Electricity price prediction method based on dynamic mode decomposition fusion LSTM + CKDE

Abstract

The invention discloses an electricity price prediction method based on dynamic mode decomposition fusion LSTM + CKDE. The method comprises the following steps of: 1, collecting data, including historical electricity prices containing time sequence characteristics and price fluctuation indexes, power generation parameters, power market supply and demand data and external environment factor parameters; 2, performing data preprocessing, abnormal value processing and missing value interpolation on the collected data; 3, performing feature input variable screening on the data processed in the step 2 by adopting a maximum information coefficient method or a Pearson correlation coefficient analysis method; 4, performing dynamic modal decomposition on the screened feature input variables to obtain dynamic feature vectors; step 5, constructing an electricity price prediction model by using an LSTM algorithm, and inputting a dynamic feature vector; and 6, evaluating the electricity price prediction model by adopting a CKDE method. According to the invention, the accuracy of electricity price prediction is improved.

Description

Technical Field

[0001] The present invention belongs to the field of renewable energy power generation technology, and specifically relates to an electricity price prediction method based on dynamic mode decomposition fusion LSTM+CKDE. Background Art

[0002] As the frequency of electricity market transactions increases significantly in the future, accurate forecasting of electricity prices in the renewable energy market is crucial for the stable operation of the power market and the effective absorption of renewable energy. However, electricity prices are highly uncertain because they are affected by factors such as supply and demand, weather changes, fuel costs, and market competition. Based on these factors, current market electricity price forecasting faces the following challenges:

[0003] (1) Dynamic feature extraction lacks universality and has high cross-site adaptation costs: Different renewable energy sites (such as photovoltaic, wind power, and energy storage) have significantly different data features (such as light intensity, wind speed, and energy storage status). Existing feature extraction methods require customized processes for a single scenario and cannot adapt to mixed sites or newly connected sites. Traditional methods rely on manual experience to screen features, which is inefficient and highly subjective. They also do not consider the dynamic correlation of multi-source data (meteorological, market, and policy), resulting in feature redundancy or omission.

[0004] (2) Prediction models are unable to capture complex multidimensional relationships: Electricity prices are affected nonlinearly by multiple factors, including meteorological fluctuations, market supply and demand, and policy regulation. Traditional models rely solely on historical electricity price sequences or simple feature combinations, ignoring the spatiotemporal correlations of multidimensional data. Single models and simple neural networks are unable to model long-term dependencies, resulting in increasing prediction errors as the period lengthens.

[0005] (3) Lack of interval prediction evaluation of electricity price forecast results: Existing technologies overly rely on point forecast frameworks and are unable to quantify market uncertainty risks. Although traditional statistical methods and machine learning models can capture electricity price trends, they ignore non-parametric modeling of forecast error distribution.

[0006] Due to the above technical difficulties, the current existing technology lacks a universal dynamic feature extraction and electricity price prediction method. Summary of the Invention

[0007] The purpose of this invention is to provide an electricity price forecasting method based on dynamic mode decomposition and fusion of LSTM and CKDE. This invention improves the accuracy of electricity price forecasting.

[0008] The technical solution of the present invention is: a method for electricity price prediction based on dynamic mode decomposition fusion LSTM+CKDE, comprising the following steps:

[0009] Step 1. Data collection, including: historical electricity prices with time series characteristics and price fluctuation indicators, power generation parameters, power market supply and demand data, and external environmental factor parameters;

[0010] Step 2. Preprocess the collected data, handle outliers, and interpolate missing values;

[0011] Step 3. Use the maximum information coefficient method or Pearson correlation coefficient analysis method to screen the characteristic input variables of the data processed in step 2;

[0012] Step 4. Perform dynamic modal decomposition on the selected characteristic input variables to obtain dynamic characteristic vectors;

[0013] Step 5. Use the LSTM algorithm to build an electricity price prediction model and input the dynamic feature vector;

[0014] Step 6. Use the CKDE method to evaluate the electricity price prediction model.

