CN101893674A

CN101893674A - A Prediction Method for Pollution Flashover Index of Regional Power Grid

Info

Publication number: CN101893674A
Application number: CN201010224050XA
Authority: CN
Inventors: 滕云; 徐建源; 林莘; 苏蔚; 李永祥
Original assignee: Shenyang University of Technology
Current assignee: State Grid Corp of China SGCC; State Grid Liaoning Electric Power Co Ltd
Priority date: 2010-07-12
Filing date: 2010-07-12
Publication date: 2010-11-24
Anticipated expiration: 2030-07-12
Also published as: CN101893674B

Abstract

A method for predicting pollution flashover index of regional power grid belongs to the technical field of power transmission and distribution monitoring. The method is as follows: 1) Apply the insulator surface equivalent salt density prediction model to predict the current value of the equivalent salt density in real time; 2) Apply the insulator pollution flashover critical voltage prediction model to predict the pollution flashover critical voltage; 3) Apply the pollution flashover classification prediction and early warning model , to predict the pollution flashover index of grid insulators; 4) judge the status. Advantages of the present invention: Propose a multivariate equivalent salt density time series prediction model based on phase space reconstruction, use the support vector machine model to solve it, solve the prediction problem in the case of small samples of equivalent salt density data and the presence of noise, Improved prediction accuracy.

Description

A Prediction Method for Pollution Flashover Index of Regional Power Grid

技术领域technical field

本发明属于输配电监测技术领域，特别涉及一种区域电网污闪指数预测方法。The invention belongs to the technical field of power transmission and distribution monitoring, and in particular relates to a method for predicting pollution flashover index of a regional power grid.

背景技术Background technique

电网在运行过程中，由于绝缘子表面发生污秽闪络对供电系统有很不利影响，目前，针对绝缘子表面污秽闪络的预测方法有很多，主要集中在对于绝缘子表面等值附盐密度的预测、绝缘子污秽闪络电压的预测、及基于泄漏电流的污秽闪络预测方面。During the operation of the power grid, the pollution flashover on the surface of the insulator has a very adverse effect on the power supply system. At present, there are many prediction methods for the pollution flashover on the insulator surface, mainly focusing on the prediction of the equivalent salt density on the surface of the insulator, the insulator Prediction of pollution flashover voltage and pollution flashover prediction based on leakage current.

其中，等值盐密的神经网络预测、污闪电压的支持向量机预测都是将描述污闪的这两个参数与环境气象参数之间的多维非线性关系用非线性建模方法来进行拟合，这种预测方法在国内外均处于领先地位，但这两种方法仍存在建模对象单一，建立的预测模型及其预测功能与电网防污工作要求之间存在一定差异，尚无法在电网的污闪防治运行管理中得到实际应用，基于泄漏电流的污闪预测方法的基础数据丰富，在此基础上应用人工神经网络等方法能够取得与工程实际比较接近的拟合效果，但泄漏电流的监测点分布范围有限，无法对电网的污闪状态进行较为全面的实时监测和预测。Among them, the neural network prediction of equivalent salt density and the support vector machine prediction of pollution flashover voltage all use nonlinear modeling methods to simulate the multidimensional nonlinear relationship between these two parameters describing pollution flashover and environmental meteorological parameters. Combined, this prediction method is in a leading position both at home and abroad, but the two methods still have a single modeling object, and there are certain differences between the established prediction model and its prediction function and the grid anti-pollution work requirements. It has been practically applied in the operation and management of pollution flashover prevention and control. The pollution flashover prediction method based on leakage current has abundant basic data. On this basis, artificial neural network and other methods can be used to obtain a fitting effect that is relatively close to the actual project. However, the leakage current The distribution of monitoring points is limited, and it is impossible to conduct more comprehensive real-time monitoring and prediction of the pollution flashover status of the power grid.

发明内容Contents of the invention

针对现有技术的不足，本发明提供一种区域电网污闪指数预测方法。Aiming at the deficiencies of the prior art, the invention provides a method for predicting the pollution flashover index of the regional power grid.

本发明一种区域电网污闪指数预测方法，步骤如下：A method for predicting pollution flashover index of regional power grid in the present invention, the steps are as follows:

步骤1、应用绝缘子表面等值盐密预测模型，实时预测等值盐密当前值；Step 1. Apply the equivalent salt density prediction model on the surface of the insulator to predict the current value of the equivalent salt density in real time;

将电网现场采集的环境参数和等值盐密历史值输入绝缘子表面等值盐密预测模型，绝缘子表面等值盐密预测模型输出即为实时预测等值盐密当前值；The environmental parameters and equivalent salt density historical values collected on the grid site are input into the insulator surface equivalent salt density prediction model, and the output of the insulator surface equivalent salt density prediction model is the real-time predicted equivalent salt density current value;

步骤2、应用绝缘子污闪临界电压预测模型，预测污闪临界电压；Step 2. Apply the insulator pollution flashover critical voltage prediction model to predict the pollution flashover critical voltage;

将实时预测等值盐密当前值和当前采集环境参数输入绝缘子的污闪临界电压预测模型，绝缘子的污闪临界电压预测模型的输出即为污闪临界电压预测值；The real-time predicted equivalent salt density current value and the current collected environmental parameters are input into the pollution flashover critical voltage prediction model of the insulator, and the output of the pollution flashover critical voltage prediction model of the insulator is the pollution flashover critical voltage prediction value;

步骤3、应用污闪分级预测预警模型，预测电网绝缘子污闪指数；Step 3. Apply the pollution flashover classification prediction and early warning model to predict the pollution flashover index of grid insulators;

将污闪临界电压预测值输入污闪分级预测预警模型，污闪分级预测预警模型的输出即为预测的电网污闪指数；Input the predicted value of pollution flashover critical voltage into the pollution flashover classification prediction and early warning model, and the output of the pollution flashover classification prediction and early warning model is the predicted power grid pollution flashover index;

步骤4、当电网污闪指数为0和5％时，不进行污闪预警；当电网污闪指数为20％时，发布污闪III级预警；当电网污闪指数为50％和85％时，污闪发生概率已经大于50％，发布污闪II级预警；当电网污闪指数为100％时，污闪发生概率已经相当大，该区域电网随时有可能发生污闪，发布污闪I级预警。Step 4. When the pollution flashover index of the power grid is 0 and 5%, no pollution flashover warning will be issued; when the pollution flashover index of the power grid is 20%, a level III warning of pollution flashover will be issued; when the pollution flashover index of the power grid is 50% and 85% , the probability of pollution flashover is greater than 50%, and a pollution flashover level II warning is issued; when the power grid pollution flashover index is 100%, the probability of pollution flashover is already quite high, and pollution flashover may occur in the regional power grid at any time, and a pollution flashover level I is issued early warning.

