A Two-Stage Method for Identifying Key Factors Affecting the Oscillation Hosting Capacity of Renewable Energy Systems Using Participation Factors and XGBoost

Abstract

With the increasing penetration of renewable energy in China’s power system, wide-band oscillations with multiple modes have emerged, posing new challenges to the assessment of renewable energy oscillation hosting capacity. At present, the construction of artificial intelligence-based assessment models still relies heavily on researchers’ subjective experience when selecting input features, which lacks theoretical justification. Moreover, the expansion of system scale increases data dimensionality and introduces a higher risk of model overfitting. To address these issues, this paper proposes a two-stage key feature selection method based on participation factors and XGBoost. First, the participation factor theory is utilized to establish the functional mapping between system electrical quantities and oscillatory characteristics, enabling an initial identification of the electrical variables most relevant to renewable energy oscillation hosting capacity. Second, to mitigate the curse of dimensionality brought by large-scale systems, a variational autoencoder is employed to compress the initial feature set and extract its latent representations. Finally, XGBoost is applied to these latent representations to further identify the most critical features that accurately reflect the oscillation hosting capacity of renewable energy. Experimental results on a wide-band oscillation dataset show that active power achieves the highest importance score among all features; moreover, a model using only active-power data attains an accuracy of approximately 97%, demonstrating its effectiveness as the most strongly correlated and least redundant key feature subset.

1. Introduction

With the rapid development of China’s power system, the penetration of renewable energy and power electronic devices has continued to increase [1,2]. The complex interactions among synchronous generators, power electronic converters, and the grid have resulted in the emergence of wide-band oscillations containing multiple oscillatory modes, posing significant challenges to secure and stable system operation [3]. Consequently, accurately assessing the oscillation hosting capacity of renewable energy sources and identifying the dominant influencing factors have become increasingly important [4,5].

In recent years, artificial intelligence (AI) techniques have progressed rapidly [6]. Leveraging massive real-time measurements provided by Wide Area Measurement Systems (WAMS), AI-based approaches can learn the dynamic behavior of power systems under diverse operating conditions without depending on detailed physical models [7]. This capability offers a promising alternative for evaluating the oscillation hosting capacity of renewable-rich power systems [8].

Meanwhile, to improve generalization and credibility in safety-critical power system applications, increasing attention has been paid to hybrid learning paradigms that integrate physical priors with data-driven models, such as physics-informed learning, model-guided learning, and system-theoretic constrained identification [9].

In modern power systems, constructing an appropriate feature set that effectively characterizes system stability is essential for efficient oscillation analysis [10]. Identifying the electrical quantities that exert the greatest influence on wide-band oscillatory behavior is a key prerequisite for improving the accuracy of AI-based assessments. However, in high-renewable-penetration systems, the large number and variety of electrical variables make it impractical to use all measurements directly [11]. Doing so leads to excessively complex model structures, increased computational burden, and a higher risk of overfitting, ultimately limiting applicability in real-world scenarios [12]. Although existing studies have explored feature selection to some extent, many rely heavily on engineering experience and lack systematic theoretical justification [13,14].

For example, Reference [15] employs Copula-based transfer entropy between internal wind turbine states and bus power measurements to infer causal propagation paths; Reference [16] utilizes low-dimensional compressed-sensing-based power measurements as inputs to a neural network; Reference [17] selects bus voltage phase angles for forced oscillation analysis; Reference [18] extracts oscillatory information from active power, reactive power, voltage magnitude, and frequency measured by PMUs; and Reference [19] analyzes ultra-low-frequency oscillations using generator speed deviations and mechanical power measurements [20].

Although these studies provide valuable insights, their feature selection largely depends on subjective judgment and does not fully explain why certain electrical quantities are more strongly related to oscillatory dynamics than others. As a result, the identification of key factors influencing oscillation hosting capacity remains insufficient and lacks rigorous system-theoretic support.

Reference [21] introduces a closed-loop interconnected modeling approach combined with participation factor analysis, demonstrating that active power, reactive power, voltage, and current at wind farm terminals are strongly correlated with system oscillatory modes. This provides a theoretically grounded feature set. Nevertheless, as system scale increases, the number of nodes and measurement variables grows substantially, leading to larger training datasets and significantly expanded neural network sizes. This results in higher computational demands, greater memory consumption, and increased overfitting risk [22], ultimately degrading the performance of learning-based models. Therefore, further dimensionality reduction and refined feature selection remain necessary.

To address these challenges, this paper proposes a two-stage key feature selection method for assessing renewable energy oscillation hosting capacity. First, participation factor theory is used to establish the functional mapping between electrical quantities and oscillatory characteristics, enabling a preliminary screening of features most relevant to oscillation hosting capacity. Although this method does not directly quantify hosting capacity, it classifies system stability under predefined disturbances, thereby indirectly supporting the evaluation of hosting capacity. Second, to mitigate the curse of dimensionality in large-scale systems, a variational autoencoder is employed to extract low-dimensional latent representations of the initially selected features [23]. Finally, XGBoost is applied to these latent representations to quantify feature importance and identify the critical electrical variables that most accurately characterize the oscillation hosting capacity of renewable energy [24]. The effectiveness and accuracy of the proposed method are validated using a wide-band oscillation dataset generated from a four-machine, two-area system with integrated wind generation.

