Source-linked AI summary
Deep learning based on Transformer architecture for power system short-term voltage stability assessment with class imbalance
Yang Li, Jiting Cao, Yan Xu, Lipeng Zhu, Zhao Yang Dong
TL;DR
Data-driven STVSA is challenged by severe class imbalance and the absence of a unified quantitative criterion for labeling stability. The paper combines CWGAN-GP, StaaT, and semi-supervised clustering to address these issues, with tests reporting strong performance under imbalance and renewable-energy penetration.
Problem
Real post-disturbance data are predominantly stable, creating severe class imbalance, while STVSA lacks a uniform quantitative criterion for accurate sample labeling.
Method
The method uses CWGAN-GP to generate balanced realistic training data, StaaT for Transformer-based STVSA, and semi-supervised clustering guided by labeled samples.
Results
The proposed method remains resilient under class imbalances up to 100:1, with CWGAN-GP achieving zero misdetection and StaaT reporting 0.18% false alarms and 0% misdetection.
Takeaways & Limitations
The approach supports STVSA with balanced synthetic data, Transformer-based assessment, and labeling assistance for imbalanced operating data.
Abstract
from arXiv · showhide
Most existing data-driven power system short-term voltage stability assessment (STVSA) approaches presume class-balanced input data. However, in practical applications, the occurrence of short-term voltage instability following a disturbance is minimal, leading to a significant class imbalance problem and a consequent decline in classifier performance. This work proposes a Transformer-based STVSA method to address this challenge. By utilizing the basic Transformer architecture, a stability assessment Transformer (StaaT) is developed {as a classification model to reflect the correlation between the operational states of the system and the resulting stability outcomes}. To combat the negative impact of imbalanced datasets, this work employs a conditional Wasserstein generative adversarial network with gradient penalty (CWGAN-GP) for synthetic data generation, aiding in the creation of a balanced, representative training set for the classifier. Semi-supervised clustering learning is implemented to enhance clustering quality, addressing the lack of a unified quantitative criterion for short-term voltage stability. {Numerical tests on the IEEE 39-bus test system extensively demonstrate that the proposed method exhibits robust performance under class imbalances up to 100:1 and noisy environments, and maintains consistent effectiveness even with an increased penetration of renewable energy}. Comparative results reveal that the CWGAN-GP generates more balanced datasets than traditional oversampling methods and that the StaaT outperforms other deep learning algorithms. This study presents a compelling solution for real-world STVSA applications that often face class imbalance and data noise challenges.
Nomenclature
This section introduces the terminology and motivation for data-driven STVSA, then presents Transformer-based assessment and CWGAN-GP-based imbalance learning as the study’s core approach.
- STVS denotes a power system’s capacity to recover voltage to an acceptable range after a disturbance.
- Transformers are introduced for STVSA because conventional algorithms are less capable of managing long-distance dependencies in data sequences.
- Real post-disturbance data are predominantly stable, creating severe stable-to-unstable class imbalance that can undermine model performance.
- The proposed method combines CWGAN-GP, which generates balanced realistic data, with StaaT, a Transformer-based STVSA model.
- CWGAN-GP remains resilient under class imbalances up to 100:1, while the proposed method maintains robust performance with increased renewable-energy penetration.
II Related algorithms
The section addresses difficult STVSA labeling by using clearly labeled samples as prior information for semi-supervised fuzzy C-means clustering of remaining samples.
- STVSA lacks a uniform quantitative criterion, making accurate sample-label acquisition difficult.
- Voltage thresholds can identify a small subset of stable and unstable samples for use as labeling prior information.
- SFCM divides an N-dimensional dataset into C clusters and represents each sample’s affiliation through fuzzy membership.
- SFCM uses labeled samples to guide iterative optimization of clustering across the dataset.
- The clustering formulation uses membership values, exponent weighting, cluster centers, and sample-to-center distances.
B. Conditional Wasserstein GAN with Gradient Penalty
The section develops conditional Wasserstein GANs to generate realistic class-conditioned samples, using Wasserstein distance and gradient penalty to improve training stability.
- GAN training pits a generator producing synthetic samples against a discriminator distinguishing generated from real data.Their competition progressively makes generated samples more similar to real samples.