所述的绝缘子表面等值盐密预测模型的应用，按如下步骤进行：The application of the insulator surface equivalent salt density prediction model is carried out as follows:

1)建立多变量等值盐密时间序列；1) Establish multivariate equivalent salt density time series;

在固定时间间隔对等值盐密数据进行测量，在一系列时刻t₁，t₂，...，t_n得到的离散有序集合{x₁，x₂，...，x_n}称为离散等值盐密时间序列，简称为等值盐密时间序列；The equivalent salt density data is measured at fixed time intervals, and the discrete ordered set {x ₁ , x ₂ , ..., x _{n }} obtained at a series of time t ₁ , t ₂ , ..., t _n is called is the discrete equivalent salt-intensive time series, referred to as the equivalent salt-intensive time series;

多变量等值盐密时间序列是由等值盐密时间序列及在相同时刻内的气象参数时间序列构成的多维等值盐密时间序列，是由包括等值盐密时间序列在内的多维等值盐密非线性动力学系统的表现形式；The multivariate equivalent salt density time series is a multidimensional equivalent salt density time series composed of the equivalent salt density time series and the meteorological parameter time series at the same time. The expression form of value-salt-dense nonlinear dynamical system;

M维等值盐密时间序列：X₁，X₂，...，X_N，N代表时刻数，其中X_i＝(x_1，i，x_2，i，...，x_M，i)，即M-dimensional equivalent salt-dense time series: X ₁ , X ₂ , ..., X _N , N represents the number of moments, where X _i = (x _{1, i} , x _{2, i} , ..., x _{M, i} ),Right now

$(\begin{matrix} {x x}_{1,1 1,1} & {x x}_{1,2 1,2} . . . . . . & {x x}_{11,, i i} . . . . . . & {x x}_{11,, N N} \\ {x x}_{2,1 2,1} & {x x}_{2,2 2,2} . . . . . . & {x x}_{22,, i i} . . . . . . & {x x}_{22,, N N} \\ . . . . . . \\ {x x}_{M m,, 11} & {x x}_{M m,, 22} . . . . . . & {x x}_{M m,, i i} . . . . . . & {x x}_{M m,, N N} \end{matrix})$

式中，i＝1，2，...，N，x_M，N表示第M个变量在N时刻的数值，x_M，i表示第M个变量在i时刻的数值；In the formula, i=1, 2, ..., N, x _{M, N} represents the value of the M variable at the time N, and x _{M, i} represents the value of the M variable at the time i;

2)重构多变量等值盐密时间序列的相空间：2) Reconstruct the phase space of the multivariate equivalent salt-dense time series:

多变量等值盐密时间序列相空间重构的相点为：The phase point of phase space reconstruction of multivariate equivalent salt density time series is:

$\{\begin{matrix} {V V}_{n no} = = (({x x}_{11,, n no},, {x x}_{11,, n no - - {τ τ}_{11}},, . . . . . .,, {x x}_{11,, n no - - ((m m 11 - - 11)) {τ τ}_{11}},, . . . . . .,, {x x}_{M m,, n no},, {x x}_{M m,, n no - - {τ τ}_{M m}},, . . . . . .,, {x x}_{M m,, n no - - (({m m}_{M m} - - 11)) {τ τ}_{M m}})) \\ . . . . . . \\ {V V}_{i i} = = (({x x}_{11,, i i},, {x x}_{11,, i i - - {τ τ}_{11}},, . . . . . .,, {x x}_{11,, i i - - ((m m 11 - - 11)) {τ τ}_{11}},, . . . . . .,, {x x}_{M m,, i i},, {x x}_{M m,, i i - - {τ τ}_{M m}},, . . . . . .,, {x x}_{M m,, i i - - (({m m}_{M m} - - 11)) {τ τ}_{M m}})) \\ . . . . . . \\ {V V}_{N N} = = (({x x}_{11,, N N},, {x x}_{11,, N N - - {τ τ}_{11}},, . . . . . .,, {x x}_{11,, N N - - ((m m 11 - - 11)) {τ τ}_{11}},, . . . . . .,, {x x}_{M m,, N N},, {x x}_{M m,, N N - - {τ τ}_{M m}},, . . . . . .,, {x x}_{M m,, N N - - (({m m}_{M m} - - 11)) {τ τ}_{M m}})) \end{matrix}$

表示第M个变量在N时刻在延迟时间为τ_M嵌入维数为m_M的重构相空间中的值； Indicates the value of the Mth variable embedded in the reconstructed phase space with dimension m _M at delay time τ _M at time N;

其中n表示第n时刻，

τ_i和m_i为第i个时间序列的延迟时间和嵌入维数，重构相空间的嵌入维数m＝m₁+m₂+...+m_M，M为时间序列的维数；where n represents the nth moment,

τ _i and m _i are the delay time and embedding dimension of the i-th time series, the embedding dimension of the reconstructed phase space m=m ₁ +m ₂ +...+m _M , M is the dimension of the time series;

多变量等值盐密时间序列的相空间重构参数延迟时间τ的选择采用互信息法，互信息法是以互信息第一次达到最小时的延时作为相空间重构的延迟时间，由

决定，R_xx((i+1)τ)是等值盐密时间序列时间跨度为(i+1)τ的自相关函数，τ为相空间重构参数延迟时间；嵌入维数m由：The phase space reconstruction parameter delay time τ of the multivariate equivalent salt-dense time series is selected using the mutual information method. The mutual information method uses the delay time when the mutual information reaches the minimum for the first time as the delay time of the phase space reconstruction.

It is determined that R _xx ((i+1)τ) is the autocorrelation function of the equivalent salt-dense time series with a time span of (i+1)τ, and τ is the delay time of phase space reconstruction parameters; the embedding dimension m is given by:

$E E. ((m m)) = = \frac{11}{N N - - mτ mτ} {Σ Σ}_{i i = = 11}^{N N - - mτ mτ} α α ((i i,, m m))$

决定，其中：decision, where:

$α α ((i i,, m m)) = = \frac{| | | | {X x}_{i i} ((m m + + 11)) - - {X x}_{n no ((i i,, m m))} ((m m + + 11)) | | | |}{| | | | {X x}_{i i} ((m m)) - - {X x}_{n no ((i i,, m m))} ((m m)) | | | |}$

X_i(m+1)是(m+1)维重构的等值盐密系统相空间中的第i个相点，n(i，m)是在m维等值盐密系统相空间中使相点X_n(i，m)(m)是相点X_i(m)的最邻近点的整数，||·||是等值盐密系统相空间上的欧式距离；X _i (m+1) is the i-th phase point in the (m+1)-dimensionally reconstructed equivalent salt-dense system phase space, n(i, m) is the phase space of the m-dimensional equivalent salt-dense system Let the phase point X _{n(i, m)} (m) be the integer of the nearest neighbor point of the phase point X _i (m), ||·|| is the Euclidean distance on the phase space of the equivalent salt-dense system;

3)等值盐密时间序列确定性检验：3) Deterministic test of equivalent salt density time series:

本发明中采用李雅谱诺夫指数法进行等值盐密时间序列的确定性检验，该指数是相空间中邻近轨道的平均指数发散率的数值表征，用以刻画混沌运动的初态敏感性，该指数作为沿轨道长期平均的结果，是一种整体特征，其值总是实数；In the present invention, the deterministic test of the equivalent salt density time series is carried out using the Lyapunov index method, which is a numerical representation of the average exponential divergence rate of adjacent orbits in phase space, and is used to describe the initial state sensitivity of chaotic motion , the index is the result of a long-term average along the orbit and is an overall characteristic whose value is always a real number;

判断等值盐密时间序列的非线性特性通过计算最大李雅普诺夫指数得到，该方法计算由y(k)曲线的回归直线斜率为最大指数，其中，

l_i(k)表示对重构的等值盐密相空间中每一对最邻近点，计算k个离散时间后的欧式距离，M为时间序列的维数；Judging the nonlinear characteristics of the equivalent salt density time series is obtained by calculating the maximum Lyapunov exponent. This method calculates the slope of the regression line from the y(k) curve is the largest exponent, where,

l _i (k) represents the Euclidean distance after calculating k discrete times for each pair of nearest neighbor points in the reconstructed equivalent salt-dense phase space, and M is the dimension of the time series;

4)全局预测多变量等值盐密时间序列：4) Global prediction of multivariate equivalent salt-dense time series:

