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Intelligent Time-Adaptive Transient Stability Assessment System

James J. Q. Yu, David J. Hill, Albert Y. S. Lam, Jiatao Gu, Victor O. K. Li

arXiv:1610.08235v2eess.SY

TL;DR

Online post-contingency transient stability assessment is needed to support timely power-system control, but existing approaches face computational, modeling, and fixed-response limitations. The paper develops an LSTM-based TSA system with a time-adaptive scheme that learns temporal dependencies, and case studies report accurate, fast, and computationally efficient assessment. The paper assumes complete PMU measurements at installation locations and identifies missing-measurement scenarios as future work.

  • Problem

    Existing time-domain and machine-learning TSA approaches face heavy computational or modeling burdens, and machine-learning systems commonly use fixed response times despite rapidly propagating instability.

  • Method

    The paper develops an LSTM-based online TSA system with a time-adaptive scheme that uses temporal dependencies in post-contingency measurements.

  • Results

    Case studies on three power systems report superior assessment accuracy within a very short time after fault clearance, with computationally efficient training and scalability for large systems.

  • Takeaways & Limitations

    The proposed system is designed to reserve more time for subsequent control actions while reducing model complexity and training cost.

  • Takeaways & Limitations

    The study assumes measurements are available at all PMU installation locations and leaves missing measurements from communication delay or loss for future work.

Abstract

from arXiv · show

Online identification of post-contingency transient stability is essential in power system control, as it facilitates the grid operator to decide and coordinate system failure correction control actions. Utilizing machine learning methods with synchrophasor measurements for transient stability assessment has received much attention recently with the gradual deployment of wide-area protection and control systems. In this paper, we develop a transient stability assessment system based on the long short-term memory network. By proposing a temporal self-adaptive scheme, our proposed system aims to balance the trade-off between assessment accuracy and response time, both of which may be crucial in real-world scenarios. Compared with previous work, the most significant enhancement is that our system learns from the temporal data dependencies of the input data, which contributes to better assessment accuracy. In addition, the model structure of our system is relatively less complex, speeding up the model training process. Case studies on three power systems demonstrate the efficacy of the proposed transient stability assessment system.

I. INTRODUCTION

Online transient stability assessment is important because disturbances can threaten synchronism and blackouts, while existing approaches face computational, modeling, and response-time limitations. The paper proposes an LSTM-based, time-adaptive TSA system intended to improve accuracy and response speed with lower implementation complexity.

  • Transient stability concerns a power system’s ability to retain synchronism after large disturbances, which can contribute to power blackouts.
  • Traditional transient-energy and time-domain methods face model simplifications, heavy computational burdens, and inaccurate system or disturbance estimates for online prediction.
  • Machine-learning TSA methods generally offer better performance than fuzzy-logic approaches, creating a trade-off with transparency.
  • Existing machine-learning TSA systems commonly use fixed response times, despite the need for faster assessments as instability can propagate across the grid.
  • The proposed work applies recurrent neural networks and LSTM to time-adaptive TSA, extracting spatial and temporal dependencies from power-system state data.
  • The system is assessed on three power-system test cases, with reported accurate assessment, reduced response time, and lower training and maintenance effort.

II. TRANSIENT STABILITY ASSESSMENT AND RECURRENT NEURAL NETWORKS

The paper frames TSA as predicting post-fault synchronism from observed system dynamics, where accuracy and response speed must be balanced. It motivates a time-adaptive machine-learning design and introduces LSTM memory for temporal information processing.

  • A. Transient Stability Assessment: TSA predicts whether a power system will maintain synchronism after fault clearance, supporting emergency control when instability is anticipated.
  • A. Transient Stability Assessment: Time-adaptive TSA seeks the earliest accurate assessment by balancing response speed against assessment accuracy across different contingencies.
  • A. Transient Stability Assessment: Machine-learning TSA systems convert post-disturbance dynamics into time-series information that produces a future system stability index.
  • B. Recurrent Neural Networks: LSTM memory cells address long-term dependency limitations in conventional recurrent neural networks by maintaining information over time.
  • A. Transient Stability Assessment: TSA response time depends on data aggregation and system computation, motivating a scheme that reduces required data while keeping calculations efficient.

B. Recurrent Neural Network and Long Short-Term Memory

RNNs model temporal sequences through recurrent hidden-state connections, while LSTM extends this approach with memory blocks and gates to preserve long-term dependencies. In TSAS, sequences of x_t data are mapped to corresponding y_t predictions.

