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STPM10 데이터시트(PDF) 39 Page - STMicroelectronics

부품명 STPM10
상세설명  Programmable single-phase energy metering IC with tamper detection
PDF  51 Pages
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제조업체  STMICROELECTRONICS [STMicroelectronics]
홈페이지  http://www.st.com
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STPM10 데이터시트(HTML) 39 Page - STMicroelectronics

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STPM10
Theory of operation
Doc ID 17728 Rev 3
39/51
Equation 13
[see Figure 26 - 11]
In this way, the AC part V•I•cos(2
ωt + 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 (Vrms, Irms) 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.
7.23.2
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
The second is to multiply the filtered DS value of the voltage channel with the value of the
filtered current channel:
Equation 15
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
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
2
cos
I
V
2
))
t
(
p
)
t
(
p
(
)
t
(
p
1
2
ϕ
⋅
⋅
=
/
−
/
=
())
t
2
sin(
sin
2
VI
t
cos(
I
)
t
sin
V
(
)
t
(
I
)
t
(
v
)
t
(
I
dt
)
t
(
v
)
t
(
Q1
ϕ
+
ω
−
ϕ
⋅
ω
=
⎟
⎠
⎞
⎜
⎝
⎛
ϕ
+
ω
ω
−
⋅
ω
=
⋅
=
⋅
′
=
∫
())
t
2
sin(
sin
2
VI
)
t
sin(
I
t
cos
V
)
t
(
i
)
t
(
v
)
t
(
Q
2
ϕ
+
ω
+
ϕ
⋅
ω
⋅
=
ϕ
+
ω
⋅
ω
ω
=
⋅
′
=
ϕ
=
ω
⋅
+
ω
⋅
⋅
=
sin
2
VI
1
)
t
(
Q
)
t
(
Q
2
1
Q
2
1



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