Steady-State Voltage Quality Early Warning Method Based on Trend Prediction and Uncertainty Analysis

Abstract

The present invention relates to a steady-state voltage quality early warning method based on trend prediction and uncertainty analysis. The method includes the following steps: decomposing the monitoring data sequence of voltage quality indicators based on VMD; performing accurate value prediction on the decomposed monitoring data sequence of voltage quality indicators based on DBN; performing interval prediction on the monitoring data sequence of voltage quality indicators; constructing a membership function for voltage quality risk early warning, and according to the accurate value prediction and interval prediction, early warning the risk of voltage quality indicators. It can overcome the problem that the traditional voltage quality risk early warning method cannot predict the development trend of voltage quality indicators. In addition to predicting the accurate value of voltage quality indicators, the proposed method also predicts its uncertainty interval, realizing the membership degree evaluation and risk early warning of voltage quality risk.

Description

Technical Field

[0001] The present invention relates to the technical field of voltage quality risk warning, and particularly to a steady-state voltage quality warning method based on trend prediction and uncertainty analysis. Background Art

[0002] With the increasing use of power electronic devices in the power system and the large-scale grid connection of non-linear loads, impact loads, etc., the voltage quality problems in the power grid have increased significantly and have received extensive attention. Since voltage quality problems will affect the power supply quality of the power grid and then affect the production and life of users, the monitoring of power grid voltage quality indicators and the accurate warning of voltage quality risks are urgent problems to be solved at present.

[0003] To monitor voltage quality problems, devices with voltage quality monitoring functions such as voltage quality monitors and fusion terminals are installed in the current power grid. They can monitor steady-state voltage quality indicators such as voltage deviation, and transient voltage quality indicators such as voltage sag. Based on these data, the accurate control of the current power grid voltage quality status can be achieved. However, many voltage quality problems have reached a relatively high level when being monitored and have caused certain impacts on the power grid and users. In contrast, predicting the development trend of voltage quality indicators based on current monitoring data and early warning of voltage quality risks are more conducive to taking early measures to suppress them.

[0004] Compared with transient voltage quality problems with strong randomness such as voltage sag, steady-state voltage quality problems such as voltage deviation have certain trend characteristics and are more predictable, which are the focus of current research. At present, many methods for warning voltage quality risks using monitoring data have been proposed at home and abroad. However, the current voltage quality risk warning still faces the following defects:

[0005] 1) Existing risk warning methods often only evaluate whether the current steady-state indicators of voltage quality exceed the limit, and cannot predict the development trend of voltage quality indicators.

[0006] 2) Existing risk warning methods do not consider the uncertainty of the development trend of voltage quality indicators and cannot characterize the potential risk of voltage quality deterioration. Summary of the Invention

[0007] Aiming at the above problems, the purpose of the present invention is to provide a steady-state voltage quality warning method based on trend prediction and uncertainty analysis, which can overcome the traditional voltage quality risk warning method that cannot predict the development trend of voltage quality indicators. In addition to predicting the accurate value of voltage quality indicators, the proposed method also predicts its uncertainty interval, realizing the membership degree evaluation and risk warning of voltage quality risks.

[0008] A steady-state voltage quality early warning method based on trend prediction and uncertainty analysis, comprising the following steps:

[0009] Decompose the monitoring data sequence of voltage quality indicators based on VMD;

[0010] Perform accurate value prediction on the decomposed monitoring data sequence of voltage quality indicators based on DBN;

[0011] Perform interval prediction on the monitoring data sequence of voltage quality indicators;

[0012] Construct a membership function for voltage quality risk early warning, and based on the accurate value prediction and interval prediction, early warn of the risk of voltage quality indicators.

[0013] Decomposing the monitoring data sequence of voltage quality indicators based on VMD specifically includes: decomposing the monitoring data sequence of voltage quality indicators into each subsequence based on VMD, and dividing the trend term, periodic term, and fluctuation term therein.