2. Preliminary Screening of Renewable Energy Oscillation Features Based on Participation Factors

To identify electrical features that are most relevant to the oscillation hosting capability of renewable energy from a physical perspective, it is necessary to clarify the relationship among oscillatory modes, internal state variables, and measurable electrical quantities. In this section, participation factor theory is employed to analyze oscillatory behavior at the state level, while the output equations are further utilized to establish a link between dominant oscillatory states and practically measurable signals, enabling a preliminary feature screening.

A typical scenario of a direct-drive wind turbine connected to an infinite-bus AC system is considered, as illustrated in Figure 1. The wind turbine together with its control system is modeled as the wind turbine subsystem, whereas the main grid and other connected components are treated as the power system subsystem.

Let $X_w$ denote the state vector of the wind turbine subsystem, including mechanical, electrical, and control-related states. The input vector is defined as

$$U_w={[\Delta V_w,\Delta I_w]}^T,$$

where $V_w$ and $I_w$ represent the terminal voltage and current at the point of connection (PoC), respectively. The incremental active and reactive power injected into the grid is defined as the output vector

$$\Delta Y_w={[\Delta P_w,\Delta Q_w]}^T.$$

The linearized state-space model of the wind turbine subsystem can be expressed as

$$\left\{\begin{array}{c}\Delta {\dot{X}}_w=A_w\Delta X_w+B_w\Delta U_w,\hfill \\ \Delta Y_w=C_w\Delta X_w+D_w\Delta U_w.\hfill \end{array}\right.$$

(1)

Let $X_g$ denote the state vector of the power system subsystem, whose linearized model is given by

$$\left\{\begin{array}{c}\Delta {\dot{X}}_g=A_g\Delta X_g+B_g\Delta U_w,\hfill \\ \Delta Y_w=C_g\Delta X_g+D_g\Delta U_w.\hfill \end{array}\right.$$

(2)

By combining the two subsystems, the overall small-signal model of the grid-connected wind turbine system can be written as

$$\left[\begin{array}{c}\Delta {\dot{X}}_w\\ \Delta {\dot{X}}_g\end{array}\right]=A_{wg}\left[\begin{array}{c}\Delta X_w\\ \Delta X_g\end{array}\right],$$

(3)

where $A_{wg}$ is the closed-loop characteristic matrix that captures the essential oscillatory dynamics around the steady-state operating point.

Based on the left and right eigenvectors of $A_{wg}$, the participation factor is calculated to quantify the contribution of each state variable to a specific oscillatory mode, which is defined as

$$p_{ki}={\displaystyle \frac{v_{ki}{u}_{ki}}{v_i^T{u}_i}},$$

(4)

where $u_{ki}$ and $v_{ki}$ denote the kth elements of the right and left eigenvectors associated with the ith mode, respectively.

It should be emphasized that participation factors characterize modal contributions at the state-variable level rather than directly at the measurement level. To relate the participation analysis to practically measurable quantities, the output equations are further considered. When an oscillatory mode exhibits large participation factors in wind-turbine-related states, and these states significantly affect the terminal electrical quantities through the output matrices $C_w$ and $D_w$, the corresponding oscillatory behavior will be observable in the terminal measurements.

Since the system matrix $A_{wg}$ depends on the steady-state operating point, which is determined by the electrical quantities at the PoC, the oscillation-related index L can be linked to measurable variables through a multi-stage mapping:

$$L=f\left(p\right)=f\left(h\right(A\left)\right)=f\left(h\right(g\left(E\right)\left)\right)=l\left(E\right),$$

(5)

where

$$E=[Y_w,U_w]=[P_w,Q_w,V_w,I_w]$$

denotes the vector of measurable electrical quantities at the PoC. Here, L represents an index characterizing the renewable energy oscillation hosting capability, and the mappings describe the relationships among operating conditions, system matrices, participation factors, and oscillation characteristics.

In summary, although participation factors are defined at the state level, their physical implications can be reflected in the terminal active power, reactive power, voltage magnitude, and current through the output equations and operating-point dependence. These quantities are directly measurable in practice and therefore constitute a suitable candidate feature set for constructing wideband oscillation samples and extracting oscillatory features in data-driven assessments of renewable energy oscillation hosting capability.

3. Fine-Grained Screening of Wide-Band Oscillation Features Based on Variational Autoencoder and XGBoost

3.1. Framework for Fine-Grained Feature Screening

Based on the preliminary screening using participation factors in the previous section, the electrical quantities identified as closely related to wide-band oscillatory behavior include active power P, reactive power Q, voltage magnitude U, and current I. However, as power system size expands and the number of generators increases, directly applying gradient-boosting methods such as XGBoost to the original high-dimensional feature space often leads to two major issues: (1) a higher risk of model overfitting due to the large dimensionality of the dataset and  (2) significantly increased training time. These issues may degrade the accuracy of key feature extraction and ultimately affect the reliability of oscillation hosting capacity assessment.

To mitigate these challenges, a variational autoencoder (VAE) is introduced as a preprocessing step prior to XGBoost. By learning the latent structure of the original electrical measurements, the VAE effectively compresses the high-dimensional data and extracts low-dimensional representations that preserve essential oscillatory information. This not only reduces data redundancy but also enhances the generalization capability of the subsequent feature evaluation process.

