Digital Non-Interleaved High-Power Totem Pole PFC Based on Double Integral Sliding Mode

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1 This article has been accepted and published on J-STAGE in advance of copyediting. Content is final as presented. IEICE Electronics Express, Vol.* No.*,*-* Digital Non-Interleaved High-Power Totem Pole PFC Based on Double Integral Sliding Mode Fei Gao, Yongjian Feng a) School of Aerospace Engineering, Xiamen University Xiamen 36005, China School of mechanical and electrical engineering, Guizhou Normal University Guiyang 55005, China a) Abstract: A PFC circuit for applications higher than kw is generally configured by an interleaved structure, which reduces component stress and the ripple of inductor currents and output ltage. However, when implemented with GaN HEMT and controlled by a double sliding mode, a high-power totem pole PFC could achieve better performance without an interleaved structure. Keywords: PFC, GaN HEMT, Totem pole, Double sliding mode. Classification: Power devices and circuits References IEICE 08 DOI: 0.587/elex Received February, 08 Accepted February 9, 08 Publicized March 7, 08 [] D. C. Hamill, J. H. B. Deane, and D. J. Jefferies, "Modeling of chaotic DC/DC converters by iterative nonlinear mappings, "IEEE Transactions on Power Electronics, l.7, pp. 5-36,99. [] V. Utkin, J. Guldner, and J. X. Shi, "Sliding Mode Control in Electromechanical Systems," ondon, U.K. Taylor and Francis,999. [3] B.Singh, V.Bist, "Improved power quality bridgeless CUK converter fed brushless dc motor drive for air conditioning system," IET Power Electron., l.6, no.5, pp , 03. [4] J.Yang, A.Faris, W.Zhang, "Small-signal model analysis and control design of a double-ended forward converter in discontinuous-capacitor-ltage mode," IET Power Electron., l.8, no.5, pp , 05. [5] S.Dian, X.Wen, X.Deng, et al. "Digital control of isolated CUK power factor correction converter under wide range of load variation," IET Power Electron., l.8, no., pp. 4 50,05. [6] B.Singh, V.Bist, B.Singh, et al."power factor correction in switched mode power supply for computers using canonical switching cell converter," IET Power Electron., l.8, no., pp , 05.

2 [7] M.Mahdavi, H.F. Fard, "Zero-ltage transition bridgeless single-ended primary inductance converter power factor correction rectifier," IET Power Electron., l.7, no.4, pp , 04. [8] M.Mahdavi, H.F. Fard, "Zero-current-transition bridgeless PFC without extra ltage and current stress," IEEE Trans. Ind. Electron., l.56, no.7,pp , 009. [9]. Balogh and R. Redl, "Power-factor correction with interleaved boost converters in continuous-inductor-current mode," in Proc. 8th Ann. IEEE Appl. Power Electron. Conf. Expo., pp , 993. [0] B. A. Miwa, "Interleaved conversion techniques for high density power supplies," Ph.D. dissertation, Massachusetts Institute of Technology. Dept.Elect. Eng. Comput. Sci., 99. [] B. A. Miwa, D. M. Otten, and M. F. Schlecht, "High efficiency power factor correction using interleaving techniques," in Proc. 7th Ann. IEEE Appl. Power Electron. Conf. Expo., pp , 99. [] R. Giral,. Martinez-Salamero, and S. Singer, "Interleaved converters operation based on CMC," IEEE Trans. Power Electron., l. 4, no. 4, pp , Jul [3] R. Giral,. Martinez-Salamero, R. eyva, and J. Maixe, "Sliding-mode control of interleaved boost converters," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., l. 47, no. 9, pp , Sep [4] Q. Huang, S.Q. Huang, "Review of GaN Totem-Pole Bridgeless PFC," CPSS Trans. Power Electronics and Applications, Vol., No. 3, Sep. 07. [5] S.C. Tan, Y. M. ai, C. K. Tse, and M. K. H. Cheung, "Adaptive feed-forward and feedback control schemes for sliding mode controlled power convert," IEEE Transactions on Power Electronics, l., no., pp.8-9,006. [6] S.C. Tan, Y. M. ai, C. K. Tse, and C.K. Wu," A Double-Integral Type of Indirect Sliding Mode Controllers for Power Converters," Proc. PESC, pp.77-83, 007. Introduction A linear small signal model is convenient for modeling and analysis; however, due to the hypothesis of a small signal, its accuracy is unsatisfactory when the PFC works over the entire load range of an operation and across the universal input ltage range. Moreover, the small signal model fails to present the stability characteristics of the whole work area of the PFC. According to [], a system whose stability is derived from a small signal model may be unstable. Sliding mode control, when applied in a variable structure control system featuring strong robustness and stability in the presence of parametric uncertainty [], is suitable for a nonlinear system such as a switch power supply. It should be mentioned that switch components of power supplies are incapable of achieving infinite switch frequency, so chattering is unaidable. To reduce the chattering, a high-switch frequency functions admirably. Compared with Si MOSFET, GaN HEMT's advantages can be summarized as a smaller driving loss, a smaller switching loss, a smaller reverse recovery loss and a smaller ltage oscillation, which yields high switch frequency without sacrificing efficiency. These characteristics make GaN HEMT suitable for applying to a totem

