Thank you, THANK you for tying this back to geometry. I have never seen the Napoleon triangle proof, nor the centroid one! One thing that didn't seem intuitive to me was why we rotate those Napoleon triangles 180° after finding them. Other than that, the extension to n-dimensions was the exact thing my brain was thinking about next! Maybe with this construction, 6-phase power is something achievable to study. Crazy to think that there are transformers that provide that. Would be interesting to see a vector treatment of Scott T and Zig Zag transformers, as proper phase rotation can mean equipment either works or blows up!
@michaelharrison1093
Ай бұрын
A great video - Pierre Fermat was a French mathematician and pronounced his last name with a silent T.
@michaelharrison1093
Ай бұрын
A really great video with some really great content. However, I think that the discussion around the AC mains powered digital clocks was a bit off and you missed the opportunity to discuss a far more interesting power systems application. Although I can't prove that spurious zero-crossing noise didn't potentially mess up the time keeping of some digital clocks, most that I had come across featured pretty robust frequency counting capability and typically were able to work reliably even with the extreme amount of allowable harmonic distortion as specified by the likes of IEEE-519, IEC-555, & EN-61000-3-2 etc. I think that the far more interesting application here relates to the fact that for several decades starting in the 1950 up to at least the turn of the 21st century (& arguably beyond) you would always find line frequency digital clocks as a center feature at any power generation facility. There would be two digital clocks - both of which would display down to the second = one of these clocks would takes its time reference from the AC frequency and the other would take it reference from some independent source - originally these would be synchronized using a radio signal that was linked back to some very accurate atomic clock. More recently the use of a GNSS (e.g., GPS in the USA) time based reference will be used. There are two very interesting details that are collectively used to set/define the frequency of the grid at any point in time. The grid frequency by definition is allowed to deviate by +/- 1Hz around the nominal frequency of 50Hz or 60Hz. The variation in frequency is a direct refection of the total load on the grid as a percentage of the current generation capacity of the grid - so if the grid frequency is 1Hz too low then this means the grid is currently loaded to the full generational capacity and if the grid is 1Hz too high then this means there is the maximum allowed over generation capacity on the grid. The other detail about the AC grid frequency is that on average over any 24Hr period then the frequency is exactly correct. Hence this is why these old digital clocks were so accurate. Lack of accuracy of these old digital clocks was not a real thing.
@eepower
3 ай бұрын
Well done! This was a great video.
@Chris-xf5og
4 ай бұрын
Extremely intuitive and interesting point of view. Congratulations on this wonderful resource. Cheers from Chile!
@dimitarhristov8704
4 ай бұрын
Awesome video! Thanks a million... saying I got the picture will be too bold a claim, but thanks to you I have a rather clarified concept as of what we are chasing with these sequences :) !
@user-ws9hj9bn7p
5 ай бұрын
So V0 is a measure to the center of the system. Would that be the 'Neutral'? Or if V0 was anything besides 0 there would be a voltage on the neutral. Trying to think of what this correlates to on the Power System. Great Video!
@nathank7569
5 ай бұрын
I find it's easiest to think about the physical nature of symmetrical components by how each component affects a 3 phase motor, which is also the reason they were invented in the first place. If the positive sequence makes a motor turn at X speed clockwise, then the same amount of negative sequence will turn the motor at X speed counter-clockwise. Since the V0 signal looks the same on all 3 phases (i.e. you never multiply it by the complex sequence operator a), the motor can't distinguish a rotational direction when only V0 is present, and so V0 is the component that doesn't turn the motor at all. Thinking about it in terms of vectors, if you start with 3 different vectors, and add the same vector V0 to all 3, this is geometrically equivalent to shifting the origin by V0, which is the same as applying basic translation symmetry. So mathematically V0 can be interpreted as a translation in the complex plane, and physically can be interpreted as a 3-phase supply that doesn't rotate a 3-phase motor. Another physical manifestation is that V0 creates circulating currents in wye-delta and zig-zag windings. More on that in a future video.
@SeeNickView
27 күн бұрын
@@nathank7569 Would it be fair to say that adding a V0 vector away from the Origin reflects adding a DC bias to a circuit, such that the AC phases don't all rotate about 0 V?
@nathank7569
26 күн бұрын
@@SeeNickView that’s correct, DC is zero sequence.
@SeeNickView
26 күн бұрын
@@nathank7569 These are the connections that were never made in my university classes. I don't think we even covered symmetrical components. Thanks for shoring this all up, coming from an EE in renewables
@nathank7569
26 күн бұрын
@@SeeNickView feel free to add me on LinkedIn (Nathan Kassees) if you want to chat about other industry stuff sometime. I’ve worked in utility distribution for 14 years, currently working on microgrids.
@jorkole1995
6 ай бұрын
Do you do you offer private tutoring?
