Test Case 21

Test Case 21 asserts that repurposing of arc capacities works as intended, including repurposing factors. The tables below describe an extended version of Test Case 9 with two commodities and years instead of one. In addition, an overview of test criteria and a graphical solution is displayed.

Sets

Set NameSet Value
$\mathcal{A}$$\{DEU\_to\_DEU,DEU\_to\_NLD,NLD\_to\_DEU,NLD\_to\_NLD\}$
$\mathcal{AC}$$\begin{aligned} \{ (DEU\_to\_DEU, CNG), (DEU\_to\_NLD, CNG), \\ (NLD\_to\_DEU, CNG), (NLD\_to\_NLD, CNG), \\ (DEU\_to\_DEU, GH2), (DEU\_to\_NLD, GH2), \\ (NLD\_to\_DEU, GH2), (NLD\_to\_NLD, GH2)\}\end{aligned}$
$\mathcal{C}$$\{CNG,GH2\}$
$\mathcal{DSB}$$\{Block 1\}$
$\mathcal{I}$$\{Natural Gas\}$
$\mathcal{IOB}$$\{Block 1\}$
$\mathcal{M}$$\{OnlyTimeStep\}$
$\mathcal{N}$$\{DEU,NLD\}$
$\mathcal{O}$$\{FES\}$
$\mathcal{P}$$\{P\_DEU,P\_NLD\}$
$\mathcal{RA}$
$\mathcal{RS}$
$\mathcal{RV}$
$\mathcal{S}$
$\mathcal{T}$$\{T\_DEU,T\_NLD\}$
$\mathcal{V}$
$\mathcal{VT}$
$\mathcal{Y}$$\{2020,2021\}$