[0015] In the aforementioned electricity price prediction method based on dynamic mode decomposition and fusion of LSTM+CKDE, step 2 is as follows:

[0016] For data with continuous features, if the value of the i-1th moment in the time series is x i -1, the value at the i+1th moment is x i +1, then the missing value x at time i i for:

[0017]

[0018] For data with discrete features, count the value with the most occurrences of the corresponding discrete feature in the data set as the mode M, and use M to fill the missing values;

[0019] The statistical Z-score method is used to identify outliers and calculate the x value of each data point. i Z i :

[0020]

[0021] Where μ is the mean, σ is the standard deviation, when |Z i ∣>3, change x i For continuous features, outliers are replaced by the median Med of the feature; for discrete features, outliers are replaced by the mode M.

[0022] In the aforementioned electricity price prediction method based on dynamic mode decomposition and fusion of LSTM+CKDE, step 3 is as follows:

[0023] Taking the market electricity price Y as the target variable, calculate each feature X j The Pearson correlation coefficient r between the target variable and jY :

[0024]

[0025] Where n is the number of samples, x ij is the value of the jth feature in the i-th sample, is the mean of the jth feature, y i is the market electricity price of the i-th sample, y is the mean of the market electricity price; select |r jY Features with a value of |>0.7 are used as preliminary screening features.

[0026] In the aforementioned electricity price prediction method based on dynamic mode decomposition and fusion of LSTM+CKDE, the decomposition method of step 4 is:

[0027] The multi-dimensional time series data is stacked into a high-dimensional state space by time slices, and the modes that characterize the key evolution laws of the system are decomposed through the DMD algorithm, and the top k dominant components are selected based on the modal energy ratio; the original high-dimensional features are then mapped to the low-dimensional modal coefficient space, retaining the dynamic coupling characteristics of non-stationary trends, periodic fluctuations and emergency response in the data, while filtering out high-frequency noise, and finally generating a feature vector that is both physically interpretable and computationally efficient.

[0028] In the aforementioned electricity price prediction method based on dynamic mode decomposition fusion LSTM+CKDE, the specific steps of step 4 are as follows:

[0029] Step 4.1. Split the state matrix X into two adjacent time window matrices:

[0030] X1=X[:,0:T-2],X2=X[:,1:T-1]

[0031] Among them, X1 represents the current state, and X2 represents the state at the previous moment;

[0032] Step 4.2. Perform SVD decomposition on X1 and retain the main energy modes:

[0033] X1=U∑V * ;

[0034] represents the left singular vector, R represents the real number domain, n represents the spatial dimension of the original feature matrix X1, and r represents the number of retained main modes;

[0035] represents a diagonal matrix of singular values

[0036] represents the right singular vector; T represents the current moment, and T-1 represents the previous moment;

[0037] V* represents the adjoint matrix of V;

[0038] Step 4.3. Calculate the approximate Koopman matrix using the SVD result after dimensionality reduction Describe the dynamic evolution of the system:

[0039]

[0040] Step 4.4. Solution The eigenvalues ​​and eigenvectors of :

[0041]

[0042] represents the eigenvalue diagonal matrix; Represents complex fields

[0043] represents the eigenvector matrix;

[0044] Step 4.5. Select the mode corresponding to the largest singular value;

[0045] Step 4.6. For each time point t, reconstruct the dynamic features through the linear combination of modes:

[0046] DMD feature vector

[0047] |φ k (t)| represents the amplitude of the kth mode at time t.

[0048] In the aforementioned electricity price prediction method based on dynamic mode decomposition and fusion of LSTM+CKDE, step 5 is as follows:

[0049] The LSTM model includes an input layer, one or more LSTM hidden layers, and an output layer. The input layer receives the feature vector X=(x1, x2,…, x m ), where m is the number of features; the hidden layer learns the long-term dependencies in the feature sequence through LSTM units; the main structure of LSTM includes input gate i t ,,,,Forget gate f t , output gate o t , candidate memory unit C~ t , memory unit C t , hidden state h t

[0050] i t =σ(W ii x t +Whi h t-1 +b i )

[0051] f t =σ(W if x t +W hf h t-1 +b f )

