Datasheet

78M6612 Data Sheet DS_6612_001
18 Rev 2
2 Functional Description
2.1 Theory of Operation
The energy delivered by a power source into a load can be expressed as:
∫
=
t
dttItVE
0
)()(
The following formulas apply for wide band mode (true RMS):
• P = ∑ (i(t) * v(t))
• Q = √(S
2
– P
2
)
• S = V * I
• V = √∑v(t)
2
• I = √∑i(t)
2
For actual measurement equations, refer to the applicable 78M6612 Firmware Description Document.
For some applications, not only voltage and current amplitudes, but also phase angles and harmonic
content may change constantly. Thus, simple RMS measurements are inherently inaccurate. A modern
solid-state electricity measurement IC such as the 78M6612 functions by emulating the integral operation
above, i.e. it processes current and voltage samples through an ADC at a constant frequency. As long
as the ADC resolution is high enough and the sample frequency is beyond the harmonic range of
interest, the current and voltage samples, multiplied with the time period of sampling will yield an accurate
quantity for the momentary energy. Summing up the momentary energy quantities over time will result in
accumulated energy.
Figure 5: Voltage, Current, Momentary and Accumulated Energy
Figure 5 shows the shapes of V(t), I(t), the momentary power and the accumulated power, resulting from
50 samples of the voltage and current signals over a period of 20 ms. The application of 240 VAC and
100 A results in an accumulation of 480 Ws (= 0.133 Wh) over the 20 ms period, as indicated by the
Accumulated Power curve. The described sampling method works reliably, even in the presence of
dynamic phase shift and harmonic distortion.
-500
-400
-300
-200
-100
0
100
200
300
400
500
0 5 10 15 20
Current [A]
Voltage [V]
Energy per Interval [Ws]
Accumulated Energy [Ws]