Test Case 10

Test Case 10 is structurally similar to Test Case 5, but 10% losses between time steps are incurred in addition to $0.1$ of extraction costs. The tables below depict the sets and parameters, respectively. Marginalized provision costs from low to high demand time step are hence $MC=1.1$. Tests are passed, if prices are $P=1.1$ and $P=0$ in high and low demand time steps.

Sets

Set NameSet 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}$$\{L,H\}$
$\mathcal{N}$$\{DEU\}$
$\mathcal{O}$$\{FES\}$
$\mathcal{P}$$\{P\_DEU\}$
$\mathcal{RA}$
$\mathcal{RS}$
$\mathcal{RV}$
$\mathcal{S}$$\{S\_DEU\}$
$\mathcal{T}$$\{T\_DEU\}$
$\mathcal{V}$
$\mathcal{VT}$
$\mathcal{Y}$$\{2020\}$

Parameters

Parameterm=Lm=H
$\frac{1}{ | \Delta |_{y}}$$1$$1$
${1}^{NC}_{T\_DEU,DEU,CNG}$$0$$0$
$r_{2020}$$1$$1$
$d_{m}$$2$$1$
$c^{P}_{P\_DEU,CNG,FES,2020}$$0.4$$0.4$
$c^{\Delta P}_{P\_DEU,CNG,FES,2020}$$1$$1$
$fi^{P}_{CNG,Natural Gas,FES}$$1$$1$
$L^{P}_{CNG,FES}$$50$$50$
$\Lambda^{P}_{P\_DEU,CNG,FES,2020}$$10$$10$
$\Lambda^{I}_{P\_DEU,Natural Gas,Block 1,2020}$$10$$10$
$\Omega^{I}_{P\_DEU,Natural Gas,Block 1,2020}$$0$$0$
$c^{\Delta^{I}}_{P\_DEU,Natural Gas,Block 1,2020}$$0$$0$
$\Lambda^{T}_{T\_DEU,DEU,CNG,FES,2020}$$10$$10$
$\Omega^{P}_{P\_DEU,CNG,FES,2020}$$10$$10$
$l^{A}_{DEU\_to\_DEU,CNG}$$0$$0$
$c^{A}_{DEU\_to\_DEU,CNG,2020}$$0$$0$
$c^{\Delta A}_{DEU\_to\_DEU,CNG,2020}$$0$$0$
$\Lambda^{A}_{DEU\_to\_DEU,CNG,2020}$$0$$0$
$L^{A}_{CNG}$$50$$50$
$l^{S}_{CNG,m,L}$$0$$0$
$l^{S}_{CNG,m,H}$$0.1$$0$
$c^{S_{in}}_{S\_DEU,CNG,2020}$$0$$0$
$c^{S}_{S\_DEU,CNG,2020}$$0.1$$0.1$
$c^{\Delta S}_{S\_DEU,CNG,2020}$$10$$10$
$\Lambda^{S}_{S\_DEU,CNG,2020}$$10$$10$
$\Omega^{S}_{S\_DEU,CNG,2020}$$10$$10$
$L^{S}_{CNG}$$10$$10$
$c^{I_{l}}_{P\_DEU,Natural Gas,Block 1,m,2020}$$0.5$$1$
$c^{I_{q}}_{P\_DEU,Natural Gas,Block 1,m,2020}$$0$$0$
$av^{I}_{P\_DEU,Natural Gas,Block 1,m}$$1$$1$
$\alpha^{D}_{DEU,CNG,Block 1,m,2020}$$0$$2$
$\beta^{D}_{DEU,CNG,Block 1,m,2020}$$0$$-1$

Test Criteria

ExpressionResult m=LResult m=H
$\tilde{P}^{T \rightarrow D}_{DEU,CNG,Block 1,m,2020}$$0.0$$1.1$

Graphical Solution

Marginalized Provision Costs and Prices for Different Time Steps

Time Step L

test_case_10a_graphic

Time Step H

test_case_10b_graphic