Datasheet

Theory of operation STPM10
42/53 Doc ID 17728 Rev 4
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
The reactive power, then, presents 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 STPM10 the reactive power is not used for meter calibration or to
generate the stepper pulses, so this ripple does not affect the overall system performance.
7.23.3 Apparent power and RMS values
The RMS values are calculated starting from the following formulas:
Equation 18
Multiplying Equation 18 by
ω , the I
RMS
value is obtained:
Equation 19
The RMS voltage value is obtained by:
Equation 20
Q
1
2
---
Q
1
t() ω Q
2
t()
1
ω
---
VI
2
------
ϕ
sin=⋅+⋅⋅=
Q
3
t()
1
2
---
Q
1
t() ω
VI
2
------
ϕ
sin 2ωt ϕ+()sin–()⋅=⋅⋅=
1
T
---
I
2
t() td
0
T
∫
I
ω 2⋅
-----------------=
I
RMS
I
2
-------=
V
RMS
1
T
---
v
2
t() td
0
T
∫
V
2
-------==