Once the latent representations are obtained, they are fed into the XGBoost model to compute importance scores for each electrical quantity, enabling more refined screening of oscillation-related features. This two-stage procedure—combining deep-learning-based dimensionality reduction with gradient-boosting-based importance evaluation—reduces model complexity, alleviates overfitting, and improves the accuracy of identifying critical electrical variables that influence the oscillation hosting capacity of renewable energy.

The overall workflow is illustrated in Figure 2, and the major steps are summarized as follows:

1.

Data acquisition and preprocessing: Collect wide-band oscillation measurements, including active power P, reactive power Q, voltage magnitude U, and current I, and perform necessary preprocessing such as normalization and noise filtering.

2.

Latent feature extraction using VAE: Input the preprocessed high-dimensional measurements into a variational autoencoder and train the model to obtain low-dimensional latent representations that capture the essential characteristics of the oscillation-related electrical quantities.

3.

Feature importance evaluation using XGBoost: Feed the latent representations into the XGBoost model to compute importance scores for each electrical feature, completing the fine-grained screening of wide-band oscillation variables.

Through this two-stage framework, the proposed method integrates the physical interpretability of participation-factor-based screening with the robustness and efficiency of data-driven learning. This ensures that the selected features are both theoretically justified and statistically reliable, providing a sound basis for subsequent modeling and evaluation of the oscillation hosting capacity of renewable energy systems.

3.2. Variational Auto-Encoder

The Variational Auto-Encoder (VAE) is a probabilistic generative model constructed using a neural-network-based encoder–decoder architecture. Unlike conventional autoencoders that learn deterministic latent representations, the VAE introduces a stochastic latent space, allowing the model to perform both dimensionality reduction and generative modeling.

The VAE consists of two main components:

1.

Encoder: Posterior distribution modeling. The encoder maps each input sample x to the parameters of a latent-variable posterior distribution $q_{\varphi }\left(z\right|x)$, where $\varphi$ denotes the encoder parameters. This posterior is typically modeled as a multivariate Gaussian whose mean and variance are learned from data.

2.

Decoder: Data reconstruction. The decoder reconstructs the input from the latent variable z according to the conditional distribution $p_{\theta }\left(x\right|z)$, where $\theta$ denotes the decoder parameters. Maximizing the likelihood of the reconstructed output enables the decoder to preserve essential characteristics of the input data.

Since the true posterior distribution of z is intractable, the VAE minimizes the Kullback–Leibler (KL) divergence between the learned posterior $q_{\varphi }\left(z\right|x)$ and a prior distribution $p\left(z\right)$, typically a standard normal distribution:

$$\underset{\varphi }{min}{D}_{\mathrm{KL}}\left(q_{\varphi }\left(z\right|x)\parallel p\left(z\right)\right).$$

(6)

The KL divergence is computed as

$$D_{\mathrm{KL}}\left(q_{\varphi }\left(z\right|x)\parallel p\left(z\right)\right)=\int q_{\varphi }\left(z\right|x)log{\displaystyle \frac{q_{\varphi }\left(z\right|x)}{p\left(z\right)}}dz.$$

(7)

To ensure faithful reconstruction, the VAE employs a reconstruction loss based on the mean squared error (MSE):

$$L_r={\displaystyle \frac{1}{n}}\sum _{i=1}^n{∥x_i-x_i^{\prime }∥}^2.$$

(8)

The overall optimization objective combines reconstruction accuracy and latent-space regularization:

$$L={\mathbb{E}}_{q_{\varphi }\left(z\right|x)}\left[-log{p}_{\theta }\left(x\right|z)\right]+D_{\mathrm{KL}}\left(q_{\varphi }\left(z\right|x)\parallel p\left(z\right)\right).$$

(9)

By minimizing the loss in (10), the VAE learns compact and informative latent representations from high-dimensional electrical measurements such as P, Q, U, and I, providing effective low-dimensional inputs for the subsequent XGBoost-based feature importance analysis.

3.3. Theoretical Foundations of XGBoost

XGBoost (eXtreme Gradient Boosting) is an efficient and scalable learning algorithm based on gradient-boosted decision trees. The model constructs an ensemble of weak learners, each trained to correct residual errors from the previous iteration.

Formally, the prediction of XGBoost is

$${\hat{y}}_i=\sum _{k=1}^K{f}_k\left(x_i\right),f_k\in F,$$

(10)

where F denotes the space of regression trees.

The objective function is

$$\mathrm{Obj}\left(\theta \right)=\sum _{i=1}^{n}l(y_i,{\hat{y}}_i)+\sum _{k=1}^K\Omega \left(f_k\right),$$

(11)

where the regularization term is defined as

$$\Omega \left(f_k\right)=\gamma T+{\displaystyle \frac{1}{2}}\lambda {\parallel w\parallel }^2,$$

(12)

with T denoting the number of leaf nodes and w the vector of leaf weights.

To optimize the t-th tree, XGBoost applies a second-order Taylor expansion to the objective:

$$\mathrm{Obj}\left(\theta \right)\approx \sum _{i=1}^n\left[g_i{f}_t\left(x_i\right)+{\displaystyle \frac{1}{2}}{h}_i{f}_t^2\left(x_i\right)\right]+\Omega \left(f_t\right),$$

(13)

where $g_i$ and $h_i$ denote the first- and second-order derivatives of the loss function.