[0014] Specifically, decomposing the monitoring data sequence of voltage quality indicators into each subsequence based on VMD and dividing the trend term, periodic term, and fluctuation term therein includes:

[0015] Step 1.1: Represent the monitoring data sequence of voltage quality indicators as the sum of several subsequences:

[0016]

[0017] In the formula: y(t) is the monitoring data sequence of voltage quality indicators to be decomposed, and voltage quality monitoring data such as voltage deviation can be taken according to early warning requirements; u k (t) is the kth subsequence after decomposition; K is the total number of subsequences after decomposition;

[0018] Step 1.2: Calculate the analytical signal expression of the subsequence

[0019] The corresponding analytical signal expression of each subsequence can be obtained by using the Hilbert transform, and its unilateral spectrum is:

[0020]

[0021] In the formula: δ(t) is the Dirac function; * represents the convolution operation; j is the unit representing the imaginary number in complex numbers; t represents the tth moment; Step 1.3: Modulate the spectrum to the baseband

[0022] By aliasing each subsequence u k (t) with the exponential term of its corresponding center frequency ω k of, modulate the unilateral spectrum of each subsequence to the corresponding baseband:

[0023]

[0024] Where: ω k is the center frequency of the k-th subsequence;

[0025] Step 1.4: Construct a variational problem

[0026] Demodulate the signal by Gaussian smoothing to obtain the bandwidth description of each subsequence u k (t). Its solution can be transformed into a variational problem with constraints:

[0027]

[0028] Where: denotes the derivative of the function in () with respect to t;

[0029] Step 1.5: Construct the Lagrangian function

[0030] Introduce the quadratic penalty factor α and the Lagrange multiplier λ into Equation (4), thereby transforming Equation (4) into an unconstrained optimization problem:

[0031]

[0032] Where: L({u k},{ω k},λ) is the constructed Lagrangian function; α is the quadratic penalty factor, λ is the Lagrange multiplier; λ(t) is the t-th Lagrange multiplier;

[0033] Step 1.6: Solve each subsequence u k (t)

[0034] Use the alternating direction method of multipliers to iteratively solve Equation (5) to obtain the specific expression of each subsequence u k (t). The iterative process is as follows:

[0035]

[0036]

[0037] Where: ω is the frequency; respectively represent the Fourier transforms of y(t), u k (t), u r (t), λ n (t); r is the counting unit; n is the number of iterations, and u r (t) is the r-th subsequence after decomposition; represents u k (t) solved by the (n + 1)-th iteration; λ nλ(t) represents the λ(t) obtained by the nth iteration solution; represents ω obtained after the (n + 1)th iteration k ;

[0038] Step 1.6: According to the obtained subsequences u k (t), divide the trend terms, periodic terms, and fluctuation terms in each subsequence u k (t)

[0039] Use the Durbin-Watson method to test the autocorrelation of each subsequence u k (t):

[0040]

[0041] In the formula: DW k is the autocorrelation value of the subsequence u k (t). If DW k is close to 2, it can be considered that u k (t) has no first-order correlation, that is, it is greatly affected by random factors and is a fluctuation term, denoted as k ∈ K0; if DW k is not close to 2, and u k (t) shows a monotonic increase or decrease trend, then it is a trend term, denoted as k ∈ K1; if DW k is not close to 2, and u k (t) shows periodic characteristics, then it is a periodic term, denoted as k ∈ K2.

[0042] Precisely predicting the monitored data sequence of voltage quality indicators based on DBN is specifically as follows:

[0043] Use DBN to predict the trend terms and periodic terms in the subsequences decomposed by VMD to obtain the precise prediction values of the monitored data sequence of voltage quality indicators.

