Update documentation

docs/src/mathematical-formulation.md

@@ -28,21 +28,23 @@ NOTE: Asset types are mutually exclusive.
 
 Name|Domain|Description|Units
  ---|---|---|---
-$p^{investment\_cost}_{a}$ | $\mathcal{A}_i$    | Investment cost  of asset units         | [kEUR/MW/year]
-$p^{unit\_capacity}_{a}$   | $\mathcal{A}$      | Capacity of asset units                 | [MW]
-$p^{peak\_demand}_{a}$     | $\mathcal{A}_c$    | Peak demand                             | [MW]
-$p^{init\_capacity}_{a}$   | $\mathcal{A}$      | Initial capacity of asset units         | [MW]
-$p^{investment\_cost}_{f}$ | $\mathcal{F}_i$    | Investment cost  of flow connections    | [kEUR/MW/year]
-$p^{variable\_cost}_{f}$   | $\mathcal{F}$      | Variable cost of flow connections       | [kEUR/MWh]
-$p^{unit\_capacity}_{f}$   | $\mathcal{F}$      | Capacity of flow connections            | [MW]
-$p^{init\_capacity}_{f}$   | $\mathcal{F}$      | Initial capacity of flow connections    | [MW]
-$p^{export\_capacity}_{f}$ | $\mathcal{F}_t$    | Export capacity of flow connections     | [MW]
-$p^{import\_capacity}_{f}$ | $\mathcal{F}_t$    | Import capacity of flow connections     | [MW]
-$p^{rp\_weight}_{rp}$      | $\mathcal{RP}$     | Representative period weight            | [h]
-$p^{profile}_{a,rp,k}$     | $\mathcal{A,RP,K}$ | Asset profile                           | [p.u.]
-$p^{profile}_{f,rp,k}$     | $\mathcal{F,RP,K}$ | Flow connections profile                | [p.u.]
-$p^{ene\_to\_pow\_ratio}_a$| $\mathcal{A}_s$    | Energy to power ratio                   | [h]
-$p^{eff}_f$                | $\mathcal{F}$      | Flow efficiency                         | [p.u.]
+$p^{investment\_cost}_{a}$     | $\mathcal{A}_i$    | Investment cost  of asset units         | [kEUR/MW/year]
+$p^{unit\_capacity}_{a}$       | $\mathcal{A}$      | Capacity of asset units                 | [MW]
+$p^{peak\_demand}_{a}$         | $\mathcal{A}_c$    | Peak demand                             | [MW]
+$p^{init\_capacity}_{a}$       | $\mathcal{A}$      | Initial capacity of asset units         | [MW]
+$p^{investment\_cost}_{f}$     | $\mathcal{F}_i$    | Investment cost  of flow connections    | [kEUR/MW/year]
+$p^{variable\_cost}_{f}$       | $\mathcal{F}$      | Variable cost of flow connections       | [kEUR/MWh]
+$p^{unit\_capacity}_{f}$       | $\mathcal{F}$      | Capacity of flow connections            | [MW]
+$p^{init\_capacity}_{f}$       | $\mathcal{F}$      | Initial capacity of flow connections    | [MW]
+$p^{export\_capacity}_{f}$     | $\mathcal{F}_t$    | Export capacity of flow connections     | [MW]
+$p^{import\_capacity}_{f}$     | $\mathcal{F}_t$    | Import capacity of flow connections     | [MW]
+$p^{rp\_weight}_{rp}$          | $\mathcal{RP}$     | Representative period weight            | [h]
+$p^{profile}_{a,rp,k}$         | $\mathcal{A,RP,K}$ | Asset profile                           | [p.u.]
+$p^{profile}_{f,rp,k}$         | $\mathcal{F,RP,K}$ | Flow connections profile                | [p.u.]
+$p^{ene\_to\_pow\_ratio}_a$    | $\mathcal{A}_s$    | Energy to power ratio                   | [h]
+$p^{init\_storage\_level}_{a}$ | $\mathcal{A}_s$    | Initial storage level                   | [MWh]
+$p^{inflow}_{a}$               | $\mathcal{A}_s$    | Energy storage inflows                  | [MWh]
+$p^{eff}_f$                    | $\mathcal{F}$      | Flow efficiency                         | [p.u.]
 
 ## [Variables](@id math-variables)
 
@@ -177,3 +179,10 @@ v^{flow}_{f,rp,k} \geq p^{profile}_{f,rp,k} \cdot \left(p^{init\_capacity}_{f} +
 0 \leq s_{a,rp,k}^{level} \leq p^{init\_storage\_capacity}_{a} + p^{ene\_to\_pow\_ratio}_a \cdot p^{unit\_capacity}_a \cdot v^{investment}_a \quad
 \\ \\ \forall a \in \mathcal{A}_s, \forall rp \in \mathcal{RP},\forall k \in \mathcal{K}
 ```
+
+#### Cycling Constraints for Storage Level
+
+```math
+s_{a,rp,k=K}^{level} \geq p^{init\_storage\_level}_{a} \quad
+\\ \\ \forall a \in \mathcal{A}_s, \forall rp \in \mathcal{RP}
+```