@SziangSziang
9 ай бұрын
Sorry, I'm having some trouble understanding. From what I understand, Way to quantify unbalance. a. Vector sum for V0 b. Rotate then vector sum and average for V1 why rotate Vb instead of Va, and why rotate 180 degrees. I'm guessing rotating Vb gives V0 and Va gives V1. Then going to 3 phase, from my understanding o symmetrical component, the "a" operator is use to multiply to rotate then sum average. So I guess it is use to find (b)? To quantify unbalance? And the notation V0 is usually reserved for zero sequence and this video it means something else? At 4:49 talking about V0 measure the distance to the N, "geometric center of the system" (is this where va,vb,vc intersects?), to the centroid "geometric mean of the triangle? Or the other way round? Can explain what's the significance of the translation symmetry? I'm kinda stuck here. Thanks
@nathank7569
9 ай бұрын
The scene around 4:49 is strictly discussing the geometrical interpretation of the zero sequence. For a triangle, the geometric center is the centroid I’m referencing. The centroid is where the center of mass would be if the triangle was a solid object. The zero sequence vector is the vector pointing from the centroid to the neutral. Now if I want to shift the triangle across the plane without changing its shape, I.e. translational motion, then I just move my centroid, which is the same as changing he zero sequence. The combination of positive and negative sequence vectors determines the shape of the triangle. The zero sequence vector does not change the shape of the triangle, but it shifts the triangle center away from the origin. Therefore the combination of all 3 sequence components allows me to draw any arbitrary triangle anywhere in the plane. I hope that answers some of your questions. Let me know if it doesn’t!
@ValleLucas
9 ай бұрын
Very nice visual interpretation! Good explanations. Very rich. Thanks for sharing all the resources. At 5:40 of the video, there’s supposed to be a j beside the sqrt(3)/2, correct?
@nathank7569
9 ай бұрын
Doh! You’re the first person to notice that mistake. Good catch.
@ValleLucas
9 ай бұрын
Holy cow. That’s amazing! Thanks so much for this work!
@clifforddicarlo9178
9 ай бұрын
Best and most understandable description of this ladder network impedance topic that I've seen.
@chrisc.6601
9 ай бұрын
Calling it now. Writing it down as proof (Hypothesized this for two years now) 10/09/2023 This method will be used to ultimately describe the equation of the perfected neural net. THE Equation to show the neural net after its been trained
@tuongnguyen9391
10 ай бұрын
Very interesting
@stijncousin4891
11 ай бұрын
Great video! This transformation has resamblance to the concept of 'space vector', which is a spatial transformation of instantaneous three-phase voltages, currents, flux-linkages, etc. The space vectors are commonly used to simplify the modelling and control of AC electrical machines. E.g. field-oriented control or space vector modulation methods. Are there any other relations between the concepts of space vectors and symmetrical components? Also, what are some good sources/textbooks on electrical fault analysis and their physical interpretation, using the method of symmetrical components?
@nathank7569
10 ай бұрын
Thanks for the comment! I had not heard of space vectors prior to this comment, and had to go look it up. I'm happy you mentioned it because I've been looking for education on inverter resources recently. From my brief review, it looks like it's used for reducing noise/increasing efficiency of PWM operation for 3-phase inversion. I saw it's associated with the Clarke Transform. I recommend multiplying the symmetrical component and Clarke transformations, such that you view the alpha and beta vectors in terms of V1 and V2. I think the result is interesting. For fault Analysis, I've found "Symmetrical Components for Power Systems Engineers" by J. Lewis Blackburn to be helpful. I'm not sure what you mean by the "physical interpretation" of faults. The physical interpretation of symmetrical components I touched on, lightly, in my first video from August 2022, "Symmetrical Components from a New Angle". I plan to make the physical interpretation of symmetrical components the main topic of one of my upcoming videos.
@jhacklack
11 ай бұрын
Very interesting video and nice animations, the harmonics causing multiple zero crossings which speed up the clock is nicely visualized. Do the symmetric component circuits correspond to physical parts of the grid or are they just an abstract way of looking at the current and voltage?
@nathank7569
11 ай бұрын
They are physical. Besides the neutral system being an important part in the zero sequence network, the negative sequence has a role with rotating machines, particularly motors. The negative sequence impedance of a running motor is much less than its positive sequence impedance, so the positive and negative sequence impedancs are important for evaluating the fault behavior of rotating machines.
@edmarsalvador2673
11 ай бұрын
Thanks
@floatingturtle2512
Жыл бұрын
I intend to develop an undergraduate thesis on the calculus of continued fractions. The result at 4:08 is quite interesting. Good video
@nathank7569
Жыл бұрын
That is based on the general definition for metallic ratios. en.wikipedia.org/wiki/Metallic_mean
@optic_edits2010
Жыл бұрын
Try explaining the per unit system. I think you could do an amazing job. 😊
@joaobaptista4610
Жыл бұрын
Please do a second video going deeper on symmetrical components of higher-than-3-phase polyphase circuits.
