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STPM13ATR Datasheet(PDF) 33 Page - STMicroelectronics

Part # STPM13ATR
Description  Single phase energy metering IC with pulsed output and digital calibration
PDF  43 Pages
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Manufacturer  STMICROELECTRONICS [STMicroelectronics]
Direct Link  http://www.st.com
Logo STMICROELECTRONICS - STMicroelectronics

STPM13ATR Datasheet(HTML) 33 Page - STMicroelectronics

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STPM11/12/13/14
Energy calculation algorithm
33/43
i(t) = I
⋅ sin(tω+ ϕ); [Eq. 2 - see (6) in Figure 6 - ]
can then be used to calculate. These digital signals are also used in two additional steps for
integration, obtaining:
dv/dt
→v(t) = V
⋅ sin tω; [Eq. 3 - see (7) in Figure 6.]
[Eq. 4 - see (8) in Figure 6]
Now four signals are available. Combining (pairing) them by two multiplication steps two
results are obtained:
[Eq. 5 - see (9) in
Figure 6.]
[Eq. 6 - see (10) in
Figure 6.]
After these two operations, another stage another step involves the subtraction of p1 from
p2 and dividing the result by 2, to obtain the active power:
[Eq. 7 - see (11) in
Figure 6.]
In this way, the AC part
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, the initial voltage signal differentiation stage is switched off. In
this case the signals coming from the A/D conversion and their consequent integrations are:
v(t) = V
⋅ sin (tω); [Eq. 8]
[Eq. 9]
)
cos(
)
(
)
(
ϕ
ω
ω
+
⋅
−
=
⋅
=
∫
t
I
dt
t
i
t
I
i(t)
⋅
2
)
2
cos(
2
cos
)
(
)
(
1
ϕ
ω
ϕ
+
⋅
⋅
−
⋅
⋅
−
=
⋅
⋅
=
/
∫
t
I
V
I
V
dt
t
i
dt
dv
t
p
2
)
2
cos(
2
cos
)
(
)
(
)
(
2
ϕ
ω
ϕ
+
⋅
⋅
−
⋅
⋅
=
⋅
=
/
t
I
V
I
V
t
i
t
v
t
p
2
cos
2
))
(
)
(
(
)
(
1
2
ϕ
⋅
⋅
=
/
−
/
=
I
V
t
p
t
p
t
p
⎟
⎠
⎞
⎜
⎝
⎛
+
⋅
⋅
2
)
2
cos(
ϕ
ωt
I
V
)
cos(
)
(
)
(
ϕ
ω
ω
+
⋅
⋅
−
=
=
′
t
I
dt
t
di
t
i
t
V
dt
t
v
t
V
ω
ω
cos
)
(
)
(
⋅
−
=
⋅
=
∫



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