A bilevel model for maintenance scheduling of power units including wind farms

  • Amir Naebi Toutounchi
  • SeyedJalal SeyedShenavaEmail author
  • Javier Contreras
  • Hossein Shayeghi
  • Seyed Saeid Taheri
  • Mahdi Nooshyar
Original Paper


This paper proposes a comprehensive bilevel model for the maintenance scheduling of power units including wind farms in a restructured environment. The maintenance-scheduling problem of generating companies (GENCOs) is constrained by technical and security constraints set by the independent system operator (ISO), who has the responsibility of operating the power system. To consider the impact of these constraints on the scheduling problem, we propose a bilevel approach with a strategic GENCO at the upper level and an ISO at the lower level. In the upper level, the scheduling problem considering the participation of wind farms is presented. The lower level, also called the ISO level, maximizes the social welfare with network security constraints. This bilevel problem is modeled as a mathematical program with equilibrium constraints (MPEC), which is then transformed into a mixed-integer linear problem through a linearization procedure. The resultant model is tested on the IEEE 24-Bus Reliability Test System considering various case studies to illustrate the effectiveness of the proposed model. The results show that the proposed model can properly schedule the outages under different strict conditions preserving system’s security.


Maintenance scheduling Bilevel model MPEC Wind farms 

List of symbols



Generator’s preventive maintenance scheduling


Independent system operator


Generation company


Mathematical program with equilibrium constraints


Mixed-integer linear program


Mixed-integer nonlinear problem




Bilevel programming problem


Locational marginal price

Indices and sets


Index for generating units


Index for demands


Index for generation blocks


Index for time


Index for demand blocks


Indices for buses


Set of lines between bus n-m


Index for the regions in the system


Set of generating units owned by producer p


Set of demands at bus n


Set of wind power units


Set of generating units at bus n


Set of generating units in region R



Reserve level at time period t


Offer bid of block b of generating unit i in period t ($/MWh)


Price bid of block c of demand j in period t ($/MWh)

\( g_{ibt}^{ {\mathrm{max}} } \)

Maximum capacity of block b of generating unit i in time period t (MW)

\( g_{i}^{ {\mathrm{max}} } \)

Maximum generation limit for unit i (MW)


Number of crew members to perform maintenance at time period t


Available number of crew members for generator maintenance at time t


Duration of maintenance for each generator


End maintenance time of each generator


Starting time of maintenance for each generator

\( {\text{NPM}}_{R}^{ {\mathrm{max}} } \)

Maximum number of power plants in maintenance allowed in region R


Number of power plants under maintenance activities in region R


Number of working hours needed for maintenance of unit i


Total number of working hours


Average percentage of the total number of hours in the time horizon for wind power plants


Working hours associated with wind power plant i in time period t


Maximum number of units simultaneously in maintenance


Not permitted maintenance plan in hour t


Susceptance of line mn



Binary variable that is equal to 1 if the generating unit is maintained during time period t and 0 otherwise


Voltage angle at bus n in time period t (rad)


Power produced by block b of generating unit i at time period t (MW)


Price (dual variable) at bus n in time period t ($/MW)


Power consumed by block c of demand j in time period t (MW)


Supplementary material

202_2019_796_MOESM1_ESM.xlsx (16 kb)
Supplementary material 1 (XLSX 16 kb)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical and Computer Engineering, Faculty of EngineeringUniversity of Mohaghegh ArdabiliArdabilIran
  2. 2.E.T.S. de Ingenieros IndustrialesUniversity of Castilla –La ManchaCiudad RealSpain

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