Grouping by leaf nodes yields

$$\mathrm{Obj}\left(\theta \right)=\sum _{j=1}^T\left[\sum _{i\in I_j}{g}_i{w}_j+{\displaystyle \frac{1}{2}}\left(\sum _{i\in I_j}{h}_i+\lambda \right)w_j^2\right]+\gamma T,$$

(14)

where $I_j$ denotes the set of samples assigned to leaf j.

Taking the derivative with respect to $w_j$ gives the optimal leaf weight

$$w_j^{*}=-{\displaystyle \frac{{\sum }_{i\in I_j}{g}_i}{{\sum }_{i\in I_j}{h}_i+\lambda }}.$$

(15)

Substituting $w_j^{*}$ back into the objective yields the optimal score for evaluating tree structure:

$${\mathrm{Obj}}^{*}\left(\theta \right)=-{\displaystyle \frac{1}{2}}\sum _{j=1}^T{\displaystyle \frac{{\left({\sum }_{i\in I_j}{g}_i\right)}^2}{{\sum }_{i\in I_j}{h}_i+\lambda }}+\gamma T.$$

(16)

This optimization criterion allows XGBoost to efficiently evaluate and construct decision trees, ultimately yielding a powerful ensemble model. In this work, XGBoost is applied to the latent representations extracted by the VAE to compute fine-grained importance scores for oscillation-related electrical variables.

4. Analysis of Simulation Results

4.1. Sample Construction

This section uses a four-machine two-area system integrated with wind generation, interfacing with the CloudPSS platform through Python 3.9 scripts for automated model modification and batch time-domain simulations. The goal is to ensure comprehensive and uniform coverage of the sample space, enhancing the generality and representativeness of the simulation results. Key factors influencing the assessment of renewable energy oscillation hosting capacity are considered, including disturbance location, frequency, amplitude, and overall system load level.

Periodic sinusoidal disturbances are applied to different generators in the system. These disturbances act either on the mechanical torque of the prime mover or on the terminal voltage of the generator, exciting wide-band oscillatory responses under various system configurations. The system load level varies between 90% and 110% of the nominal load, in increments of 5%. The disturbance amplitude ranges from 0.1 p.u. to 0.5 p.u., with steps of 0.05 p.u. The disturbance frequency spans two ranges, 10–40 Hz and 70–100 Hz, with a resolution of 0.2 Hz. These variations ensure a broad exploration of operating conditions and disturbance impacts, providing a robust sample space for oscillation hosting capacity analysis.

Python-based automation scripts invoke the CloudPSS time-domain simulation engine to generate the required samples. For each simulation case, measurements are collected from the generator terminal buses, including active power, reactive power, voltage magnitude, and current. These measurements are then analyzed to determine the system’s stability under the applied disturbances.

Time-domain simulations use a fixed time step of 1 ms, corresponding to a sampling frequency of 1000 Hz, ensuring strict adherence to the Nyquist–Shannon sampling theorem. Given that the highest frequency component of the applied disturbances is 100 Hz, the minimum required sampling frequency would be 200 Hz. The chosen sampling rate of 1000 Hz, with a Nyquist frequency of 500 Hz, is well above the minimum, fully eliminating any risk of aliasing and ensuring accurate capture of the frequency content in the 10–100 Hz range. For each simulation case, 500 consecutive data points are recorded, corresponding to a 0.5-s data window. This window length provides sufficient time resolution for capturing oscillations. For a 10 Hz oscillation, the window captures approximately 5 full cycles, and for a 100 Hz oscillation, approximately 50 full cycles, ensuring reliable modal identification and feature extraction.

The disturbance frequency bands of 10–40 Hz and 70–100 Hz are selected based on the dynamics of high-penetration renewable energy systems. The 10–40 Hz range typically encompasses sub-synchronous and super-synchronous oscillations, often associated with shaft torsional interactions, converter-grid impedance interactions, and control-induced resonances. The 70–100 Hz range targets high-frequency oscillations potentially excited by power electronic switching characteristics and associated control dynamics. For the studied four-machine two-area system with a direct-drive wind turbine, oscillation modes and interactions relevant to oscillation hosting capacity are expected to occur within these frequency ranges or be influenced by them, making the selected frequency bands both physically meaningful and relevant to the dynamics under study.

Sample labeling is performed based on the system’s operating conditions and the disturbance configuration. Specifically, the damping coefficient ($\sigma$) is extracted from the active power response at the generator terminal using the Prony method. The damping coefficient, an important parameter reflecting the oscillation characteristics and trends of the system, is calculated as follows:

$$x\left(t\right)=A_k{e}^{-\sigma (t-t_k)}sin(2\pi ft+\theta ),t\in [t_k,t_k+m{T}_s]$$

(17)

where $A_k$ is the modal amplitude, f is the oscillation frequency, $\theta$ is the initial phase, k is the number of sampling points, m is the data window length, $T_s$ is the sampling period, and $t_k$ is the current sampling time.

