IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 27, NO. 1, FEBRUARY 2012 181 Optimal Self-Scheduling of Thermal Units During Commissioning Christos K. Simoglou, Student Member, IEEE, Pandelis N. Biskas, Member, IEEE, and Anastasios G. Bakirtzis, Senior Member, IEEE Abstract—This paper addresses the problem of the self-sched- uling of thermal generating units during commissioning. A 0/1 mixed-integer linear formulation is presented, which allows an accurate and realistic modeling for the scheduling of the com- missioning tests that should be performed once the construction of the thermal unit has been completed and prior to entering its commercial operation. A flexible contract between the producer and the contractor regarding the performing period of the com- missioning tests is proposed. The model presented can be used by a producer with thermal units in commissioning, who acts either as a price-taker or a price-maker in the day-ahead energy market. Test results on a medium-scale real test system address the effect that the implementation of the proposed model has on the producer profits as well as on the day-ahead market clearing prices. Index Terms—Commissioning tests, day-ahead energy market, mixed-integer linear programming, self-scheduling. NOMENCLATURE Index (set) of steps of the residual demand curve. Index (set) of steps of the marginal cost function of unit . Index (set) of thermal generating units in commissioning. Index (set) of commissioning tests of unit . Index (set) of unit start-up types , where : hot, : warm, and : cold start-up. Index (set) of intervals (steps) of test of unit . Index (set) of hours of the planning horizon. Forecasted price of energy in hour , in /MWh. Residual demand curve in hour , expressed as a stepwise monotonically non-increasing function that represents the market clearing price as a function of the producer quota . Price of step of the residual demand curve in hour in /MWh. Marginal cost of step of unit marginal cost function, in /MWh. Manuscript received October 07, 2010; revised March 31, 2011; accepted June 03, 2011. Date of publication July 05, 2011; date of current version January 20, 2012. This work was supported by the State Scholarships Foundation of Greece. Paper no. TPWRS-00803-2010. The authors are with the Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece (e-mail: chsi- moglou@ee.auth.gr; pbiskas@auth.gr; bakiana@eng.auth.gr). Digital Object Identifier 10.1109/TPWRS.2011.2159521 Total production cost of unit in hour at level , in . Size of step of the residual demand curve in hour , in MW. Summation of power blocks from step 1 to step of the residual demand curve in hour in MW . Portion of step of the residual demand curve that corresponds to the quantity accepted by the ISO in hour , in MW. Minimum down time of unit in h. Size of step of unit marginal cost function, in MW. Portion of step of the th unit’s marginal cost function loaded in hour , in MW. No-load cost of unit (for one hour operation), in . Power output of unit corresponding to the th interval (step) of commissioning test , in MW. Power output of unit scheduled in hour in the day-ahead energy auction, in MW. Shut-down cost of unit , in . Start-up cost of test of unit , in . Start-up cost of unit from type- standby, in . Time off-load before going into longer standby conditions ( : hot to warm, : hot to cold) of unit , in h. Duration of commissioning test of unit , in h. Binary variable which is equal to 1 if unit is committed during hour . Binary variable which is equal to 1 if unit is in test during hour . Binary variable which is equal to 1 if unit is started-up during hour . Binary variable which is equal to 1 if test of unit is initiated during hour . Binary variable which is equal to 1 if unit is shut-down during hour . Binary variable which is equal to 1 if test of unit is terminated during hour . Set defining the feasible operating region of unit . Vector of the continuous and the binary decision variables associated with the operation of unit during hour . 0885-8950/$26.00 © 2011 IEEE