135 include all assets (#161)

* WIP: first update in the formulation

* Update the formulation, first draft

* Change the markdown to latex command

* Update formulation with bounds for flows associated to assets

* Updated input data

* Update documentation

* Updated the schema to include new parameters

* Updated schema for different efficiency

* Updated data with efficiency

* Implement all constraints from the mathematical formulation (#1)

* Change code and input data to have the flows with names instead of id

* Change the variable cost data from the assets to the flows

* Fix model funtion to create it properly with the new constraints

* Update solution of the tiny example

* Add write_lp_file option in the creation of the model

* Fix Julia files format

* Add all assets types in the sets structure

* Changes in the model and input to include new assets data

* Update tiny case study data files

* Update tiny case test result and output file

* Update Norse case study input data files

* Change the flow capacity to import/export capacity to set flows bounds

* Update formulation in the documentation with latest changes

* Add test for Norse case study

* Changes to cover all the options in test for the Norse case study

* Changes according to review comments

---------

Co-authored-by: datejada <[email protected]>
Co-authored-by: Abel Soares Siqueira <[email protected]>

docs/src/mathematical-formulation.md

@@ -5,75 +5,164 @@ The full mathematical formulation is also freely available in the [preprint](htt
 
 ## [Sets](@id math-sets)
 
+NOTE: Asset types are mutually exclusive.
 Name|Description|Elements
  ---|---|---:
-$\mathcal{A}$           | Energy assets                         | $a \in \mathcal{A}$
-$\mathcal{A_c}$         | Consumer energy assets                | $\mathcal{A_c} \subseteq \mathcal{A}$
-$\mathcal{A_p}$         | Producer energy assets                | $\mathcal{A_p} \subseteq \mathcal{A}$
-$\mathcal{A_i}$         | Energy assets with investment method  | $\mathcal{A_i} \subseteq \mathcal{A}$
-$\mathcal{A_b}$         | Energy assets with balance method     | $\mathcal{A_b} \subseteq \mathcal{A}$
-$\mathcal{RP}$          | Representative periods                | $rp \in \mathcal{RP}$
-$\mathcal{K}$           | Time steps within the $rp$            | $k \in \mathcal{K}$
-$\mathcal{F}$           | Flow connections between two assets   | $f \in \mathcal{F}$
-$\mathcal{F_{rec}}(a)$  | Set of flows with receiving asset $a$ | $\mathcal{F_{rec}}(a) \subseteq \mathcal{F}$
-$\mathcal{F_{snd}}(a)$  | Set of flows with sending asset $a$   | $\mathcal{F_{snd}}(a) \subseteq \mathcal{F}$
+$\mathcal{A}$           | Energy assets                           | $a \in \mathcal{A}$
+$\mathcal{A}_c$         | Consumer energy assets                  | $\mathcal{A}_c   \subseteq \mathcal{A}$
+$\mathcal{A}_p$         | Producer energy assets                  | $\mathcal{A}_p   \subseteq \mathcal{A}$
+$\mathcal{A}_s$         | Storage energy assets                   | $\mathcal{A}_s   \subseteq \mathcal{A}$
+$\mathcal{A}_h$         | Hub energy assets (e.g., transshipment) | $\mathcal{A}_h   \subseteq \mathcal{A}$
+$\mathcal{A}_{cv}$      | Conversion energy assets                | $\mathcal{A}_{cv}\subseteq \mathcal{A}$
+$\mathcal{A}_i$         | Energy assets with investment method    | $\mathcal{A}_i   \subseteq \mathcal{A}$
+$\mathcal{F}$           | Flow connections between two assets     | $f \in \mathcal{F}$
+$\mathcal{F}_t$         | Transport flow between two assets       | $\mathcal{F}_t   \subseteq \mathcal{F}$
+$\mathcal{F}_i$         | Transport flow with investment method   | $\mathcal{F}_i   \subseteq \mathcal{F}_t$
+$\mathcal{F}_{in}(a)$   | Set of flows going into asset $a$       | $\mathcal{F}_{in}(a) \subseteq \mathcal{F}$
+$\mathcal{F}_{out}(a)$  | Set of flows going out of asset $a$     | $\mathcal{F}_{out}(a) \subseteq \mathcal{F}$
+$\mathcal{RP}$          | Representative periods                  | $rp \in \mathcal{RP}$
+$\mathcal{K}$           | Time steps within the $rp$              | $k \in \mathcal{K}$
 
