.. _PhasorMeasurement:

================================================================================
PhasorMeasurement
================================================================================
Phasor measurements

Common Parameters: u, name

Common Variables: am, vm

Available models:
PMU_

.. _PMU:

--------------------------------------------------------------------------------
PMU
--------------------------------------------------------------------------------
Simple phasor measurement unit model.

This model tracks the bus voltage magnitude and phase angle, each using
a low-pass filter.

Parameters
----------

+-------+-------------+------------------------------+---------+--------+------------+
| Name  |   Symbol    |         Description          | Default |  Unit  | Properties |
+=======+=============+==============================+=========+========+============+
|  idx  |             | unique device idx            |         |        |            |
+-------+-------------+------------------------------+---------+--------+------------+
|  u    | :math:`u`   | connection status            | 1       | *bool* |            |
+-------+-------------+------------------------------+---------+--------+------------+
|  name |             | device name                  |         |        |            |
+-------+-------------+------------------------------+---------+--------+------------+
|  bus  |             | bus idx                      |         |        | mandatory  |
+-------+-------------+------------------------------+---------+--------+------------+
|  Ta   | :math:`T_a` | angle filter time constant   | 0.100   |        |            |
+-------+-------------+------------------------------+---------+--------+------------+
|  Tv   | :math:`T_v` | voltage filter time constant | 0.100   |        |            |
+-------+-------------+------------------------------+---------+--------+------------+

Variables
---------

+------+------------+----------+-------------------------------+------------+------------+
| Name |   Symbol   |   Type   |          Description          |    Unit    | Properties |
+======+============+==========+===============================+============+============+
|  am  | :math:`am` | State    | phase angle measurement       | *rad.*     | v_str      |
+------+------------+----------+-------------------------------+------------+------------+
|  vm  | :math:`vm` | State    | voltage magnitude measurement | *p.u.(kV)* | v_str      |
+------+------------+----------+-------------------------------+------------+------------+
|  a   | :math:`a`  | ExtAlgeb | Bus voltage phase angle       |            |            |
+------+------------+----------+-------------------------------+------------+------------+
|  v   | :math:`v`  | ExtAlgeb | Bus voltage magnitude         |            |            |
+------+------------+----------+-------------------------------+------------+------------+

Initialization Equations
------------------------

+------+------------+----------+---------------+
| Name |   Symbol   |   Type   | Initial Value |
+======+============+==========+===============+
|  am  | :math:`am` | State    | :math:`a`     |
+------+------------+----------+---------------+
|  vm  | :math:`vm` | State    | :math:`v`     |
+------+------------+----------+---------------+
|  a   | :math:`a`  | ExtAlgeb |               |
+------+------------+----------+---------------+
|  v   | :math:`v`  | ExtAlgeb |               |
+------+------------+----------+---------------+

Differential Equations
-----------------------------

+------+------------+-------+----------------------------------+-------------+
| Name |   Symbol   | Type  | RHS of Equation "T x' = f(x, y)" |   T (LHS)   |
+======+============+=======+==================================+=============+
|  am  | :math:`am` | State | :math:`a - am`                   | :math:`T_a` |
+------+------------+-------+----------------------------------+-------------+
|  vm  | :math:`vm` | State | :math:`v - vm`                   | :math:`T_v` |
+------+------------+-------+----------------------------------+-------------+

Algebraic Equations
-----------------------------

+------+-----------+----------+-------------------------------+
| Name |  Symbol   |   Type   | RHS of Equation "0 = g(x, y)" |
+======+===========+==========+===============================+
|  a   | :math:`a` | ExtAlgeb | :math:`0`                     |
+------+-----------+----------+-------------------------------+
|  v   | :math:`v` | ExtAlgeb | :math:`0`                     |
+------+-----------+----------+-------------------------------+


Config Fields in [PMU]

+---------------+--------+-------+---------------------------------------+-----------------+
|    Option     | Symbol | Value |                 Info                  | Accepted values |
+===============+========+=======+=======================================+=================+
|  allow_adjust |        | 1     | allow adjusting upper or lower limits | (0, 1)          |
+---------------+--------+-------+---------------------------------------+-----------------+
|  adjust_lower |        | 0     | adjust lower limit                    | (0, 1)          |
+---------------+--------+-------+---------------------------------------+-----------------+
|  adjust_upper |        | 1     | adjust upper limit                    | (0, 1)          |
+---------------+--------+-------+---------------------------------------+-----------------+