| The thermal electric is a major electric energy in our country, and the operation sitation of electric power industry published by China Electricity Council show that, by the end of August 2015, the coal-fired thermal units in our country account for 68.6% of the toal 6000 kw and above generation units capacity. Under the world consensus for reducing of energy consumption and pollutant emissions as well as developing positively the low-carbon economy, it has important theoretical and practical significance for the optimal operation of unit, that is, the units which have the minimum cost are kept on line, while some of the more expensive units are kept as standby.The unit commitment (UC) problem in power system is defined as determining the start-up and shut-down schedules of units, the output of units to meet the forecast load demand and spinning reserve as well as the other constraints over a scheduling period so that the total production cost is minimized. The UC problem is formulated as a large-scale mixed-integer nonlinear optimization problem in mathematics, which has a lot of 0-1 integer variables denoting the on or off states of units, and many continuous variables denoting the output of units. The UC problem is one of the most difficult optimization problems to be solved in power system, and it can be considered as two linked optimization problems:the unit scheduling problem and the economic dispatch problem. The unit scheduling problem is the 0-1 combinatorial optimization, and the economic dispatch problem is a non-linearly constrained optimization problem. The quick and efficient solving for the two linked optimization problems will directly affect the solving efficiency of the UC problem. On the one hand, this paper aims to study some efficient methods for solving the UC problem, which are based on the Benders decomposition method for solving the complex problems and cuts. On the other hand, the sequential quadratic programming that is SQP algorithm has been carried out in-depth, which is effective for solving nonlinear constrained optimization problem, and can be expected to provide numerical method from the perspective of mathematical method for the UC problem in power system.Firstly, the paper proposes respectively an improved relaxed Benders decomposition method and an accelerated generalized Benders decomposition method for solving the UC problem, which are based on the Benders decomposition method and cuts. Secondly, a cut-and-branch method is proposed for solving the UC problem, which is based on the branch-and-bound and cuts techniques for solving mixed integer programming as well as combing with the heuristic method. Finally, with the aim of exploring an algorithm with less amount of calculation and the same convergence property under some weaker assumptions, this paper puts forward a new and globally convergent norm-relaxed SQP algorithm for solving inequality constrained optimization problem. This thesis contains 7 chapters. Chapter 1 is the introduction, which elaborates the theory and practice significance of the research, reviews and sums up the solution methods for the UC problem, introduces the basic ideas and the research status of SQP algorithm. Chapter 2 discusses the basic problem and relative mathematical theory foundations used in this paper, which provide support for subsequent chapters in both the theory analysis and algorithm. Chapter 3 to Chapter 6 are devoted to the main works. The conclusions and the future works are discussed in Chapter 7. The main works and contributions are as follows:1) Based on Benders decomposition and cover inequalities, an improved relaxed Benders decomposition method is proposed for solving the UC problem. Taking using of the perspective cuts and linearization technique, the classical UC problem which only contains thermal units is formulated as an approximate mixed-integer linear programming model. Combining with the cover inequalities, an improved relaxed Benders decomposition method is proposed for solving mixed-integer programming with 0-1 integer variables. The improved relaxed Benders decomposition method is used to solve the classical UC problem. The simulation results for multiple systems of up to 1000 units and 24 hours show that the computational time of the proposed improved relaxed Benders decomposition method for solving the UC problem is reduced greatly, which is compared with the classical Benders decomposition method. The comparison result with other methods also illustrates that the proposed method is effective.2) An accelerated generalized Benders decomposition is proposed for solving the UC problem with CO2 emission, which is based on integer cuts and strengthening technique. By using of linearization technique, an approximate mixed integer quadratic model is presented for the corresponding UC problem. The simple but highly efficient integer cuts are proposed for the relevant UC problem, which are obtained by solving some auxiliary linear programming problems. The accelerated generalized Benders decomposition method which combines with integer cuts and strengthening technique is proposed for solving the UC problem, and the simulation results for six systems up to 100 units and 24 hours show that the proposed method is effective and stable.3) A cut-and-branch method is proposed for solving the UC problem with plug-in electric vehicle, which is based on cuts and branch-and-bound search as well as heuristic technique. Two classes of cuts are introduced in the proposed method, that is the integer cuts and the generalized flow cover inequalities (GFCIs) as well as the complementary class of GFCIs, which can give a tighter representation of the corresponding continuous relaxed problem for the UC problem. Furthermore, taking using of the heuristic technique and the solution of the continuous relaxed problem incorporating the proposed cuts can obtain a better feasible solution. Based on the two points, the proposed cut-and-branch method can reduce the numbers of nodes during the branch-and-bound search. In addition, the computational efficiency of famous commercial software CPLEX for solving UC problem is greatly improved with the proposed cuts adding. The simulation results for six systems with up to 100 units and 24 hours without the plug-in electric vehicles, and the one for the system with 10 units and 24 hours as well as 50000 plug-in electric vehicles show that the proposed method has nice convergence, which can find global optimal solution in theory.4) A new globally convergent norm-relaxed SQP method is proposed for solving non-linear inequality constrained optimization problem. In each iteration of the proposed algorithm, a feasible descent direction can be obtained by solving only one norm-relaxed quadratic programming sub-problem, and the the l∞ penalty function is used as the merit function. In addition, the proposed algorithm considers the maximal violated constraints function in line search. Because the proposed SQP algorithm uses a new penalty parameter updated formulation and a new search mode, it is globally convergent under some weak assumptions which have not the boundedness on any of the iterative sequences and linear independent. |
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