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The Price of a Cycle: A Phasor -vs- Sampled-Value Comparison for Streaming Fault Classification on the IEEE 9-Bus System

Emad Abukhousa, Khaled Muhmmed Nor Muhmmed, Abdulaziz Qwbaiban, Saman Zonouz, A. P. Sakis Meliopoulos

arXiv:2610.04167v1eess.SYcs.SY

TL;DR

Transmission-line fault classification must identify the faulted phases and grounding quickly, yet input representation can impose a measurement-window delay. The paper compares sampled-value and one-cycle phasor inputs under a controlled streaming evaluation. Sampled-value inputs reach the correct class earlier in every model pair, while the 40-sample MLP leads the reported metrics.

  • Problem

    Streaming fault classifiers must identify involved phases and grounding quickly, but static accuracy alone does not show when a causal input representation permits a decision.

    Source: §I · p. 1

  • Method

    The study compares six sampled-value and one-cycle phasor configurations on the synchronous IEEE/WSCC 9-bus system while holding the system, channels, taxonomy, training, models, and decision layer constant.

    Source: §I · p. 2, A. Synchronous Test System and… · p. 2

  • Results

    All configurations identified every event, and sampled-value inputs reached the correct class earlier in every model pair; the 40-sample sampled-value MLP had a 2.807 ms mean first-correct delay.

    Source: A. Model-Level Performance · p. 4, D. Accuracy-Delay Tradeoff · p. 5, §V · p. 7

  • Takeaways & Limitations

    On this clean synchronous benchmark, the one-cycle phasor representation’s timing cost was not offset by an accuracy or stability benefit, while the 40-sample sampled-value MLP Pareto-dominated the other configurations.

    Source: §IV · pp. 6–7, §V · p. 7

    The conclusions are bounded by fixed-location bolted faults, a fixed operating condition, no noise sweep, and no hardware-in-the-loop timing.

    Source: §IV · p. 7

Abstract

from arXiv · show

Transmission-line fault classification is a time-critical protection function, and recent machine-learning methods classify fault type directly from voltage and current measurements. The input to such a classifier can be supplied as sampled-value windows of raw measurements, which preserve sub-cycle structure, or as phasor-domain sequence components, which are physically interpretable but require a causal one-cycle observation window before a phasor estimate is available. This paper measures the cost of that observation window, the price of a cycle, through a controlled comparison of the two representations for streaming fault-family classification on the standard synchronous WSCC/IEEE 9-bus system. The comparison holds the simulated system, the measured channels, the eleven-class event-family taxonomy, the training procedure, and the streaming decision layer constant, and uses six configurations: 40- and 80-sample sampled-value inputs and one-cycle phasor inputs, each evaluated with a multilayer perceptron (MLP) and a one-dimensional convolutional neural network (CNN). All six configurations classify every event successfully, yet the sampled-value representation reaches the correct class earlier in every model pair. The 40-sample sampled-value MLP attains the strongest result, with 99.34% fault-window accuracy, 99.79% normal accuracy, a 0.21% false-fault rate, a 0.65% false-normal rate, and a 2.81 ms mean first-correct delay, and it Pareto-dominates the other five configurations. A matched-window comparison at eighty samples confirms that the timing advantage follows from the representation rather than from the window length. On this clean synchronous benchmark, the one-cycle phasor representation does not return an accuracy or stability benefit sufficient to offset its delay.

I. INTRODUCTION

The paper asks whether one-cycle phasor estimation earns its timing cost in streaming fault classification, and isolates representation in a controlled comparison. It treats streaming decision timing, rather than static accuracy alone, as part of classifier quality.

I. INTRODUCTION

  • At 60 Hz, a one-cycle sliding DFT needs approximately 16.67 ms of samples before producing the first causal phasor; causal raw sampled-value windows preserve sub-cycle fault transients.Source: §I · p. 1
  • Prior work leaves open whether sampled-value windows or one-cycle phasor sequence components are preferable when phasor-estimation time is included in streaming evaluation.The paper identifies its contribution as isolating input representation, rather than introducing the benchmark, taxonomy, or features.Source: §I · p. 2
  • The study holds the system, channels, eleven-class taxonomy, training, model families, and decision layer constant while comparing six sampled-value and phasor configurations.The model axis serves as a robustness control, and the phasor-estimation window is counted in the decision timeline.Source: §I · p. 2
  • Faults are applied at the midpoint of line 7–8, with three-phase voltages measured at buses 7 and 8 and bidirectional three-phase and neutral line currents.The diagram depicts the synchronous WSCC/IEEE 9-bus test system.Source: Figure 1 · p. 2

II. METHODOLOGY

The methodology isolates input representation by holding the simulated system, measured channels, taxonomy, training, models, and streaming decision layer constant. It uses the synchronous WSCC/IEEE 9-bus benchmark and terminal voltage and current measurements.

