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 Andrs Ramos Galn

[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.