Datasheet

STPM01 Theory of operation
Doc ID 10853 Rev 8 47/60
Equation 11
Equation 12
[
The signals process flow will be the same as shown in the previous case, and even with the
formulas above, the result will be the same.
The absence of any AC component allows a very fast calibration procedure: it requires just
to set (using the internal device programming registers) the voltage and current sensor
conversion constants, using the effective voltage and current (V
RMS
, I
RMS
) readings
provided by the device built-in communication port, avoiding the time-averaged readings of
the active power or need for line synchronization.
8.24.2 Reactive power
The reactive power is produced using the already computed signals. In case of shunt sensor
the voltage signal is derived while the current signal is not. A first computation is to multiply
DS value of integrated voltage channel with the value of integrated current channel, which
yields:
Equation 13
The second is to multiply filtered DS value of voltage channel with the value of filtered
current channel,
Equation 14
From the above results, Q1(t) is proportional to 1/
ω while Q2(t) is proportional to ω. The
correct reactive power would result from the following formula:
Equation 15
Since the above computation would need significant additional circuitry, the Reactive Power
in the STPM01 is calculated using only the Q1(t) multiplied by
ω, it means:
tcos
V
dt)t(v)t(V ω⋅
ω
−=⋅=
∫
)tsin(I)t(idt)t(i)t
(
ϕ+ω⋅−==⋅
′
=
∫
()
)t2sin(sin
2
VI
tcos(
I
)tsinV()t(I)t(v)t(Idt)t(v)t(Q
1
ϕ+ω−ϕ⋅
ω
=
⎟
⎠
⎞
⎜
⎝
⎛
ϕ+ω
ω
−⋅ω=⋅=⋅
′
=
∫
()
)t2sin(sin
2
VI
)tsin(ItcosV)t(i)t(v)t(Q
2
ϕ+ω+ϕ⋅ω⋅=ϕ+ω⋅ωω=⋅
′
=
ϕ=
ω
⋅+ω⋅⋅= sin
2
VI1
)t(Q)t(Q
2
1
Q
21