Table 9 Overview of expansion planning models in power system
Objectives | Constraints | Types of uncertainties | Model framework | Expansion planning model | Solver/software/system configuration | Inertia Consideration | Refs. |
|---|---|---|---|---|---|---|---|
Minimize cost comprising operating, investment, and environmental costs | Unit commitment and DC-Optimal power flow (OPC) constraints | Not Considered (NC) | Deterministic MILP | GTEP | CPLEX 12.9.0.0. solver.:2.67 GHz processor and 64 GB RAM | No | [36] |
Minimize emission, and maximize profit | Operational constraints | Varying capacity of wind turbine | LP | GTEP | CPLEX solver in GAMS. Core i5,3 GHz processor and 16 GB of RAM | No | [140] |
Minimize cost, energy losses, and voltage violation | DC-OPF | NC | MILP | GEP | CPLEX solver in GAMS. Intel Core i7-4770 processor | No | [143] |
Minimize investment costs | DC-OPF | NC | MILP | GTEP | LINPROG function in MATLAB and CPLEX Solver in GAMS. 2.5 GHz CPU, Core i5 and 4- GB memory | No | [44] |
Minimize cost, and energy not supplied (ENS) | DC-OPF, N-1 constraints | NC | MILP | TEP | CPLEX Solver in GAMS. Core-i7, 2.81-GHz processor and 16-GB RAM | No | [46] |
Minimizing cost | DC-OPF | Load demand | Stochastic two-stage MILP optimization model | GSTEP | NG | No | [47] |
Minimize investment, maintenance, and CO2 emission cost | AC–OPF and renewable energy policy constraints | Load demand and RES variations | MINLP | TGSEP | Accelerated Benders Dual Decomposition algorithm | No | [48] |
Minimize cost and energy not served (ENS) | Security and resilience constraints | NC | MILP | TEP | Benders Decomposition algorithm | No | [49] |
Minimize cost and emission | N-1 contingency constraints | PV generation and load variations | Scenario-based stochastic MILP | IEGNEP | CPLEX’s solver in GAMS 25.1.2 1.60 GHz CPU; core i7 and 4 GB memory | No | [51] |
Minimize cost and carbon emission | Generation and transmission limits, ramp constraints | load demand variations | Deterministic MILP | GTEP | Branch:and bound method and weighted sum bisection method (WSBM) | No | [52] |
Minimize cost | Reliability constraints | NC | Multi-level game theory model | GEP | Game theory and bi-level modeling in MATLAB. 8 GB RAM computer | No | |
Minimize cost and CO2 emission | AC–OPF | Load demand and generation variations | MINLP | DSEP | CPLEX solver using the branch-and-bound algorithm | No | [54] |
Minimize investment, operation, and transmission service cost | DC-OPF | Nil | MILP | GTEP | BONMIN solver in GAMS | No | [37] |
Minimize the investment costs while considering system uncertainties | DC-OPF | NC | MILP | DSEP | Gurobi solver in Python.:8 cores and 32 GB of RAM | No | [56] |
Minimize investment and operational cost | Ramping, DC-DC-OPF constraints | Water flow variations | LP | GEP | Progressive Hedging Algorithm (PHA) and Gurobi 7.0 solver in Python 24-core computer and 32 GB RAM | No | [145] |