Electric power system short-term inertia point prediction method based on feature dimensionality reduction and multiple models

Abstract

A power system short-term inertia point prediction method based on feature dimensionality reduction and multiple models comprises the following steps: determining original multi-dimensional input features of power system short-term inertia prediction, and screening the original multi-dimensional input features by adopting a mode of combining a maximum correlation minimum redundancy mRMR algorithm and a random forest RF algorithm, obtaining an optimal feature subset which is strongly correlated with a short-term inertia prediction target and is low in redundancy; a CNN-BiLSTM-MHAM hybrid prediction model is constructed; and through the constructed CNN-BiLSTM-MHAM hybrid prediction model, the obtained optimal feature subset is utilized to predict the short-term inertia point of the power system. According to the method, the problem of high-precision prediction of the short-term inertia point of the electric power system is researched, the problems of high dimension, redundancy and fuzzy association among characteristics of original characteristic data in inertia prediction and the characteristics of high nonlinearity, strong time sequence and complex fluctuation of the inertia data of the electric power system are considered, and the economical efficiency and the safety of a scheduling scheme are improved.

Description

Technical Field

[0001] This invention relates to the field of power system inertia prediction technology, specifically to a method for predicting short-term inertia points in power systems based on feature reduction and multiple models. Background Technology

[0002] Accurate prediction of short-term trends in power system inertia is crucial for identifying periods of inertia vulnerability and quantifying risk levels. It also provides essential data support for optimizing inertia resource allocation and formulating emergency frequency control strategies. Most existing inertia prediction research is based on idealized simulation scenarios, focusing on inertia level analysis under transient disturbances. Research on modeling the time-series characteristics of inertia under quasi-steady-state operation scenarios is insufficient. Furthermore, existing models largely rely on macroscopic statistical patterns from meteorological parameters and power system operating data, lacking in-depth exploration of the nonlinear correlations between inertia and other characteristics, leading to significant feature redundancy. Therefore, extracting key features from high-dimensional heterogeneous data and constructing a prediction model suitable for the dynamic characteristics of the power system is a critical issue for improving the accuracy of inertia prediction.

[0003] The core challenges in predicting short-term inertia points in current power systems stem primarily from the inherent high dimensionality, redundancy, and ambiguity in the interrelationships between features in most of the raw data. These data characteristics often limit the accuracy of prediction models, making it difficult to accurately capture the complex inertia dynamics under actual load fluctuations. Consequently, the maximum system reserve demand identified by generating units deviates significantly from the actual demand. Traditional discrete strategies fail to adequately consider the complexity of such data and lack theoretically sound and feasible methods for selecting discrete scales for continuous quantities, further impacting prediction accuracy and the optimization of dispatch decisions. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for predicting short-term inertia points in power systems based on feature dimensionality reduction and multiple models. This method studies the problem of high-precision prediction of short-term inertia points in power systems, considering the high dimensionality, redundancy, and fuzzy correlations between features in the original feature data during inertia prediction, as well as the highly nonlinear, strong temporal sequence, and complex fluctuation characteristics of power system inertia data. This improves the economy and security of dispatching schemes. Especially in the context of load fluctuations and increased penetration of new energy sources, it provides more accurate system inertia assessment and avoids prediction bias.

[0005] The technical solution adopted in this invention is as follows:

[0006] A method for predicting the short-term inertia point of a power system based on feature reduction and multiple models includes the following steps:

[0007] Step 1: Determine the original multidimensional input features for short-term inertia prediction of the power system, and use a combination of the maximum correlation minimum redundancy (mRMR) algorithm and the random forest (RF) algorithm to screen the original multidimensional input features to obtain the optimal feature subset that is strongly correlated with the short-term inertia prediction target and has low redundancy, thereby constructing the input of the dimensionality-reduced prediction model.

[0008] Step 2: Construct a CNN-BiLSTM-MHAM hybrid prediction model;

[0009] Step 3: Using the CNN-BiLSTM-MHAM hybrid prediction model constructed in Step 2, the short-term inertia point of the power system was predicted using the optimal feature subset obtained in Step 1.

[0010] In step 1, in order to solve the problem of decreased classification accuracy and waste of computing resources caused by shallow statistical features, the maximum relevance minimum redundancy (mRMR) algorithm is used for feature selection. mRMR is based on the mutual information principle and selects the feature subset with the highest relevance to the final output but the lowest redundancy between features from the original feature set.