根据泰肯斯延时嵌入定理，只要嵌入维数m和延迟时间τ选择合理，重构相空间在嵌入空间的轨迹就与微分同胚意义下的等值盐密动力学系统等价，且存在光滑映射f：

使得：V_i+1＝f(V_i)，V_i+1表示重构相空间中第i+1个相点，应用非线性逼近方法构造映射

来近似逼近f，并使

满足：

最小，其中

表示表示第M个变量在n时刻在延迟时间为τ_M嵌入维数为m_M的重构相空间中的值，τ_M表示第M个变量的延迟时间，m_M表示第M个变量的嵌入维数；According to the Tekens time-delay embedding theorem, as long as the embedding dimension m and delay time τ are selected reasonably, the trajectory of the reconstructed phase space in the embedding space is equivalent to the equivalent salt-dense dynamical system in the sense of diffeomorphism, and there exists Smooth map f:

Make: V _i+1 = f(V _i ), V _i+1 represents the i+1th phase point in the reconstructed phase space, and the nonlinear approximation method is used to construct the map

to approximate f, and make

satisfy:

minimum, of which

Indicates the value of the Mth variable in the reconstructed phase space with a delay time of τ _M embedding dimension m _M at time n, where τ _M represents the delay time of the M variable, and m _M represents the embedding of the M variable dimension;

5)利用支持向量机模型求解多变量等值盐密时间序列预测模型：5) Use the support vector machine model to solve the multivariate equivalent salt density time series prediction model:

通过求解预测模型中的非线性映射

确定等值盐密时间序列预测模型，并使预测模型在求得的非线性映射

下的预测误差满足要求，支持向量机理论可以有效地解决等值盐密数据样本容量偏小的情况下的等值盐密非线性时间序列预测模型中非线性映射

的求解问题，用于逼近等值盐密时间序列预测模型中非线性映射关系的支持向量机方法是支持向量回归；By solving nonlinear mappings in predictive models

Determine the equivalent salt-dense time series forecasting model, and make the forecasting model in the obtained nonlinear mapping

The prediction error below meets the requirements, and the support vector machine theory can effectively solve the nonlinear mapping in the equivalent salt density nonlinear time series prediction model under the condition that the equivalent salt density data sample capacity is too small

The solution problem of , the support vector machine method used to approximate the nonlinear mapping relationship in the equivalent salt density time series prediction model is support vector regression;

设等值盐密系统相空间相点构成的样本集为：S＝{(x_i，y_i)，i＝1，2，...，M}，(x_i，y_i)表示重构相空间中的任一相点，若存在一个超平面g(x)＝<w·x>+b，w∈Rⁿ，b∈R，w、b表示向量参数，为了构造超平面g(x)，使得：|y_i-g(x_i)|≤ε成立，其中，<·>表示向量内积，i＝1，2，...，M，M为等值盐密时间序列的维数，则样本集S＝{(x_i，y_i)，i＝1，2，...，M}为ε的近似集，有：|<w·x>+b-y_i|≤ε，即

i＝1，2，...，M；Assume that the sample set composed of phase points in the phase space of the equivalent salt-dense system is: S={(xi _, y _i ), i=1, 2,..., M}, ( _xi , y _i ) means the reconstruction For any phase point in the phase space, if there is a hyperplane g(x)=<w·x>+b, w∈R ⁿ , b∈R, w and b represent vector parameters, in order to construct the hyperplane g(x ), so that: |y _i -g(xi ₎ |≤ε holds, where <·> represents the vector inner product, i=1, 2, ..., M, M is the dimension of the equivalent salt-dense time series number, then the sample set S={(x _i , y _i ), i=1, 2,..., M} is an approximate set of ε, which has: |<w·x>+by _i |≤ε, that is

i=1,2,...,M;

其中，

为S的点到超平面f(x)的距离d_i，则有：i＝1，2，...，M，即集合S中的点到超平面的距离最大值为

通过最大化S中的点到超平面距离的上界可得到集合S的最优近似超平面，则最优近似超平面可通过最大化式

得到，因此求解||w||²的最小化问题即可得到集合S的最优近似超平面，由于等值盐密系统是非线性系统，必须用一个非线性映射

把等值盐密系统相空间中的相点x_i映射到一个高维空间，然后在高维空间里进行线性回归，由于优化过程中涉及到高维空间的内积运算，为了避免内积运算，用核函数Ψ(x_i，x_i+1)代替内积

来实现等值盐密系统相空间中非线性回归，此时，等值盐密系统相空间上的支持向量回归问题可转化为如下的||w||²优化问题：in,

is the distance d _i from the point of S to the hyperplane f(x), then: i=1, 2,..., M, that is, the maximum distance between the points in the set S and the hyperplane is

The optimal approximate hyperplane of the set S can be obtained by maximizing the upper bound of the distance between the points in S and the hyperplane, then the optimal approximate hyperplane can be obtained by maximizing the formula

Therefore, by solving the minimization problem of ||w|| ² , the optimal approximation hyperplane of the set S can be obtained. Since the equivalent salt density system is a nonlinear system, a nonlinear mapping must be used

Map the phase point x _i in the phase space of the equivalent salt-dense system to a high-dimensional space, and then perform linear regression in the high-dimensional space. Since the inner product operation of the high-dimensional space is involved in the optimization process, in order to avoid the inner product operation , replace the inner product with the kernel function Ψ( _xi ,xi ₊₁ )

To realize the nonlinear regression in the phase space of the equivalent salt density system, at this time, the support vector regression problem on the phase space of the equivalent salt density system can be transformed into the following ||w|| ² optimization problem:

其中，i＝1，2，...，M，上式为二次规划问题，其Lagrange函数为：Among them, i=1, 2,..., M, the above formula is a quadratic programming problem, and its Lagrange function is:

$\{\begin{matrix} \underset{α α,, {α α}^{* *}}{min min} \frac{11}{22} {Σ Σ}_{i i = = 11}^{M m} (({α α}_{i i}^{* *} - - {α α}_{i i})) (({α α}_{i i + + 11}^{* *} - - {α α}_{i i + + 11})) Ψ Ψ (({x x}_{i i},, {x x}_{i i + + 11})) + + ϵ ϵ {Σ Σ}_{i i = = 11}^{M m} (({α α}_{i i}^{* *} - - {α α}_{i i})) - - {Σ Σ}_{j j = = 11}^{M m} {y the y}_{j j} (({α α}_{i i}^{* *} - - {α α}_{i i})),, j j = = 1,2 1,2,, . . . . . .,, M m \\ s the s . . t t . . {Σ Σ}_{i i = = 11}^{M m} (({α α}_{i i}^{* *} - - {α α}_{i i})) = = 00,, {α α}_{i i} &GreaterEqual; &Greater Equal; 00,, {α α}_{i i}^{* *} &GreaterEqual; &Greater Equal; 00,, i i = = 1,2 1,2,, . . . . . .,, M m \end{matrix}$

其中，α_i和

被称为拉格朗日乘子，对任何i＝1，2，...，M，都有等式

α_i≥0，

成立；Among them, α _i and

Known as the Lagrange multiplier, for any i=1, 2, ..., M, there is an equation

α _i ≥ 0,

established;

在进行等值盐密系统相空间中非线性映射函数逼近时，由于求得的回归函数与实际函数之间不可避免的存在误差，因此引入松弛变量：When approximating the nonlinear mapping function in the phase space of the equivalent salt-density system, due to the inevitable error between the obtained regression function and the actual function, the slack variable is introduced:

ξ_i≥0，

i＝1，2，...，M，ξ_i表示松弛变量；ξ _i ≥ 0,

i=1, 2,..., M, _ξi represents a slack variable;

此时的优化为：The optimization at this time is:

式中c为惩罚参数，且c＞0；In the formula, c is a penalty parameter, and c>0;

可得Lagrange对偶问题为：The Lagrange dual problem can be obtained as:

