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Design Criteria for Sepic and Cuk Converters as Power Factor Preregulators in Discontinuous Conduction Mode D.S.L. Simonetti, J. Sebastiin, F. S. dos Reis and J. Uceda * Division de Electronica - E.T.S.I. Industriales Universidad Politecnica de Madrid c/ Jose Gutierrez Abascal, 2 - 28006 - Madrid - Spain Phone: (0341) 4117517 FAX: (0341) 5645966 ABSTRACT There are two major approaches in implementing control circuits in PFP: the multiplier approach and the voltage-follower approach. The multiplier approach is used when the converter is operating in continuous conduction mode. In this case, there are two control loops: one, controls the output voltage; the other, controls the input current. To provide output voltage regulation, a multiplier circuit is used to control the amplitude of the sinusoidal current reference signal in accordance with the output voltage error (Figura 1.a). Power Factor Preregulators (PFP) have been used to improve input current waveform of off-line power supplies. There are two major approaches in implementing control circuits in PFP: the multiplier approach and the voltage-follower approach. The simplest one is the voltage-follower approach because the converter operates in discontinuous conduction mode (DCM), and only one loop control is required. SEPIC and CUK converters present a great advantage over boost and fly-back topologies in DCM: an input current with low harmonic content can be obtained by correctly choosing inductors L, and L, of the converter with a fixed operation frequency, as is demonstrated here. Also some discussion about the intermedium capacitor C, as well some advantages and disadvantages of the aplication is done. Simulation and experimental results support the approach. Therefore, SEPIC and CUK converters in DCM seem to be good choices to use as PFP. a) 1. INTRODUCTION Conventional off-line power supply usually include at its input a full-bridge rectifier and a large input filter capacitor, which produces a high level of harmonic distortion on the line and excesive peak input currents, leading to a bad power factor. Recently, this problem has been overcome by using a Power Factor Preregulator (PFP), which draws a sinusoidal-current at the input of converters [l-71. In general, boost, buck-boost (flyback), SEPIC or CUK converters can be used as PFP. In Table I, the advantages and disadvantages can be seen of each one. Despite its problems, the most popular topology used as PFP is the boost converter. Although, SEPIC and CUK converter present several important advantages to be used as PFP. I I I 1 Figure 1 . Control Circults in PFP (a) multiplier approach; (b) Voltage-follower approach In voltage-follower approach the converter operates in discontinuous conduction mode, where the on-time of the switched converter is controlled by the output voltage error signal (Figure 1.b). As the average value of the input inductor current in a switching period is determined by the input voltage, this current naturally fol~ows the sinusoidal line voltage waveform. The voltage-follower approach provides a simple control scheme, loop' requiring Only One Using boost or buck-boost converter as PFP in discontinuous conduction mode requires an input filter, C,, because a large Table 1. Characteristics of converters for PFP - Domingos S . L. Simonetti is a professor at the Departament of Electrical Engineering, Universidade Federal do Espinto Santo, Brazil. Femando S . dos Reis is a professor at the Department of Electronics, Pontificia Universidade Cat6lica do R.G.do Sul, Brazil. Both are perforaling their doctoral course at Universidad Politknica de Madrid with a scholarship from the Brazilian Agency CAPES. 