Datasheet

Theory of operation STPM01
46/60 Doc ID 10853 Rev 8
Equation 6
dv/dt → v(t) = V
⋅sin ωt; [see Figure 28 - 7]
i(t) →
[see Figure 28 - 8]
Now four signals are available. Combining (pairing) them by means of two multiplying stages
two results are obtained:
Equation 7
[see Figure 28 - 9]
Equation 8
[see Figure 28 - 10]
After these two operations, another stage performs the subtraction between the results p2
and p1 and a division by 2, obtaining the active power:
Equation 9
[see Figure 28 - 11]
In this way, the AC part V•I•cos(2
ωt + ϕ)/2 has been then removed from the instantaneous
power.
In the case of current sensors like “Rogowski coils”, which provide the rate of the
instantaneous current signal (di/dt), the initial voltage signal differentiated stage will be
switched off. In this case the signals coming from the A/D conversion and their consequent
integrations will be:
Equation 10
v(t) = V•sin
ωt
)tcos(
I
dt)t(i)t(I ϕ+ω⋅
ω
−=⋅=
∫
2
)t2cos(IV
2
cosIV
dt)t(i
dt
dv
)t(p
1
ϕ+ω⋅⋅
−
ϕ⋅⋅
−=⋅⋅=
/
∫
2
)t2cos(IV
2
cosIV
)t(i)t(v)t(p
2
ϕ+ω⋅⋅
−
ϕ⋅⋅
=⋅=
/
2
cosIV
2
))t(p)t(p(
)t(p
12
ϕ⋅⋅
=
/
−
/
=
)tcos(I
dt
)t(di
)t(i ϕ+ω⋅ω⋅−==
′