Power system non-stationary time sequence prediction method

Abstract

The invention discloses a power system non-stationary time sequence prediction method, which is realized based on a non-stationary prediction enhancement module, and the non-stationary prediction enhancement module comprises a time domain-frequency domain conversion sub-module and a non-stationary trend extraction sub-module. Firstly, a time domain-frequency domain conversion sub-module is used for extracting periodic characteristics of time sequence data of a power system; subtracting the periodic features from the time sequence data of the power system to obtain non-stationary features; then, performing non-stationary trend fitting on the non-stationary features by using a non-stationary trend extraction sub-module to obtain non-stationary trend features; and finally, taking the periodic features as the input of the basic prediction model, and superposing the output of the basic prediction model and the non-stationary trend features as a final prediction result. The non-stationary prediction enhancement module can be compatible with any time sequence prediction model, the prediction precision of the non-stationary time sequence is remarkably improved compared with that of an original model when the non-stationary time sequence is processed, and the prediction performance of the original model in a non-stationary time sequence scene can be enhanced.

Description

Technical Field

[0001] The invention relates to a method for predicting non-stationary time series of an electric power system, and belongs to the field of time series prediction of an electric power system. Background Art

[0002] Non-stationary time series refers to time series data whose statistical properties (such as mean, variance, covariance, etc.) change significantly over time. Unlike stationary series, the distribution pattern of non-stationary series changes over time, which makes it difficult to directly apply traditional time series prediction methods. In power systems, time series data such as photovoltaic, wind power, and load often exhibit significant non-stationarity. To address the prediction problem of non-stationary time series, the current main method is to normalize the series to a mean of 0 and a variance of 1 to solve the problem of inconsistent statistics at different time steps. However, this method will cause the data to lose personalized information. The normalized series may cause the attention matrix in the Transformer model to converge, resulting in excessive stationarity and reduced model expressiveness. Summary of the Invention

[0003] The present invention aims to address the shortcomings of existing technologies and provide a method for predicting non-stationary time series in power systems. This method is compatible with any time series prediction model and significantly improves the prediction accuracy of non-stationary time series compared to the original model, thereby enhancing the prediction performance of the original model in non-stationary time series scenarios.

[0004] The object of the present invention is achieved through the following technical solutions:

[0005] A method for predicting non-stationary time series of a power system is provided. The method is implemented based on a non-stationary prediction enhancement module. The non-stationary prediction enhancement module includes a time domain-frequency domain conversion submodule and a non-stationary trend extraction submodule, specifically comprising the following steps:

[0006] The power system time series data is used as the input of the time domain-frequency domain conversion submodule, and the time domain-frequency domain conversion submodule is used to extract the periodic characteristics of the power system time series data; and the periodic characteristics output by the time domain-frequency domain conversion submodule are subtracted from the power system time series data to extract the non-stationary characteristics as the input of the non-stationary trend extraction submodule, and the non-stationary trend extraction submodule fits the non-stationary trend to obtain the non-stationary trend characteristics; the periodic characteristics extracted by the time domain-frequency domain conversion submodule are used as the input of the basic prediction model, and the output of the basic prediction model is superimposed with the non-stationary trend characteristics obtained by fitting the non-stationary trend extraction submodule as the final prediction result.

[0007] In the above technical solution, further, the time domain-frequency domain conversion submodule is used to extract the periodic characteristics of the power system time series data, and the specific method is:

[0008] First, the input power system time series data is converted into discrete fundamental frequency components in the frequency domain through fast discrete Fourier transform;

[0009] Secondly, extracting K frequencies with the largest amplitudes from the discrete fundamental frequency components in the frequency domain and recording the corresponding amplitude and phase information;

[0010] Finally, the K fundamental frequency components are summed up, and based on the amplitude and phase information, the reconstruction from the frequency domain components to the time domain is completed through the inverse Fourier transform, the time series is restored, and the periodic characteristics of the power system time series data are obtained.

[0011] In the process of extracting the periodic characteristics of power system time series data, since only the most significant frequency domain components are extracted, non-stationary trend information and random fluctuation information are filtered out. The reconstructed and restored time series is the periodic characteristics of the input sequence and is passed into the prediction basic prediction model.

[0012] Furthermore, the non-stationary trend extraction submodule performs fitting of the non-stationary trend, and the specific method is: the non-stationary feature includes non-stationary random fluctuations and non-stationary trend information; a polynomial fitting method is used to filter out the non-stationary random fluctuations to obtain the non-stationary trend information, which is the non-stationary trend feature.

