Pag. 55 di 152
8.2.2 Measurement Formulas:
Phase-phase Voltages:
31
23
12
,
,
U
U
U
( )
∑
−
=
=
1
0
2
12
12
1
M
n
n
U
M
U
;
( )
∑
−
=
=
1
0
2
23
23
1
M
n
n
U
M
U
;
( )
∑
−
=
=
1
0
2
31
31
1
M
n
n
U
M
U
( )
( )
( )
n
U
n
U
n
U
31
23
12
,
,
are the Phase to phase Voltages samples.
M is the number of samples taken over a period (64)
Phase to phase Voltages THD
12
U
THD
,
23
U
THD
,
31
U
THD
in %
1
2
sin
)
(
2
cos
)
(
2
)
(
100
2
1
0
12
2
1
0
12
1
0
2
12
12
−
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
+
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
=
∑
∑
∑
−
=
−
=
−
=
N
n
N
n
N
n
U
N
n
n
U
N
n
n
U
N
n
U
THD
π
π
1
2
sin
)
(
2
cos
)
(
2
)
(
100
2
1
0
23
2
1
0
23
1
0
2
23
23
−
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
+
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
=
∑
∑
∑
−
=
−
=
−
=
N
n
N
n
N
n
U
N
n
n
U
N
n
n
U
N
n
U
THD
π
π
1
2
sin
)
(
2
cos
)
(
2
)
(
100
2
1
0
31
2
1
0
31
1
0
2
31
31
−
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
+
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
=
∑
∑
∑
−
=
−
=
−
=
N
n
N
n
N
n
U
N
n
n
U
N
n
n
U
N
n
U
THD
π
π
Phase Current:
3
2
1
,
,
I
I
I
( )
∑
−
=
=
1
0
2
1
1
1
M
n
n
I
M
I
;
( )
∑
−
=
=
1
0
2
2
2
1
M
n
n
I
M
I
;
( )
∑
−
=
=
1
0
2
3
3
1
M
n
n
I
M
I
( ) ( ) ( )
n
I
n
I
n
I
3
2
1
,
,
are the line current samples.
Phase Current THD:
1
I
THD
,
2
I
THD
,
3
I
THD
1
2
sin
)
(
2
cos
)
(
2
)
(
100
2
1
0
1
2
1
0
1
1
0
2
1
1
−
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
+
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
=
∑
∑
∑
−
=
−
=
−
=
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
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