[0044] Use DBN to predict the trend terms and periodic terms in the subsequences decomposed by VMD to obtain the precise prediction values of the monitored data sequence of voltage quality indicators, specifically as follows:

[0045] Step 2.1: Select the trend terms {u k (t), k ∈ K1} or periodic terms {u k (t), k ∈ K2} in the subsequence for prediction, and denote the sequence input into DBN as {u(1), u(2), ···, u(T)}, where T is the sequence length of the subsequence u k (t);

[0046] Step 2.2: Construct the Boltzmann machine of DBN, as shown in the following formula (9), which includes one visible layer v = (v1, v2, …, v n1) and a hidden layer h = (h1, h2, …, h n2 );

[0047]

[0048] where: θ = (w, a, b) are the parameters of the Boltzmann machine; p, q, n1, n2 are counting units; v p is the p-th unit of the visible layer; h q is the q-th unit of the hidden layer; w pq , a p , b q are the weights of the Boltzmann machine units; a p , b q are the bias values of the Boltzmann machine units;

[0049] Step 2.3: Construct the joint probability distribution of the parameters (v, h) in the Boltzmann machine:

[0050]

[0051] where: Z(θ) is the partition function;

[0052] Step 2.4: Select the sigmoid function as the activation function and calculate the activation probability of the hidden layer units of the Boltzmann machine:

[0053]

[0054] Step 2.5: Calculate the activation probability of the visible layer units of the Boltzmann machine:

[0055]

[0056] Step 2.6: Obtain the model parameters θ and fit the training samples by maximizing the log-likelihood function L s (θ) of the Boltzmann machine on the samples to complete the construction of the DBN model:

[0057]

[0058] Step 2.7: Perform backpropagation supervised fine-tuning on the network parameters of the DBN model. By comparing the output with the data labels and calculating the error, the biases and connection weights of each layer node of the DBN model are fine-tuned backward;

[0059] Step 2.8: Use the constructed DBN model to predict the value of the sequence u k (t) at time t + 1 to obtain the accurate prediction value Using the prediction values of each subsequence, reconstruct the accurate prediction value of y(t) at time t + 1 :

[0060]

[0061] Perform interval prediction on the monitoring data sequence of voltage quality indicators, specifically: calculate the variance of the fluctuation terms in the subsequences decomposed by VMD to obtain the uncertainty prediction interval of the monitoring data sequence of voltage quality indicators.

[0062] Calculate the variance of the fluctuation terms in the subsequences decomposed by VMD to obtain the uncertainty prediction interval of the monitoring data sequence of voltage quality indicators, specifically:

[0063] Step 3.1: Calculate the variance of the fluctuation terms {u k (t), k ∈ K0}

[0064]

[0065] Step 3.2: Calculate the uncertainty prediction interval of y(t) at time t + 1:

[0066]

[0067] In the formula: respectively represent the upper and lower bounds of the prediction interval with probability ε of y(t) at time t + 1; R ε is the quantile corresponding to the standard normal distribution and probability ε.

[0068] Construct the membership function for voltage quality risk warning. Based on the accurate value prediction and interval prediction, warn of the risk of voltage quality indicators, specifically: use the kernel density estimation method to estimate the probability function of voltage quality indicators to construct the membership function for voltage quality risk warning, and substitute the accurate prediction value and the uncertainty prediction interval into the constructed risk membership function to warn of the risk of voltage quality indicators.

[0069] Use the kernel density estimation method to estimate the probability function of voltage quality indicators to construct the membership function for voltage quality risk warning, and substitute the accurate prediction value and the uncertainty prediction interval into the constructed risk membership function to warn of the risk of voltage quality indicators, specifically:

[0070] Step 4.1: Select the Gaussian kernel as the kernel function for kernel density estimation:

[0071]

[0072] In the formula: y represents the random variable of voltage quality indicators;

[0073] Step 4.2: To ensure that the probability density function of voltage quality indicators estimated by the kernel density estimation method can reflect the characteristics of the original data as much as possible while maintaining smoothness, select the bandwidth as:

[0074]

[0075] Where: σ g is the standard deviation of the kernel function G(y); f″(y) represents the second derivative of y; w is the bandwidth length.

