, adjustment constantly plays damping action for t, when rising and falling suddenly appears in the error curved surface, can reduce vibration trend, improve training speed;

Learning rate to the BP method in the modeling of pollution flashover critical voltage prediction artificial neural network carries out the self-adaptation adjustment, learning rate η ∈ (0,1) represents scale-up factor, establishes an initial learn rate, if through total error is increased, then this adjustment is invalid; If through total error is descended, then this is adjusted effectively;

4) on the basis of artificial nerve network model, introduce steepness factor, make the weights adjustment break away from the flat region;

In pollution flashover critical voltage prediction artificial nerve network model training process, introduce steepness factor, exist flat site on the error curved surface, it is that the pollution flashover critical voltage predicts that the neuron output of artificial neural network has entered the saturation region of transfer function that the weights adjustment enters the flat region representative, if after entering the flat region, manage to compress neuronic clean input, make its output and withdraw from the saturation region of transfer function, just can change the shape of error function, thereby make to adjust and break away from the flat region, specific practice is, in former transfer function, introduce a steepness factor ζ, make to be output as:

$o=\frac{1-e^{-\frac{\mathrm{net}}{\mathrm{\ξ}}}}{1+e^{-\frac{\mathrm{net}}{\mathrm{\ξ}}}}$

Wherein, net is the output valve of each node layer, when the d-o value is still big when finding Δ E approaching zero, promptly thinks to enter the flat region this seasonal ζ＞1; After withdrawing from the flat region, make ζ=1 again, when ζ＞1, the net coordinate has compressed doubly, the sensitive segment of the neuronic transfer function curve of pollution flashover critical voltage prediction artificial neural network is elongated, thereby makes the net value withdraw from saturation value, when ζ=1, transfer function restores to the original state, and less net value is had higher sensitivity;

Set up improved BP neural network prediction model, solution formula O (j)=f (net (j)) can obtain the pollution flashover critical voltage predicted value of insulator, j=1 wherein, 2, ..., l, l are the node number of output layer, the input summation of net (j) expression pollution flashover critical voltage prediction neuron j, f represents a kind of Nonlinear Mapping relation.

4. by the described pollution flashover index forecasting method for regional power grid of claim 1, it is characterized in that: the application of described pollution flashover classification prediction Early-warning Model, carry out as follows:

Determine the pollution flashover index of insulator, the pollution flashover index forecast model passes through formula

Decision, wherein κ is a pollution flashover index; U _FFPredicted value for the pollution flashover critical voltage; U _OPBe working voltage, the predicted value of pollution flashover critical voltage is the input of this model, and κ is the output of this model, is the pollution flashover index of prediction.

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