تحلیل ثبات با توجه به فاصله گذار برای مبدل های DC-DC PWM بر اساس روش تابع توصیف Stability Analysis with Considering the Transition Interval for PWM DC-DC Converters Based on Describing Function Method

I. INTRODUCTION As the most common and practical topology of the power converters, DC-DC converters have the advantages on simple structure, low cost and high conversion efficiency. DC-DC converters have been widely used in household appliances, electrical industries, aerospace and other fields [1-5]. Today, pulse width modulation (PWM) is widely adopted in DC-DC converters. In addition, the traditional linear modeling and stability analysis methods are usually used for DC-DC converters, such as the average state space method [6]. But as the rapid development of power electronic technologies, the requirements of power electronic systems or equipment on stability, reliability and electrical performance have become stricter and stricter. The traditional linear modeling and analysis methods more and more cannot satisfy these requirements due to the nonlinearity of power converters [7]. In recent decades, the nonlinear behaviors of the power converters have been gradually revealed [8, 9]. The application of nonlinear theories in the field of power electronics has become a hot topic and received wide attention both at home and abroad [10-14]. At present, the common nonlinear analysis methods include analytical method [15, 16], phase plane method [17], switch signal flow graph method [18, 19], describing function method [20, 21], etc. The analytical method solves the state-space averaged equations directly, which is suitable for the one or secondorder system. But, the analytical method is very complicated for the high order systems [22]. The phase plane method is a graphic analysis method, and it transforms the movement of the first or second order system to a trajectory about position and velocity in phase plane, which is intuitive but also disabled for the high order systems [23]. The switch signal flow graph method is a nonlinear graphical modeling method, by which, the switching process can be equivalent as two linear branches in turn-on or turn-off periods [18, 19]. But the dedicated graphic computer simulation software is needed for the analysis. The three methods mentioned above all use the concept of averaging for system modeling and analysis, which can neither reflect the frequency characteristic of the nonlinear link nor be used in high order system.