APIC-Net

Author: Utkarsh Tyagi · IEEE 39-Bus VSM Cyberattack Detection

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Research Goal

Challenging and improving upon Khaleghi et al. 2025 (PI-LSTM) by showing that a simple physics-residual approach — requiring zero training — dramatically outperforms a complex federated LSTM trained for hours.

The project uses the Φ (Phi) Tensor framework as an analytical tool to identify which physical constraints carry detection signal for each attack type.

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Key Result

A single physics residual r4 = |ω_C − ω_local|, thresholded at its 95th normal percentile, achieves AUC = 0.931 on all 4 attack types with zero training.
Combined with the swing-equation residual r_phys, it reaches AUC = 0.959 — compared to PI-LSTM's AUC = 0.525 after 50 federated training rounds.

Full Comparison Table (V2 Dataset)

Method	Overall AUC	freq	coi	power	voltage	Training
PI-LSTM (50 FL rounds)	0.525	~0.4	~0.36	~0.63	~0.62	~24h
Pure r_phys	0.632	0.998	0.500	0.500	0.500	None
r4-only	0.931	0.891	0.931	0.919	0.976	None
r4 + r_phys	0.959	0.997	0.931	0.920	0.976	None

Results on V2 dataset (calibrated amplitudes: freq SNR=1.78×, power SNR=2.69×, voltage large-disturbance class).
COI attack fix (Option A1 — upstream spoof) is in progress.

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Why PI-LSTM Fails

Report report_02d_closure.md diagnosed the root cause:

• PI-LSTM learns reconstruction error (r_data = |x - x̂|)
• Under attack, signals become more predictable (attacks are smooth, structured perturbations)
• Score is inverted: normal=0.84, attack=0.56–0.58 → random-chance AUC

The physics component (r_phys) is present in the architecture but contributes negligibly because r_data >> r_phys in magnitude.

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Why Pure Physics (r_phys) Is Structurally Blind to 3/4 Attacks

The swing-equation Euler residual:

r_phys(t) = |ω(t+1) − [ω(t) + dt·(1/2H)·(p*·ω* − P_e·ω* + D·(ω*−ω) + F·(ω_C−ω))]|

Attack	Corrupts	r_phys response
freq	ω (output of physics)	✅ Detects — Euler prediction diverges from observation
coi	ω_C (input to swing eq.)	❌ Blind — corrupted input used in prediction → residual cancels
power	p* (input to swing eq.)	❌ Blind — same reason
voltage	v_ref (input to voltage controller)	❌ Blind — same reason

This is not a bug — it is the fundamental limit of single-VSM physics verification. If the inputs to the equation are compromised, the equation faithfully computes with corrupted data. r_phys is mathematically guaranteed to be zero for these attack types.

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What r4 Detects and Why

r4 = |ω_C_received − ω_local| measures the consistency between the COI feedback signal and the local frequency. In normal operation this difference is small (≈0.13 rad/s mean).

Attack	Why r4 detects it
freq	ω_local is spoofed → diverges from ω_C
coi	ω_C_received is corrupted → diverges from ω_local
power	p* injection drives ω_local away from network average → ω_C−ω_local grows
voltage	v_ref perturbation causes large ω deviation via controller → diverges from ω_C

r4 is the COI consistency residual — it detects attacks via their cross-VSM signature rather than single-VSM physics violation. This is why it where r_phys is blind.

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Dataset (V2 — Calibrated)

Attack Injection Method

Attack	Signal	Amplitude	Waveforms
freq	ω (frequency sensor spoof)	1–5 rad/s (unchanged)	constant, sine, square, ramp
coi	Outgoing ω to aggregator (upstream spoof)	calibrated	random walk bias
power	p* (setpoint injection)	0.285–0.76 rad/s	constant, sine, square, ramp
voltage	v_ref (voltage reference tamper)	1–5 rad/s	constant, sine, square, ramp

V2 Audit Results

Attack	Normal r4_std	Attack r4_mean	SNR	Detection Rate	Verdict
freq	0.510	0.911	1.78×	67%	REALISTIC
coi	0.510	0.834	1.63×	83%	REALISTIC (fix in progress)
power	0.510	1.374	2.69×	79%	REALISTIC
voltage	0.510	8.343	16.35×	94%	HIGH-SEVERITY (accepted)

Voltage attacks cause inherently large omega deviations due to VSM controller nonlinearity.
Categorised as a high-severity rather than stealthy attack class.

