Test Case 2

Test Case 2 adds multiple years and tests for prices in both, while also including conversion costs. As before, relevant sets and parameters can be seen from the tables below. Marginalized costs for given factor intensities are $MC=c^{Pl} + c^{P} + c^{V} + \beta^{P} \cdot Q$, while prices are $P(Q) = \alpha^{D} + \beta^{D} Q$. Hence, as stated and illustrated below, tests pass if prices in both years are $P=1.25$ for CNG and $P=0.0$ for GH2.

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}$$\{Electricity\}$
$\mathcal{IOB}$$\{Block 1\}$
$\mathcal{M}$$\{OnlyTimeStep\}$
$\mathcal{N}$$\{DEU\}$
$\mathcal{O}$$\{RES\}$
$\mathcal{P}$$\{P\_DEU\}$
$\mathcal{RA}$
$\mathcal{RS}$
$\mathcal{RV}$
$\mathcal{S}$
$\mathcal{T}$$\{T\_DEU\}$
$\mathcal{V}$$\{V\_DEU\}$
$\mathcal{VT}$$\{(GH2,CNG)\}$
$\mathcal{Y}$$\{2020,2021\}$

Parameters

Parametery=2020y=2021
$\frac{1}{ | \Delta |_{y}}$$1$$1$
${1}^{NC}_{T\_DEU,DEU,CNG}$$0$$0$
${1}^{NC}_{T\_DEU,DEU,GH2}$$0$$0$
$r_{y}$$1$$1$
$d_{OnlyTimeStep}$$2$$2$
$c^{P}_{P\_DEU,GH2,RES,y}$$0.1$$0.1$
$c^{P}_{P\_DEU,CNG,RES,y}$$0.0$$0.0$
$c^{\Delta P}_{P\_DEU,GH2,RES,y}$$10$$10$
$c^{\Delta P}_{P\_DEU,CNG,RES,y}$$10$$10$
$fi^{P}_{GH2,Electricity,RES}$$1$$1$
$fi^{P}_{CNG,Electricity,RES}$$1$$1$
$L^{P}_{GH2,RES}$$50$$50$
$L^{P}_{CNG,RES}$$50$$50$
$\Lambda^{P}_{P\_DEU,GH2,RES,y}$$10$$10$
$\Lambda^{P}_{P\_DEU,CNG,RES,y}$$0$$0$
$\Lambda^{I}_{P\_DEU,Electricity,Block 1,y}$$10$$10$
$\Omega^{I}_{P\_DEU,Electricity,Block 1,y}$$0$$0$
$c^{\Delta^{I}}_{P\_DEU,Electricity,Block 1,y}$$0$$0$
$\Lambda^{T}_{T\_DEU,DEU,GH2,RES,y}$$10$$10$
$\Lambda^{T}_{T\_DEU,DEU,CNG,RES,y}$$10$$10$
$\Omega^{P}_{P\_DEU,GH2,RES,y}$$10$$10$
$\Omega^{P}_{P\_DEU,CNG,RES,y}$$10$$10$
$fi^{V}_{GH2,CNG}$$1$$1$
$l^{A}_{DEU\_to\_DEU,GH2}$$0$$0$
$l^{A}_{DEU\_to\_DEU,CNG}$$0$$0$
$c^{V}_{V\_DEU,GH2,CNG,y}$$0.1$$0.1$
$c^{\Delta V}_{V\_DEU,GH2,CNG,y}$$10$$10$
$\Lambda^{V}_{V\_DEU,GH2,CNG,y}$$10$$10$
$L^{V}_{GH2,CNG}$$10$$10$
$c^{A}_{DEU\_to\_DEU,GH2,y}$$0$$0$
$c^{A}_{DEU\_to\_DEU,CNG,y}$$0$$0$
$c^{\Delta A}_{DEU\_to\_DEU,GH2,y}$$0$$0$
$c^{\Delta A}_{DEU\_to\_DEU,CNG,y}$$0$$0$
$\Lambda^{A}_{DEU\_to\_DEU,GH2,y}$$0$$0$
$\Lambda^{A}_{DEU\_to\_DEU,CNG,y}$$0$$0$
$L^{A}_{GH2}$$50$$50$
$L^{A}_{CNG}$$50$$50$
$c^{I_{l}}_{P\_DEU,Electricity,Block 1,OnlyTimeStep,y}$$0.3$$0.3$
$c^{I_{q}}_{P\_DEU,Electricity,Block 1,OnlyTimeStep,y}$$1$$1$
$av^{I}_{P\_DEU,Electricity,Block 1,OnlyTimeStep}$$1$$1$
$\alpha^{D}_{DEU,GH2,Block 1,OnlyTimeStep,y}$$0$$0$
$\beta^{D}_{DEU,GH2,Block 1,OnlyTimeStep,y}$$0$$0$
$\alpha^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$2$$2$
$\beta^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$-1$$-1$

Test Criteria

ExpressionResult y=2020Result y=2021
$\tilde{P}^{T \rightarrow D}_{DEU,GH2,Block 1,OnlyTimeStep,y}$$0.00$$0.00$
$\tilde{P}^{T \rightarrow D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$1.25$$1.25$

Graphical Solution

Inverse Demand and Marginalized Cost Curves

GH2 2020

test_case_2a_graphic

GH2 2021

test_case_2b_graphic

CNG 2020

test_case_2a_graphic

CNG 2021

test_case_2b_graphic