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Symmetrical Components - How power system analysis gives insight into Napoleon Triangles
About the author
(My name is Nathan Kassees. I'm a battery storage and microgrid engineer in Colorado. I've spent years investigating power quality issues for utilities and have made it a hobby to explore the math used in power system analysis.)
Quick Summary
(In the branch of electrical engineering that educates on power and energy systems, there is a concept called Symmetrical Components that is relevant to all power grids worldwide and is taught to all power system BS students. It is an obscure topic for most students, including myself originally, and most of the time the professor only presents the bare mathematical techniques necessary to solve the problems. The conceptual background is left out in school, and yet the background is a deep rabbit hole that sheds light on Discrete Fourier Transforms, Napoleon Triangles, various Triangle Centers, and a novel construction of the Golden Ratio that I think everyone would enjoy. Almost all of what I’ve written in the storyboard is not presented in any power engineering textbook, but I think it should be. Lacking ability to directly edit textbooks, I have structured outlines for lessons and Geogebra simulators that I have passed on to other engineers when I've had the opportunity to present the topic. I have not learned to make videos yet, and professionally and personally I’m too busy to learn Manim and give it the kind of quality 3B1B has in time for August. In my storyboard I've provided a summary of my work on this topic, along with links to the Geogebra simulators I've created, which should provide good starting points for illustrations. Those simulators are linked below in this post. I would love to have the opportunity to work with an animator who can the add extra quality to make the lessons more visually appealing.)
Target medium
(I'm looking for a video to illustrate concepts similar to 3B1B's videos on discrete Fourier transforms and using complex numbers to solve counting problems. My goal is to have a video with the same quality as those videos to present to an audience of power system engineers, students, or anyone curious about transformation of vector spaces and geometry.)
More details
(My storyboard can be found at the google drive link below. If it doesn’t work I can share in an email. https://docs.google.com/document/d/1X1WR34W_PXlXYGW8H-XihfnPj87VWT7s/edit?usp=sharing&ouid=107952479991480160738&rtpof=true&sd=true )
(If you have an outline or storyboard for the topic, include it here. The more detail the better.)
Contact details
(Email: [email protected] Phone: +1-972-743-8684)
Additional context
(Here are the links to my Geogebra simulators: https://www.geogebra.org/m/kznambqh - Wave-Vector Relationship – Manipulate the magnitude and phase of 3 voltage signals in a 3 phase power system and see the corresponding effect on the wave and associated phasor
https://www.geogebra.org/m/c3dfnj3d - 3-Phase Symmetrical Components Vx -> Vn - Change System Phasors to determine Symmetrical Component phasors
https://www.geogebra.org/m/yxaq6bck - 3-Phase Symmetrical Component Simulator Vn -> Vx – Change Symmetrical Component phasors to determine system phasors
https://www.geogebra.org/m/chntv6kh - 6-Phase AC Symmetrical Component Simulator - Change Symmetrical Component phasors to determine system phasors
https://www.geogebra.org/m/amarfxe8 - 12-phase AC power system simulator - Change Symmetrical Component phasors to determine system phasors
https://www.geogebra.org/m/zkbnwvdv - Zero Sequence Component – This simulator illustrates the triangle centroid and explains its connection to the zero sequence component of 3-phase systems.
https://www.geogebra.org/m/jdza87bg - Outer Napoleon Triangle / Positive Sequence Component – Just a basic Outer Napoleon triangle simulator that illustrates the connection to the positive sequence component in 3-phase systems.
https://www.geogebra.org/m/vthbgtxy - Inner Napoleon Triangle / Negative Sequence Component – Just a basic Inner Napoleon triangle simulator that illustrates the connection to the negative sequence component in 3-phase systems.
https://www.geogebra.org/m/ncqwvj68 - 1-√n-√n Triangle – Napoleon Triangles – This simulator displays the interesting Napoleon Triangle solutions found when a triangle has side lengths 1-√n-√n, n any positive integer. )
(I’ve reached out to Geogebra and received written approval that their simulators can be used in Youtube Videos, even if ads are turned on. I can provide their email if needed.)
