The Effect of Ripple Steering on Control Loop Stability for a CCM PFC Boost Converter

Transcription

1 The Effect of Ripple Steering on Control Loop Stability for a CCM PFC Boost Converter Fariborz Musavi, Murray Edington Department of Research, Engineering Delta-Q Technologies Corp. Burnaby, BC, Canada fmusavi@delta-q.com, medington@delta-q.com 1 Wilson Eberle, William G. Dunford Department of Electrical and Computer Engineering University of British Columbia 1 Okanagan Vancouver 1 Kelowna, BC, Canada Vancouver, BC, Canada 1 wilson.eberle@ubc.ca wgd@ece.ubc.ca Abstract In this paper, an average switch model approach to the power stage modeling, feedback compensation and dynamic analysis of PFC boost converters with coupled magnetic filter is presented. The model is expressed by derivation of power stage transfer functions for a conventional boost converter, and then followed by the power stage transfer functions for a PFC boost converter with coupled magnetic filter. Experimental and simulation results of a prototype boost converter converting universal AC input voltage to V DC at 1.8 kw are given to verify the proof of concept, and analytical work reported. The experimental results demonstrate that the model can correctly predict the steadystate and large signal dynamic behavior of a CCM PFC boost converter with coupled magnetic filter. I. INTRODUCTION Coupled magnetics filter techniques, known also as ripple steering techniques [1], have existed for many years, and have been applied to several topologies [, 3]. As shown in Figure 1, this technique replaces a series smoothing inductor with a pair of coupled inductors and a blocking capacitor. The circuit works by allowing the DC component of the input current to pass through the series winding, at the input, while the high frequency ripple component is filtered by steering it through the additional coupled inductor and capacitor combination. Figure 1. Smoothing transformer in a coupled filter. Ripple steering for PFC boost converters has been presented in [, 5]. Figure illustrates the modified PFC boost converter with a coupled inductor. The ripple-steering technique has several advantages in a PFC boost converter. Since it eliminates most of the differential-mode conducted noise, it enables the reduction in EMI filter size and complexity, especially in its differential filtering section, which includes Cx capacitors and differential mode inductors. Reducing the Cx capacitors to a minimal size has an additional benefit for applications with tight specifications on standby power consumption. Cx capacitors cause a considerable reactive current to flow through the filter, which is a source of additional and unwanted loss. Furthermore, with ripple steering, the discharge resistor that must be placed in parallel to Cx for safety reasons can be higher. As a result, both losses are minimized. With ripple steering, the control strategy for the PFC stage is similar to that of a conventional boost converter, but the power stage transfer functions are different. This paper proposes a model to verify the effect of the added coupled filter to the power stage transfer functions, which can be used to design the feedback loop compensation. Figure. Modified PFC boost converter with coupled inductors. II. AVERAGE SWITCH MODEL A Model for the PWM-switch was first introduced in [, 7]. It was then adopted for different converters in [8-1]. For the average switch model of a converter, the active and passive switches shown in Figure 3 are replaced with the PWM-switch equivalent circuits shown in Figures and 5. Figure 3. One active switch and one passive switch. This work has been sponsored and supported by Delta-Q Technologies Corporation.

2 Figure. PWM-Switch. Figure 7. Circuit of coupled inductors. () (5) () From above equations, Figure 7 can be replaced with its equivalent circuit shown in Figure 8 []. Figure 5. PWM-Switch with dependant voltage and current sources. Applying this model to a modified boost converter with coupled inductors, any of the transfer functions between the output variables (output voltage and inductor current) and the input variables (input voltage and duty ration) can be derived. Applying the PWM switch model results in the equivalent circuit shown in Figure, and by application of superposition and circuit theory, the power stage transfer functions can be derived:.. (1)..... () The low voltage loop cut off frequency of around 1 Hz is well below the L B C o resonant frequency (around 1 Hz), so the voltage loop transfer function can be approximated by:... (3) Figure 8. Equivalent circuit of coupled inductors. The equivalent circuit of coupled inductor can be modeled as: (7) (8) Figure 9. Modified boost converter with coupled inductors. Figure 9 shows the equivalent circuit of boost converter with a coupled inductor, where active and passive switches are replaced by the averaged model of PWM switch. By application of superposition and other circuit theory, the power stage transfer functions can be derived: Figure. Conventional boost converter with PWM switch. III. PWM SWITCH MODEL OF BOOST CONVERTER WITH COUPLED INDUCTOR In order to model the boost converter with coupled inductors, the winding arrangements shown in Figure 7 can be described mathematically by:..... (9) (1) (11)

