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Recording Merge & Alignment

Time synchronization and waveform alignment algorithms for merging multi-source COMTRADE recordings.

In Detego

See the Merging Recordings Guide for how to use this feature in the app. This page covers the mathematical theory.

Overview

When two COMTRADE recordings capture the same power system event from different devices, their timelines must be aligned before the channels can be meaningfully combined. The core problem is that relay clocks are often not synchronized -- even with NTP, clock offsets of tens or hundreds of milliseconds are common. GPS-synced relays have sub-millisecond accuracy, but many installations lack GPS timing.

The alignment algorithm uses a three-layer approach:

Coarse alignment -- establish an initial offset using either timestamps or fault inception detection
Cross-correlation refinement -- refine the offset to sub-sample precision using waveform correlation
Cross-validation -- compare timestamp-based and fault-based offsets to assess clock synchronization quality

Timestamp Alignment

The simplest alignment method uses the recording start timestamps embedded in the COMTRADE CFG header. Each recording has a start time $T_{\text{start}}$ and a trigger time $T_{\text{trigger}}$ . The alignment uses start times rather than trigger times because trigger times include variable relay processing delays that differ between devices.

Timestamp offset

\Delta t_{\text{ts}} = T_{\text{start,B}} - T_{\text{start,A}}

Where

$\Delta t_{\text{ts}}$ Time offset to apply to recording B relative to recording A
$T_{\text{start,A}}$ Start timestamp of recording A
$T_{\text{start,B}}$ Start timestamp of recording B

Timezone Correction

Relays at different substations may be configured with different timezone settings, or one relay may record in UTC while another uses local time. The timezone correction algorithm detects and removes these offsets by checking whether the computed offset is close to a multiple of 15 minutes (the smallest timezone granularity in use worldwide, accounting for zones like UTC+5:45 Nepal and UTC+9:30 Australia).

If the offset falls within a tolerance window of a 15-minute multiple, the nearest multiple is subtracted. This preserves the sub-minute timing difference (which reflects actual clock drift) while removing the timezone component.

Alignment pipeline: File A (purple) and File B before alignment (dotted orange) show a 13 ms timing difference at fault inception. After applying the computed offset, File B (solid orange) aligns with File A — both fault inception points coincide. The opposite current polarity is expected (current flows into the fault from both line ends).

Fault Inception Alignment

When a fault event is present in both recordings, the fault inception point provides a physical anchor that is independent of clock settings. The algorithm detects fault inception in each recording independently using the superimposed delta method, then aligns the two inception points.

Superimposed delta

\Delta I(t) = I(t) - I(t - T)

Where

$\Delta I(t)$ Change component at time t
$T$ One power frequency cycle period

The coarse fault-based offset is simply the difference between the two inception times (expressed in their respective local timelines):

Fault inception offset

\Delta t_{\text{fi}} = t_{\text{inception,A}} - t_{\text{inception,B}}

Where

$\Delta t_{\text{fi}}$ Time offset derived from fault inception
$t_{\text{inception,A}}$ Fault inception time in recording A (relative to start)
$t_{\text{inception,B}}$ Fault inception time in recording B (relative to start)

The detection runs independently on all current and voltage channels in each file. The earliest detected inception across all channels is used. This provides roughly 10-15 ms accuracy, limited by differences in relay ADC processing, anti-aliasing filter delays, and the fact that the fault wavefront arrives at the two line terminals at slightly different times (propagation delay).

Cross-Correlation Refinement

After coarse alignment, the offset is refined using cross-correlation of the superimposed delta signals. This exploits the fact that the same fault produces similar transient waveforms at both line terminals (with possible polarity inversion due to opposite CT conventions).

Channel Matching

The algorithm finds matching channel pairs by phase -- voltage channels are matched with voltage channels and current channels with current channels. Phase extraction uses the channel naming conventions from the COMTRADE header to identify which channels correspond to phases A, B, and C.

