Dynamic Optimal Power Flow Problems With Unit Commitment

With the emergence of policies in saving energy, quantitative goal in reducing greenhouse gas emissions and innovation in power markets, market competition mechanism and measures have been introduced for many basic industries, including power, aviation and railway etc., to improve the energy efficiency. Under this background, it is important in theoretical and practical to study the operation and dispatch of power system for energy saving and environment protection.Based on the quickly interior point method in continuous domain and the lift-and-project in discrete domain, this thesis aims to study the optimal power flow, dynamic optimal power flow, unit commitment and dynamic optimal power flow with unit commitment in models and methods. A tight relaxation of a mixed integer programming feasible region can be gotten by using the relaxation of the feasible region, and the solutions of the tight relaxation problem are the good approximations of the solutions of the origin mixed integer programming. The tight relaxation of the mixed integer set can be constructed in high dimension space with lift-and-project. Interior point method is a polynomial time complexity algorithm for solving convex programming, and this method and many related algorithms have been widely used in power system. With the increasing in the size of problems and the demand for computing speed, parallel interior point methods have been introduced into power system computing.This thesis proposes a new quickly interior point method based on the techniques of optimal centering parameter and improved multiple centrality corrections, and the optimal power flow, dynamic optimal power flow problems all can be solved with this new method. Then, several tight mixed integer programming models for the unit commitment problems are presented by using lift-and-project, and the continuous relaxations of these proposed models can be solved to achieve the sub-optimal solutions for the unit commitment problems. At last, the complicated dynamic optimal power flow with unit commitment problems can be solved in3steps; all the important sub problems can be solved with the aforementioned method. This thesis contains8chapters as follows:In chapter1, the optimal power flow, dynamic optimal power flow, unit commitment and dynamic optimal power flow with unit commitment problems are discussed briefly at first. The necessity and importance of studying the dynamic optimal power flow problems with unit commitment problems are presented. Meanwhile, some methods, solving the aforementioned problems, are reviewed briefly for the following discussion. Theory and practice of interior point method are discussed in chapter2, and parallel interior point method has been shown too. In this chapter, the procedure of life-and-project has been explained and extended to mixed integer programming problem.In chapter3, a new quickly interior point algorithm was presented for solving optimal power flow problem based on the techniques of optimal centering parameter and improved multiple centrality corrections. The proposed method involves integrating equilibrium distance-quality function to establish a mathematical model for evaluating centering parameter, and the approximate expression of this model, which can be solved with fewer computations than the original one, was proposed using the linearization technique. After solving the approximate model with the line search technique, the optimal centering parameters can be obtained for the proposed method to own more dominant steps and less number of iterations than other interior point methods.Chapter4presents a new parallel algorithm to solve dynamic optimal power flow based on the methods of improved multiple centrality corrections and decoupling. A parallel decoupling-factorization-substitution method for the correction equation of dynamic optimal power flow was proposed by integrating interior point method framework and the block arrow correction equation, and then, the methods of dynamic increasing step length and adaptive corrections were given. A longer iteration step length and a better central point, which can be obtained by the proposed algorithm, give on the reduction in the number of iterations and savings in computing time than other interior point methods. Most of operations in proposed method can be processed in parallel with decoupling.In chapter5, a new tighter continuous relaxation model of the ramp rate constrained unit commitment problem is presented by integrating the techniques of convex hull transformation and lift-and-project cone relaxation. The proposed model can be solved directly to get the sub-optimal solutions of the unit commitment problem.In chapter6, a novel method for the ramp rate constrained unit commitment problem is presented by solving a sequence of increasingly tight continuous relaxations based on the techniques of convex hull transformation and lift-and-project tight relaxation. The proposed method provides excellent performance and sub-optimal solutions.A method with3steps based on proposed quickly interior point method and lift-and-project method for solving dynamic optimal power flow with unit commitment problem has been discussed in chapter7. The two continuous sub problems, feasible problem for dynamic optimal power flow and classic dynamic optimal power flow problem, can be solved using the parallel improved multiple center corrections interior point method, and the discrete sub problem can be solved with the lift-and-project method.The conclusions and remained questions are given in chapter8.