Studies On Theory And Arithmetic Of Unit Commitment

With the development of the national economy and the reform of enterprises, the scale and the operation mechanism of power systems are rapid developing every day. The degrees of areal and time difference between energy generation and consumption, the uncertainty and the difference between peak and valley load, the electricity market competition are all increasing which make the operation dispatch decision-makings ever more complicated. Against this background, the theory of power system operation and dispatch is facing challenge and must be improved to accommodate the situation. So it is of important theoretical and practical significance to make an in-depth study on the theory. The thesis, based on mathematical optimization theories and guided by power system operation and dispatch theory, performs meticulous and thorough work of research and practice. At the same time, the work summarized by the thesis is also the important content of the project entitled 'Rigid Optimization and Flexible Decision-making in Electrical Power System' and supported by National Natural Science Foundation of China. There are 8 chapters in the thesis. The first chapter is the introduction. Chapter 2 to chapter 7 are the main works based on the accumulated research and practice. Chapter 8 is the conclusion and future works. The main works and innovative achievements of the thesis are as follows:1. On the basis of expounding the difference between Largrangian multipliers in ED and the ones in UC and their mechanisms of action, a new method of modifying Largrangian multipliers in unit decommitment (UD) method is proposed to reduce the burden of numerous economic dispatch computations. The proposed method not only reduces the search range but also improves economical indices of units correspondingly. Thus the accuracy and calculation speed of the original method are evidently enhanced.2. The relation between unit commitment risk and unit forced outage capacity is discrete, which leads to a difficult combination with the Lagrangian relaxation method of unit commitment. Two kinds of curve fitting of the unit commitment risk are analyzed. They are the Gauss function fitting and exponential function fitting. The research shows that the results of Gauss function fitting are more accurate than those of the exponential function fitting. By incorporating the analytic expressed unit commitment risk constraints into the Lagrangian relaxation method of unit commitment, the probability reserve constrained unit commitment problem can be truly achieved and optimized.3. The security-constrained unit commitment problem is decomposed into two subproblems. The constraint expression of connection and coordination between them is built, by which an alternative algorithm is proposed. The two subproblems are the unit commitment problem without security constraints and the optimal power flow problem considering security constraints. Virtual variables are introduced into the latter to reflect the restriction and influence of the unit commitment to transmission elements. Hence complementary constraint conditions correlating the two subproblems are set up by the use of the virtual variables and generation shift factors. They form the influence mechanism that the former subproblem varies according to the latter one and the means to modify the optimizing direction. The proposed algorithm is sufficiently compatible to the present method but also conforms to the reality of the power system. Thus it is quite adaptive to solve the security restraint phenomenon of the unit commitment and to evaluate the results of unit commitment problems.4. Based on the traditional research on the unit commitment considering active power security constraints, the voltage and reactive power constraints are further introduced to build a relatively comprehensive model. Using Benders decomposition, the optimization problem is decomposed into a master problem and a subproblem and the corresponding iterative process is also proposed. The master problem solves unit commitment considering security constraints based on the DC power flow model, the subproblem is composed of a series of reactive power optimization problems. Benders cuts guided by the subproblem form the additional constraints correlating the master problem and the subproblem. With the proposed optimization mechanism, all kinds of present methods are applicable, and a flexible decision-making mechanism, from unit commitment without network constraints to one with active power security constraints and finally to one with voltage and reactive power constraints is set up. It is applicable to the large scale power system in practice as well.5. For the security economic dispatch problems considering generator ramp rate limits, a master-slave optimization model and iterative solving mechanism based on Dantzig-Wolfe decomposition are proposed. In the master problem, only time correlation constraints are considered with the solution areas determined by slave problems. Depending on the study periods, the slave problems are made up of some static optimization sub-problems. In order to decouple the time correlation constraints indirectly, the slave problems objective functions are modified with the Lagrangian multipliers corresponding to the optimal solution of the master problem. Based on the convergence conditions and examples of the iterative solutions, the detailed algorithm and special problem solutions are proposed. The proposed method can solve the kind of security economic dispatch problems considering time correlation constraints effectively and also has the prospect of large scale application in practice.6. Under the condition that the operation pattern of the power system is given (active power and reactive power are given), analyzing Jacobian matrix eigenstructure variation mode of the power flow finds that the eigenvector determined by the minimum eigenvalue is closely related to reactive power distribution. This is the basis of searching weak links of voltage support, network partition in secondary voltage control and also can be used to test whether the unit commitment result and the active power distribution are reasonable.