.. _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:`\theta_{m}` | State    | phase angle measurement       | *rad.*     | v_str      |
+------+--------------------+----------+-------------------------------+------------+------------+
|  vm  | :math:`V_{m}`      | State    | voltage magnitude measurement | *p.u.(kV)* | v_str      |
+------+--------------------+----------+-------------------------------+------------+------------+
|  a   | :math:`\theta`     | ExtAlgeb | Bus voltage phase angle       |            |            |
+------+--------------------+----------+-------------------------------+------------+------------+
|  v   | :math:`V`          | ExtAlgeb | Bus voltage magnitude         |            |            |
+------+--------------------+----------+-------------------------------+------------+------------+

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

+------+--------------------+----------+----------------+
| Name |       Symbol       |   Type   | Initial Value  |
+======+====================+==========+================+
|  am  | :math:`\theta_{m}` | State    | :math:`\theta` |
+------+--------------------+----------+----------------+
|  vm  | :math:`V_{m}`      | State    | :math:`V`      |
+------+--------------------+----------+----------------+
|  a   | :math:`\theta`     | ExtAlgeb |                |
+------+--------------------+----------+----------------+
|  v   | :math:`V`          | ExtAlgeb |                |
+------+--------------------+----------+----------------+

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

+------+--------------------+-------+----------------------------------+-------------+
| Name |       Symbol       | Type  | RHS of Equation "T x' = f(x, y)" |   T (LHS)   |
+======+====================+=======+==================================+=============+
|  am  | :math:`\theta_{m}` | State | :math:`\theta - \theta_{m}`      | :math:`T_a` |
+------+--------------------+-------+----------------------------------+-------------+
|  vm  | :math:`V_{m}`      | State | :math:`V - V_{m}`                | :math:`T_v` |
+------+--------------------+-------+----------------------------------+-------------+

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

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