620IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 19, NO. 1, FEBRUARY 2004Unit Commitment by Enhanced Adaptive Lagrangian RelaxationWeerakorn Ongsakul, Member, IEEE, and Nit PetcharaksAbstract—This paper proposes an enhanced adaptive Lagrangian relaxation (ELR) for a unit commitment (UC) problem. ELR consists of adaptive LR (ALR) and heuristic search. The ALR algorithm is enhanced by new on/off decision criterion, new initialization of Lagrangian multipliers, unit classification, identical marginal unit decommitment, and adaptive adjustment of Lagrangian multipliers. After the ALR best feasible solution reached is obtained, the heuristic search consisting of unit substitution and unit decommitment is used to fine tune the solution. The proposed ELR is tested and compared to conventional Lagrangian relaxation (LR), genetic algorithm (GA), evolutionary programming (EP), Lagrangian relaxation and genetic algorithm (LRGA), and genetic algorithm based on unit characteristic classification (GAUC) on the systems with the number of generating units in the range of 10 to 100. ELR total system production costs are less expensive than the others especially for the large number of generating units. Furthermore, the computational times of ELR are much less than the others and increase linearly with the system size, which is favorable for large-scale implementation. Index Terms—Heuristic search, Lagrangian relaxation, unit commitment.NOMENCLATURE Cold startup cost of unit (in dollars). Current unit at hour . Value of the on/off decision criteria of unit at hour . Ramp down rate limit of unit (in megawatts per minute). Generator fuel cost function in a quadratic form. Average production cost of unit at hour , (in dollars per megawatt-hour). Full load average production cost of unit at hour , (in dollars per megawatt-hour).Manuscript received March 3, 2003. This work is supported in part by the Energy Conservation Promotion Fund under Contract 029/2545, Energy Policy and Planning Office of Thailand. W. Ongsakul is with Energy Field of Study, School of Environment, Resources and Development, Asian Institute of Technology, Pathumthani 12120, Thailand (e-mail: ongsakul@ait.ac.th). N. Petcharaks is with Energy Field of Study, School of Environment, Resources and Development, Asian Institute of Technology, Pathumthani 12120, Thailand, on leave from the Electrical Engineering Department, Dhurakijpundit University, Bangkok 10210, Thailand (e-mail: nitp@dpu.ac.th). Digital Object Identifier 10.1109/TPWRS.2003.820707 0885-8950/04$20.00 © 2004 IEEERelative duality gap at iteration . th local peak load hour. Hot startup cost of unit (in dollars). Best total economic dispatch production cost reached (in dollars). Total economic dispatch production cost at iteration (in dollars). ALR iteration counter. Maximum allowable number of iterations. Total number of generator units. Number of major load peaks over the scheduled time horizon. Highest possible power output of unit at hour (in megawatts). Lowest possible power output of unit at hour (in megawatts). Minimum real power generation of unit (in megawatts). Maximum real power generation of unit (in megawatts). Generation output power of unit at hour (in megawatts). Economic dispatch generation output of unit at hour (in megawatts). Load demand at hour (in megawatts). Unit reserve contribution at hour , (in megawatts). Spinning reserve at hour (in megawatts). Set of identical marginal units at hour . Startup ramp rate limit of unit (in megawatts). Set of committed units at hour sorted in the descending order of negative value of . Set of committed units at hour sorted . in the descending order of Set of uncommitted units at hour sorted in the ascending order of . Startup cost of unit at hour (in dollars). Total number of hours. Continuously on time of (in hours). Cold start hour unit (in hours). Minimum down time of unit (in hours).

ONGSAKUL AND PETCHARAKS: UNIT COMMITMENT BY ENHANCED ADAPTIVE LAGRANGIAN RELAXATION621,,Continuously off time of unit (in hours). Continuously on time of unit (in hours). Minimum uptime of unit (in hours). Status of unit at hour ( , ). Best feasible solution reached. Solution at iteration . Ramp up rate limit of unit (in megawatts per minute). Duality gap tolerance. Reserve response time frame (i.e., 10–15 min). Initial Lagrangian multipliers at hour (in dollars per megawatt hour, dollars per megawatt). Lagrangian multipliers at hour at iteration (in dollars per megawatt hour, dollars per megawatt). Initial Lagrangian multiplier of unit at hour (in dollars per megawatt). I. INTRODUCTIONUNIT COMMITMENT (UC) is used to schedule the generators such that the total system production cost over the scheduled time horizon is minimized under the spinning reserve and operational constraints of generator units. UC problem is a nonlinear, mixed integer combinatorial optimization problem. The global optimal solution can be obtained by complete enumeration, which is not applicable to large power systems due to its excessive computational time requirements [1]. Lagrangian relaxation (LR) for UC problem [2]–[5] was superior to dynamic programming [6] due to its higher solution quality and faster computational time. However, numerical convergence and solution quality of LR are not satisfactory in the presence of identical heat rate units since they will be committed as a group on a pro-rata basis, apportioning dispatched power to their megawatt quantity [7]. Therefore, there was an attempt to differentiate identical units by slightly adjusting the heat rate of the identical units [3]. However, adjusting the heat rate may not be justified due to contractual agreement of energy payment between generator companies and a utility in a single buyer model. In [4], they combined LR, sequential unit commitment (SUC) based on the least reserve cost index and unit decommitment (UD) based on the highest average spinning reserve cost index. However, this …… 此处隐藏：35940字，全部文档内容请下载后查看。喜欢就下载吧 ……