II. METHODOLOGY

  • Input representation is the sole experimental variable; the system, channels, taxonomy, training procedure, model families, and streaming decision layer are held constant.This controls the comparison across sampled-value and phasor inputs.Source: §II · p. 2

A. Synchronous Test System and Measurement Vector

  • The synchronous WSCC/IEEE 9-bus system is simulated in RSCAD with a 100 MVA base, three synchronous generators, and three constant-power loads, without inverter-based resources.Faults are applied at the midpoint of line 7–8 with bolted resistance, and measurements are taken at both line terminals.Source: A. Synchronous Test System and… · p. 2
  • The measurement vector comprises fourteen electrical channels: three-phase voltages at buses 7 and 8 and bidirectional three-phase and neutral line currents.Time is used for indexing, event alignment, and timing, not as a model feature; replay labels are absent.Source: A. Synchronous Test System and… · p. 2

B. Data Streams and Scoring Windows

The study uses separate training and testing streams, with the replay changing event order, start times, and durations while retaining the same fault families. Testing event windows are specified for scoring and figure shading.

B. Data Streams and Scoring Windows

  • The labeled training stream contains normal operation and eleven one-second bolted midpoint faults, with ABC and ABCG mapped to one ABC Family class.The training stream supports model fitting, scaler estimation, and validation.Source: B. Data Streams and Scoring Windows · pp. 2–3
  • Table I lists the testing replay event windows used for streaming evaluation and figure shading.The windows are defined in stream time.Source: Table I · p. 3, B. Data Streams and Scoring Windows · p. 3
  • The testing replay changes event order, start times, and durations relative to training, testing temporal, onset, and duration robustness under the same fixed electrical condition.It does not test generalization to unseen locations, resistances, topologies, or loading conditions; normal intervals show clearing and return-to-normal behavior.Source: B. Data Streams and Scoring Windows · p. 3
  • The sampled-value rate is 80 samples per 60 Hz cycle, making the 40-sample input a half-cycle window and the 80-sample input a one-cycle window.The one-cycle phasor estimator uses 80 samples.Source: B. Data Streams and Scoring Windows · p. 3

C. Sampled-Value and Phasor Representations

Both representations are causal and present the same channels differently to the classifier. Sampled-value inputs retain recent raw measurements, whereas phasor inputs use a trailing one-cycle estimate resolved into symmetrical components.

C. Sampled-Value and Phasor Representations

  • The causal sampled-value input stacks the most recent L measurement vectors, and the two representations differ only in how the fourteen channels are presented to an identical classifier.Both representations are causal.Source: C. Sampled-Value and Phasor… · p. 3
  • A 40-sample sampled-value window spans approximately 8.33 ms, while the 80-sample window spans approximately 16.67 ms and serves as a matched-window control.Training-split statistics standardize each channel, and each window receives the label of its final sample.Source: C. Sampled-Value and Phasor… · p. 3
  • The phasor input uses a trailing one-cycle DFT and resolves three-phase phasors into symmetrical components, whose sequence content distinguishes fault families by physics.The feature vector concatenates real and imaginary sequence-component parts for four three-phase groups and two neutral-current phasors, giving 28 dimensions.Source: C. Sampled-Value and Phasor… · p. 3
  • The eleven-class taxonomy merges the ABC and ABCG three-phase labels into one ABC Family class.The paper states that the ground/no-ground distinction is physically marginal for fast event-family classification under bolted three-phase faults.Source: C. Sampled-Value and Phasor… · p. 3

D. Model Families and Training

The MLP and CNN provide architecture controls across models without and with temporal structure. Their sampled-value and phasor-specific input arrangements are trained with class-weighted cross-entropy and a shared training procedure.