[0011] In mRMR, mutual information I(x,y) is used as a fundamental metric to measure the correlation between variables. For any two random variables x and y, their mutual information is defined as:

[0012]

[0013] In equation (1), I(x,y) represents the mutual information between random variables x and y; the marginal probability density function of random variable x is defined as p(x), the marginal probability density function of random variable y is defined as p(y), and the joint probability density function between x and y is defined as p(x,y);

[0014] Suppose we have obtained m-1 features, and the feature set formed by these features is S. Then, in the m-th iteration, we select the other features f from the original feature set that have not yet been selected into S. j In the process, the next optimal feature f is selected and added to form S:

[0015]

[0016] In equation (2), This represents the incremental mutual information evaluation value of each candidate feature f calculated in the current m-th round; Represents all candidate features f j middle The highest rating; This represents the mRMR mutual information quotient evaluation value calculated for each candidate feature f in the m-th round. Indicates all candidate features f j middle The most important feature is the optimal feature that simultaneously possesses high relevance and low redundancy; I(f j c) represents the mutual information between the candidate feature and the target category c; I(f j ,f i ) represents candidate feature f j With the selected feature f i Mutual information between Representing candidate features f j With the selected feature set S m-1 Each feature f in i Mutual information I(f) between j ,f i ) and.

[0017] f j The original feature set does not contain S m-1 Other features of the feature quantity; c represents the target category.

[0018] In step 1, after the mRMR initially screens out the effective feature subset, this stage further refines the effective feature subset using the average precision descent method of random forest (RF) to identify the key features that have the most significant impact on the model's classification or prediction performance. The specific steps are as follows:

[0019] 1) Suppose that the constructed random forest model contains m' decision trees, and let the i-th decision tree be T. i = (i = 1, 2, ..., m'), input the out-of-bag (OOB) data of each decision tree into matrix X. OOB The predicted value is defined as Y i The true value is defined as Y, and the mean square error between the two is defined as...

[0020] 2) While ensuring X OOB With the feature variables unchanged, the sample at feature j is randomly modified, and the predicted value Y after the sample modification is re-evaluated. i j That is, the predicted value Y i j The mean squared error between the true value Y and the actual value Y

[0021] 3) Calculate the feature variable X in the i-th decision tree. n The accuracy decrease value A, where n = 1, 2, ..., N, n represents the feature index, and N represents the total number of features;

[0022]

[0023] 4) Calculate the characteristic variable X n All average precision decrease value A n :

[0024]

[0025] The average accuracy decrease value A n This quantifies the overall importance of feature X to the prediction performance of the entire random forest model. The larger the value, the more significant the decrease in model prediction accuracy when the feature is disturbed, i.e., the greater its contribution to prediction performance.

[0026] 5) Feature ranking and secondary selection:

[0027] Based on the average accuracy decrease value A n The features are ranked by importance, and a threshold θ or an upper limit K for the number of features is set to select those that satisfy the following:

[0028] A n The key feature set S consists of features ≥θ or n≤K (5). final ;

[0029] 6) mRMR–RF fusion:

[0030] Calculate the feature importance scores A for mRMR and RF respectively. mRMR (X i ) and A RF (X i After normalizing both results to the same scale, a linear weighted superposition method is used to obtain the final comprehensive feature importance. The normalization is as follows:

[0031]

[0032] Among them, A k (X i ) represents the original feature importance score of the i-th feature X calculated by algorithm k (mRMR or RF); min represents the normalized feature importance value; j A k (X j ) represents the minimum importance score among all features under the current algorithm k; max j A k (X j ) represents the maximum importance score among all features under the current algorithm k; the subscript j in the formula represents the feature index variable, which is used to traverse the entire input feature set {X,X,…,X}.

[0033] The normalized results are then weighted and combined:

[0034]

[0035] Where: X i Let λ represent the i-th input feature variable; λ1 and λ2 are weight coefficients (usually taken as 0.5); Representing feature X i The normalized feature importance score calculated in the mRMR algorithm; Representing feature X i The normalized feature importance score calculated using the RF average precision reduction method; A final (X i ) represents feature X i The final overall importance score. (Based on A) final (X i The features are sorted, and the top K features or those above the threshold are selected as the final feature set, thus completing the feature selection process.

[0036] Step 2 includes:

[0037] 2.1: Using the optimal feature subset as input to the CNN network. CNN networks essentially mimic biological visual mechanisms, capturing local spatial features in data through convolutional operations. Convolutional layers use convolutional kernels of a specific size W. (d) For the input feature mapping x (") Perform convolution and summation, then add a bias b to the convolution result. d This yields the net input to the convolutional layer; finally, the output mapping y is obtained through a nonlinear activation function φ. (d) ;

[0038]

[0039] In equation (8), d = 1, ..., D, where D represents the total number of biases;

[0040] Pooling layers sample based on local statistical information on feature maps to reduce the number of parameters involved in model computation.

[0041] The fully connected layer, located at the end of the network, integrates, compresses, and non-linearly maps the high-dimensional features extracted by the preceding convolutional and pooling layers, thereby outputting the final classification or regression result. This can be expressed as:

[0042] y=σ(w*x+b) (9);

[0043] In equation (9), y is the output vector; σ is the activation function; w is the weight matrix; b is the bias vector; and x is the input feature vector, with dimensions x = [x1, x2, ..., x...]. n ] T, where each x is a feature extracted from the previous layer; 2.2: The local features extracted by the CNN network are then input into the BiLSTM network to further mine the temporal dependencies and global semantic features of the features.

