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Sliding one-cycle root-mean-square magnitude for fault current and voltage measurement.
In Detego
The Root Mean Square (RMS) value gives the effective (heating) value of an AC waveform. A 100 A RMS alternating current delivers the same heating energy to a resistor as a 100 A direct current. In protection engineering, RMS is the fundamental magnitude measurement underpinning overcurrent, undervoltage, and distance protection schemes.
Detego computes RMS using a sliding one-cycle window that advances sample-by-sample through the recording. At each position, the window captures exactly one full cycle of the fundamental frequency, ensuring that the sinusoidal component integrates cleanly to its true RMS value.
Discrete RMS (sliding window)
Where
The window length is determined by the system frequency and the recording sample rate.
This is the discrete-time equivalent of the continuous RMS integral. By squaring each sample, averaging, and taking the square root, we obtain the effective value regardless of waveform shape -- it works correctly for sinusoidal, distorted, or non-periodic signals.
For a 50 Hz system, one cycle is . At a sample rate of 4000 samples/second, the window contains samples.
For a 60 Hz system, one cycle is . At 4800 samples/second, the window contains samples.
The computed window length is validated to be within 80-120% of the expected cycle duration. This guard prevents obviously wrong RMS values when the sample rate and nominal frequency produce a non-integer number of samples per cycle. A minimum of 2 samples per window is enforced to avoid degenerate cases in very low sample rate recordings.
The diagram below shows an instantaneous current waveform with its RMS envelope overlaid. Before the fault, the RMS value tracks the steady-state load current. At fault inception, the RMS steps up to reflect the increased fault current magnitude.
Instantaneous waveform with RMS envelope overlay. The RMS value is computed using a sliding one-cycle window. At fault inception, the RMS steps up reflecting the increased fault current magnitude.
The RMS Peak annotation tool places a dot and label at the point of highest RMS value within the visible time range. You may notice that this dot does not always sit on the tallest visible peak of the waveform. This is expected behavior — here is why.
The instantaneous peak is the single tallest point on the waveform — the tip of one specific half-cycle. The RMS peak is the time at which the one-cycle RMS envelope reaches its maximum — the cycle with the highest overall energy content.
During a fault, two effects cause these to diverge:
The diagram below illustrates a fault with decaying DC offset. Notice how the tallest instantaneous peak (purple diamond) occurs early — inflated by the DC component — while the peak of the RMS envelope (red circle) occurs later when the full AC fault current has developed.
During a fault with DC offset, the peak instantaneous value (purple diamond) occurs at the first tall crest — inflated by the decaying DC component. The peak RMS (red circle) occurs later, once the fundamental AC component has fully ramped up, representing the true maximum energy per cycle.
The annotation dot is placed on the nearest waveform crest to the peak RMS time, so it visually sits on top of the envelope. The displayed RMS value is computed at that exact point, ensuring it matches the tooltip value when you hover over the dot.
RMS vs Peak — Which to Use?
RMS is the base measurement for most protection functions:
Why RMS, not peak?
The one-cycle window means the RMS value has a settling time of one full cycle after any transient event. During the first cycle after fault inception, the RMS value is transitioning and does not yet represent the true fault-level magnitude. For sub-cycle detection, consider using the superimposed delta signal instead, which responds within a single sample of the fault.