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8.4.2 Measurement Formulas:
1
M
U12 =
Phase-phase Voltages: U12
Where: U12 (n ) are the samples of the chained values.
M is the number of sampling on a period (64)
Phase to phase Voltages THD
M −1
∑U (n )
n =0
2
12
THDU 23 in %
N −1
THDU12 = 100
∑U
n =0
2
N
Line Currents :
2
12
( n)
2
2
⎧⎪⎡ N −1
⎛ 2πn ⎞⎤ ⎫⎪
⎛ 2πn ⎞⎤ ⎡ N −1
⎟⎥ ⎬
⎟⎥ + ⎢∑U12 (n) sin ⎜
⎨⎢∑U12 (n) cos ⎜
⎝ N ⎠⎦ ⎪⎭
⎝ N ⎠ ⎦ ⎣ n =0
⎪⎩⎣ n=0
I3 =
I3
I 1 (n ) are the samples of the line currents.
THD of the phase currents:
1
M
−1
M −1
∑ I (n )
2
3
n =0
THDI 3
N −1
THDI3 = 100
∑I
n =0
2
N
2
3
( n)
2
2
⎧⎪⎡ N −1
⎛ 2πn ⎞⎤ ⎡ N −1
⎛ 2πn ⎞⎤ ⎫⎪
I
n
I
n
(
)
cos
(
)
sin
+
⎜
⎟
⎜
⎟
⎨ ⎢∑ 3
⎥ ⎢∑ 3
⎥ ⎬
⎝ N ⎠ ⎦ ⎣ n =0
⎝ N ⎠⎦ ⎪⎭
⎪⎩⎣ n=0
Three phase Active Power:
1 ⎡ M −1
⎤
U 23 (n + M 4) I 1 (n )⎥ 3
∑
⎢
M ⎣ n =0
⎦
M −1
1 ⎡
⎤
QΣ =
U 23 (n ) I 1 (n )⎥ 3
∑
⎢
M ⎣ n =0
⎦
PΣ =
PΣ
Three phase reactive Power: QΣ
S Σ = PΣ2 + QΣ2
Three phase apparent Power: S Σ
Three phase Power Factor:
−1
λΣ
λΣ =
where sign(x) is equal to 1 with x > 0, to -1 with x < 0.
Pag. 51 di 80
PΣ
sign (QΣ )
SΣ