Two sided PWM control of switching power factor correction ac-dc converter

M Mahesh* IEEE Student Member Prof. Anup Kumar Panda† Department of Electrical Engineering

National Institute of Technology Rourkela – 769008, Orissa, India

matadamahesh1@rediffmail.com* anuppanda64@gmail.com†

Abstract- A novel PWM technique in active power factor correction converter for power supplies with a 1-phase front end diode rectifier is proposed and analyzed. Regarding PFC converters as highly non-linear plants with inherence parameter uncertainties, the deleterious effects due to large disturbances in line voltage and load resistance are tackled by two sided latched PWM technique with sophisticated feedback control loops. Two sided latched PWM control approach which owns merits in both fast response and cost-effectiveness. The performance of the power factor correction converter for variable input voltage is observed by simulating in PSIM. The resulting input voltage and current waveforms show that design is successful.

Key words: Pulse Width Modulation (PWM), Power Factor Correction (PFC), Continuous Conduction Mode (CCM).

I. INTRODUCTION

The power factor correction techniques in switch-mode supplies have been improving, due to the increasing demand for improved power quality. In addition to unity power factor, fast response, high efficiency, high power density & size also are important. Many new topologies have been discussed in recent literature for achieving the required unity power factor. Most switching power supplies always use closed-loop negative feed-back systems with PWM technique to achieve objectives for line and load regulation. Most PWM controllers use a clock-edge to set one edge of the PWM signal and feed-back to set the other edge of the PWM signal. But, one edge available for control remains unused. This direct duty cycle control has disadvantages like slow response to sudden input changes, poor audio susceptibility and poor open loop line regulation [1]. In both current mode and voltage mode control [1-3] of PWM is restricted that it uses one of two edges available for control.

Controller with hysteresis based of power converters makes

use of both edges but the switching frequency is allowed to vary and control scheme is sensitive to commutation noises [4-7]. Variation in the switching frequency makes it difficult to filter the ripple components in the input and output waveforms of the converters [3]. Therefore, it is essential to have constant switching frequency to obtain unity power factor in power supplies to increase the efficiency of the electrical power grid and to meet the specifications of

Fig. 1 Two Sided Latched PWM Schematic for PFC ac-dc Converter. International standards. Employing two sided PWM to active PFC converter is not known to be present in the literature. [4-7, 10-15].

Saw-tooth ramp generator is required in PFC ac-dc

converters to stabilize fixed frequency PWM control. Many commercial PWM controller ICs are available with/without saw-tooth generator. ICs with a saw-tooth generator are limited in switching frequency and ICs that do not include the saw-tooth ramp generator are available that operate at much higher switching frequency. Still there exists a challenging task for power supply design engineers in generation of the high frequency saw-tooth ramp with the fast reset. Employing two sided PWM technique improves the dynamic response of the power factor correction circuit & it is most suitable for high frequency applications [7].

II. OPERATION OF TWO SIDED PWM:

The two sided latched PWM [8] proposed scheme for active PFC ac-dc converter is shown in figure1 which achieves modulation of both edges while maintaining fully latched operation. In this PWM scheme two comparators are used instead of one to set and to reset the switch. One comparator is used for the comparison between the feedback signal Sign and ramp to set the switch while another

comparison between an offset feed-back signal and ramp is used to reset the switch.

The ramp is not a saw-tooth, which is hard to generate at high frequencies, but a triangular ramp wave with equal rising and falling slopes is used to stabilize the duty ratio of the switch and to set the switching frequency. The ramp amplitude is chosen to meet the equal ramp slope criteria for optimal current mode control. Fig1 shows a sensor-less current mode control implementation, in an inner current mode control of active PFC ac-dc converter.

Fig 2 shows the timing diagram of the signals in this proposed PWM scheme for active PFC ac-dc converter. There is a triangular ramp with equal rising and falling slopes. This ramp is compared to the feedback signal with an appropriate offset. The resulting pulse width modulation signal is shown below. Note that the delay between consecutive rising and falling edges are Tsw. The ramp slope is chosen to be equal to the feedback signal at duty ratio of half. This is a design choice and depends on the nominal duty ratio.

III. TIME DOMAIN ANALYSIS:

A Assuming the continuous mode of operation and using the switch set and reset criteria, the following analysis is made [8, 9]. Fig 2 shows the timing diagram for the two sided PWM technique.

During the nth switching cycle, the crossing point of the signal+0.5 current feedback and rising ramp signals causes the switch transition to occur at time tsw = (2n+Dr(n))Tsw.

Therefore, the nominal duty ratio is given by Dn = Dr (n) +Dl (n). Where Dr (n) is the duty ratio provided from the control loop by rising ramp only in the nth cycle and Dl (n) is the duty ratio provided from the control loop by falling ramp in the nth cycle.

Fig 2 Timing Diagram

The magnitudes of two signals at transition are given by

Sign1 (tsw) = Dr (n) Tsw mramp Sign2 (tsw) = Dl (n) Tsw mramp Where mramp = V (pk) ramp/Tsw. (slope of ramp). The signal Sign is obtained as the integral of the difference of the Iref and the actual boost inductor current waveform. The gain of the integral is obtained using the equal slope criteria when the reference is the half the input voltage.

IV. Control Circuit Considerations

Generally, active power factor correction (APFC) systems

are designed at high frequency converters that are controlled by two feedback loops. Voltage loop is the outer loop which regulates the output voltage with slow-response and the inner loop that shapes the input current, is a much faster loop. Average current mode control method is employed to achieve high power factor. Bode plots of the transfer functions discussed below are obtained in MATLAB.