283 0-7803-0582-5 /92$3.0001992 IEFE Authorized licensed use limited to: IEEE Xplore. Downloaded on April 12, 2009 at 15:40 from IEEE Xplore. Restrictions apply. v2 . harmonic content is present. Besides, when using boost converter in voltage-follower approach its input current is distorted . As shown in , SEPIC converter [lo] in discontinuous conduction mode (DCM) presents an input current with a "sinusoidal dc level", under constant duty cycle, not requiring input filter. This is because the discontinuity is present at the output, and not at input. In this paper, design criteria for applying SEPIC and CUK converter as PFP-voltage-follower approach will be studied, demonstrating their advantages. 'm1 = d2Vg rvg = K.r (8) Where i,, is the average input current in a switching period. Substituting equations (4), (5) and (7) in (8): d 2 Vglsino tl zln1 = 2 Kasin2 t 2. STUDY OF SEPIC AND CUK CONVERTERS IN DCM AS PFP . ~ R 2sinzot 2.1. SEPIC Converter The basic structure of the SEPIC converter with a transformer is shown in figure 2. Applying volt-second balance to the converter in DCM we obtain: Equation (9) shows that the SEPIC converter when operating in DCM as PFP and with constants switching frequency and duty cycle presents an averaged input current in a switching period proportional to the input voltage. Therefore, SEPIC converter is indicated to operate as PFP in "voltage follower approach". The duty cycle is obtained by : Where: (3) Where M is the voltage relation in DCM; d is the duty cycle (transistor on); d' is related to the time diode is on; and T, is the switching period. To operate in DCM, K, must verify [l 11: The input current, in a switching period, can be drawn as in K = (5) 2K, sin'ot IO - i _ t The load r "seen" by the converter is: r = - R 2sinzot (7) TS Considering unity power factor, we have the following power balance equation in a switching period (switching frequency is assumed much greater than line frequency): Pi, = Po,, . =) V*'lml = Figure 3. Input current (i,,) and iL,, in a switching period. Normally a PFP contains a rectifier at the input; therefore the design of a converter which allows I,, < 0 means distortion at the input current. From figure 3, writing the average current &,,: -P r 284 Authorized licensed use limited to: IEEE Xplore. Downloaded on April 12, 2009 at 15:40 from IEEE Xplore. Restrictions apply. To guarantee I, > 0 in the CUK converter: iml = Io + vsdTs (d + d') 2Ll d L, > - ndlsinotl -~ L 2 M nM From (9), (17) and (19) we can obtain the desired relation between average current and ripple current in a switching period: (3), (9) and (14) in (13): To guarantee I, > 0: L ' nL >z M The equation (16) is the limit condition that equation (9) is valid. The ripple current i, (figure 3) is: Using (3), (9) and (17), the desired relation between average current and ripple current in a switching period can be obtained: The same comment made to equation (18) is valid to equation (22). Using equations (6), (lo), (12) and (22) inductor L, and L, are designed for CUK converter as PFP in DCM. 2.3. Some comements about the intermedium capacitor C, In conventional CUK and SEPIC converters, the capacitor C, is assumed to have a constant voltage. When operating as PFP, the capacitor voltage has two constraints: to have a nearly constant value in a switching period; and follows the input voltage in a line period. Its value has a great influence in the input current waveform. The resonant frequency of C,, L, and must be much greater than line frequency, to avoid input current oscilations each half cycle. Besides, if the resonant frequency is near the switching frequency, the characteristic of good power factor is lost achieving distorted waveforms. As a general rule, we can use: As the relation of equation (18) is an inverse fuction of the duty cycle, some applications can require to calculate it for minimum load. Using equations (6), (IO), (12) and (18), we can design inductors L, and for SEPIC converter as PFP in DCM. where component values are referred to primary side and 2, = 2 ~ f . From (23) we can choose an initial value for capacitor C, and, by simulation, to adjust it to obtain a better response. 