Window Extraction and Normalization

For each matched channel pair, the algorithm:

Computes the superimposed delta signal for both channels
Extracts a 3-cycle window centered on the fault inception point
Normalises each window by subtracting the mean and dividing by the standard deviation, producing zero-mean unit-variance signals

Correlation Computation

The normalised cross-correlation function is computed for both polarities to handle the case where CTs at opposite ends of a line produce currents of opposite sign:

Normalised cross-correlation

R(\tau) = \frac{1}{N} \sum_{t=0}^{N-1} A(t) \cdot B(t + \tau)

Where

$R(\tau)$ Correlation coefficient at lag \tau
$A(t)$ Normalised delta signal from recording A
$B(t + \tau)$ Normalised delta signal from recording B, shifted by \tau
$N$ Number of samples in the correlation window

The correlation is computed for both $B(t)$ and $-B(t)$ (polarity inversion). The polarity that produces the higher peak correlation is selected.

Sub-Sample Parabolic Interpolation

The cross-correlation function has integer-sample resolution. To achieve fractional-sample precision, a parabolic (quadratic) interpolation is fitted to the three samples around the peak:

Parabolic peak refinement

\tau_{\text{refined}} = \tau_{\text{best}} + \frac{R(\tau_{\text{best}}-1) - R(\tau_{\text{best}}+1)}{2\bigl(2R(\tau_{\text{best}}) - R(\tau_{\text{best}}-1) - R(\tau_{\text{best}}+1)\bigr)}

Where

$\tau_{\text{refined}}$ Sub-sample lag estimate
$\tau_{\text{best}}$ Integer lag with the highest correlation
$R(\tau)$ Correlation values at three adjacent lags

This achieves fractional-sample alignment precision, significantly better than the sample-rate limit.

Cross-Validation

When both timestamp and fault inception offsets are available, the algorithm cross-validates them by comparing the two independently derived offsets. This provides a measure of clock synchronization quality.

Agreement -- if the two offsets agree within 2 power frequency cycles, the clocks are considered synchronized. The estimated accuracy is the absolute difference between the two offsets: $|\Delta t_{\text{ts}} - \Delta t_{\text{fi}}|$ .
Disagreement -- if the offsets differ by more than 2 cycles, the relay clocks are not synchronized. In this case, fault-based alignment is recommended because it is independent of clock settings.

Confidence Estimation

The alignment confidence reflects how reliably the fault inception was detected. It is based on the RMS change at the inception point -- a larger change means a more clearly defined fault onset and therefore a more reliable alignment anchor.

The confidence is measured as the maximum relative RMS change across all channels:

RMS change ratio

\rho = \max_{\text{channels}} \frac{|I_{\text{RMS,fault}} - I_{\text{RMS,pre}}|}{I_{\text{RMS,pre}}}

Where

$\rho$ Maximum relative RMS change across all channels
$I_{\text{RMS,fault}}$ RMS magnitude during the fault
$I_{\text{RMS,pre}}$ Pre-fault RMS magnitude

The ratio $\rho$ is then mapped to a confidence score on a scale from 0 to 1. Higher RMS changes (indicating more severe faults with clearly defined inception points) produce higher confidence scores.

Resampling

When the two recordings have different sample rates, the lower-rate recording is resampled to match the higher rate. The target sample rate is:

Target sample rate

f_s = \max(f_{s,A},\; f_{s,B})

Where

$f_s$ Output sample rate
$f_{s,A}$ Sample rate of recording A
$f_{s,B}$ Sample rate of recording B

Analog Channel Resampling

Analog channels (voltages and currents) are resampled using linear interpolation between adjacent samples:

Linear interpolation

y(t) = y_0 + \frac{t - t_0}{t_1 - t_0} \cdot (y_1 - y_0)

Where

$y(t)$ Interpolated value at the target time t
$y_0,\; y_1$ Sample values at times t_0 and t_1 bracketing the target
$t_0,\; t_1$ Times of the two bracketing source samples

Boundary samples at the edges of the recording are clamped to the nearest available source sample to avoid extrapolation artifacts.

