Paul Alciatore

03-09-2017, 02:57 PM

As some of you may have noticed, I have been trying for some time now to learn more about the various AC motors and their use. In this effort I have purchased several books and am presently reading "Three-Phase Conversion" by Graham Astbury. It is Number 47 in the "Workshop Practice Series" published by Special Interest Model Books. It is one of the later books in this excellent series, first published in 2011 and appears to be be fairly up to date.

I first have a caution for anyone who may also read this book. I am really trying to get the most from it so I am carefully working the Questions that the author has included at the end of the chapters. Unfortunately, the author's answer to the first question at the end of the first chapter as shown in the back of the book is in error. In that question he states that the value of a choke is 10 mH (milliHenry). But in showing how it is solved, in the back of the book, he enters that value as 0.1 meaning 0.1 Henry. He has clearly multiplied the value of that choke by a factor of ten. That value is squared, then added to another value and then a square root is taken, so it took me several passes through the math to finally realize that the error was his, not mine. If you do work through that problem you can either use the 100mH value and you will get his answers or, if you use the stated value of 10mH, then the correct answers are I = 0.372 A and Power Factor = 0.707.

OK, my question. So far I have read half way through Chapter 5, "The Steinmetz Connection". For those who are not familiar with this terminology, the Steinmetz connection refers to the use of a single capacitor to power the third phase of a three phase motor when it is connected to a single phase supply. This is perhaps the simplest and least expensive way for running a three phase motor with single phase power. Anyway, I was very interested in how this capacitor's value was determined and as far as I can see, his method is simply stated as "... the capacitor has to provide the full load current at the supply voltage, so ...". That is his sole basis for calculating the value of this capacitor. He uses Ohms law to find the capacitive reactance needed using the rated Voltage and rated maximum current of the motor. Then from that capacitive reactance, he uses the frequency of the power line with that capacitive reactance in the standard equation for capacitive reactance to fine the value of the capacitor in Farads. My question is, is this really all there is to it? Maximum current and rated Voltage of the three phase motor and the line frequency frequency? Has anyone seen a better derivation of the value of this capacitor?

In the book the author dismisses the rule of thumb used by some: 70 uF per KW. He claims that his calculation is more accurate. Of course, he also admits that this value is only good at full load and if the motor is not operated at the full load condition, then the size of the capacitor could/should be adjusted. But I am interested in the logic behind that primary calculation. The justification for doing it that way. How, with all the other impedances in the circuit (motor coils) does that value insure a proper Voltage and phase angle for that third motor connection point? It would seem to me that the calculation would be a lot more complicated.

Anybody have any real insight into this? Or know of a good reference work that does?

I first have a caution for anyone who may also read this book. I am really trying to get the most from it so I am carefully working the Questions that the author has included at the end of the chapters. Unfortunately, the author's answer to the first question at the end of the first chapter as shown in the back of the book is in error. In that question he states that the value of a choke is 10 mH (milliHenry). But in showing how it is solved, in the back of the book, he enters that value as 0.1 meaning 0.1 Henry. He has clearly multiplied the value of that choke by a factor of ten. That value is squared, then added to another value and then a square root is taken, so it took me several passes through the math to finally realize that the error was his, not mine. If you do work through that problem you can either use the 100mH value and you will get his answers or, if you use the stated value of 10mH, then the correct answers are I = 0.372 A and Power Factor = 0.707.

OK, my question. So far I have read half way through Chapter 5, "The Steinmetz Connection". For those who are not familiar with this terminology, the Steinmetz connection refers to the use of a single capacitor to power the third phase of a three phase motor when it is connected to a single phase supply. This is perhaps the simplest and least expensive way for running a three phase motor with single phase power. Anyway, I was very interested in how this capacitor's value was determined and as far as I can see, his method is simply stated as "... the capacitor has to provide the full load current at the supply voltage, so ...". That is his sole basis for calculating the value of this capacitor. He uses Ohms law to find the capacitive reactance needed using the rated Voltage and rated maximum current of the motor. Then from that capacitive reactance, he uses the frequency of the power line with that capacitive reactance in the standard equation for capacitive reactance to fine the value of the capacitor in Farads. My question is, is this really all there is to it? Maximum current and rated Voltage of the three phase motor and the line frequency frequency? Has anyone seen a better derivation of the value of this capacitor?

In the book the author dismisses the rule of thumb used by some: 70 uF per KW. He claims that his calculation is more accurate. Of course, he also admits that this value is only good at full load and if the motor is not operated at the full load condition, then the size of the capacitor could/should be adjusted. But I am interested in the logic behind that primary calculation. The justification for doing it that way. How, with all the other impedances in the circuit (motor coils) does that value insure a proper Voltage and phase angle for that third motor connection point? It would seem to me that the calculation would be a lot more complicated.

Anybody have any real insight into this? Or know of a good reference work that does?