[0013] Furthermore, the polynomial fitting method is used to filter out non-stationary random fluctuations to obtain non-stationary trend information, which is the non-stationary trend feature. The specific method is:

[0014] The periodic features extracted by the time-frequency domain conversion submodule are subtracted from the power system time series data to obtain the non-stationary features X containing random fluctuations and non-stationary trend information. noise :

[0015] X noise =XX period

[0016] With non-stationary feature X noise For the non-stationary trend extraction submodule input, X is first converted through the convolution layer Conv1D and the activation layer Sigmoid noise Mapping to polynomial coefficient space C coe :

[0017] C coe =Sigmoid(Conv1D(X noise ))

[0018] Among them, the input dimension of the convolutional layer is X noiseThe output dimension is the degree of the polynomial. The degree of the polynomial can be set to n (usually an integer between 3 and 5) based on the complexity of the non-stationary trend in the specific application scenario. The output dimension pred_len of the non-stationary trend extraction submodule is much larger than 5.

[0019] Construct the polynomial basis function space lin_space based on the output dimension pred_len of the non-stationary trend extraction submodule:

[0020]

[0021] According to the set polynomial degree n, the first n basis functions are selected from the polynomial basis function space to construct the polynomial space poly_space as follows:

[0022] poly_space=[lin_space(1),lin_space(2),...,lin_space(n)]

[0023] Finally, the polynomial basis function is used to map the non-stationary features into non-stationary trend features. This process is achieved by multiplying the polynomial coefficient space with the polynomial space. The mathematical process is expressed as follows:

[0024] X trend =matmul(C coe ,poly_space)

[0025] Furthermore, a trend feature prediction layer based on polynomial fitting is constructed in the non-stationary trend extraction submodule. This layer of network takes non-stationary features (specifically including non-stationary random fluctuations and non-stationary trend information) as input and outputs non-stationary trend features of the prediction window. The core logic of the prediction method using polynomial fitting is that non-stationary change trends are mostly presented in the form of slow increases, decreases or horizontal fluctuations. Polynomial fitting can not only ensure that there are sufficient nonlinear degrees of freedom in the fitting process, but also has excellent performance in resisting random fluctuations (i.e., high-frequency noise) contained in the input sequence. The predicted non-stationary trend features are the output of the non-stationary trend extraction submodule.

[0026] In the present invention, in order to better be compatible with and adapt to the access of the non-stationary prediction enhancement module proposed by the present invention and applicable to the non-stationary time series prediction scenario, the basic prediction model is processed as follows: First, the data input of the basic prediction model is adjusted, and the input data must first be processed by the non-stationary prediction enhancement module. After the modification, the prediction input of the basic prediction model is the periodic feature output of the time domain-frequency domain conversion submodule in the non-stationary prediction enhancement module; secondly, the prediction output of the basic prediction model is adjusted, and the prediction result of the basic prediction model is no longer regarded as the final prediction output, but is linearly superimposed with the non-stationary trend feature extracted by the non-stationary trend extraction submodule in the non-stationary prediction enhancement module and then output. Finally, except for the input and output layers, the core prediction algorithm and unique structure of the basic prediction model are completely retained, which makes the non-stationary prediction enhancement module proposed by the present invention compatible with time series prediction models with different structures and principles.

[0027] The beneficial effects of the present invention are:

[0028] This paper designs a concise and effective non-stationary prediction enhancement module that is compatible with basic prediction models of different algorithms and structures, and has good generalizability and universality. Based on the technical difficulties of non-stationary time series prediction scenarios, the integration of the non-stationary prediction enhancement module eliminates the interference of random fluctuations and non-stationary trends on model predictions, fully leveraging the correlation analysis and periodic modeling capabilities of the basic prediction model; the introduction of the non-stationary trend extraction submodule can specifically enhance the model's prediction performance in non-stationary scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a flowchart of non-stationary time series prediction of power system.