3 The voltage loop transfer function approximation is also valid here, enabling (1) to be simplified as (3). Figure 1 shows the Bode plot of current loop transfer functions for the modified boost converter with coupled inductor and a conventional boost converter. 5 5 Conventional Boost Plant Transfer Function Modified Boost Plant Transfer Function Figure 1. Current loop plant Bode plots. L B = µh, C o = 1 µf, R L = 88 Ω, L dc = µh, L ac = µh, M = µh, C s = 1 µf The open loop bode plot is given in Figure 13. As it can be seen, at cross over frequency, the open loop has a phase margin of 5, providing for a stable design. 5 5 Controller Type II Plant Transfer Function Figure 11. Current loop plant and Compensator Type II Bode plots. L B = µh, C o = 1 µf, R L = 88 Ω, R = 11.5 kω, C =.7 nf and C 3 = 3 pf. 3 9 As it can be noted that the phase margins for both converters are the same and steady at -9. But, the main difference is at the crossover frequencies, where for the conventional boost it is significantly lower. If the same feedback compensation network were to be used for both converters, the steady state and large signal responses would be inadequate for the coupled inductor boost. IV. FEEDBACK COMPENSATION DESIGN The compensation is selected so that the open-loop transfer function achieves the following criteria: 1. A high gain at low frequency in order to compensate the steady state error.. A gain slope maintained at - db/dec around the crossover frequency in order to ensure enough phase margin and, therefore, closed-loop stability. 3. A very small gain at high frequency in order to reduce the influence of the switching harmonics and overall noise. A. Current Loop Compensation for the Conventional Boost Converter Figure 11 illustrates the current loop plant and a type II compensator Bode plots. The current loop power stage has a cross over frequency at 1 khz, so a type II compensator was chosen with a pole and zero, as shown in Figure 1. The compensator has a pole at zero frequency, and another pole at: f (1) R C C C C and one zero at: f (13) R C Figure 1. Type II compensator network. Compensated Current Loop Plant (Open Loop) Figure 13. Open loop Bode plot for current loop. L B = µh, C o = 1 µf, R L = 88 Ω, R = 11.5 kω, C =.7 nf and C 3 = 3 pf. B. Voltag Loop Compensation for the Conventional Boost Converter The voltage loop transfer function and compensator network Bode plot is given in Figure 1. The compensator 9

4 for the voltage is a type II compensator. In the compensator network, the voltage error amplifier gain is adjusted with compensation components to attenuate the double-line frequency ripple on the output capacitor to obtain the desired reduction of the 3rd harmonic THD. C 3 sets the reduction level, R sets the phase margin to 5 degrees at cross over frequency, and C sets the beginning of the phase boost. The desired cross over frequency for voltage loop is around 1 Hz, where the line frequency varies from 5 Hz to Hz Modified boost Plant Transfer Function Controller Type II Plant Transfer Function Controller Type II Figure 1. Current loop plant and compensator Bode plots for boost converter with coupled inductor. R L = 88 Ω, L dc = µh, L ac = µh, M = µh, C s = 1 µf, R =.1 kω, C = 1 nf and C3 = 15 pf Figure 1. Voltage loop plant and compensator type II Bode plots. L B = µh, C o = 1 µf, R L = 88 Ω, R = kω, C = 1 µf and C 3 = 1 nf. 1 8 Compensated Current Loop Plant (Open Loop) Compensated Current Loop Plant (Open Loop) Figure 17. Open loop plant Bode plot for boost converter with coupled inductor. R L = 88 Ω, L dc = µh, L ac = µh, M = µh, C s = 1 µf, R =.1 kω, C = 1 nf and C3 = 15 pf Figure 15. Open loop plant Bode plot for voltage loop. L B = µh, C o = 1 µf, R L = 88 Ω, R = kω, C = 1 µf and C 3 = 1 nf. Figure 15 shows the open loop Bode plot of compensated voltage loop. As it can be seen, it has a high gain at low frequencies, and at cross over frequency, the open loop has a phase margin of 55 which is a stable design. C. Current Loop Compensation for Boost Converter with Coupled Inductor Figure 1 shows the current loop plant and a type II compensator Bode plots. The current loop power stage has a cross over frequency at KHz. The open loop Bode plot is given in Figure 17. As it can be seen, at the cross over frequency, the open loop has a phase margin of 5 which is a stable design. D. Voltag Loop Compensation for Boost Converter with Coupled Inductor The voltage loop transfer function approximation is also valid here, so the voltage loop plant transfer function does not change with coupled inductor in a boost converter. As a result, the voltage loop compensation network is the same as in section B. V. SIMULATION RESULTS PSIM simulation was used to verify the feedback loop design for steady state and large signal perturbation. Figure 18 shows the simulation results of boost converter with coupled inductors, converting universal AC input voltage at V to a load at V DC and 1. kw. Figure 19 illustrates: Top: The boost inductor current in a conventional boost converter - No Filtering technique. Middle: The boost inductor current with ripple steering technique applied, and Bottom: Series capacitor current in the coupled inductor filter.