Sample Scenarios

r4 Signal Distribution (V2 Audit)

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Φ Tensor Analysis

The Φ Tensor framework defines 4 physical residuals per VSM per timestep:

Residual	Definition	Detects
r1	|Δω − dt·swing_eq|	freq attacks (via r_phys)
r2	|p − p_approx|	power injection (weak, collapses in attack)
r3	|v_dc − v_dc_model|	voltage attacks (weak)
r4	|ω_C − ω_local|	All 4 attack types

Signal check finding (report_03b): r4 dominates all other residuals. The Φ off-diagonal structure (cross-constraint inconsistency) reduces to r4 for COI/power/voltage and r_phys for freq. The Φ MLP does not outperform the analytical combination.

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Open Problem — COI Correlation

Status: Fix in progress (Option A1)

For COI attacks any additive injection into ω_C mathematically ensures:

r4 = ω_C_received − ω_local = injected_bias + natural_gap

When amplitude >> noise, pearsonr(injection, r4) → 1.0 regardless of injection shape. This makes r4 a direct readout of the attack, not a physical detection.

Fix (Option A1 — self-exclusion): VSM j spoofs its outgoing omega to the aggregator. Other 5 VSMs detect the inconsistency via their r4. VSM j itself receives the honest omega_C (computed without its own spoof) — breaking the correlation at j by construction.

This is physically realistic: the attacker manipulates what they report outward but cannot alter what was last received.

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Project Structure

APIC-Net/
├── simulation/
│   ├── vsm_simulator.py        # Euler VSM swing equation + COI aggregation
│   ├── attack_generator.py     # Attack injection (V2: calibrated amplitudes)
│   └── generate_dataset.py     # Full generation pipeline (3500 scenarios)
│
├── configs/
│   └── simulation_config.py   # All hyperparameters
│
├── models/
│   ├── pi_lstm/               # Baseline (Khaleghi et al. reproduction)
│   │   ├── model.py, train.py, federated.py
│   │   └── pure_physics_baseline.py    # r_phys (no training)
│   └── phi_tensor/
│       ├── residuals.py       # r1–r4 per-VSM per-timestep
│       ├── phi_tensor.py      # Φ matrix + gradients
│       ├── features.py        # 20-dim feature extraction
│       ├── r4_baseline.py     # r4-only + r4+r_phys combined detector
│       └── dataset_audit.py   # Validity audit (SNR, correlation, detection rate)
│
├── data/                      # vsm_{0..5}.npz — per-VSM scenario arrays
├── results/                   # JSON results + plots
│   └── plots/                 # Audit plots
├── reports/                   # Numbered research reports (see below)
└── .agent/                    # Task files, system context, status reports

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Reports Index

Report	Key Finding
report_01_dataset.md	Initial dataset generation and spec
report_02d_closure.md	PI-LSTM root cause: r_data score inversion (AUC=0.507)
report_02e_physics_baseline.md	r_phys: freq AUC=0.998, COI/power/voltage AUC=0.5 (structural blindness)
report_03_phi_tensor.md	Φ Tensor implementation + spec conflicts resolved
report_03b_decision_gate.md	r4 AUC=0.946 dominates — Φ MLP adds no value
report_03c_dataset_audit.md	V1 audit: power/voltage SNR too high, COI correlation=0.99
report_04_dataset_v2.md	V2 dataset: calibrated amplitudes, verdict VALID
report_04b_coi_diagnosis.md	COI correlation diagnosis: additive injection always correlates
.agent/report.md	Current status: COI Option A1 fix in progress

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Setup

python -m venv .venv
.venv\Scripts\activate        # Windows
pip install -r requirements.txt

Generate dataset:

python -m simulation.generate_dataset

Run baselines (no training):

python -m models.pi_lstm.pure_physics_baseline   # r_phys
python -m models.phi_tensor.r4_baseline          # r4-only + combined

Audit dataset:

python -m models.phi_tensor.dataset_audit

Requirements: Python 3.10+, NumPy, PyTorch, scikit-learn, SciPy, matplotlib