Updating mathematical formulations for GENESYS-2

doc/source/frameworks/genesys2.rst

@@ -10,11 +10,11 @@ Objective function
 
 	\pi^{\text{objective}} = C_{\text{real}}(\pi^{inv,capa,g},\pi^{omf,capa,g},\pi^{omv,gen,g}) + C_{\text{penalty}}(\varepsilon^{\text{deviation}})
 
-	\pi^{\text{objective}} = \sum_{T_{interval}}^{} \sum_{regions}^{} \sum_{components}^{} \pi^{inv,capa,g} + \pi^{omf,capa,g} + \pi^{omv,gen,g} + \sum_{years}^{} \sum_{regions}^{} \pi^{penalty,unsupplied\_load} \varepsilon^{\text{unsupplied}} + \pi^{penalty,selsupplied\_quota} \varepsilon^{\text{selfsupply}}
+	\pi^{\text{objective}} = \sum_{T_{interval}}^{} \sum_{regions}^{} \sum_{components}^{} \pi^{inv,capa,g} + \pi^{omf,capa,g} + \pi^{omv,gen,g} + \sum_{years}^{} \sum_{regions}^{} \pi^{penalty,unsupplied\_load} (\varepsilon^{\text{unsupplied}})^2 + \pi^{penalty,selsupplied\_quota} \varepsilon^{\text{selfsupply}}
 
-	\pi^{\text{objective}} = \sum_{T_{interval}}^{} \sum_{regions}^{} \sum_{components}^{} ANF*[\pi^{inv,capa,g} + \pi^{inv,capa,g} \gamma^{inv,capa,g}] + \pi^{omv,gen,g} + \sum_{T_{interval}}^{} \sum_{regions}^{} \pi^{penalty,unsupplied\_load} \varepsilon^{\text{unsupplied}} + \pi^{penalty,selsupplied\_quota} \varepsilon^{\text{selfsupply}}
+	\pi^{\text{objective}} = \sum_{T_{interval}}^{} \sum_{regions}^{} \sum_{components}^{} ANF*[\pi^{inv,capa,g} + \pi^{inv,capa,g} \gamma^{inv,capa,g}] + \pi^{omv,gen,g} + \sum_{T_{interval}}^{} \sum_{regions}^{} \pi^{penalty,unsupplied\_load} (\varepsilon^{\text{unsupplied}})^2 + \pi^{penalty,selsupplied\_quota} \varepsilon^{\text{selfsupply}}
 	
-	\pi^{\text{objective}} = \sum_{T_{interval}}^{} \sum_{regions}^{} \sum_{components}^{} \frac{(1+i)^{n}i}{(1+i)^{n}-1}*[\pi^{inv,capa,g} + \pi^{inv,capa,g} \gamma^{inv,capa,g}] + [\pi^{fuel,f}+\pi^{emi,e}] \varepsilon^{gen,t} + \sum_{T_{interval}}^{} \sum_{regions}^{} \pi^{penalty,unsupplied\_load} \varepsilon^{\text{unsupplied}} + \pi^{penalty,selsupplied\_quota} \varepsilon^{\text{selfsupply}}
+	\pi^{\text{objective}} = \sum_{T_{interval}}^{} \sum_{regions}^{} \sum_{components}^{} \frac{(1+i)^{n}i}{(1+i)^{n}-1}*[\pi^{inv,capa,g} + \pi^{inv,capa,g} \gamma^{inv,capa,g}] + [\pi^{fuel,f}+\pi^{emi,e}] \varepsilon^{gen,t} + \sum_{T_{interval}}^{} \sum_{regions}^{} \pi^{penalty,unsupplied\_load} (\varepsilon^{\text{unsupplied}})^2 + \pi^{penalty,selsupplied\_quota} \varepsilon^{\text{selfsupply}}
 
 Constraints
 ***********

doc/source/frameworks/technologies.rst

@@ -45,6 +45,16 @@ Uses generic process equations. Only difference is that additionally the input d
     &\forall t \in T_m, ~y \in Y, ~r \in R, ~g \in G, ~c \in C^{\text{supIm}}
 
 
+GENESYS-2
+''''''''''
+Capacity factor (CF) ist used to calculate generation of VRE-units. \Delta t always equals one hour.
+
+.. math::
+
+	{v^{gen}_{y,r,g,t}}  = v^{capa}_{y,r,g} \cdot CF^{in,gen}_{y,r,g,t} \cdot \Delta t \quad \forall y \in Y, r\in R, g\in G, t\in T
+    
+
+
 
 Electricity-only units
 **********************
@@ -74,6 +84,15 @@ Urbs
 Uses generic process equations.
 