The damping coefficient, $\sigma$, is then computed by comparing the modal amplitudes extracted from two adjacent time windows (data segments) of the generator terminal active-power response.

$$\sigma \left(t_k\right)={\displaystyle \frac{ln\left(\frac{A\left(t_0\right)}{A\left(t_k\right)}\right)}{2\pi (k-1)}}\sqrt{1+{\left({\displaystyle \frac{1}{2\pi (k-1)}}ln\left({\displaystyle \frac{A\left(t_0\right)}{A\left(t_k\right)}}\right)\right)}^2}$$

(18)

Based on the calculated damping coefficient, the labeling rule is as follows: if $\sigma >0$ (indicating positive damping), the system is stable and can “host” the disturbance, and the sample is labeled “1” (stable). If $\sigma \le 0$ (indicating non-positive damping), the system is unstable, and the sample is labeled “0” (unstable). This process completes the construction of the dataset, which is then used for analysis and modeling.

For example, if the damping coefficient is found to be $\sigma =0.15$, the oscillation shows a decaying trend, indicating that the system is stable under the given operating conditions and disturbance, and is labeled “1” (stable). Conversely, if the damping coefficient is $\sigma =-0.05$, the system exhibits instability, and the sample is labeled “0” (unstable).

4.2. Electrical Feature Dimensionality Reduction Based on Variational Autoencoder

To accelerate the convergence of neural network training and reduce the overall computational cost, data normalization is an effective preprocessing technique. In this work, a max–min normalization approach is adopted to scale the collected electrical measurements into the interval $[0, 1]$. The normalization process is expressed as:

$$p^{\prime }(x,t)={\displaystyle \frac{p(x,t)-p{\left(x\right)}_{min}}{p{\left(x\right)}_{max}-p{\left(x\right)}_{min}}},$$

(19)

where $p(x,t)$ denotes the value of the x-th sample at time t, $p^{\prime }(x,t)$ is the corresponding normalized value, and $p{\left(x\right)}_{max}$ and $p{\left(x\right)}_{min}$ represent the maximum and minimum values of the x-th sample, respectively.

The variational autoencoder (VAE) is then applied to the wide-band oscillation waveform dataset to perform dimensionality reduction. The network is trained using the Adam optimizer, where the learning rate governs the magnitude of parameter updates. A batch size of 32 is adopted, indicating that 32 samples are fed into the network during each training iteration. The total number of training epochs is set to 500, ensuring that the entire dataset is repeatedly traversed to achieve stable convergence.

To effectively extract compact yet informative features from the high-dimensional oscillation waveforms, a two-stage feature extraction and fusion process is designed.

Stage 1: Deep Feature Encoding. For each electrical quantity (active power P, reactive power Q, voltage magnitude U, and current I), its 500-point time series (spanning 0.5 s) is independently processed by a dedicated VAE encoder. The encoder maps the high-dimensional sequence into a 25-dimensional latent vector $\mathbf{z}\in {\mathbb{R}}^{25}$, which compactly captures the essential oscillatory patterns and dynamic characteristics of the original waveform. This intermediate latent representation ensures the representativeness of the extracted features. Figure 3 visually illustrates such a 25-dimensional latent vector generated for an exemplary electrical quantity.

Stage 2: Feature Fusion and Aggregation. To transform the information-rich 25-dimensional latent representation into a fixed-dimensional scalar feature suitable for subsequent machine learning models (e.g., XGBoost) while preserving its core information, a feature fusion step is introduced. Specifically, the first principal component (FPC) is extracted from each 25-dimensional latent vector $\mathbf{z}$, serving as the final scalar feature f for that electrical quantity. The first principal component represents the direction of maximum variance in the latent space, thereby summarizing the most significant variation pattern with a single value.

Mathematically, PCA is performed on mean-centered latent vectors. Let ${\mathit{\mu }}_z$ denote the mean of $\mathbf{z}$ over the training fold, and define $\tilde{\mathbf{z}}=\mathbf{z}-{\mathit{\mu }}_z$. The scalar feature is then computed as

$$f={\mathbf{w}}^T\tilde{\mathbf{z}},$$

(20)

where $\mathbf{w}$ is the eigenvector corresponding to the largest eigenvalue of the covariance matrix of $\tilde{\mathbf{z}}$ estimated on the training fold. The same ${\mathit{\mu }}_z$ and $\mathbf{w}$ are then applied to the corresponding test fold to avoid information leakage.

Through this two-stage process, each electrical quantity’s 500-point sequence is transformed into a single, physically meaningful scalar feature ($f_P$, $f_Q$, $f_U$, $f_I$). These four scalars are then concatenated to form a 4-dimensional feature vector $\mathbf{f}={[f_P,f_Q,f_U,f_I]}^T$ for each oscillation sample. Consequently, for a dataset with M samples, the final feature matrix input to XGBoost has a shape of $(M,4)$. This design enables a direct and interpretable assessment of the importance of the four original electrical quantities.

The VAE is implemented with a symmetric encoder–decoder structure. All data normalization parameters, VAE models, and PCA-based aggregation operators are fitted exclusively using the training folds in each cross-validation iteration, and then applied to the corresponding test fold. The encoder for each electrical quantity consists of fully connected (Dense) layers that progressively reduce the dimensionality from 500 to 25. The decoder mirrors this structure, reconstructing the original 500-point sequence from the 25-dimensional latent vector. After obtaining the latent vector, an additional aggregation layer (implemented via principal component analysis) is applied to produce the final scalar feature. The detailed layer-by-layer architecture for processing a single electrical quantity sequence is summarized in

Table 1. Layer-wise architecture of a single VAE branch for one electrical quantity (input length = 500). The same branch is applied independently to P, Q, U, and I.

