Add initial storage level and storage inflows

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}
+```

src/input-tables.jl

@@ -9,6 +9,7 @@ struct AssetData
     initial_capacity::Float64         # MW
     peak_demand::Float64              # MW
     initial_storage_capacity::Float64 # MWh
+    initial_storage_level::Float64    # MWh
     energy_to_power_ratio::Float64    # Hours
 end
 

src/io.jl

@@ -85,10 +85,12 @@ function create_parameters_and_sets_from_file(input_folder::AbstractString)
 
     # Parameters for storage
     initial_storage_capacity = Dict{String,Float64}()
+    initial_storage_level    = Dict{String,Float64}()
     energy_to_power_ratio    = Dict{String,Float64}()
     for row in eachrow(assets_data_df)
         if row.name in assets_storage
             initial_storage_capacity[row.name] = row.initial_storage_capacity
+            initial_storage_level[row.name]    = row.initial_storage_level
             energy_to_power_ratio[row.name]    = row.energy_to_power_ratio
         end
     end
@@ -134,6 +136,7 @@ function create_parameters_and_sets_from_file(input_folder::AbstractString)
         flows_is_transport = flows_is_transport,
         peak_demand = peak_demand,
         initial_storage_capacity = initial_storage_capacity,
+        initial_storage_level = initial_storage_level,
         energy_to_power_ratio = energy_to_power_ratio,
         rp_weight = rp_weight,
         rp_resolution = rp_resolution,

src/model.jl

@@ -126,6 +126,21 @@ function create_model(graph, params, sets; verbose = false, write_lp_file = fals
         )
     )
 
+    @expression(
+        model,
+        energy_limit[a ∈ As∩Ai],
+        params.energy_to_power_ratio[a] *
+        params.assets_unit_capacity[a] *
+        assets_investment[a]
+    )
+
+    @expression(
+        model,
+        storage_inflows[a ∈ As, rp ∈ RP, T ∈ P[(a, rp)]],
+        sum(get(params.assets_profile, (a, rp, k), 0.0) for k ∈ T) *
+        (params.initial_storage_capacity[a] + (a ∈ Ai ? energy_limit[a] : 0.0))
+    )
+
     # Balance equations
     # - consumer balance equation
     @constraint(
@@ -136,12 +151,12 @@ function create_model(graph, params, sets; verbose = false, write_lp_file = fals
     )
 
     # - storage balance equation
-    # TODO: Add p^{inflow}
     @constraint(
         model,
         storage_balance[a ∈ As, rp ∈ RP, (k, B) ∈ enumerate(P[(a, rp)])],
         storage_level[a, rp, B] ==
-        (k > 1 ? storage_level[a, rp, P[(a, rp)][k-1]] : 0.0) +
+        (k > 1 ? storage_level[a, rp, P[(a, rp)][k-1]] : params.initial_storage_level[a]) +
+        storage_inflows[a, rp, B] +
         incoming_flow_w_efficiency[(a, rp, B)] - outgoing_flow_w_efficiency[(a, rp, B)]
     )
 
@@ -228,20 +243,21 @@ function create_model(graph, params, sets; verbose = false, write_lp_file = fals
 
     # Extra constraints
     # - upper bound constraints for storage level
-    @expression(
-        model,
-        energy_limit[a ∈ As∩Ai],
-        params.energy_to_power_ratio[a] *
-        params.assets_unit_capacity[a] *
-        assets_investment[a]
-    )
     @constraint(
         model,
         upper_bound_for_storage_level[a ∈ As, rp ∈ RP, B ∈ P[(a, rp)]],
         storage_level[a, rp, B] ≤
         params.initial_storage_capacity[a] + (a ∈ Ai ? energy_limit[a] : 0.0)
     )
 
