Index

# RELAYS 101

### RELAYS 101 Lecture Notes Assorted Calculations

Screen Shots of various concepts presented on classroom whiteboard.
Phasor Diagram (X-Y Quadrant Diagram)
An X-Y quadrant diagram is the general mathematics diagram used to plot values with horizontal (X) and vertical (Y) coordinates. In the electrical fields the X-Y diagram is used to plot the values (magnitudes and angles) of the three phases of the 3-Phase power system. You CANNOT plot voltages and currents on R-X (Impedance) or P-Q (Power) quadrant diagrams. Likewise you CANNOT plot S (Volt-Amps) or Z (Impedance) on the X-Y diagram. The math that you apply on an X-Y diagram is the same math that will be used on the other quadrant diagrams (rectangular to polar conversions and vice-versa). You must be able to move between the various diagrams to understand what is happening on the power system.
Impedance Diagram (R-X Quadrant Diagram)
R (horizontal axis) and X (vertical axis). This is strictly the R-X diagram, a quadrant diagram that allows for the plotting (and understanding) of Impedance (Z). Z = R+jX Z = √((R*R)+(X*X)) Z= V / I So many ways to calculate Z shows just how important Z is to the Protective Relay business. As "I" increases, "Z" decreases. So simple. If the fault is close to the bus (or generator) there is more current involved than if the fault were farther away from the bus. Note that you cannot plot voltages and currents on this quadrant diagram. "Z" is voltage divided by current. This is the quadrant diagram for displaying voltage divided by current.
Power Diagram (P-Q Quadrant Diagram)
P (horizontal axis) and Q (vertical axis). This is strictly the P-Q diagram, a quadrant diagram that allows for the plotting (and understanding) of Power. S = P+jQ Volt-Amps (S) = Watts (P) + (j)VARs (Q) Apparent Power = Real Power + Reactive Power. This is where one would plot the "Power Triangle". "S" (apparent power) = voltage TIMES the current. S = V x I = P + jQ You cannot plot voltages and currents on the P-Q diagram. You also cannot plot impedances on this P-Q diagram. It takes three quadrant diagrams to capture all of the ins and outs of the values that run through a substation bus and power line.
Z-Primary to Z-Secondary Conversion explained
Visit the "Z primary to Z secondary" conversions page to learn how to calculate (to learn the formula). This display shows the mathematics behind the "formula".
Symmetrical Components Invented circa 1921
When you're trying to teach yourself how to calculate Symmetrical Components you will eventually run into this page of math. It is enough to scare away many people. But, it simply shows us a new "factor". This page shows the resolution of the "a" operator.
It doesn't have to be hard.
There is an easier way!
"A" and "A2" Operators
When you run into the "a" operator you will simply add 120 degrees to the vector. For example if "VB" = 67 volts at -120 degrees then "aVB" = 67 volts at (-120 + 120) degrees. (67 at 0 degrees). "a2" (a-squared) operator means ADD 240 degrees. "VC" = 67v at -240 degrees. "a2VC" = 67v at -240+240 degrees (=67 at 0)
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