Test Case 18

Test Case 18 is similar to Test Case 13, only that T_NLD is able to exercise market power in DEU. The tables below depict the sets and parameters, respectively. As the trader acts as a Cournot monopolist, the necessary capacity expansion in 2020 reduces to $0.5$. The test is passed, if only NLD_to_DEU and reverse is expanded by $0.5$ in 2020, while no other expansions take place. In addition, prices in DEU must be 0, 1.5 and 0.98 in 2020, 2025 and 2030, respectively, while those in NLD must be equal to zero. 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}$$1$$1$$1$
${1}^{NC}_{T\_NLD,DEU,CNG}$$1$$1$$1$
${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}$$0$$1.5$$0.99$
$\tilde{P}^{T \rightarrow D}_{NLD,CNG,Block 1,OnlyTimeStep,y}$$0.0$$0.0$$0.0$
$\Delta^{A}_{DEU\_to\_DEU,CNG,y}$$0.0$$0.0$$0.0$
$\Delta^{A}_{DEU\_to\_NLD,CNG,y}$$0.5$$0.0$$0.0$
$\Delta^{A}_{NLD\_to\_DEU,CNG,y}$$0.5$$0.0$$0.0$
$\Delta^{A}_{NLD\_to\_NLD,CNG,y}$$0.0$$0.0$$0.0$

Graphical Solution

Marginalized Provision Costs, Revenues and Prices

NLD 2020

test_case_18a_graphic

DEU 2020

test_case_18b_graphic

NLD 2025

test_case_18c_graphic

DEU 2025

test_case_18d_graphic

NLD 2030

test_case_18e_graphic

DEU 2030

test_case_18f_graphic