$\{\begin{matrix} \underset{α α,, {α α}^{* *}}{min min} \frac{11}{22} {Σ Σ}_{i i = = 11}^{M m} (({α α}_{i i}^{* *} - - {α α}_{i i})) (({aα aα}_{i i + + 11}^{* *} - - {aα aα}_{i i + + 11})) Ψ Ψ (({x x}_{i i},, {x x}_{i i + + 11})) + + ϵ ϵ {Σ Σ}_{i i = = 11}^{M m} (({α α}_{i i}^{* *} - - {α α}_{i i})) - - {Σ Σ}_{i i = = 11}^{M m} {y the y}_{i i} (({α α}_{i i}^{* *} - - {α α}_{i i})) \\ s the s . . t t . . {Σ Σ}_{i i = = 11}^{M m} (({α α}_{i i}^{* *} - - {α α}_{i i})) = = 00,, {α α}_{i i} &GreaterEqual; &Greater Equal; c c,, {α α}_{i i}^{* *} &GreaterEqual; &Greater Equal; 00,, i i = = 1,2 1,2,, . . . . . .,, M m \end{matrix}$

上式作为绝缘子表面等值盐密的预测；The above formula is used as the prediction of the equivalent salt density on the surface of the insulator;

求解上式即可得等值盐密系统相空间中非线性映射

的回归函数g(x)，核函数与y_i作为输入量，即可得到下一时刻的等值盐密值，核函数中的参数和支持向量机模型参数中的惩罚因子是决定支持向量机方法求得的非线性映射

预测性能的最主要因素，采用交叉验证法进行支持向量机模型参数的选择。By solving the above formula, the nonlinear mapping in the phase space of the equivalent salt-dense system can be obtained

The regression function g(x) of the kernel function and y _i are used as input quantities, and the equivalent salt density value at the next moment can be obtained. The parameters in the kernel function and the penalty factor in the model parameters of the support vector machine are the factors that determine the support vector machine nonlinear mapping

The most important factor of predictive performance, using the cross-validation method to select the parameters of the support vector machine model.

所述的绝缘子的污闪临界电压预测模型的应用，按如下步骤进行：The application of the pollution flashover critical voltage prediction model of the insulator is carried out as follows:

1)污闪临界电压的确定：1) Determination of pollution flashover critical voltage:

污闪临界电压值选用50％污闪电压试验获得的数据U_50％，对等值盐密及气象参数与污闪临界电压值U_50％之间的多维非线性关系进行人工神经网络建模，实现对已知等值盐密及气象参数的绝缘子污闪临界电压U_50％进行预测；The critical voltage value of pollution flashover is selected from the data U _50% obtained from the 50% pollution flashover voltage test, and the multi-dimensional nonlinear relationship between the equivalent salt density and meteorological parameters and the critical voltage value U _50% of pollution flashover is modeled by artificial neural network. Realize the prediction of the insulator pollution flashover critical voltage U _50% of the known equivalent salt density and meteorological parameters;

2)人工神经网络模型的建立：2) Establishment of artificial neural network model:

本发明中采用基于BP方法的污闪临界电压预测人工神经网络模型；In the present invention, the pollution flashover critical voltage prediction artificial neural network model based on the BP method is adopted;

确定污闪临界电压预测BP人工神经网络模型的输入层、隐层和输出层三层；Determine the three layers of input layer, hidden layer and output layer of pollution flashover critical voltage prediction BP artificial neural network model;

污闪临界电压预测BP人工神经网络模型包括输入层、隐层和输出层三层结构，根据不同的人工污秽实验数据，隐层分别为两层或三层节点组成；The pollution flashover critical voltage prediction BP artificial neural network model includes a three-layer structure of input layer, hidden layer and output layer. According to different artificial pollution experimental data, the hidden layer is composed of two or three layers of nodes;

x₁，x₂，...，x_n为输入层节点，包括等值盐密值、温度、湿度、气压、风速和雨量，h₁，h₂，...，h_m为隐层节点，o为输出层节点，是绝缘子污闪临界电压预测值；V₁，V₂，...，V_m为输入层至隐层的权值，W₁，W₂，...，W_m为隐层至输出层权值，污闪临界电压人工神经网络模型的训练使用人工污秽耐压试验数据作为训练数据，整个网络的结构和参数由训练进行优化，网络的输入层维数为n，输出维数为一维即相关预测值的输出，隐层单元维数m在网络训练学习中优化确定，预测模型的预测值与实际人工污秽耐压试验的结果进行比较，进而对网络结构和权值进行修正和完善；x ₁ , x ₂ ,..., x _n are input layer nodes, including equivalent salt density value, temperature, humidity, air pressure, wind speed and rainfall, h ₁ , h ₂ ,..., h _m are hidden layer nodes , o is the output layer node, which is the predicted value of the insulator pollution flashover critical voltage; V ₁ , V ₂ ,..., V _m are the weights from the input layer to the hidden layer, W ₁ , W ₂ ,..., W _m is the weight value from the hidden layer to the output layer. The artificial neural network model training of the pollution flashover critical voltage uses the artificial pollution withstand voltage test data as the training data. The structure and parameters of the entire network are optimized by training. The input layer dimension of the network is n, The output dimension is one-dimensional, that is, the output of the relevant predicted value. The hidden layer unit dimension m is optimized and determined during network training and learning. The predicted value of the predicted model is compared with the results of the actual artificial pollution withstand voltage test, and then the network structure and weight Values are corrected and improved;

3)在人工神经网络模型的基础上增设动量项并对对BP方法的学习率进行自适应调整：3) On the basis of the artificial neural network model, a momentum item is added and the learning rate of the BP method is adaptively adjusted:

为提高污闪临界电压预测人工神经网络的训练速度，在权值调整公式中增加一个动量项，若用W代表污闪临界电压预测人工神经网络中某层的权值矩阵，X代表某层输入向量，则含有动量项的污闪临界电压预测人工神经网络权值调整向量表达式为：In order to improve the training speed of the pollution flashover critical voltage prediction artificial neural network, a momentum term is added to the weight adjustment formula. If W represents the weight matrix of a certain layer in the pollution flashover critical voltage prediction artificial neural network, X represents the input of a certain layer vector, the expression of the weight adjustment vector of the pollution flashover critical voltage prediction artificial neural network including the momentum item is:

ΔW(t)＝ηδX+αΔW(t-1)，公式中字母表示意思α是动量系数，设α∈(0，1)，η是神经网络的学习率，ΔW(t-1)是前一次的权值调整量，ΔW(t)是本次的权值调整量，动量项反映了以前的调整经验，对于t时刻的调整起阻尼作用，当误差曲面出现骤然起伏时，可减小振荡趋势，提高训练速度；ΔW(t)=ηδX+αΔW(t-1), the letters in the formula mean α is the momentum coefficient, let α∈(0,1), η is the learning rate of the neural network, ΔW(t-1) is the previous time The weight adjustment amount, ΔW(t) is the weight adjustment amount this time, the momentum item reflects the previous adjustment experience, and plays a damping role for the adjustment at time t. When the error surface fluctuates suddenly, it can reduce the oscillation trend , to increase the training speed;

在污闪临界电压预测人工神经网络建模中对BP方法的学习率进行自适应调整，学习率η∈(0，1)表示比例系数，设一个初始学习率，若经过一次权值调整后使总误差增加，则本次调整无效；若经过一次权值调整后使总误差下降，则本次调整有效；In the artificial neural network modeling of pollution flashover critical voltage prediction, the learning rate of BP method is adaptively adjusted. The learning rate η∈(0, 1) represents the proportional coefficient. An initial learning rate is set. If the total error increases, this adjustment will be invalid; if the total error decreases after a weight adjustment, this adjustment will be valid;