Digital Channel Resampling

Digital channels (binary signals such as trip contacts, breaker status, protection flags) use nearest-neighbor resampling. Each output sample takes the value of the closest source sample in time. This preserves the binary nature of the signal -- interpolating between 0 and 1 would produce fractional values that have no physical meaning for contact status signals.

CFF Serialization

The merged output is serialized as an IEEE C37.111-1999 CFF file (Combined File Format), which embeds both the CFG configuration header and the ASCII DAT sample data in a single file.

Channel metadata: Each channel retains its original unit, phase designation, CT/VT ratios, and scaling factors from the source file.
Channel naming: Channel names are prefixed with the source station or device name to avoid duplicates (e.g., "StationA_IA", "StationB_IA").
Provenance: The CFG header text includes merge provenance information documenting which source files were combined and the alignment offset applied.

Engineering Applications

Merged recordings enable several important analyses:

Differential protection verification: With currents from both terminals on the same timeline, you can compute operate and restraint quantities and verify that differential protection would have operated correctly.
Two-ended fault location: Using voltage and current from both line terminals eliminates the fault resistance error inherent in single-ended methods, providing more accurate fault distance estimates.
Protection coordination review: Comparing trip times and relay operations from multiple devices on a common timeline reveals whether protection coordination is working as designed.

Alignment Accuracy

The accuracy of merged-file analysis depends directly on alignment quality. For differential protection analysis where sub-cycle precision matters, GPS-synced timestamps are strongly recommended. Fault-detection alignment provides 10-15 ms accuracy, which is sufficient for fault location and event correlation but may introduce small errors in differential current calculations.

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Recording Merge & Alignment

Time synchronization and waveform alignment algorithms for merging multi-source COMTRADE recordings.

In Detego

See the Merging Recordings Guide for how to use this feature in the app. This page covers the mathematical theory.

Overview

The alignment algorithm uses a three-layer approach:

Coarse alignment -- establish an initial offset using either timestamps or fault inception detection
Cross-correlation refinement -- refine the offset to sub-sample precision using waveform correlation
Cross-validation -- compare timestamp-based and fault-based offsets to assess clock synchronization quality

Timestamp Alignment

Timestamp offset

\Delta t_{\text{ts}} = T_{\text{start,B}} - T_{\text{start,A}}

Where

$\Delta t_{\text{ts}}$ Time offset to apply to recording B relative to recording A
$T_{\text{start,A}}$ Start timestamp of recording A
$T_{\text{start,B}}$ Start timestamp of recording B

Timezone Correction

Fault Inception Alignment

Superimposed delta

\Delta I(t) = I(t) - I(t - T)

Where

$\Delta I(t)$ Change component at time t
$T$ One power frequency cycle period

The coarse fault-based offset is simply the difference between the two inception times (expressed in their respective local timelines):

Fault inception offset

\Delta t_{\text{fi}} = t_{\text{inception,A}} - t_{\text{inception,B}}

Where

$\Delta t_{\text{fi}}$ Time offset derived from fault inception
$t_{\text{inception,A}}$ Fault inception time in recording A (relative to start)
$t_{\text{inception,B}}$ Fault inception time in recording B (relative to start)

Cross-Correlation Refinement

Channel Matching

Window Extraction and Normalization

For each matched channel pair, the algorithm:

Computes the superimposed delta signal for both channels
Extracts a 3-cycle window centered on the fault inception point
Normalises each window by subtracting the mean and dividing by the standard deviation, producing zero-mean unit-variance signals

Correlation Computation

The normalised cross-correlation function is computed for both polarities to handle the case where CTs at opposite ends of a line produce currents of opposite sign:

Normalised cross-correlation

R(\tau) = \frac{1}{N} \sum_{t=0}^{N-1} A(t) \cdot B(t + \tau)

Where

$R(\tau)$ Correlation coefficient at lag \tau
$A(t)$ Normalised delta signal from recording A
$B(t + \tau)$ Normalised delta signal from recording B, shifted by \tau
$N$ Number of samples in the correlation window

The correlation is computed for both $B(t)$ and $-B(t)$ (polarity inversion). The polarity that produces the higher peak correlation is selected.