[0030] Figure 2 It is a flowchart for constructing a non-stationary prediction enhancement module and performing non-stationary time series prediction of the power system based on the module. DETAILED DESCRIPTION

[0031] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0032] The present invention provides a method for predicting non-stationary time series of a power system, comprising the following steps:

[0033] like Figure 1 As shown, suppose the input power system time series data is X={x1,x2,...,x T}, where T is the time series step. The input data no longer passes directly through the basic prediction model, but first passes through the non-stationary prediction enhancement module Adapter, which first decomposes the input data into periodic features X period and non-stationary trend characteristics X trendTwo parts:

[0034] X period ,X trend =Adapter(X)

[0035] Adjust the basic prediction model structure and set the basic prediction model after removing the input layer and output layer network to f base (·), and its prediction process can be expressed as:

[0036] Y base =f base (X peroid )

[0037] Y base It represents the prediction result obtained by the basic prediction model based on the periodic characteristics of the output of the time-frequency domain conversion submodule of the non-stationary prediction enhancement module. In this framework, f base (·) can be used to represent any time series prediction model with different structures, different algorithms and different principles, thereby making the method of the present invention extremely compatible and having a wide range of applications.

[0038] The prediction results of the basic prediction model are linearly superimposed with the non-stationary trend features extracted by the non-stationary trend extraction submodule and then output as the non-stationary time series of the power system.

[0039] like Figure 2 As shown in the figure, a non-stationary prediction enhancement module is constructed, and based on it, non-stationary time series prediction of the power system is performed, which specifically includes three sub-steps:

[0040] Sub-step 1: Construct a time domain-frequency domain conversion sub-module to realize the periodic feature extraction of time series.

[0041] First, we construct an input layer based on discrete Fourier transform and perform fast discrete Fourier transform (FFT) on the input time series data X to convert it from time domain to frequency domain information:

[0042] X freq =FFT(X)

[0043] At this time X freq is the frequency domain representation of the input time series and contains only positive frequency components.

[0044] Then, according to the pre-set low-frequency threshold, X freq Filter and remove the high-frequency components in the frequency domain (i.e., non-stationary random fluctuation characteristics), so that the periodic characteristics of the remaining frequency domain components are more obvious. Extract the K components with the largest amplitude from the frequency domain:

[0045] X top =TopK(X freq )

[0046] In the formula, the working principle of TopK(·) function is: according to the amplitude of X freq The frequency domain components in are arranged in descending order, and the first K components are selected from large to small, X top That is the main periodic component extracted from it.

[0047] By inverse Fourier transforming X top The frequency domain signal in is restored to the time domain signal, and the periodic feature X is obtained. period , its formula is expressed as follows:

[0048]

[0049] amp(k)=abs(X top (k))

[0050] phase(k)=angle(X top (k))

[0051] In the formula, the inverse Fourier transform from frequency domain to time domain is for X top Each component in is processed one by one, amp(k) and phase(k) represent the amplitude and phase angle of the kth component respectively, and the periodic feature X is finally extracted and output. period By X top It is obtained by superimposing the inverse transform results of all frequency domain components in; f represents frequency and t represents time.

[0052] Sub-step 2: Construct a non-stationary trend extraction sub-module to realize non-stationary trend feature extraction.

[0053] Subtract the periodic features extracted in step 1 from the input time series to obtain the non-stationary feature X containing random fluctuations and non-stationary trend information. noise .

[0054] X noise =XX period

[0055] Construct a trend feature prediction layer based on polynomial fitting. This layer takes random fluctuation and non-stationary trend information as input. First, it maps the input features to the polynomial coefficient space through the convolution layer Conv1D and the activation layer Sigmoid:

[0056] C coe =Sigmoid(Conv1D(X noise ))

[0057] Where, the input dimension of the convolutional layer is X noiseThe output dimension is the degree of the polynomial, which can be set to n (usually an integer from 3 to 5) based on the complexity of the non-stationary trend. The output dimension of the non-stationary trend extraction submodule is pred_len, which is generally much larger than 5.

[0058] Construct the polynomial basis function space lin_space based on the output dimension pred_len (i.e. the predicted length of the output sequence) of the non-stationary trend extraction submodule:

[0059]

[0060] Accordingly, according to the set polynomial degree n, the first n basis functions are selected from the polynomial basis function space (each term in the polynomial basis function space is a basis function), and the polynomial space poly_space is constructed as follows:

[0061] poly_space=[lin_space(1),lin_space(2),...,lin_space(n)]

[0062] Finally, the polynomial basis function is used to map the non-stationary features into non-stationary trend features. This process is achieved by multiplying the polynomial coefficient space with the polynomial space. The mathematical process is expressed as follows:

[0063] X trend =matmul(C coe ,poly_space)

[0064] The non-stationary feature X containing random fluctuations and non-stationary trend information noise The convolution map is the polynomial coefficient C coe , which can effectively reduce the interference of high-frequency random noise in the trend learning process, and the polynomial coefficient C coe Multiplication with the polynomial space poly_space can ensure the nonlinear degrees of freedom of trend information in the fitting process and achieve accurate non-stationary trend prediction.

