STPM10 Datasheet, PDF (39/51 Pages) STMicroelectronics – Programmable single-phase energy metering IC with tamper detection

STPM10
Equation 13
Theory of operation
7.23.2
p(t) = ^{(p/ 2(t) − p/ 1(t))} = ^{V ⋅ I ⋅ cos ϕ}
2
2
[see Figure 26 - 11]
In this way, the AC part V•I•cos(2ωt + ϕ)/2 has been removed from the instantaneous
power.
The absence of any AC component allows for a very fast calibration procedure. It requires
only the setting of (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’s built-in communication port, avoiding the time-averaged readings of
the active power or the need for line synchronization.
Reactive power
The reactive power is produced using the previously-computed signals. In case of shunt
sensor the voltage signal is derived while the current signal is not. A first computation is to
multiply the DS value of the integrated voltage channel with the value of the integrated
current channel, which yields:
Equation 14
∫ ^{Q1(t) =}
v′(t)dt ⋅ I(t) =v(t) ⋅ I(t) = (V sin ωt) ⋅ ⎜⎛ − ^I cos( ωt + ϕ ⎟⎞ = ^VI ⋅ (sin ϕ − sin( 2ωt + ϕ))
⎝ω
⎠ ^2ω
The second is to multiply the filtered DS value of the voltage channel with the value of the
filtered current channel:
Equation 15
Q ₂ (t)
=
v′(t) ⋅ i(t)
=
Vω cos ωt ⋅ Isin( ωt + ϕ)
=
VI
2
⋅ ω ⋅ (sin ϕ + sin( 2ωt +
ϕ))
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 16
Q
=
1
2
⋅ Q₁(t) ⋅ ω + Q₂ (t) ⋅
1
ω
=
VI
2
sin ϕ
Since the above computation would need significant additional circuitry, the reactive power
in the STPM10 is calculated using only the Q1(t) multiplied by ω, which means:
Equation 17
Doc ID 17728 Rev 3
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