Vector 1 (orange color) + Vector 2 (blue color) + Vector 3 (green color)
Using complex number addition the resultant is Vector 4 (red color)

Step 1: Add the x-coordinate of vector 1 + vector 2 + vector 3
= vector 4 ( x-coordinate)
Step 2: Add the y-coordinate of vector 1 + vector 2 + vector 3
= vector 4 (y-coordinate)

To edit, go to bottom right hand corner of the graph and click edit graph on Desmos

Note: Letter A, B, and C are the values of vectors magnitude
letter a, b, and c are the corresponding angles in degree notation.

Initial condition: all angles are a = 0 deg; b=120 deg ; c=240 deg

A = 120 B = 100 and C = 110

By Sam Ortega, Created with Desmos Graphing

Practice set all angles in 360 degress a=360 ; b=360; c= 360

You should get this answer



Go to bottom right hand corner of the graph and click edit graph on Desmos

Change the value of magnitude of vector A = 105 Ampere , B = 103 Ampere, and C = 108 Ampere and make all the angles equal to 30 degrees a = 30 b= 30 and c = 30
Answer in rectangular form (273.7, 158)
You should get this answer.

Answer in polar form 316 Ample ∠ 30 °

Another solution in adding three vectors using waveform

Given A = 105 A ∠ 30° Here p1 represents A phase angle
Given B = 103 A ∠ 30° Here p2 represents B phase angle
Given C = 108 A ∠ 30° Here p3 represents BCphase angle

Answer ( x axis is degree, y axis is magnitude in Ampere)
Answer (30, 316) which is the peak of the sine wave.



What will happen if Bank A transformer phase angle is no longer averaging at 30 degrees? Change the value of a = 70 meaning the average angle is 70 degrees. Compute the new total current. Answer 299 Ampere ∠ 43 °



Answer is the peak value (43, 299) in Cartesian coordinates where x is in degrees and y is ampere



As you can see observing the phase angle shifting from 30° to 70° could possibly be used as a predictor that there is internal movement inside the transformer. This is not expensive machine learning possible application and no outage requirements.

Can we use machine learning to watch the trending of transformer phase angle shifting as a predictive variable to compute the remaining life of the transformer?
This will be my hypothesis that I would like to test using Phasor Measurement Units where transformer currents are measured in polar coordinates. For example 299 Ampere ∠ 43 °

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