[0052] o t =σ(W io x t +W ho h t-1 +b o )

[0053] C~t=tanh(W ic x t +W hc h t-1 +b c )

[0054] C t =f t ⊙C t-1 +i t ⊙C~t

[0055] h t =o t ⊙tanh(C t )

[0056] Among them, x t is the input vector at time t, h t-1 is the hidden state at time t-1, C t-1 is the memory unit at time t-1, W is the weight matrix, b is the bias vector, σ is the sigmoid function, tanh is the hyperbolic tangent function, and ⊙ represents element-by-element multiplication. The output layer outputs the predicted market electricity price y^t, which is obtained through linear transformation:

[0057] y^t=W hy h t +b y

[0058] Among them, W hy is the output layer weight matrix, b y is the output layer bias vector;

[0059] The feature vector after dynamic mode decomposition in step 4 is used as the LSTM model input variable set, and the market electricity price is used as the model output; the model is trained to obtain the mapping relationship between the input variable set and the output market electricity price:

[0060]

[0061] Use mean squared error (MSE) as the loss function:

[0062]

[0063] Where n is the number of samples, y i is the real market electricity price, is the predicted market electricity price;

[0064] The Adam optimizer is used to update the model parameters; during the network model training process, the LSTM network parameters are updated to minimize the joint loss function.

[0065] In the aforementioned electricity price prediction method based on dynamic mode decomposition and fusion of LSTM+CKDE, step 6 is as follows:

[0066] First, a conditional kernel density estimation model is constructed based on the predicted residuals and conditional variables. The dynamic distribution of the residuals is fitted by the kernel function, and the conditional quantiles are extracted to generate dynamic confidence intervals. Then, the interval coverage, average interval width and Winkler score are calculated.

[0067] The advantages of the present invention are: (1) The present invention solves the problem of the lack of a universal method for dynamic feature extraction. The present invention proposes a dynamic feature extraction method applicable across sites. Combined with DMD dynamic modal decomposition, it solves the problem of large differences in data features between different new energy sites (photovoltaic, wind power, energy storage) and the lack of a universal dynamic feature extraction method. The dynamic feature extraction framework supports cross-site deployment (such as photovoltaic, wind power, and energy storage hybrid power stations), reduces model customization costs, and retains the dynamic characteristics of multidimensional feature vectors (meteorological, load, etc.), thereby improving prediction accuracy.

[0068] (2) Electricity prices in the new energy market are affected by complex factors such as weather, policies, and supply and demand fluctuations. Point predictions (such as single LSTM outputs) cannot reflect potential risks. To address this problem, the present invention introduces the CKDE method to generate probability intervals (such as 95% confidence intervals) by estimating the residual distribution, intuitively displaying the fluctuation range of the prediction results, and assisting decision makers in assessing risks. In addition, although LSTM is good at capturing nonlinear relationships, it may ignore sudden events (such as extreme weather). Therefore, the present invention introduces CKDE to dynamically adjust the interval width by analyzing the conditional distribution of historical prediction errors (such as based on the current electricity price level, volatility, etc.) to enhance robustness to abnormal events.

[0069] In summary, the present invention specifically solves the three core problems in the prediction of new energy electricity prices: the difficulty in extracting dynamic features, weak multidimensional relationship modeling, and low reliability of prediction results. The prediction results can assist market participants in making decisions, reduce the operating costs of the system, promote the consumption of new energy and optimize energy scheduling plans, and provide support for the stability of the power market and the efficient consumption of new energy. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is the overall flow chart of the present invention;

[0071] Figure 2 This is the data preprocessing flow chart;

[0072] Figure 3 Flowchart for feature screening;

[0073] Figure 4 This is the dynamic modal decomposition flow chart;

[0074] Figure 5 LSTM prediction flow chart;

[0075] Figure 6 Flowchart for CKDE interval prediction evaluation. DETAILED DESCRIPTION

[0076] The present invention will be further described below with reference to the accompanying drawings and examples, but they are not intended to limit the present invention.

