Test Case 9

Test Case 9 is used to verify functionality and losses on transportation arcs with time step weights. The tables below depict the sets and parameters, respectively. Production costs in $DEU$ are much too high. However, $NLD$ has no own demand and can export to $DEU$ with operational cost of $0.1$ and losses of 10%. In addition to production and conversion costs of $1$, 10% must be produced on top, and operational costs of $0.1$ follow. Marginalized provision costs are hence $1.2$. Tests are passed, if prices are $1.2$ and $0$ in $DEU$ and $NLD$, respectively. Further, $0.88$ must be produced in $NLD$, corresponding to a consumption quantity of $0.8$ in $DEU$.

The implementation in the testing routine features two separate runs for shipping and pipelines (denoted by case 9a and 9b), however, mathematical model data remain unchanged.

Sets

Set NameSet Value
$\mathcal{A}$$\{DEU\_to\_DEU,DEU\_to\_NLD,NLD\_to\_DEU,NLD\_to\_NLD\}$
$\mathcal{AC}$$\begin{aligned}\{(DEU\_to\_DEU, CNG),(DEU\_to\_NLD, CNG), \\ (NLD\_to\_DEU, CNG),(NLD\_to\_NLD, CNG)\} \end{aligned}$
$\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\}$

Parameters

Parametery=2020
$\frac{1}{ | \Delta |_{y}}$$1$
${1}^{NC}_{T\_DEU,DEU,CNG}$$0$
${1}^{NC}_{T\_DEU,NLD,CNG}$$0$
${1}^{NC}_{T\_NLD,DEU,CNG}$$0$
${1}^{NC}_{T\_NLD,NLD,CNG}$$0$
$r_{y}$$1$
$d_{OnlyTimeStep}$$2$
$c^{P}_{P\_DEU,CNG,FES,y}$$0.5$
$c^{\Delta P}_{P\_DEU,CNG,FES,y}$$1$
$c^{P}_{P\_NLD,CNG,FES,y}$$0.5$
$c^{\Delta P}_{P\_NLD,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$
$\Lambda^{T}_{T\_DEU,NLD,CNG,FES,y}$$10$
$\Omega^{P}_{P\_DEU,CNG,FES,y}$$10$
$\Lambda^{P}_{P\_NLD,CNG,FES,y}$$10$
$\Lambda^{I}_{P\_NLD,Natural Gas,Block 1,y}$$10$
$\Omega^{I}_{P\_NLD,Natural Gas,Block 1,y}$$0$
$c^{\Delta^{I}}_{P\_NLD,Natural Gas,Block 1,y}$$0$
$\Lambda^{T}_{T\_NLD,DEU,CNG,FES,y}$$10$
$\Lambda^{T}_{T\_NLD,NLD,CNG,FES,y}$$10$
$\Omega^{P}_{P\_NLD,CNG,FES,y}$$10$
$l^{A}_{DEU\_to\_DEU,CNG}$$0.0$
$l^{A}_{DEU\_to\_NLD,CNG}$$0.0$
$l^{A}_{NLD\_to\_DEU,CNG}$$0.1$
$l^{A}_{NLD\_to\_NLD,CNG}$$0.0$
$c^{A}_{DEU\_to\_DEU,CNG,y}$$0.0$
$c^{A}_{DEU\_to\_NLD,CNG,y}$$0.0$
$c^{A}_{NLD\_to\_DEU,CNG,y}$$0.1$
$c^{A}_{NLD\_to\_NLD,CNG,y}$$0.0$
$c^{\Delta A}_{DEU\_to\_DEU,CNG,y}$$0$
$c^{\Delta A}_{DEU\_to\_NLD,CNG,y}$$0$
$c^{\Delta A}_{NLD\_to\_DEU,CNG,y}$$0$
$c^{\Delta A}_{NLD\_to\_NLD,CNG,y}$$0$
$\Lambda^{A}_{DEU\_to\_DEU,CNG,y}$$0$
$\Lambda^{A}_{DEU\_to\_NLD,CNG,y}$$0$
$\Lambda^{A}_{NLD\_to\_DEU,CNG,y}$$10$
$\Lambda^{A}_{NLD\_to\_NLD,CNG,y}$$0$
$L^{A}_{CNG}$$50$
$c^{I_{l}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$$2$
$c^{I_{q}}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$$0$
$av^{I}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep}$$1$
$c^{I_{l}}_{P\_NLD,Natural Gas,Block 1,OnlyTimeStep,y}$$0.5$
$c^{I_{q}}_{P\_NLD,Natural Gas,Block 1,OnlyTimeStep,y}$$0$
$av^{I}_{P\_NLD,Natural Gas,Block 1,OnlyTimeStep}$$1$
$\alpha^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$2$
$\beta^{D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$-1$
$\alpha^{D}_{NLD,CNG,Block 1,OnlyTimeStep,y}$$0$
$\beta^{D}_{NLD,CNG,Block 1,OnlyTimeStep,y}$$-1$

Test Criteria

ExpressionResult y=2020
$\tilde{P}^{T \rightarrow D}_{DEU,CNG,Block 1,OnlyTimeStep,y}$$1.2$
$\tilde{P}^{T \rightarrow D}_{NLD,CNG,Block 1,OnlyTimeStep,y}$$0.0$
$q^{I}_{P\_DEU,Natural Gas,Block 1,OnlyTimeStep,y}$$0.0$
$q^{I}_{P\_NLD,Natural Gas,Block 1,OnlyTimeStep,y}$$0.88$

Graphical Solution

Marginalized Provision Costs and Prices for Different Nodes

NLD

test_case_9a_graphic

DEU

test_case_9b_graphic