+    # - cycling condition for storage level
+    for a ∈ As, rp ∈ RP
+        set_lower_bound(
+            storage_level[a, rp, P[(a, rp)][end]],
+            params.initial_storage_level[a],
+        )
+    end
+
     if write_lp_file
         write_to_file(model, "model.lp")
     end

test/inputs/Norse/assets-data.csv

@@ -1,24 +1,24 @@
-,,{producer;consumer;storage;hub;conversion},{true;false},{true;false},kEUR/MWh,kEUR/MW/year,MW,MW,MW,MW/unit,MW/unit,MW,MW,MWh,h,kEUR/MW/year,year,0
-id,name,type,active,investable,variable_cost,investment_cost,capacity,initial_capacity,peak_demand,charging_capacity,discharging_capacity,initial_charging_capacity,initial_discharging_capacity,initial_storage_capacity,energy_to_power_ratio,fixed_cost,lifetime,efficiency
-1,Asgard_Battery,storage,true,true,0.003,300,10,0,0,1,1,0,0,0,100,3,10,0
-2,Asgard_Solar,producer,true,true,0.001,350,100,0,0,0,0,0,0,0,0,8,25,0
-3,Asgard_E_demand,consumer,true,false,0,0,0,0,65787.17792,0,0,0,0,0,0,0,0,0
-4,Asgard_CCGT,conversion,true,true,0.0015,650,500,0,0,0,0,0,0,0,0,10,30,0.6
-5,G_imports,producer,true,false,0.08,0,0,75000,0,0,0,0,0,0,0,0,0,0
-6,Midgard_Wind,producer,true,true,0.002,1300,3,0,0,0,0,0,0,0,0,15,25,0
-7,Midgard_Hydro,storage,true,false,0.0012,1600,0,250,0,3,3,0,0,4000,0,16,50,0
-8,Midgard_Nuclear_SMR,producer,true,true,0.015,6000,150,1000,0,0,0,0,0,0,0,101,60,0
-9,Midgard_E_imports,producer,true,false,0.02,0,0,500,0,0,0,0,0,0,0,0,0,0
-10,Midgard_CCGT,conversion,true,true,0.0015,650,500,0,0,0,0,0,0,0,0,10,30,0.6
-11,Midgard_E_demand,consumer,true,false,0,0,0,0,19604.76443,0,0,0,0,0,0,0,0,0
-12,Valhalla_H2_generator,conversion,true,true,0,479,100,0,0,0,0,0,0,0,0,10,20,0.6
-13,Valhalla_H2_storage,storage,true,true,0,0.1,500,0,0,3,3,0,0,0,10000,0.005,50,0
-14,Valhalla_H2_demand,consumer,true,false,0,0,0,0,745.735,0,0,0,0,0,0,0,0,0
-15,Valhalla_Electrolyser,conversion,true,true,0,1260,100,500,0,0,0,0,0,0,0,60,25,0.704
-16,Valhalla_E_balance,hub,true,false,0,0,0,0,0,0,0,0,0,0,0,0,0,0
-17,Valhalla_E_exports,consumer,true,false,0.09,0,0,0,50,0,0,0,0,0,0,0,0,0
-18,Valhalla_Fuel_cell,conversion,true,true,0,800,100,0,0,0,0,0,0,0,0,40,25,0.5
-19,Valhalla_Heat_pump,conversion,true,true,0,300,100,0,0,0,0,0,0,0,0,15,20,4
-20,Valhalla_Waste_heat,producer,true,false,0.0025,1450,200,0,0,0,0,0,0,0,0,0,30,0
-21,Valhalla_Heat_demand,consumer,true,false,0,0,0,0,3548.42445,0,0,0,0,0,0,0,0,0
-22,Valhalla_GT,conversion,true,true,0.0015,400,500,0,0,0,0,0,0,0,0,3.85,30,0.6
+,,{producer;consumer;storage;hub;conversion},{true;false},{true;false},kEUR/MWh,kEUR/MW/year,MW,MW,MW,MW/unit,MW/unit,MW,MW,MWh,MWh,h,kEUR/MW/year,year,0
