Test Case 1

This test case comprises a simple example. The tables below depict the model sets and relevant parameters. If the model is solved correctly, marginalized production costs should be equal to the price. Test Case 1 passes, if prices in the single node are equal to the intersection of marginalized provision cost and inverse demand, see also the graphical solution below. Marginalized provision cost at factor intensities of 1:1 are $MC=c^{I_{l}} + c^{I_{q}} Q + c^{P}$, while prices are $P(Q) = \alpha^{D} + \beta^{D} Q$. Hence, for the given data, prices should be $P=1.5$, see also the overview of tested criteria.

Sets

Set NameSet Value
$\mathcal{A}${DEU_to_DEU}
$\mathcal{AC}${(DEU_to_DEU, CNG)}
$\mathcal{C}${CNG}
$\mathcal{DSB}${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}
$\mathcal{V}$
$\mathcal{VT}$
$\mathcal{Y}${2020}

Parameters

Parametery=2020
$\frac{1}{ | \Delta |_{y}}$$1$
${1}^{NC}_{T\_DEU,DEU,CNG}$$0$
$r_{y}$$1$
$d_{OnlyTimeStep}$$1$
$c^{P}_{P\_DEU,CNG,FES,y}$$0.5$
$c^{\Delta P}_{P\_DEU,CNG,FES,y}$$1$
$fi^{P}_{CNG,Natural Gas,FES}$$1$
$L^{P}_{CNG,FES}$$50$
$\Lambda^{P}_{P\_DEU,CNG,FES,y}$$10$
$\Lambda^{I}_{P\_DEU,Natural Gas,Block 1,y}$$10$
$\Omega^{I}_{P\_DEU,Natural Gas,Block 1,y}$$0$
$c^{\Delta^{I}}_{P\_DEU,Natural Gas,Block 1,y}$$0$
$\Lambda^{T}_{T\_DEU,DEU,CNG,FES,y}$$10$
$\Omega^{P}_{P\_DEU,CNG,FES,y}$$10$
$l^{A}_{DEU\_to\_DEU,CNG}$$0$
$c^{A}_{DEU\_to\_DEU,CNG,y}$$0$
$c^{\Delta A}_{DEU\_to\_DEU,CNG,y}$$0$
$\Lambda^{A}_{DEU\_to\_DEU,CNG,y}$$0$
$L^{A}_{CNG}$$50$
$c^{I_{l}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$$0.5$
$c^{I_{q}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$$1.0$
$av^{I}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep}$$1.0$
$\alpha^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$2$
$\beta^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$-1$

Test Criteria

ExpressionResult y=2020
$\tilde{P}^{T \rightarrow D}_{\text{DEU,CNG,Block 1,OnlyTimeStep,y}}$$1.5$

Graphical Solution

Inverse Demand and Marginalized Cost Curves

test_case_1_graphic