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slaa391+Reactive power measurement+phase shift of 90 deg?

In the application note(SLAA391)  for 3 Phase energy meter design, it is mentioned that the true rms measurement is done by accumulating the samples for V1,V2,V3,I1,I2,I3,P1,P2,P3 ,Q1,Q2,Q3 in different 48 bit registers  in interrupt of Timer A1 at the rate of 3.2768Ksps. Since squared values are accumulated every Interrupt, there is no problem for RAm. However, inorder to calculate Q1,Q2 and Q3 (reactive Power), the application note mentions that we need to shift the voltage samples by 90 deg and multiply with corresponding current input . If this is to be done, you cannot use accumulated squared values but you need  to store individual samples of  V(90+n)   and I (n) and multiply them before accumulating  per sample . In the application note, the method of trms calculation requires us to collect one second data and appropriate sample count for calculating TRMS. One seconds data means 3276 samples at sampling rate of 65 samples per cycle. This means we need to store 3276 samples  each for 3 voltages and 3 currents. If individual samples are available then we can phase shift the Voltge samples by 90 deg by collecting samples at T/4 .However 3276 x 6  samples would need large RAm making the scheme unrealistic. 

 Can anybody explain how to implement reactive energy measurement  as per the recommendations of Ti  SLAA391 but without consuming huge RAM

  • If you’re accumulating squared U and I values, you’re calculating Urms and Irms. Whose product will be apparent power. To get active power, you can also accumulate (U*I) momentary values (note that this is a signed multiplication!). The difference between the two methods, over a period, will be reactive power. And their relation gives you the power factor.
    However, when using current transformers, you’ll need to delay the voltage for U’I by the same delay the current transformer induces (usually given as an angle error in the CT datasheet).

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