2.2. CUK Converter 2.4. Figure 4 shows the CUK converter with an isolation transformer . The operation in DCM without transformer can be seen in When operating with a little ripple, the current of input diodes and inductor L, are easily aproximated. To the input diodes: Some comments about other components ~31. Ll Ca Cll 12 Figure 4. CUK converter with an isolation transformer. Equations (1-2) and (4-14) are the same for SEPIC and CUK converter, as well as figure 3. For CUK converter, the equivalent inductance is: Le* = L, L2 n2L, + L~ To the inductor L,: 4% ZL,w = '8 (9). (14) and (19) in (13): The turn-on of the switch is with zero-current, but the turn-off Authorized licensed use limited to: IEEE Xplore. Downloaded on April 12, 2009 at 15:40 from IEEE Xplore. Restrictions apply. is dissipative. The maximum current and voltage are: Using K, = 0,05 and from equations (3), (6) and (10): = Vs- d = 0,632 v, + v, (31) At the turn-off of the switch spikes can be present. L, = 75 p H The output diode presents a dissipative turn-on, and non dissipative turn-off. The maximum value of current and voltage L, = 150pH are: From (23), choosing a resonant frequency about 5 KHz: C, = 4,7pF VD.3, = v, + v, = "Smax A simulation using Analog Workbench was performed for this situation. In figure 5.a the line current during a line cycle is shown, and in figure 5.b a detail at maximum current can be seen, demonstrating the operation at discontinuity limit. (33) The peak-to-peak current is high. The average current is: ............................................ ........................... Also the inductor L, presents a high peak-to-peak current value. Its maximum and minimum current values are: ............ .A..?&&.. (35) .......... .___ .......................... rms mi-142 3 . 2 4 a ....................................... a) 4 The equations were derived for non-isolated converters, and must be adapted if a transformer is used. Other values of current and voltage in the components can be obtained by simulation. 3. DESIGN EXAMPLE AND SIMULATION RESULTS I," As an example, a SEPIC converter with the following characteristics will be designed: v, = 50 sin 2aft V f = 50 Hz v = 1oov P o = l W W ( R = loon) fs = 50 KHz, T, = 20 ps n = l 3 Mal" . . . Figure 5. (a) Input current with limit condition of DCM; @) A detail. Another simulation is performed considering K, = 0,02. From (6) and (10): To operate in DCM, we must have (equation 12): L, = 20 pH d = 0,4 Using a relation of 0 , l in equation (18) (considering nominal load): 3.1. Analysis of inductors' influence First, will be used the limit condition (16): 286 Authorized licensed use limited to: IEEE Xplore. Downloaded on April 12, 2009 at 15:40 from IEEE Xplore. Restrictions apply. L, = 1 mH L, = 20,4 pH resonant frequency of 10 KHz, C, = 0,22 pF, and a distorted input current is obtained (figure 7.b) Choosing a resonant frequency about 2500 Hz: C, = 3,9 p F The input current is shown in figure 6.a, and a detail at maximum current is shown in figure 6.b, where can be seen the ripple obtained as well the operation in DCM. The good frequency spectrum can be seen in figure 6.c. The power factor obtained by simulation is > 0.99. 2 4/dl" a) I- I 11" h) I ' I J l ' 1 ~ 10 m [ ' 1 ~ 1 ' 1 ~ 15m 'I I ' ~I ~ ' I ' I ' I ~ I ' I ~ 20m 9 x AX?-: me A m I l -b-I Figure 7. Influence of capacitor C, (a) w , = 500 Hz, C , (b) w , = 10 KHz, C , = 0 2 2 pF = m ms = 100 pF; 4. EXPERIMENTAL RESULTS 1. 1. ..I. .... . ..... . .. . ...... . . 1 A/div . .. . , M l 4.11 .. . ~.. . . The situation simulated and shown in figure 6 was experimentally performed. As there are losses in the components, the duty cycle was adjusted to obtain nominal output voltage. Good results were achieved, as can be seen in figure 8, where input current and voltage (a), output voltage (b) and a detail of the operation in DCM (c) are shown. A . 