5 Figure shows a coupled inductor used. The inductor values are: L dc = uh, L ac = uh, M = uh and the series capacitor C s = 1 uf. Figure 18. PSIM simulation circuit for ripple steering technique applied to PFC boost converter I(M1_1) 1 Figure 1. Inductor current I dc ripple at 1 V input and 8 W output I(M1_) Figure 19. Inductor Current - No Filtering technique (Top) Ripple Steering Technique (Middle), Series cap current (Bottom). VI. EXPERIMENTAL RESULTS Prototypes of the boost converter with coupled inductors and conventional boost converter were built to verify the proof-of-concept and analytical work presented and to benchmark the proposed compensation network design. Figure. Inductor current I dc ripple at 1 V input and 8 W output - Figure 1 and Figure show the experimental and simulation ripple current waveforms in the dc inductor under the following operating conditions: V in = 1 V, I in = 15 A, P o = 8 W, V o = V and 7 khz. Figure 3 and Figure show the experimental current waveforms in the ac inductor under the same test condition. Figure. Coupled inductors used in experimental circuit. Figure and Figure show the experimental and simulation ripple current waveforms in the dc inductor under the following operating conditions: f sw = 7 khz, V in = V, I in = 15 A, P o = 1 W and V o = V.

6 Figure 3. Inductor current I ac at 1 V input and 8 W output - Figure. Inductor current I dc ripple at V input and 1 W output - ac Inductor Current Time (s) Figure. Inductor current I ac at 1 V input and 8 W output - Figure 7. Inductor current I ac at V input and 1 W output - Figure. Inductor current I dc ripple at V input and 1 W output - Figure 8. Inductor current I ac at V input and 1 W output -

7 Figure 7 and Figure 8 show the experimental and simulation low frequency current waveforms in the ac inductor under the following operating conditions: f sw = 7 khz, V in = V, I in = 15 A, P o = 1 W and V o = V. VII. CONCLUSIONS An averaged PWM model for boost converters with the ripple steering technique has been developed and the effect of ripple steering on the design of the current loop compensation network has been studied. Analytical and simulation results were compared with experimental results for a prototype converter circuit converting the universal AC input voltage to a load at V DC and 1. kw. The proposed model shows an accurate prediction of steady state and large transient behavior for the boost converter with coupled inductors. REFERENCES [1] D.C. Hamill ;P.T.Krein, "A `zero' ripple technique applicable to any DC converter " in IEEE Power Electronics Specialists Conference, PESC. vol., 1999, pp [] J.W. Kolar ; H. Sree ; N. Mohan ; F.C. Zach, "Novel aspects of an application of `zero'-ripple techniques to basic converter topologies " in Power Electronics Specialists Conference, PESC. vol. 1, 1997, pp [3] N.K. Poon ; J.C.P. Liu ; C.K. Tse ; M.H. Pong, "Techniques for input ripple current cancellation: classification and implementation," IEEE Transactions on Power Electronics, vol. 15, pp [] J. Wang ; W.G. Dunford ; K. Mauch, "Analysis of a ripple-free inputcurrent boost converter with discontinuous conduction characteristics " IEEE Transactions on Power Electronics, vol. 1, pp. 8-9, [5] E. Chou ; F. Chen; C. Adragna ; B. Lu, "Ripple steering AC-DC converters to minimize input filter " in IEEE Energy Conversion Congress and Exposition, ECCE, 9, pp [] V. Vorperian, "Simplified analysis of PWM converters using model of PWM switch, Part I: Continuous conduction mode " IEEE Transactions on Aerospace and Electronic Systems, vol., pp [7] V. Vorperian, "Simplified analysis of PWM converters using model of PWM switch, Part II: Discontinuous conduction mode," IEEE Transactions on Aerospace and Electronic Systems, vol., pp [8] F. Musavi ; K. Al-Haddad ; H.Y. Kanaan, "A large signal averaged modelling and control of paralleled DC/DC converters with automatic load sharing," in IEEE Applied Power Electronics Conference and Exposition, APEC. vol.,, pp [9] E. Van Dijk ; J.N. Spruijt ; D.M. O'Sullivan ; J.B. Klaassens, "PWMswitch modeling of DC-DC converters " IEEE Transactions on Power Electronics, vol. 1, pp [1] Y.W. Lu ; W. Zhang ; Yanfei Liu, "A large signal dynamic model for single-phase AC-to-DC converters with power factor correction " IEEE Power Electronics Specialists Conference, PESC, vol., pp ,. [11] Yan-Fei Liu ; P.C. Sen, "Large-signal modeling of hysteretic currentprogrammed converters " IEEE Transactions on Power Electronics, vol. 11, pp. 3-3, 199. [1] Byungcho Choi ; Sung-Soo Hong ; Hyokil Park, "Modeling and small-signal analysis of controlled on-time boost power-factorcorrection circuit " IEEE Transactions on Industrial Electronics, vol. 8, pp. 13-1, 1.