IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 24, NO. 4, NOVEMBER 2009 1841 Stochastic Multiobjective Market Clearing of Joint Energy and Reserves Auctions Ensuring Power System Security Nima Amjady, Member, IEEE, Jamshid Aghaei, and Heidar Ali Shayanfar Abstract—In this paper, a stochastic multiobjective framework is proposed for day-ahead joint market clearing. The proposed multiobjective framework can concurrently optimize competing objective functions including augmented generation offer cost and security indices (overload index, voltage drop index, and voltage stability margin). Besides, system uncertainties including generating units and branches contingencies and load uncertainty are explicitly considered in the stochastic market clearing scheme. The solution methodology consists of two stages, which firstly, employs roulette wheel mechanism and Monte Carlo simulation (MCS) for random adaptive 24-h scenario generation wherein the stochastic multiobjective market clearing procedure is converted into its respective deterministic equivalents (scenarios). In the second stage, for each deterministic scenario, a multiobjective mathematical programming (MMP) formulation based on the -constrained approach is implemented for provision of spinning reserve (SR) and nonspinning reserve (NSR) as well as energy. The MMP formulation of the market clearing process is optimized while meeting ac power flow constraints and expected interruption cost (EIC). The IEEE 24-bus Reliability Test System (RTS 24-bus) is used to demonstrate the performance of the proposed method. Index Terms—Joint market clearing, multiobjective mathemat- ical programming, stochastic optimization. NOMENCLATURE Indices of bus. Index of unit in each bus. Index of scenario. Index of time. Index for different load levels. Number of system buses. Number of units in th bus. Number of scenarios in each hour of the scenario generation stage after scenario reduction. Number of time intervals. Number of load levels. Probability of the th scenario up to time . Manuscript received August 25, 2008; revised March 18, 2009. First pub- lished October 16, 2009; current version published October 21, 2009. Paper no. TPWRS-00669-2008. N. Amjady is with the Department of Electrical Engineering, Semnan Uni- versity, Semnan, Iran (e-mail: amjady@tavanir.org.ir). J. Aghaei and H. A. Shayanfar are with the Center of Excellence for Power System Automation and Operation, Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran (e-mail: aghaei@iust.ac.ir; hashayanfar@yahoo.com). Digital Object Identifier 10.1109/TPWRS.2009.2030364 Probability of th load level at time . Binary variable obtained from the roulette wheel mechanism in the scenario generation stage indicating whether th load level in the th scenario is occurred or not at time . Forced outage rate of th unit in th bus. Forced outage rate of branch between th and th buses. Status of the th unit of th bus at time in the th scenario obtained from MCS in the scenario generation stage (forced outage state or available). Status of branch between th and th buses at time in the th scenario obtained from MCS in the scenario generation stage (forced outage state or available). A binary variable indicating that the th unit of th bus at time in the th scenario accepted or not in the energy market. Energy output of th unit in th bus at time in th scenario of the joint market. and Capacity assigned to up and down spinning reserves for the th unit of th bus at time in the th scenario, respectively. Capacity assigned to nonspinning reserve for the th unit of th bus at time in the th scenario. Bid price of the th unit of th bus at time for energy. and Bid price of the th unit of th bus at time for up and down spinning reserves, respectively. Bid price of the th unit of th bus at time for nonspinning reserve. Market clearing price of energy auction at time in the th scenario. Active load error of th bus at time in the th scenario. Reactive load error of th bus at time in the th scenario corresponding to assuming constant power factor. Active load shedding of th bus at time in the th scenario. Reactive load shedding of th bus at time in the th scenario corresponding to assuming constant power factor. 0885-8950/$26.00 © 2009 IEEE