[0044] BiLSTM networks are an extension of LSTM networks, combining forward and backward LSTM layers to achieve a mechanism for information flow in both directions. LSTM introduces an input gate i t Forgotten Gate t Output gate O t Three types of gated logic units enable it to maintain the persistence and accuracy of information when processing long sequences of data;

[0045] f t =σ(W f ·[h t-1 ,x t ]+b f (10);

[0046] In equation (10), σ is the bipolar sigmoid activation function; W f and b f These are the recursive weights and biases of the forget gate, respectively; h t-1 Let x represent the hidden state vector from the previous time step. t This represents the input vector at the current moment;

[0047] Memory cell C t It is a core component of LSTM, used to store, transmit, and update sequence information over time. Input gate i t The process of controlling the writing of new information determines the memory cell C t The information retained in the memory. First, candidate memory cells are calculated:

[0048]

[0049] In equation (11), W C b C These represent the weight matrix and bias term of the memory cell, respectively; tanh is the hyperbolic tangent activation function.

[0050] i t =σ(W i ·[h t-1 ,x t ]+b i (12);

[0051] In equation (12), W i b i These are the weights and bias terms of the input gate, respectively;

[0052] Finally, combining the input gate i t and candidate memory cells Update memory cells C t :

[0053]

[0054] In equation (13), C t-1 This indicates the state of the memory cell at the previous moment. This represents the Hadamard product (the multiplication of corresponding elements of two matrices);

[0055] Output gate O t Control the output information of the LSTM, i.e., the current hidden state h. t The calculation formula is as follows:

[0056] O t =σ(W O ·[h t-1 ,x t ]+b O (14);

[0057]

[0058] In the above formula, W O b O These are the weight matrix and bias term of the output gate, respectively;

[0059] Unlike unidirectional LSTM, the BiLSTM model has two sets of LSTM units to achieve bidirectional learning and optimization of time series data. BiLSTM consists of two LSTM layers, one forward and one backward, processing the input data in normal and reverse order respectively. The two sets of LSTM units have different outputs. and BiLSTM ultimately outputs the sum of these two sets of predictions, as shown below:

[0060]

[0061] In the formula: and x represents the output hidden state vectors of the forward and backward LSTMs at time step t, respectively; t This represents the feature vector input into the network at time t; This represents the hidden state of the feedforward LSTM at time t-1; This represents the hidden state of the backward LSTM at time t+1; LSTM f () represents the mapping function of the forward LSTM unit; LSTM b () represents the mapping function of the backward LSTM unit; h tThe output vector of the BiLSTM is [h1,h2,…,h t A matrix composed of ] .

[0062] 2.3: To address the potential information loss issue in BiLSTM modeling of long sequences, a Multi-Head Self-Attention (MHAM) mechanism is introduced. MHAM enhances the ability to capture dependencies in long sequences through parallelized feature association analysis. The hidden state features output from the BiLSTM network layers are transformed into d-dimensional features through three independent linear transformations. k Given three input matrices: query Q, key K, and value V, the attention output matrix is ​​as follows:

[0063]

[0064] In equation (18), Attention(Q,K,V) represents weighted fusion of information in V based on the similarity between Q and K; softmax(i) represents the normalization operation, mapping the attention weights to a probability distribution; and K... T d represents the transpose of the key matrix K; k The feature dimension of each key is used for weight scaling and is normalized to the [0,1] interval by softmax.

[0065] The Multi-Head Self-Attention (MHAM) mechanism divides the temporal feature space into h independent subspaces, with each subspace performing self-attention computation in parallel. The outputs of each head are concatenated, and feature fusion is achieved through a linear transformation layer.

[0066] head i =Attention(QW i Q ,KW i K VW i V (19);

[0067] In equation (19), head i W represents the output of the i-th attention head; i Q W i K W i V Let Q, K, and V represent the weight matrices, respectively.

[0068] MultHead(Q,K,V)=Concat(head1,...,head h )W0(20);

[0069] In equation (20), W0 represents the weights of the linear transformation; head i This represents the i-th head in the multi-head attention module, where i = 1, 2, ..., h, and h is the total number of attention heads; Concat represents the concatenation operation; MultHead(Q, K, V) is the final output result.