4)在人工神经网络模型的基础上引入陡度因子，使权值调整脱离平坦区：4) Introduce the steepness factor on the basis of the artificial neural network model to make the weight adjustment out of the flat area:

在污闪临界电压预测人工神经网络模型训练过程中引入陡度因子，误差曲面上存在着平坦区域，权值调整进入平坦区代表是污闪临界电压预测人工神经网络的神经元输出进入了转移函数的饱和区，如果在进入平坦区后，设法压缩神经元的净输入，使其输出并退出转移函数的饱和区，就可以改变误差函数的形状，从而使调整脱离平坦区，具体做法是，在原转移函数中引入一个陡度因子ζ，使输出为：The steepness factor is introduced in the training process of the pollution flashover critical voltage prediction artificial neural network model. There is a flat area on the error surface, and the adjustment of weights into the flat area means that the neuron output of the pollution flashover critical voltage prediction artificial neural network has entered the transfer function. If after entering the flat area, try to compress the net input of the neuron to make its output and exit the saturation area of the transfer function, the shape of the error function can be changed, so that the adjustment can be out of the flat area. The specific method is, in the original A steepness factor ζ is introduced into the transfer function, so that the output is:

$o o = = \frac{11 - - {e e}^{- - \frac{net net}{ξ ξ}}}{11 + + {e e}^{- - \frac{net net}{ξ ξ}}}$

其中，net为各层节点的输出值，当发现ΔE接近零而d-o值仍较大时，即认为进入平坦区，此时令ζ＞1；当退出平坦区后，再令ζ＝1，当ζ＞1时，net坐标压缩了倍，污闪临界电压预测人工神经网络的神经元的转移函数曲线的敏感段变长，从而使net值退出饱和值，当ζ＝1时，转移函数恢复原状，对较小的net值具有较高的灵敏度；Among them, net is the output value of the nodes in each layer. When it is found that ΔE is close to zero and the value of d-o is still large, it is considered to enter the flat area, and at this time, ζ>1; after exiting the flat area, let ζ=1, when When >1, the net coordinates are compressed twice, and the sensitive section of the transfer function curve of neurons in the pollution flashover critical voltage prediction artificial neural network becomes longer, so that the net value exits the saturation value. When ζ = 1, the transfer function returns to its original state. Higher sensitivity to smaller net values;

建立改进的BP人工神经网络预测模型，求解公式O(j)＝f(net(j))即可得到绝缘子的污闪临界电压预测值，其中j＝1，2，...，l，l为输出层的节点数，net(j)表示污闪临界电压预测神经元j的输入总和，f表示一种非线性映射关系。Establish an improved BP artificial neural network prediction model and solve the formula O(j)=f(net(j)) to get the predicted value of the pollution flashover critical voltage of the insulator, where j=1, 2,..., l, l is the number of nodes in the output layer, net(j) represents the input sum of the pollution flashover critical voltage prediction neuron j, and f represents a nonlinear mapping relationship.

所述的污闪分级预测预警模型的应用，按如下步骤进行：The application of the pollution flashover classification prediction and early warning model is carried out as follows:

确定绝缘子的污闪指数，污闪指数预测模型通过公式

决定，其中κ为污闪指数；U_FF为污闪临界电压的预测值；U_OP为运行电压，污闪临界电压的预测值为该模型的输入，κ为该模型的输出，即为预测的污闪指数。Determine the pollution flashover index of insulators, and the pollution flashover index prediction model uses the formula

κ is the pollution flashover index; U _FF is the predicted value of the pollution flashover critical voltage; U _OP is the operating voltage, the predicted value of the pollution flashover critical voltage is the input of the model, and κ is the output of the model, which is the predicted Pollution flashover index.

本发明的优点：提出了基于相空间重构的多变量等值盐密时间序列的预测模型，并且用支持向量机模型对其求解，解决了在等值盐密数据小样本且存在噪声情况下的预测问题，提高了预测精度。Advantages of the present invention: a multivariate equivalent salt density time series prediction model based on phase space reconstruction is proposed, and the support vector machine model is used to solve it, which solves the problem of small samples of equivalent salt density data and the presence of noise prediction problems, improving the prediction accuracy.

附图说明：Description of drawings:

图1(a)本发明区域电网污闪指数预测方法流程图；Fig. 1 (a) regional grid pollution flashover index prediction method flowchart of the present invention;

图1(b)本发明应用绝缘子表面等值盐密的预测模型流程图；Fig. 1 (b) the present invention applies the predictive model flowchart of insulator surface equivalent salt density;

图1(c)本发明应用绝缘子的污闪临界电压预测模型流程图；Fig. 1 (c) the present invention applies the flow chart of the pollution flashover critical voltage prediction model of insulator;

图2本发明人工神经网络模型图；Fig. 2 artificial neural network model figure of the present invention;

图3本发明等值盐密监测点等值盐密测量值与计算值比较；Fig. 3 compares the equivalent salt density measured value and calculated value of the equivalent salt density monitoring point of the present invention;

图4本发明污闪临界电压测量值与计算值比较图；Fig. 4 compares the measured value and the calculated value of the pollution flashover critical voltage of the present invention;

图5本发明污闪指数预测预警模型图。Fig. 5 is a model diagram of the pollution flashover index prediction and early warning model of the present invention.

具体实施方式：Detailed ways:

本发明一种区域电网污闪指数预测方法结合实施例和附图加以说明。A method for predicting the pollution flashover index of a regional power grid according to the present invention is described in conjunction with embodiments and accompanying drawings.

该方法，步骤如下，如图1(a)所示：In this method, the steps are as follows, as shown in Figure 1(a):

其中现场采集的环境参数包括风速值、温度值、气压值、雨量值、湿度值和等值盐密历史值；风速、温度、气压、降雨量、湿度的测量数据和等值盐密历史值构成一个六维的等值盐密多变量时间序列，选取这六个变量的同一时间段的20个不同时刻值构成时间序列Among them, the environmental parameters collected on site include wind speed, temperature, air pressure, rainfall, humidity and equivalent salt density historical value; wind speed, temperature, air pressure, rainfall, humidity measurement data and equivalent salt density historical value constitute A six-dimensional equivalent salt-dense multivariate time series, select 20 different time values of the six variables in the same time period to form a time series

具体参数见下式See the following formula for specific parameters

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

上式中：第一行为风速值，单位为m/s；第二行为温度值，单位为℃；第三行为气压值，单位为hPa；第四行为雨量值，单位为mm；第五行为相对湿度值，单位为％；In the above formula: the first behavior is the wind speed value, the unit is m/s; the second behavior is the temperature value, the unit is ℃; the third behavior is the air pressure value, the unit is hPa; the fourth behavior is the rainfall value, the unit is mm; the fifth behavior is relative Humidity value in %;

第六行为等值盐密值，单位为mg/cm²。The sixth line is equivalent salt density value, the unit is mg/cm ² .

步骤2、应用污闪临界电压预测模型，预测污闪临界电压；Step 2. Apply the pollution flashover critical voltage prediction model to predict the pollution flashover critical voltage;

步骤4、当电网污闪指数为0和5％时，不进行污闪预警；当电网污闪指数为20％时，发布污闪III级预警；当电网污闪指数为50％和85％时，污闪发生概率已经大于50％，发布污闪II级预警；当电网污闪指数为100％时，污闪发生概率已经相当大，该区域电网随时有可能发生污闪，发布污闪I级预警，如图5所示。Step 4. When the pollution flashover index of the power grid is 0 and 5%, no pollution flashover warning will be issued; when the pollution flashover index of the power grid is 20%, a level III warning of pollution flashover will be issued; when the pollution flashover index of the power grid is 50% and 85% , the probability of pollution flashover is greater than 50%, and a pollution flashover level II warning is issued; when the power grid pollution flashover index is 100%, the probability of pollution flashover is already quite high, and pollution flashover may occur in the regional power grid at any time, and a pollution flashover level I is issued Early warning, as shown in Figure 5.

