=============
Impedance
=============

.. seealso::
    :ref:`Unit Systems and Conventions <conventions>`

Create Function
=====================

.. autofunction:: pandapower.create_impedance

Input Parameters
=====================

*net.impedance*

.. tabularcolumns:: |p{0.10\linewidth}|p{0.10\linewidth}|p{0.15\linewidth}|p{0.4\linewidth}|
.. csv-table:: 
   :file: impedance_par.csv
   :delim: ;
   :widths: 10, 10, 15, 40

\*necessary for executing a power flow calculation.

.. _impedance_model:

Electric Model
=================

The impedance is modelled as a longitudinal per unit impedance with :math:`\underline{z}_{ft} \neq \underline{z}_{tf}` :

.. image:: impedance.png
	:width: 25em
	:alt: alternate Text
	:align: center

The per unit values given in the parameter table are assumed to be relative to the rated voltage of from and to bus as well as to the apparent power given in the table.
The per unit values are therefore transformed into the network per unit system:

.. math::
   :nowrap:

   \begin{align*}
    \underline{z}_{ft} &= (rft\_pu + j \cdot xft\_pu) \cdot \frac{S_{N}}{sn\_mva} \\
    \underline{z}_{tf} &= (rft\_pu + j \cdot xtf\_pu) \cdot \frac{S_{N}}{sn\_mva} \\
    \end{align*}

where :math:`S_{N}` is the reference power of the per unit system (see :ref:`Unit Systems and Conventions<conventions>`). 

The asymmetric impedance results in an asymmetric nodal point admittance matrix:

.. math::
   :nowrap:
   
    \begin{bmatrix} Y_{00} & \dots & \dots  & Y_{nn} \\
    \vdots & \ddots & \underline{y}_{ft} & \vdots \\
    \vdots &  \underline{y}_{tf} & \ddots & \vdots \\
    \underline{Y}_{n0} & \dots & \dots & \underline{y}_{nn}\\
    \end{bmatrix}


Optionally, the impedance element can also have conductance and susceptance at the "from" and "to" buses. In this case,
the electric model becomes similar to the line model. It is possible to have different values of susceptance and
conductance for the "from" and "to" bus, as is in the case of the resistance and reactance. This provides for
flexibility in modeling an impedance branch element, which will be especially useful when modeling grid equivalents.


Result Parameters
==========================
*net.res_impedance*

.. tabularcolumns:: |p{0.10\linewidth}|p{0.1\linewidth}|p{0.55\linewidth}|
.. csv-table:: 
   :file: impedance_res.csv
   :delim: ;
   :widths: 10, 10, 55

.. math::
   :nowrap:
   
   \begin{align*}
    i\_from\_ka &= i_{from}\\
    i\_to\_ka &= i_{to}\\
    p\_from\_mw &= Re(\underline{v}_{from} \cdot \underline{i}^*_{from}) \\    
    q\_from\_mvar &= Im(\underline{v}_{from} \cdot \underline{i}^*_{from}) \\
    p\_to\_mw &= Re(\underline{v}_{to} \cdot \underline{i}^*_{to}) \\
    q\_to\_mvar &= Im(\underline{v}_{to} \cdot \underline{i}^*_{to}) \\
	pl\_mw &= p\_from\_mw + p\_to\_mw \\
	ql\_mvar &= q\_from\_mvar + q\_to\_mvar \\
    \end{align*}