# Solving a flow matrix with one of the nodes as constant.

1. Feb 1, 2012

### Mamed

Hi

I am trying to solve a flow chart that has one of the nodes a constant/ambient/ground. I dont know how to go about to design this in the matrix.

What i have is kinda like the attached image.
I have that V0 is constant, and i have set the flow matrix as.

$\left[ \begin{array}{cccc} \frac{1}{R_1} & \frac{1}{R_1} & 0 & 0 \\ -\frac{1}{R_1} & \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_4} & -\frac{1}{R_2} &-\frac{1}{R_4} \\ 0 & -\frac{1}{R_2} & \frac{1}{R_2}+\frac{1}{R_3} & -\frac{1}{R_3} \\ 0 & -\frac{1}{R_4} &-\frac{1}{R_3} & \frac{1}{R_4}+\frac{1}{R_3} \\ \end{array} \right]$
And by having the currents in as
$\left[ \begin{array}{c} I0 \\ I1 \\ I2 \\ I3 \end{array} \right]$
Where P0 is the negative sum of all the other values at steady state. But this will make the voltage V0 be dependant on the slow but I want it to be constant but don’t know how to make it work. I have though about just ignoring the node and thus taking away the first row and column but again I want it to somehow depend on the fact that we have a slack there.

What i wanna find out are the Voltages at the different nodes. But i cant just do V = A\I because the first one in V is to be constant.

Thanks for any comment.

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