5. CONCLUSIONS C) X 11Il1~ 100 Rx19: F r e o I I IIIII// I I I H I I I fit 50 H7 I 10K 1K Ilw at - 2 I lllllll KH, I I h = I I I 1 100K SEPIC and CUK converters operating in voltage-follower approach (discontinuous conduction mode) have advantages over other converters that are used as Power Factor Preregulators. By correctly choosing inductors L, and L, (considering the current ripple) and capacitor C, (considering frequencies involved in the converter), a line current with little harmonic content can be achieved, in steady-state. Comparing SEPIC and CUK converters with boost and fly-back converters in discontinuous conduction mode as PFP, a good current waveform is achieved without an input filter. In addition, comparing them with converters as PFP in continuous conduction mode, similar current waveform is obtained with only one control loop (operation in CCM requires two control loops). Some disadvantages can be found in the comparison. For example, a greater number of components, with a high peak-topeak current in the indutor L, and capacitor C,. Nevertheless, a HZ RI9 I KHL 3.2. Analysis of capacitor's influence In the simulations made above, a good choice of capacitor C, was made. Now, will be shown two other situations, both considering the second simulation performed. If we choose a resonant frequency of 500 Hz, we have C, = 100 pF. In figure 7.a the input current for this situation is shown, where the transitory response obtained can be seen. Choosing a 287 Authorized licensed use limited to: IEEE Xplore. Downloaded on April 12, 2009 at 15:40 from IEEE Xplore. Restrictions apply. I ' I ~ U __ - 1 [51 M. ALBACH, "An ac-to-dc Converter with Low Mains Current Distortion and Minimized Conducted Emissions", EPE 1989, pp. 457-460. 161 C. P. HENZE and N. MOHAN. "A Digitally Controlled ac-todc Power Conditioner that Draws Sinusoidal Input Current", IEEE PESC 1986. pp. 531-537.  C. A. CANESIN and I. BARBI, "A Unity Power Factor Multiple Isolated Outputs Switching Mode Power Supply Using a Single Switch", lEEE APEC 1991, pp. 430-436.  K. H. LIU and Y. L. LIN, "Current Waveform Distortion in Power Factor Correction Circuits Employing Discontinuous Mode Boost Converter", lEEE PESC 1989, pp. 825-829.  J . SEBASTIAN, J. UCEDA, J. A. COBOS, J. ARAU and F. ALDANA, "Improving Power Factor Correction in Distributed Power Supply Systems Using PWM and ZCS-QR SEPIC Topologies", lEEE PESC 1991, pp. 780-791. 20 V/di.v level 50 V f T f I [lo] R. P. MASSEY and E. C. SNYDER, "High Voltage Single-Ended DC-DC Converter", lEEE PESC 1977, pp. 156-159. [ll] J. SEBASTIAN, J. A. COBOS, P. GIL and J. UCEDA, "The Determination of the Boundaries between Continuous and Discontinuous Conduction Modes in PWM dc-todc Converters Used as Power Factor Preregulators", lEEE PESC 1992, pp. 1061 - 1070.  R.D. MIDDLEBROOK and S. CUK, "Isolation and Multiple Output Extensions of a New Optimum Topology Switching DCto-DC converter", IEEE PESC 1978, pp. 256-264. [I31 S. CUK, "Discontinuous Inductor Current Mode in the Optimum Topology Switching Converter", lEEE PESC 1978, pp. 105-123. I 1 f level 2 A i Figure 8. Experimental results (a) input current and voltage; (b) Output voltage; (c) A detail at maximum current. good design and implementation can overcome these problems. As shown by simulation and experimentation, the described approach to design inductors L,, and capacitor C,, in DCM, is valid. Besides, the input current obtained is of high quality. Therefore, SEPIC and CUK converters in DCM seem to be good choices to use as PFP. 6. REFERENCES M. J. KOCHER and R. L. STEIGERWALD, "An ac-to-dc Converter with High Quality Input Waveforms", lEEE Trans. 1. A., vol. IA-19, no 4, pp. 586-599, JulylAugust, 1983. L. H. DIXON, "High Power Factor Preregulators for Off-line Power Supplies", Unitrode Power Supply Design Seminar, pp. 6.1-6.16, 1988. I. BARBI and S.A.O. da SILVA, "Sinusoidal Line Current Rectification at Unity Power Factor with Boost Quasi-Resonant Converters", lEEE APEC 1993, pp. 553-562. C. ZHOV, R. B. RIDLEY and F. C. LEE, "Design and Analysis of a Histerestic Boost Power Factor Correction Circuit", lEEE PESC 19p0, pp. 800-807. 288 Authorized licensed use limited to: IEEE Xplore. Downloaded on April 12, 2009 at 15:40 from IEEE Xplore. Restrictions apply.