[0076] Step 4.3: Calculate the probability density function of the voltage quality index:

[0077]

[0078] Step 4.4: Calculate the cumulative probability function of the voltage quality index:

[0079]

[0080] Step 4.5: Establish the membership functions for voltage quality risk warning with low-risk warning level, medium-risk warning level, and high-risk warning level:

[0081]

[0082]

[0083]

[0084] Where: M1(y), M2(y), and M3(y) are the low-risk membership, medium-risk membership, and high-risk membership respectively; a, b, c, and d are the risk boundaries;

[0085] Select the risk boundaries a, b, c, and d according to Equation (24):

[0086]

[0087] Step 4.6: Substitute the accurate predicted value and prediction interval of y(t) calculated in Steps 2 and 3 into the risk membership function constructed in Step 4.5, and based on the prediction of the voltage quality index and the risk warning membership function, give a warning about the risk of the voltage quality index at time t + 1.

[0088] The beneficial effects of the present invention are:

[0089] 1) The present invention uses VMD to decompose the voltage quality index monitoring data sequence into each subsequence, and divides the trend term, periodic term, and fluctuation term among them, and respectively performs accurate value prediction and interval prediction for different types of subsequences, which not only improves the prediction accuracy but also considers the uncertainty of the development trend of the voltage quality index.

[0090] 2) After predicting the voltage quality index, the present invention constructs a membership function for voltage quality risk, thereby determining the membership degrees of the index prediction value and the prediction interval to each voltage quality risk level, and can achieve accurate early warning of voltage quality risk. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 is the basic flow chart of the present invention; Figure 2 is the structure of the DBN adopted by the present invention; Figure 3 is the measured voltage deviation data; Figure 4 is the voltage deviation prediction result; Figure 5 is the risk membership degree of the voltage deviation prediction result. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0092] The present invention will be further described in detail below with reference to the drawings and specific embodiments. The voltage quality problems in the power system are increasing day by day. In order to accurately predict the voltage quality index risk, the present invention proposes a steady-state voltage quality early warning method based on trend prediction and uncertainty analysis. The basic flow chart is as Figure 1 shown, which is divided into four steps S1-S4:

[0093] S1: Decompose the voltage quality index monitoring data sequence based on VMD:

[0094] Based on VMD, the voltage quality index monitoring data sequence is decomposed into each subsequence, and the trend term, periodic term and fluctuation term are divided.

[0095] Specifically: The voltage quality index monitoring data sequence is expressed as the sum of several subsequences:

[0096]

[0097] where: y(t) is the voltage quality index monitoring data sequence to be decomposed, and voltage quality monitoring data such as voltage deviation can be taken according to the early warning requirements; u k (t) is the k-th subsequence after decomposition; K is the total number of subsequences after decomposition.

[0098] Calculate the analytical signal expression of the subsequence. The analytical signal expressions corresponding to each subsequence can be obtained by using the Hilbert transform, and its unilateral spectrum is:

[0099]

[0100] where: δ(t) is the Dirac function; * represents the convolution operation; j is the unit representing the imaginary number in the complex number; t represents the t-th moment.

[0101] Modulate the spectrum to the baseband. By multiplying u k (t) with its corresponding center frequency ωk Exponential term Aliasing, modulating the spectrum of each subsequence to the corresponding base frequency band:

[0102]

[0103] where: ω k is the center frequency of the k-th subsequence.

[0104] Construct a variational problem. Demodulate the signal through Gaussian smoothing to obtain the bandwidth description of u k (t), and its solution can be transformed into a variational problem with constraints:

[0105]

[0106] where: denotes taking the derivative of the function in () with respect to t.

[0107] Construct the Lagrangian function. Introduce the quadratic penalty factor α and the Lagrange multiplier λ into equation (4), thus transforming equation (4) into an unconstrained optimization problem:

[0108]

[0109] where: L({u k},{ω k},λ) is the constructed Lagrangian function; α is the quadratic penalty factor, λ is the Lagrange multiplier; λ(t) is the t-th Lagrange multiplier.