(a) Current Loop Compensator

Excellent references exist on current loop design [1, 10-12]. The objective of this loop is to track a reference waveform (Iref) whose frequency is twice the line frequency. The bandwidth of the current loop needs to be much greater than twice the line frequency. This reference signal has a high dv/dt around the zero crossings of the line. Therefore the loop needs gain at frequencies corresponding to the higher order Fourier coefficients needed to recreate the reference waveform. This implies high bandwidth for the current loop. In this case, a 10 kHz bandwidth is considered which is usually adequate. In order to design a compensator loop properly, the model of the converter is needed. A small signal model of the converter based on the PWM switch model is shown in Figure 3.

Fig. 3 Model of Boost Converter

The transfer function of the exact model of boost PFC is

. ..

. ω

ω . ω

-- (1)

ω2

,ω 1√

, 1

The simplified current loop transfer function is give by G s V .RSENSE

.L .VSE -- (2)

Where VSE is the triangular voltage peak to peak.

The Bode plot of (1) is plotted in Fig. 5 for high line and

low line input voltages. At higher frequencies the plot converges to the simplified model as shown in fig.5 (a). The simplified model approach is easier to use and is adequate to design the current loop. The exact model is shown to explain what is seen if one measures the loop.

(a)

(b)

Fig. 5 Gain & Phase Plots of Exact Model at high & low line voltages, Simplified Model & Current Error Amplifier. The current loop error amplifier is shown in fig 4 and its transfer function is

AV 1 SR C

sR CP CZ 1 R CP||C

Fig. 4 Current Loop error amplifier Its Bode plot is developed in MATLAB the same is shown

in Fig. 5.

(b) Voltage Loop Compensator: There are some trade-offs inherent in the voltage loop design that are particular to PFC applications. The fundamental requirement of power balance, on the line frequency time scale requires that the voltage loop’s bandwidth must be less than the half the line frequency. Otherwise, the voltage loop will distort the line current in order to regulate the output voltage. 10Hz is considered in this case. The proportional integrator is considered which suits for PFC applications. The feedback loop PI compensator is shown in below Fig. & its transfer function is Av.

Fig. 6 Gm amplifier configuration

||

---- (3)

V Design Criteria

The design criteria of PFC ac-dc converter follow those of the corresponding single-phase boost PFC’s operating in CCM. The only difference is in the way switch is driven by two sided PWM technique which results in the fast dynamic response compare to PWM technique. In the current loop controller, IMO (reference current) is obtained from multiplier whose equation is (4)

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feedback current & voltage loops are discussed. The whole system has been tested by means of simulation using Power-Sim Power Electronics & Drives simulation package. Even though the simulator restricted the implementation of the control law, the results are encouraging. Reduced Total Harmonic Distortion (THD) over the conventional boost converter is significant at low line. Better regulated dc voltage on constant power load is observed. Here the results are encouraging; there is indication that if a practical system is realized with the freedom of practical hardware, excellent results will be achieved.

REFERENCES [1] L H Dixon, “Closing the Feedback Loop”, in

Unitrode Power Supply Design Seminar Manual, pages C1-1 to C1-7, 1986.

[2] R B Ridley, “A new, Continuous-Time Model for Current-Mode Control, in IEEE Transactions on Power Electronics, Vol.6 pages 271-280, 1990. [3] Mohan, Undeland, Robbins, “Power Electronics Converters,

Applications & Design”, Third Edition, John Wiley & sons,, INC. [4] C Zhou, R B Ridley and F C Lee, “Design and Analysis of a

Hysteretic Boost Power factor Correction Circuit”, PESC Conf. Proc. , pages 800-807,1990.

[5] C A Canesin, I Barbi, “A Unity Power Factor Multiple Isolated Outputs Switching Mode Power Supply Using a single Switch”, APEC Conf. Proc., 1991, pages 430-436.

[6] Xu Yang and Zhaoan Wang, “Research on quasi-constant frequency hysteresis PWM current mode control”, Proceedings of the International Conference on Power electronics and Drive Systems, vol.2, pages 1124-1127, 1999.

[7] L Rossetto, G Spiazzi, P Tenti, “Control Techniques for Power Factor Correction Converters”, Department of Electrical egg, University of Padova, Padova – Italy.

[8] P Midya, K Haddad “Two sided Latched Pulse Width Modulation Control”, Power Electronics Specialists Conference, vol.2, pages 628-633, 2000.

[9] Midya P and Krein P T, “Closed-loop noise properties of pulse-width modulated power converters”, Proceedings of the Power Electronics Specialists Conference, vol 2, pages 1710-1716, 1995.

[10] A Abramovitch, S Ben-Yaakov, “Analysis and Design of the feedback and Feed forward Paths of Active Power Factor Correction Systems for minimum Input Current Distortion”, PESC, 1995.

[11] C Zhou, M M Jovanovic, “Design Trade-Offs in Continuous Current-Mode Controlled Boost Power Factor Correction Circuit”, High Frequency Power Conversion Conference, May-1992.

[12] James P, Noon and Dhaval D, “Practical Design Issues for PFC Circuits”, APEC-1997, vol 1, pages 51-58, 1997.

[13] P N Ekemezie, “Design of A Power Factor Correction AC-DC Converter”, AFRICON, IEEE – 2007.

[14] Yungtaek J, M M Jovanovic and David L D,”Soft-Switched PFC Boost Rectifier with Integrated ZVS Two-Switch Forward Converter”, IEEE Trans on Power Electronics, Vol.21, No. 6, Nov-2006.

[15] H M Suryawanshi, M R Ramteke K L Thakre and V B Borghate, “Unity-Power-Factor Operation of Three-Phase AC-DC Soft Switched Converter Based On Boost Active Clamp Topology in Modular Approach”, IEEE Trans on Power Electronics, Vol.23, No.1, Jan-2008.