Solving linear overdetermined systems. +and in a Flow matrix.

Hi

I have two problems, both that have to do with linear systems.

First:

I have an equation in the form c1*y1 + c2*y1*w = 1, where c1 and c2 are unknowns. As I cant really measure with w as zero i thought that i would set up an equation with

[y1  y1*w1  ][c1] = [1]
[..   ...   ][c2]   [.]
[yn  yn*wn  ]       [1]

As I am measuring i thought that it would be best to have more values as there can be errors in the measuring. I thought of using A'*A \ A'*b to solve the results as that will give the but apparently matlab does that automatically, with A\b. But i did it on a test matrix and the results where way off. So

How trustworthy is it to using that method on finding the solution and is there another way to do it?

My second question is regarding loadflow. I have in my system of nodes, 0-3. Node 1-3 are connected in a delta/triangle and node 0 is connected to node 1. There is a flow into the nodes, P0-P3. Where P0 is the outflow, that is -(P1+P2+P3).

So i have a Y-bus matrix set up. And the equation looks like

Ybus * X = P, and X = Ybus \ P.

The thing here is that the reference of node 0 is know, that is X0 is known.

So i multiply that with the value in Ybus and move it over to the other side. So I will have

Pnew = [P(1)-Ybus(1,1)*X0]

So now i will have one of the nodes in X gone and also the first row in Ybus but this gives us an Overdetermined matrix and I'm again confused as to how to solve this.

Because it should have a unique solution as its a physical problem but matlab doesn't give that.

Hi I set up KCL for the node and it turns out that one of the equations could be eliminated and hence there is a unique answer. matlab was giving me a non 0 e-11 when i looked at the diff and therefore i was a bit skeptical.

Thanks for any help if you need any more clarification please ask.