.. _Cost:

================================================================================
Cost
================================================================================
Common Parameters: u, name, idx, gen

Available models:
GCost_,
SFRCost_,
SRCost_,
NSRCost_,
VSGCost_,
DCost_

.. _GCost:

--------------------------------------------------------------------------------
GCost
--------------------------------------------------------------------------------
Generator cost model, similar to MATPOWER ``gencost`` format.

``type`` is the cost model type. 1 for piecewise linear, 2 for polynomial.

In piecewise linear cost model, cost function f(p) is defined by a set of points:
(p0, c0), (p1, c1), (p2, c2), where p0 < p1 < p2.

In quadratic cost model, cost function f(p) is defined by a set of coefficients:
f(p) = c2 * p^2 + c1 * p + c0.

Parameters
----------

+-------+-----------------+-----------------------------------------------------------+---------+----------------+------------+
| Name  |     Symbol      |                        Description                        | Default |      Unit      | Properties |
+=======+=================+===========================================================+=========+================+============+
|  idx  |                 | unique device idx                                         |         |                |            |
+-------+-----------------+-----------------------------------------------------------+---------+----------------+------------+
|  u    | :math:`u`       | connection status                                         | 1       | *bool*         |            |
+-------+-----------------+-----------------------------------------------------------+---------+----------------+------------+
|  name |                 | device name                                               |         |                |            |
+-------+-----------------+-----------------------------------------------------------+---------+----------------+------------+
|  gen  |                 | static generator index                                    |         |                | mandatory  |
+-------+-----------------+-----------------------------------------------------------+---------+----------------+------------+
|  type | :math:`t_{ype}` | Cost model type. 1 for piecewise linear, 2 for polynomial | 2       |                |            |
+-------+-----------------+-----------------------------------------------------------+---------+----------------+------------+
|  csu  | :math:`c_{su}`  | startup cost in US dollars                                | 0       | *$*            |            |
+-------+-----------------+-----------------------------------------------------------+---------+----------------+------------+
|  csd  | :math:`c_{sd}`  | shutdown cost in US dollars                               | 0       | *$*            |            |
+-------+-----------------+-----------------------------------------------------------+---------+----------------+------------+
|  c2   | :math:`c_{2}`   | coefficient 2                                             | 0       | *$/(p.u.*h)^2* |            |
+-------+-----------------+-----------------------------------------------------------+---------+----------------+------------+
|  c1   | :math:`c_{1}`   | coefficient 1                                             | 0       | *$/p.u.*h*     |            |
+-------+-----------------+-----------------------------------------------------------+---------+----------------+------------+
|  c0   | :math:`c_{0}`   | coefficient 0                                             | 0       | *$*            |            |
+-------+-----------------+-----------------------------------------------------------+---------+----------------+------------+


.. _SFRCost:

--------------------------------------------------------------------------------
SFRCost
--------------------------------------------------------------------------------
Linear SFR cost model.

Parameters
----------

+-------+---------------+------------------------+---------+--------------+------------+
| Name  |    Symbol     |      Description       | Default |     Unit     | Properties |
+=======+===============+========================+=========+==============+============+
|  idx  |               | unique device idx      |         |              |            |
+-------+---------------+------------------------+---------+--------------+------------+
|  u    | :math:`u`     | connection status      | 1       | *bool*       |            |
+-------+---------------+------------------------+---------+--------------+------------+
|  name |               | device name            |         |              |            |
+-------+---------------+------------------------+---------+--------------+------------+
|  gen  |               | static generator index |         |              | mandatory  |
+-------+---------------+------------------------+---------+--------------+------------+
|  cru  | :math:`c_{r}` | cost for RegUp reserve | 0       | *$/(p.u.*h)* |            |
+-------+---------------+------------------------+---------+--------------+------------+
|  crd  | :math:`c_{r}` | cost for RegDn reserve | 0       | *$/(p.u.*h)* |            |
+-------+---------------+------------------------+---------+--------------+------------+


.. _SRCost:

--------------------------------------------------------------------------------
SRCost
--------------------------------------------------------------------------------
Linear spinning reserve cost model.

