minimum up and down times and ramping limits. The mentioned formulation, mixed-integer linear programming algorithm has been used commercially to solve the unit commitment problem effectively in large-scale cases. NOMENCLATURE Constants A j Factor of the piecewise linear production cost function of j aj, bj, cj Coefficients of the startup cost function of unit j.ccj, bcj,tjcold Coefficients of the startup cost function of unit jCj The unit j shutdown cost.D(k) Demand of load in period kDTj Unit j minimum down timeFj Block slope l of the piecewise linear production cost function of unit jGj This represents the number of period’s unit j that should be primarily online as a result of its minimum up time constraints. Ktj Interval cost of the unit j stair wise startup cost function. Lj Unit j figure of periods that needs to be offline as a result of the minimum down time constraints.NDj Amount of periods of unit j starwise startup cost function.NLj Amount of segments of the piecewise linear production cost function of unit jPj Unit j sizePj Unit j minimum power outputR(k) The spinning reserve needed by period kRDj Unit j ramp-down limitRUj Unit j ramp- up limitSj (O) Amount of period’s unit j stayed offline prior to the period of the time duration.SDj Unit j shutdown ramp limitSUj Unit j startup ramp limitT Number of periods of the time duration.Uoj Amount of time unit j has stayed online aforementioned to the firstly period of time duration.UTj Unit j minimum up timeVj (0) Unit j initial commitment stateVariablescjd (k) Unit j shutdown cost in period k.cjp (k) Unit j production cost in period k

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Unit Commitment Optimization with MILP

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