+id,name,type,active,investable,variable_cost,investment_cost,capacity,initial_capacity,peak_demand,charging_capacity,discharging_capacity,initial_charging_capacity,initial_discharging_capacity,initial_storage_capacity,initial_storage_level,energy_to_power_ratio,fixed_cost,lifetime,efficiency
+1,Asgard_Battery,storage,true,true,0.003,300,10,0,0,1,1,0,0,0,0,100,3,10,0
+2,Asgard_Solar,producer,true,true,0.001,350,100,0,0,0,0,0,0,0,0,0,8,25,0
+3,Asgard_E_demand,consumer,true,false,0,0,0,0,65787.17792,0,0,0,0,0,0,0,0,0,0
+4,Asgard_CCGT,conversion,true,true,0.0015,650,500,0,0,0,0,0,0,0,0,0,10,30,0.6
+5,G_imports,producer,true,false,0.08,0,0,75000,0,0,0,0,0,0,0,0,0,0,0
+6,Midgard_Wind,producer,true,true,0.002,1300,3,0,0,0,0,0,0,0,0,0,15,25,0
+7,Midgard_Hydro,storage,true,false,0.0012,1600,0,250,0,3,3,0,0,4000,2000,0,16,50,0
+8,Midgard_Nuclear_SMR,producer,true,true,0.015,6000,150,1000,0,0,0,0,0,0,0,0,101,60,0
+9,Midgard_E_imports,producer,true,false,0.02,0,0,500,0,0,0,0,0,0,0,0,0,0,0
+10,Midgard_CCGT,conversion,true,true,0.0015,650,500,0,0,0,0,0,0,0,0,0,10,30,0.6
+11,Midgard_E_demand,consumer,true,false,0,0,0,0,19604.76443,0,0,0,0,0,0,0,0,0,0
+12,Valhalla_H2_generator,conversion,true,true,0,479,100,0,0,0,0,0,0,0,0,0,10,20,0.6
+13,Valhalla_H2_storage,storage,true,true,0,0.1,500,0,0,3,3,0,0,0,0,10000,0.005,50,0
+14,Valhalla_H2_demand,consumer,true,false,0,0,0,0,745.735,0,0,0,0,0,0,0,0,0,0
+15,Valhalla_Electrolyser,conversion,true,true,0,1260,100,500,0,0,0,0,0,0,0,0,60,25,0.704
+16,Valhalla_E_balance,hub,true,false,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
+17,Valhalla_E_exports,consumer,true,false,0.09,0,0,0,50,0,0,0,0,0,0,0,0,0,0
+18,Valhalla_Fuel_cell,conversion,true,true,0,800,100,0,0,0,0,0,0,0,0,0,40,25,0.5
+19,Valhalla_Heat_pump,conversion,true,true,0,300,100,0,0,0,0,0,0,0,0,0,15,20,4
+20,Valhalla_Waste_heat,producer,true,false,0.0025,1450,200,0,0,0,0,0,0,0,0,0,0,30,0
+21,Valhalla_Heat_demand,consumer,true,false,0,0,0,0,3548.42445,0,0,0,0,0,0,0,0,0,0
+22,Valhalla_GT,conversion,true,true,0.0015,400,500,0,0,0,0,0,0,0,0,0,3.85,30,0.6

test/inputs/Norse/assets-profiles.csv

@@ -504,6 +504,174 @@ id,rep_period_id,time_step,value
 6,1,166,0.654
 6,1,167,0.673
 6,1,168,0.681
+7,1,1,0.0001
+7,1,2,0.0001
+7,1,3,0.0001
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 11,1,1,0.688597416
 11,1,2,0.676090883
 11,1,3,0.654860035
@@ -1080,6 +1248,30 @@ id,rep_period_id,time_step,value
 6,2,22,0.7542
 6,2,23,0.7677
 6,2,24,0.7785
+7,2,1,0.00005
+7,2,2,0.00005
+7,2,3,0.00005
+7,2,4,0.00005
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+7,2,21,0.00005
+7,2,22,0.00005
+7,2,23,0.00005
+7,2,24,0.00005
 11,2,1,0.964036382
 11,2,2,0.946527236
 11,2,3,0.916804049