Test Case 16

Test Case 16 is similar to Test Case 14, except that storage capacity expansion is disallowed. The tables below depict the sets and parameters, respectively. Since no storage is possible now, prices must be equal to inverse demand intercepts. Tests are passed, if high demand prices in 2020, 2025 and 2030 are 0, 2 and 0.98, respectively and zero during low demand time steps. Further, no capacity expansions are allowed to happen for the test to pass. Passing criteria can be seen below, while the figure depicts a graphical solution.

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}$$\{2020,2025,2030\}$

Parameters

Parameterm=Lm=H
$\frac{1}{ | \Delta |_{y}}$$1$$1$
${1}^{NC}_{T\_DEU,DEU,CNG}$$0$$0$
$r_{2020}$$1$$1$
$r_{2025}$$1$$1$
$r_{2030}$$1$$1$
$d_{m}$$2$$1$
$c^{P}_{P\_DEU,CNG,FES,2020}$$0.4$$0.4$
$c^{P}_{P\_DEU,CNG,FES,2025}$$0.4$$0.4$
$c^{P}_{P\_DEU,CNG,FES,2030}$$0.4$$0.4$
$c^{\Delta P}_{P\_DEU,CNG,FES,2020}$$1$$1$
$c^{\Delta P}_{P\_DEU,CNG,FES,2025}$$1$$1$
$c^{\Delta P}_{P\_DEU,CNG,FES,2030}$$1$$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^{P}_{P\_DEU,CNG,FES,2025}$$10$$10$
$\Lambda^{P}_{P\_DEU,CNG,FES,2030}$$10$$10$
$\Lambda^{I}_{P\_DEU,Natural Gas,Block 1,2020}$$10$$10$
$\Lambda^{I}_{P\_DEU,Natural Gas,Block 1,2025}$$10$$10$
$\Lambda^{I}_{P\_DEU,Natural Gas,Block 1,2030}$$10$$10$
$\Omega^{I}_{P\_DEU,Natural Gas,Block 1,2020}$$0$$0$
$\Omega^{I}_{P\_DEU,Natural Gas,Block 1,2025}$$0$$0$
$\Omega^{I}_{P\_DEU,Natural Gas,Block 1,2030}$$0$$0$
$c^{\Delta^{I}}_{P\_DEU,Natural Gas,Block 1,2020}$$0$$0$
$c^{\Delta^{I}}_{P\_DEU,Natural Gas,Block 1,2025}$$0$$0$
$c^{\Delta^{I}}_{P\_DEU,Natural Gas,Block 1,2030}$$0$$0$
$\Lambda^{T}_{T\_DEU,DEU,CNG,FES,2020}$$10$$10$
$\Lambda^{T}_{T\_DEU,DEU,CNG,FES,2025}$$10$$10$
$\Lambda^{T}_{T\_DEU,DEU,CNG,FES,2030}$$10$$10$
$\Omega^{P}_{P\_DEU,CNG,FES,2020}$$10$$10$
$\Omega^{P}_{P\_DEU,CNG,FES,2025}$$10$$10$
$\Omega^{P}_{P\_DEU,CNG,FES,2030}$$10$$10$
$l^{A}_{DEU\_to\_DEU,CNG}$$0$$0$
$c^{A}_{DEU\_to\_DEU,CNG,2020}$$0$$0$
$c^{A}_{DEU\_to\_DEU,CNG,2025}$$0$$0$
$c^{A}_{DEU\_to\_DEU,CNG,2030}$$0$$0$
$c^{\Delta A}_{DEU\_to\_DEU,CNG,2020}$$0$$0$
$c^{\Delta A}_{DEU\_to\_DEU,CNG,2025}$$0$$0$