 ## [Parameters](@id math-parameters)
 
-Name|Description|Units
- ---|---|---
-$p^{investment\_cost}_{a}$ | Investment cost  of asset units      | [kEUR/MW/year]
-$p^{variable\_cost}_{a}$   | Variable cost of asset units         | [kEUR/MWh]
-$p^{unit\_capacity}_{a}$   | Capacity of asset units              | [MW]
-$p^{rp\_weight}_{rp}$      | Representative period weight         | [h]
-$p^{profile}_{a,rp, k}$    | Asset production/consumption profile | [p.u.]
-$p^{peak\_demand}_{a}$     | Peak demand                          | [MW]
-$p^{init\_capacity}_{a}$   | initial capacity of asset units      | [MW]
+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.]
 
 ## [Variables](@id math-variables)
 
-Name|Description|Units
- ---|---|---
-$v^{flow}_{f,rp,k} \in \mathbb{R}$     | Flow between two assets         |[MW]
-$v^{investment}_{a} \in \mathbb{Z^{+}}$| Number of installed asset units |[units]
+Name|Domain|Description|Units
+ ---|---|---|---
+$v^{flow}_{f,rp,k}  \in \mathbb{R}$    | $\mathcal{F,RP,K}$    | Flow between two assets                      |[MW]
+$v^{investment}_{a} \in \mathbb{Z}^{+}$| $\mathcal{A}_i$       | Number of installed asset units              |[units]
+$v^{investment}_{f} \in \mathbb{Z}^{+}$| $\mathcal{F}_i$       | Number of installed units between two assets |[units]
+$s^{level}_{a,rp,k} \in \mathbb{R}$    | $\mathcal{A_s,RP,K}$  | Storage level                                |[MWh]
 
 ## [Objective Function](@id math-objective-function)
 
 Objective function:
 
 ```math
-\text{{minimize}} \quad investment\_cost + variable\_cost
+\begin{aligned}
+\text{{minimize}} \quad & assets\_investment\_cost + flows\_investment\_cost \\
+                        & + flows\_variable\_cost
+\end{aligned}
 ```
 
 Where:
 
 ```math
 \begin{aligned}
-investment\_cost &= \sum_{a \in \mathcal{Ai}} p^{investment\_cost}_a \cdot p^{unit\_capacity}_a \cdot v^{investment}_a \\
-variable\_cost &= \sum_{a \in \mathcal{Ap}} \sum_{f \in \mathcal{F_{snd}}(a)} \sum_{rp \in \mathcal{RP}} \sum_{k \in \mathcal{K}} p^{rp\_weight}_{rp} \cdot p^{variable\_cost}_a \cdot v^{flow}_{f,rp,k}
+assets\_investment\_cost &= \sum_{a \in \mathcal{Ai}} p^{investment\_cost}_a \cdot p^{unit\_capacity}_a \cdot v^{investment}_a \\
+flows\_investment\_cost &= \sum_{f \in \mathcal{Fi}} p^{investment\_cost}_f \cdot p^{unit\_capacity}_f \cdot v^{investment}_f \\
+flows\_variable\_cost &= \sum_{f \in \mathcal{F}} \sum_{rp \in \mathcal{RP}} \sum_{k \in \mathcal{K}} p^{rp\_weight}_{rp} \cdot p^{variable\_cost}_f \cdot v^{flow}_{f,rp,k}
 \end{aligned}
 ```
 
