Test Case 27
Test Case 27 is used to assert correct working of adjacency structures for arc capacity expansion. All parameters are the same as in Test Case 13, however commodity-specific adjacency prohibits flows (since $\mathcal{AC}$ is empty). The tables below depict the sets and parameters. In addition, tests and a graphical solution are depicted.
The implementation in the testing routine features two separate runs for shipping and pipelines (denoted by case 27a and 27b), however, mathematical model data remain unchanged.
Sets
| Set Name | Set Value |
|---|---|
| $\mathcal{A}$ | $\{DEU\_to\_DEU,DEU\_to\_NLD,NLD\_to\_DEU,NLD\_to\_NLD\}$ |
| $\mathcal{AC}$ | ∅ |
| $\mathcal{C}$ | $\{CNG\}$ |
| $\mathcal{DSB}$ | $\{Block 1\}$ |
| $\mathcal{I}$ | $\{Natural Gas\}$ |
| $\mathcal{IOB}$ | $\{Block 1\}$ |
| $\mathcal{M}$ | $\{OnlyTimeStep\}$ |
| $\mathcal{N}$ | $\{DEU,NLD\}$ |
| $\mathcal{O}$ | $\{FES\}$ |
| $\mathcal{P}$ | $\{P\_DEU,P\_NLD\}$ |
| $\mathcal{RA}$ | ∅ |
| $\mathcal{RS}$ | ∅ |
| $\mathcal{RV}$ | ∅ |
| $\mathcal{S}$ | ∅ |
| $\mathcal{T}$ | $\{T\_DEU,T\_NLD\}$ |
| $\mathcal{V}$ | ∅ |
| $\mathcal{VT}$ | ∅ |
| $\mathcal{Y}$ | $\{2020,2025,2030\}$ |
Parameters
| Parameter | y=2020 | y=2025 | y=2030 |
|---|---|---|---|
| $\frac{1}{ | \Delta |_{y}}$ | $1$ | $1$ | $1$ |
| ${1}^{NC}_{T\_DEU,DEU,CNG}$ | $0$ | $0$ | $0$ |
| ${1}^{NC}_{T\_DEU,NLD,CNG}$ | $0$ | $0$ | $0$ |
| ${1}^{NC}_{T\_NLD,DEU,CNG}$ | $0$ | $0$ | $0$ |
| ${1}^{NC}_{T\_NLD,NLD,CNG}$ | $0$ | $0$ | $0$ |
| $r_{y}$ | $1$ | $1$ | $1$ |
| $d_{OnlyTimeStep}$ | $1$ | $1$ | $1$ |
| $c^{P}_{P\_DEU,CNG,FES,y}$ | $0.4$ | $0.4$ | $0.4$ |
| $c^{\Delta P}_{P\_DEU,CNG,FES,y}$ | $1$ | $1$ | $1$ |
| $c^{P}_{P\_NLD,CNG,FES,y}$ | $0.5$ | $0.5$ | $0.5$ |
| $c^{\Delta P}_{P\_NLD,CNG,FES,y}$ | $1$ | $1$ | $1$ |
| $fi^{P}_{CNG,Natural Gas,FES}$ | $1$ | $1$ | $1$ |
| $L^{P}_{CNG,FES}$ | $50$ | $50$ | $50$ |
| $\Lambda^{P}_{P\_DEU,CNG,FES,y}$ | $10$ | $10$ | $10$ |
| $\Lambda^{I}_{P\_DEU,Natural Gas,Block 1,y}$ | $10$ | $10$ | $10$ |
| $\Omega^{I}_{P\_DEU,Natural Gas,Block 1,y}$ | $0$ | $0$ | $0$ |
| $c^{\Delta^{I}}_{P\_DEU,Natural Gas,Block 1,y}$ | $0$ | $0$ | $0$ |
| $\Lambda^{T}_{T\_DEU,DEU,CNG,FES,y}$ | $10$ | $10$ | $10$ |
| $\Lambda^{T}_{T\_DEU,NLD,CNG,FES,y}$ | $10$ | $10$ | $10$ |
| $\Omega^{P}_{P\_DEU,CNG,FES,y}$ | $10$ | $10$ | $10$ |
| $\Lambda^{P}_{P\_NLD,CNG,FES,y}$ | $10$ | $10$ | $10$ |
| $\Lambda^{I}_{P\_NLD,Natural Gas,Block 1,y}$ | $10$ | $10$ | $10$ |
| $\Omega^{I}_{P\_NLD,Natural Gas,Block 1,y}$ | $0$ | $0$ | $0$ |
| $c^{\Delta^{I}}_{P\_NLD,Natural Gas,Block 1,y}$ | $0$ | $0$ | $0$ |
