How to Use

In julia REPL, add the environment variable for your Gurobi installation

ENV["GUROBI_HOME"] = "PATH_TO_GUROBI"

Then go to the package mode by pressing ], and activate the environment in the current directory:

pkg> activate .
pkg> add Gurobi
pkg> develop ./GenerationExpansionPlanning

Press backspace to return to Julia REPL.

You should be able to run main.jl or your own scripts using GenerationExpansionPlanning module now.

Mathematical formulation

Sets

Name	Description
$N$	locations (nodes)
$G$	generation technologies
$NG \subseteq N \times G$	generation units
$T$	time steps
$L$	transmission lines

Parameters

Name	Symbol	Index Sets	Description	Unit
demand	$D$	$N \times T$	Demand	MW
generation_availability	$A$	$NG \times T$	Generation availability (load factor)	1/unit
investment_cost	$I$	$NG$	Investment cost	EUR/MW
variable_cost	$V$	$NG$	Variable production cost	EUR/MWh
unit_capacity	$U$	$NG$	Capacity per each invested unit	MW/unit
ramping_rate	$R$	$NG$	Ramping rate	1/unit
export_capacity	$L^{\text{exp}}$	$L$	Maximum transmission export capacity (A->B)	MW
import_capacity	$L^{\text{imp}}$	$L$	Maximum transmission import capacity (A<-B)	MW
data.value_of_lost_load	$V^{\text{loss}}$		Value of lost load	EUR/MWh
data.relaxation			Solve the LP relaxation?	Bool

Variables

Name	Symbol	Index Sets	Domain	Description	Unit
total_investment_cost	$c^{\text{inv}}$		$\mathbb{R}_+$	Total investment cost	EUR
total_operational_cost	$c^{\text{op}}$		$\mathbb{R}_+$	Total operatinal cost	EUR
investment	$i$	$NG$	$\mathbb{Z}_+$	Generation investment	units
production	$p$	$NG \times T$	$\mathbb{R}_+$	Generation production	MW
line_flow	$f$	$L \times T$	$[-L^{\text{imp}}, L^{\text{exp}}]$	Transmission line flow	MW
loss_of_load	$p^{\text{loss}}$	$N \times T$	$\mathbb{R}_+$	Loss of load	MW

Problem Formulation

$$\begin{aligned} \text{minimize} && c^{\text{inv}} &+ c^{\text{op}} \\ \text{subject to:} \\ \text{investment cost} && c^{\text{inv}} &= \sum_{(n, g) \in NG} I_{n,g} \cdot U_{n,g} \cdot i_{n,g} \\ \text{operational cost} && c^{\text{op}} &= \sum_{(n, g) \in NG} \sum_{t \in T} V_{n,g} \cdot p_{n,g,t} + \sum_{n \in N} \sum_{t \in T} V^{\text{loss}} \cdot p^{\text{loss}}_{n,t} \\ \end{aligned}$$

$$\begin{aligned} \text{node balance} && D_{n,t} &= \sum_{g \in G: (n,g) \in NG} p_{n,g,t} + \sum_{(n^{\text{from}}, n^{\text{to}}) \in L : n^{\text{to}} = n} f_{n^{\text{from}}, n^{\text{to}}, t} - \sum_{(n^{\text{from}}, n^{\text{to}}) \in L : n^{\text{from}} = n} f_{n^{\text{from}}, n^{\text{to}}, t} + p^{\text{loss}}_{n,t} && \forall n \in N, \forall t \in T \\ \end{aligned}$$

$$\begin{aligned} \text{maximum capacity} && p_{n, g, t} &\leq A_{n, g, t} \cdot U_{n,g} \cdot i_{n,g} && \forall (n, g) \in NG, \forall t \in T \\ \text{ramping up} && p_{n, g, t} - p_{n, g, t-1} &\leq R_{n,g} \cdot U_{n,g} \cdot i_{n,g} && \forall (n, g) \in NG, \forall t \in T \setminus { 1 } \\ \text{ramping down} && p_{n, g, t} - p_{n, g, t-1} &\geq -R_{n,g} \cdot U_{n,g} \cdot i_{n,g} && \forall (n, g) \in NG, \forall t \in T \setminus { 1 } \\ \end{aligned}$$