[0070] In step 2, the constructed CNN-BiLSTM-MHAM hybrid prediction model is trained using the Adaptive Moment Estimation (ADAM) optimization algorithm:

[0071] The ADAM optimization algorithm combines the core advantages of AdaGrad and RMSProp in principle, possessing adaptive learning rate adjustment capabilities and convergence stability, enabling efficient optimization of complex objective functions. Its specific parameter update method is as follows:

[0072] t = t + 1 (21);

[0073] In equation (21), t represents the current iteration number;

[0074]

[0075] In equation (22), g t The gradient of the random objective function; f represents the gradient operator, which is the partial derivative with respect to the parameter θ; t (θ t-1 θ represents the stochastic objective function at the current time step; t-1 Parameters to be updated;

[0076] m t =β1m t-1 +(1-β1)g t (twenty three);

[0077] In equation (23), m t β1 is the first-moment estimate; m is the exponential decay rate of the first-moment estimate; t-1 G represents the previous first-moment estimate; t The gradient of the random objective function;

[0078]

[0079] In equation (24), v t β1 is the partial second moment estimate; v is the exponential decay rate of the partial second moment estimate; t-1 This represents the second-order moment estimate from the previous iteration;

[0080]

[0081] In equation (25), θ tThis represents the model parameter vector after the current iteration; α is the learning rate. ε represents the deviation correction coefficient corresponding to the first-order and second-order moment estimates; ε represents the numerical stability constant.

[0082] Keep updating until θ t Convergence occurs, ending the loop; initial values ​​m0 = 0, v0 = 0, ε > 0 and close to 0. This process is repeated iteratively until convergence.

[0083] This invention provides a method for predicting the short-term inertia point of a power system based on feature reduction and multiple models. The technical advantages are as follows:

[0084] 1) This invention performs feature importance analysis on the inertia feature set based on the mRMR and RF methods, and extracts 22 key features with high feature importance ranking from the original 83-dimensional features. Compared with other four feature selection methods such as RF, mRMR, GR, and CFS, this hybrid feature selection method has higher accuracy and a larger AUC value, indicating that the method effectively reduces model complexity and improves data utilization efficiency.

[0085] 2) This invention designs a CNN-BiLSTM-MHAM combined prediction model, which combines a time series prediction model with a deep learning network to better uncover the complex nonlinear relationship between the system's equivalent inertia and other relevant features. By comparing with SVR, RF, CNN, BiLSTM, and the CNN-BiLSTM combined model, the CNN-BiLSTM-MHAM combined prediction model proposed in this invention outperforms all other models and can better fit the trend of inertia.

[0086] 3) This method studies the problem of high-precision prediction of short-term inertia points in power systems, aiming to solve the challenges posed by the high dimensionality, redundancy, and fuzzy feature correlation of the original data. It considers the highly nonlinear, strongly temporal, and complex fluctuation characteristics of inertia data, and strives to improve the prediction accuracy and robustness of the model under complex operating conditions. Ultimately, the accurate short-term inertia point prediction data provided by the method of this invention provides key input for optimized scheduling with real-time power balance constraints, supports the optimization of reserve decision-making mechanisms, and thus improves the economy and security of power system scheduling schemes.

[0087] 4) By analyzing two special scenarios where the output of wind power and photovoltaic power is relatively large and relatively small at different times, the method of this invention can also obtain relatively accurate inertia results. Attached Figure Description

[0088] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0089] Figure 1 This is a distribution map of the importance of mRMR features.

[0090] Figure 2 This is a distribution map of the importance of RF features.

[0091] Figure 3 This diagram illustrates the impact of the number of features on the model's AUC value.

[0092] Figure 4 The prediction results are for the CNN-BiLSTM combined prediction model.

[0093] Figure 5 The results are predictions from the CNN-BiLSTM-MHAM combined prediction model of this invention. Detailed Implementation

[0094] This invention proposes a method for predicting short-term inertia points in power systems based on feature dimensionality reduction and multiple models. First, to address the high-dimensional redundancy, ambiguous feature correlations, and complexity caused by load fluctuations in the original data, this method innovatively combines the Maximum Relevance Minimum Redundancy (mRMR) algorithm with the Random Forest (RF) feature selection method. This collaboratively sorts and refines the initial multidimensional input features, aiming to select the optimal feature subset with high importance scores and lowest redundancy. This effectively reduces data dimensionality and provides the model with more representative and stable input, avoiding the problem of increased prediction bias caused by feature noise or redundancy in traditional methods. Next, a CNN network is used to extract features from the input data, capturing its spatial and local features. The extracted feature vectors are then input into a BiLSTM network for training, capturing global information and long-term dependencies in the time series. By introducing a Multi-Head Self-Attention (MHAM) mechanism into the BiLSTM network layer, the weights of different features are dynamically adjusted to select key features.

