Test Case 12

Test Case 12 is structurally similar to Test Case 11, but this time conversion capacities are non-existent instead of production capacities. The tables below depict the sets and parameters, respectively. The solution is the same as in Test Case 11, only that conversion capacity should be expanded instead of production capacity (at the same cost). Passing criteria can be seen below, while the figure depicts the graphical solution.

Sets

Set NameSet Value
$\mathcal{A}$$\{DEU\_to\_DEU\}$
$\mathcal{AC}$$\{(DEU\_to\_DEU, CNG), (DEU\_to\_DEU, GH2)\}$
$\mathcal{C}$$\{CNG,GH2\}$
$\mathcal{DSB}$$\{Block 1\}$
$\mathcal{I}$$\{Natural Gas\}$
$\mathcal{IOB}$$\{Block 1\}$
$\mathcal{M}$$\{OnlyTimeStep\}$
$\mathcal{N}$$\{DEU\}$
$\mathcal{O}$$\{FES\}$
$\mathcal{P}$$\{P\_DEU\}$
$\mathcal{RA}$
$\mathcal{RS}$
$\mathcal{RV}$
$\mathcal{S}$
$\mathcal{T}$$\{T\_DEU\}$
$\mathcal{V}$$\{V\_DEU\}$
$\mathcal{VT}$$\{(CNG,GH2)\}$
$\mathcal{Y}$$\{2020,2025,2030\}$

Parameters

Parametery=2020y=2025y=2030
$\frac{1}{ | \Delta |_{y}}$$0.2$$0.2$$0.2$
${1}^{NC}_{T\_DEU,DEU,CNG}$$0$$0$$0$
$r_{y}$$1$$1$$1$
$d_{OnlyTimeStep}$$1$$1$$1$
$c^{P}_{P\_DEU,CNG,FES,y}$$0.3$$0.3$$0.3$
$c^{\Delta P}_{P\_DEU,CNG,FES,y}$$0.5$$0.5$$0.5$
$fi^{P}_{CNG,Natural Gas,FES}$$1$$1$$1$
$L^{P}_{CNG,FES}$$50$$50$$50$
$\Lambda^{P}_{P\_DEU,CNG,FES,y}$$10$$10$$10$
$c^{P}_{P\_DEU,GH2,FES,y}$$1.3$$1.3$$1.3$
$c^{\Delta P}_{P\_DEU,GH2,FES,y}$$0.5$$0.5$$0.5$
$fi^{P}_{GH2,Natural Gas,FES}$$1$$1$$1$
$L^{P}_{GH2,FES}$$50$$50$$50$
$\Lambda^{P}_{P\_DEU,GH2,FES,y}$$10$$10$$10$
$\Lambda^{I}_{P\_DEU,Natural Gas,Block 1,y}$$10$$10$$10$
$\Omega^{I}_{P\_DEU,Natural Gas,Block 1,y}$$0$$0$$0$
$c^{\Delta^{I}}_{P\_DEU,Natural Gas,Block 1,y}$$0$$0$$0$
$\Lambda^{T}_{T\_DEU,DEU,CNG,FES,y}$$10$$10$$10$
$\Lambda^{T}_{T\_DEU,DEU,GH2,FES,y}$$10$$10$$10$
$\Omega^{P}_{P\_DEU,CNG,FES,y}$$10$$10$$10$
$\Omega^{P}_{P\_DEU,GH2,FES,y}$$10$$10$$10$
$fi^{V}_{CNG,GH2}$$1$$1$$1$
$l^{A}_{DEU\_to\_DEU,CNG}$$0$$0$$0$
$l^{A}_{DEU\_to\_DEU,GH2}$$0$$0$$0$
$c^{V}_{V\_DEU,CNG,GH2,y}$$0.3$$0.3$$0.3$
$c^{\Delta V}_{V\_DEU,CNG,GH2,y}$$0.5$$0.5$$0.5$
$\Lambda^{V}_{V\_DEU,CNG,GH2,y}$$0$$0$$0$
$L^{V}_{CNG,GH2}$$5$$5$$5$
$c^{A}_{DEU\_to\_DEU,CNG,y}$$0$$0$$0$
$c^{\Delta A}_{DEU\_to\_DEU,CNG,y}$$0$$0$$0$
$\Lambda^{A}_{DEU\_to\_DEU,CNG,y}$$0$$0$$0$
$L^{A}_{CNG}$$50$$50$$50$
$c^{A}_{DEU\_to\_DEU,GH2,y}$$0$$0$$0$
$c^{\Delta A}_{DEU\_to\_DEU,GH2,y}$$0$$0$$0$
$\Lambda^{A}_{DEU\_to\_DEU,GH2,y}$$0$$0$$0$
$L^{A}_{GH2}$$50$$50$$50$
$c^{I_{l}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$$0.3$$0.3$$0.3$
$c^{I_{q}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$$0$$0$$0$
$av^{I}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep}$$1$$1$$1$
$\alpha^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$0$$0$$0$
$\beta^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$-1$$-1$$-1$
$\alpha^{D}_{DEU,GH2,Block 1,OnlyTimeStep,y}$$0$$2$$0.99$
$\beta^{D}_{DEU,GH2,Block 1,OnlyTimeStep,y}$$-1$$-1$$-1$

Test Criteria

ExpressionResult y=2020Result y=2025Result y=2030
$\tilde{P}^{T \rightarrow D}_{DEU,GH2,Block 1,OnlyTimeStep,y}$$0$$1$$0.99$
$\Delta^{V}_{V\_DEU,CNG,GH2,y}$$1$$0$$0$
$\tilde{P}^{T \rightarrow D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$0$$0$$0$

Graphical Solution

Marginalized Provision Costs and Prices

CNG 2020

test_case_12a_graphic

GH2 2020

test_case_12b_graphic

CNG 2025

test_case_12c_graphic

GH2 2025

test_case_12d_graphic

CNG 2030

test_case_12e_graphic

GH2 2030

test_case_12f_graphic