[0077] Example 1. A method for predicting electricity prices based on dynamic mode decomposition and fusion of LSTM+CKDE, see Figure 1-6 , including the following steps:

[0078] Step 1: Data collection.

[0079] Collect historical electricity price data, including time series characteristics and price fluctuation indicators (electricity price volatility, peak-valley price difference, historical highest and lowest electricity prices); collect power generation related parameters, including photovoltaic output related characteristic parameters (such as light intensity, temperature, solar radiation, cloud coverage), wind turbine processing related characteristic parameters (such as wind speed, wind direction, air density, turbulence intensity), energy storage system status (energy storage capacity, charging and discharging efficiency, remaining power); collect electricity market supply and demand data, including power load demand (historical load curve, real-time load forecast value), conventional power output (power generation of traditional power sources such as thermal power, hydropower, nuclear power, etc.), grid constraints (transmission line capacity, node electricity price difference, system backup capacity); collect external environmental factor parameters (temperature, humidity, air pressure, precipitation).

[0080] Step 2: Data preprocessing, outlier processing and missing value interpolation.

[0081] For continuous features, such as light intensity, wind speed, etc., if the value of the i-1th moment in the time series is x i -1, the value at the i+1th moment is x i +1, then the missing value x at time i i The filling formula is:

[0082]

[0083] For discrete features, such as holiday signs, weather types, etc., count the values ​​of the feature that appear the most times in the data set as the mode M, and use M to fill the missing values. Use the statistical Z-score method to identify outliers. Calculate the value of each data point x i Z i , the formula is:

[0084]

[0085] Among them, μ is the mean of the feature, σ is the standard deviation of the feature. i ∣>3, change x i For continuous features, outliers are replaced by the median Med of the feature; for discrete features, outliers are replaced by the mode M.

[0086] Step 3: Feature screening and correlation analysis.

[0087] The maximum information coefficient method or Pearson correlation coefficient analysis method is used to screen the candidate feature input variables and calculate the X j The Pearson correlation coefficient r between the target variable (new energy market electricity price Y) jY , the formula is:

[0088]

[0089] Where n is the number of samples, x ij is the value of the jth feature in the i-th sample, is the mean of the jth feature, y i is the market electricity price of the i-th sample, is the mean of the market electricity price. jY Features with |>0.7 are used as preliminary screening features, that is, feature variables with strong correlation are retained as feature input variables.

[0090] Step 4: Perform dynamic mode decomposition on the screened multidimensional eigenvectors to obtain dynamic eigenmodes.

[0091] The feature extraction process of dynamic modal decomposition (DMD) for multidimensional electricity price forecasting constructs a joint state matrix containing multi-source data such as historical electricity prices, renewable energy output, and meteorological factors, and uses singular value decomposition (SVD) and feature projection to extract the dominant spatiotemporal modes: first, the multidimensional time series data is stacked into a high-dimensional state space by time slices, and the modes that characterize the key evolution laws of the system are decomposed through the DMD algorithm, and the top k dominant components are selected based on the modal energy ratio; then the original high-dimensional features are mapped to a low-dimensional modal coefficient space, retaining the dynamic coupling characteristics of non-stationary trends, periodic fluctuations and emergency response in the data, while filtering out high-frequency noise, and finally generating a feature vector that is both physically interpretable and computationally efficient, which is used as the input of the neural network to improve the generalization ability of electricity price forecasting and the accuracy of uncertainty modeling.

[0092] Step 4.1 splits the time delay matrix.

[0093] Split the state matrix X into two adjacent time window matrices:

[0094] X1=X[:,0:T-2],X2=X[:,1:T-1]

[0095] X1 represents the current state, and X2 represents the state at the previous moment.

[0096] Step 4.2 Singular Value Decomposition (SVD).

[0097] Perform SVD decomposition on X1, retaining the main energy modes (usually truncated to the first singular value):

[0098] X1=U∑V *

[0099] Left singular vector (spatial mode), R represents the real number domain, n represents the spatial dimension of the original feature matrix X1 (i.e., the number of input variables), and r represents the number of retained main modes;

[0100] Singular value diagonal matrix

[0101] Right singular vectors (time-evolving modes)

[0102] Step 4.3 Approximate Koopman matrix calculation.