Parameters

Parametery=2020y=2021
$\frac{1}{ | \Delta |_{y}}$$1$$1$
${1}^{NC}_{T\_DEU,DEU,CNG}$$0$$0$
${1}^{NC}_{T\_DEU,NLD,CNG}$$0$$0$
${1}^{NC}_{T\_NLD,DEU,CNG}$$0$$0$
${1}^{NC}_{T\_NLD,NLD,CNG}$$0$$0$
${1}^{NC}_{T\_DEU,DEU,GH2}$$0$$0$
${1}^{NC}_{T\_DEU,NLD,GH2}$$0$$0$
${1}^{NC}_{T\_NLD,DEU,GH2}$$0$$0$
${1}^{NC}_{T\_NLD,NLD,GH2}$$0$$0$
$r_{y}$$1$$1$
$d_{OnlyTimeStep}$$1$$1$
$c^{P}_{P\_DEU,CNG,FES,y}$$0.5$$0.5$
$c^{\Delta P}_{P\_DEU,CNG,FES,y}$$1$$1$
$c^{P}_{P\_NLD,CNG,FES,y}$$0.5$$0.5$
$c^{\Delta P}_{P\_NLD,CNG,FES,y}$$1$$1$
$fi^{P}_{CNG,Natural Gas,FES}$$1$$1$
$L^{P}_{CNG,FES}$$50$$50$
$\Lambda^{P}_{P\_DEU,CNG,FES,y}$$10$$10$
$c^{P}_{P\_DEU,GH2,FES,y}$$0.4$$0.4$
$c^{\Delta P}_{P\_DEU,GH2,FES,y}$$1$$1$
$c^{P}_{P\_NLD,GH2,FES,y}$$0.5$$0.5$
$c^{\Delta P}_{P\_NLD,GH2,FES,y}$$1$$1$
$fi^{P}_{GH2,Natural Gas,FES}$$1$$1$
$L^{P}_{GH2,FES}$$50$$50$
$\Lambda^{P}_{P\_DEU,GH2,FES,y}$$10$$10$
$\Lambda^{I}_{P\_DEU,Natural Gas,Block 1,y}$$10$$10$
$\Omega^{I}_{P\_DEU,Natural Gas,Block 1,y}$$0$$0$
$c^{\Delta^{I}}_{P\_DEU,Natural Gas,Block 1,y}$$0$$0$
$\Lambda^{T}_{T\_DEU,DEU,CNG,FES,y}$$10$$10$
$\Lambda^{T}_{T\_DEU,NLD,CNG,FES,y}$$10$$10$
$\Lambda^{T}_{T\_DEU,DEU,GH2,FES,y}$$10$$10$
$\Lambda^{T}_{T\_DEU,NLD,GH2,FES,y}$$10$$10$
$\Omega^{P}_{P\_DEU,CNG,FES,y}$$10$$10$
$\Omega^{P}_{P\_DEU,GH2,FES,y}$$10$$10$
$\Lambda^{P}_{P\_NLD,CNG,FES,y}$$10$$10$
$\Lambda^{P}_{P\_NLD,GH2,FES,y}$$10$$10$
$\Lambda^{I}_{P\_NLD,Natural Gas,Block 1,y}$$10$$10$
$\Omega^{I}_{P\_NLD,Natural Gas,Block 1,y}$$0$$0$
$c^{\Delta^{I}}_{P\_NLD,Natural Gas,Block 1,y}$$0$$0$
$\Lambda^{T}_{T\_NLD,DEU,CNG,FES,y}$$10$$10$
$\Lambda^{T}_{T\_NLD,DEU,GH2,FES,y}$$10$$10$
$\Lambda^{T}_{T\_NLD,NLD,CNG,FES,y}$$10$$10$
$\Lambda^{T}_{T\_NLD,NLD,GH2,FES,y}$$10$$10$
$\Omega^{P}_{P\_NLD,CNG,FES,y}$$10$$10$
$\Omega^{P}_{P\_NLD,GH2,FES,y}$$10$$10$
$l^{A}_{DEU\_to\_DEU,CNG}$$0.0$$0.0$
$l^{A}_{DEU\_to\_NLD,CNG}$$0.0$$0.0$
$l^{A}_{NLD\_to\_DEU,CNG}$$0.1$$0.1$
$l^{A}_{NLD\_to\_NLD,CNG}$$0.0$$0.0$
$l^{A}_{DEU\_to\_DEU,GH2}$$0.0$$0.0$
$l^{A}_{DEU\_to\_NLD,GH2}$$0.0$$0.0$
$l^{A}_{NLD\_to\_DEU,GH2}$$0.1$$0.1$
$l^{A}_{NLD\_to\_NLD,GH2}$$0.0$$0.0$
$c^{A}_{DEU\_to\_DEU,CNG,y}$$0.0$$0.0$
$c^{A}_{DEU\_to\_NLD,CNG,y}$$0.0$$0.0$
$c^{A}_{NLD\_to\_DEU,CNG,y}$$0.1$$0.1$
$c^{A}_{NLD\_to\_NLD,CNG,y}$$0.0$$0.0$
$c^{A}_{DEU\_to\_DEU,GH2,y}$$0.0$$0.0$
$c^{A}_{DEU\_to\_NLD,GH2,y}$$0.0$$0.0$
$c^{A}_{NLD\_to\_DEU,GH2,y}$$0.1$$0.1$
$c^{A}_{NLD\_to\_NLD,GH2,y}$$0.0$$0.0$
$c^{\Delta A}_{DEU\_to\_DEU,CNG,y}$$0$$0$
$c^{\Delta A}_{DEU\_to\_NLD,CNG,y}$$10$$10$
$c^{\Delta A}_{NLD\_to\_DEU,CNG,y}$$10$$10$
$c^{\Delta A}_{NLD\_to\_NLD,CNG,y}$$0$$0$
$c^{\Delta A}_{DEU\_to\_DEU,GH2,y}$$0$$0$
$c^{\Delta A}_{DEU\_to\_NLD,GH2,y}$$10$$10$
$c^{\Delta A}_{NLD\_to\_DEU,GH2,y}$$10$$10$
$c^{\Delta A}_{NLD\_to\_NLD,GH2,y}$$0$$0$
$c^{\Delta^{RA}}_{DEU\_to\_DEU,CNG,GH2,y}$$0$$0$
$c^{\Delta^{RA}}_{DEU\_to\_NLD,CNG,GH2,y}$$0$$0$
$c^{\Delta^{RA}}_{NLD\_to\_DEU,CNG,GH2,y}$$0.055$$0.055$
$c^{\Delta^{RA}}_{NLD\_to\_NLD,CNG,GH2,y}$$0$$0$
$f^{RA}_{CNG,GH2}$$0.5$$0.5$
$\Lambda^{A}_{DEU\_to\_DEU,CNG,y}$$0$$0$
$\Lambda^{A}_{DEU\_to\_NLD,CNG,y}$$10$$10$
$\Lambda^{A}_{NLD\_to\_DEU,CNG,y}$$10$$10$
$\Lambda^{A}_{NLD\_to\_NLD,CNG,y}$$0$$0$
$\Lambda^{A}_{DEU\_to\_DEU,GH2,y}$$0$$0$
$\Lambda^{A}_{DEU\_to\_NLD,GH2,y}$$0$$0$
$\Lambda^{A}_{NLD\_to\_DEU,GH2,y}$$0$$0$
$\Lambda^{A}_{NLD\_to\_NLD,GH2,y}$$0$$0$
$L^{A}_{CNG}$$50$$50$
$L^{A}_{GH2}$$50$$50$
$c^{I_{l}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$$2$$2$
$c^{I_{q}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$$0$$0$
$av^{I}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep}$$1$$1$
$c^{I_{l}}_{P\_NLD,Natural Gas,Block 1,OnlyTimeStep,y}$$0.5$$0.5$
$c^{I_{q}}_{P\_NLD,Natural Gas,Block 1,OnlyTimeStep,y}$$0$$0$
$av^{I}_{P\_NLD,Natural Gas,Block 1,OnlyTimeStep}$$1$$1$
$\alpha^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$2$$0$
$\beta^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$-1$$0$
$\alpha^{D}_{NLD,CNG,Block 1,OnlyTimeStep,y}$$0$$0$
$\beta^{D}_{NLD,CNG,Block 1,OnlyTimeStep,y}$$-1$$0$
$\alpha^{D}_{DEU,GH2,Block 1,OnlyTimeStep,y}$$0$$2$
$\beta^{D}_{DEU,GH2,Block 1,OnlyTimeStep,y}$$0$$-1$
$\alpha^{D}_{NLD,GH2,Block 1,OnlyTimeStep,y}$$0$$0$
$\beta^{D}_{NLD,GH2,Block 1,OnlyTimeStep,y}$$0$$-1$

