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Strategic generation expansion planning considering prohibited operating zones: a game-theoretic analysis

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Abstract

Generation expansion planning (GEP) is a pivotal problem for power system planners due to increasing electric power consumption. This article aims to construct a methodology for GEP in power networks while incorporating the prohibited operating zones (POZ) and multi-fuel option (MFO) into the problem. The POZ and MFO are not considered in the existing GEP models, whereas these factors might considerably change the optimal planning scheme. A decentralized framework that relies on a generalized Nash equilibrium problem (GNEP) is considered in this paper, where several rival generation companies (Gencos) compete with each other to specify their own optimal decisions. Due to modeling the POZ and MFO in the GEP problem, integer variables are introduced, leading to a discretely constrained GNEP (DC-GNEP). Employing Karush–Kuhn–Tucker (KKT) optimality conditions, the DC-GNEP is recast as mixed-integer linear programming, which commercial branch-and-cut solvers can efficiently solve. Numerical experiments are performed on the IEEE 118-bus system to analyze and compare optimal GEP solutions. The numerical results point to the effectiveness of the proposed model considering POZ and MFO.

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Abbreviations

\(f\) :

Index for fuel types.

g :

Index for generators.

G :

Index for Gencos.

\(i, j\) :

Index for buses.

\(ij\) :

Index for transmission line connected to buses i and j.

\(z\) :

Index for operating zones.

\({\Omega }^{G},{\Omega }^{-G}\) :

Set of all Gencos and set of all Genco except Genco G.

\({\Omega }_{g}^{F}\) :

Set of fuel types used by generator g.

\({\Omega \mathrm{g}}_{i}^{e},{\Omega \mathrm{g}}_{i}^{c}\) :

Set of all existing and candidate generators connected to bus i.

\({\Omega \mathrm{g}}^{e},{\Omega \mathrm{g}}^{c}\) :

Set of all existing and candidate generators \(\left({\Omega \mathrm{g}}^{e}={\bigcup }_{i\in {\Omega }^{N}}{\Omega \mathrm{g}}_{i}^{e}\right)\) and \(\left({\Omega \mathrm{g}}^{c}={\bigcup }_{i\in {\Omega }^{N}}{\Omega \mathrm{g}}_{i}^{c}\right)\).

\({\Omega \mathrm{g}}_{G}^{e},{\Omega \mathrm{g}}_{G}^{c}\) :

Set of all existing and candidate generators belonging to Genco G.

\({\Omega }^{L}\) :

Set of all lines.

\({\Omega }^{N}\) :

Set of all nodes.

\({\Omega }_{gf}^{Z}\) :

Set of available operating zones when fuel type f of generator g is activated.

\(A_{i} ,B_{i} ,A,B\) :

Coefficients associated with demand functions.

\(a_{gf}^{e} ,b_{gf}^{e} \) :

Generation cost coefficients of existing generator g and fuel type f ($/MWh) and ($/h).

\(a_{gf}^{c} ,b_{gf}^{c} \) :

Generation cost coefficients of candidate generator g and fuel type f ($/MWh) and ($/h).

\(I_{g}^{{}}\) :

Investment cost of generator g ($/MWh).

\(M_{1} ,M_{2} ,M_{3} ,M_{g}\) :

Disjunctive parameters.

\(P_{\rm gfz}^{\rm Gmin} ,P_{\rm gfz}^{\rm G{\rm max}}\) :

Minimum and maximum generation of generator g while operating with fuel type f at zone z (MW).

\(PL_{ij}^{\rm {\rm max}}\) :

Thermal capacity of line ij (MW).

\(x_{ij}\) :

Reactance of line ij (per unit).

\({a}_{g}^{\prime},{b}_{g}^{\prime}\) :

Auxiliary continuous variables used to define the new cost coefficients of generator g ($/MWh) and ($/h).

\({PD}_{i}\) :

Electric demand at bus i in scenario s (MW).

\({\rm PG}_{g}^{e}, {\rm PG}_{g}^{c}\) :

Power production by existing/candidate generator g (MW).

\({\rm PG}_{\rm gfz}^{e},{\rm PG}_{\rm gfz}^{c}\) :

Power production by existing/candidate generator g while using fuel type f at zone z (MW).

\({\rm PG}_{g}^{c,{\rm max}}\) :

Capacity of generator g to be installed.

\({PL}_{ij}\) :

Power flow of line ij (MW).

\({\mathrm{Pr}}_{G}\) :

Profit of Genco G.

\({TG}^{G},{TG}^{-G}\) :

Total generation of Genco G and total generation of all Gencos except Genco G.

\({u}_{\rm gfz}^{e},{u}_{\rm gfz}^{c}\) :

Binary variable that is equal to 1 if existing/candidate generator g is operated with fuel type f at operating zone z.

\({y}_{g}\) :

Binary variable indicating the installation status of generator g. (If generator g is built \({y}_{g}=1\), otherwise \({y}_{g}=0\))

\(\lambda \) :

Electricity price ($/MWh).

\({\delta }_{i}\) :

Voltage angle at node i (rad).

\({\Pi }_{\rm gfz}^{e},{\Pi }_{\rm gfz}^{c}\) \({\Psi 1}_{g},{\Psi 2}_{\rm gfz},\) \({\Psi 3}_{\rm gfz}\) :

Continuous auxiliary variables introduced in the linearization process

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Acknowledgements

The authors extend their appreciation to King Saud University, Saudi Arabia for funding this work through Researchers Supporting Project Number (RSP2023R305), King Saud University, Riyadh, Saudi Arabia.

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  1. Statistics and Operations Research Department, College of Science, King Saud University, Riyadh, 11451, Kingdom of Saudi Arabia

    Ahmad M. Alshamrani, Adel F. Alrasheedi & Khalid A. Alnowibet

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  3. Khalid A. Alnowibet
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Contributions

AMA: Conceptualization, Visualization, Writing (Original draft preparation). AFA: Investigation, Methodology, Data curation, Software. KA: Supervision, Project administration, Writing (Editing). All authors reviewed the manuscript. Manuscript is approved by all authors who contributed to the study and design.

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Correspondence to Khalid A. Alnowibet.

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Alshamrani, A.M., Alrasheedi, A.F. & Alnowibet, K.A. Strategic generation expansion planning considering prohibited operating zones: a game-theoretic analysis. Electr Eng 105, 1747–1760 (2023). https://doi.org/10.1007/s00202-023-01757-y

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