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STPM01FTR Arkusz danych(PDF) 45 Page - STMicroelectronics

Numer części STPM01FTR
Szczegółowy opis  Programmable single phase energy metering IC
PDF  56 Pages
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Producent  STMICROELECTRONICS [STMicroelectronics]
Strona internetowa  http://www.st.com
Logo STMICROELECTRONICS - STMicroelectronics

STPM01FTR Arkusz danych(HTML) 45 Page - STMicroelectronics

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STPM01
Theory of operation
45/56
DS value of integrated voltage channel with the value of integrated current channel, which
yields:
[Eq. 13]
The second is to multiply filtered DS value of voltage channel with the value of filtered
current channel,
[Eq. 14]
From the above results, Q1(t) is proportional to 1/
ωwhile Q2(t) is proportional to ω. The
correct reactive power would result from the following formula:
[Eq. 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:
[Eq. 16]
The Reactive Power will present then a ripple at twice the line frequency. Since the average
value of a sinusoid is 0, this ripple does not contribute to the reactive energy calculation over
time, moreover, in the STPM01 the reactive power is not used for meter calibration or to
generate the stepper pulses, then this ripple will not affect the overall system performances.
In case of Rogowsky coil, the same procedure is applied, but the current channel will be
proportional to the derived of the current and the differentiated is bypassed in the voltage
channel, so we have:
[Eq. 17]
[Eq. 18]
The reactive power is then calculated:
[Eq. 19]
())
2
sin(
sin
2
cos(
)
sin
(
)
(
)
(
)
(
)
(
)
(
1
ϕ
ω
ϕ
ω
ϕ
ω
ω
ω
+
−
⋅
=
⎟
⎠
⎞
⎜
⎝
⎛
+
−
⋅
=
⋅
=
⋅
′
=
∫
t
VI
t
I
t
V
t
I
t
v
t
I
dt
t
v
t
Q
())
2
sin(
sin
2
)
sin(
cos
)
(
)
(
)
(
2
ϕ
ω
ϕ
ω
ϕ
ω
ω
ω
+
+
⋅
⋅
=
+
⋅
=
⋅
′
=
t
VI
t
I
t
V
t
i
t
v
t
Q
ϕ
ω
ω
sin
2
1
)
(
)
(
2
1
2
1
VI
t
Q
t
Q
Q
=
⋅
+
⋅
⋅
=
())
2
sin(
sin
2
)
(
2
1
)
(
1
3
ϕ
ω
ϕ
ω
+
−
⋅
=
⋅
⋅
=
t
VI
t
Q
t
Q
()
())
2
sin(
sin
2
)
sin(
)
cos(
)
(
)
(
)
(
)
(
)
(
1
ϕ
ω
ϕ
ω
ϕ
ω
ω
ω
+
+
=
+
−
⋅
⎟
⎠
⎞
⎜
⎝
⎛−
=
⋅
=
′
⋅
=
∫∫
t
VI
t
I
t
V
t
i
t
V
dt
t
i
dt
t
v
t
Q
()
())
2
sin(
sin
2
)
cos(
)
(
sin
)
(
)
(
)
(
1
ϕ
ω
ϕ
ω
ϕ
ω
ω
ω
+
−
⋅
⋅
−
=
+
−
⋅
=
′
⋅
=
t
VI
t
I
t
t
V
t
i
t
v
t
Q
())
2
sin(
sin
2
)
(
2
1
)
(
1
3
ϕ
ω
ϕ
ω
+
+
⋅
=
⋅
⋅
=
t
VI
t
Q
t
Q



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