Neutral Voltage Ratio (NVR) and Earth Tangent Angle (ETA)

  Instantaneous Neutral Voltage (Vn) is the Phasor sum of all phase voltages. It is Zero in Three phase three wire system, and Three phase Four wire  Balanced System. 

Let us introduce the New Factor namely 'Neutral Voltage Ratio (NVR)' which is the Ratio between the RMS of Neutral Voltage and Sum of All Phase voltage RMSs.

It is approximately equal to the sine of ETA. ETA is the Angular Symmetrical Component represents the zero sequence voltage. Sine of ETA is the ratio between Zero sequence Voltage and SEL Voltage. Zero sequence voltage is 57.735% of Neutral Voltage. SEL Voltage is 1.732 times of the Quadratic Mean of Phase Voltage RMS values. Mean square of Phase Voltages are equal to the square of Average phase voltage and  Square of Standard deviation (Variance) of phase voltages. 

Sine of ETA is apparently equal to the NVR defined above after detailed derivation given below. So, ETA will apparently determined as Arc Sine of NVR. Hence, NVR is also called as "SETA (Sine of Earth Tangent Angle)".

Example:

NVR is the ratio between Vectorial sum of all phase voltages and Arithmetic Sum of all Phase Voltages. It is the approximate value of Sine of ETA.

ETA is also determined without sine Function: ETA is nearly equal to the percentage of Zero sequence component to the Total Phase voltage.

Conclusion:

 ETA is apparently equal to the 100 times ratio between Zero Sequence Voltage and Total Phase Voltage. The error is very small for smaller neutral voltages.