Nonlinear dynamic analysis and robust controller design for Francis hydraulic turbine regulating system with a straight-tube surge tank

A method is presented for determining the aeroelastic stability boundaries of a cascade with aerodynamic, inertial, and structural coupling between the bending and torsional degrees of freedom. A computer program has been written to systematically investigate the effect of this coupling on cascade stability over a wide range of design parameters. Results presented illustrate that the bending-torsion interaction has a pronounced effect on the cascade flutter boundary, despite no appreciable tendency toward frequency coalescence as flutter is approached. The analysis also indicates that bending flutter is possible even in the absence of finite mean lift.

Coupled bending-torsion flutter in cascades.

The sliding mode control for an airfoil system driven by harmonic and colored Gaussian noise excitations

Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.

Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect

A reduced three-degree-of-freedom model simulating the fluid-structure interactions (FSI) of the turbine blades and the oncoming air flows is proposed. The equations of motions consist of the coupling of bending and torsion of a blade as well as a van der Pol oscillation which represents the time-varying of the fluid. The 1:1 internal resonance of the system is analyzed with the multiple scale method, and the modulation equations are derived. The two-parameter bifurcation diagrams are computed. The effects of the system parameters, including the detuning parameter and the reduced frequency, on responses of the structure and fluid are investigated. Bifurcation curves are computed and the stability is determined by examining the eigenvalues of the Jacobian matrix. The results indicate that rich dynamic phenomena of the steady-state solutions including the saddle- node and Hopf bifurcations can occur under certain parameter conditions. The parameter region where the unstable solutions occur should be avoided to keep the safe operation of the blades. The analytical solutions are verified by the direct numerical simulations.

Gang Han

Papers

Nonlinear dynamic analysis of a single-machine infinite-bus power system

Flutter analysis of bending–torsion coupling of aero-engine compressor blade with assembled clearance