DS_6613_018
78M6613 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
The following formulae apply for wide band mode (true RMS):
•
•
•
•
P = ∑ (i(t) * v(t))
Q = √(S2 – P2)
S = V * I
V = √∑v(t)2
•
I = √∑i(t)2
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,
and true RMS measurements must be utilized. A modern solid-state electricity Power and Energy
Measurement IC such as the Teridian 78M6613 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 4: Voltage. Current, Momentary and Accumulated Energy
Figure 4 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.
For actual measurement equations, refer to the applicable firmware documentation.
Rev. 1.1
11
TERIDIAN [ TERIDIAN SEMICONDUCTOR CORPORATION ]