Test Criteria

ExpressionResult y=2020Result y=2021
$\tilde{P}^{T \rightarrow D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$1.2$$0$
$\tilde{P}^{T \rightarrow D}_{NLD,CNG,Block 1,OnlyTimeStep,y}$$0.0$$0.0$
$\tilde{P}^{T \rightarrow D}_{DEU,GH2,Block 1,OnlyTimeStep,y}$$0$$1.2$
$\tilde{P}^{T \rightarrow D}_{NLD,GH2,Block 1,OnlyTimeStep,y}$$0.0$$0.0$
$q^{I}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$$0.0$$0.0$
$q^{I}_{P\_NLD,Natural Gas,Block 1,OnlyTimeStep,y}$$0.88$$0.88$

Graphical Solution

Marginalized Provision Costs and Prices for Different Nodes

Node NLD in 2020 for CNG

test_case_21a_graphic

Node DEU in 2020 for CNG

test_case_21b_graphic

Node NLD in 2021 for CNG

test_case_21c_graphic

Node DEU in 2021 for CNG

test_case_21d_graphic

Node NLD in 2020 for GH2

test_case_21e_graphic

Node DEU in 2020 for GH2

test_case_21f_graphic

Node NLD in 2021 for GH2

test_case_21g_graphic

Node DEU in 2021 for GH2

test_case_21h_graphic