From data to decision: a holistic data-driven method for HVDC commutation failure pre-judgement

1 Introduction

Commutation failure (CF) prediction is critical to the operation of HVDC transmission systems, as it enables early identification of potential risks and provides a valuable time window for timely control actions to prevent fault propagation, protect equipment, and maintain system stability. Existing CF prediction methods are typically based on commutation voltage or extinction angle assessment, which can be summarized as follows. (i) Critical voltage based methods: the indicators are typically designed based on empirical experience or quasi-steady-state equations (Wang et al., 2025). However, limited accuracy is observed in complex systems or under fault conditions. (ii) Waveform transformation: for example, ABB's CFPREV module applies an abc–αβ transformation to commutation voltage during faults and compares the results with preset criteria to predict CF. However, the criteria are ill-suited to complex scenarios (He et al., 2023), and the sensitivity degrades under phase-to-phase faults or faults through large zero-sequence impedance (Zhang Y. L. et al., 2024). (iii) Component detection and comparison method: More precise CF prediction can be achieved by detecting specific waveform components and comparing them to reference values (Kuang et al., 2026). Yet, these references still require empirical or trial-based determination.

In summary, commutation voltage based methods primarily consider external disturbances, but neglect complex characteristics of the AC system and HVDC control behavior. Extinction angle based methods better reflect the physical essence of CF. For example, (Li et al., 2021) derives extinction angle estimation formulas under various fault types and commutation voltages. However, such models typically oversimplify primary systems and DC control, limiting the accuracy.

Therefore, the CF prediction should integrate both external disturbances and system response, treating the HVDC system as a complex AC–DC coupled, non-linear, high-dimensional and time-varying system (Zhang G. et al., 2024). Data-driven approaches have achieved remarkable success in solving numerous high-dimensional, complex non-linear problems (Liu et al., 2023). Leveraging the abundance of simulation and field operation data, data-driven modeling has the potential to essentially improve CF prediction accuracy.

Literature (Wang et al., 2019) proposes extinction angle estimation based on harmonic components in the commutation voltage, extracted by Fourier analysis, but the timeliness is poor. (Cui et al., 2020) estimates the commutation voltage via data-driven models incorporating multi-infeed factors and compares the result to a threshold to predict CF, though the data-driven model is merely used to predict the fundamental component in the commutation voltage. (Huang et al., 2020) combines a physical model to predict commutation voltage and DC current with a data-driven model for extinction angle estimation. However, simplifications in the physical model still compromise accuracy. Furthermore, these studies show that data-driven methods mainly support state estimation or specific submodules in the CF prediction scenes, rather than achieving end-to-end prediction from raw measurements. Thus, data-driven CF predictions face several challenges: (i). there is a lack of evaluation on the suitability of mature classification algorithms for CF prediction, (ii). in real systems commutation voltage waveforms are complex and highly correlated with CF processes, extracting informative and timely features is non-trivial, and (iii). engineering applications demand both high accuracy and low missed detection rates. However, real HVDC operation datasets are lopsided, with few samples near the CF/non-CF boundary.

Aiming at the challenges, this paper proposes a data-driven CF prediction method that considers both DC control and AC system dynamic responses. First, performance evaluation criteria for CF classification algorithms are designed, and suitable data-driven classifiers are selected. A feature matrix is constructed using four sampling points from the commutation voltage, and then a rapid feature extraction method is proposed. To address the sample imbalance problem and meet engineering performance requirements, a solution combining cost-sensitive learning and efficient sample generation is introduced. Finally, results from a case study validate the proposed feature extraction method's efficiency and accuracy and demonstrate the proposed method's superiority in both speed and precision compared to conventional approaches.

2 Performance evaluation of classification algorithms to predict CF

The commutation-status prediction is cast as a binary classification task in supervised learning (Goodfellow et al., 2016), where sampled signal features serve as the classifier inputs and their labels as the outputs. A classifier model is then obtained through supervised training.

