Abstract
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.
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Abbreviations
- t :
-
Time period
- i :
-
Individual conventional power plant
- j :
-
Individual wind farm
- sc:
-
Individual scenario
- k :
-
Individual load
- r :
-
Individual transmission line
- n :
-
Individual node/bus
- ω :
-
Individual scenario
- Nt :
-
Total time period
- Ng :
-
Total number of conventional power plants
- Nω :
-
Total scenarios considered
- Nj :
-
Total wind farms
- Nl :
-
Total loads in the system
- Nr :
-
Total number of transmission lines in the system
- Ng n :
-
Total number of generators on bus n
- Nw n :
-
Total number of wind generators on bus n
- Nr n :
-
Total number of transmission lines on bus n
- Nl n :
-
Total number of load on bus n
- \( C_{it}^{\text{su}} ,C_{it\omega }^{\text{su}} \) :
-
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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Heistrene, L., Mishra, P., Lokhande, M. (2020). Recourse-based Stochastic Market Clearing Algorithm. In: Mehta, A., Rawat, A., Chauhan, P. (eds) Advances in Electric Power and Energy Infrastructure. Lecture Notes in Electrical Engineering, vol 608. Springer, Singapore. https://doi.org/10.1007/978-981-15-0206-4_6
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DOI: https://doi.org/10.1007/978-981-15-0206-4_6
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