[0110] Solve for the subsequence u k (t). Use the alternating direction method of multipliers to iteratively solve equation (5) to obtain the specific expression of each subsequence u k (t). The iterative process is as follows:

[0111]

[0112]

[0113] where: ω is the frequency; respectively represent the Fourier transforms of y(t), u k (t), u r (t), λ n (t); r is the counting unit; n is the number of iterations, and u r (t) is the r-th subsequence after decomposition; represents u k (t) solved in the (n + 1)-th iteration; λ n (t) represents λ(t) solved in the n-th iteration; It represents ω obtained after the (n + 1)-th iteration k .

[0114] Divide the subsequence u k (t) into trend term, periodic term and fluctuation term. Use the Durbin-Watson method to test the autocorrelation of each subsequence u k (t):

[0115]

[0116] Where: DW k is the autocorrelation value of the subsequence u k (t). If DW k is close to 2, it can be considered that u k (t) has no first-order correlation, that is, it is greatly affected by random factors and is a fluctuation term, denoted as k ∈ K0; if DW k is not close to 2, and u k (t) shows a monotonic increasing or decreasing trend, then it is a trend term, denoted as k ∈ K1; if DW k is not close to 2, and u k (t) shows periodic characteristics, then it is a periodic term, denoted as k ∈ K2.

[0117] S2: Based on DBN, perform accurate value prediction on the decomposed voltage quality index monitoring data sequence:

[0118] Use DBN to predict the trend term and periodic term in the subsequence decomposed by VMD to obtain the accurate prediction value of the voltage quality index monitoring data sequence y(t). The DBN structure is as shown in the appendix Figure 2 .

[0119] Specifically: Select the trend term {u k (t), k ∈ K1} or the periodic term {u k (t), k ∈ K2} in the subsequence for prediction. Denote the sequence input into DBN as {u(1), u(2), ···, u(T)}, where T is the length of the u k (t) sequence.

[0120] Construct the Boltzmann machine of DBN, which includes a visible layer v = (v1, v2, …, v n1 ) and a hidden layer h = (h1, h2, …, h n2 ), as shown in Equation (9).

[0121]

[0122] Where: θ = (w, a, b) are the parameters of the Boltzmann machine; p, q, n1, n2 are counting units; v pis the p-th unit of the visible layer; h q is the q-th unit of the hidden layer; w pq , a p , b q are the weights of the Boltzmann machine units; a p , b q are the bias values of the Boltzmann machine units.

[0123] Construct the joint probability distribution of the parameters (v, h) in the Boltzmann machine:

[0124]

[0125] In the formula: Z(θ) is the partition function.

[0126] Select the sigmoid function as the activation function and calculate the activation probability of the hidden layer units:

[0127]

[0128] Calculate the activation probability of the visible layer units:

[0129]

[0130] By maximizing the log-likelihood function L s (θ) of the Boltzmann machine on the samples, obtain the model parameters θ and fit the training samples to complete the construction of the DBN model:

[0131]

[0132] Perform backpropagation supervised fine-tuning on the DBN network parameters. By comparing the output with the data labels and calculating the error, the biases and connection weights of each layer of nodes are fine-tuned in reverse.

[0133] Use the constructed DBN model to predict the value of the sequence u k (t) at time t + 1 to obtain the predicted value Using the predicted values of each subsequence, the predicted value of y(t) at time t + 1 is reconstructed:

[0134]

[0135] S3: Conduct interval prediction on the voltage quality index monitoring data sequence:

[0136] Calculate the variance of the fluctuation terms in the subsequences obtained by VMD decomposition to obtain the uncertainty prediction interval of the voltage quality index monitoring data sequence y(t).

[0137] Specifically: Calculate the variance of the fluctuation terms {u k (t), k ∈ K0}

[0138]

[0139] Calculate the prediction interval of y(t) at time t + 1:

[0140]

[0141] Where: respectively represent the upper and lower bounds of the prediction interval of y(t) at time t + 1 with a probability of ε; R ε is the quantile corresponding to the standard normal distribution and the probability ε.