污闪预测模型总的输入条件为气象数据，包括历史记录数据和预报，输出为污秽闪络电压等级，根据污秽闪络电压等级即可对污秽闪络发生风险做出判断。The general input condition of the pollution flashover prediction model is meteorological data, including historical record data and forecast, and the output is the pollution flashover voltage level. According to the pollution flashover voltage level, the risk of pollution flashover can be judged.

所述的绝缘子表面等值盐密预测模型的应用，按如下步骤进行，如图1(b)所示：The application of the equivalent salt density prediction model on the insulator surface is carried out according to the following steps, as shown in Figure 1(b):

具体参数见下式See the following formula for specific parameters

以延迟时间τ＝3和嵌入维数m＝6对等值盐密多变量时间序列进行相空间重构，在重构的等值盐密相空间中，以相空间中的所有相点构成等值盐密时间序列支持向量机模型的训练样本，建立支持向量机模型，对等值盐密时间序列全局预测模型中的非线性映射

进行拟合；Phase space reconstruction of equivalent salt-dense multivariate time series with delay time τ=3 and embedding dimension m=6, in the reconstructed equivalent salt-dense phase space, all phase points in the phase space constitute the equivalent The training samples of the value-salt-dense time series support vector machine model, the establishment of the support vector machine model, and the non-linear mapping in the global prediction model of the equivalent salt-dense time series

to fit;

相空间中的全部相点构成的训练样本为：The training samples composed of all phase points in the phase space are:

其中相点总数为N＝6(n-(m-1)τ)；Wherein the total number of phase points is N=6(n-(m-1)τ);

通过改进方法计算最大Lyapunov指数，结果约等于0.047，由最大Lyapunov指数大于零可判断：等值盐密时间序列为非线性混沌时间序列；The maximum Lyapunov exponent is calculated by the improved method, and the result is approximately equal to 0.047. It can be judged from the fact that the maximum Lyapunov exponent is greater than zero: the equivalent salt density time series is a nonlinear chaotic time series;

4)全局预测多变量等值盐密时间序列4) Global prediction of multivariate equivalent salt-dense time series

基于以上的三个步骤，建立了多变量等值盐密是时间序列全局预测模型；Based on the above three steps, a multi-variable equivalent salt density time series global prediction model is established;

5)利用支持向量机模型求解多变量等值盐密时间序列预测模型5) Using the support vector machine model to solve the multivariate equivalent salt density time series prediction model

根据等值盐密时间序列重构相空间相点构成的支持向量机模型训练样本集容量及等值盐密非线性系统特性，应用交叉检验法，选择支持向量机模型核函数及模型各参数为：核函数选择高斯核函数；核函数参数γ＝0.6；惩罚c＝50；不敏感损失函数参数ε＝0.29；According to the equivalent salt density time series reconstruction of the phase space phase points of the support vector machine model training sample set capacity and equivalent salt density nonlinear system characteristics, the cross-check method is used to select the support vector machine model kernel function and model parameters as : Kernel function chooses Gaussian kernel function; kernel function parameter γ=0.6; penalty c=50; insensitive loss function parameter ε=0.29;

部分等值盐密监测点等值盐密时间序列支持向量机预测模型的预测结果如图3所示，所建立的等值盐密预测模型中，等值盐密预测值的误差基本上控制在12％之内。The prediction results of the equivalent salt density time series support vector machine prediction model for some equivalent salt density monitoring points are shown in Figure 3. In the established equivalent salt density prediction model, the error of the equivalent salt density prediction value is basically controlled within within 12%.

所述的绝缘子的污闪临界电压预测模型的应用，按如下步骤进行，如图1(c)所示：The application of the pollution flashover critical voltage prediction model of the insulator is carried out according to the following steps, as shown in Figure 1(c):

其中污闪电压试验获得的数据如下：The data obtained from the pollution flashover voltage test are as follows:

气压的标准化值Standardized value of air pressure 湿度的标准化值Normalized value of humidity 温度的标准化值Normalized value of temperature ESDD的标准化值Standardized value of ESDD U_50％的标准化值U _50% normalized value 0.39130.3913 0.87800.8780 0.53540.5354 0.49000.4900 0.30700.3070 0.86690.8669 0.87850.8785 0.62830.6283 0.15800.1580 0.65800.6580 0.43320.4332 0.75600.7560 0.44860.4486 0.08000.0800 0.65880.6588 0.61000.6100 0.69180.6918 0.65140.6514 0.63600.6360 0.23430.2343

标准化值是由以下公式确定的：Normalized values are determined by the following formula:

i为获得的U_50％数据的个数；

i is the number of obtained U _50% data;

a_i为某一参数的标准化值，b_i为该参数的任一值，b_min为该参数所有值中的最小值，b_max为该参数所有值中的最大值；选择一组数据作为检验样本，其它数据作为人工神经网络的训练样本；a _i is the standardized value of a certain parameter, b _i is any value of this parameter, b _min is the minimum value of all values of this parameter, b _max is the maximum value of all values of this parameter; select a set of data as the test Samples, other data are used as training samples for artificial neural networks;

2)针对处理后的人工污秽试验数据，建立如附图2的人工神经网络模型；2) for the artificial pollution test data after processing, set up the artificial neural network model as accompanying drawing 2;

以步骤1)中的标准化数据为训练样本，设定网络参数初始值和网络输出误差允许值，对网络进行训练，当网络输出误差小于允许值后，保持相应的网络结构参数；With the standardized data in step 1) as the training sample, set the initial value of the network parameters and the allowable value of the network output error, train the network, and keep the corresponding network structure parameters when the network output error is less than the allowable value;

4)在人工神经网络模型的基础上引入陡度因子，使权值调整脱离平坦区，得到污闪临界电压预测模型：4) On the basis of the artificial neural network model, the steepness factor is introduced to make the weight adjustment out of the flat area, and the pollution flashover critical voltage prediction model is obtained:

部分污闪临界电压预测模型的预测结果与实测值比较如图4所示，所建立的污闪临界电压预测模型中，污闪临界电压值的误差基本上控制在±6％之内；The comparison between the prediction results of some pollution flashover critical voltage prediction models and the measured values is shown in Figure 4. In the established pollution flashover critical voltage prediction model, the error of the pollution flashover critical voltage value is basically controlled within ±6%.

污闪指数预测模型通过公式

决定，其中κ为污闪指数；U_FF为污闪临界电压的预测值；U_OP为运行电压。Pollution flashover index prediction model through the formula

κ is the pollution flashover index; U _FF is the predicted value of the pollution flashover critical voltage; U _OP is the operating voltage.

