DS_6612_001
78M6612 Data Sheet
2 Functional Description
2.1 Theory of Operation
The energy delivered by a power source into a load can be expressed as:
t
E = V (t)I(t)dt
∫
0
Assuming phase angles are constant, the following formulae apply (for narrow band mode):
.
.
P = Real Energy [Wh] = V * A * cos φ* t
Q = Reactive Energy [VARh] = V * A * sin φ * t
P2 + Q2
.
S = Apparent Energy [VAh] =
For actual measurement equations, refer to the applicable 78M6612 Firmware Description Document.
For a practical measurement, 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 Power and Energy Measurement IC such as the Teridian 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.
500
400
300
200
100
0
0
5
10
15
20
-100
-200
-300
-400
-500
Current [A]
Voltage [V]
Energy per Interval [Ws]
Accumulated Energy [Ws]
Figure 15: Voltage. Current, Momentary and Accumulated Energy
Figure 15 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.
Rev. 1.2
51
TERIDIAN [ TERIDIAN SEMICONDUCTOR CORPORATION ]