[0142] Figure 3 is the measured voltage deviation data recorded by the voltage quality monitor at the point of common coupling of a certain residential load in southern China, Figure 4 showing the voltage deviation prediction results of the embodiments of the present invention.

[0143] S4: Construct a membership function for voltage quality risk warning, and based on the accurate value prediction and interval prediction, warn of the risk of voltage quality indicators:

[0144] Estimate the probability function of the voltage quality indicator using the kernel density estimation method to construct a membership function for voltage quality risk warning and warn of the risk of voltage quality indicators.

[0145] Specifically: Select a kernel function. Select the Gaussian kernel as the kernel function for kernel density estimation:

[0146]

[0147] Where: y represents the random variable of the voltage quality indicator.

[0148] Select a bandwidth. To ensure that the probability density function of the voltage quality indicator estimated by the kernel density estimation method can reflect the characteristics of the original data as much as possible while maintaining smoothness, select the bandwidth as:

[0149]

[0150] Where: σ g is the standard deviation of the kernel function G(y); f″(y) represents the second derivative of y; w is the bandwidth length.

[0151] Calculate the probability density function of the voltage quality indicator:

[0152]

[0153] Calculate the cumulative probability function of the voltage quality indicator:

[0154]

[0155] The membership functions for voltage quality risk warning are established based on low-risk warning, medium-risk warning, and high-risk warning, as shown in Equations (21)-(23).

[0156]

[0157]

[0158]

[0159] Where: M1(y), M2(y), and M3(y) are the low-risk membership degree, medium-risk membership degree, and high-risk membership degree respectively; a, b, c, and d are the risk boundaries.

[0160] Select the risk boundaries a, b, c, and d according to Equation (24) as shown in the appendix Figure 5 as follows:

[0161]

[0162] Substitute the accurately predicted value and prediction interval of y(t) calculated into the constructed risk membership function, and based on the prediction of voltage quality indicators and the risk warning membership function, warn of the risk of voltage quality indicators at the t+1 moment. The appendix Figure 5 shows the risk membership degree and warning results of the voltage deviation prediction results. According to the predicted value of the voltage quality indicator at the t+1 moment (orange dots in the appendix Figure 5 ) and the upper and lower bounds of the prediction interval (red dots in the appendix Figure 5 ), (green dots in the appendix Figure 5 ), judge the risk level of the voltage quality indicator. In the appendix Figure 5 , 60% of the accurate value prediction belongs to high risk, 40% belongs to medium risk; the upper bound of the prediction interval belongs to high risk; the lower bound of the prediction interval belongs to low risk.

[0163] In summary, the present invention provides a steady-state voltage quality warning method based on trend prediction and uncertainty analysis, which can overcome the drawback that traditional risk warning methods fail to fully consider the uncertainty of the development trend of voltage quality indicators. The proposed method not only predicts the accurate value of voltage quality, but also conducts interval prediction on it, realizing the risk warning of steady-state voltage quality indicators.

Claims

1. A steady-state voltage quality early warning method based on trend prediction and uncertainty analysis, characterized in that The steps include the following: Decompose the voltage quality index monitoring data sequence based on VMD: Based on VMD, decompose the voltage quality index monitoring data sequence into each subsequence, and divide the trend term, periodic term, and fluctuation term therein; Perform accurate value prediction on the decomposed voltage quality index monitoring data sequence based on DBN: Use DBN to predict the trend term and periodic term in the subsequence decomposed by VMD to obtain the accurate prediction value of the voltage quality index monitoring data sequence; Perform interval prediction on the voltage quality index monitoring data sequence: Calculate the variance of the fluctuation term in the subsequence decomposed by VMD to obtain the uncertainty prediction interval of the voltage quality index monitoring data sequence; Construct the membership function for voltage quality risk warning, and based on the accurate value prediction and interval prediction, give a warning about the risk of the voltage quality index.