[0095] Figure 1 To determine the original multidimensional input features for power system short-term inertia prediction through step 1, the maximum correlation minimum redundancy (mRMR) algorithm is used to perform information correlation analysis on the original input features, resulting in a ranking of feature importance. Figure 1It can be seen that the feature importance exhibits a clear long-tail distribution: a few features (such as h74, h62, h67, etc.) have significantly higher weight values ​​and contribute the most to the model's predictive performance, while the importance of most features gradually decays or even approaches zero. This indicates that inertia prediction mainly relies on a few key input features. These high-weight variables usually correspond to the system frequency change rate, unit output fluctuations, or virtual inertia control parameters, and are closely coupled with the dynamic changes of system inertia; while low-weight features are mostly weakly correlated or redundant indicators, and their effect on improving the prediction results is limited. This demonstrates that the mRMR algorithm is based on the mutual information criterion, measuring the "independent information content" provided by each input feature to the target variable, and showing the ranking of features in terms of "information contribution".

[0096] Figure 2 To initially screen the original features using the mRMR algorithm to obtain a high-information-density candidate feature set, the Random Forest (RF) algorithm is then used to evaluate the importance of the screened features at the model level through the Mean Precision Degradation (MDA) method. Figure 2 It can be seen that the feature importance distribution is steeper, indicating that the model performance mainly depends on a few key features. RF uses the Mean Precision Decrease (MDA) method to calculate the change in out-of-bag error by perturbing individual features, quantitatively measuring the contribution of each feature to the prediction accuracy, thus demonstrating its nonlinear mapping capability.

[0097] Table 1 Ranking of the Importance of Each Feature

[0098]

[0099]

[0100] Table 1 shows the final ranking of feature importance after normalizing the feature importance results obtained from the two algorithms to eliminate the influence of dimensions. A higher feature importance score indicates that the feature has stronger explanatory power in the model and contributes more to it.

[0101] Figure 3 Since the choice of feature dimension directly affects the prediction accuracy of the model, the feature dataset needs to be filtered after ranking the feature importance. To select the optimal input dimension k in the feature space, different dimensions k are established for comparative analysis. The candidate dimension parameters are quantitatively evaluated using the model classification performance index AUC, and the experimental results are obtained after determining the optimal dimension k. Figure 3 The results show that the AUC value reaches its peak when k is set to 22. Therefore, the 22 features with the highest importance ranking are selected as the model input.

[0102] Table 2 Comparison of characteristics of four different feature selection methods

[0103]

[0104] Table 2 compares the performance of four different feature selection methods to verify the effectiveness of the proposed feature selection algorithm. As shown in Table 2, the mRMR-RF feature selection fusion architecture constructed in this invention exhibits certain advantages in the test, achieving a classification accuracy of 93.374% and an AUC evaluation index of 87.9. This indicates that the method proposed in this invention is significantly superior to the four feature selection algorithms: RF, mRMR, GR, and CFS. Although RF and GR perform well in feature dimensionality reduction, they are prone to excessive removal of effective features, resulting in insufficient distribution of original information and reduced accuracy of the prediction model.

[0105] Table 3 Evaluation Indicators for Four Different Feature Selection Methods

[0106] Table 3 shows the 22 dimensions selected as the final input after feature filtering. To verify the effectiveness of the proposed method, four other methods—SVR, RF, CNN, BiLSTM, and CNN-BiLSTM—were compared with the proposed method. RMSE, MAE, MAPE, and R... 2 A comparison of the error results of each model after evaluating the models using four error assessment metrics.

[0107] MAE reflects the average absolute error. The smaller the MAE, the more accurate the prediction. Its mathematical formula can be expressed as:

[0108]

[0109] In equation (26), i is the sample number, N is the sample size, and x i Let x be the true value of the system's inertia. i ′ represents the system inertia value predicted by the model.

[0110] RMSE describes the dispersion of prediction error. The smaller the RMSE, the more accurate the prediction. Its mathematical formula can be expressed as:

[0111]

[0112] In equation (27), MAPE measures the average deviation between the predicted result and the actual value by calculating the average absolute percentage error between each predicted value and the actual value. The smaller the value, the closer the predicted value is to the actual value and the better the model performance.

[0113]

[0114] In equation (28), R 2It is a statistic of the goodness of fit, reflecting the degree of explanation. R 2 The closer the result is to 1, the higher the prediction accuracy. The mathematical formula for this is:

[0115]

[0116] In equation (29), This is the average value of the true system inertia.

[0117] Error results show that the CNN-BiLSTM-MHAM model exhibits the best prediction performance on the test set, with R0... 2 The MAE of 0.973 indicates that the model can accurately fit the short-term inertia variation trend of the power system. In contrast, SVR, due to its simple model structure, is prone to underfitting when dealing with some complex nonlinear problems, resulting in poor prediction performance. Although RF's prediction performance is slightly better than other single models, it is highly sensitive to feature distribution. CNN extracts local spatial features through convolutional kernels but lacks the ability to model the dynamic evolution of time series. CNN's MAE is as high as 0.0963, and R... 2 With an R value of only 0.761, it is significantly lower than that of the time series model BiLSTM. 2 The RMSE of 0.928 indicates that CNNs are insufficient in fitting temporal patterns. BiLSTM excels at modeling temporal dependencies, but it has low sensitivity to the spatial local features of the input data. BiLSTM's RMSE is 0.0826, significantly higher than CNN-BiLSTM, indicating that a single BiLSTM model struggles to effectively integrate spatiotemporal features. While the CNN-BiLSTM model achieves better prediction results than a single model, it uses fixed weights for the spatiotemporal importance of features, which cannot be adaptively adjusted. The importance of features may change dynamically across different time periods; introducing MHAM (Hyper-Mean-Age Algorithm) through dynamic weighting can effectively improve accuracy in such scenarios.

