Datasheet

Energy calculation algorithm STPMC1
72/77 Doc ID 15728 Rev 7
The DSP performs also an integration of powers (P, Q) into energies:
Equation 54
AW = U
RMS
I
RMS
cos ϕ k
P
k
UD
Equation 55
AW = U
RMS
I
RMS
sin ϕ k
P
k
UD
These integrators are implemented as up/down counters and they can roll over.
20-bit output buses of the counters are assigned as the most significant part of the energy
data records. It is a responsibility of the application to read the counters at least every
second so as not to miss any rollover. The integration of power can be suspended due to
detected error on the source signals or due to no load condition. From AW, stepper output
signals are generated.
10.5 Fundamental power calculation
The fact that integration suppresses all but fundamental components of signals is used to
compute the fundamental active power, which is in case of Rogowski coil:
Equation 56
F
1
= v
uic
v
iiic
= - ABk
INT
cos (ω t) cos (ω t + ϕ) = - ABk
INT
[cos ϕ + cos (2 ω t + ϕ)] / 2
Equation 57
F
2
= v
iic
v
uiic
= - ABk
INT
sin (ω t) sin (ω t + ϕ) = ABk
INT
[cos ϕ - cos (2 ω t + ϕ)] / 2
Equation 58
F = (F
2
- F
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
Similar result are found in case of non Rogowski sensor:
Equation 59
F
1
= v
dic
v
siic
= - AC sin (ω t) sin (ω t + ϕ) = - AC [cos ϕ - cos (2 ω t + ϕ)] / 2
Equation 60
F
2
= v
sic
v
diic
= - ACk
DIF
k
INT
cos (ω t) cos (ω t + ϕ) = - AC [cos ϕ + cos (2 ω t + ϕ)] / 2
Equation 61
F = (F
2
- F
1
) / 2 = - AC cos (2 ω t + ϕ) = Uk
D
Ik
s
cos (2 ω t + ϕ) / 2 = U
RMS
I
RMS
cos (2 ω t +
ϕ) k
P
The fundamental reactive power in case of a Rogowski coil is:
Equation 62
Q = v
uiic
v
iiic
ω / k
INT
= - ABk
INT
cos (ω t) sin (ω t + ϕ) = ABk
INT
[sin ϕ - sin (2 ω t + ϕ)] / 2
Similar results are found in cases of non Rogowski sensors:
Equation 63
Q = v
diic
v
siic
ω / k
INT
= - AC cos (ω t) sin (ω t + ϕ) = AC [sin ϕ - sin (2 ω t + ϕ)] / 2.