Research On Decomposition Method For Solving Unit Commitment Problem

Unit commitment(UC)problem is an important economic dispatching problem in power system.Its mathematical model is a complex large-scale mixed integer nonlinear programming(MINLP)problem,and it is difficult to obtain the theoretical optimal solution.Therefore,it is of great practical significance to obtain high quality sub-optimal solution of UC problem within a reasonable computation time.In order to reduce the difficulty and complexity of UC problem,three decomposition methods are presented: alternating direction method of multipliers(ADMM),piecewise linear approximation(PLA)method and outer-inner approximation(OIA)method.1.An ADMM is presented for UC problem.According to the characteristics of UC problem,the method copies three groups of integer variables in UC problem to realize the block requirement of ADMM.Then the UC problem is decomposed into two easily solved subproblems which can be solved alternatively.As a result,the optimal solution of the UC problem can be approximated.Finally,numerical simulation is carried out,and the numerical results verify the effectiveness of the presented ADMM.2.A PLA method is presented for UC problem.In this method,the convex quadratic objective function of the UC problem is approximated by piecewise linear approximation.Based on the σ method and γ method of piecewise linear approximation,two PLAs of the UC problem are established,so that the UC problem is decomposed into an approximate mixed integer linear programming(MILP)and quadratic programming(QP).Finally,numerical simulation is carried out and compared with other methods.The results show that the presented PLA method can obtain high quality sub-optimal solutions of UC problems in less computational time.3.An OIA method is presented for UC problem.This method is based on linear inner approximation and outer approximation of convex quadratic objective function of UC problem,and obtains a MILP approximation based on outer-inner approximation of UC problem.Therefore,the UC problem is decomposed into a tighter constrained MILP and QP.Finally,numerical simulation is carried out and compared with other methods.The results show that the presented OIA method can obtain high quality sub-optimal solutions in less computational time.