Aspects Of Stability Analysis Research Articles

Qualitative analysis of two systems of nonlinear first‐order ordinary differential equations for biological systems

We consider two systems of nonlinear first‐order ordinary differential equations proposed to describe ‐levels in renal vascular smooth muscle cells and in liver cells. Initially, we present the models and its assumptions. We next investigate an approach to local solvability by Picard–Lindelöf 's Theorem. Further, we prove nonnegativity of the systems' possible solutions and we especially conclude global unique existence of the models' solutions by Gronwall‐type arguments and the concept of trapping regions. After finishing our theoretical part with some aspects of stability analysis, we provide evidence of our findings by some numerical experiments.

A survey on development and prospect of wind turbines virtual synchronous control technology

The ongoing energy revolution has led to the gradual replacement of traditional synchronous generators by renewable enecorresponding authorrgy. This transformation of power generation mode reshapes power system dynamics and poses many challenges to reliable and efficient grid operation. With the continuous improvement of the penetration level of renewable energy represented by wind power in the power system, the synchronous mode of wind turbine will gradually become one of the main modes of system synchronization. In the case of coexistence of multiple synchronization modes, the synchronization mechanism of the whole power system will be fundamentally changed; at the same time, due to the response characteristics of wind turbine to the frequency and voltage dynamics of power grid and the traditional power supply, the synchronous mode of wind turbine will gradually become one of the main modes of system synchronization The frequency and voltage stability of power system also faces new challenges. The virtual synchronous generation technology can make the grid connected inverter simulate the operation mechanism of step generator and provide an effective method to solve the above problems. In this paper, the main technical routes to realize virtual synchronous control of wind turbines are summarized. From the aspects of stability analysis, control system optimization, performance analysis and evaluation, the research and engineering status of virtual synchronization technology in wind turbines are introduced, and the problems to be solved and technical requirements are prospected.