Electronic – Calculate total apparent, average and reactive power in 3-phase

Real power is based on the difference in phase between the voltage and the current waveforms. You mainly see it in calculation of power factor. From wikipedia:

The ratio between real power and apparent power in a circuit is called the power factor. It's a practical measure of the efficiency of a power distribution system. For two systems transmitting the same amount of real power, the system with the lower power factor will have higher circulating currents due to energy that returns to the source from energy storage in the load. These higher currents produce higher losses and reduce overall transmission efficiency. A lower power factor circuit will have a higher apparent power and higher losses for the same amount of real power. The power factor is one when the voltage and current are in phase. It is zero when the current leads or lags the voltage by 90 degrees. Power factors are usually stated as "leading" or "lagging" to show the sign of the phase angle of current with respect to voltage.

In your application I believe they are using shiftedV as a way to see how much the phase has changed since the last value. With a purely resistive load, the power factor would be 1...so the real power=apparent power. So you are probably suppose to use a resistive load to determine your phasecal number(set it so real=apparent). Then you can find the power factor for various loads.

Edit: If you take the time average of the instantaneous product of voltage and current, you will surely have a real power measurement. As I (poorly) implied above, I believe the shiftedV is used to adjust for any reactance elements introduced by the measurement process. As a way to null out the effects of the electronics, so you get the real power of the load. Here good reading and pictures National Instruments

If you have resistors from red to blue, from blue to yellow and from yellow to red (i.e. a delta formation load) then the power is the sum of the individual line voltages (squared) divided by the individual resistance across each line:

$$P = \frac{V_{RB}^2}{R_{RB}} + \frac{V_{BY}^2}{R_{BY}} + \frac{V_{YR}^2}{R_{YR}}$$

If you have resistors in a star formation this is more difficult unless you have a neutral wire commoning the three resistors. If you do then measure the individual phase voltages and do individual power calculations then add the three powers to give total load power.

If you don't have a neutral then you will have to calculate the star-point voltage relative to red, blue and yellow respectively. Then you'll have three voltages and three resistors and power is the sum of the individual powers.