Pag. 52 di 152
1
2
sin
)
(
2
cos
)
(
2
)
(
100
2
1
0
2
2
1
0
2
1
0
2
2
2
−
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
+
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
=
∑
∑
∑
−
=
−
=
−
=
N
n
N
n
N
n
I
N
n
n
I
N
n
n
I
N
n
I
THD
π
π
1
2
sin
)
(
2
cos
)
(
2
)
(
100
2
1
0
3
2
1
0
3
1
0
2
3
3
−
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
+
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
=
∑
∑
∑
−
=
−
=
−
=
N
n
N
n
N
n
I
N
n
n
I
N
n
n
I
N
n
I
THD
π
π
Phase Active Powers:
3
2
1
,
,
P
P
P
;
( ) ( )
∑
−
=
=
1
0
1
1
1
1
M
n
N
n
I
n
U
M
P
;
( ) ( )
∑
−
=
=
1
0
2
2
2
1
M
n
N
n
I
n
U
M
P
;
( ) ( )
∑
−
=
=
1
0
3
3
3
1
M
n
N
n
I
n
U
M
P
Phase reactive Powers:
3
2
1
,
,
Q
Q
Q
(
) ( )
n
I
M
n
U
M
Q
M
n
N
1
1
0
1
1
4
1
∑
−
=
+
=
;
(
) ( )
n
I
M
n
U
M
Q
M
n
N
2
1
0
2
2
4
1
∑
−
=
+
=
;
(
) ( )
n
I
M
n
U
M
Q
M
n
N
3
1
0
3
3
4
1
∑
−
=
+
=
Phase apparent Powers:
3
2
1
,
,
S
S
S
1
1
1
I
U
S
=
2
2
2
I
U
S
=
3
3
3
I
U
S
=
Phase Power Factors:
3
2
1
,
,
λ
λ
λ
( )
1
1
1
1
Q
sign
S
P
=
λ
( )
2
2
2
2
Q
sign
S
P
=
λ
( )
3
3
3
3
Q
sign
S
P
=
λ
where
sign
(
x
) is equal to 1 with
x
> 0, to -1 with
x
< 0.
Average star Voltage
λ
U
3
3
2
1
N
N
N
U
U
U
U
+
+
=
λ
Mean phase-phase Voltage
∆
U
3
31
23
12
U
U
U
U
+
+
=
∆
Average THD of the star voltages:
λ
U
THD
3
3
2
1
N
N
N
U
U
U
U
THD
THD
THD
THD
+
+
=
λ
Three phase Current
Σ
I
3
∆
Σ
Σ
=
U
S
I
Average THD of the phase currents:
Σ
I
THD
3
3
2
1
I
I
I
I
THD
THD
THD
THD
+
+
=
Σ
Total Active Power:
Σ
P
3
2
1
P
P
P
P
+
+
=
Σ
Total reactive Power:
Σ
Q
3
2
1
Q
Q
Q
Q
+
+
=
Σ
Total apparent Power:
Σ
S
2
2
Σ
Σ
Σ
+
=
Q
P
S
3 Phase Power Factor:
Σ
λ
( )
Σ
Σ
Σ
Σ
=
Q
sign
S
P
λ
where
sign
(
x
) is equal to 1 with
x
> 0, to -1 with
x
< 0.