Parameters
----------

+-------+----------------+---------------------------+---------+--------------+------------+
| Name  |     Symbol     |        Description        | Default |     Unit     | Properties |
+=======+================+===========================+=========+==============+============+
|  idx  |                | unique device idx         |         |              |            |
+-------+----------------+---------------------------+---------+--------------+------------+
|  u    | :math:`u`      | connection status         | 1       | *bool*       |            |
+-------+----------------+---------------------------+---------+--------------+------------+
|  name |                | device name               |         |              |            |
+-------+----------------+---------------------------+---------+--------------+------------+
|  gen  |                | static generator index    |         |              | mandatory  |
+-------+----------------+---------------------------+---------+--------------+------------+
|  csr  | :math:`c_{sr}` | cost for spinning reserve | 0       | *$/(p.u.*h)* |            |
+-------+----------------+---------------------------+---------+--------------+------------+


.. _NSRCost:

--------------------------------------------------------------------------------
NSRCost
--------------------------------------------------------------------------------
Linear non-spinning reserve cost model.

Parameters
----------

+-------+-----------------+-------------------------------+---------+--------------+------------+
| Name  |     Symbol      |          Description          | Default |     Unit     | Properties |
+=======+=================+===============================+=========+==============+============+
|  idx  |                 | unique device idx             |         |              |            |
+-------+-----------------+-------------------------------+---------+--------------+------------+
|  u    | :math:`u`       | connection status             | 1       | *bool*       |            |
+-------+-----------------+-------------------------------+---------+--------------+------------+
|  name |                 | device name                   |         |              |            |
+-------+-----------------+-------------------------------+---------+--------------+------------+
|  gen  |                 | static generator index        |         |              | mandatory  |
+-------+-----------------+-------------------------------+---------+--------------+------------+
|  cnsr | :math:`c_{nsr}` | cost for non-spinning reserve | 0       | *$/(p.u.*h)* |            |
+-------+-----------------+-------------------------------+---------+--------------+------------+


.. _VSGCost:

--------------------------------------------------------------------------------
VSGCost
--------------------------------------------------------------------------------
Linear cost model for VSG emulated inertia (M) and damping (D).

Parameters
----------

+-------+---------------+-------------------------------+---------+----------+------------+
| Name  |    Symbol     |          Description          | Default |   Unit   | Properties |
+=======+===============+===============================+=========+==========+============+
|  idx  |               | unique device idx             |         |          |            |
+-------+---------------+-------------------------------+---------+----------+------------+
|  u    | :math:`u`     | connection status             | 1       | *bool*   |            |
+-------+---------------+-------------------------------+---------+----------+------------+
|  name |               | device name                   |         |          |            |
+-------+---------------+-------------------------------+---------+----------+------------+
|  reg  |               | Renewable generator idx       |         |          | mandatory  |
+-------+---------------+-------------------------------+---------+----------+------------+
|  cm   | :math:`c_{r}` | cost for emulated inertia (M) | 0       | *$/s*    |            |
+-------+---------------+-------------------------------+---------+----------+------------+
|  cd   | :math:`c_{r}` | cost for emulated damping (D) | 0       | *$/p.u.* |            |
+-------+---------------+-------------------------------+---------+----------+------------+


.. _DCost:

--------------------------------------------------------------------------------
DCost
--------------------------------------------------------------------------------
Linear cost model for dispatchable loads.

Parameters
----------

+-------+-----------------+-------------------------------+---------+--------------+------------+
| Name  |     Symbol      |          Description          | Default |     Unit     | Properties |
+=======+=================+===============================+=========+==============+============+
|  idx  |                 | unique device idx             |         |              |            |
+-------+-----------------+-------------------------------+---------+--------------+------------+
|  u    | :math:`u`       | connection status             | 1       | *bool*       |            |
+-------+-----------------+-------------------------------+---------+--------------+------------+
|  name |                 | device name                   |         |              |            |
+-------+-----------------+-------------------------------+---------+--------------+------------+
|  pq   |                 | static load index             |         |              | mandatory  |
+-------+-----------------+-------------------------------+---------+--------------+------------+
|  cdp  | :math:`c_{d,p}` | cost for unserve load penalty | 999     | *$/(p.u.*h)* |            |
+-------+-----------------+-------------------------------+---------+--------------+------------+