$c^{\Delta A}_{DEU\_to\_DEU,CNG,2030}$$0$$0$
$\Lambda^{A}_{DEU\_to\_DEU,CNG,2020}$$0$$0$
$\Lambda^{A}_{DEU\_to\_DEU,CNG,2025}$$0$$0$
$\Lambda^{A}_{DEU\_to\_DEU,CNG,2030}$$0$$0$
$L^{A}_{CNG}$$50$$50$
$l^{S}_{CNG,m,L}$$0$$0$
$l^{S}_{CNG,m,H}$$0$$0$
$c^{S}_{S\_DEU,CNG,m,H,2020}$$0.05$$0.05$
$c^{S}_{S\_DEU,CNG,m,H,2025}$$0.05$$0.05$
$c^{S}_{S\_DEU,CNG,m,H,2030}$$0.05$$0.05$
$c^{S}_{S\_DEU,CNG,m,L,2020}$$0.05$$0.05$
$c^{S}_{S\_DEU,CNG,m,L,2025}$$0.05$$0.05$
$c^{S}_{S\_DEU,CNG,m,L,2030}$$0.05$$0.05$
$c^{\Delta S}_{S\_DEU,CNG,2020}$$0.25$$0.25$
$c^{\Delta S}_{S\_DEU,CNG,2025}$$0.25$$0.25$
$c^{\Delta S}_{S\_DEU,CNG,2030}$$0.25$$0.25$
$\Lambda^{S}_{S\_DEU,CNG,2020}$$0$$0$
$\Lambda^{S}_{S\_DEU,CNG,2025}$$0$$0$
$\Lambda^{S}_{S\_DEU,CNG,2030}$$0$$0$
$\Omega^{S}_{S\_DEU,CNG,2020}$$0$$0$
$\Omega^{S}_{S\_DEU,CNG,2025}$$0$$0$
$\Omega^{S}_{S\_DEU,CNG,2030}$$0$$0$
$L^{S}_{CNG}$$5$$5$
$c^{I_{l}}_{P\_DEU,Natural Gas,Block 1,m,2020}$$0.5$$1.6$
$c^{I_{l}}_{P\_DEU,Natural Gas,Block 1,m,2025}$$0.5$$1.6$
$c^{I_{l}}_{P\_DEU,Natural Gas,Block 1,m,2030}$$0.5$$1.6$
$c^{I_{q}}_{P\_DEU,Natural Gas,Block 1,m,2020}$$0$$0$
$c^{I_{q}}_{P\_DEU,Natural Gas,Block 1,m,2025}$$0$$0$
$c^{I_{q}}_{P\_DEU,Natural Gas,Block 1,m,2030}$$0$$0$
$av^{I}_{P\_DEU,Natural Gas,Block 1,m}$$1$$1$
$\alpha^{D}_{DEU,CNG,Block 1,m,2020}$$0$$2$
$\alpha^{D}_{DEU,CNG,Block 1,m,2025}$$0$$2$
$\alpha^{D}_{DEU,CNG,Block 1,m,2030}$$0$$2$
$\beta^{D}_{DEU,CNG,Block 1,m,2020}$$0$$-1$
$\beta^{D}_{DEU,CNG,Block 1,m,2025}$$0$$-1$
$\beta^{D}_{DEU,CNG,Block 1,m,2030}$$0$$-1$

Test Criteria

ExpressionResult m=LResult m=H
$\tilde{P}^{T \rightarrow D}_{DEU,CNG,Block 1,m,2020}$$0.0$$0.0$
$\tilde{P}^{T \rightarrow D}_{DEU,CNG,Block 1,m,2025}$$0.0$$2.0$
$\tilde{P}^{T \rightarrow D}_{DEU,CNG,Block 1,m,2030}$$0.0$$0.99$
$\Delta^{S}_{S\_DEU,CNG,2020}$$0$$0$
$\Delta^{S}_{S\_DEU,CNG,2025}$$0$$0$
$\Delta^{S}_{S\_DEU,CNG,2030}$$0$$0$

Graphical Solution

Marginalized Provision Costs and Prices

Time Step L 2020

test_case_16a_graphic

Time Step H 2020

test_case_16b_graphic

Time Step L 2025

test_case_16c_graphic

Time Step H 2025

test_case_16d_graphic

Time Step L 2030

test_case_16e_graphic

Time Step H 2030

test_case_16f_graphic