Spectral Discretization Based Eigenvalue Computation Methods For Large Time Delayed Power System

The inter-area low frequency oscillation is the key factor which bottlenecks the capacity of long distance power transmission for large scale interconnected power system. The synchronous phasor measurement unit-based wide-area measurement system can sample the dynamic operating conditions of the whole grid in real-time, which therefore brings good chance for effectively damping inter-area low frequency oscillations in large scale power system. However, non-neglectable time delays are introduced during the transmission and process of wide-area measurements. Therefore, it is necessary to intensively study the time-delay impact on system stability, which is of great theoretical and practical significances for enhancing the security and stability of power systems.Aiming at large scale power system with multiple time delays, spectral discretization-based methods for computing critical eigenvalues of the system are studies in this thesis. The main work and some results of the thesis are addressed as follows.(1) The linearized mathematical model of the time delayed power system is established. Its eigenvalue computation problem is then raised and sparsities in augmented system matrices are finally analyzed. The mathematical model and its characteristic lay the basis of test and analysis of the performance of the spectral discretization-based critical eigenvalue computation method.(2) An explicit infinitesimal generator discretization method (EIGD) is proposed to calculate critical eigenvalues of large time delayed power system. Firstly, delay differential equations describing the time delayed power system is transformed to a homogeneous linear differential equations by using the infinitesimal generator. Secondly, according to pseudo-spectral discretization scheme of infinitesimal generator, the sparsity of the discretized approximate matrix and its explicit expression characteristic about system state matrix have been analyzed. Subsequently, critical techniques for applying EIGD to large time delayed power systems are presented, including the shift-invert transformation, sparse eigenvalue technique and Newton correction. Lastly, the accuracy, efficiency and scalability of EIGD are validated by the simulation results of the two-area four-machine test system and the real-life Shandong power system.(3) A solution operator discretization method under the linear multi-step scheme (SOD-LMS) is presented for calculating critical eigenvalues and determining the stability of large time delayed power system. Firstly, the unique spectral mapping property of solution operator is studied and the rationale behind SOD-LMS is analyzed in detail. Considering eigenvalues of the solution operator exponentially related to those of the time delayed power system, critical eigenvalues of the system with the largest real parts can be restored from those of the solution operator. Secondly, a highly sparse discretized approximate matrix of the solution operator is constructed under the linear multi-step discretization scheme. Thirdly, critical techniques for applying SOD-LMS to large time delayed power systems are presented, including axis-rotation, sparse eigenvalue techniques and Newton correction method. Lastly, the accuracy and scalability of SOD-LMS are investigated on the two-area four-machine test system and the real-life Shandong power system.The proposed EIGD and SOD-LMS methods for calculating critical eigenvalues of large scale power system build solid foundations for designing wide-area damping controllers while time delay impacts are considered. Future work will focus on studying discretized approximate matrices for spectral operators those are with better accuracies and in more concise forms so that both the accuracy and the efficiency of eigenvalue computation are achieved.