Rainbow Electronics 71M6542G - Manual (Page 80)

80 © 2008–2011 Teridian Semiconductor Corporation v1.1
3 Functional Description
3.1 Theory of Operation
The energy delivered by a power source into a load can be expressed as:
∫ =
t
dt t I t V E
0
) ( ) (
Assuming phase angles are constant, the following formulae apply:

P = Real Energy [Wh] = V * A * cos
φ* t

Q = Reactive Energy [VARh] = V * A * sin
φ * t

S = Apparent Energy [VAh] = 2 2 Q P
+
For a practical meter, 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 meter IC such as the Teridian 71M654x 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 yield an accurate quantity for the
momentary energy. Summing up the momentary energy quantities over time results in very accurate
results for accumulated energy.
Figure 28: Voltage, Current, Momentary and Accumulated Energy
Figure 28 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]