D. Model Families and Training

  • The MLP and CNN serve as architecture controls, contrasting a model without temporal structure with one that has it.Both produce 11-class logits followed by a softmax.Source: D. Model Families and Training · p. 3
  • Sampled-value CNNs convolve across time with fourteen measurement channels, whereas phasor CNNs convolve over ordered real/imaginary features.Sampled-value MLPs flatten their inputs; phasor MLPs use a 28-dimensional vector.Source: D. Model Families and Training · pp. 3–4
  • Training uses class-weighted cross-entropy and AdamW, with early stopping based on validation macro-F1.The learning rate is 10^-3, weight decay 10^-4, batch size 256, and training runs for at most 50 epochs.Source: D. Model Families and Training · p. 4

E. Streaming Decision Layer and Metrics

The streaming layer turns per-sample probabilities into emitted decisions using causal smoothing and confidence gating. The section defines event-window accuracy and first-correct delay for assessing those decisions.

E. Streaming Decision Layer and Metrics

  • A causal trailing moving average smooths per-sample probabilities without using future samples.The smoothed prediction is the highest-probability class, and confidence is its maximum probability.Source: E. Streaming Decision Layer and Metrics · p. 4
  • The decision layer emits the smoothed class when confidence meets the 0.60 threshold; otherwise it can abstain, with optional persistence.The prose identifies −1 as the abstention value.Source: E. Streaming Decision Layer and Metrics · p. 4
  • Event-window accuracy measures the fraction of samples in an event window whose emitted class matches the true class.Aggregate fault-window accuracy pools samples across fault windows.Source: E. Streaming Decision Layer and Metrics · p. 4
  • First-correct delay can be shorter than the input-window length because the trailing window accumulates post-onset samples as each sample arrives.A correct decision can occur before the window contains only post-onset data.Source: E. Streaming Decision Layer and Metrics · p. 4

III. RESULTS

The evaluation compares six configurations on an unlabeled replay stream using a common streaming decision layer and event-window scoring. It asks which representation and model reaches the correct class earliest after fault onset, and what fault-window accuracy it sustains.

III. RESULTS

  • The six configurations are evaluated on the unlabeled replay stream under common decision-layer and event-window-scoring procedures.Source: §III · p. 4
  • The central timing question is which representation and model family reaches the correct class earliest after a fault begins.Source: §III · p. 4
  • The evaluation also asks what fault-window accuracy each configuration sustains.Source: §III · p. 4

A. Model-Level Performance

All six configurations classify every test event, but they differ in fault-window accuracy and first-correct delay. Sampled-value inputs reach correct decisions earlier, including in matched 80-sample comparisons; the 40-sample sampled-value MLP leads on the reported metrics.

A. Model-Level Performance

  • 11/11 event classification success is shared by all six configurations, while they differ in fault-window accuracy, false-normal rate, and first-correct delay.S40 and S80 denote sampled-value windows of 40 and 80 samples; P80 denotes the 80-sample one-cycle phasor representation.Source: A. Model-Level Performance · p. 4
  • 99.338% fault-window accuracy and 2.807 ms mean first-correct delay make the 40-sample sampled-value MLP the leader on every reported axis.It also records 99.792% normal accuracy, a 0.208% false-fault rate, and a 0.652% false-normal rate.Source: A. Model-Level Performance · p. 4
  • Sampled-value configurations have consistently earlier decisions, but their accuracy advantage is clearest for MLPs and depends on window length for CNNs.The 40-sample sampled-value CNN is slightly less accurate than its phasor counterpart, whereas the 80-sample sampled-value CNN is both faster and more accurate.Source: A. Model-Level Performance · p. 4

B. Matched-Window Comparison

  • At 80 samples, sampled-value configurations have lower delay and higher fault-window accuracy than their matched phasor counterparts.The comparison pairs S80-MLP with P80-MLP and S80-CNN with P80-CNN, isolating representation from window length.Source: B. Matched-Window Comparison · p. 4, Table II · p. 5
  • The full-stream overlay identifies the eleven scored event windows, confidence traces, and emitted classes across all six configurations.Source: Figure 2 · p. 5

C. Full-Stream Behavior

The full-stream replay aligns emitted decisions with physical event windows, while the accuracy-delay comparison favors S40-MLP and identifies timing as the larger difference.

