Test Case 4 asserts that discounting works as intended. It depicts a perfectly competitive version of Test Case 3 over the course of two years, where the second period is discounted by 50\%. Prices should be $P=1.0$ in both years. Social welfare corresponds to the gray triangle in the graphical solution, where the second period must be discounted accordingly. Hence, the total objective value (corresponding to social welfare in the absence of strategic behavior) must be $0.75$. Both, prices and objective values, are tested against.
| Set Name | Set Value |
|---|
| $\mathcal{A}$ | $\{DEU\_to\_DEU\}$ |
| $\mathcal{AC}$ | $\{(DEU\_to\_DEU,CNG)\}$ |
| $\mathcal{C}$ | $\{CNG\}$ |
| $\mathcal{DSB}$ | $\{Block 1\}$ |
| $\mathcal{I}$ | $\{Natural Gas\}$ |
| $\mathcal{IOB}$ | $\{Block 1\}$ |
| $\mathcal{M}$ | $\{OnlyTimeStep\}$ |
| $\mathcal{N}$ | $\{DEU\}$ |
| $\mathcal{O}$ | $\{FES\}$ |
| $\mathcal{P}$ | $\{P\_DEU\}$ |
| $\mathcal{RA}$ | ∅ |
| $\mathcal{RS}$ | ∅ |
| $\mathcal{RV}$ | ∅ |
| $\mathcal{S}$ | ∅ |
| $\mathcal{T}$ | $\{T\_DEU\}$ |
| $\mathcal{V}$ | ∅ |
| $\mathcal{VT}$ | ∅ |
| $\mathcal{Y}$ | $\{2020,2021\}$ |
| Parameter | y=2020 | y=2021 |
|---|
| $\frac{1}{ | \Delta |_{y}}$ | $1$ | $1$ |
| ${1}^{NC}_{T\_DEU,DEU,CNG}$ | $0$ | $0$ |
| $r_{y}$ | $1$ | $0.5$ |
| $d_{OnlyTimeStep}$ | $1$ | $1$ |
| $c^{P}_{P\_DEU,CNG,FES,y}$ | $0.5$ | $0.5$ |
| $c^{\Delta P}_{P\_DEU,CNG,FES,y}$ | $1$ | $1$ |
| $fi^{P}_{CNG,Natural Gas,FES}$ | $1$ | $1$ |
| $L^{P}_{CNG,FES}$ | $50$ | $50$ |
| $\Lambda^{P}_{P\_DEU,CNG,FES,y}$ | $10$ | $10$ |
| $\Lambda^{I}_{P\_DEU,Natural Gas,Block 1,y}$ | $10$ | $10$ |
| $\Omega^{I}_{P\_DEU,Natural Gas,Block 1,y}$ | $0$ | $0$ |
| $c^{\Delta^{I}}_{P\_DEU,Natural Gas,Block 1,y}$ | $0$ | $0$ |
| $\Lambda^{T}_{T\_DEU,DEU,CNG,FES,y}$ | $10$ | $10$ |
| $\Omega^{P}_{P\_DEU,CNG,FES,y}$ | $10$ | $10$ |
| $l^{A}_{DEU\_to\_DEU,CNG}$ | $0$ | $0$ |
| $c^{A}_{DEU\_to\_DEU,CNG,y}$ | $0$ | $0$ |
| $c^{\Delta A}_{DEU\_to\_DEU,CNG,y}$ | $0$ | $0$ |
| $\Lambda^{A}_{DEU\_to\_DEU,CNG,y}$ | $0$ | $0$ |
| $L^{A}_{CNG}$ | $50$ | $50$ |
| $c^{I_{l}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$ | $0.5$ | $0.5$ |
| $c^{I_{q}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$ | $0$ | $0$ |
| $av^{I}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep}$ | $1$ | $1$ |
| $\alpha^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$ | $2$ | $2$ |
| $\beta^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$ | $-1$ | $-1$ |
| Expression | Result y=2020 | y=2021 |
|---|
| $\tilde{P}^{T \rightarrow D}_{DEU,CNG,Block 1,OnlyTimeStep,2020}$ | $1.0$ | $1.0$ |
| Objective Value | | 0.75 |
