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docs: capitalizing just the first and fix grammar
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Signed-off-by: Victor Garcia Reolid <victor@seita.nl>
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victorgarcia98 committed Jul 21, 2023
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42 changes: 21 additions & 21 deletions documentation/concepts/device_scheduler.rst
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Expand Up @@ -29,24 +29,24 @@ Symbol Variable in the Code

.. note::
The time index :math:`j` has two interpretations: a time period or an instantaneous moment at the end of time period :math:`j`.
For example, :math:`j` in flow constraints correspond to time periods, whereas :math:`j` used in a stock constraint refers end of time period :math:`j`.
For example, :math:`j` in flow constraints correspond to time periods, whereas :math:`j` used in a stock constraint refers to the end of time period :math:`j`.

Parameters
^^^^^^^^^^
================================ ================================================ ==============================================================================================================
Symbol Variable in the Code Description
================================ ================================================ ==============================================================================================================
:math:`Price_{up}(c,j)` up_price Price of incurring an upwards deviations in commitment :math:`c` during :math:`j` time period.
:math:`Price_{down}(c,j)` down_price Price of incurring a downwards deviations in commitment :math:`c` during :math:`j` time period.
:math:`Price_{up}(c,j)` up_price Price of incurring an upwards deviations in commitment :math:`c` during time period :math:`j`.
:math:`Price_{down}(c,j)` down_price Price of incurring a downwards deviations in commitment :math:`c` during time period :math:`j`.
:math:`\eta_{up}(d,j)` device_derivative_up_efficiency Upwards conversion efficiency.
:math:`\eta_{down}(d,j)` device_derivative_down_efficiency Downwards conversion efficiency.
:math:`Stock_{min}(d,j)` device_min Minimum quantity for the stock of device :math:`d` at the end of :math:`j` time period.
:math:`Stock_{max}(d,j)` device_max Maximum quantity for the stock of device :math:`d` at the end of :math:`j` time period.
:math:`Stock_{min}(d,j)` device_min Minimum quantity for the stock of device :math:`d` at the end of time period :math:`j`.
:math:`Stock_{max}(d,j)` device_max Maximum quantity for the stock of device :math:`d` at the end of time period :math:`j`.
:math:`\epsilon(d,j)` efficiencies Stock energy losses.
:math:`P_{max}(d,j)` device_derivative_max Maximum flow of device :math:`d` during :math:`j` time period.
:math:`P_{min}(d,j)` device_derivative_min Minimum flow of device :math:`d` during :math:`j` time period.
:math:`P^{ems}_{min}(j)` ems_derivative_min Minimum flow of the EMS during :math:`j` time period.
:math:`P^{ems}_{max}(j)` ems_derivative_max Maximum flow of the EMS during :math:`j` time period.
:math:`P_{max}(d,j)` device_derivative_max Maximum flow of device :math:`d` during time period :math:`j`.
:math:`P_{min}(d,j)` device_derivative_min Minimum flow of device :math:`d` during time period :math:`j`.
:math:`P^{ems}_{min}(j)` ems_derivative_min Minimum flow of the EMS during time period :math:`j`.
:math:`P^{ems}_{max}(j)` ems_derivative_max Maximum flow of the EMS during time period :math:`j`.
:math:`Commitment(c,j)` commitment_quantity Commitment c (at EMS level) over time step :math:`j`.
================================ ================================================ ==============================================================================================================

Expand All @@ -56,15 +56,15 @@ Variables
================================ ================================================ ==============================================================================================================
Symbol Variable in the Code Description
================================ ================================================ ==============================================================================================================
:math:`\Delta_{up}(c,j)` commitment_upwards_deviation Upwards deviation from the power commitment :math:`c` of the EMS during :math:`j` time period.
:math:`\Delta_{down}(c,j)` commitment_downwards_deviation Downwards deviation from the power commitment :math:`c` of the EMS during :math:`j` time period.
:math:`\Delta Stock(d,j)` n/a Change of stock of device :math:`d` at the end of :math:`j` time period.
:math:`P_{up}(d,j)` device_power_up Upwards power of device :math:`d` during :math:`j` time period.
:math:`P_{down}(d,j)` device_power_down Downwards power of device :math:`d` during :math:`j` time period.
:math:`P^{ems}(j)` ems_power Aggregated power of all the devices during :math:`j` time period.
:math:`\Delta_{up}(c,j)` commitment_upwards_deviation Upwards deviation from the power commitment :math:`c` of the EMS during time period :math:`j`.
:math:`\Delta_{down}(c,j)` commitment_downwards_deviation Downwards deviation from the power commitment :math:`c` of the EMS during time period :math:`j`.
:math:`\Delta Stock(d,j)` n/a Change of stock of device :math:`d` at the end of time period :math:`j`.
:math:`P_{up}(d,j)` device_power_up Upwards power of device :math:`d` during time period :math:`j`.
:math:`P_{down}(d,j)` device_power_down Downwards power of device :math:`d` during time period :math:`j`.
:math:`P^{ems}(j)` ems_power Aggregated power of all the devices during time period :math:`j`.
================================ ================================================ ==============================================================================================================

Cost Function
Cost function
--------------

The cost function quantifies the total cost of upwards and downwards deviations from the different commitments.
Expand All @@ -75,7 +75,7 @@ The cost function quantifies the total cost of upwards and downwards deviations
\min [\sum_{c,j} \Delta _{up}(c,j) \cdot Price_{up}(c,j) + \Delta_{down}(c,j) \cdot Price_{down}(c,j)]
State Dynamics
State dynamics
---------------

To simplify the description of the model, the auxiliary variable :math:`\Delta Stock(d,j)` is introduced in the documentation. It represents the
Expand All @@ -94,15 +94,15 @@ change of :math:`Stock(d,j)`, taking into account conversion efficiencies but no
Stock_{min}(d,j) \leq Stock(d,j) - Stock(d,-1)\leq Stock_{max}(d,j)
Perfect Efficiency
Perfect efficiency
^^^^^^^^^^^^^^^^^^^

.. math::
:name: efficiency_e1
Stock(d, j) = Stock(d, j-1) + \Delta Stock(d,j)
Left Efficiency
Left efficiency
^^^^^^^^^^^^^^^^^
First apply the stock change, then apply the losses (i.e. the stock changes on the left side of the time interval in which the losses apply)

Expand All @@ -113,7 +113,7 @@ First apply the stock change, then apply the losses (i.e. the stock changes on t
Stock(d, j) = (Stock(d, j-1) + \Delta Stock(d,j)) \cdot \epsilon(d,j)
Right Efficiency
Right efficiency
^^^^^^^^^^^^^^^^^
First apply the losses, then apply the stock change (i.e. the stock changes on the right side of the time interval in which the losses apply)

Expand All @@ -122,7 +122,7 @@ First apply the losses, then apply the stock change (i.e. the stock changes on t
Stock(d, j) = Stock(d, j-1) \cdot \epsilon(d,j) + \Delta Stock(d,j)
Linear Efficiency
Linear efficiency
^^^^^^^^^^^^^^^^^
Assume the change happens at a constant rate, leading to a linear stock change, and exponential decay, within the current interval

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