RELAYS 101

Mho Math

This routine allows you to see and predict the distance (in ohms) to a fault plot that falls on the border of the Mho Characteristic.
For any given reach (to border of characteristic) at the Max Torque Angle (MTA) then there is a prediction one can accomplish to prove that the characteristic is indeed a Mho (circular) characteristic. With modern protective relays the characteristic is driven by mathematics within the relays' programming. With older electromechanical or solid-state relays the characteristic was created in other manners. After one proves the Max Torque Angle (MTA) then a test is done to find the reach at the MTA. Finally, a reach test is done at angular points on either side of the MTA. A circle characteristic can thus be proven. The math to prove a circular characteristic is: Reach at Test Angle (TA) = Reach at MTA x cos(MTA-TA). On this display one can view that the characteristic is circular by looking for a right angle between the test angle and the max torque angle. To make it easier to view a right angle between MTA and TA, this mho characteristic display draws the line from the reach at the TA to the reach at the MTA. An example that demonstrates the proper reaches and test angles is: MTA = 5 ohms at 75 degrees and TA = 3.5 ohms at 30 degrees. Thus the example math is: 3.5 ohms at 30 degrees = 5 ohms x cos(75-30). And that checks out because 3.5 = 5 x 0.7071. Note that a right triangle is seen. Try another example of MTA = 10 at 90 degrees and TA = 7.1 at 45 degrees. Note that a right triangle is formed.