  • Recurrent Neural Network: RNNs process temporal input vectors and produce corresponding sequences of hidden-state vectors.The recurrent formulation is applied for each time step t = 1, 2, ···, T.
  • Recurrent Neural Network: Recurrent hidden-layer connections retain previous information, enabling RNNs to capture time-domain dependencies.These connections provide the network with memory capabilities unavailable in ordinary feedforward ANNs.
  • Long Short-Term Memory: Gradient-based RNN training can suffer from vanishing gradients, weakening performance on long temporal dependencies.LSTM was proposed as an alternative architecture to address this defect.
  • Long Short-Term Memory: LSTM uses memory blocks containing cells to maintain a long-term state over time.The architecture combines these memory blocks with a typical RNN.
  • Long Short-Term Memory: LSTM gates cooperate with memory to update the network’s output representation.The architecture includes input, forget, and output gates; its parameters include W, U, and b.
  • TSAS Structure: TSAS maps a sequence of x_t data to corresponding y_t predictions.This figure summarizes the system’s sequence-to-prediction structure.

III. LSTM-BASED TSAS

The LSTM-based TSAS learns a nonlinear stability classifier from simulated post-contingency voltage-phasor sequences and rotor-angle-based labels. Its observation-window length T controls the trade-off between model complexity and assessment accuracy.

  • System Structure: TSAS uses an LSTM classifier to relate post-contingency measurements, such as bus voltage phasors, to system stability.The approach assumes measurements can indicate stability soon after a disturbance and that temporal dependencies can reduce the data needed for accurate assessment.
  • System Structure: The model combines an LSTM memory-block layer, a dense hidden layer for dimensionality reduction, and a final sigmoid output.The LSTM processes power-system measurements and produces h_t features with the same dimensionality as x_t.
  • Time-Series Simulation: Offline training uses time-series simulations of different transient contingencies to generate training data.The simulated measurements are intended to represent responses to varied disturbances.
  • Time-Series Simulation: Positive-sequence voltage phasors from all buses are sampled at 50/60 Hz as real-time-compatible input measurements.Each time-step vector contains voltage magnitudes and angles for the system’s B buses.
  • Time-Series Simulation: T denotes the post-contingency observation-window length and controls the trade-off between TSAS complexity and assessment accuracy.A large T increases nonlinearity, whereas a small T may reduce input completeness and weaken accuracy.
  • Offline Training: Training labels are derived from δmax, the maximum angle deviation between any two generators at any time.The stability label uses η = (360−δmax)/(360+δmax), assigning stable when η > 0 and unstable when η ≤ 0.
  • Offline Training: The offline objective is to learn W, U, and b using Adam with binary cross-entropy error.The trained system’s classification result is denoted by ŷ(n).

C. Online Assessment

Online assessment applies the trained TSAS to post-contingency PMU voltage-phasor measurements. The resulting output is converted into a binary stability decision using a threshold of 0.5.

  • Online Classification: Online TSAS classifies test cases from post-contingency PMU voltage-phasor measurements of length T.These measurements are used to calculate h_T and the system output ŷ_T.
  • Online Classification: 0.5 is the bipartite threshold: ŷ_T < 0.5 indicates unstable, while ŷ_T ≥ 0.5 indicates stable.The trained system output lies in the interval (0, 1) before thresholding.

A. Time Adaptive Implementation

The time-adaptive TSAS updates stability assessment as post-contingency PMU measurements arrive, balancing assessment speed against accuracy through a threshold-based decision process.

  • The proposed time-adaptive TSAS seeks reliable stability assessment as fast as possible by trading off assessment speed and accuracy.The scheme is intended to allow earlier control actions to avoid possible system failures.
  • LSTM recurrent connections incorporate temporal dependencies from the input data into system stability assessment.The approach addresses potential information loss from discarding intermediate outputs by using additional temporal information.
  • After fault clearance, the system begins assessment when the first PMU measurement arrives and calculates a stability index from the available output.Subsequent measurements are incorporated if the initial result is not reliable.
  • The threshold δ ∈ (0, 0.5) controls the speed–accuracy trade-off: larger values can assess earlier, whereas smaller values can improve accuracy at lower speed.The decision rule labels outputs as Stable, Unstable, or Unknown according to the threshold.
  • When the result is Unknown, the system waits for the next time instance and repeats the calculation until reliability is achieved or T max is reached.The flow chart describes the repeated measurement-and-assessment process.
  • Compared with the multi-ELM system, the single-LSTM design extracts temporal data-dependency features and reduces training complexity.Both systems support online time-adaptive transient stability assessment.

B. Discussion

The discussion presents LSTM-based TSAS as suitable for online assessment because training is offline and power-dynamics data can support prediction without fully accurate system models. The evaluation uses simulated contingencies and load levels, while the neural network remains a black-box model.