[0118] from Figure 4 and Figure 5 The prediction results show that, compared with CNN-BiLSTM and the method used in this invention,

[0119] The CNN-BiLSTM-MHAM algorithm, while exhibiting relatively poor curve fitting performance, particularly at inflection points, achieves significantly lower MAE (Maximum Effect) by 56.3%, RMSE (Recovery Time Per Second) by 54.01%, and MAPE (Maximum Effect Per Second) by 55.39% compared to the CNN-BiLSTM model. 2The improvement was 0.011. This indicates that the method proposed in this invention has stronger characterization capabilities when dealing with highly nonlinear and temporally sequential inertia feature data. It also reduces the problems of gradient vanishing and gradient exploding, and better solves the problem of large inflection point fluctuations. It can improve the reliability of prediction results while ensuring the accuracy of model prediction.

[0120] from Figure 4 and Figure 5 The data shows that the system's equivalent inertia exhibits a significant diurnal cycle: during the daytime, wind turbine output is lower while electricity load is higher, resulting in a higher level of equivalent inertia; from nightfall to dawn, the inertia value decreases significantly. The prediction results clearly reproduce this intraday fluctuation characteristic. Because the system's equivalent inertia is influenced by multiple factors, including the output of renewable energy generation and the grid load level, and because both renewable energy generation and user energy consumption behavior exhibit significant randomness, the inertia value shows a clear dynamic change throughout the day.

[0121] Table 4. Prediction results for 3 test samples in each of the 4 operating scenarios.

[0122] Table 4 explores the impact of new energy output power on the system's equivalent inertia. From 235 test samples, inertia predictions were selected for special operating scenarios, such as those with a high and low proportion of wind power output, and those with a high and low proportion of photovoltaic power output, and compared with the actual inertia values. Table 4 lists the prediction results for three test samples in each of the four operating scenarios, with prediction accuracy exceeding 99.85%. This indicates that even in special scenarios, the proposed method can still obtain relatively accurate system inertia prediction results, validating the method's effectiveness.

Claims

1. A method for predicting the short-term inertia point of a power system based on feature reduction and multiple models, characterized in that... The steps include: Step 1: Determine the original multidimensional input features for short-term inertia prediction of the power system, and use a combination of the maximum correlation minimum redundancy (mRMR) algorithm and the random forest (RF) algorithm to screen the original multidimensional input features in order to obtain the optimal feature subset that is strongly correlated with the short-term inertia prediction target and has low redundancy. Step 2: Construct a CNN-BiLSTM-MHAM hybrid prediction model; Step 3: Using the CNN-BiLSTM-MHAM hybrid prediction model constructed in Step 2, the short-term inertia point of the power system was predicted using the optimal feature subset obtained in Step 1.

2. The method for predicting the short-term inertia point of a power system based on feature dimensionality reduction and multiple models according to claim 1, characterized in that: In step 1, the maximum relevance minimum redundancy (mRMR) algorithm is used for feature selection. Based on the mutual information principle, mRMR selects the subset of features from the original feature set that has the highest relevance to the final output but the lowest redundancy between features, as follows: In mRMR, mutual information I(x,y) is used as a fundamental criterion for measuring the correlation between variables; for any two random variables x and y, their mutual information is defined as: In equation (1), I(x,y) represents the mutual information between random variables x and y; the marginal probability density function of random variable x is defined as p(x), the marginal probability density function of random variable y is defined as p(y), and the joint probability density function between x and y is defined as p(x,y); Suppose we have obtained m-1 features, and the feature set formed by these features is S. m-1 In the m-th iteration, the features that have not yet been selected from the original feature set will be included in S. m-1 Other features f j In the middle, select the next optimal feature f m Add to form S m : In equation (2), This represents the incremental mutual information evaluation value of each candidate feature f calculated in the current m-th round; Represents all candidate features f j middle The highest rating; This represents the mRMR mutual information quotient evaluation value calculated for each candidate feature f in the m-th round. Indicates all candidate features f j middle The most important feature is the optimal feature that simultaneously possesses high relevance and low redundancy; I(f j c) represents the mutual information between the candidate feature and the target category c; I(f j ,f i ) represents candidate feature f j Mutual information between the selected feature f and the selected feature f Represents the candidate feature f and the selected feature set S m-1 Each feature f in i Mutual information I(f) between j ,f i The sum of f j The original feature set does not contain S m-1 Other features of the medium feature quantity; c represents the target category.