[0065] Sub-step 3: Based on the above sub-steps 1 and 2, it can be seen that the non-stationary prediction enhancement module takes the power system time series data X as input, and outputs the learned periodic features X through the time domain-frequency domain conversion sub-module and the non-stationary trend extraction sub-module. period and the non-stationary trend characteristics X of the prediction window trend Among them, the periodic feature output is used as the input of the basic prediction model; the non-stationary trend feature of the prediction window and the output of the basic prediction model are linearly superimposed to form the final prediction result Y pred .

[0066] Y pred=Y base +α·X trend

[0067] Where α is a trainable weight coefficient, which is used to adjust the impact of non-stationary trend characteristics on the final prediction results. The initial value can be set to 0.5.

Claims

1. A method for predicting non-stationary time series of power system, characterized by: The method is implemented based on a non-stationary prediction enhancement module, which includes a time-domain-frequency domain conversion submodule and a non-stationary trend extraction submodule. The method comprises: using power system time series data as input to the time-domain-frequency domain conversion submodule, and the time-domain-frequency domain conversion submodule is used to extract the periodic characteristics of the power system time series data; and using the power system time series data to subtract the periodic characteristics output by the time domain-frequency domain conversion submodule to extract non-stationary characteristics as input to the non-stationary trend extraction submodule, and the non-stationary trend extraction submodule performs non-stationary trend fitting to obtain non-stationary trend characteristics; The periodic features extracted by the time domain-frequency domain conversion submodule are used as the input of the basic prediction model, and the output of the basic prediction model is superimposed with the non-stationary trend features obtained by fitting the non-stationary trend extraction submodule as the final prediction result.

2. A method for predicting non-stationary time series of a power system according to claim 1, characterized in that: The time domain-frequency domain conversion submodule is used to extract the periodic characteristics of the power system time series data. The specific method is as follows: First, the input power system time series data is converted into discrete fundamental frequency components in the frequency domain through fast discrete Fourier transform; Secondly, extracting K frequencies with the largest amplitudes from the discrete fundamental frequency components in the frequency domain and recording the corresponding amplitude and phase information; Finally, the K fundamental frequency components are summed up, and based on the amplitude and phase information, the reconstruction from the frequency domain components to the time domain is completed through the inverse Fourier transform, the time series is restored, and the periodic characteristics of the power system time series data are obtained.

3. A method for predicting non-stationary time series of a power system according to claim 1, characterized in that: The non-stationary trend extraction submodule performs non-stationary trend fitting, and the specific method is: the non-stationary feature includes non-stationary random fluctuations and non-stationary trend information; a polynomial fitting method is used to filter out non-stationary random fluctuations to obtain non-stationary trend information, which is the non-stationary trend feature.

4. A method for predicting non-stationary time series of a power system according to claim 3, characterized in that: The polynomial fitting method is used to filter out non-stationary random fluctuations and obtain non-stationary trend information, which is the non-stationary trend feature. The specific method is: The periodic features extracted by the time-frequency domain conversion submodule are subtracted from the power system time series data to obtain the non-stationary features X containing random fluctuations and non-stationary trend information. noise : X noise =X-X period With non-stationary feature X noise For the non-stationary trend extraction submodule input, X is first converted through the convolution layer Conv1D and the activation layer Sigmoid noise Mapping to polynomial coefficient space C coe : C coe =Sigmoid(Conv1D(X noise )) Among them, the input dimension of the convolutional layer is X noise The length of the output dimension is the degree n of the polynomial; the output dimension of the non-stationary trend extraction submodule is pred_len; Construct the polynomial basis function space lin_space based on the output dimension pred_len of the non-stationary trend extraction submodule: Select the first n basis functions from the polynomial basis function space to construct the polynomial space poly_space, specifically: poly_space=[lin_space(1),lin_space(2),...,lin_space(n)] Finally, the polynomial basis function is used to map the non-stationary features into non-stationary trend features. This process is achieved by multiplying the polynomial coefficient space with the polynomial space. The mathematical process is expressed as follows: X trend =matmul(C coe ,poly_space)。

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