Claims

1. A regional grid pollution flashover index prediction method is characterized in that: the steps are as follows:

Step 1. Apply the equivalent salt density prediction model on the surface of the insulator to predict the current value of the equivalent salt density in real time;

The environmental parameters and equivalent salt density historical values collected on the grid site are input into the insulator surface equivalent salt density prediction model, and the output of the insulator surface equivalent salt density prediction model is the real-time predicted equivalent salt density current value;

Step 2. Apply the insulator pollution flashover critical voltage prediction model to predict the pollution flashover critical voltage;

The real-time predicted equivalent salt density current value and the current collected environmental parameters are input into the pollution flashover critical voltage prediction model of the insulator, and the output of the pollution flashover critical voltage prediction model of the insulator is the pollution flashover critical voltage prediction value;

Step 3. Apply the pollution flashover classification prediction and early warning model to predict the pollution flashover index of grid insulators;

Input the predicted value of pollution flashover critical voltage into the pollution flashover classification prediction and early warning model, and the output of the pollution flashover classification prediction and early warning model is the predicted power grid pollution flashover index;

Step 4. When the pollution flashover index of the power grid is 0 and 5%, no pollution flashover warning will be issued; when the pollution flashover index of the power grid is 20%, a level III warning of pollution flashover will be issued; when the pollution flashover index of the power grid is 50% and 85% , the probability of pollution flashover is greater than 50%, and a pollution flashover level II warning is issued; when the power grid pollution flashover index is 100%, the probability of pollution flashover is already quite high, and pollution flashover may occur in the regional power grid at any time, and a pollution flashover level I is issued early warning.

2. by the regional grid pollution flashover index prediction method of claim 1, it is characterized in that: the application of the equivalent salt density prediction model on the surface of the insulator is carried out as follows:

1) Establish multivariate equivalent salt density time series;

The equivalent salt density data is measured at fixed time intervals, and the discrete ordered set {x ₁ , x ₂ , ..., x _{n }} obtained at a series of time t ₁ , t ₂ , ..., t _n is called is the discrete equivalent salt-intensive time series, referred to as the equivalent salt-intensive time series;

The multivariate equivalent salt density time series is a multidimensional equivalent salt density time series composed of the equivalent salt density time series and the meteorological parameter time series at the same time. The expression form of value-salt-dense nonlinear dynamical system;

M-dimensional equivalent salt-dense time series: X ₁ , X ₂ , ..., X _N , N represents the number of moments, where X _i = (x _{1, i} , x _{2, i} , ..., x _{M, i} ),Right now

(\begin{matrix} {x x}_{1,1 1,1} & {x x}_{1,2 1,2} . . . . . . & {x x}_{11,, i i} . . . . . . & {x x}_{11,, N N} \\ {x x}_{2,1 2,1} & {x x}_{2,2 2,2} . . . . . . & {x x}_{22,, i i} . . . . . . & {x x}_{22,, N N} \\ . . . . . . \\ {x x}_{M m,, 11} & {x x}_{M m,, 22} . . . . . . & {x x}_{M m,, i i} . . . . . . & {x x}_{M m,, N N} \end{matrix})

In the formula, i=1, 2, ..., N, x _{M, N} represents the value of the M variable at the time N, and x _{M, i} represents the value of the M variable at the time i;

2) Reconstruct the phase space of the multivariate equivalent salt density time series;

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

\{\begin{matrix} {V V}_{n no} = = (({x x}_{11,, n no},, {x x}_{11,, n no - - {τ τ}_{11}},, . . . . . .,, {x x}_{11,, n no - - ((m m 11 - - 11)) {τ τ}_{11}},, . . . . . .,, {x x}_{M m,, n no},, {x x}_{M m,, n no - - {τ τ}_{M m}},, . . . . . .,, {x x}_{M m,, n no - - (({m m}_{M m} - - 11)) {τ τ}_{M m}})) \\ . . . . . . \\ {V V}_{i i} = = (({x x}_{11,, i i},, {x x}_{11,, i i - - {τ τ}_{11}},, . . . . . .,, {x x}_{11,, i i - - ((m m 11 - - 11)) {τ τ}_{11}},, . . . . . .,, {x x}_{M m,, i i},, {x x}_{M m,, i i - - {τ τ}_{M m}},, . . . . . .,, {x x}_{M m,, i i - - (({m m}_{M m} - - 11)) {τ τ}_{M m}})) \\ . . . . . . \\ {V V}_{N N} = = (({x x}_{11,, N N},, {x x}_{11,, N N - - {τ τ}_{11}},, . . . . . .,, {x x}_{11,, N N - - ((m m 11 - - 11)) {τ τ}_{11}},, . . . . . .,, {x x}_{M m,, N N},, {x x}_{M m,, N N - - {τ τ}_{M m}},, . . . . . .,, {x x}_{M m,, N N - - (({m m}_{M m} - - 11)) {τ τ}_{M m}})) \end{matrix}

Indicates the value of the Mth variable embedded in the reconstructed phase space with dimension m _M at delay time τ _M at time N;

where n represents the nth moment,

The phase space reconstruction parameter delay time τ of the multivariate equivalent salt-dense time series is selected using the mutual information method. The mutual information method uses the delay time when the mutual information reaches the minimum for the first time as the delay time of the phase space reconstruction.

E E. ((m m)) = = \frac{11}{N N - - mτ mτ} {Σ Σ}_{i i = = 11}^{N N - - mτ mτ} α α ((i i,, m m))

decision, where:

α α ((i i,, m m)) = = \frac{| | | | {X x}_{i i} ((m m + + 11)) - - {X x}_{n no ((i i,, m m))} ((m m + + 11)) | | | |}{| | | | {X x}_{i i} ((m m)) - - {X x}_{n no ((i i,, m m))} ((m m)) | | | |}

X _i (m+1) is the i-th phase point in the (m+1)-dimensionally reconstructed equivalent salt-dense system phase space, n(i, m) is the phase space of the m-dimensional equivalent salt-dense system Let the phase point X _{n(i, m)} (m) be the integer of the nearest neighbor point of the phase point X _i (m), ||·|| is the Euclidean distance on the phase space of the equivalent salt-dense system;

3) Deterministic test of equivalent salt density time series;

In the present invention, the deterministic test of the equivalent salt density time series is carried out using the Lyapunov index method, which is a numerical representation of the average exponential divergence rate of adjacent orbits in phase space, and is used to describe the initial state sensitivity of chaotic motion , the index is the result of a long-term average along the orbit and is an overall characteristic whose value is always a real number;

Judging the nonlinear characteristics of the equivalent salt density time series is obtained by calculating the maximum Lyapunov exponent. This method calculates the slope of the regression line from the y(k) curve

is the largest exponent, where,

4) Global prediction of multivariate equivalent salt density time series;

According to the Tekens time-delay embedding theorem, as long as the embedding dimension m and delay time τ are selected reasonably, the trajectory of the reconstructed phase space in the embedding space is equivalent to the equivalent salt-dense dynamical system in the sense of diffeomorphism, and there exists Smooth map f:

to approximate f, and make

satisfy:

minimum, of which

5) Using the support vector machine model to solve the multivariate equivalent salt density time series prediction model;

By solving nonlinear mappings in predictive models

Assume that the sample set composed of phase points in the phase space of the equivalent salt-dense system is: S={(xi _, y _i ), i=1, 2,..., M}, ( _xi , y _i ) means the reconstruction For any phase point in the phase space, if there is a hyperplane g(x)=<w·x>+b, w∈R ⁿ , b∈R, w and b represent vector parameters, in order to construct the hyperplane g(x ), so that: |y _i -g(xi ₎ |≤ε holds, where <·> represents the vector inner product, i=1, 2, ..., M, M is the dimension of the equivalent salt-dense time series number, then the sample set S={(x _i , y _i ), i=1, 2,..., M} is an approximate set of ε, which has: |<w·x>+by _i |≤ε, that is

i=1,2,...,M;

in,

The optimal approximate hyperplane of the set S can be obtained by maximizing the upper bound of the distance between the points in S and the hyperplane, then the optimal approximate hyperplane can be obtained by maximizing the formula Therefore, by solving the minimization problem of ||w|| ² , the optimal approximation hyperplane of the set S can be obtained. Since the equivalent salt density system is a nonlinear system, a nonlinear mapping must be used

Among them, i=1, 2,..., M, the above formula is a quadratic programming problem, and its Lagrange function is:

