Recourse-based Stochastic Market Clearing Algorithm

  • Leena HeistreneEmail author
  • Poonam Mishra
  • Makarand Lokhande
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 608)


Solutions obtained from the deterministic market-clearing problem may be feasible only for those conditions when point forecasts of random variables such as load and renewable sources of energy are within a tight range of accuracy. Unfortunately, point forecasts of renewable sources of energy have a higher error percentage. Under such circumstances, dynamism associated with renewable sources such as wind must be formulated as stochastic formulations which would encompass feasible solutions for a broader spectrum of forecast possibilities. This paper describes stochastic formulation for market clearing using recourse method. This method gives twofold solutions—the first being day-ahead market schedules obtained as here-and-now variables while the second being reserves applicable for different scenarios of wind forecast obtained as wait-and-see variables. This recourse-based stochastic formulation is validated for modified 24-node IEEE reliability test system.


Stochastic market clearing Recourse method Renewable energy Here-and-now variables Wait-and-see variables 




Time period


Individual conventional power plant


Individual wind farm


Individual scenario


Individual load


Individual transmission line


Individual node/bus


Individual scenario


Total time period


Total number of conventional power plants

Total scenarios considered


Total wind farms


Total loads in the system


Total number of transmission lines in the system


Total number of generators on bus n


Total number of wind generators on bus n


Total number of transmission lines on bus n


Total number of load on bus n

Here-and-now and wait-and-see variables

\( C_{it}^{\text{su}} ,C_{it\omega }^{\text{su}} \)

Start-up cost of conventional generator i at time t

\( P_{it}^{g} ,P_{it\omega }^{g} \)

Power generated by conventional generator i at time t

\( R_{it}^{U} \)

Up reserve of conventional generator i at time t

\( R_{it}^{D} \)

Down reserve of conventional generator i at time t

\( R_{it}^{\text{NS}} \)

Non-spinning reserve of conventional generator i at time t

\( rG_{it\omega } \)

Additional power to be generated by conventional generator i at time t under scenario ω

\( P_{jt}^{\text{wind}} ,P_{jt\omega }^{\text{wind}} \)

Power generated by wind farm j at time t

\( S_{t\omega }^{\text{wind}} \)

Curtailment due to scenario ω in time t

\( U_{it} ,U_{it\omega } \)

Unit commitment status binary variable

\( f_{\omega } (n,r) \)

Transmission line flow between bus n and bus r

\( rG_{it\omega }^{U} \)

Up reserve for generator i at time t under scenario ω

\( rG_{it\omega }^{D} \)

Down reserve for generator i at time t under scenario ω


\( \lambda_{it} \)

Offer cost of conventional generator i at time t

\( \lambda_{it}^{\text{su}} \)

Cost for starting the conventional generator i at time t

\( \lambda_{it}^{\text{RU}} \)

Cost for up reserve of conventional generator i at time t

\( \lambda_{it}^{\text{RD}} \)

Cost for down reserve of conventional generator i at time t

\( \lambda_{it}^{\text{RNS}} \)

Cost for non-spinning reserve of conventional generator i at t

\( \pi_{\omega } \)

Probability of scenario ω

\( L_{kt} \)

Demand of load \( k \) at time t

\( P_{{{ \min },i}}^{g} \)

Minimum generation limit of generator i

\( P_{{{\max}, i}}^{g} \)

Maximum generation limit of generator i

\( R^{{{system}}} \)

System reserve


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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Leena Heistrene
    • 1
    Email author
  • Poonam Mishra
    • 1
  • Makarand Lokhande
    • 2
  1. 1.Pandit Deendayal Petroleum UniversityGandhinagarIndia
  2. 2.Visvesvaraya National Institute of TechnologyNagpurIndia

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