This paper shows how the Lagrange Relaxation dual optimization algorithm is incorporated in solving a thermal unit commitment problem. The Lagrange relaxation procedure solves the unit commitment problem by temporarily relaxing the coupling constraints and solving the problem as if they do not exist. The performance of this technique is tested by running the algorithm on MATLAB using a 10-unit system with a 24-hour load requirement data. The same problem is solved using Priority listing method on MATLAB and the results obtained are compared with the results obtained through the dual optimization algorithm to check the performance of the relaxation technique. Minimum up time, down time constraints and startup costs are considered in this case study. Ramp rate constraints and reserve capacity constraints are ignored and shut down cost is taken as zero.
Abstract-This paper shows how the total fuel cost generated by the distributed generating units of a microgrid is minimized by the application of unit commitment problem. The microgrid taken for case study consists of a wind power unit, a photovoltaic unit, a microturbine, a diesel generator and a battery bank. The unit commitment problem is solved using priority listing method. The priority is assigned on the basis of emissions released by each unit. The 24 hour forecasted power output of the renewable energy sources is subtracted from the given 24 hour load requirement and is not considered in the unit commitment problem. The fuel cost coefficients and generating constraints of the conventional units and the battery bank specifications are taken as data for solving the unit commitment problem. Minimum up time, minimum down time and startup costs of the conventional units are considered in this case study. Ramp rate constraints and reserve capacity constraints are ignored and shut down cost is taken as zero. Operating costs of the renewable units are taken as zero and the cost of energy delivered during battery discharge is considered as profit. The economic dispatch problem is solved using Quadratic Programming approach. Losses in the system are ignored while solving the economic dispatch problem. From the results obtained we can conclude that even if the unit commitment schedule generated may not be most economic, it still ensures an environment friendly operation by the microgrid.Index Terms-Microgrid, priority listing, quadratic programming, unit commitment problem. I. INTRODUCTIONThe unit commitment problem is generally applied in the field of power systems to find out the optimum generating schedule of the generating units to satisfy the load demand. The optimal scheduling of power is to be done in a way such that all constraints of the generating systems and the network are met. The unit commitment time period generally varies from one day to one week. It requires solving the unit commitment problem for each hour. Various optimization algorithms are applied in this problem to achieve the optimum power generation. The optimal fuel cost generated is calculated with the help of the power output obtained by the application of the optimization techniques.The technique used for solving the unit commitment problem mainly depends on the data that is available and the constraints in the problem. Sometimes the fuel cost function is quadratic or convex in nature and hence in such cases Priority Listing method or Lagrange method can be applied to solve the problem. However if the problem is non-convex, we need to use dynamic programming or other meta-heuristic Manuscript received November 30, 2014; revised April 23, 2015. The authors are with the Electrical Engineering Department, National Institute of Technology Kurukshetra, India (e-mail: vinodmraj1@gmail.com, s_chanana@rediffmail.com).approaches to solve the problem.In recent times, the traditional power system network is gradually transforming from a centralized...
This paper shows how the Lagrange Relaxation dual optimization algorithm is incorporated in solving a thermal unit commitment problem. The Lagrange relaxation procedure solves the unit commitment problem by temporarily relaxing the coupling constraints and solving the problem as if they do not exist. The performance of this technique is tested by running the algorithm on MATLAB using a 10-unit system with a 24-hour load requirement data. The same problem is solved using Priority listing method on MATLAB and the results obtained are compared with the results obtained through the dual optimization algorithm to check the performance of the relaxation technique. Minimum up time, down time constraints and startup costs are considered in this case study. Ramp rate constraints and reserve capacity constraints are ignored and shut down cost is taken as zero.
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