How to Use

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

julia 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 | | `totaloperationalcost` | $c^{\text{op}}$ | | $\mathbb{R}+$ | 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

$$\begin{aligned} \text{minimize} && c^{\text{inv}} &+ c^{\text{op}} \ \text{subject to:} \ \text{investment cost} && c^{\text{inv}} &= \sum{(n, g) \in NG} I{n,g} \cdot U{n,g} \cdot i{n,g} \ \text{operational cost} && c^{\text{op}} &= \sum{(n, g) \in NG} \sum{t \in T} V{n,g} \cdot p{n,g,t} + \sum{n \in N} \sum{t \in T} V^{\text{loss}} \cdot p^{\text{loss}}_{n,t} \ \end{aligned}$$

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

$$\begin{aligned} \text{maximum capacity} && p{n, g, t} &\leq A{n, g, t} \cdot U{n,g} \cdot i{n,g} && \forall (n, g) \in NG\, \forall t \in T \ \text{ramping up} && p{n, g, t} - p{n, g, t-1} &\leq R{n,g} \cdot U{n,g} \cdot i{n,g} && \forall (n, g) \in NG\, \forall t \in T \setminus { 1 } \ \text{ramping down} && p{n, g, t} - p{n, g, t-1} &\geq -R{n,g} \cdot U{n,g} \cdot i{n,g} && \forall (n, g) \in NG\, \forall t \in T \setminus { 1 } \ \end{aligned}$$