[0103] Calculate the approximate Koopman matrix using the SVD result after dimensionality reduction Describe the dynamic evolution of the system:

[0104]

[0105] Step 4.4 Feature decomposition.

[0106] Solution The eigenvalues ​​and eigenvectors of :

[0107]

[0108] Eigenvalue diagonal matrix (reflecting the amplitude and frequency of the mode)

[0109] Eigenvector matrix

[0110] Step 4.5: Modality selection.

[0111] Energy screening: select the mode corresponding to the largest singular value (usually the first 3 to 5 modes are the most interpretable)

[0112] Step 4.6 Feature vector construction.

[0113] For each time point t, the dynamic features are reconstructed by linear combination of modes:

[0114] DMD feature vector

[0115] |φ k (t)| represents the amplitude of the kth mode at time t (modulus length)

[0116] Step 5: Use the LSTM algorithm to build a new energy market electricity price prediction model and input the dynamic feature vector after dynamic mode decomposition.

[0117] The LSTM model consists of an input layer, multiple LSTM hidden layers, and an output layer. The input layer receives the feature vector X=(x1, x2,…, x m ), where m is the number of features. The hidden layer learns the long-term dependencies in the feature sequence through LSTM units. The main structure of LSTM includes input gate i t ,,,,Forget gate f t , output gate o t , candidate memory unit C~ t , memory unit C t , hidden state h t

[0118] i t =σ(W ii x t +W hi h t-1 +b i )

[0119] f t =σ(W if x t +W hfh t-1 +b f )

[0120] o t =σ(W io x t +W ho h t-1 +b o )

[0121] C~t=tanh(W ic x t +W hc h t-1 +b c )

[0122] C t =f t ⊙C t-1 +i t ⊙C~t

[0123] h t =o t ⊙tanh(C t )

[0124] Among them, x t is the input vector at time t, h t-1 is the hidden state at time t-1, C t-1 is the memory unit at time t-1, W is the weight matrix, b is the bias vector, σ is the sigmoid function. tanh is the hyperbolic tangent function, and ⊙ represents element-by-element multiplication. The output layer outputs the predicted new energy market electricity price y^t, which is obtained through linear transformation:

[0125] y^t=W hy h t +b y

[0126] Among them, W hy is the output layer weight matrix, b y is the output layer bias vector. The feature vectors obtained through dynamic mode decomposition in step 4 are used as the LSTM model input variable set, and the renewable energy market electricity price is used as the model output. The data set is rationally divided into a training set, a validation set, and a test set (e.g., in a ratio of 7:2:1) for model training to determine the mapping relationship between the input variable set and the output renewable energy market electricity price.

[0127]

[0128] The mean square error (MSE) is used as the loss function, and the formula is:

[0129]

[0130] Where n is the number of samples, y i is the real market electricity price, is the predicted market electricity price. The Adam optimizer is used to update the model parameters. During network model training, the LSTM network parameters are updated to minimize the joint loss function.

[0131] Step 6: Use the CKDE method to establish a photovoltaic power station market electricity price range prediction model.

[0132] To evaluate the accuracy of LSTM electricity price forecasts using the CKDE method, it is necessary to first construct a conditional kernel density estimation model based on the prediction residuals and conditional variables (such as load and renewable energy output), fit the dynamic distribution of the residuals through a kernel function (such as a Gaussian kernel), extract the conditional quantiles and generate a dynamic confidence interval; then calculate indicators such as the interval coverage ratio (ICP), average interval width (IAW) and Winkler score to quantify the coverage and accuracy of the prediction interval for the actual electricity price.

[0133] Example 2. A method for predicting electricity prices based on dynamic mode decomposition and fusion of LSTM+CKDE, with the attached Figure 1 Take Python as an example to illustrate the overall implementation process of the present invention:

[0134] (1) Data acquisition module: Acquires data related to electricity prices in the new energy market, including historical new energy power generation, grid load data, and corresponding time series information.

