# Re: Admittance formula for branches with transformers

```Itâ€™s a simple summation of the corresponding diagonal elements from the branch
admittance matrix in (3.2), plus any bus shunt elements.```
```
Ray

> On Sep 3, 2016, at 11:59 AM, davor sutic <davor.su...@gmail.com> wrote:
>
> I did a thorough study of makeYbus() (both a code analysis and step-by-step
> executions) and was able to answer the majority of my questions. However, I
> still can't get the mathematical sense on how a diagonal element with
> multiple transformers is treated.
>
> As an example consider case14.m bus 4, here is stripped down version of its
> portion of the branch input matrix:
>
> fbus |  tbus |  r       | x       | b      |  ratio  |  angle
> 2    |  4    |  0.05811 | 0.17632 | 0.034  |  0      |  0
> 3    |  4    |  0.06701 | 0.17103 | 0.0128 |  0      |  0
> 4    |  5    |  0.01335 | 0.04211 | 0      |  0      |  0
> 4    |  7    |  0       | 0.20912 | 0      |  0.978  |  0
> 4    |  9    |  0       | 0.55618 | 0      |  0.969  |  0
>
> There are 5 lines that meet at bus 4, 2 have transformers (albeit with no
> phase shift, but that shouldn't be important) and of the remaining 3, 2 have
> line charging.
>
> What is the general formula for a diagonal element?
>
> Thanks a lot
>
>
> On Fri, Aug 26, 2016 at 7:58 PM, Abhyankar, Shrirang G. <abhy...@anl.gov
> <mailto:abhy...@anl.gov>> wrote:
> Please take a look at the function makeYbus().
>
> > On Aug 26, 2016, at 10:05 AM, davor sutic <davor.su...@gmail.com
> > <mailto:davor.su...@gmail.com>> wrote:
> >
> > I'm trying to understand the effects of having a transformer connected to a
> > branch on the implicated admittance matrix. In the MatPower manual, section
> > 3.2, equation 3.2 describes such a relation for a 2x2 branch admittance
> > matrix.
> >
> > I'm interested in the general form of the (diagonal and off-diagonal)
> > elements of an admittance matrix, when multiple branches have transformers
> > attached. Particularly the diagonal elements are confusing, how are the
> > elements summed up, if multiple have transformers?
> >
> > Further, in the test case files, the absence of a transformer is indicated
> > with its ratio and angle set to 0. In the mentioned equation (3.2) that
> > would cause problems when dividing with 0. So another question is how are
> > those elements treated in the light of formula 3.2?
> >
> > Thanks a lot.
>
>
>

```