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Versor Algebra

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Volume 1 – Versor Algebra As Applied To Polyphase Power Systems

Charles Proteus Steinmetz’s original math model is a natural outgrowth of Nikola Tesla’s polyphase power systems. Tesla was the discoverer, but Steinmetz was the builder who first applied Versor Algebra to the analysis of alternating current power systems.

In my presentation and book Four Quadrant Representation Of Electricity, my extension of Steinmetz’s work is presented in the most simple way possible using very simple analogies, pictures and diagrams. It was a very difficult task as the goal was to facilitate an understanding for the layman.

That presentation was given at the 2013 Energy Science & Technology Conference and shortly thereafter, the book version was released, which went into more detail that was not covered in the presentation.

Tesla’s polyphase power system was originally four poles or four phases. Steinmetz is the one who adapted it into a three pole or three phase system, which is the prominent system of today. The complication is that three phase systems cannot be explained by conventional mathematics. With three phase systems, there is no plus or minus and that is the reason why the conventional math doesn’t work any more.

That left a big gap in polyphase power systems until Dr. Fortescue came up with the system of Symmetrical Coordinates. This laid the groundwork for polyphase mathematics for any number of phases. And ultimately, it can be extended into the Pythagorean understanding of numbers.

The “Fortescue Method” was never fully developed because of its complexity. The proper name for this is “Sequence Algebra” and the rudiments were presented in my presentation and book Four Quadrant Representation Of Electricity.

Even though the system has become adopted for general engineering usage, Versor Algebra Volume 1 and Versor Algebra Volume 2 is the first theoretical basis that has ever been presented on the subject.

Versor Algebra Voume 1 and Versor Algebra Volume 2 is the next logical step after Four Quadrant Representation of Electricity as it takes the reader into the mathematical journey of the mathematical model and theory that is necessary to realize the unique electrical waves that exist in polypahse power systems. These waves are actually beyond the original understanding of Tesla and Steinmetz with regard to polyphase power systems.

It is important to understand that this is all possible with simple 9th grade algebra. I take the reader through a step-by-step process from very basic algebra and logarithms into the more complex subject. The process involves very simple but numerous steps to guide the reader into the understanding of polyphase mathematics.

Through my own journey in writing this Versor Algebra book, I have been able to unify the polyphonic music of Bach and his contemporaries as this music follows the logic of sequence algebra perfectly.

In fact, the book was written when listening to this music, which aided the process greatly.

(146 page downloadable ebook)

Volume 2 – Special Theories Of Sequence Operators As Applied To Power Engineering

In Versor Algebra Volume 2, the general theory presented in the first volume is actually applied to any number of phases.

Each set of phases has its own mathematical manifestation. If there are eight phases, the math is very different from the math necessary to analyze three phases. The general theory is basically being developed into special theory for multiple number of phases.

The second volume covers a plurality of phases including eight phases, which is necessary for the proper mathematical analysis of polyphase music. It also covers the very usual true single or monopolar phase developed by Nikola Tesla for his telluric ground transmission systems. We also review the more common three and four phase power systems.

What is commonly misunderstood as single phase is actually a two phase system that is common in your home. This is not a true polyphase system because it is not rotational like a four phase system but is included for continuity.

You will be able to observe the mathematical process without being sidetracked by numerous subscripts and the use of the same letter for a multiplicity of terms, which is the flaw in the available textbooks on the subject. This is necessary to establish the clarity of the process so that in the future third volume, it is possible to understand its application and extension.

(193 page downloadable ebook)

Fault has been found with these articles that they are hard to read. They were harder, perhaps, to write.

Oliver Heaviside – Electromagnetic Theory Volume 1, 1893


The complete set of ebooks is also available as a combo package

Save $7 when you buy both ebooks together!

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1 review for Versor Algebra

  1. Simon (verified owner)

    In his latest offering to the engineering community, Eric Dollard presents his unique method of analysing polyphase electrical systems through developing and translating difficult theory and mathematics into a form that can easily be followed by someone at any level of experience. He clearly explains the processes involved step-by-step, with examples and diagrams that ensure the reader understands and sets out on the right path in applying the information. Although someone who is not too familiar or comfortable with mathematics may at first expect it to be too difficult to follow or understand, Eric Dollard’s deep understanding of the subject is illustrated through the clarity of this work and extends to the reader to enable anyone who understands basic algebra, and perhaps knows how to use a calculator, to be able to analyse pholyphase electrical systems with relative ease. Not only does he present the information clearly, he also does a remarkable job of teaching the reader how to calculate the equations in the process, making this an invaluable book.

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