Test Case 15

Test Case 15 is similar to Test Case 11, except that production capacity expansion is disallowed. The tables below depict the sets and parameters, respectively. Since no production is possible now, prices must be equal to inverse demand intercepts. The test is passed, if prices in 2020, 2025 and 2030 are 0, 2 and 0.99, respectively and no capacities are invested in. Passing criteria can be seen in below, while the figure depicts a 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}$$0$$0$$0$
$c^{P}_{P\_DEU,GH2,FES,y}$$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$$50$
$\Lambda^{P}_{P\_DEU,GH2,FES,y}$$0$$0$$0$
$\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$$10$
$\Omega^{P}_{P\_DEU,CNG,FES,y}$$0$$0$$0$
$\Omega^{P}_{P\_DEU,GH2,FES,y}$$0$$0$$0$
$fi^{V}_{CNG,GH2}$$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$$0.3$
$c^{\Delta V}_{V\_DEU,CNG,GH2,y}$$10$$10$$10$
$\Lambda^{V}_{V\_DEU,CNG,GH2,y}$$10$$10$$10$
$L^{V}_{CNG,GH2}$$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,CNG,Block 1,OnlyTimeStep,y}$$0$$0$$0$
$\tilde{P}^{T \rightarrow D}_{DEU,GH2,Block 1,OnlyTimeStep,y}$$0$$2$$0.99$
$\Delta^{P}_{P\_DEU,CNG,FES,y}$$0$$0$$0$
$\Delta^{P}_{P\_DEU,CNG,FES,y}$$0$$0$$0$

Graphical Solution

Marginalized Provision Costs and Prices for Different Time Steps

CNG 2020

test_case_15a_graphic

GH2 2020

test_case_15b_graphic

CNG 2025

test_case_15c_graphic

GH2 2025

test_case_15d_graphic

CNG 2030

test_case_15e_graphic

GH2 2030

test_case_15f_graphic