3. The method for predicting the short-term inertia point of a power system based on feature dimensionality reduction and multiple models according to claim 2, characterized in that: After obtaining a subset of effective features through initial screening using mRMR, the average precision descent method of Random Forest (RF) is further used to refine the subset of effective features in order to identify the key features that have the most significant impact on the model's classification or prediction performance. The specific steps are as follows: 1) Suppose that the constructed random forest model contains m' decision trees, and let the i-th decision tree be T. i = (i = 1, 2, ..., m'), input the data outside the bag of each decision tree into matrix X. OOB The predicted value is defined as Y i The true value is defined as Y, and the mean square error between the two is defined as... 2) While ensuring X OOB With the feature variables unchanged, the sample at feature j is randomly modified, and the predicted value Y after the sample modification is re-evaluated. i j That is, the predicted value Y i j The mean squared error between the true value Y and the actual value Y 3) Calculate the feature variable X in the i-th decision tree. n The decrease in accuracy A in Where n = 1, 2, ..., N, n represents the feature index, and N represents the total number of features; 4) Calculate the characteristic variable X n All average precision decrease value A n : The average accuracy decrease value A n Quantified feature X n The overall importance of this feature to the prediction performance of the entire random forest model is such that a larger value indicates that the feature causes a more significant decrease in the model's prediction accuracy when it is disturbed, i.e., a greater contribution to the prediction performance. 5) Feature ranking and secondary selection: Based on the average accuracy decrease value A n Rank the features by importance and set a threshold θ or an upper limit K for the number of features, selecting those that satisfy: A n ≥θ or n≤K (5); The key feature set S is composed of features. final .

4. The method for predicting the short-term inertia point of a power system based on feature dimensionality reduction and multiple models according to claim 3, characterized in that: It also includes mRMR–RF fusion: Calculate the feature importance scores A for mRMR and RF respectively. mRMR (X i ) and A RF (X i After normalizing both results to the same scale, a linear weighted superposition method is used to obtain the final comprehensive feature importance. The normalization is as follows: Among them, A k (X i ) represents the i-th feature X i The original feature importance score is calculated using the mRMR or RF algorithm; min represents the normalized feature importance value; j A k (X j ) represents the minimum importance score among all features under the current algorithm k; max j A k (X j () represents the maximum importance score among all features under the current algorithm k; In the formula, the subscript j represents the feature index variable, used to traverse the entire input feature set {X1,X2,…,X...} n }; The normalized results are then weighted and combined: Where: X i Let λ represent the i-th input feature variable; λ1 and λ2 are weight coefficients (usually taken as 0.5); Representing feature X i The normalized feature importance score calculated in the mRMR algorithm; Representing feature X i The normalized feature importance score calculated using the RF average precision reduction method; A final (X i ) represents feature X i The final overall importance score; according to A final (X i Sort the features and select the top K features or those above the threshold as the final feature set to complete the feature selection process.

5. The method for predicting the short-term inertia point of a power system based on feature dimensionality reduction and multiple models according to claim 4, characterized in that: Step 2 includes: The optimal feature subset is used as input to the CNN network, and the convolutional layers use convolutional kernels of a specific size W. (d) For the input feature mapping x (p) Perform convolution and summation, then add a bias b to the convolution result. d This yields the net input to the convolutional layer; finally, the output mapping y is obtained through a nonlinear activation function φ. (d) ; In equation (8), d = 1, ..., D, where D represents the total number of biases; The pooling layer samples based on local statistical information on the feature map; The fully connected layer, located at the end of the network, integrates, compresses, and nonlinearly maps the high-dimensional features extracted by the preceding convolutional and pooling layers, thereby outputting the final classification or regression result; represented as: y=σ(w*x+b) (9); In equation (9), y is the output vector; σ is the activation function; w is the weight matrix; b is the bias vector; and x is the input feature vector with dimensions x = [x1, x2, ..., x]. n ] T , where each x i It is a feature extracted from the previous layer.