 ## [Constraints](@id math-constraints)
 
-### Balance Constraint
+### Balancing Contraints for Asset Type
+
+#### Constraints for Consumers Energy Assets $\mathcal{A}_c$
+
+```math
+\begin{aligned}
+\sum_{f \in \mathcal{F}_{in}(a)} v^{flow}_{f,rp,k} - \sum_{f \in \mathcal{F}_{out}(a)} v^{flow}_{f,rp,k} \left\{\begin{array}{l} = \\ \geqslant \\ \leqslant \end{array}\right\} p^{profile}_{a,rp,k} \cdot p^{peak\_demand}_{a} \quad \forall a \in \mathcal{A}_c, \forall rp \in \mathcal{RP},\forall k \in \mathcal{K}
+\end{aligned}
+```
+
+#### Constraints for Storage Energy Assets $\mathcal{A}_s$
+
+```math
+\begin{aligned}
+s_{a,rp,k}^{level} = s_{a,rp,k-1}^{level} + p_{a,rp,k}^{inflow} + \cdot \sum_{f \in \mathcal{F}_{in}(a)} p^{eff}_f \cdot v^{flow}_{f,rp,k} - \sum_{f \in \mathcal{F}_{out}(a)} \frac{1}{p^{eff}_f} \cdot v^{flow}_{f,rp,k} \quad \forall a \in \mathcal{A}_s, \forall rp \in \mathcal{RP},\forall k \in \mathcal{K}
+\end{aligned}
+```
+
+#### Constraints for Hub Energy Assets $\mathcal{A}_h$
+
+```math
+\begin{aligned}
+\sum_{f \in \mathcal{F}_{in}(a)} v^{flow}_{f,rp,k} = \sum_{f \in \mathcal{F}_{out}(a)} v^{flow}_{f,rp,k} \quad \forall a \in \mathcal{A}_h, \forall rp \in \mathcal{RP},\forall k \in \mathcal{K}
+\end{aligned}
+```
+
+#### Constraints for Conversion Energy Assets $\mathcal{A}_{cv}$
+
+```math
+\begin{aligned}
+\sum_{f \in \mathcal{F}_{in}(a)} p^{eff}_f \cdot {v^{flow}_{f,rp,k}} = \sum_{f \in \mathcal{F}_{out}(a)} \frac{v^{flow}_{f,rp,k}}{p^{eff}_f}  \quad \forall a \in \mathcal{A}_{cv}, \forall rp \in \mathcal{RP},\forall k \in \mathcal{K}
+\end{aligned}
+```
+
+### Constraints that Define Bounds of Flows Related to Energy Assets $\mathcal{A}$
+
+#### Contraint for the Overall Output Flows from an Asset
+
+```math
+\begin{aligned}
+\sum_{f \in \mathcal{F}_{out}(a)} v^{flow}_{f,rp,k} \leq p^{profile}_{a,rp,k} \cdot \left(p^{init\_capacity}_{a} + p^{unit\_capacity}_a \cdot v^{investment}_a \right)  \quad \forall a \in \mathcal{A}_{cv} \cup \mathcal{A_{s}} \cup \mathcal{A_{p}}, \forall rp \in \mathcal{RP},\forall k \in \mathcal{K}
+\end{aligned}
+```
+
+#### Contraint for the Overall Input Flows from an Asset
+
+```math
+\begin{aligned}
+\sum_{f \in \mathcal{F}_{in}(a)} v^{flow}_{f,rp,k} \leq p^{profile}_{a,rp,k} \cdot \left(p^{init\_capacity}_{a} + p^{unit\_capacity}_a \cdot v^{investment}_a \right)  \quad \forall a \in \mathcal{A_{s}}, \forall rp \in \mathcal{RP},\forall k \in \mathcal{K}
+\end{aligned}
+```
+
+#### Upper Bound Constraint for Associated with Asset
 
 ```math
 \begin{aligned}
-\sum_{f \in \mathcal{F_{rec}}(a)} v^{flow}_{f,rp,k} - \sum_{f \in \mathcal{F_{snd}}(a)} v^{flow}_{f,rp,k} = p^{profile}_{a,rp,k} \cdot p^{peak\_demand}_{a} \quad \forall a \in \mathcal{A_b}, \forall rp \in \mathcal{RP},\forall k \in \mathcal{K}
+v^{flow}_{f,rp,k} \leq p^{profile}_{a,rp,k} \cdot \left(p^{init\_capacity}_{a} + p^{unit\_capacity}_a \cdot v^{investment}_a \right)  \quad \forall a \notin \mathcal{A}_h, \forall f \in \mathcal{F}_{out}(a), \forall rp \in \mathcal{RP},\forall k \in \mathcal{K}
 \end{aligned}
 ```
 
