User Manual
87
Negative-sequence unbalance factor of the phase-to-phase voltages in a distribution system without neutral
+
−
Urms
Urms
=Uunb
Remark: The following quantities are saved with the negative-sequence unbalance factor in a trend recording: Uns = |Urms-| and
Ups = |Urms+| (the norms of the negative-sequence and positive-sequence fundamental symmetrical components,
respectively).
Positive-sequence fundamental symmetrical current (vector)
[ ] [ ] [ ]
)2AFrmsa1AFrmsa0AFrms(
3
1
Arms
2
⋅+⋅+=
+
Reverse-sequence fundamental symmetrical current (vector)
[ ] [ ] [ ]
)2AFrmsa1AFrmsa0AFrms(
3
1
Arms
2
⋅+⋅+=
−
Negative-sequence unbalance rate of the current
+
−
Arms
Arms
=Aunb
Remark: The following quantities are saved with the negative-sequence unbalance factor in a trend recording: Ans = |Arms-| and
Aps = |Arms+| (the norms of the negative-sequence and positive-sequence fundamental symmetrical components,
respectively).
16.1.2.9. Fundamental rms values (excluding neutral – over one second)
These are calculated from the filtered vector (instantaneous) values. A digital filter made up of 6 low-pass order 2 infinite pulse
response Butterworth filters and one high-pass order 2 infinite pulse response Butterworth filter is used to extract the fundamental
components.
16.1.2.10. Fundamental angular values (excluding neutral – over one second)
These are calculated from the filtered vector (instantaneous) values. A digital filter made up of 6 low-pass order 2 infinite pulse
response Butterworth filters and one high-pass order 2 infinite pulse response Butterworth filter is used to extract the fundamental
components. The angular values calculated are those between:
2 phase-to-neutral voltages
2 line currents
2 phase-to-phase voltages
One phase-to-neutral voltage and one line current (distribution systems with neutral)
One phase-to-phase voltage and one line current (2-wire two-phase distribution systems)
16.1.3. HARMONIC MODE
16.1.3.1. FFT (excluding neutral – over 4 consecutive periods every second)
These calculations are carried out by FFT (16 bits), 1024 points over four cycles, with a rectangular window (see IEC61000-4-
7). From the real parts b
k
and the imaginary parts a
k
, the harmonic factor is calculated for each order (j) and for each phase (i)
Vharm[i][j], Uharm[i][j] and Aharm[i][j] with respect to the fundamental and the angles Vph[i][j], Uph[i][j] and Aph[i][j] with respect
to the fundamental.
Note: The calculations are performed sequentially: {V1; A1} then {V2; A2} then {V3; A3} then {U1; U2} and finally {U3}. In the case
of a 2-wire two-phase distribution source, the couple {V1; A1} is replaced by the couple {U1; A1}.
The level in % with respect to the fundamental [% f] ⇔
100
4
c
c
k
k
=
τ
The level in % with respect to the total RMS value [% r] ⇔
100
50
0
2
4
∑
=
=
m
m
k
k
C
c
τ
50