Electrex X3M, Руководство пользователя

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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.