### New Mixed Integer Linear Formulation

Added on - 21 Apr 2020

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AbstractThis sheet discuss new mixed-integer linear formulation for the unit commitment problem for thermalunits is presented in this paper. Fewer constraints and binary variables needed by the proposed formulationhelps in yielding helpful computational savings. The new formulation provides a background for modellingwhich permits a detailed explanation of time-dependent start-up cost and intertemporal constraints namely

minimum up and down times and ramping limits. The mentioned formulation, mixed-integer linearprogramming algorithm has been used commercially to solve the unit commitment problem effectively inlarge-scale cases.NOMENCLATUREConstantsAjFactor of the piecewise linear production cost function of jaj, bj, cj Coefficients of the startup cost function of unit j.ccj, bcj,tjcoldCoefficients of the startup cost function of unit jCjThe unit j shutdown cost.D(k) Demand of load in period kDTj Unit j minimum down timeFjBlock 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 itsminimum up time constraints.KtjInterval cost of the unit j stair wise startup cost function.LjUnit j figure of periods that needs to be offline as a result of the minimum down time constraints.NDjAmount of periods of unit j starwise startup cost function.NLjAmount of segments of the piecewise linear production cost function of unit jPjUnit j sizePjUnit j minimum power outputR(k) The spinning reserve needed by period kRDjUnit j ramp-down limitRUjUnit j ramp- up limitSj (O) Amount of period’s unit j stayed offline prior to the period of the time duration.SDjUnit j shutdown ramp limitSUjUnit j startup ramp limitT Number of periods of the time duration.UojAmount of time unit j has stayed online aforementioned to the firstly period of time duration.UTjUnit 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

cjuUnit j start up cost in period kPj,(k) Unit j power output in period k.I.INTRODUCTIONAccurate and efficient tools are needed in the new competitive environment power system to help insupporting decision for resource scheduling. Certain issues such as determining when to shut down or shutup generating units and dispatching online generators to attain the demand of the system has been solvedtraditionally in thermal unit commitment problem. The problems associated with scheduling of generation inthe recent market are solved by independent system operator (ISO) and these problems are identical to thoseof unit commitment in unified non-competitive. There is relevancy in the competitive power industry when itcomes to solving traditional and centralized unit commitment problems.The potential savings in operating cost has led to active research on mixed- integer, large scale, non-linear programming and combinatorial problem. Many techniques for example dynamic programming,heuristics, mixed-integer linear programming and Langrangian relaxation simulated annealing were enactedto solve the issue of savings in operating cost. As a result of solving large-scale problems, lagragrian is themost widely used technique among the mentioned techniques.The solving of unit commitment problem was the first action to be carried out by the Mixed-integerlinear programming (MILP and its assurances merging to be the best solution involving a few number ofsteps and giving out modelling framework which is accurate and flexible. Developing a branch-and-cutalgorithm which is an example of an effective example of mixed integer linear software has enhancedcommercial solvers with large-scale proficiencies. Its formation was grounded on binary variables which arethree sets correspondingly, the shutdown, and startup and on/off states for every time period and every unit.The paper's objective is to provide a substitute mixed- integer formulation for the thermal unitcommitment problem represented as MILP-UC. This model is also used in setting up problems incurred inplace dealing with electricity such as market-clearing procedure which is solved by ISO. Thus, MILP-UC isbeneficial to the market agents. This paper aims at solving realistic application through numerical experienceand formulation of MILP_UC demanding less binary variables and constraints to help in decreasing thecomputational problem of current MILP approaches.Models lacking quadratic features are referred to as mixed integer linear programming problems andthey are solved as a result of algorithm description. Mixed- integer linear program is a problem having;Bounds and linear constraints with exclusion of nonlinear constraints.Limiting some components to have integer values.Objective function in linearIntlinprog AlgorithmIt constitutes ofAlgorithm overviewLinear Program Pre-processingBranch and boundsCut GenerationLinear ProgrammingMixed- integer Program pre-processingHeuristics for Finding Feasible Solutions

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