Datasheet

Energy calculation algorithm STPMC1
70/77 Doc ID 15728 Rev 7
compensated stream of 16-bit voltage from the 2
nd
stage of filter ( Equation 18 or Equation
26
) is multiplied by the 16-bit current stream from the 2
nd
stage ( Equation 16 or Equation
25
) yielding:
Equation 40
Q
1
= v
uiic
v
i
= ABk
INT
sin (ω t) cos (ω t + ϕ) = - ABk
INT
[sin ϕ - sin (2 ω t + ϕ)] / 2
Equation 41
Q
2
= ω / k
INT
v
ui
v
ii
= ABk
INT
cos (ω t) sin (ω t + ϕ) = ABk
INT
[sin ϕ + sin (2 ω t + ϕ)] / 2
In case of non Rogowski sensor, the corresponding products are:
Equation 42
Q
1
= v
diic
v
s
= ACk
DIF
k
INT
cos (ω t) sin (ω t + ϕ) = AC [sin ϕ + sin (2 ω t + ϕ)] / 2
Equation 43
Q
2
= ω / k
INT
v
di
v
si
= - ACk
DIF
k
INT
sin (ω t) cos (ω t + ϕ) = - AC [sin ϕ - sin (2 ω t + ϕ)] / 2
Then a subtraction of Q
1
from Q
2
is performed:
Equation 44
Q = (Q
2
- Q
1
) / 2 = (AB sin ϕ) k
INT
/ 2 = (Uk
D
Ik
L
sin ϕ) k
INT
/ 2 = U
RMS
I
RMS
sin ϕ k
P
This gives the same result for Q in case of non Rogowski sensor, substituting B and k
L
k
INT
with C and k
S
:
Equation 45
Q = (Q
2
- Q
1
) / 2 = (AC sin ϕ) = (Uk
D
Ik
S
sin ϕ) / 2 = U
RMS
I
RMS
sin ϕ k
P
The artificial reactive power (ART = 1) of line is computed as follows.
The inter-phase voltage sigma-delta stream is computed from voltage stream from the 1
st
stage as follows:
Equation 46
Δv
uR
= (v
uS
- v
uT
) / 2
Δv
uS
= (v
uT
- v
uR
) / 2
Δv
uT
= (v
uR
- v
uS
) / 2
The inter-phase voltage sigma-delta stream (
Equation 46 ), the 16-bit current from the 2
nd
stage (
Equation 16 or Equation 25 ) and the value of 1 / √3 are multiplied yielding:
Equation 47
Q = Δv
u
v
ii
1 / √3 = AB k
INT
[sin ϕ + sin (2 ω t + ϕ)] / 2
or in case of non Rogowski sensor, the corresponding products are:
Equation 48
Q = Δv
d
v
si
1 / √30 = AC [sin ϕ + sin (2 ω t + ϕ)] / 2