- A CGAN adds conditional information y to both generated and real-data discrimination.The conditional objective evaluates real samples and generated samples given y.
- WGAN replaces GAN classification with distance fitting using 1-Lipschitz functions and Wasserstein distance.This addresses cases where KL and JS divergences provide neither meaningful distance nor gradients for nearly non-overlapping distributions.
- WGAN-GP avoids weight truncation by using a gradient penalty, whose coefficient is λ and whose interpolation samples lie between real and generated data.The penalty is applied independently to samples to constrain the discriminator during generation.
C. Transformer
The Transformer is presented as an encoder-decoder sequence architecture built around self-attention, with multi-head attention extracting information from different sequence locations.
- The Transformer uses stacked encoder layers containing multi-head self-attention and feed-forward networks, while the decoder adds encoder-decoder attention.
- Scaled dot-product attention replaces each sequence element with a weighted combination of the remaining sequence elements.Queries, keys, and values are represented by input feature matrices.
- Multi-head attention processes features from distinct positions with different weights and concatenates the resulting heads.This allows the Transformer to gather information from diverse locations rather than relying on a single attention mechanism.
III Class imbalance learning based on CWGAN-GP
The CWGAN-GP training procedure uses labeled noise to generate samples, evaluates them alongside real data, and iteratively trains a generator capable of producing balanced STVSA training data.
- The CWGAN-GP generator is a four-layer fully connected network, while the discriminator has three fully connected layers with 512, 256, and 1 neurons.Both networks use LeakyReLU activations, and generated samples train the classifier.
- Step 1 feeds random noise z and labels y into the generator to produce samples aligned with real-sample distributions.
- Step 2 mixes generated and real data before presenting them to the discriminator for real-versus-fake evaluation.
- Step 3 repeatedly optimizes the models until the trained generator can produce a balanced training set for STVSA.
IV Proposed STVSA model
The proposed STVSA model uses a simplified Transformer encoder, StaaT, to classify power-system time-series samples as stable or unstable. The overall scheme generates and labels data, trains StaaT offline, and performs real-time assessment using PMU measurements.
- Stability assessment Transformer: StaaT removes the Transformer decoder and connects encoder layers to fully connected and Softmax layers for classification.This adaptation focuses on feature learning rather than decoder-based prediction.
- Stability assessment Transformer: PMU time-series samples are positionally embedded, processed by multi-head self-attention and feedforward networks, then classified as stable or unstable.The input contains real-time power-system data, and the encoder output passes through a fully connected layer and Softmax function.
- Proposed STVSA scheme: The proposed scheme first generates normalized voltage, active-power, and reactive-power samples, labels unlabeled data with SFCM, and partitions the dataset into training and test sets.The training-to-test split is 4:1.
- Proposed STVSA scheme: During offline training, StaaT learns from the generated training set, while the test set evaluates performance and the optimal parameters are saved for online assessment.The saved parameters are used in subsequent assessments.
- Proposed STVSA scheme: During online assessment, PMUs transmit U, P, and Qr after a disturbance; unstable classifications trigger control measures, while stable classifications continue monitoring.The online process uses real-time electrical quantities captured after a large disturbance.
1) Silhouette coefficient
The section introduces clustering evaluation and broader experimental settings for assessing the proposed STVSA approach. It emphasizes that accuracy alone is inadequate when stable and unstable classification errors have unequal consequences.
- Silhouette coefficient: The silhouette coefficient evaluates clustering quality through sample aggregation within clusters and separation from other clusters.The average within-cluster distance is denoted by aj, while the minimum average distance to other clusters is bj.
- Evaluation criteria: Misclassifying an unstable sample as stable can contribute to voltage collapse by preventing necessary control measures.Because misclassification costs differ, the section identifies accuracy as insufficient for comprehensive STVSA evaluation.
- Evaluation criteria: CWGAN-GP performance is evaluated using Wasserstein distance, maximum mean difference, and Fréchet incidence distance, with lower values indicating better performance.These metrics assess the quality of generated data.
- Case study: Experiments use the IEEE 39-bus test system with a third-order exciter model and data generated through PSD-BPA simulations.The implementation uses PyTorch 1.7 and TensorFlow 1.14 in Python 3.7.
