App-4
IM 760201-01E
Measurement Functions Used in Harmonic Measurement
P(k)
S(k)
F
(
k) = tan
–1
Q(k)
P(k)
dc
(when k = 0)
Total Value (Total)
(No parentheses)
k
(when k = 1 to max)
Numbers and Characters in the Parentheses
I
r
(k)
2
+
I
j
(k)
2
I(dc) = I
r
(0)
I(k) =
U
r
(k)
2
+
U
j
(k)
2
Voltage U( ) [V]
Current I( ) (A)
U(dc) =U
r
(0)
U(k) =
Active power P( ) [W]
P(dc) = U
r
(0)
•
I
r
(0)
P(k) =
U
r
(k)
•
I
r
(k) +
U
j
(k)
•
I
j
(k)
S(dc) = P(dc)
Reactive power Q( ) [var]
(TYPE3)*
Apparent power S( ) [VA]
(TYPE3)*
Q(k) =
U
r
(k)
•
I
j
(k) –
U
j
(k)
•
I
r
(k)
Q(dc) = 0
—
—
S(k) = P(k)
2
+ Q(k)
2
S = P
2
+ Q
2
Power factor
L
( )
Phase difference
F
( ) [
°
]
Phase difference with U(1)
F
U(
) [°]
Phase difference with I(1)
F
I(
) [°]
F
U(k) = The phase difference
between U(k) and U(1)
—
—
—
F
I(k) = The phase difference
between I(k) and I(1)
L
(k) =
Measurement Functions
Used in Harmonic
Measurement
Methods of Computation and Determination
(Table 1/2)
(Continues on next page)
L
(dc) =
P(dc)
S(dc)
U(k)
2
k = min
max
U =
I(k)
2
k = min
max
I =
P(k)
k = min
max
P
=
Q(k)
k = min
max
Q
=
F
= tan
–1
(
)
P
S
P
L
=
S
* For details about the S and Q formula type settings, see section 5.4.
Note
• k denotes a harmonic order, r denotes the real part, and j denotes the imaginary part.
• U(k), Ur(k), Uj(k), I(k), Ir(k), and Ij(k) are expressed using rms values.
• The minimum harmonic order is denoted by min. min can be set to either 0 (the dc
component) or 1 (the fundamental signal). For details, see section 6.4.
• The upper limit of harmonic analysis is denoted by max. max is determined automatically
according to the PLL source frequency. It can go up to the 50
th
harmonic order.
Appendix 1 Symbols and Determination of Measurement Functions