[0135] (2) Data preprocessing module: The pandas library is used to handle missing values ​​in the data. For a small amount of missing power generation data, interpolation is used to fill in the missing values. For abnormal price data, corrections are made based on the reasonable fluctuation range of the industry. StandardScaler in sklearn.preprocessing is used to standardize data of different dimensions to facilitate subsequent analysis.

[0136] (3) Feature screening module: Use the pearsonr function in the scipy.stats library to calculate the maximum information correlation coefficient between each feature and the electricity price in the new energy market. Set a reasonable threshold (such as 0.7) and eliminate features with an absolute value of the correlation coefficient less than the threshold, retaining features with a high correlation with the electricity price.

[0137] (4) Dynamic mode decomposition module: The filtered time series feature data related to electricity prices are input and decomposed into different modes to analyze the potential dynamic laws of electricity price changes in the new energy market. Examples are shown in Table 1.

[0138] Table 1 Physical meaning analysis (example)

[0139]

[0140] (5) LSTM prediction module: Build an LSTM neural network based on TensorFlow and Keras. Reasonably set the network hyperparameters, organize the data after dynamic modal decomposition into an input format with an appropriate time step, train the model, and predict the electricity price in the new energy market.

[0141] (6) CKDE interval prediction evaluation module: Based on the prediction results and historical error data, the prediction interval is determined through kernel density estimation (CKDE), and the accuracy of the prediction is measured using indicators such as interval coverage probability (ICP) and average interval width (IAW). Among them, ICP refers to the probability that the prediction interval covers the actual value interval. Generally, the higher the ICP value, the better, and it should be close to the confidence level, because it means that the prediction result is more accurate. For example, when the confidence level is 95%, the expected ICP value should be between 0.90 and 0.95. IAW refers to the average width of the prediction interval, which can evaluate the uncertainty of the interval prediction model. Generally, the smaller the IAW value, the more accurate the prediction result.

Claims

1. A method for electricity price prediction based on dynamic mode decomposition fusion LSTM+CKDE, characterized by: The steps include: Step 1. Data collection, including: historical electricity prices with time series characteristics and price fluctuation indicators, power generation parameters, power market supply and demand data, and external environmental factor parameters; Step 2. Preprocess the collected data, handle outliers, and interpolate missing values; Step 3. Use the maximum information coefficient method or Pearson correlation coefficient analysis method to screen the characteristic input variables of the data processed in step 2; Step 4. Perform dynamic modal decomposition on the selected characteristic input variables to obtain dynamic characteristic vectors; Step 5. Use the LSTM algorithm to build an electricity price prediction model and input the dynamic feature vector; Step 6. Use the CKDE method to evaluate the electricity price prediction model.

2. The electricity price prediction method based on dynamic mode decomposition fusion LSTM+CKDE according to claim 1 is characterized in that: Step 2 is as follows: For data with continuous features, if the value of the i-1th moment in the time series is x i -1, the value at the i+1th moment is x i +1, then the missing value x at time i i for: For data with discrete features, count the value with the most occurrences of the corresponding discrete feature in the data set as the mode M, and use M to fill the missing values; The statistical Z-score method is used to identify outliers and calculate the x value of each data point. i Z i : Where μ is the mean, σ is the standard deviation, when |Z i ∣>3, change x i For continuous features, outliers are replaced by the median Med of the feature; for discrete features, outliers are replaced by the mode M.

3. The electricity price prediction method based on dynamic mode decomposition fusion LSTM+CKDE according to claim 1 is characterized in that: Step 3 is as follows: Taking the market electricity price Y as the target variable, calculate each feature X j The Pearson correlation coefficient r between the target variable and jY : Where n is the number of samples, x ij is the value of the jth feature in the i-th sample, is the mean of the jth feature, y i is the market electricity price of the i-th sample, is the mean of the market electricity price; select |r jY Features with a value of |>0.7 are used as preliminary screening features.

