Understanding Electric Power Systems: Minus Signs in the Admittance Matrix

[badgers]

http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-061-introduction-to-electric-power-systems-spring-2007/assignments/ps1ans.pdf
Problem #3

Where do the minus signs come from in the admittance matrix?

also, there is this statement
"Thus it is clear that R3 = 1/3 and"
and later the statement
"R12 = R3 =1"

Homework Equations

The Attempt at a Solution

From what I think it would be that the T circiut would be 1ohm for all three resistors, but that isn't what the solution is.
Can someone help me please understand?
thank you for your time and have a good day

 

[gneill]

The negative values in the admittance matrix are there because of the definitions of the current and voltage directions that define the ports. Port currents are always taken to be INTO the port terminal (and out of the return path for the given port).

Regarding the "R3 = 1 or R3 = 1/3" question, it would appear that there is a mistake in the question document; the author took the value from the matrix as written, but failed to multiply by the constant 1/3 that was factored out of the matrix.

 

[badgers]

thank you for your help