Why remove the mean?
Mean removal suppresses a constant DC component inside the selected window before fundamental correlation. It is not a complete decaying-DC compensation algorithm.
Implementation sequence
The estimator follows four explicit steps.
01Require a complete one-cycle window
02Remove the arithmetic mean
03Correlate with cosine and sine at bin 1
04Scale the complex result to RMS
05Build phase and residual phasors
06Derive sequence quantities
07Evaluate protection under trust gates
Mathematical form
A DC-removed fundamental DFT bin produces a complex RMS phasor.
For a window of N samples, ARVREL subtracts the sample mean and accumulates the real and imaginary correlations at the nominal fundamental bin.
mean = (1/N) Σ x[k] X1 = (√2/N) Σ (x[k] - mean) · (cos(-2πk/N) + j·sin(-2πk/N)) Result: complex RMS phasor X1
Why a single bin?
The implemented protection functions require the nominal fundamental phasor, not a complete frequency spectrum. A single-bin estimator is simpler to review and deterministic for the tested nominal-frequency fixtures.
Derived quantities
The phasor set supports residual and symmetrical-component calculations.
IA, IB, IC and VA, VB, VC
Each available channel is converted into a complex RMS phasor using the same one-cycle estimator.
IN/3I0 and VN/3V0 provenance
An explicitly decoded fourth channel is preferred. When unavailable, residual quantities can be calculated from the three phase phasors and must retain fallback provenance.
Positive, negative, and zero sequence
The conventional complex a-operator transformation derives sequence currents and voltages from the phase phasors.
Deterministic evidence
SIG-001 checks magnitude and balanced positive sequence.
The current test constructs 80 samples per cycle of balanced synthetic sine waves, evaluates current and voltage RMS, checks positive-sequence magnitude, and restrains negative sequence for the balanced fixture.
| Input | Expected result | Automated anchor |
|---|---|---|
| 80 samples/cycle, 2 A RMS balanced current | IA ≈ 2 A RMS; I1 ≈ 2 A; I2 near zero | FundamentalEstimator_ReturnsRmsMagnitudeAndBalancedPositiveSequence |
| 80 samples/cycle, 63.5 V RMS balanced voltage | VA ≈ 63.5 V RMS; V1 ≈ 63.5 V | FeederProtectionTests.cs |
Current limitations
State the estimator boundary before interpreting results.
Not currently claimed
- Full FFT or harmonic spectrum
- Adaptive frequency tracking
- Off-nominal-frequency accuracy characterization
- Decaying-DC removal beyond mean subtraction
- Anti-aliasing or merging-unit analog performance
- IEC 60255 measurement or timing type tests
Future validation track
- Frequency sweep around 50 and 60 Hz
- Harmonic and interharmonic injection
- Decaying-DC and CT-saturation fixtures
- Noise and quantization sensitivity
- Alternative windows and estimator comparison
- Runtime and allocation benchmarks
Interpretation boundary: a synthetic nominal-frequency unit test verifies the implemented calculation for that fixture. It does not establish calibrated accuracy across all process-bus, merging-unit, operating, or timing conditions.