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 |
|---|
| $\mathcal{A}$ | {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 |
|---|
| $\tilde{P}^{T \rightarrow D}_{\text{DEU,CNG,Block 1,OnlyTimeStep,y}}$ | $1.5$ |
