# HARMONIC ANALYSIS USE CASE: FEEDER A

## 📊 Telemetry Scenario
- **Client**: SGBA plant.
- **Feeder**: Main Raw Mill feeder A.
- **Inquiry**: *"What is the voltage harmonic distortion rate of feeder A?"*

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## ⚙️ Automated 12-Step Mitigation Pipeline

### Step 1: Telemetry Acquisition
Ingest active registers from Feeder A Modbus power analyzers:
- Phase A Current: $I_A = 422\text{ A}$ | Voltage: $V_A = 401\text{ V}$
- Phase B Current: $I_B = 418\text{ A}$ | Voltage: $V_B = 398\text{ V}$
- Phase C Current: $I_C = 425\text{ A}$ | Voltage: $V_C = 402\text{ V}$

### Step 2: FFT Spectral Scan
Compute 1024-point Fast Fourier Transform (FFT) on active waves:
- Main fundamental load ($I_1$): $380\text{ A}$
- 5th Harmonic ($I_5$ at 250Hz): $52.1\text{ A}$
- 7th Harmonic ($I_7$ at 350Hz): $15.4\text{ A}$

### Step 3: THD Calculations
$$\text{THDI} = \frac{\sqrt{I_5^2 + I_7^2}}{I_1} = \frac{\sqrt{52.1^2 + 15.4^2}}{380} = 14.28\%$$

### Step 4: IEEE 519 Standard Check
Verify limits (IEEE 519 Table 1):
- Voltage Distortion (THDV = 3.12% < 5.0% limit): **COMPLIANT**
- Current Distortion (THDI = 14.28% > 8.0% limit): **CRITICAL NON-COMPLIANCE**

### Step 5: Root Cause Isolation
Correlate THDI peaks with raw mill VFD cycles. Source identified: VFD switching loops on raw mill motors #3 and #4.

### Step 6: Sizing Correction
Determine Active Harmonic Filter (AHF) capacity to eliminate 5th harmonic:
- Projected filter injection: $52\text{ A}$ of anti-phase 5th harmonic current.
- Sized filter capacity: **150 kVAR AHF** tuned to 250Hz.

### Step 7: Waveform Mitigation Simulation
Simulate AHF activation. The mathematical model projects a THDI drop from $14.28\%$ down to **$3.82\%$**, restoring a smooth sinusoidal current waveform.