2. The steady-state voltage quality early warning method based on trend prediction and uncertainty analysis according to claim 1, wherein Based on VMD, decomposing the voltage quality index monitoring data sequence into each subsequence, and dividing the trend term, periodic term, and fluctuation term therein specifically includes: Step 1.1: Represent the voltage quality index monitoring data sequence as the sum of several subsequences: Where: y(t) is the monitoring data sequence of the voltage quality index to be decomposed, and the voltage deviation voltage quality monitoring data is taken according to the early warning requirements; u k (t) is the k-th subsequence after decomposition; K is the total number of subsequences after decomposition; Step 1.2: Calculate the analytical signal expression of the subsequence The corresponding analytical signal expression of each subsequence can be obtained by using the Hilbert transform, and its unilateral spectrum is: In the formula: δ(t) is the Dirac function; * represents the convolution operation; j is the unit representing the imaginary number in the complex number; t represents the t-th moment; Step 1.3: Modulate the spectrum to the baseband By aliasing each subsequence u k (t) with its corresponding center frequency ω k to the exponential term of, the one-sided spectrum of each subsequence is modulated to the corresponding baseband: where: ω k is the center frequency of the k-th subsequence; Step 1.4: Construct a variational problem Demodulate the signal through Gaussian smoothing to obtain each subsequence u k (t) bandwidth description, and its solution can be transformed into a variational problem with constraints: In the formula: represents the derivative of the function in () with respect to t; Step 1.5: Construct the Lagrangian function Introduce the quadratic penalty factor α and the Lagrange multiplier λ into formula (4), so as to transform formula (4) into an unconstrained optimization problem: where: L({u k},{ω k},λ) is the constructed Lagrangian function; α is the quadratic penalty factor, λ is the Lagrange multiplier; λ(t) is the t-th Lagrange multiplier; Step 1.6: Solve for each subsequence u k (t) The multiplicative alternating direction method is used to iteratively solve Equation (5) to obtain the specific expressions of each subsequence u k (t), and the iterative process is as follows: Where: ω is the frequency; respectively represent y(t), u k (t), u r (t), λ n (t) is the Fourier transform; r is the counting unit; n is the number of iterations, u r (t) is the r-th subsequence after decomposition; represents u k (t) solved in the (n + 1)-th iteration; λ n (t) represents λ(t) solved in the n-th iteration; represents ω solved after the (n + 1)-th iteration k ; Step 1.6: According to the obtained subsequences u k (t), divide each subsequence u k (t) into trend terms, periodic terms, and fluctuation terms. Use the Durbin-Watson method to test the autocorrelation of each subsequence u k (t): where: DW k is the autocorrelation value of the subsequence u k (t). If DW k is close to 2, it is considered that u k (t) has no first-order correlation, that is, it is greatly affected by random factors and is a fluctuation term, denoted as k ∈ K0; if DW k is not close to 2, and u k (t) shows a monotonically increasing or decreasing trend, then it is a trend term, denoted as k ∈ K1; if DW k is not close to 2, and u k (t) shows periodic characteristics, then it is a periodic term, denoted as k ∈ K2.

