Generation Expansion Planning (GEP) models considering uncertainties on renewable energy resources (RES)

Files description

The following files solve the GEP problem for three scenarios of wind and solar production using different approaches:

Stochastic-GEP.gms: Two-Stage Stochastic Generation Expansion Planning
Stochastic-GEP-Benders.gms: Two-Stage Stochastic Generation Expansion Planning - Using Benders
Stochastic-GEP-Benders-Multicut.gms: Two-Stage Stochastic Generation Expansion Planning - Using Benders Multicut
Stochastic-GEP-LR.gms: Two-Stage Stochastic Generation Expansion Planning - Using Lagrangian Relaxation (LR)
Stochastic-GEP-Multistage.gms: Multi-Stage Stochastic Generation Expansion Planning
SRO-GEP.gms: Single-Stage Static Robust Optimization (SRO) or Scenario-based RO -Generation Expansion Planning (GEP)
ARO-GEP.gms: Two-Stage Adaptive Robust Optimization (ARO)-Generation Expansion Planning (GEP)
WCS-GEP.gms: Worst Case Scenario -Generation Expansion Planning (GEP)
Bilevel-Centralized-GEPM.gms: The Bilevel formulation Deterministic Single-Node Static Generation Expansion Planning Model (GEPM)

The models are developed in GAMS and solved with CPLEX, but you could use any other solver (e.g., GUROBI, Cbc).

GEP Formulation

Indices

Name	Description
$p$	time periods
$g$	generation technologies
$r(g)$	subset of renewable techonologies
$sc$	scenarios

Parameters

Name	Domains	Description
$pVOLL $		Value of Lost Load [$/MWh]
$pWeight $		Representative period weight [hours]
$pInvCost$	$g$	Investment cost [$/MW]
$pVarCost$	$g$	Variable production cost [$/MWh]
$pUnitCap$	$g$	Capacity per each invested unit [MW/unit]
$pRenProf$	$r,p,sc$	Renewable profile (e.g., load factor) [p.u.]
$pDemand $	$p$	Demand [MW]
$pScProb $	$sc$	Scenario probability [p.u.]

Variables

Name	Domains	Description
$vTotCost $		Total system cost [$]
$vInvCost $		Total investment cost [$]
$vOpeCost $		Total operating cost [$]
$vGenInv $	$g$	Generation investment [1..N]
$vGenProd $	$g,p,sc$	Generation production [MW]
$vLossLoad$	$p,sc$	Loss of load [MW]

Equations

Name	Domains	Description
eObjFun		Total system cost [$]
eInvCost		Total investment cost [$]
eOpeCost		Total operating cost [$]
eBalance	$p,sc$	Power system balance [MWh]
eMaxProd	$g,p,sc$	Maximum generation production [MW]
eRenProd	$r,p,sc$	Maximum renewable production [MW]

eObjFun

$$ \displaystyle{\min{vTotCost = vInvCost + vOpeCost}} $$

eInvCost

$$ vInvCost = \displaystyle \sum_{g}(pInvCost_{g} \cdot pUnitCap_{g} \cdot vGenInv_{g}) $$

eOpeCost

$$ vOpeCost = pWeight \cdot {\left(\displaystyle \sum_{sc}pScProb_{sc}\cdot{\left(\sum_{g,p}pVarCost_{g} \cdot vGenProd_{g,p,sc} + \sum_{p,sc}pVOLL \cdot vLossLoad_{p,sc}\right)}\right)} $$

eBalance

$$ \displaystyle \sum_{g}vGenProd_{g,p,sc} + vLossLoad_{p,sc} = pDemand_{p} \quad \forall{p,sc} $$

eMaxProd

$$ vGenProd_{g,p,sc} \leq pUnitCap_{g} \cdot vGenInv_{g} \quad \forall{g,p,sc} $$

eRenProd

$$ vGenProd_{r,p,sc} \leq pRenProf_{r,p,sc} \cdot pUnitCap_{r} \cdot vGenInv_{r} \quad \forall{r,p,sc} $$

Bounds

$vGenProd_{g,p,sc}\geq 0 ~ \forall g, p, sc $

$vLossLoad_{p,sc}\geq 0 ~ \forall p, sc $

$vGenInv_{g} \in \mathbb{Z}^{+} ~ \forall g $

References

The main references to model the optimization problems are:

[1] Optimization Techniques by Andrés Ramos Galán

[2] A. J. Conejo, L. Baringo, S. J. Kazempour and A. S. Siddiqui, Investment in Electricity Generation and Transmission, Cham, Zug, Switzerland:Springer, 2016.

[3] Sun X.A., Conejo A.J. (2021) Static Robust Optimization. In: Robust Optimization in Electric Energy Systems. International Series in Operations Research & Management Science, vol 313. Springer, Cham.

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