Stability analysis of nonlinear power electronics systems utilizing periodicity and introducing auxiliary state vector

Variable-structure piecewise-linear nonlinear dynamic feedback systems emerge frequently in power electronics. This paper is concerned with the stability analysis of these systems. Although it applies the usual well-known and widely used approach, namely, the eigenvalues of the Jacobian matrix of the Poincare/spl acute/ map function belonging to a fixed point of the system to ascertain the stability, this paper offers two contributions for simplification as well that utilize the periodicity of the structure or configuration sequence and apply an alternative simpler and faster method for the determination of the Jacobian matrix. The new method works with differences of state variables rather than derivatives of the Poincare/spl acute/ map function (PMF) and offers geometric interpretations for each step. The determination of the derivates of PMF is not needed. A key element is the introduction of the so-called auxiliary state vector for preserving the switching instant belonging to the periodic steady-state unchanged even after the small deviations of the system orbit around the fixed point. In addition, the application of the method is illustrated on a resonant dc-dc buck converter

Bifurcation Analysis with Applications to Power Electronics

The problem of sudden loss of stability (more precisely, sudden change of operating behaviour) is frequently encountered in power electronics. A classic example is the current-mode controlled dc/dc converter which suffers from unwanted subharmonic operations when some parameters are not properly chosen. For this problem, power electronics engineers have derived an effective solution approach, known as ramp compensation, which has become the industry standard for current-mode control of dc/dc converters. In this chapter, the problem is reexamined in the light of bifurcation analysis. It is shown that such an analysis allows convenient prediction of stability boundaries and facilitates the selection of parameter values to guarantee stable operation. It also permits new phenomena to be discovered. An example is given at the end of the chapter to illustrate how some bizarre operation in a power-factor-correction (PFC) converter can be systematically explained

Iu, “Bifurcation analysis of a powerfactor-correction boost converter: uncovering fast-scale instability

Bifurcation analysis is performed to a power-factor-correction (PFC) boost converter to examine the fast-scale instability problem. Computer simulations and analysis reveal the possibility of period-doubling for some intervals within the line cycle. The results allow convenient prediction of stability boundaries. Analytical equations and design curves are given to facilitate the selection of parameter values to guarantee stable operation. Index Terms — Bifurcation analysis, dc/dc converters, power factor correction

Stability analysis of a feedback controlled resonant dc-dc converter

This paper reports on the stability analysis of one member of a dual-channel resonant DC-DC converter family. The study is confined to the buck configuration in symmetrical operation. The output voltage of the converter is controlled by a closed loop applying constant-frequency pulsewidth modulation. The dynamic analysis reveals that a bifurcation cascade develops as a result of increasing the loop gain. The trajectory of the variable-structure piecewise-linear nonlinear system pierces through the Poincare plane at the fixed point in state space when the loop gain is small. For stability criterion the positions of the characteristic multipliers of the Jacobian matrix belonging to the Poincare map function defined around the fixed point located in the Poincare plane is applied. In addition to the stability analysis, a bifurcation diagram is developed showing the four possible states of the feedback loop: the periodic, the quasi-periodic, the subharmonic, and the chaotic states. Simulation and test results verify the theory

Scaling of unsteady magnetic convection boundary layer growth for Pr>1 fluids

The scaling to characterize unsteady boundary layer development for thermo-magnetic convection of paramagnetic fluids with the Prandtl number greater than one is developed. Under the consideration is a square cavity with initially quiescent isothermal fluid placed in microgravity condition (g = 0) and subject to a uniform, vertical gradient magnetic field. A distinct magnetic thermal-boundary layer is produced by sudden imposing of a higher temperature on the vertical sidewall and as an effect of magnetic body force generated on paramagnetic fluid. The transient flow behavior of the resulting boundary layer is shown to be described by three stages: the start-up stage, the transitional stage and the steady state. The scaling is\ud verified by numerical simulations with the magnetic momentum parameter m variation and the parameter γRa variation

Bifurcation in parallel-connected buck converters under current-mode control

This paper studies a system of parallel-connected dc/dc buck converters under current-mode control. The effects of variations of the reference current are studied. It has been observed that the system exhibits low-frequency bifurcation behaviour while period-doubling at switching frequency is suppressed. Extensive simulations are used to capture the behaviour. Time-domain waveforms, stroboscopic maps and trajectories are shown. The paper reveals the drastic alteration of bifurcation behaviour of dc/dc converters due to subtle coupling