3.3.3 Accumulated Voltage Quantities Between Phases

The metrology module generates the following accumulated phase voltage (V) quantities between phases: V_AB, V_BC, V_CA, V_AB_F, V_BC_F, and V_CA_F.

They are in units of [Volt²samp scaled]. They are scaled accumulated voltage quantities between phases in the whole integration period. They are calculated according to the following formula:

Where,

• V_x_sample_i is i^th sampled phase voltage value of phase x in present integration period
• V_y_sample_i is i^th sampled phase voltage value of phase y in present integration period
• x = [A, B, C]
• y = [B, C, A]
• N is the number of samples in the last measurement interval.

They are used to calculate the RMS value of voltage between phases.

V_xy and V_xy_F are stored in uQ24.40 format.

These accumulators are useful for calculating the phase shift between voltages by applying the Law of Cosines. Depending on the application requirements, it can be utilized either the fundamental plus harmonics or the fundamental only, ended in "_F", registers.

The following numerical example demonstrates the angle computation:

• Data from Metrology Accumulator Registers:
  • V_A: 0x15219DA3DFFC
  • V_B: 0x1521A8F07EDF
  • V_C: 0x1522518EAC3A
  • V_AB: 0x3F63899CA42A
  • V_BC: 0x3F67221A3C5C
  • V_CA: 0x3F661B94C8D4
• The units of these registers are in Volt² samp scaled, with a uQ24.40 format. To convert these to decimal values, divide by 2⁴⁰:
  • V_A: 21.13131165
  • V_B: 21.13148406
  • V_C: 21.13405697
  • V_AB: 63.38881854
  • V_BC: 63.40286411
  • V_CA: 63.39885836
• Application of the Law of Cosines:
  • Angle between phases A and B (AB_phase):

    AB_phase = arccos((V_AB - V_A - V_B) / (-2 * sqrt(V_A * V_B)) = 119.992º

  • Angle between phases B and C (BC_phase):

    BC_phase = arccos((V_BC - V_B - V_C) / (-2 * sqrt(V_B * V_C)) = 120.007º

  • Angle between phases C and A (CA_phase):

    CA_phase = arccos((V_CA - V_A - V_C) / (-2 * sqrt(V_A * V_C)) = 120.001º