Study On Subsynchronous Torsional Dynamics

With the implementation of the strategic plan of "transmission of electricity from the west to the east, exchange electricity between the south and the north, and the interconnection of power grids", the coal power bases have been commissioned one after another. They have commonly employed the turbine-generators with the unit capacity from 600 MW to 1000 MW. Series capacitive compensation measure has been widely used for enhancing the transmission capability of the corridors. The interactions of the high-capacity generator units and the large-scale grid, especially the series capacitive compensation transmission lines, readily lead to turbine-generator shaft torsional fatigue. Thus, subsynchronous torsional dynamics is an imperative problem for the implementation of the strategic plan and the security operation of large-scale interconnected power system and high-capacity units. In this dissertation, the modelling and analysis methodologies of subsynchronous torsional dynamics are studied, which is mainly composed of following parts.The three categories of parameter translations between measured parameters and equivalent circuit parameters for synchronous machines, including the classic parameter, the approximate accurate parameter and the iterative parameter translations, are given, and their drawbacks are revealed. The accurate translations are respectively established based on standstill-frequency-response tests and sudden short-circuit tests. The relations and differences between all kinds of the above mentioned parameter translations are clarified. The effect of parameter translations on torsional dynamics are analyzed by using the frequency-response characteristics for operational reactance and the eigenvalues method. The analysis results show that it is necessary to adopt the accurate translations for subsynchronous torsional dynamics analysis.The fifth-order dynamic equation for induction motors is derived in the dq-coordinates of synchronous machines. This equation can interface with the dynamic equations including the electromagnetic transients of electrical networks. Furthermore, the linear equations including fifth-order induction motors and constant impedance (Z), constant current (I), constant power (P) load models, are established for investigating subsynchronous torsional dynamics. Effects of different loads on the damping torsional modes are analyzed. The results show that the effect of loads on the damping of torsional modes can be neglected under the system with the very small equivalent impedance; the loads have the important effect on the damping of torsional modes under the system with the average equivalent impedance. The calculated damping of torsional modes can be overly optimistic without the consideration of load models under the average equivalent impedance.The linear solutions of torsional torques are derived based on the electromechanical coupling model, and then they are used to define mode shapes and mode contribution factors of torques, which directly relate the electromechanical system modes to shaft torsional dynamics. Thus, the analytical method is established for analyzing small-signal torsional dynamics. Additionally, all-mode shapes and torsional mode shapes are defined. The solutions of forced vibration model are developed under the same electrical torque for the electromechanical coupling model. By using the above analyses, the three questions are answered:whether the three models of "electromechanical coupling model", "free vibration model" and "forced vibration model" are equivalent or not, why there is large deviation between the calculated and measured values for mode shapes and natural torsional frequencies, how shaft torsional dynamics can be directly represented.Based on the modal series method, the second-order solutions of torsional torques are derived, and the nonlinearity modal indices and contributor factors of torques are defined to quantify the effects of nonlinear modal interactions on torsional dynamics. The analytical method is established for investigating nonlinear torsional dynamics directly from the physical concepts. Moreover, the principle of modal superposition is developed and it is used to establish a methodology for predicting transient torque amplification based on the second-order solutions of torques.Finally, the proposed modelling and analysis methodologies are used to investigate the torsional dynamics for an actual series compensation system with six turbine-generators from the China Grid. The numerical results shows that the parameter translations have the significant effect on the damping for the calculated torsional modes for the actual system; all kinds of parameter translations can not make sure that they are conservative for the calculated torsional modes. Additionally, there exist a lot of oscillation modes. The proposed analysis method for investigating the large (small) disturbance torsional dynamics can establish the direct relationships of the fundamental modes of the electromechanical system and the large (small) disturbance torsional dynamics, and it can provide the quantitative analysis for the large (small) disturbance torsional dynamics. These quantitative analyses can provide recommendations for the actual operation and lay the foundation for developing the measures for suppressing the subsynchronous shaft torsional dynamics problems. The advantages for employing the proposed modelling and analysis methodologies are shown in the actual systems.