2.4 RMS Voltage Measurement

For the AC power supply, RMS is equal to the value of the direct current that would produce the same average power dissipation in a resistive load. The RMS value gives the equivalent DC measurement of the AC power. Mathematically, the root mean square is defined as the square root of the mean square (the arithmetic mean of the squares of a set of numbers). In alternating signals, RMS can be defined as an integral of the squares of the instantaneous values during a cycle.

In the application, the RMS voltage is calculated by the arithmetic mean of the square of a set of numbers on each phase of the three-phase input signal.

The equations used for calculating RMS voltage are:

$V_{r m s} = \sqrt{\frac{(s u m o f t h e s q u a r e d v o l t a g e s a m p l e s)}{n u m b e r o f s a m p l e s}}$
$V_{r m s} = \sqrt{\frac{{V 1}^{2} + {V 2}^{2} + {V 3}^{2} + ............ + {V n}^{2}}{n}}$

Here, n is number of samples and V1,V2,V3.….Vn are the voltage samples acquired from the input signal using ADC.

Figure 2-3 shows the signal, which is divided into 24 number of equal samples.

Figure 2-3. RMS Voltage Calculation Signal

AN3607

2.4 RMS Voltage Measurement