Trajectory-based Stability Preserving Dimension Reduction Methodology And Its Application In Transient Stability Analysis Of Power System

The security of power system is of significant importance for social economy and culture while stability is the key for the system to run safely. Due to more and more strict confinements of the environment and zoology it becomes very difficult to build new generation and transmission units. So it's very important to make full use of the existing facilities. Besides the developments of power market and interconnection of large areas also make the equipments to run near the thermal limits. It increases the uncertain and insecure factors in system plan and operation. It brings more rigorous challenges to the intelligence and real-time ability of the stability evaluation algorithm. It also requires the algorithm to be more valid and robust.The bifurcation and chaos phenomena in power systems come from the intrinsic nonlinear and non-autonomous characters. They have important impacts in the static performance and security. The basic concepts of chaos and bifurcation are introduced in this paper and an overview of the researches in power system is given. Voltage instability has close relationships with various bifurcations and different generator and load models will result different bifurcation processes and instability mechanism. As a reliable statistical index to describe chaos Lyapunov exponent is applied extensively. The definition and algorithm are discussed in this paper. Only in the one-mass Hamiltonian system Lyapunov exponent equals to the eigenvalue. For Hamilton systems under small disturbance Melnikov method may be used to determine whether the chaotic motions will happen in the system. The applications of this method in power system is introduced and it is pointed out especially that for systems with two degrees of motion freedom and more than two degrees of motion freedom they will exhibit essentially different chaotic motions.The trajectory-based stability preserving dimension reduction (TSPDR) methodology is described in detail. Dynamics of an one-mass-spring Hamilton system under two different periodical excitations,Lorenz-like systems withadditional nonlinear terms,Rossler system and Lii&Chen system are analyzed with TSPDR as examples. When analyzing the bounded stability it is the well-known complementary cluster energy barrier criterion (CCEBC). In this paper the CCEBC is applied in the analysis of one-mass-spring system and the switches between the left and right centers in the Lorenz strange attractor. Quantitative indices are introduced and good results are got from sensitivity analyzing. When applied in the analysis of high-dimensional bifurcations and structural stabilities a series of coordinate plane projection (CPP) transformations are done firstly. Then investigate the property of the original system through these 2 dimensional time-varying linear subsystems. The fine structure and mechanism are explored with TSPDR. It is proved the chaotic motions are composed of continuous bifurcations in the subsystems.These research also approve some inherent phenomena in nonlinear systems such as the interleaving of stability region and instability region,the parameter sensibility of the instable modes,divergence after a relatively long time of chaotic swings (transient chaos),a cascade of period double bifurcations to chaos and etc. These phenomena are of great importance to both theoretical research and engineering practice.TSPDR is also used in the analysis of multi-swing instability in power system. The essential reason lies in the non-Hamiltonian character in the controlling image subsystem. In classical models the primary effect comes from the incoherence in complementary clusters. It reflects mainly in the non-periodical of the P-8 curve. To terminate integrations as early as possible we should predict the stability of the following movement with the known trajectories. The reason why characters in the frequency domains can't be used to determine the future stability is discussed. Based on EEAC a novel method is proposed for long term stability evaluation. The maximal changes...