@2000watts2
Жыл бұрын
Perfect explanation I have ever seen.👍
@speedbird7587
Жыл бұрын
very interesting !
@WaltSlade-hv3lg
Жыл бұрын
I'm getting the impression you think something like Isaac Newton did.
@nathank7569
Жыл бұрын
Oh no! I hope I don’t end up poking a needle in my eye for science.
@WaltSlade-hv3lg
Жыл бұрын
@@nathank7569 Wow, hardly anyone knows about the weird needle-in-the-eye incident. Amazing he didn't blind himself one way or another.
@1sesh
Жыл бұрын
Wish I had this video to look at when I was in college!
@beilkster
Жыл бұрын
Great explanation again! I would recommend thickening some of the line segments as I had to raise the streaming quality to get a consistent line. Keep it up
@nathank7569
Жыл бұрын
Thanks!
@alexwang982
Жыл бұрын
I’m a synthetic geometer and this video taught me the practical use of Napoleon and Van Aubel(and their ugly complex proofs)
@kams2520
Жыл бұрын
Amazing
@rkalle66
Жыл бұрын
AC power calculus is just the beginning. The next step is to calculate elecronics like buck/boost/pwm and so on for driving brushless motors and understanding capacitors and inductors.
@devrimturker
Жыл бұрын
You may find interesting videos on rational tangles and continued fractions
@DeclanMBrennan
Жыл бұрын
The elegance of your phasors stunned me. Thanks for all the effort you put into those animations.
@nathank7569
Жыл бұрын
Thank you! To make the phasors, I worked with an animator who was proficient with Manim, the python library developed by Grant Sanderson for his YT channel 3blue1brown. My animator is mentioned in the description.
@newerstillimproved
Жыл бұрын
Oh, please do give some credit to Galileo Ferraris, 1847-1897, professor in Turin. The IEEE (Institute of Electrical and Electronics Engineers, they are the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity) in their Milestone program unveiled a plaque in 2021 at the Politecnico di Torino for the Milestone “Rotating Fields and Early Induction Motors, 1885-1888” with citation: “Galileo Ferraris, professor at the Italian Industrial Museum (now Polytechnic) of Turin, conceived and demonstrated the principle of the rotating magnetic field. Ferraris’ field, produced by two stationary coils with perpendicular axes, was driven by alternating currents phase-shifted by 90 degrees. Ferraris also constructed prototypes of two-phase AC motors. Rotating fields, polyphase currents, and their application to induction motors had a fundamental role in the electrification of the world.” Apparently, there was a series of court cases about the inventor of the polyphase motor and obviously the validity of Tesla/Westinghouse's patent, when Ferraris was long dead. Tesla won the final court case, allegedly thanks to a statement by three colleagues who testified that he invented it in the fall of 1887, before Ferraris' publication. Tesla and Westinghouse obviously then got all the fame and money. Stanley (the one who you mention) commented on the court cases. One of his comments stated apparently "I myself have seen the original motors, models, and drawings made by Ferraris in 1885, have personally talked with the men who saw these models in operation and heard Ferraris explain them at that date." - from a letter to the Electrical Review on March 16, 1903 [Electrical Review, Volume 42. 1903. Pg. 415 Well I am not an expert on the court cases and the statements, but at least the IEEE does recognize Ferraris.
@newerstillimproved
Жыл бұрын
And yes, I'd rather drive a Ferraris than a Tesla 🙂
@nathank7569
Жыл бұрын
There were a lot of people to consider for that scene, including Ferraris, but I had limited space and time. I intentionally said Tesla “patented” and not “invented” the two phase motor. The main reason I mentioned Tesla is because his association with Westinghouse influenced the wide adoption of that system.
@newerstillimproved
Жыл бұрын
@@nathank7569 Thank you.
@Rotem_S
Жыл бұрын
Hmm, so it's just a discrete Fourier transform? And it's useful because the DFT is phase-invariant, so anything else which is phase-invariant like a motor only depends on the relevant components? Like, it's cool, I just wasn't sure what we're trying to get exactly
@nathank7569
Жыл бұрын
You’re correct, the system can be treated at phase invariant, and relative components provide the information needed to understand system state.
@beilkster
Жыл бұрын
It's clear you put a lot of work into this video. Great job
@CognitiveOffense
Жыл бұрын
Delightful! Thank you for offering this lecture, I learned lovely truths.
@quadrannilator
Жыл бұрын
This is really wonderful. Although my core background is in mechanical engineering, I do understand electrical theory from time to time, and I fit into the same category of being able to work with the system but not really understanding it intuitively. Animations, Clarity of ideas and approach as well as the overall Teaching was spot on. Thank you, much appreciated. 👍
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