A New Approach to the Stability Analysis of Boost Power-Factor-Correction Circuits

Abstract

We analyze the stability of a boost power-factor-correction (PFC) circuit using a hybrid model. We consider two multi-loop controllers to control the power stage. For each closed-loop system, we treat two separate cases: one for which the switching frequency is approaching infinity and the other for which it is finite but large. Unlike all previous analyses, the analysis in this paper investigates the stability of the converter in the saturated and unsaturated regions of operation. Using concepts of discontinuous systems, we show that the global existence of a smooth hypersurface for the boost PFC circuit is not possible. Subsequently, we develop conditions for the local existence of each of the closed-loop systems using a Lyapunov function. In other words, we derive the conditions for which a trajectory will reach a smooth hypersurface. If the trajectories do not reach the sliding surface, then the system saturates. As such, the stability of the period-one orbit is lost. Using the conditions for existence and the concept of equivalent control, we show why, for the second closed-loop system, the onset of the fast-scale instability occurs when the inductor current approaches zero. For this system, we show that the onset of the fast-scale instability near zero-inductor current occurs for a lower line voltage. Besides, when the peak of the line voltage approaches the bus voltage, the fast-scale instability may occur not only at the peak but also when the inductor current approaches zero. We develop a condition which ensures that the saturated region does not have any stable orbits. As such, a solution that leaves the sliding surface (if existence fails) cannot stabilize in the saturated region. Finally, we extend the analysis to the case in which the converter operates with a finite but large switching frequency. As such, the system has two fundamental frequencies: the switching and line frequencies. Hence, the dynamics of the system evolve on a torus. We show two different approaches to obtaining a solution for the closed-loop system. For the second closed-loop system, using the controller gain for the current loop as a bifurcation parameter, we show (using a Poincaré map) the mechanism of the torus breakdown. If the mechanism of the torus breakdown is known, then, depending on the post-instability dynamics, a designer can optimize the design of the closed-loop converter.

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References

Alfayyoumi, M., Nayfeh, A.H., and Borojević, D., 1999, “Input filter interactions in dc-dc switching regulators,” in IEEE Power Electronics Specialists Conference pp. 926-932 .

Andreycak, B., 1997, “Advanced power factor correction control ICs,” Unitrode Inc., Design Note DN-44.

Chang, L.W., 1990, “A MIMO sliding control with a second order sliding condition.” in ASME WAM, Paper No 90-WA/DSC-5, Dallas, TX.

Elmali, H. and Olgac, N., 1992, “Robust output tracking control of nonlinear MIMO systems via sliding mode technique.” Automatica 28, 145-151 .

Erickson, R.W., Ćuk, S., and Middlebrook, R.D., 1982, “Large-signal modelling and analysis of switching regulators,” in IEEE Power Electronics Specialists Conference pp. 240-250 .

Filippov, A.F., 1988, Differential Equations with Discontinuous Righthand Sides, Kluwer, Dordrecht .

Hahn, W., 1963, Theory and Application of Liapunovs Direct Method, Prentice-Hall, Englewood Cliffs, NJ .

Henze, C.P. and Mohan, N., 1986, “A digitally controlled AC to DC power conditioner that draws sinusoidal input current,” in IEEE Power Electronics Specialists Conference pp 531-540 .

Huliehel, F.A., Lee, F.C., and Cho, B.H., 1992, “Small-signal modeling of the single-phase boost high factor converter with constant frequency control,” in IEEE Power Electronics Specialists Conference pp. 475-482 .

10.

Kaas-Petersen, C., 1986, “Computation of quasi-periodic solutions of forced dissipative systems,” Journal of Computational Physics 58, 395-408 .

11.

Khalil, H.K., 1995, Nonlinear Systems, 2nd edition, Prentice-Hall, Englewood Cliffs, NJ .

12.

Mazumder, S.K., Nayfeh, A.H., and Borojević, D., 2001, “A theoretical and experimental investigation of the fast- and slow-scale instabilities of a dc-dc converter.” in IEEE Transactions on Power Electronics 16, 201-216 .

13.

Mazumder, S.K., Nayfeh, A.H., and Borojević, D., 2002, “Robust control of parallel dc-dc buck converters by combining integral-variable-structure and multiple-sliding-surface control schemes,” IEEE Transactions on Power Electronics Vol. 17, no. 3, pp. 428-437 .

14.

Mohan, N., Undeland, T.M., and Ferraro, R.J., 1984, “Sinusoidal line current rectification ith a 100kHz B-SIT step-up converter,” in IEEE Power Electronics Specialists Conference pp. 92-98 .

15.

Nayfeh, A.H. and Balachandran, B., 1995, Applied Nonlinear Dynamics, Wiley, New York .

16.

Ridley, R.B., 1989, “Average small-signal analysis of the boost power factor correction circuit,” in Proceedings of the Virginia Power Electronics Seminar pp. 108-120 .

17.

Simonetti, D., Sebastiań J., Cobos, J.A., and Uceda, J., 1995, “The continuous-discontinuous conduction boundary of a boost PFP fed by universal input,” in CIEP pp. 20-24.

18.

Todd, P., 1999, “UC3854 controlled power factor correction circuit design,” Unitrode Inc., Application Note U-134.

19.

Utkin, V.I., 1992, Sliding Modes in Control Optimization, Springer-Verlag, New York .

20.

Wang, X., 1997, “Analytical methods of nonsynchronous response and bifurcation in nonlinear rotordynamics with applications,” Ph.D. Dissertation, Department of Mechanical Engineering, Texas A&M University, College Station, TX.

21.

Williams J.B., 1989, “Design of feedback loop in unity power factor ac to dc converter,” in IEEE Power Electronics Specialists Conference pp. 959-967 .

22.

Zhou, C. and Jovanović, M.M., 1992, “Design trade-offs in continuous current-mode controlled boost power factor correction circuits,” in Proceedings of the High-Frequency Power Conversion Conference pp. 209-220 .

23.

Zhou, C., Ridley, R.B., and Lee, F.C., 1990, “Design and analysis of a hysteretic boost power factor correction circuit,” in IEEE Power Electronics Specialists Conference pp. 800-807 .