4. The electricity price prediction method based on dynamic mode decomposition fusion LSTM+CKDE according to claim 1 is characterized in that: The decomposition method of step 4 is: The multi-dimensional time series data is stacked into a high-dimensional state space by time slices, and the modes that characterize the key evolution laws of the system are decomposed through the DMD algorithm, and the top k dominant components are selected based on the modal energy ratio; the original high-dimensional features are then mapped to the low-dimensional modal coefficient space, retaining the dynamic coupling characteristics of non-stationary trends, periodic fluctuations and emergency response in the data, while filtering out high-frequency noise, and finally generating a feature vector that is both physically interpretable and computationally efficient.

5. The electricity price prediction method based on dynamic mode decomposition fusion LSTM+CKDE according to claim 1 is characterized in that: The specific steps of step 4 are as follows: Step 4.

1. Split the state matrix X into two adjacent time window matrices: X1=X[:,0:T-2],X2=X[:,1:T-1] Among them, X1 represents the current state, and X2 represents the state at the previous moment; Step 4.

2. Perform SVD decomposition on X1 and retain the main energy modes: X1=U∑V * ; represents the left singular vector, R represents the real number domain, n represents the spatial dimension of the original feature matrix X1, and r represents the number of retained main modes; represents a diagonal matrix of singular values represents the right singular vector; T represents the current moment, and T-1 represents the previous moment; V* represents the adjoint matrix of V; Step 4.

3. Calculate the approximate Koopman matrix using the SVD result after dimensionality reduction Describe the dynamic evolution of the system: Step 4.

4. Solution The eigenvalues ​​and eigenvectors of : represents the eigenvalue diagonal matrix; Represents complex fields represents the eigenvector matrix; Step 4.

5. Select the mode corresponding to the largest singular value; Step 4.

6. For each time point t, reconstruct the dynamic features through the linear combination of modes: DMD feature vector |φ k (t)| represents the amplitude of the kth mode at time t.

6. The electricity price prediction method based on dynamic mode decomposition fusion LSTM+CKDE according to claim 1 is characterized in that: Step 5 is as follows: The LSTM model includes an input layer, one or more LSTM hidden layers, and an output layer. The input layer receives the feature vector X=(x1, x2,…, x m ), where m is the number of features; the hidden layer learns the long-term dependencies in the feature sequence through LSTM units; the main structure of LSTM includes input gate i t ,,,,Forget gate f t , output gate o t , candidate memory unit C~ t , memory unit C t , hidden state h t i t =σ(W ii x t +W hi h t-1 +b i ) f t =σ(W if x t +W hf h t-1 +b f ) o t =σ(W io x t +W ho h t-1 +b o ) C~t=tanh(W ic x t +W hc h t-1 +b c ) C t =f t ⊙C t-1 +i t ⊙C~t h t =o t ⊙tanh(C t ) Among them, x t is the input vector at time t, h t-1 is the hidden state at time t-1, C t-1 is the memory unit at time t-1, W is the weight matrix, b is the bias vector, σ is the sigmoid function, tanh is the hyperbolic tangent function, and ⊙ represents element-by-element multiplication. The output layer outputs the predicted market electricity price y^t, which is obtained through linear transformation: y^t=W hy h t +b y Among them, W hy is the output layer weight matrix, b y is the output layer bias vector; The feature vector after dynamic mode decomposition in step 4 is used as the LSTM model input variable set, and the market electricity price is used as the model output; the model is trained to obtain the mapping relationship between the input variable set and the output market electricity price: Use mean squared error (MSE) as the loss function: Where n is the number of samples, y i is the real market electricity price, is the predicted market electricity price; The Adam optimizer is used to update the model parameters; during the network model training process, the LSTM network parameters are updated to minimize the joint loss function.

7. The electricity price prediction method based on dynamic mode decomposition fusion LSTM+CKDE according to claim 1 is characterized in that: Step 6 is as follows: First, a conditional kernel density estimation model is constructed based on the predicted residuals and conditional variables. The dynamic distribution of the residuals is fitted by the kernel function, and the conditional quantiles are extracted to generate dynamic confidence intervals. Then, the interval coverage, average interval width and Winkler score are calculated.

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