Problem with Three Phase Power Factor

Hello All.

I am Sudarshan from India. I recently finished my final year B.E from PES Institute of Technology, Bangalore in Electrical and Electronics branch. I want to further my final year project now and I am facing few hurdles in the process and it would help me a lot if you guys could help me. I am going to give you my final year project details now.

M/s: SUDARSHAN ELECTRONICS (my father’s company) manufacture AC-AC Power Controllers from the smallest Rating of 20 Amps right up to 500 Amps as a Standard Product. These Controllers basically have Two Sections – Power Section and Control Section.

My objective was to to convert a part of the existing analog control section to DIGITAL CONTROL and find the values like Power, Power Factor, etc.

The input is 3-phase 415 V which is then stepped down to 10 V using a step down transformer for each phase. This signal is shifted above the zero value and is then reduced to 5 V before sending it to the Analog pin of the Arduino. The load is purely resistive (incandescent bulbs - 3 bulbs for each phase, so a total of 9 bulbs). I am able to find the power factor for single phase (the value is in the range of 0.91-0.98) but I am finding it difficult to get the same for Three phase. I will also share the code for the single phase power factor.

void setup() {
  Serial.begin(9600);

}
int v,i,n=0;
double inst_power,inst_voltage,inst_current;
double voltage,current,power;
double p,sum_p,real_power;
double square_voltage,sum_square_voltage,mean_square_voltage,root_mean_square_voltage;
double square_current,sum_square_current,mean_square_current,root_mean_square_current;
double apparent_power,power_factor;
void loop() {
v = analogRead(A0);
i = analogRead(A1);
inst_voltage = v;
inst_current = i;
inst_power = v*i;
Serial.print("inst_power = ");
Serial.println(inst_power);
Serial.println("       ");



//REAL POWER CALCULATION

for(n=0; n<4131; n++)
    {
      p = inst_voltage * inst_current;
      sum_p += p;
    }
    real_power = sum_p / 4131;

//ROOT MEAN SQUARE VOLTAGE CALCULATION

for(n=0; n<8261; n++)
    {
      square_voltage = inst_voltage * inst_voltage;
      sum_square_voltage += square_voltage;
    }
    mean_square_voltage = sum_square_voltage / 8261;
    root_mean_square_voltage = sqrt(mean_square_voltage);


//ROOT MEAN SQUARE CURRENT CALCULATION

for(n=0; n<8621; n++)
     {
       square_current = inst_current * inst_current;
       sum_square_current += square_current;
     }
     mean_square_current = sum_square_current / 8261;
     root_mean_square_current = sqrt(mean_square_current);

//APPARENT POWER CALCULATION
      apparent_power = root_mean_square_voltage * root_mean_square_current;


//POWER FACTOR CALCULATION
      power_factor = real_power / apparent_power;
      Serial.print("Power factor =  ");
      Serial.println(power_factor);
      delay(500);

It would help me a lot if you guys could shed some light on the same.

Thank you.

Best regards,
Sudarshan.

This code is not useful:

for(n=0; n<4131; n++)
    {
      p = inst_voltage * inst_current;
      sum_p += p;
    }
    real_power = sum_p / 4131;

It does nothing more than: real_power = inst_voltage * inst_current;

You need to sum up the actual sampled points in time… Something more like:

unsigned long timestamp = 0L ;
float power_summed = 0.0 ;
void loop ()
{
  if (micros () - timestamp >= 1250)
  { 
    timestamp += 1250 ;  // allows 16 samples per 50Hz cycle
    float inst_voltage = Vscale * (analogRead (A0) - zero_voltage) ;  // need to subtract zero offset and scale
    float inst_current = Iscale * (analogRead (A1) - zero_current);

    power_summed +=inst_voltage * inst_current ;
    N_samples += 1 ;

    if (N_samples >= 1000)  // periodically average and print
    {
      Serial.println (power_summed / N_samples) ;
      power_summed = 0.0 ;
      N_samples = 0 ;
    }
  }
}

Thank you Mark for your valuable inputs.

However, I would like to know how to solve for power factor for all the three phases (R, Y & B).

Thank you.

There power factor for each phase is independently measurable. They should be the same, if not you
have asymmetry which is not good.

Once you are summing power you can sum V-squared and I-squared as well to get rms voltage and current
averages, power factor can be derived from true power and these rms values.