6. The method for predicting the short-term inertia point of a power system based on feature dimensionality reduction and multiple models according to claim 5, characterized in that: The local features extracted by the CNN network are then input into the BiLSTM network. The BiLSTM network is an extension of the LSTM network, combining two LSTM network layers, forward and backward, to realize the flow mechanism of information propagation in both directions. The LSTM introduces an input gate i. t Forgotten Gate t Output gate O t Three types of gated logic units; f t =σ(W f ·[h t-1 ,x t ]+b f ) (10); In equation (10), σ is the bipolar sigmoid activation function; W f and b f These are the recursive weights and biases of the forget gate, respectively; h t-1 Let x represent the hidden state vector from the previous time step. t This represents the input vector at the current moment; Memory cell C t It is a core component of LSTM, used to store, transmit, and update sequence information in the time dimension; input gate i t The process of controlling the writing of new information determines the memory cell C t The information retained in the memory cells; first, calculate the candidate memory cells: In equation (11), W C b C These represent the weight matrix and bias term of the memory cell, respectively; tanh is the hyperbolic tangent activation function. i t =σ(W i ·[h t-1 ,x t ]+b i ) (12); In equation (12), W i b i These are the weights and bias terms of the input gate, respectively; Finally, combining the input gate i t and candidate memory cells Update memory cells C t : In equation (13), C t-1 This indicates the state of the memory cell at the previous moment. This represents the multiplication of corresponding elements in two matrices; Output gate O t Control the output information of the LSTM, i.e., the current hidden state h. t The calculation formula is as follows: The t =σ(W O ·[h t-1 ,x t ]+b O ) (14); In the above formula, W O b O These are the weight matrix and bias term of the output gate, respectively.

7. The method for predicting the short-term inertia point of a power system based on feature dimensionality reduction and multiple models according to claim 6, characterized in that: The BiLSTM model employs two sets of LSTM units to achieve bidirectional learning and optimization of time series data. BiLSTM consists of two LSTM layers, one forward and one backward, processing the input data in normal and reverse order respectively. The two sets of LSTM units have different outputs. and BiLSTM ultimately outputs the sum of these two sets of predictions, as shown below: In the formula: and x represents the output hidden state vectors of the forward and backward LSTMs at time step t, respectively; t This represents the feature vector input into the network at time t; This represents the hidden state of the feedforward LSTM at time t-1; This represents the hidden state of the backward LSTM at time t+1; LSTM f () represents the mapping function of the forward LSTM unit; LSTM b () represents the mapping function of the backward LSTM unit; h t The output vector of the BiLSTM is [h1,h2,…,h t A matrix composed of ] .

8. The method for predicting the short-term inertia point of a power system based on feature dimensionality reduction and multiple models according to claim 7, characterized in that: The Multi-Head Self-Attention (MHAM) mechanism is introduced to generate d-dimensional hidden state features from the output of the BiLSTM network layers through three independent linear transformations. k Given three input matrices: query Q, key K, and value V, the attention output matrix is ​​as follows: In equation (18), Attention(Q,K,V) represents weighted fusion of information in V based on the similarity between Q and K; softmax(i) represents the normalization operation, mapping the attention weights to a probability distribution; and K... T d represents the transpose of the key matrix K; k The feature dimension of each key is used for weight scaling and is normalized to the [0,1] interval by softmax. The Multi-Head Self-Attention (MHAM) mechanism divides the temporal feature space into h independent subspaces, with each subspace performing self-attention computation in parallel. The outputs of each head are concatenated, and feature fusion is achieved through a linear transformation layer. head i =Attention(QW i Q ,KW i K ,VW i V ) (19); In equation (19), head i W represents the output of the i-th attention head; i Q W i K W i V These represent the weight matrices for Q, K, and V, respectively. MultHead(Q,K,V)=Concat(head1,...,head h )W0 (20); In equation (20), W0 represents the weights of the linear transformation; head i This represents the i-th head in the multi-head attention module, where i = 1, 2, ..., h, and h is the total number of attention heads; Concat represents the concatenation operation; MultHead(Q, K, V) is the final output result.

9. The method for predicting the short-term inertia point of a power system based on feature dimensionality reduction and multiple models according to claim 8, characterized in that: In step 2, the constructed CNN-BiLSTM-MHAM hybrid prediction model is trained using the adaptive moment estimation ADAM optimization algorithm.

10. The method for predicting the short-term inertia point of a power system based on feature dimensionality reduction and multiple models according to claim 9, characterized in that: The ADAM optimization algorithm can efficiently optimize complex objective functions. Its specific parameter update method is as follows: t = t + 1 (21); In equation (21), t represents the current iteration number; In equation (22), g t The gradient of the random objective function; f represents the gradient operator, which is the partial derivative with respect to the parameter θ; t (θ t-1 θ represents the stochastic objective function at the current time step; t-1 Parameters to be updated; m t =β1m t-1 +(1-β1)g t (23); In equation (23), m t β1 is the first-moment estimate; m is the exponential decay rate of the first-moment estimate; t-1 G represents the previous first-moment estimate; t The gradient of the random objective function; In equation (24), v t β1 is the partial second moment estimate; v is the exponential decay rate of the partial second moment estimate; t-1 This represents the second-order moment estimate from the previous iteration; In equation (25), θ t This represents the model parameter vector after the current iteration; α is the learning rate. ε represents the deviation correction coefficient corresponding to the first-order and second-order moment estimates; ε represents the numerical stability constant. Keep updating until θ t Convergence occurs, ending the loop; initial values ​​m0 = 0, v0 = 0, ε > 0 and close to 0; this process is repeated iteratively until convergence.

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