Sub-Sample Parabolic Interpolation

The cross-correlation function has integer-sample resolution. To achieve fractional-sample precision, a parabolic (quadratic) interpolation is fitted to the three samples around the peak:

Parabolic peak refinement

\tau_{\text{refined}} = \tau_{\text{best}} + \frac{R(\tau_{\text{best}}-1) - R(\tau_{\text{best}}+1)}{2\bigl(2R(\tau_{\text{best}}) - R(\tau_{\text{best}}-1) - R(\tau_{\text{best}}+1)\bigr)}

Where

$\tau_{\text{refined}}$ Sub-sample lag estimate
$\tau_{\text{best}}$ Integer lag with the highest correlation
$R(\tau)$ Correlation values at three adjacent lags

This achieves fractional-sample alignment precision, significantly better than the sample-rate limit.

Cross-Validation

Agreement -- if the two offsets agree within 2 power frequency cycles, the clocks are considered synchronized. The estimated accuracy is the absolute difference between the two offsets: $|\Delta t_{\text{ts}} - \Delta t_{\text{fi}}|$ .
Disagreement -- if the offsets differ by more than 2 cycles, the relay clocks are not synchronized. In this case, fault-based alignment is recommended because it is independent of clock settings.

Confidence Estimation

The confidence is measured as the maximum relative RMS change across all channels:

RMS change ratio

\rho = \max_{\text{channels}} \frac{|I_{\text{RMS,fault}} - I_{\text{RMS,pre}}|}{I_{\text{RMS,pre}}}

Where

$\rho$ Maximum relative RMS change across all channels
$I_{\text{RMS,fault}}$ RMS magnitude during the fault
$I_{\text{RMS,pre}}$ Pre-fault RMS magnitude

Resampling

When the two recordings have different sample rates, the lower-rate recording is resampled to match the higher rate. The target sample rate is:

Target sample rate

f_s = \max(f_{s,A},\; f_{s,B})

Where

$f_s$ Output sample rate
$f_{s,A}$ Sample rate of recording A
$f_{s,B}$ Sample rate of recording B

Analog Channel Resampling

Analog channels (voltages and currents) are resampled using linear interpolation between adjacent samples:

Linear interpolation

y(t) = y_0 + \frac{t - t_0}{t_1 - t_0} \cdot (y_1 - y_0)

Where

$y(t)$ Interpolated value at the target time t
$y_0,\; y_1$ Sample values at times t_0 and t_1 bracketing the target
$t_0,\; t_1$ Times of the two bracketing source samples

Boundary samples at the edges of the recording are clamped to the nearest available source sample to avoid extrapolation artifacts.

Digital Channel Resampling

CFF Serialization

The merged output is serialized as an IEEE C37.111-1999 CFF file (Combined File Format), which embeds both the CFG configuration header and the ASCII DAT sample data in a single file.

Channel metadata: Each channel retains its original unit, phase designation, CT/VT ratios, and scaling factors from the source file.
Channel naming: Channel names are prefixed with the source station or device name to avoid duplicates (e.g., "StationA_IA", "StationB_IA").
Provenance: The CFG header text includes merge provenance information documenting which source files were combined and the alignment offset applied.

Engineering Applications

Merged recordings enable several important analyses:

Differential protection verification: With currents from both terminals on the same timeline, you can compute operate and restraint quantities and verify that differential protection would have operated correctly.
Two-ended fault location: Using voltage and current from both line terminals eliminates the fault resistance error inherent in single-ended methods, providing more accurate fault distance estimates.
Protection coordination review: Comparing trip times and relay operations from multiple devices on a common timeline reveals whether protection coordination is working as designed.

Alignment Accuracy

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