Among the various supervised classification methods, the support vector machine (SVM) (Hao et al., 2022; Li and Yang, 2022), constructs a hyperplane in the feature space to approximate the target function. Thus, it overcomes issues of local optima and the “curse of dimensionality” and effectively controls the global generalization error—striking a balance between learning accuracy and generalization capability under limited samples. In online applications, the SVM needs only store a small set of support vectors, making it well suited to the learning on small-sample datasets, and well match the real-time CF prediction requirement.

Given a training set *S* = {(x₁, y₁), (x₂, y₂), …, (x_*n*, y_*n*)}, we define the functional margin γi^ of each sample as in Equation 1. By normalizing the functional margin of each sample with respect to the hyperplane S(w, b) using the hyperplane's normal vector w, we obtain the geometric margin γ_*i* of sample i to the hyperplane, as shown in Equation 2. If a sample is correctly classified, its geometric margin is positive, otherwise negative. The geometric margin thus quantifies both the correctness and confidence of the classification (Quan, 2025).

γ^i=yi(w·xi+b)(1)

γi=γ^i||w||=yi(w||w||·xi+b||w||)(2)

The objective of the SVM is to identify a hyperplane that not only correctly classifies all training samples but also maximizes the geometric margin. To account for the influence of outliers or misclassified samples in the training set, slack variables ξ_*i* and a penalty term C are introduced, transforming the optimization problem into the form shown in Equation 3:

minw,b,ξ12‖w‖2+C∑i=1nξi s.t. yi(wxi+b) ≥1−ξi ξi≥0, C>0 i=1, 2,…n(3)

Furthermore, a non-linear transformation using a kernel function K(x1,x2)=ϕ(x1)·ϕ(x2) can be applied, which maps the input data into a higher-dimensional feature space. This allows the model to transform a linearly inseparable problem in the input space into a linearly separable problem in the feature space.

For the binary classification problem of commutation status prediction, the performance of the classifier can be evaluated using a confusion matrix, as shown in Table 1. Based on the parameters in the confusion matrix, performance metrics such as Accuracy, Miss, and False can be computed to intuitively assess the classification results (Rachana et al., 2024). The formulas are given in Equation 4.

Accuracy=NTCF+NTNCFNCF+NNCF

Miss=NFNCFNCF+NNCF(4)

False=NFCFNCF+NNCF

Table 1. Confusion matrix for transient time-series dataset.

Here, Accuracy measures the proportion of correctly classified samples out of all samples, without distinguishing between classes. In contrast, the Miss and False reflect the classifier's performance for positive and negative samples, respectively. Under lopsided datasets, using all three metrics together provides a more comprehensive evaluation of classifier performance across different classes.

3 Feature extraction based on second-order determinant

3.1 Feature design

By mining disturbance-intrinsic features directly from raw measurements as classifier inputs, one can increase the information density of inputs and reduce the required size of the training set. This paper proposes a second-order determinant feature-extraction method based on sinusoidal shift-invariance theory. Consider an ideal sinusoid, sampled at constant interval. Define the sequence of recent samples and let the window length be 4. For each time index k, form the 2 × 2 feature-calculation matrix.

Let y = Asin(ωnΔt), n = 1, 2, 3, … be a sinusoidal signal sampled at interval Δt. Ordering the samples in time yields the sequence S={y_*T*, y_*T*−1, …y_*k*, y_*k*−1, y_*k*−2, y_*k*−3, …y₁}. Using a sliding window of length 4, each set of four consecutive samples forms the feature—calculation matrix M_*k*, defined as Equation 6:

Mk=[yk yk-1yk-2 yk-3](5)

The second-order determinant of the feature-calculation matrix defines the feature value F_*k* for the sampling window at time k, as given in Equation 6:

Fk=|Mk|=|yk yk-1yk-2 yk-3|=ykyk-3-yk-1yk-2=2A2

(sinωΔt)2cosωΔt(6)

Under periodic sampling of a pure sinusoid, F_*k* depends only on the amplitude A. After a disturbance, however, F_*k* immediately reflects any change in signal amplitude.

