Datasheet

STPMC1 Energy calculation algorithm
Doc ID 15728 Rev 7 67/77
10 Energy calculation algorithm
For the purpose of simplicity the energy computation shown below is relative to only one
phase.
Given line voltage and current as:
Equation 12
u = U sin (ω t) i = I sin(ω t + ϕ)
The voltage divider, AD converter and calibrator produce the value:
Equation 13
v
u
= u (R
2
/(R
1
+R
2
) (A
U
/V
REF
) k
U
= u k
D
= A sin (ω t)
The Rogowski coil preamplifier, AD converter and calibrator produce the value:
Equation 14
v
i
= - L (di/dt) (A
I
/V
REF
) k
I
= - I k
L
ω cos (ω t + ϕ) = - B ω cos (ω t + ϕ)
The 2
nd
stage internal integrations produce the values:
Equation 15
v
ui
= ∫ v
u
dt = - (A / ω) cos (ω t) k
INT
Equation 16
vii = ∫ v
i
dt = - B sin (ω t + ϕ) k
INT
From signs of v
u
and v
ui
the base frequency of line can be produced:
Equation 17
ω / k
INT
= k / T
This result is used to compensate Eq. 41, Eq. 44, Eq. 45 and Eq. 54.
The frequency compensated values are:
Equation 18
v
uic
= ω / k
INT
v
ui
= - A cos (ω t)
Equation 19
v
iic
= ω / k
INT
v
ii
= - B ω sin (ω t + ϕ)
The 3
rd
stage internal integrations and DC cancellations produce the values:
Equation 20
v
uiic
= ∫ v
uic
dt = - (A / ω) sin (ω t) k
INT
Equation 21
v
iiic
= ∫ v
iic
dt = B cos (ω t + ϕ) k
INT