5 move optimisation model variables to own module

README.md

@@ -1 +1,31 @@
 # Home-Battery-Optimiser
+
+## Optimisation Model
+The optimisation model is a linear program (LP) that minimises the cost of electricity consumption over
+a given time horizon based on optimal dispatch of a battery. The model is formulated as follows:
+
+
+[//]: # (read the optimisation problem)
+$$
+\begin{aligned}
+& \underset{Cost_{t}^{battery} + Cost_{t}^{grid} + Cost_{t}^{renewable} - Sales_{t}^{grid}}{\text{minimise}}
+& & \sum_{t=1}^{T} \left(Cost_{t}^{battery} + Cost_{t}^{grid} + Cost_{t}^{renewable} - Sales_{t}^{grid} \right) \\
+& \text{subject to}
+& & E_{t}^{battery} = E_{t-1}^{battery} + \eta_{t}^{charge} P_{t}^{charge} - \frac{1}{\eta_{t}^{discharge}} P_{t}^{discharge} \\
+& & & E_{t}^{battery} \leq E_{t}^{battery, max} \\
+& & & E_{t}^{battery} \geq E_{t}^{battery, min} \\
+& & & P_{t}^{charge} \leq P_{t}^{charge, max} \\
+& & & P_{t}^{discharge} \leq P_{t}^{discharge, max} \\
+& & & P_{t}^{charge} \geq P_{t}^{charge, min} \\
+& & & P_{t}^{discharge} \geq P_{t}^{discharge, min} \\
+& & & \eta_{t}^{charge} \leq \eta_{t}^{charge, max} \\
+& & & \eta_{t}^{discharge} \leq \eta_{t}^{discharge, max} \\
+& & & \eta_{t}^{charge} \geq \eta_{t}^{charge, min} \\
+& & & \eta_{t}^{discharge} \geq \eta_{t}^{discharge, min} \\
+& & & \forall t \in \{1, \dots, T\} \\
+\end{aligned}
+$$
+
+Where $Cost_{t}^{battery}$ is the unit cost of electricity from the battery, $Cost_{t}^{grid}$ is the unit cost of
+electricity from the grid, $Cost_{t}^{renewable}$ is the unit cost of electricity from renewable sources,
+$Sales_{t}^{grid}$ is the unit revenue from selling electricity to the grid,