3. The steady-state voltage quality early warning method based on trend prediction and uncertainty analysis according to claim 1, characterized in that Use DBN to predict the trend term and periodic term in the subsequence decomposed by VMD to obtain the accurate prediction value of the voltage quality index monitoring data sequence, specifically including: Step 2.1: Select the trend terms {u k (t), k ∈ K1} or periodic terms {u k (t), k ∈ K2} in the subsequence for prediction. Denote the sequence input into the DBN as {u(1), u(2), ···, u(T)}, where T is the sequence length of the subsequence u k (t); Step 2.2: Construct the Boltzmann machine of the DBN, as shown in Equation (9) below, which includes a visible layer v = (v1, v2, …, v n1 ) and a hidden layer h = (h1, h2, …, h n2 ); Where: θ = (w, a, b) are the parameters of the Boltzmann machine; p, q, n1, n2 are counting units; v p is the p-th unit of the visible layer; h q is the q-th unit of the hidden layer; w pq is the weight of the Boltzmann machine unit; a p , b q are the bias values of the Boltzmann machine unit; Step 2.3: Construct the joint probability distribution of the parameters (v, h) in the Boltzmann machine: In the formula: Z(θ) is the partition function; Step 2.4: Select the sigmoid function as the activation function and calculate the activation probability of the hidden layer units of the Boltzmann machine; Step 2.5: Calculate the activation probability of the visible layer units of the Boltzmann machine; Step 2.6: Obtain the model parameter θ by maximizing the log-likelihood function L s (θ) of the Boltzmann machine on the samples and fit the training samples to complete the construction of the DBN model: Step 2.7: Perform reverse supervised fine-tuning on the network parameters of the DBN model. By comparing the output with the data label and calculating the error, reverse fine-tune the biases and connection weights of each layer node of the DBN model; Step 2.8: Use the constructed DBN model to predict the value of the sequence u k at time t + 1 to obtain an accurate predicted value Use the predicted values of each subsequence to accurately predict the value of y(t) at time t + 1 for reconstruction:

4. The steady-state voltage quality early warning method based on trend prediction and uncertainty analysis according to claim 3, characterized in that Calculate the variance of the fluctuation term in the subsequence decomposed by VMD to obtain the uncertainty prediction interval of the voltage quality index monitoring data sequence, specifically including: Step 3.1: Calculate the variance of the fluctuation terms {u k (t), k ∈ K0} Step 3.2: Calculate the uncertainty prediction interval of y(t) at the t+1 moment: Wherein: respectively represent the upper and lower bounds of the prediction interval with a probability of ε for y(t) at the moment t + 1; R ε is the quantile corresponding to the standard normal distribution and the probability ε.

5. The steady-state voltage quality early warning method based on trend prediction and uncertainty analysis according to claim 1, characterized in that: Construct the membership function for voltage quality risk warning, and based on the accurate value prediction and interval prediction, give a warning about the risk of the voltage quality index, specifically including: Use the kernel density estimation method to estimate the probability function of the voltage quality index to construct the membership function for voltage quality risk warning, and substitute the accurate prediction value and the uncertainty prediction interval into the constructed risk membership function to give a warning about the risk of the voltage quality index.

6. The steady-state voltage quality early warning method based on trend prediction and uncertainty analysis according to any one of claims 1-5, characterized in that: Estimate the probability function of voltage quality indicators using the kernel density estimation method to construct the membership function for voltage quality risk early warning. Substitute the accurate prediction value and the uncertainty prediction interval into the constructed risk membership function to early warn the risk of voltage quality indicators. Specifically: Step 4.1: Select the Gaussian kernel as the kernel function for kernel density estimation: In the formula: y represents the random variable of voltage quality indicators; Step 4.2: To ensure that the probability density function of voltage quality indicators estimated by the kernel density estimation method can reflect the characteristics of the original data as much as possible while maintaining smoothness, select the bandwidth as: where: σ g is the standard deviation of the kernel function G(y); f″(y) represents the second derivative of y; w is the bandwidth length; Step 4.3: Calculate the probability density function of voltage quality indicators: Step 4.4: Calculate the cumulative probability function of voltage quality indicators: Step 4.5: Establish the membership function for voltage quality risk early warning with low risk early warning level, medium risk early warning level, and high risk early warning level: In the formula: M1(y), M2(y), and M3(y) are the low risk membership, medium risk membership, and high risk membership respectively; a, b, c, d are the risk boundaries; Select the risk boundaries a, b, c, d according to Equation (24): Step 4.6: Substitute the accurate prediction value and the prediction interval of y(t) calculated into the risk membership function constructed in Step 4.5, and early warn the risk of voltage quality indicators at the (t + 1)th moment based on the prediction of voltage quality indicators and the risk early warning membership function.

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