C. Full-Stream Behavior

  • During event windows, emitted classes move from Normal to the corresponding fault family after onset and return to Normal after clearing.The shaded replay intervals align with visible voltage and current disturbances used for scoring.Source: C. Full-Stream Behavior · p. 5
  • Confidence decreases near event onsets and clearings, where causal windows mix pre-event with event samples or event with post-event samples.The best configuration's false-fault rate is 0.208%.Source: C. Full-Stream Behavior · p. 5

D. Accuracy-Delay Tradeoff

  • S40-MLP has the highest fault-window accuracy and shortest mean first-correct delay, Pareto-dominating the other five configurations.The accuracy-delay plot places it at the preferred upper-left position.Source: D. Accuracy-Delay Tradeoff · p. 5, Figure 3 · p. 5
  • S40-MLP exceeds P80-MLP by 0.699 percentage points, while phasor MLP and CNN delays exceed their sampled-value counterparts by 2.799 ms and 3.687 ms.The paper characterizes timing, rather than accuracy, as the dominant difference.Source: D. Accuracy-Delay Tradeoff · pp. 5–6
  • All six configurations enter the ABC three-phase-family class shortly after onset, while phasor traces for the BG fault show slower, more oscillatory confidence than sampled-value traces.The BG event is classified as its specific single-line-to-ground family.Source: Figure 5 · p. 6, Figure 4 · p. 6

E. Event Case Studies

The event case studies show family-specific decisions at fault onset, consistent configuration ordering across multiple events, and greater trace fluctuation in the 40-sample CNN.

E. Event Case Studies

  • Across a wider window containing two successive fault events, the relative configuration ordering is consistent from one fault family to another.The window spans 15.25–19.00 s.Source: E. Event Case Studies · p. 6, Figure 6 · p. 6
  • The ABC Family grouping classifies a three-phase event as one family rather than splitting it between ABC and ABCG.All six configurations enter the three-phase-family class shortly after onset.Source: E. Event Case Studies · p. 6
  • For the BG event, configurations identify the specific single-line-to-ground family; phasor traces show slower, more oscillatory confidence than the fastest sampled-value traces.Source: E. Event Case Studies · p. 6
  • At the CA fault onset, S40-MLP transitions first, the other sampled-value configurations follow, and phasor configurations transition last.The CA fault is a line-to-line fault involving phases C and A.Source: E. Event Case Studies · p. 6
  • The 40-sample sampled-value CNN detects and classifies the event, but its confidence and class trace fluctuate more than the corresponding MLP response.This is why event success alone is insufficient; fault-window accuracy and false-normal rate are also needed to characterize streaming performance.Source: E. Event Case Studies · p. 6

IV. DISCUSSION

The discussion frames the one-cycle phasor cost as delayed decisions rather than classification failure: sampled-value inputs are earlier, while this clean benchmark shows no offsetting phasor accuracy or stability benefit. The conclusion reports a Pareto-leading 40-sample MLP and bounds claims to the tested synchronous setting.

IV. DISCUSSION

  • The timing advantage is universal across model pairs, but accuracy ordering is mixed for CNNs and clearest for MLPs.The discussion identifies timing, not accuracy, as the universal claim.Source: §IV · pp. 6–7
  • First-correct delays are shorter than nominal window lengths because trailing-window decisions are emitted at every sample, making delay an empirical streaming-transition quantity.A correct decision can arrive before the window fills entirely with post-onset data.Source: §IV · p. 7
  • One-cycle DFT averaging may suppress noise, harmonics, and short disturbances, potentially benefiting phasors under noise, missing channels, or broader operating conditions absent here.These conditions are not part of the present clean benchmark.Source: §IV · p. 7
  • The study fixes faults at the midpoint of line 7–8, uses bolted resistance and fixed operating conditions, and omits noise, out-of-zone faults, load or dispatch variation, and hardware-in-the-loop timing.The taxonomy combines ABC and ABCG into one ABC Family class rather than distinguishing three-phase ground involvement.Source: §IV · p. 7

V. CONCLUSION

  • 99.34% fault-window accuracy, 99.79% normal accuracy, 0.21% false-fault rate, 0.65% false-normal rate, and 2.81 ms mean first-correct delay: the 40-sample sampled-value MLP Pareto-dominated the other five configurations.A matched-window comparison at eighty samples confirmed that the timing advantage follows from the representation rather than the window length.Source: §V · p. 7

IV. DISCUSSION

  • Across six configurations, every classifier identified every event, and sampled-value inputs reached the correct class earlier in every model pair.On this clean synchronous benchmark, the one-cycle phasor representation did not provide enough accuracy or stability benefit to offset its delay.Source: §IV · p. 6, §V · p. 7

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