Datasheet

STPMC1 Energy calculation algorithm
Doc ID 15728 Rev 7 69/77
In case of a non Rogowski sensor, the corresponding products are:
Equation 32
P
1
= v
d
v
si
= - AC k
DIF
k
INT
cos (ω t) cos (ω t + ϕ) = - AC [cos ϕ + cos (2 ω t + ϕ)] / 2
Equation 33
P
2
= v
di
v
s
= AC k
DIF
k
INT
sin (ω t) sin (ω t + ϕ) = AC [cos ϕ - cos (2 ω t + ϕ)] / 2
Then a subtraction of P
1
from P
2
is performed:
Equation 34
P = (P
2
- P
1
) / 2 = (AB cos ϕ) k
INT
/ 2 = (Uk
D
Ik
L
cos ϕ) k
INT
/ 2 = U
RMS
I
RMS
cos ϕ k
P
where:
Equation 35
k
P
= k
D
k
L
k
INT
This gives the same result for P in case of non Rogowski sensor, substituting B and k
L
k
INT
with C and k
S
:
Equation 36
P = (P
2
- P
1
) / 2 = (AC cos ϕ) / 2 = (Uk
D
Ik
S
cos ϕ) / 2 = U
RMS
I
RMS
cos ϕ k
P
where:
Equation 37
k
P
= k
D
k
S
The result in Equation 35 and Equation 36 is proportional to the DC part of active power of
line. The division by 2 is a feature of ΔΣ subtractor. The absence of harmonic components
eliminates the spread of results due to asynchronism with the line. This fact enables fast a
calibration procedure which is used to set the target constant of meter k
P
.
A sensitivity analysis of k
P
yields:
Equation 38
Δk
P
/k
P
= ΔL/L + R
1
/ (R
1
+R
2
)(ΔR
2
/R
2
- ΔR
1
/R
1
) + ΔA
U
/A
U
+ ΔA
I
/A
I
- 2 ΔV
REF
/V
REF
Equation 39
Δk
P
/k
P
= ΔR
S
/ R
S
+ R
1
/ (R
1
+R
2
)(ΔR
2
/R
2
- ΔR
1
/R
1
) + ΔA
U
/A
U
+ ΔA
I
/A
I
- 2 ΔV
REF
/V
REF
It is clear that the device is responsible for A
U
, A
I
and V
REF
parts. The parts k
U
, k
I
and k
INT
are omitted, because they are not subject to aging or temperature variations due to digital
implementation.
10.2 Reactive energy calculation
The natural reactive power (ART = 0) of the line is computed as follows.
First, 16-bit voltage from the 3
rd
stage ( Equation 20 or Equation 28 ) is multiplied by the
current stream from the 1
st
stage ( Equation 14 or Equation 23 ) and the frequency