Dynamic Stability Analysis of Size-Dependent Viscoelastic/Piezoelectric Nano-beam

This paper analyzes the dynamic stability of an isotropic viscoelastic Euler–Bernoulli nano-beam using piezoelectric materials. For this purpose, the size-dependent theory was used in the framework of the modified couple stress theory (MCST) for piezoelectric materials. In order to capture the geometrical nonlinearity, the von Karman strain displacement relation was applied. Hamilton’s principle was also employed to obtain the governing equations. Furthermore, the Galerkin method was used in order to convert the governing partial differential equations (PDEs) to a nonlinear second-order ordinary differential one. Dynamic stability analysis was performed and the effects of such parameters as viscoelastic coefficients, size effect, and piezoelectric coefficient were investigated. The results showed that in this system, saddle points, central points, Hopf bifurcation points, and fork bifurcation points could be created, and the phase portraits connecting these equilibrium points exhibit periodic orbits, heteroclinic orbits, and homoclinic orbits.

Robust Power Designing of Supplementary Damping Controller in VSC HVDC System to Improve Energy Conversion Efficiency of Wind Turbine and Power System Stability

Because of low losses and voltage drop, fast control of power, limitless connection distance, and isolation issues, using high-voltage direct-current (HVDC) transmission system is recommended to transfer power in the power systems, including wind farms. This paper aims to propose a supplementary damping controller (SDC) based on the HVDC to improve not only power system dynamic stability but also energy conversion efficiency and torsional vibration damping in the wind power plants (WPPs). When the WPPs are working in power control mode, the active power is set to its reference value, which is extracted from power-speed curve. This paper shows that torsional oscillations associated with the poorly torsional modes can be affected by different operating regions of the power-speed curve of WPP. Therefore, it is essential to employ an SDC to have the optimum energy conversion efficiency in the wind turbine and the most dynamic stability margin in the power system. The SDC is designed using a fractional-order PID controller (FOPID) based on the multiobjective bat-genetic algorithm (MOBGA). The simulation results show that the proposed control strategy effectively works in minimizing the torsional and electromechanical oscillations in power system and optimizing the energy conversion efficiency in the wind turbine.