Assume that at time kΔt the phase of the sinusoidal signal undergoes an increment of θ. The phase jump will alter the modified determinants F~k′~F~k+3′. Specifically, F′k can be calculated as shown in Equation 7:

F˜k=[2yksin2θ2+Asinθcos(ωkΔt)]yk−3+F(7)

3.2 Feature extraction scheme

The scheme for feature extraction on consecutive sampled data is illustrated in Figure 1. Four overlapping sliding windows constitute one sampling unit; by applying Equation 6 to each window, four feature values are obtained to form a single feature vector. Computing all the features for one sampling unit therefore requires seven consecutive samples.

In terms of algorithmic complexity, Table 2 compares the proposed determinant-based method with several common feature extraction techniques:

Table 2. Comparison of common feature-extraction algorithms.

Compared with these traditional methods, the proposed determinant-based feature-extraction scheme offers clear advantages in both computational simplicity and windowing latency.

4 Data supplementation and balancing for lopsided samples

4.1 Sample labeling

The first CF occurring during 2/3 to 4/3 fundamental cycles after a disturbance has only a minor, unavoidable impact (Zhang and Wang, 2025). What merit attention are CFs that persist during the fault or recur after fault clearance. Accordingly, we label the following situations.

(i) Negative: CF occurs during the fault but recovers within 1.5 cycles.

(ii) Positive: CF during the fault that lasts longer than 1.5 cycles.

(iii) Negative: No CF occurs after the fault.

(iv) Positive: CF recurs following fault clearance.

4.2 Hybrid simulation based data supplementation and balancing

When training a classifier on field-measured data, two major issues arise. (i). A representative dataset must cover diverse disturbances and operating conditions—but collecting such data in a real system is time and cost prohibitive. (ii). CF is a rare event in practice, so measured data inevitably produce a strong class imbalance between “CF” and “no-CF” samples.

Training directly on a lopsided dataset degrades performance, primarily through missed detections of the minority class. Broadly, three families of solutions exist. (i). Data-level: Augment the minority class with new samples. This retains true physical semantics, unlike purely synthetic or interpolated data. (ii). Sampling-level: Apply over- or under-sampling to rebalance. Over-sampling can blur class boundaries and induce misclassification (Liang and Liang, 2024), while under-sampling discards useful data and reduces overall information (Liu et al., 2022). (iii). Algorithm-level: Use cost-sensitive learning or ensemble methods that assign higher misclassification penalties to the minority class (Mansouri et al., 2025; Wang, 2022).

Here, we combine data- and algorithm-level strategies. Data-level augmentation is performed via numerical simulation, which offers two advantages: (i) samples retain clear physical meaning, and (ii) we can tailor the disturbance set to improve classifier performance near decision boundaries. For large-scale AC–DC hybrid transmission systems, electromagnetic–electromechanical co-simulation (Zhu et al., 2021) achieves both high efficiency and sample fidelity, enabling bulk sample generation with low modeling complexity and time cost.

Algorithm-level adaptation employs a cost-sensitive classifier that penalizes missed CFs more heavily, enhancing the predictor's conservativeness in line with engineering requirements.

The combined simulated and measured dataset structure is illustrated in Figure 2.

At each bus node, faults of varying types, severities, and initiation times are applied to generate a comprehensive sample set. This ensures full coverage of all potential AC bus faults in the real system and guarantees the sufficiency of the sample set.

5 Cost-sensitive classification

5.1 Cost-sensitive analysis

In CF prediction, misclassifying a positive sample as negative (i.e., a miss) severely endangers DC transmission and system stability, whereas misclassifying a negative sample as positive (i.e., a false alarm) has comparatively minor consequences. Therefore, we adopt a cost-sensitive SVM that minimizes the total misclassification cost (Liang and Liang, 2024). For the CF-prediction task, we define the objective function and introduce a hierarchical model to quantify the positive-sample misclassification cost.