 
+GENESYS-2
+''''''''''
+Generation is calculated by using overall plant efficiencies, that are time-independent. \Delta t always equals one hour.
+
+.. math::
+
+	{v^{gen}_{y,r,g,t}}  = v^{fuse}_{y,r,g,t} \cdot \gamma^{total,gen}_{g} \cdot \Delta t \quad \forall y \in Y, r\in R, g\in G, t\in T
+
+
 Heat-only units
 ***************
 
@@ -97,6 +116,11 @@ Urbs
 Uses generic process equations.
 
 
+GENESYS-2
+''''''''''
+Currently not modelled with this framework.
+
+
 CHP units: backpressure
 ***********************
 
@@ -132,6 +156,11 @@ Urbs
 Not modeled in urbs.
 
 
+GENESYS-2
+''''''''''
+Currently not modelled with this framework.
+
+
 CHP units: extraction
 *********************
 
@@ -171,6 +200,11 @@ Urbs
 Not modeled in urbs.
 
 
+GENESYS-2
+''''''''''
+Currently not modelled with this framework.
+
+
 Storages
 ********
 
@@ -227,6 +261,36 @@ oemof.tabular
   & t_0, t_{\infty} \in T
   \\
   & \forall y \in Y, r\in R, g\in G, t\in T\setminus\{t_0\}
+  
+  
+
+GENESYS-2
+''''''''''
+Generally, storages in GENESYS-2 always require a storage unit connected to a charger/discharger unit. Charger and discharger can either be one unit called 'Bicharger' or can be modelled seperately with diffrent efficiencies.
+
+initial storage level
+----------------------
+.. math::
+	{v^{sto,vol}_{y,r,g,t=0}}  = 0 \quad \forall y \in Y, r\in R, g\in G, t\in T \\
+	
+charge/discharge processes
+--------------------------
+.. math::
+	{v^{gen,load}_{y,r,g,t}}  = v^{sto,charge}_{y,r,g,t} \cdot \gamma^{in,gen}_{y,r,g,t} \cdot \Delta t \quad \forall y \in Y, r\in R, g\in G, t\in T \\
+	{v^{gen,unload}_{y,r,g,t}}  = v^{sto,discharge}_{y,r,g,t} \cdot \gamma^{out,gen}_{y,r,g,t} \cdot \Delta t \quad \forall y \in Y, r\in R, g\in G, t\in T \\
+	Condition: v^{gen,load}_{y,r,g,t} >= 0 + v^{gen,unload}_{y,r,g,t} > 0 = 1
+
+storage level
+--------------------------
+.. math::
+	{v^{sto,vol}_{y,r,g,t}}  = v^{sto,vol}_{y,r,g,t-1} + v^{gen,load}_{y,r,g,t} \cdot \gamma^{total,gen,sto}_{y,r,g,t} - v^{gen,unload}_{y,r,g,t} \quad \forall y \in Y, r\in R, g\in G, t\in T \\
+
+total losses
+--------------------------
+.. math::
+	{\gamma^{loss,con}_{y,r,g,t}}  = v^{sto,charge}_{y,r,g,t} \cdot (1 - \gamma^{in,gen}_{y,r,g,t}) + v^{sto,discharge}_{y,r,g,t} \cdot (1 - \gamma^{out,gen}_{y,r,g,t}) + v^{gen,load}_{y,r,g,t} \cdot (1 - \gamma^{total,gen,sto}_{y,r,g,t})  \quad \forall y \in Y, r\in R, g\in G, t\in T \\
+ 
+ 
 
 Generation
 **********
@@ -324,6 +388,15 @@ urbs
 
    & v^{\text{trans,out}}_{t,y,r_{in},r_{out},x,c}= v^{\text{trans,in}}_{t,y,r_{in},r_{out},x,c}\cdot \gamma^{\text{trans}}_{y,r_{in},r_{out},x,c}\\
     &\forall t\in T_m,~y\in Y,~r_{in}\in R,~r_{out}\in R,~x\in X,~c\in C
+	
+
+GENESYS-2
+''''
+
+.. math::
+
+   & v^{\text{trans,out}}_{t,y,r_{in},r_{out},x,c}= v^{\text{trans,in}}_{t,y,r_{in},r_{out},x,c}\cdot \gamma^{\text{trans}}_{y,r_{in},r_{out},x,c}\\
+    &\forall t\in T_m,~y\in Y,~r_{in}\in R,~r_{out}\in R,~x\in X,~c\in C
 
 
 Generic processes