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.
Set Name | Set Value |
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$\mathcal{A}$ | {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} |
Parameter | y=2020 |
---|
$\frac{1}{ | \Delta |_{y}}$ | $1$ |
${1}^{NC}_{T\_DEU,DEU,CNG}$ | $0$ |
$r_{y}$ | $1$ |
$d_{OnlyTimeStep}$ | $1$ |
$c^{P}_{P\_DEU,CNG,FES,y}$ | $0.5$ |
$c^{\Delta P}_{P\_DEU,CNG,FES,y}$ | $1$ |
$fi^{P}_{CNG,Natural Gas,FES}$ | $1$ |
$L^{P}_{CNG,FES}$ | $50$ |
$\Lambda^{P}_{P\_DEU,CNG,FES,y}$ | $10$ |
$\Lambda^{I}_{P\_DEU,Natural Gas,Block 1,y}$ | $10$ |
$\Omega^{I}_{P\_DEU,Natural Gas,Block 1,y}$ | $0$ |
$c^{\Delta^{I}}_{P\_DEU,Natural Gas,Block 1,y}$ | $0$ |
$\Lambda^{T}_{T\_DEU,DEU,CNG,FES,y}$ | $10$ |
$\Omega^{P}_{P\_DEU,CNG,FES,y}$ | $10$ |
$l^{A}_{DEU\_to\_DEU,CNG}$ | $0$ |
$c^{A}_{DEU\_to\_DEU,CNG,y}$ | $0$ |
$c^{\Delta A}_{DEU\_to\_DEU,CNG,y}$ | $0$ |
$\Lambda^{A}_{DEU\_to\_DEU,CNG,y}$ | $0$ |
$L^{A}_{CNG}$ | $50$ |
$c^{I_{l}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$ | $0.5$ |
$c^{I_{q}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$ | $1.0$ |
$av^{I}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep}$ | $1.0$ |
$\alpha^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$ | $2$ |
$\beta^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$ | $-1$ |
Expression | Result y=2020 |
---|
$\tilde{P}^{T \rightarrow D}_{\text{DEU,CNG,Block 1,OnlyTimeStep,y}}$ | $1.5$ |