Let the training set be S={(xi, yi)}i=1n with n_*P* positive samples and n_*N* negative samples. Each xi∈ℝd, y_*i*∈{+1, −1}. Define index sets I_*P* = {i:y_*i* = 1} and I_*N* = {i:y_*i* = − 1}.

Assign positive and negative sample weights w_*P* and w_*N* according to the misclassification costs expressed in Equation 8:

wP=CPnCNnN+CPnP(8)

wN=CNnCNnN+CPnP

Here, C_*p* is misclassification cost and C_*N* is false-alarm cost, the standard SVM assumes C_*N* = C_*P*; in our problem C_*N*≠C_*P*. The cost-sensitive SVM optimization becomes (Equation 9):

minw,b,ξ12‖w‖2+CN∑i∈INξi+CP∑i∈IPξi s.t. yi(wTϕ(xi)+b) ≥1−ξi ξi≥0 i=1, 2,…n CN≥0, CP≥0(9)

5.2 Hierarchical-model-based misclassification cost quantification

Because multiple factors influence the cost of misclassifying CF events, we convert domain knowledge into a three-level hierarchical model (Figure 3) to determine C_*P*:

The model comprises three levels:

(i) Goal layer (O): Determine the miss cost for positive samples.

(ii) Criteria layer: Three key factors affecting that cost:

A₁: Equipment damage (e.g., converter valves); A₂: Power-transfer loss during the disturbance; A₃: Post-disturbance recovery cost.

(iii) Scheme layer: Two error types:

E₁: Missing a true CF (miss); E₂: Raising a false CF alarm (false alarm).

Pairwise-comparison matrices are constructed to quantify each layer's relative influences. For example, if a miss E₁ causes twice the equipment damage of a false alarm E₂, the comparison matrix for the Scheme layer against criterion A₁ is given by Equation 10:

ME-A1=[1&21/2&1](10)

Let the principal eigenvector of M_*E*−*A*1 be l₁, whose components give the relative weights of E₁ and E₂ on A₁. Similarly, we form M_*E*−*A*2, M_*E*−*A*3, and M_*A*−*O*, yielding eigenvectors l₂, l₃, and l₄.

Combining these, we compute the final cost C_*P* using Equation 11:

{CP=sE1/sE2[sE1, sE2]T=[l1,l2,l3]•l4(11)

6 Case study

6.1 Case design

To validate the proposed CF prediction method, we use the test system shown in Figure 4. The DC side employs the CIGRÉ benchmark HVDC transmission system. The network between the inverter bus and the main AC grid is modeled as segmented lines to simulate faults at various electrical distances from the converter bus. Faults of differing types, severities, and onset times are applied at five bus locations, as detailed in Table 3, generating a dataset of 1,600 samples. The labeling results are summarized in Table 4.

Table 3. Disturbance configuration for dataset.

Table 4. Sample labeling results.

Regarding the dataset construction, The grounding resistance range (0.1–35 Ω) is selected to cover the spectrum from severe metallic faults to high-impedance faults. Eight discrete values are chosen to define a clear decision boundary for the SVM without introducing data redundancy. The total dataset of 1,600 samples is generated through a full factorial combination of 4 fault types, 5 fault locations, 10 initial phases, and 8 grounding resistances (4 × 5 × 10 × 8 = 1,600). Since SVM is highly effective in high-dimensional spaces with limited samples, this dataset provides sufficient coverage of the critical fault regions.

In terms of data composition, Each sample in the dataset consists of a feature vector and a corresponding label. The feature vector is constructed from the three-phase instantaneous voltages at the inverter AC bus, specifically using 4 consecutive sampling points per phase (total 12 dimensions). The ground truth label (y_i∈{+1, −1}) is determined by the measured extinction angle γ: a sample is labeled positive if γ < γ_min commutation failure occurs) and remains low for more than 1.5 cycles, ensuring the model focuses on persistent or recurring CFs.

