Test Case 13

Test Case 13 is similar to Test Case 9, only that this time transport capacity is limited. The tables below depict the sets and parameters, respectively. Production costs in DEU are much too high. However, NLD has no own demand and can export to DEU with operational cost of $0.05$ if capacity is invested. In addition to production and conversion costs of in total $0.9$, rescaled investment costs of 0.05 must be added. Marginalized provision costs are hence $1.0$. Tests are passed, if DEU prices are $P=0$, $P=1$, $P=0.99$, in 2020, 2025 and 2030 respectively. In addition, capacity of 1 on arc NLD_to_DEU and reverse should be invested in 2020, while no investments should be made in 2025 and 2030. No other arc capacities should be expanded, and prices in NLD must be $0$. Passing criteria can be seen below, while the figure depicts a graphical solution.

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)\}\end{aligned}$
$\mathcal{C}$$\{CNG\}$
$\mathcal{DSB}$$\{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}$$\{T\_DEU,T\_NLD\}$
$\mathcal{V}$
$\mathcal{VT}$
$\mathcal{Y}$$\{2020,2025,2030\}$

Parameters

Parametery=2020y=2025y=2030
$\frac{1}{ | \Delta |_{y}}$$1$$1$$1$
${1}^{NC}_{T\_DEU,DEU,CNG}$$0$$0$$0$
${1}^{NC}_{T\_DEU,NLD,CNG}$$0$$0$$0$
${1}^{NC}_{T\_NLD,DEU,CNG}$$0$$0$$0$
${1}^{NC}_{T\_NLD,NLD,CNG}$$0$$0$$0$
$r_{y}$$1$$1$$1$
$d_{OnlyTimeStep}$$1$$1$$1$
$c^{P}_{P\_DEU,CNG,FES,y}$$0.4$$0.4$$0.4$
$c^{\Delta P}_{P\_DEU,CNG,FES,y}$$1$$1$$1$
$c^{P}_{P\_NLD,CNG,FES,y}$$0.5$$0.5$$0.5$
$c^{\Delta P}_{P\_NLD,CNG,FES,y}$$1$$1$$1$
$fi^{P}_{CNG,Natural Gas,FES}$$1$$1$$1$
$L^{P}_{CNG,FES}$$50$$50$$50$
$\Lambda^{P}_{P\_DEU,CNG,FES,y}$$10$$10$$10$
$\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,NLD,CNG,FES,y}$$10$$10$$10$
$\Omega^{P}_{P\_DEU,CNG,FES,y}$$10$$10$$10$
$\Lambda^{P}_{P\_NLD,CNG,FES,y}$$10$$10$$10$
$\Lambda^{I}_{P\_NLD,Natural Gas,Block 1,y}$$10$$10$$10$
$\Omega^{I}_{P\_NLD,Natural Gas,Block 1,y}$$0$$0$$0$
$c^{\Delta^{I}}_{P\_NLD,Natural Gas,Block 1,y}$$0$$0$$0$
$\Lambda^{T}_{T\_NLD,DEU,CNG,FES,y}$$10$$10$$10$
$\Lambda^{T}_{T\_NLD,NLD,CNG,FES,y}$$10$$10$$10$
$\Omega^{P}_{P\_NLD,CNG,FES,y}$$10$$10$$10$
$l^{A}_{DEU\_to\_DEU,CNG}$$0.0$$0.0$$0.0$
$l^{A}_{DEU\_to\_NLD,CNG}$$0.0$$0.0$$0.0$
$l^{A}_{NLD\_to\_DEU,CNG}$$0.1$$0.1$$0.1$
$l^{A}_{NLD\_to\_NLD,CNG}$$0.0$$0.0$$0.0$
$c^{A}_{DEU\_to\_DEU,CNG,y}$$0.0$$0.0$$0.0$
$c^{A}_{DEU\_to\_NLD,CNG,y}$$0.0$$0.0$$0.0$
$c^{A}_{NLD\_to\_DEU,CNG,y}$$0.05$$0.05$$0.05$
$c^{A}_{NLD\_to\_NLD,CNG,y}$$0.0$$0.0$$0.0$
$c^{\Delta A}_{DEU\_to\_DEU,CNG,y}$$0.25$$0.25$$0.25$
$c^{\Delta A}_{DEU\_to\_NLD,CNG,y}$$0.25$$0.25$$0.25$
$c^{\Delta A}_{NLD\_to\_DEU,CNG,y}$$0.25$$0.25$$0.25$
$c^{\Delta A}_{NLD\_to\_NLD,CNG,y}$$0.25$$0.25$$0.25$
$\Lambda^{A}_{DEU\_to\_DEU,CNG,y}$$0$$0$$0$
$\Lambda^{A}_{DEU\_to\_NLD,CNG,y}$$0$$0$$0$
$\Lambda^{A}_{NLD\_to\_DEU,CNG,y}$$0$$0$$0$
$\Lambda^{A}_{NLD\_to\_NLD,CNG,y}$$0$$0$$0$
$L^{A}_{CNG}$$50$$50$$50$
$c^{I_{l}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$$2$$2$$2$
$c^{I_{q}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$$0$$0$$0$
$av^{I}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep}$$1$$1$$1$
$c^{I_{l}}_{P\_NLD,Natural Gas,Block 1,OnlyTimeStep,y}$$0.5$$0.5$$0.5$
$c^{I_{q}}_{P\_NLD,Natural Gas,Block 1,OnlyTimeStep,y}$$0$$0$$0$
$av^{I}_{P\_NLD,Natural Gas,Block 1,OnlyTimeStep}$$1$$1$$1$
$\alpha^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$2$$2$$2$
$\beta^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$-1$$-1$$-1$
$\alpha^{D}_{NLD,CNG,Block 1,OnlyTimeStep,y}$$0$$0$$0$
$\beta^{D}_{NLD,CNG,Block 1,OnlyTimeStep,y}$$-1$$-1$$-1$

Test Criteria

ExpressionResult y=2020Result y=2025Result y=2030
$\tilde{P}^{T \rightarrow D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$0$$1$$0.99$
$\tilde{P}^{T \rightarrow D}_{NLD,CNG,Block 1,OnlyTimeStep,y}$$0.0$$0.0$$0.0$
$\Delta^{A}_{DEU\_to\_DEU,CNG,y}$$0.0$$0.0$$0.0$
$\Delta^{A}_{DEU\_to\_NLD,CNG,y}$$1.0$$0.0$$0.0$
$\Delta^{A}_{NLD\_to\_DEU,CNG,y}$$1.0$$0.0$$0.0$
$\Delta^{A}_{NLD\_to\_NLD,CNG,y}$$0.0$$0.0$$0.0$

Graphical Solution

Marginalized Provision Costs and Prices

NLD 2020

test_case_13a_graphic

DEU 2020

test_case_13b_graphic

NLD 2025

test_case_13c_graphic

DEU 2025

test_case_13d_graphic

NLD 2030

test_case_13e_graphic

DEU 2030

test_case_13f_graphic