Layer	Input Dimension	Neurons	Output Dimension
Input	$1\times 500$		$1\times 500$
Dense	$1\times 500$	256	$1\times 256$
Dense	$1\times 256$	64	$1\times 64$
Dense (Encoder output)	$1\times 64$	25	$1\times 25$
Dense	$1\times 25$	64	$1\times 64$
Dense	$1\times 64$	256	$1\times 256$
Dense (Reconstruction)	$1\times 256$	500	$1\times 500$

.

As illustrated in Figure 4, the reconstructed waveform closely matches the original waveform, demonstrating that the encoder effectively captures essential oscillatory characteristics and that the decoder successfully restores waveform details. This confirms that the proposed method can reliably compress and reconstruct wide-band oscillation signals while extracting compact and meaningful latent features.

4.3. Key Feature Extraction Based on XGBoost

The feature matrix $\mathbf{Z}\in {\mathbb{R}}^{M\times 4}$ obtained from the process described in Section 4.2—where each row is a sample’s directly interpretable feature vector $[f_P,f_Q,f_U,f_I]$—serves as the input to the XGBoost model. This setup allows for the evaluation of the relative contribution of each of the four original electrical quantity features to the classification of oscillation hosting capacity.

It should be noted that no independent hold-out test set is used in this study. All reported test results correspond to the test folds in the five-fold cross-validation procedure. K-fold cross-validation, originally proposed by Seymour Geisser, is a widely used method for model evaluation and selection. As illustrated in Figure 5, this study adopts five-fold cross-validation (i.e., $K=5$). Compared with choosing $K=3$ or $K=10$, selecting $K=5$ achieves a desirable balance between bias and variance, thereby improving the accuracy and reliability of model assessment while keeping computational complexity at a reasonable level. The procedure of K-fold cross-validation can be summarized as follows:

1.

The dataset is randomly partitioned into K subsets of equal size.

2.

Each subset is used once as the test fold, while the remaining $K-1$ subsets are combined to form the training folds.

3.

Each iteration yields a model and its corresponding prediction error. The cross-validation score is then obtained by averaging the K prediction errors.

4.3.1. Selection of the Number of Trees for Model Evaluation

To evaluate the performance of the XGBoost model, the Random Forest (RF) algorithm is used as a comparative baseline. Random Forest is also a widely adopted and powerful machine learning method within the family of ensemble learning algorithms. It is composed of multiple decision trees, and aggregates their predictions to enhance overall accuracy and generalization capability.

Five-fold cross-validation is employed to assess the model performance. The cross-validation scores of XGBoost and Random Forest under different numbers of trees (n_estimators) are shown in Figure 6. As illustrated in the figure, the five-fold cross-validation score of XGBoost consistently exceeds that of Random Forest. Notably, even when n_estimators = 1, XGBoost already achieves a relatively high score of approximately 0.8. The highest cross-validation score for XGBoost occurs at n_estimators = 18, reaching approximately 0.9826. Therefore, the number of trees in this study is set to 18.

4.3.2. Learning Curve Analysis

To further evaluate the performance of XGBoost, the learning_curve function is employed to generate the learning curves. This function directly outputs the number of training samples, the training scores, and the validation scores, illustrating how the model’s performance on both the training set and the validation set changes with increasing training data size. The learning curve provides an effective means to assess the model’s generalization ability and to determine whether it suffers from overfitting or underfitting.

The learning curves of XGBoost and Random Forest are shown in Figure 7 and Figure 8, respectively. The training score represents the performance obtained on each training subset, while the validation score corresponds to the five-fold cross-validation score for the same subset size. As shown in the figures, both the training and validation scores of XGBoost and Random Forest improve as the number of training samples increases. Moreover, the gap between the training and validation scores gradually narrows, indicating that increasing the training data significantly enhances the generalization capability of both models and that neither model exhibits overfitting nor underfitting.

However, for any given training set size, the training and validation scores of XGBoost remain consistently higher than those of Random Forest, demonstrating that XGBoost provides superior predictive performance in this task.

4.3.3. Feature Importance Ranking

The larger the importance score of an electrical feature, the greater its contribution to the model’s predictive decision making, indicating a stronger correlation with the target variable. As shown in Figure 9, active power exhibits the highest importance score (0.422), reflecting its crucial role in capturing the system’s real work. While active power is highly informative, it should not be regarded as a complete substitute for multi-signal measurements. Other features such as voltage, current, and reactive power together provide a more comprehensive understanding of the system’s behavior, making them preferred when available.

In contrast, line current shows the lowest importance score (0.204), possibly because variations in current exert only limited direct influence on the overall system stability; current fluctuations are often mitigated by the system’s internal control and regulation mechanisms. The importance scores of bus voltage and reactive power fall between these two extremes.

From a theoretical perspective, both reactive and active power are products of voltage and current, meaning that their coupling inherently contains complete voltage–current information. However, reactive power receives a lower importance score than active power. This may be attributed to its primary role in voltage regulation rather than directly reflecting oscillatory behavior. These observations suggest that, although both quantities arise from voltage–current coupling, the strength and nature of their coupling coefficients lead to different degrees of relevance to oscillation-source locations, and thus different importance scores.

