impedance circle calc help

[meeko]

hey, looking for some way to figure out the answer to this problem. but a source to learn it or an explained answer would be greatly appreciated.

" - A simple single phase impedance relay is set for Z=(R-1)^2 + (X-2)^2 = 4. It protects 2 lines. The first line has an impedance of Z =.5 +j2. The second line (in series) has an impedance of Z = 1 + j3. What percentage of the second line is protected. Draw the R-X diagram and use it to illustrate your solution.

Any help is appreciated, and also I'm a Technologist trying to learn protective relaying and stumbled across this

 

[collies99]

I can give you part of the answer. The second transmission line has a straight line equation of y=3x+.5.

you have to sub y into your circle formula(x-1)^2+(y-2)^2=4, it should become a quadratic formula that is solveable with 2 answers.

That's as far as my smarts can take me which is not very far.

 

[collies99]

Ok I tried it, intersection at 1.1644+j3.99. I think it is incorrect.

 

[collies99]

Reach on line 2 is 66.5% ... I can go to bed now.

 

[meeko]

that's awesome, thanks for the reply! do you know any book that I can read to help me learn this to see how you got your answer?

 

[xnuke]

[ol 1]
[li]Draw a sketch that has the mho circle on it, then plot the first line from the origin of the R-X plane to the endpoint given for it, and then plot the second line starting from the first line's endpoint to its own endpoint now given by the sum of the x and sum of the y coordinates of both lines. Always draw a sketch, if possible - especially since the question tells you to in the given problem.[/li]
[li]You need to find the equation of the second line (collies99 gave you this; you should confirm it), then the coordinates of the intersection of the second line with the circle (which collies99 told you how to do by substitution, and gave you the correct answer), then find the distance from the beginning of the second line to the intersection point. This is the length of the line covered by the nho characteristic circle.[/li]
[li]Once you have that distance, you can divide it by the total length of the second line (only) and multiply by 100 to turn it into a percentage.[/li]
[/ol]

I'm not wild about the way the question was asked. As I remember, circular mho characteristics are usually defined in terms of a maximum reach impedance and a maximum torque angle, not using the standard formula for a circle given in the question. It looks like an academic wrote the question rather than a practicing protection engineer.

Protective Relaying: Principles and Applications by Blackburn and Domin is considered by some to be the best text on the subject of relaying. The fourth edition is due out in the beginning 2014, so you may want to wait to purchase it. However, the book will not tell you how to do what collies99 or I did for this particular problem; we simply figured it out by knowing the theory (from that text and/or others) and applying the mathematics.

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[collies99]

The math book was grade 11 or 12, can't remember that far back.

Cirle and line intersection solutions is available on line.

http://www.youtube.com/watch?v=c8nBAY9iMKI

http://www.math.com/students/calculators/source/quadratic.htm

 

[xnuke]

The fact that the circle is tangent to the point (1,0) on the R-X plane also bothers me a bit. Typical mho or impedance relays are usually either tangent to the origin of the R-X plane, or if it is desired for them to have some reach in the reverse direction, enter the third quadrant of the R-X plane where both R and X are negative. The circle given does neither. Where did you get this question?

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[meeko]

Thank you, this means a lot, I have been trying to learn relaying for a while and am currently on the subject of distance relaying, and the resources and help you guys gave me is greatly appreciated. The hardest thing for me is the resources, to find the right resources is tough to me. I have purchased many books but its tough when you don't have help to guide you.
Thanks,

ps, I got the question from the link below , from a pdf file "worksheet"

http://www.ece.mtu.edu/faculty/bamork/EE5223/#Texts