Study On Tighter Outer Approximation And Outer-Inner Approximation Model And Approaches For Unit Commitment Problems And Optimization Problem QP-Free Algorithm

Under the background of developing positively the low-carbon economy all over the world, the reduction of the energy consumption is the most direct and important way to realize low-carbon economy. In recent years, the development of China's power industry is rapid, and the most part of the consumed electricity is from coal-fired power plants. Therefore, it has important realistic significance to study the dispatch of coal-fired power plants on the premise of ensuring the safe and stable operation of the power system and reliable power supply.This thesis aims to study the unit commitment (UC) problem in power systems. On the one hand, this paper aims to study some efficient methods for solving the large-scale, nonlinear unit commitment problems with many integer and continuous varibles. On the other hand, in the process of solving the unit commitment problems, it needs to solve its continuous relaxation problem which is a smooth nonlinear programming (NLP) problem. The QP-free algorithm for solving nonlinear programming problem has been carried out in-depth and meticulous research at the same time.Firstly, based on the review and summary of the application of the existing generation dispatching, the paper proposes a new convex separable model for the unit commitment problem, and the tighter outer approximation and outer-inner approximation approaches for this model. These two methods can effectively solve the nonlinear, nonsmooth, large-scale and multi-period unit commitment problem with mixed variables, and provide methods and means for achieving the energy-saving generation dispatching. Secondly, with the aim of searching an algorithm with a simple structure, less amount of calculation, fast convergence rate and better numerical performance for the nonlinear programming problems to be suitable for large-scale power system optimization problems, this paper put forward a new method of structuring system of linear equations and a new type of QP-free algorithm for optimization problem with inequality constraints. This thesis contains6chapters as follows:Chapter1presents the meaning of theory research and practice through the analysis of the requirements of the generation dispatching. This chaper reviews and sums up the status of solution methods of UC problem and around the QP-free algorithm for solving NLP problem around two main lines of the solution methods of UC problem and the smooth NLP problem, and extracts the key issues that still need to be studied and solved. The main research and expectations are described based on these. Chapter2discusses the mathematical theory foundations used in this paper. For the special convex separable model, this chapter gives a tighter outer approximation method and its algorithm steps, and elaborates the thought and basic principle of the outer-inner approximation method in detail and some theoretical basis of designing specific algorithm for smooth NLP problem. All of them provide support for subsequent chapters in both the theory analysis and algorithm.Chapter3presents a new convex separable model and a tighter outer approximation methodology which is a deterministic global optimization method based on it by studying the characteristics and mathematical models of UC problem. By decomposing a multivariate function into several univariate functions, a tighter mixed integer linear programming (MILP) master problem is obtained by several step outer approximation using subgradient inequalites of the separated univariate functions. The optimal solution of UC problem is approached by alternately solving the MILP master problems and the NLP subproblems.In chapter4, an outer-inner approximation approach is presented to solve UC problem by further reducing the relaxation gaps. This chapter gives an improved initial outer approximation subproblem and presents a new inner approximation MILP subproblem. A sequence of MILP outer approximation subproblem and.inner approximation subproblem are solved alternately to yield better lower bound and upper bound. Both the iteration gap and the solutions'quality have been improved by taking advantages of the effectiveness of inner and outer approximation subproblems. Some numerical simulations are carried out on the systems of up to300units with24h, and systems of up to100units with24?96h.In chapter5, a new feasible QP-free algorithm for solving the smooth nonlinear constrained optimization problems based on the perturbation for the gradients of the constraint functions is presented. It reserves all the advantages of previous algorithms, and there are some other interesting features of the algorithm. At each iteration, only three systems of linear equations with the same coefficient matrix need to be solved, which decreases largely the amount of computations. A feasible descent direction can be obtained by solving only one system of linear equations, while the previous algorithms need to solve one linear system to get a feasible direction and another one to obtain a descent direction, and an improving direction is obtained by doing a convex combination. The iteration points are all feasible without requiring to be strictly interior points. The exploratory line search is introduced to the algorithm, and the computational cost can be further reduced. The parameters in the proposed algorithm are few, and some numerical results for math test problems illustrate that the proposed algorithm is efficient and stable.Chapter6summarizes the main research work and achievements of this paper and points out the further research works in the future.