In this paper, a stochastic multiobjective framework is proposed for a day-ahead short-term Hydro Thermal Self-Scheduling (HTSS) problem for joint energy and reserve markets. An efficient linear formulations are introduced in this paper to deal with the nonlinearity of original problem due to the dynamic ramp rate limits, prohibited operating zones, operating services of thermal plants, multi-head power discharge characteristics of hydro generating units and spillage of reservoirs. Besides, system uncertainties including the generating units’ contingencies and price uncertainty are explicitly considered in the stochastic market clearing scheme. For the stochastic modeling of probable multiobjective optimization scenarios, a lattice Monte Carlo simulation has been adopted to have a better coverage of the system uncertainty spectrum. Consequently, the resulting multiobjective optimization scenarios should concurrently optimize competing objective functions including GENeration COmpany's (GENCO's) profit maximization and thermal units’ emission minimization. Accordingly, the ɛ-constraint method is used to solve the multiobjective optimization problem and generate the Pareto set. Then, a fuzzy satisfying method is employed to choose the most preferred solution among all Pareto optimal solutions. The performance of the presented method is verified in different case studies. The results obtained from ɛ-constraint method is compared with those reported by weighted sum method, evolutionary programming-based interactive Fuzzy satisfying method, differential evolution, quantum-behaved particle swarm optimization and hybrid multi-objective cultural algorithm, verifying the superiority of the proposed approach. thermal unit index hydro unit index time interval (hour) index. For instance, p(j,t,s) is the power output of hydro unit j at hour t in the sth scenario (MW) scenario index network area index probability of kth price level bilateral contract price ($/MWh) emission price ($/lbs) number of periods in the planning horizon shut-down cost of unit i ($) start-up cost of unit j ($) slope of block n of fuel cost curve of unit i ($/MWh) slope of the volume block n of the reservoir associated to unit j (m3/s/Hm3) slope of the block n of the performance curve k of unit j (MW/m3/s) slope of segment n in emission curve of unit i (lbs/MWh) coefficients of valve loading cost function generated emission by off-unit while providing non-spinning reserve (lbs) generated emission of n −1th upper limit in the emission curve of unit i (lbs) emission group (SO2orNO x ) emission quota (lbs) generation cost of n-1th upper limit in the fuel cost curve of unit i ($/h) forecasted natural water inflow of the reservoir associated to unit j (Hm3/h) number of performance curves number of prohibited operating zones number of blocks of the piecewise linearized start-up fuel function number of price levels number of scenario after scenario reduction number of areas in the network power capacity of bilateral contract (MW) probability of scenario s normalized probability of scenario s minimum and maximum power output of unit i (MW) minimum power output of unit j for performance curve n (MW) capacity of unit j (MW) lower limit of nth prohibited operating zone of unit i (MW) upper limit of n −1th prohibited operating zone of unit i (MW) minimum and maximum water discharge of unit j (m3/s) ramp down and ramp up limit for block n (MW) start-up and shut-down emission generated by unit i (lbs) start-up and shut-down ramp rate limit of unit i (MW/h) ramping down and ramping up limit of unit i (MW) minimum content of the reservoir associated to unit j (Hm3) maximum content of the reservoir j associated to nth performance curve (Hm3) generation of block n of fuel cost curve for unit i (MW) generation of block n of unit i for valve loading effect curve (MW) market price for energy, spinning and non-spinning reserve ($/MWh), respectively individual membership function (the degree of optimality) for the nth objective function in the rth Pareto optimal solution the weight factor of the nth objective function in the MMP problem total membership function of the rth Pareto optimal solution start-up cost of unit i ($) valve loading effect cost of unit i ($) fuel cost of unit i ($) main objective function (expected profit of GENCO) GENCO's total expected profit in dollars after arbitrage expected generated emission for each Pareto optimal solution (lbs) non-spinning reserve of thermal unit i in the spot market when unit is off and on, respectively (MW) non-spinning reserve of a hydro unit j in the spot market when unit is off and on, respectively (MW) power output of thermal unit i (MW) maximum power output of unit i (MW) power output of hydro unit j (MW) power for bid on the spot market (MW) profit of scenario s water discharge of hydro unit j and block n (m3/s) spinning reserve of a thermal unit i and hydro unit j in the spot market (MW), respectively water content of the reservoir associated with unit j (Hm3) 1 if thermal unit i is on 1 if hydro unit j is on 1 if unit i provide non-spinning reserve when unit is off. 1 if block n of fuel cost curve of unit i is selected 1 if volume of reservoir water is greater than v n (j) 1 if power output of unit i has exceeded block n of valve loading effect curve obtained from the roulette wheel mechanism in the scenario generation stage indicating whether kth price level in the sth scenario occurred ( w k , t , s P = 1 ) or not ( w k , t , s P = 0 ) status of the ith thermal and jth hydro unit obtained from LMCS in the scenario generation stage (forced outage state, i.e. W =0 or available, i.e. W =1). 1 if thermal unit i is started-up 1 if hydro unit j is started-up 1 if unit i is shut-down thermal units hydro units set of indices of blocks of piecewise linearized hydro unit performance curve the blocks of piecewise linearized thermal unit emission curve the periods of market time horizon T ={1, 2, …, NT} scenario 
Uncertainty management in multiobjective hydro-thermal self-scheduling under emission considerations