Test Case 17

Test Case 17 is similar to Test Case 13, only that T_NLD is not allowed to sell natural gas from FES in DEU. The tables below depict the sets and parameters, respectively. For the test to pass, capacity expansions of all arcs must be zero, and prices must be equal to inverse demand intercepts, i.e. for DEU 0, 2 and 0.98 in 2020, 2025 and 2030, respectively, and 0 in NLD in all years. 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}$$0$$0$$0$
$\Lambda^{T}_{T\_NLD,NLD,CNG,FES,y}$$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}$$0$$2$$0.99$
$\tilde{P}^{T \rightarrow D}_{NLD,CNG,Block 1,OnlyTimeStep,y}$$0.0$$0.0$$0.0$
$\Delta^{A}_{DEU\_to\_DEU,CNG,y}$$0.0$$0.0$$0.0$
$\Delta^{A}_{DEU\_to\_NLD,CNG,y}$$0.0$$0.0$$0.0$
$\Delta^{A}_{NLD\_to\_DEU,CNG,y}$$0.0$$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_17a_graphic

DEU 2020

test_case_17b_graphic

NLD 2025

test_case_17c_graphic

DEU 2025

test_case_17d_graphic

NLD 2030

test_case_17e_graphic

DEU 2030

test_case_17f_graphic