\{\begin{matrix} \underset{α α,, {α α}^{* *}}{min min} \frac{11}{22} {Σ Σ}_{i i = = 11}^{M m} (({α α}_{i i}^{* *} - - {α α}_{i i})) (({α α}_{i i + + 11}^{* *} - - {α α}_{i i + + 11})) Ψ Ψ (({x x}_{i i},, {x x}_{i i + + 11})) + + ϵ ϵ {Σ Σ}_{i i = = 11}^{M m} (({α α}_{i i}^{* *} - - {α α}_{i i})) - - {Σ Σ}_{j j = = 11}^{M m} {y the y}_{j j} (({α α}_{i i}^{* *} - - {α α}_{i i})),, j j = = 1,2 1,2,, . . . . . .,, M m \\ s the s . . t t . . {Σ Σ}_{i i = = 11}^{M m} (({α α}_{i i}^{* *} - - {α α}_{i i})) = = 00,, {α α}_{i i} &GreaterEqual; &Greater Equal; 00,, {α α}_{i i}^{* *} &GreaterEqual; &Greater Equal; 00,, i i = = 1,2 1,2,, . . . . . .,, M m \end{matrix}

Among them, α _i and

Known as the Lagrange multiplier, for any i=1, 2, ..., M, there is an equation α _i ≥ 0,

established;

When approximating the nonlinear mapping function in the phase space of the equivalent salt-density system, due to the inevitable error between the obtained regression function and the actual function, the slack variable is introduced:

ξ _i ≥ 0,

i=1, 2,..., M, _ξi represents a slack variable;

The optimization at this time is:

In the formula, c is a penalty parameter, and c>0;

The Lagrange dual problem can be obtained as:

\{\begin{matrix} \underset{α α,, {α α}^{* *}}{min min} \frac{11}{22} {Σ Σ}_{i i = = 11}^{M m} (({α α}_{i i}^{* *} - - {α α}_{i i})) (({a a}_{i i + + 11}^{* *} - - {a a}_{i i + + 11})) Ψ Ψ (({x x}_{i i},, {x x}_{i i + + 11})) + + ϵ ϵ {Σ Σ}_{i i = = 11}^{M m} (({α α}_{i i}^{* *} - - {α α}_{i i})) - - {Σ Σ}_{i i = = 11}^{M m} {y the y}_{i i} (({α α}_{i i}^{* *} - - {α α}_{i i})) \\ s the s . . t t . . {Σ Σ}_{i i = = 11}^{M m} (({α α}_{i i}^{* *} - - {α α}_{i i})) = = 00,, {α α}_{i i} &GreaterEqual; &Greater Equal; c c,, {α α}_{i i}^{* *} &GreaterEqual; &Greater Equal; 00,, i i = = 1,2 1,2,, . . . . . .,, M m \end{matrix}

The above formula is used as the prediction of the equivalent salt density on the surface of the insulator;

By solving the above formula, the nonlinear mapping in the phase space of the equivalent salt-dense system can be obtained

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

1) Determination of pollution flashover critical voltage;

The critical voltage value of pollution flashover is selected from the data U _50% obtained from the 50% pollution flashover voltage test, and the multi-dimensional nonlinear relationship between the equivalent salt density and meteorological parameters and the critical voltage value U _50% of pollution flashover is modeled by artificial neural network. Realize the prediction of the insulator pollution flashover critical voltage U _50% of the known equivalent salt density and meteorological parameters;

2) Establishment of artificial neural network model;

In the present invention, the pollution flashover critical voltage prediction artificial neural network model based on the BP method is adopted;

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

The pollution flashover critical voltage prediction BP artificial neural network model includes a three-layer structure of input layer, hidden layer and output layer. According to different artificial pollution experimental data, the hidden layer is composed of two or three layers of nodes;

x ₁ , x ₂ ,..., x _n are input layer nodes, including equivalent salt density value, temperature, humidity, air pressure, wind speed and rainfall, h ₁ , h ₂ ,..., h _m are hidden layer nodes , o is the output layer node, which is the predicted value of the insulator pollution flashover critical voltage; V ₁ , V ₂ ,..., V _m are the weights from the input layer to the hidden layer, W ₁ , W ₂ ,..., W _m is the weight value from the hidden layer to the output layer. The artificial neural network model training of the pollution flashover critical voltage uses the artificial pollution withstand voltage test data as the training data. The structure and parameters of the entire network are optimized by training. The input layer dimension of the network is n, The output dimension is one-dimensional, that is, the output of the relevant predicted value. The hidden layer unit dimension m is optimized and determined during network training and learning. The predicted value of the predicted model is compared with the results of the actual artificial pollution withstand voltage test, and then the network structure and weight Values are corrected and improved;

3) On the basis of the artificial neural network model, a momentum item is added and the learning rate of the BP method is adaptively adjusted;

In order to improve the training speed of the artificial neural network for predicting the critical voltage of pollution flashover, a momentum item is added to the weight adjustment formula. vector, the expression of the weight adjustment vector of the pollution flashover critical voltage prediction artificial neural network including the momentum item is:

ΔW(t)=ηδX+αΔW(t-1), the letters in the formula mean α is the momentum coefficient, let α∈(0,1), η is the learning rate of the neural network, ΔW(t-1) is the previous time ΔW(t) is the weight adjustment amount of this time, and the momentum item reflects the previous adjustment experience, which plays a damping role for the adjustment at time t, and can reduce the oscillation trend when the error surface fluctuates suddenly , to increase the training speed;

In the artificial neural network modeling of pollution flashover critical voltage prediction, the learning rate of the BP method is adaptively adjusted. The learning rate η∈(0, 1) represents the proportional coefficient. An initial learning rate is set. If the total error increases, this adjustment will be invalid; if the total error decreases after a weight adjustment, this adjustment will be valid;

4) On the basis of the artificial neural network model, the steepness factor is introduced to make the weight adjustment out of the flat area;

The steepness factor is introduced in the training process of the pollution flashover critical voltage prediction artificial neural network model. There is a flat area on the error surface, and the adjustment of weights into the flat area means that the neuron output of the pollution flashover critical voltage prediction artificial neural network has entered the transfer function. If after entering the flat region, try to compress the net input of the neuron to make its output and exit the saturation region of the transfer function, the shape of the error function can be changed, so that the adjustment can be out of the flat region. The specific method is, in the original A steepness factor ζ is introduced into the transfer function, so that the output is:

o o = = \frac{11 - - {e e}^{- - \frac{net net}{ξ ξ}}}{11 + + {e e}^{- - \frac{net net}{ξ ξ}}}

Among them, net is the output value of the nodes in each layer. When it is found that ΔE is close to zero and the value of d-o is still large, it is considered to enter the flat area, and at this time, ζ>1; after exiting the flat area, let ζ=1, when When >1, the net coordinates are compressed twice, and the sensitive section of the transfer function curve of neurons in the pollution flashover critical voltage prediction artificial neural network becomes longer, so that the net value exits the saturation value. When ζ = 1, the transfer function returns to its original state. Higher sensitivity to smaller net values;

Establish an improved BP artificial neural network prediction model and solve the formula O(j)=f(net(j)) to get the predicted value of the pollution flashover critical voltage of the insulator, where j=1, 2,..., l, l is the number of nodes in the output layer, net(j) represents the input sum of the pollution flashover critical voltage prediction neuron j, and f represents a nonlinear mapping relationship.

4. by the regional grid pollution flashover index prediction method of claim 1, it is characterized in that: the application of described pollution flashover grading prediction early warning model is carried out as follows:

Determine the pollution flashover index of insulators, and the pollution flashover index prediction model uses the formula