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16. APPENDICES
This section presents the mathematical formulae used in calculating various parameters.
16.1. MATHEMATICAL FORMULAE
16.1.1. NETWORK FREQUENCY AND SAMPLING
Sampling is controlled by (locked to) the network frequency so as to deliver 256 samples per cycle from 40 Hz to 70 Hz. This
locking is essential for many calculations, including reactive power, distorting power, fundamental power factor, unbalance, and
harmonic factors and angles.
The instantaneous frequency is measured by analysing eight consecutive positive-going zero crossings on the signal in question
after digital low-pass filtering and digital suppression of the DC component (i.e. 7 periods filtered). The time of the zero crossing
is determined precisely by linear interpolation between two samples to achieve resolution better than 0.002%.
The device is capable of calculating an instantaneous frequency simultaneously on each of the 3 phases in voltage (phase-to-
neutral for distribution systems with neutral and phase-to-phase for distribution systems without neutral) or in current. It then
chooses one from among two or three of them as the official instantaneous frequency.
The network frequency over one second is determined (approximately) as the reciprocal of the arithmetic mean of the instantane-
ous periods.
The signals are acquired using a 16-bit converter and (for current acquisition) dynamic gain switches.
16.1.2. WAVEFORM MODE
16.1.2.1. RMS values of half-cycle voltage and current (excluding neutral)
Half-cycle RMS phase-to-neutral voltage of phase (i+1) with i ∈ [0; 2].
[ ] [ ][ ]
1
Vdem
1) (
2
∑
−
=
⋅=
suivantZéro
Zéron
niV
NechDemPer
i
Half-cycle RMS phase-to-phase voltage of phase (i+1) with i ∈ [0 ; 2].
[ ] [ ][ ]
1
Udem
1) (
2
∑
−
=
⋅=
suivantZéro
Zéron
niU
NechDemPer
i
Half-cycle RMS current of phase (i+1) with i ∈ [0 ; 2].
[ ] [ ][ ]
∑
−
=
⋅=
1) (
2
1
Adem
suivantZéro
Zéron
niA
NechDemPer
i
Notes: these values are calculated for each half-cycle so as not to miss any fault.
NechDemPer is the number of samples in the half cycle.
16.1.2.2. Minimum and maximum half-cycle RMS values (excluding neutral)
Minimum and maximum RMS phase-to-neutral voltages of phase (i+1) with i ∈ [0 ; 2].
Vmax [i] = max(Vdem[i]), Vmin[i] = min(Vdem[i])
Minimum and maximum RMS phase-to-phase voltages of phase (i+1) with i ∈ [0 ; 2].
Umax [i] = max(Udem[i]), Umin[i] = min(Udem[i])
Minimum and maximum RMS currents of phase (i+1) with i ∈ [0 ; 2].
Amax [i] = max(Adem[i]), Amin[i] = min(Adem[i])
Note: The duration of the evaluation is left to the user’s discretion (reset by pressing the
key in the MAX-MIN mode).
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