A sampling frequency of 2.5 kHz (400 μs interval) [National Energy Administration of China (NEA), 2021] is adopted to match the standard execution cycle of industrial HVDC controllers (e.g., ABB MACH or NARI systems). This ensures that the proposed method can be integrated into existing DSP-based hardware without requiring specialized high-speed acquisition units. Furthermore, this frequency provides sufficient resolution for the second-order determinant to capture voltage waveform distortions within the 1.6 ms (4-sample) observation window.

6.2 Feature-extraction scheme validation

We randomly select 1,200 samples for training and 400 for validation. Four feature-extraction methods are compared as classifier inputs—instantaneous values, DFT amplitudes, wavelet-energy features, and the proposed second-order-determinant features. All 1,600 samples are processed on an Intel Core i5-6200U 2.3 GHz, 16 GB RAM machine. Table 5 reports the total feature—computation time and classification performance.

Table 5. Comparison of classification performance with different features.

Table 5 shows that the proposed method achieves the shortest computation time and, despite a window latency of only four samples, delivers the highest classification accuracy.

6.3 Comparison with CFPREV prediction module

We further compare our data-driven prediction module against ABB's CFPREV commutation-failure prediction block. The CFPREV structure is illustrated in Figure 5.

Its key parameter is the reference voltage magnitude U_αβ. At a sampling rate of 2.5 kHz, Figure 6A shows CFPREV's miss and false-alarm rates under various U_αβ thresholds.

As the U_αβ threshold decreases, the miss rate falls but the false-alarm rate rises sharply. We set the U_αβ threshold as an optimized value 0.6324, and get a miss rate of 3.5% and a false-alarm rate of 7.5%. Figure 6B shows that CFPREV's response time varies by fault condition, with an average of 6.67 sampling step and a maximum value of 47 sampling steps.

By contrast, the proposed method using second-order-determinant features with a conventional (non-cost-sensitive) classifier achieves, under three-phase symmetric faults, a miss rate of 1%, a false-alarm rate of 1.25%, and a maximum response time of four sampling steps. Thus, for severe three-phase faults, the proposed approach outperforms CFPREV in both speed and accuracy.

While the model is trained on simulation data, its practical applicability is supported by three factors. First, the CIGRE benchmark system is a globally recognized standard that maintains high physical isomorphism with real HVDC projects. Second, the second-order determinant feature focuses on the rate of change and distortion shape of the waveform rather than absolute magnitudes, which is inherently robust against system parameter variations. Third, the cost-sensitive framework (C_*P*>C_*N*) builds in a “safety margin,” making the model conservatively biased toward over-detection, which aligns with engineering requirements for failure prevention.

7 Conclusion

This paper proposes a fully data-driven failure prediction method, demonstrating exceptional timeliness and a remarkably low missed detection rate, with significant potential for practical engineering applications. The key technical methodologies and distinctive features are outlined as follows.

Using the second-order determinant of sampled data as the input feature for the commutation-status prediction classifier yields a feature-extraction method with low computational complexity, fast response, and invariance to fault occurrence timing. A labeling scheme is devised that ignores the first CF immediately following a disturbance; by comparing each sample's extinction angle to the minimum extinction angle, samples are classified in a way that meets the needs of real-time failure blocking and preventive control. The dataset is constructed and augmented using a hybrid simulation platform based on refined interface techniques, ensuring balanced class proportions. Finally, a hierarchical analysis method is employed to determine the cost ratio between missed and false alarms, thereby making the commutation-status predictor more conservative.

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Footnotes

Edited by: Najib Essounbouli, Université de Reims Champagne-Ardenne, France

Reviewed by: Ningyi Dai, University of Macau, China

Tarek Aounallah, Université de Reims Champagne-Ardenne, France