Within each cross-validation iteration, feature importance estimation and threshold-based feature selection are performed using the training folds only. Since the model parameters have already been learned, the threshold serves as the criterion for determining which features are considered important—only those whose importance scores exceed the threshold are retained.

As shown in

Table 2. Feature threshold filtering.

Threshold	Features	Selected Features	Accuracy (%)	F1-Score
0.162	4	U, I, P, Q	97.14	0.971
0.204	3	U, P, Q	97.51	0.974
0.212	2	U, P	96.60	0.959
0.422	1	P	96.54	0.957

, when the threshold is set to 0.162, all features with importance scores greater than 0.162 are selected, resulting in four retained features: voltage U, current I, active power P, and reactive power Q. When the threshold is increased to 0.422, only active power P remains above the threshold and is therefore considered as a single-feature baseline for evaluating model performance.

The results in Table 2 reveal that using three features $(U,P,Q)$ yields even higher accuracy than using all four features $(U,I,P,Q)$. This suggests that reducing the feature set not only decreases model complexity and accelerates training, but also improves prediction accuracy by removing less informative features. However, it is emphasized that, when multi-signal measurements are available, the combination of $(U,P,Q)$ should be prioritized, as it provides a more robust and accurate model. In contrast, when resources are limited, active power P can serve as a baseline, but it is explicitly acknowledged that performance will degrade when used alone. Moreover, when only feature P is selected, the model achieves an accuracy of 96.54%, which is approximately 1% lower than when all features are used. This suggests that using P alone incurs a measurable performance loss compared with the best-performing multi-feature input $(U,P,Q)$, although it still provides a reasonably competitive baseline.

Therefore, $(U,P,Q)$ is preferred when multi-signal measurements are available, whereas P alone is reported only as a lightweight baseline (or a fallback option under strict measurement/communication constraints), with the associated performance loss explicitly acknowledged.

Overall, a leakage-free evaluation pipeline is adopted. For each fold of the five-fold cross-validation, the dataset is split into training and test folds. All preprocessing steps, including normalization, VAE training, latent feature aggregation, feature importance estimation, and threshold-based feature selection, are performed exclusively on the training folds. The trained models are then evaluated on the corresponding test fold. Final performance metrics are obtained by averaging the results across all folds.

4.4. Ablation Study and Analysis

This section conducts a two-level ablation study to validate (i) the effectiveness and interpretability of the proposed VAE–PCA feature engineering scheme and (ii) the independent contribution of each module in the overall pipeline. All experiments are performed on the same simulation dataset using an identical training strategy and a nested $5\times 4$-fold cross-validation protocol to ensure a fair comparison.

We first compare different feature construction strategies under a controlled setting where each method produces a four-dimensional feature vector, and each dimension explicitly corresponds to one electrical quantity in $\{P,Q,U,I\}$. Specifically, three feature sets are considered:

• Baseline A (Mean Features): The arithmetic mean of each 500-point time series is used as the feature value, yielding $[\overline{P},\overline{Q},\overline{U},\overline{I}]$.
• Baseline B (Damping-Coefficient Features): The Prony method is applied to the oscillatory response of each quantity to extract the damping coefficient $\sigma$ of the dominant mode, yielding $[{\sigma }_P,{\sigma }_Q,{\sigma }_U,{\sigma }_I]$.
• Proposed (VAE-PCA Features): Following the two-stage procedure in Section 4.2, we extract $[f_P,f_Q,f_U,f_I]$, where each f is an aggregated latent descriptor that preserves a direct correspondence to the original quantity.

Table 3. Performance comparison of different feature construction methods.

Feature Set	Selected Quantities	Accuracy (%)	F1-Score
Mean Features	$\{I,P,Q\}$	$95.87$	0.959
Damping-Coefficient Features	$\{U,I,Q\}$	$96.61$	0.966
VAE–PCA Features	$\{U,P,Q\}$	$97.51$	0.974

reports the average performance. The results show that VAE–PCA features consistently outperform both intuitive statistics and physics-inspired damping descriptors, indicating that the proposed representation captures more discriminative dynamics while maintaining per-quantity interpretability.

To quantify the marginal benefit of each component—participation-factor (PF) screening, VAE-based representation learning, PCA-based aggregation, and the XGBoost-based ranking/classification stage—we construct several pipeline variants by progressively removing or replacing key modules, while keeping the dataset, training protocol, and evaluation procedure unchanged.

We consider four representative configurations: (A) An end-to-end 1D-CNN that directly ingests the raw wide-band oscillation waveforms of size $4\times 500$, serving as a deep-learning baseline without physics priors or explicit feature engineering; (B)PF + XGBoost, which bypasses the VAE stage and feeds PF-screened signals into XGBoost to isolate the contribution of representation learning; (C) PF + VAE + SVM, which replaces XGBoost with SVM to assess the discriminability of the learned latent representations without XGBoost’s nonlinear ranking capability; and (D) the full proposed pipeline PF + VAE–PCA + XGBoost. The results are summarized in

Table 4. Performance comparison of different pipeline configurations under nested $5\times 4$-fold cross-validation.