| $\Lambda^{T}_{T\_NLD,DEU,CNG,FES,y}$ | $10$ | $10$ | $10$ |
| $\Lambda^{T}_{T\_NLD,NLD,CNG,FES,y}$ | $10$ | $10$ | $10$ |
| $\Omega^{P}_{P\_NLD,CNG,FES,y}$ | $10$ | $10$ | $10$ |
| $l^{A}_{DEU\_to\_DEU,CNG}$ | $0.0$ | $0.0$ | $0.0$ |
| $l^{A}_{DEU\_to\_NLD,CNG}$ | $0.0$ | $0.0$ | $0.0$ |
| $l^{A}_{NLD\_to\_DEU,CNG}$ | $0.1$ | $0.1$ | $0.1$ |
| $l^{A}_{NLD\_to\_NLD,CNG}$ | $0.0$ | $0.0$ | $0.0$ |
| $c^{A}_{DEU\_to\_DEU,CNG,y}$ | $0.0$ | $0.0$ | $0.0$ |
| $c^{A}_{DEU\_to\_NLD,CNG,y}$ | $0.0$ | $0.0$ | $0.0$ |
| $c^{A}_{NLD\_to\_DEU,CNG,y}$ | $0.05$ | $0.05$ | $0.05$ |
| $c^{A}_{NLD\_to\_NLD,CNG,y}$ | $0.0$ | $0.0$ | $0.0$ |
| $c^{\Delta A}_{DEU\_to\_DEU,CNG,y}$ | $0.25$ | $0.25$ | $0.25$ |
| $c^{\Delta A}_{DEU\_to\_NLD,CNG,y}$ | $0.25$ | $0.25$ | $0.25$ |
| $c^{\Delta A}_{NLD\_to\_DEU,CNG,y}$ | $0.25$ | $0.25$ | $0.25$ |
| $c^{\Delta A}_{NLD\_to\_NLD,CNG,y}$ | $0.25$ | $0.25$ | $0.25$ |
| $\Lambda^{A}_{DEU\_to\_DEU,CNG,y}$ | $0$ | $0$ | $0$ |
| $\Lambda^{A}_{DEU\_to\_NLD,CNG,y}$ | $0$ | $0$ | $0$ |
| $\Lambda^{A}_{NLD\_to\_DEU,CNG,y}$ | $0$ | $0$ | $0$ |
| $\Lambda^{A}_{NLD\_to\_NLD,CNG,y}$ | $0$ | $0$ | $0$ |
| $L^{A}_{CNG}$ | $50$ | $50$ | $50$ |
| $c^{I_{l}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$ | $2$ | $2$ | $2$ |
| $c^{I_{q}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$ | $0$ | $0$ | $0$ |
| $av^{I}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep}$ | $1$ | $1$ | $1$ |
| $c^{I_{l}}_{P\_NLD,Natural Gas,Block 1,OnlyTimeStep,y}$ | $0.5$ | $0.5$ | $0.5$ |
| $c^{I_{q}}_{P\_NLD,Natural Gas,Block 1,OnlyTimeStep,y}$ | $0$ | $0$ | $0$ |
| $av^{I}_{P\_NLD,Natural Gas,Block 1,OnlyTimeStep}$ | $1$ | $1$ | $1$ |
| $\alpha^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$ | $2$ | $2$ | $2$ |
| $\beta^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$ | $-1$ | $-1$ | $-1$ |
| $\alpha^{D}_{NLD,CNG,Block 1,OnlyTimeStep,y}$ | $0$ | $0$ | $0$ |
| $\beta^{D}_{NLD,CNG,Block 1,OnlyTimeStep,y}$ | $-1$ | $-1$ | $-1$ |
Test Criteria
| Expression | Result y=2020 | Result y=2025 | Result y=2030 |
|---|---|---|---|
| $\tilde{P}^{T \rightarrow D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$ | $0$ | $2$ | $0.99$ |
| $\tilde{P}^{T \rightarrow D}_{NLD,CNG,Block 1,OnlyTimeStep,y}$ | $0.0$ | $0.0$ | $0.0$ |
| $\Delta^{A}_{DEU\_to\_DEU,CNG,y}$ | N.E. | N.E. | N.E. |
| $\Delta^{A}_{DEU\_to\_NLD,CNG,y}$ | N.E. | N.E. | N.E. |
| $\Delta^{A}_{NLD\_to\_DEU,CNG,y}$ | N.E. | N.E. | N.E. |
| $\Delta^{A}_{NLD\_to\_NLD,CNG,y}$ | N.E. | N.E. | N.E. |
Graphical Solution
Marginalized Provision Costs and Prices
Note: Marginalized costs are depicted as if adjacency was given.