- Case study: The CWGAN-GP and StaaT hyperparameters are selected by trial and error, with ncritic balancing CWGAN-GP training convergence speed.The settings are listed in Tables II and III.
A. Dataset generation
Dataset generation simulates operating conditions and post-fault measurements, producing time-series samples for STVSA. Semi-supervised fuzzy C-means labeling uses limited labeled information to assign labels across the dataset, and clustering performance is compared with other approaches.
- Dataset generation: The simulations use induction-motor and static ZIP loads across varied operating conditions, fault types, and fault locations.The induction-motor model reflects the study’s focus on post-fault short-term voltage instability.
- Dataset generation: The resulting time-domain simulations provide voltage amplitude, active power, and reactive power measurements for constructing the time-series dataset S.The measurements are denoted U, P, and Qr and are obtained using PSD-BPA.
- Dataset structure: The dataset S is organized into n subsets, each containing sequences of U, P, and Qr across the system buses.Each subset has dimension d, and L denotes the number of system buses.
- Dataset structure: 5500 samples are generated, with unstable samples comprising 9.09% of the total.This distribution creates a substantially imbalanced dataset for the subsequent assessment experiments.
- Sample labeling: SFCM uses a small set of known labels as prior information to cluster and label the remaining samples, addressing limited availability of labels.The resulting label sets are compared using COP-k-means and engineering criteria.
- Sample labeling: SFCM achieves nearly double the efficiency of the engineering criterion and exceeds COP-k-means in the reported clustering comparison.The results are presented in Table V.
C. Performance tests of CWGAN-GP
The CWGAN-GP is evaluated against resampling and generative baselines for class-imbalanced STVSA. It performs strongly across imbalance ratios, although performance becomes unacceptable at 100:1.
- CWGAN-GP outperforms SMOTE, ROS, and ADASYN across all reported indices, with zero misdetection and MCC at least 0.04 higher.MCC is emphasized as a clearer indicator of performance under class imbalance.
- CWGAN-GP has lower WD, MMD, and FID than CGAN, including a WD 38.4% lower than CGAN.Lower values indicate better performance for each metric.
- At 100:1 imbalance, the investigated approach degrades to an unacceptable efficiency level, while ACC changes little with increasing imbalance.The results caution against evaluating the method solely with accuracy.
D. Performance test at different observation times
The study examines observation-window length and StaaT classification performance. A 0.03 s window balances assessment speed and accuracy, while StaaT achieves very low false alarms and misdetections and outperforms other tested deep-learning models.
- Performance at different observation times: A 0.03 s observation-time window provides high accuracy and is selected to balance assessment speed with accuracy.Training and testing accuracies remain relatively stable as the window length increases.
- StaaT performance: StaaT records a 0.18% false-alarm rate and 0% misdetection rate in the confusion-matrix evaluation.These outcomes are reported as satisfying practical instability-assessment requirements.
- StaaT performance: StaaT outperforms LSTM, CNN, and BiGRU on ACC, MCC, F1-score, and Mis, with the highest MCC and smallest Mis.The comparison attributes this performance to StaaT’s self-attentive mechanism for learning information at each data position.
F. Performance test with renewable energy integration
The proposed method is tested under renewable-energy integration and noisy measurement conditions. Performance declines with renewable penetration but remains commendable at 30%, while varying noise levels do not significantly affect the classifier.
- Renewable energy integration: The proposed approach’s performance declines as renewable-energy penetration increases but remains commendable at 30%.The paper attributes the decline to increasingly complex post-disturbance dynamics that are harder to learn.
- Noisy conditions: Under varying SNR noise conditions, the proposed classifier maintains superior performance without significant degradation as noise increases.The results are presented as evidence of robustness to measurement noise.
- Overall findings: The method combines CWGAN-GP and StaaT to address class imbalance in STVSA and remains robust across varying sample ratios and noisy environments.The conclusion also reports consistent effectiveness with increased renewable-energy penetration.
- Scope and future work: Future work will address missing PMU data, larger power-system models, and integration of data-driven with model-driven techniques.The proposed combination is intended to provide more insight into voltage-instability causes and corrective measures.