Configuration	Accuracy (%)	F1-Score
(A) 1D-CNN on raw waveforms	$94.20$	$0.940$
(B) PF + XGBoost	$95.50$	$0.953$
(C) PF + VAE + SVM	$96.40$	$0.962$
(D) PF + VAE–PCA + XGBoost	$97.51$	$0.974$

.

The results demonstrate that each module contributes measurably to the final performance. In particular, removing the VAE stage leads to a clear degradation, while replacing XGBoost with SVM also reduces performance, confirming the necessity of combining physics-guided screening with learned representations and robust nonlinear ranking/classification.

4.5. Generalization Study on the IEEE 39-Bus System

To further evaluate the generalizability of the proposed framework beyond the four-machine two-area benchmark, an additional case study is conducted on the IEEE 39-bus system. This system is widely adopted as a representative large-scale interconnected power network and exhibits more complex topology, diverse generator dynamics, and richer modal interactions, thereby providing a suitable testbed for assessing scalability to large and heterogeneous power systems.

In this study, the IEEE 39-bus system is configured to emulate a renewable-rich operating scenario by replacing a subset of conventional synchronous generators with renewable energy units interfaced via power electronic converters. Importantly, the sample construction procedure, disturbance design, sampling strategy, and labeling rule are kept exactly the same as those described in Section 4.1 to ensure a fair and consistent evaluation across different systems. Specifically, periodic sinusoidal disturbances are injected at selected generator buses, acting either on the mechanical torque or the terminal voltage. The system load level varies from 90% to 110% of the nominal value (step: 5%), the disturbance amplitude ranges from 0.1 p.u. to 0.5 p.u. (step: 0.05 p.u.), and the disturbance frequency spans two bands (10–40 Hz and 70–100 Hz) with a resolution of 0.2 Hz.

Time-domain simulations are performed with a fixed time step of 1 ms, corresponding to a sampling frequency of 1000 Hz. For each disturbance scenario, 500 consecutive samples (0.5 s window) of terminal active power P, reactive power Q, voltage magnitude U, and current I are recorded. Sample labels are generated using the same Prony-based damping criterion as in the benchmark system: samples with positive damping are labeled as stable (label $=1$), while those with non-positive damping are labeled as unstable (label $=0$).

The proposed two-stage feature extraction pipeline (VAE encoding followed by PCA-based aggregation) and the XGBoost classifier are applied without any modification to the network architecture, hyperparameters, or training strategy. A leakage-free five-fold cross-validation protocol is adopted. In each fold, all preprocessing steps—including normalization, VAE training, PCA-based aggregation, feature-importance estimation, and threshold-based feature selection—are fitted exclusively on the training folds and then applied to the corresponding test fold.

Table 5. Generalization results on the IEEE 39-bus system (five-fold cross-validation).

System	Selected Features	Accuracy (%)	F1-Score
Four-machine two-area	$\{U,P,Q\}$	97.51	0.974
IEEE 39-bus system	$\{U,P,Q\}$	96.83	0.968
IEEE 39-bus system (P only)	$\left\{P\right\}$	95.92	0.956

summarizes the classification performance on the IEEE 39-bus system, along with the benchmark results for comparison. The results show that the proposed method maintains high performance on a larger and more heterogeneous system. Moreover, the feature-importance ranking exhibits the same trend as that observed in the four-machine two-area system: active power remains the most influential feature, followed by voltage magnitude and reactive power, while current is relatively less informative. Although a slight performance degradation is observed due to the increased system complexity and richer modal interactions, the decrease is marginal, supporting the scalability and robustness of the proposed framework.

5. Conclusions

This study proposes a two-stage method for extracting key wide-band oscillatory response features to support renewable energy oscillation hosting capacity assessment. The work is motivated by the fact that existing AI-based assessment models often rely on operators’ subjective judgment when selecting input variables, and that high-dimensional system measurements in large-scale power grids significantly increase the risk of model overfitting. By integrating participation-factor analysis with the XGBoost framework, the proposed approach provides both theoretical grounding and data-driven refinement for identifying the most informative electrical quantities.

Using wide-band oscillation data generated from a four-machine two-area benchmark system with wind integration, the effectiveness of the proposed method is demonstrated through systematic simulations. Participation-factor analysis reveals that generator terminal active power, reactive power, voltage magnitude, and current exhibit the strongest sensitivity to oscillatory behavior, forming a physics-based preliminary feature set. A variational autoencoder is then employed to compress large volumes of oscillatory measurement data into compact latent representations while preserving essential waveform characteristics, indicating that the learned low-dimensional features successfully capture the intrinsic oscillatory patterns. On this basis, XGBoost performs fine-grained feature importance ranking, identifying active power as the most informative and least redundant variable in relation to oscillation propagation and dynamic response, while also demonstrating that eliminating less important features can reduce model complexity without degrading assessment accuracy.

Overall, the proposed two-stage screening framework establishes a reliable and theoretically interpretable pathway for feature selection in renewable-energy-dominated systems. Although this method indirectly supports hosting capacity evaluation through stability classification, future research could explore how this approach can be integrated with more precise hosting capacity quantification methods. Future research may further explore how the extracted active-power-based features, combined with advanced neural architectures and spatiotemporal characteristics of wide-band oscillations, can enhance the accuracy, generalization ability, and interpretability of oscillation hosting capacity evaluations in high-renewable power grids.