Model Formulation

E4ST.setup_model — Method

setup_model(config, data) -> model

Sets up a JuMP Model for E4ST using config and data.

Parameters

Name	Symbol	Letter
$N_G$	:num_gen	Number of generators
$N_B$	:num_bus	Number of buses
$N_L$	:num_branch	Number of branches
$G = \{1,2,...,N_G \}$	N/A	Set of generator indices
$B = \{1,2,...,N_B \}$	N/A	Set of bus indices
$L = \{1,2,...,N_L \}$	N/A	Set of branch indices
$g \in G$	:gen_idx	Generator index
$b \in B$	:bus_idx	Bus index
$l \in L$	:branch_idx	Branch index
$y \in Y$	:year_idx	Year index
$y_{S_g} \in Y$	:yearonidx	Starting Year index for generator `g`

Variables

These are the decision variables to be optimized over. Can be accessed by model[symbol]

Name	Symbol	Unit	Description
$\theta_{b,y,h}$	`:θ_bus`	Radians	Hourly voltage angle of each bus. Reference buses fixed to 0.0
$P_{G_{g,y,h}}$	`:pgen_gen`	MW	Hourly avg. power generated by each generator
$P_{C_{g,y}}$	`:pcap_gen`	MW	Annual power generation capacity of each generator
$P_{S_{b,y,h}}$	`:plserv_bus`	MW	Hourly avg. power served to each bus

Expressions

Expressions are calculated as linear combinations of variables. Can be accessed by model[symbol]

Name	Symbol	Unit	Description
$P_{F_{l,y,h}}$	`:pflow_branch`	MW	Hourly avg. power flowing through each branch
$P_{F_{b,y,h}}$	`:pflow_bus`	MW	Hourly avg. net power flowing out of each bus
$P_{U_{b,y,h}}$	`:plcurt_bus`	MW	Hourly avg. power curtailed at each bus
$P_{G_{b,y,h}}$	`:pgen_bus`	MW	Hourly avg. power generated at each bus

Constraints

Name	Constraint	Symbol	Unit	Description
$C_{PB_{b,y,h}}$	$P_{G_{b,y,h}} - P_{S_{b,y,h}} \geq P_{F_{b,y,h}}$	`:cons_pbal_geq`	MW	Constrain the power flow at each bus
$C_{PB_{b,y,h}}$	$P_{G_{b,y,h}} - P_{S_{b,y,h}} \leq P_{F_{b,y,h}}$	`:cons_pbal_leq`	MW	Constrain the power flow at each bus
$C_{PG_{g,y,h}}^{\text{min}}$	$P_{G_{g,y,h}} \geq P_{C_{b,y}}^{\text{min}}$	`:cons_pgen_min`	MW	Constrain the generated power to be above minimum capacity factor, if given.
$C_{PG_{g,y,h}}^{\text{max}}$	$P_{G_{g,y,h}} \leq P_{C_{b,y}}^{\text{max}}$	`:cons_pgen_max`	MW	Constrain the generated power to be below min(availability factor, max capacity factor)
$C_{PS_{g,y,h}}^{\text{min}}$	$P_{S_{b,y,h}} \geq 0$	`:cons_plserv_min`	MW	Constrain the served power to be greater than zero
$C_{PS_{g,y,h}}^{\text{max}}$	$P_{S_{b,y,h}} \leq P_{D_{b,y,h}}$	`:cons_plserv_max`	MW	Constrain the served power to be less than or equal to load power.
$C_{PC_{g,y}}^{\text{min}}$	$P_{C_{g,y}} \geq P_{C_{g,y}}^{\text{min}}$	`:cons_pcap_min`	MW	Constrain the power generation capacity to be less than or equal to its minimum.
$C_{PC_{g}}^{\text{max}}$	$P_{C_{g,y}} \leq P_{C_{g,y}}^{\text{max}}\quad \forall y = y_{S_g}$	`:cons_pcap_max`	MW	Constrain the power generation capacity to be less than or equal to its minimum for its starting year.
$C_{PL_{l,y,h}}^{+}$	$P_{F_{l,y,h}} \leq P_{L_{l,y,h}}^{\text{max}}$	`:cons_branch_pflow_pos`	MW	Constrain the branch power flow to be less than or equal to its maximum.
$C_{PL_{l,y,h}}^{-}$	$-P_{F_{l,y,h}} \leq P_{L_{l,y,h}}^{\text{max}}$	`:cons_branch_pflow_neg`	MW	Constrain the negative branch power flow to be less than or equal to its maximum.
$C_{PCGPB_{g,y}}$	$P_{C_{g,y}} = 0 \quad \forall \left\{ y<y_{S_g} \right\}$	`N/A`	MW	Constrain the power generation capacity to be zero before the start year. Implemented by fixing the variable.
$C_{PCGNA_{g,y}}$	$P_{C_{g,y+1}} <= P_{C_{g,y}} \quad \forall \left\{ y >= y_{S_g} \right\}$	`:cons_pcap_gen_noadd`	MW	Constrain the power generation capacity to be non-increasing after the start year. Generation capacity is only added when building new generators in their start year.
$C_{PCGE_{g,y}}$	$P_{C_{g,y}} == P_{C_{0_{g}}} \quad \forall \left\{ first y >= y_{S_g} \right\}$	`:cons_pcap_gen_exog`	MW	Constrain unbuilt exogenous generators to be built to `pcap0` in the first year after `year_on`.

Objective

The objective is a single expression that can be accessed via model[:obj]. In general, we add things to the objective via:

source