-### Upper Bound Constraint for Flows
+#### Lower Bound Constraint Flows Associated with Asset
+
+```math
+v^{flow}_{f,rp,k} \geq 0 \quad \forall f \notin \mathcal{F}_t, \forall rp \in \mathcal{RP}, \forall k \in \mathcal{k}
+```
+
+### Constraints that Define Bounds for a Transport Flow $\mathcal{F}_t$
+
+#### Upper Bound Constraint for Transport Flows
 
 ```math
 \begin{aligned}
-v^{flow}_{f,rp,k} \leq p^{profile}_{a,rp,k} \cdot \left(p^{init\_capacity}_{a} + p^{unit\_capacity}_a \cdot v^{investment}_a \right)  \quad \forall a \in \mathcal{Ap}, \forall f \in \mathcal{F_{snd}}(a), \forall rp \in \mathcal{RP},\forall k \in \mathcal{K}
+v^{flow}_{f,rp,k} \leq p^{profile}_{f,rp,k} \cdot \left(p^{init\_capacity}_{f} + p^{export\_capacity}_f \cdot v^{investment}_f \right)  \quad \forall f \in \mathcal{F}_t, \forall rp \in \mathcal{RP},\forall k \in \mathcal{K}
 \end{aligned}
 ```
 
-### Lower Bound Constraint for Flows
+#### Lower Bound Constraint for Transport Flows
+
+```math
+\begin{aligned}
+v^{flow}_{f,rp,k} \geq p^{profile}_{f,rp,k} \cdot \left(p^{init\_capacity}_{f} + p^{import\_capacity}_f \cdot v^{investment}_f \right)  \quad \forall f \in \mathcal{F}_t, \forall rp \in \mathcal{RP},\forall k \in \mathcal{K}
+\end{aligned}
+```
+
+### Extra Constraints for Energy Storage Assets $\mathcal{A}_s$
+
+#### Upper and Lower Bound Constraints for Storage Level
 
 ```math
-v^{flow}_{f,rp,k} \geq 0 \quad \forall f \in \mathcal{F}, \forall rp \in \mathcal{RP}, \forall k \in \mathcal{k}
+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}
 ```

src/input_tables.jl

@@ -1,44 +1,48 @@
 struct AssetData
-    id::Int                     # Asset ID
-    name::String                # Name of Asset (geographical?)
-    type::String                # Producer/Consumer - maybe an enum?
-    active::Bool                # Active or decomissioned
-    investable::Bool            # Whether able to invest
-    variable_cost::Float64      # kEUR/MWh
-    investment_cost::Float64    # kEUR/MW/year
-    capacity::Float64           # MW
-    initial_capacity::Float64   # MW
-    peak_demand::Float64        # MW
+    id::Int                           # Asset ID
+    name::String                      # Name of Asset (geographical?)
+    type::String                      # Producer/Consumer - maybe an enum?
+    active::Bool                      # Active or decomissioned
+    investable::Bool                  # Whether able to invest
+    investment_cost::Float64          # kEUR/MW/year
+    capacity::Float64                 # MW
+    initial_capacity::Float64         # MW
+    peak_demand::Float64              # MW
+    initial_storage_capacity::Float64 # MWh
+    energy_to_power_ratio::Float64    # Hours
 end
 
 struct FlowData
     id::Int                     # Flow ID
     carrier::String             # (Optional?) Energy carrier
-    from_asset_id::Int           # Asset ID
-    to_asset_id::Int             # Asset ID
+    from_asset::String          # Name of Asset
+    to_asset::String            # Name of Asset
     active::Bool                # Active or decomissioned
+    is_transport::Bool          # Whether a transport flow
     investable::Bool            # Whether able to invest
     variable_cost::Float64      # kEUR/MWh
     investment_cost::Float64    # kEUR/MW/year
-    capacity::Float64           # MW
+    export_capacity::Float64    # MW
+    import_capacity::Float64    # MW
     initial_capacity::Float64   # MW
+    efficiency::Float64         # p.u. (per unit)
 end
 
 struct FlowProfiles
     id::Int                     # Flow ID
-    rep_period_id::Int
-    time_step::Int
-    value::Float64              # p.u.
+    rep_period_id::Int          # Representative period ID
+    time_step::Int              # Time step ID
+    value::Float64              # p.u. (per unit)
 end
 
 struct AssetProfiles
     id::Int                     # Asset ID
-    rep_period_id::Int
-    time_step::Int
-    value::Float64              # p.u.
+    rep_period_id::Int          # Representative period ID
+    time_step::Int              # Time step ID
+    value::Float64              # p.u. (per unit)
 end
 
 struct RepPeriodData
-    id::Int
-    weight::Float64
+    id::Int                     # Representative period ID
+    weight::Float64             # Hours
 end