  • Offline training allows the online TSA testing process to run effectively using trained neural-network parameters.The computationally expensive training process is performed before online operation.
  • Neural networks can model transient stability from power-dynamics data, relaxing the requirement for accurate power-system models.This is presented as addressing traditional methods' complete-model and real-time computational-burden problems.
  • Discussion: The neural network is a black-box model because its internal parameters and variables generally lack explicit physical meanings.The discussion states that only algebraic calculations are needed to produce the output stability status from PMU-sampled dynamics.
  • Evaluation setup: The evaluation generates training and testing cases with time-domain simulations covering nominal topology, N−1 contingencies, and 80%, 100%, and 120% load levels.Contingencies remove one transmission line or transformer, and three-phase short-circuit faults are considered.
  • Evaluation setup: Simulated bus-voltage phasors serve as PMU measurements, although utilities could alternatively train TSAS with historical operation data.The simulations use TSAT, and accurate PMU sampling is assumed unless specified otherwise.
  • Evaluation setup: Contingency cases are randomly split 3:1 into training and testing sets, with testing measuring accuracy on unknown contingencies.Only training cases are used to train TSAS.
  • Training and discussion: The simulations report no observed inferior testing accuracy attributed to overfitting after using the training procedure and early stopping.The network is trained for up to 100 epochs with early stopping, using two 128-block LSTM layers and T max = 20.

A. TSA Accuracy and Response Time

TSAS combines high early assessment accuracy with short, adaptive response times, outperforming or matching existing methods across tested systems. Its sensitivity depends on balancing the stability threshold and observation-window length.

  • Around two thirds of New England system instances are assessed at the first post-contingency cycle, with perfect early accuracy for training and testing cases.
  • All testing instances are correctly assessed within seven post-contingency cycles, while only around 4% remain unassessed after two cycles.
  • TSAS maintains superior accuracy over another time-adaptive approach when test instances require more information, attributed to LSTM extraction of temporal dependencies.
  • 1.448 cycles with 100% testing accuracy and 1.412 cycles with 99.97% training accuracy are reported for TSAS on the New England system.
  • TSAS matches accurate competing methods with much shorter response times and achieves better accuracy than ELM-based comparison on the tested systems.
  • Stability threshold values around 0.4 are preferred, while observation window T = 5 offers an accuracy–ART trade-off.

C. PMU Placement Analysis

The PMU placement analysis seeks effective measurement locations because TSAS uses voltage phasors from all buses and therefore requires broad observability. Sequential feature selection evaluates placements using accuracy and average response time.

  • TSAS uses real-time voltage magnitudes and angles from all buses, requiring many high-speed PMUs for full observability.
  • Sequential forward and backward selection assess candidate PMU placements by comparing transient-stability accuracy and average response time.
  • With fewer than 10 PMUs, increasing installations decreases response time and increases assessment accuracy; later, accuracy stays at 100%.
  • After the initial improvement phase, average response time fluctuates around 1.5 cycles for both selection algorithms.

D. PMU Measurement Accuracy Sensitivity

TSAS remains accurate under noisy PMU measurements and scales to larger power systems, though response speed depends on system size. Its fast training supports updates, while retraining implementation remains outside this paper’s scope.

  • Noisy PMU data slightly worsens accuracy and ART, with noisy ARTs of 1.423 training cycles and 1.466 testing cycles versus 1.412 and 1.448 noiseless cycles.
  • Most larger-system test cases are identified within one cycle, with ARTs of 1.901 cycles for 162 buses and 2.047 cycles for 145 buses.
  • Assessment accuracy remains perfect for both larger systems except for one test case in the 145-bus system.
  • Assessment speed is closely related to system size, while generator and bus counts jointly explain similar speeds between the two larger systems.
  • Training time is roughly linear with the number of training cases, which is closely related to system size.
  • TSAS can be updated with newly measured variables, but detailed retraining implementation is deferred to future work.

VI. CONCLUSION AND FUTURE WORK

The proposed LSTM-based transient stability assessment system combines temporal self-adaptation with a relatively simple model to support rapid, accurate post-contingency assessment. Tests across three power systems, parameter sensitivities, and PMU selection support its potential deployment, while missing-measurement scenarios and online retraining remain future work.

  • The system uses LSTM networks and a time-adaptive scheme to improve assessment accuracy while preserving response-time performance.It learns temporal dependencies and seeks assessment at the earliest possible time for subsequent control actions.
  • A single LSTM-based network reduces model complexity and makes training less computationally expensive than an ensemble design.
  • Three test cases include the New England 10-machine system, a 17-generator 162-bus system, and a 50-generator 145-bus system.
  • The proposed model achieves superior assessment accuracy shortly after fault clearance and is computationally efficient to train using existing measurements.The authors describe the resulting model as highly scalable for TSA tasks in large power systems.
  • Sensitivity studies examine the stability threshold, training observation window, and PMU measurements, identifying a promising configuration and PMU selection for the tested grid.Future work will address missing PMU measurements, alternative predictors, and online retraining.
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