3 pole PFC controlled by a sliding mode. Researchers and engineers have made efforts to improve the performance of PFCs, primarily paying attention to high efficiency, high power density and total harmonic distortion (THD) [3]-[8] related to the power factor and EMI. The trend in PFC development is to apply fewer components while achieving better performance and satisfying the proposed requirements. Among all PFC topologies, totem pole PFC has the fewest components, which means the least conduction loss. However, before the industry application of GaN HEMT, totem pole PFC was hardly ever used in practice due to the unaidable drawbacks of Si MOSFET. The large switch loss and parasitic ringing derived from the reverse recovery effect of the body diode limits the application of totem pole PFC with Si MOSFET to low power levels and low frequency in either discontinuous conduction mode (DCM) or critical conduction mode (CRM) operation rather than to the high power levels and high frequency in hard switching CCR that are required by high-power PFC. Interleaved structure, which is usually applied to PFCs that are more than kw [9]-[], consists of two or more sets of boost converter cells, which operate in phase-shift mode. As a result, the superposition of current waveforms has lower ripple than each individual current waveform generated by a single boost converter cell. This technique reduces not only component stress and lume but also current ripple and EMI [], [3]; however, it also increases the number of components and the lume of PFC and reduces power density by adding one or more sets of boost converter cells. Nevertheless, totem pole PFC with GaN HEMT controlled by DSP can be made without interleaved structure, even when the power is as high as.4 kw, due to low EMI caused by the smaller ltage oscillation of GaN HEMT and the low current ripple caused by high switch frequency. Compared with traditional interleaved PFC with Si MOSFET, non-interleaved totem pole PFC with HEMT has better performance in such areas as efficiency, THD and power density. A.4-kW prototype was made to verify the theoretical analysis; the peak efficiency is 99.07% (50 khz), and the minimum values of THD are.8% (5 V) and.7% (30 V). In addition to high efficiency and low THD, totem pole PFC with GaN HEMT could achieve high power density; according to [4], 30 W per prototype. 3 inch has been obtained by a 3. kw. Design of Algorithm The transfer function of a boost converter working in continuous conduction mode (CCM) has zero points in the right half plane (RHPZ), which causes the dynamic response of the controlled system to be hysteretic, especially when controlled only by ltage. Current control is usually applied to improve the dynamic response of an RHPZ system. Although integral control could improve steady error, sliding mode with integral control could hardly ever do a satisfactory job in improving steady error [5], [6]. Usually, increasing the control order of a system contributes to improving steady error, so double integral items would be 3

4 introduced. The topology and algorithm of totem pole PFC are shown in Fig.. Q and Q are GaN HEMTs, and T and T are Si MOSFETs. Fig. Topology and Algorithm of Totem Pole PFC The analysis of the case in which vi 0 is similar to the analysis when vi 0 : when vi 0, we obtain the absolute value of i v, i. In this paper, we only analyze the case in which vi 0. When we have vi 0, T on, Q on, Q and off, then v vi and u ; with T on, Q off, Q on, then v vi, and u 0 v vi u.. So The controlled state variables are current error x ; ltage error x ; integral of current and ltage error x 3 ; and double integral of current and ltage error x 4 ; they are written as follows: x iref i x Vref x3 ( x x) x4 ( x x) () where iref K( Vref ), K vi / ViRMS, and v i and V irms are the absolute values of instantaneous value and RMS of input ltage, respectively. The sliding manifold is expressed as: S x x x x () Taking the derivatives of the variables in (), the result is: 4

5 K vi u x ic C x ic C (3) x3 ( K )( Vref ) i x4 [( K )( Vref ) i ] Assume S x x 3 x3 4 x4 0 (4) Then, the equivalent sliding control law u eq could be written as: u K i K ( V v ) K ( V v ) K [ K( V v ) eq C ref o 3 ref o ref o where i ] K [ K( V v ) i ] v 3 ref o i K ( K ), K, K C (5) To guarantee the existence of sliding state, lims 0 SS 0 should be satisfied; according (3) and (4), the existence condition is: where o( ss) K i K ( x x ) K x v v K ic (min) K( x(max) x(max) ) K3x3(max) vi (min) C(max) (min) (min) 3 3(min) o( ss) i(max) v is the steady output ltage and i C(max) and i C(min) are the maximum (6) value and the minimum value of a steady capacitor current. The value of vi (min) not 0 but 4.5 V; if the input ltage is less than 4.5 V, then the switch components shut off to aid calculation error, and the capacitor then supplies power to the load. The variables the steady current error, x(max) and x (min) are the maximum value and minimum value of value of the steady ltage error, and x3(max) x (max) and x (min) are the maximum value and minimum and x 3(min) are the maximum value and minimum value of the steady integral of ltage error and current error. The designed parameters must satisfy equation (6). The stability of a power converter controlled by double integral sliding could be achieved by guaranteeing that all the eigenvalues of the Jacobian matrix of the system have a negative real part. The stability condition could be derived by two steps: first, deduce the ideal sliding dynamics of the system; second, analyze the stability on its equilibrium [6]. According to the ltage of the inductor and the current of the capacitor of the is 5

6 system, the stability can be derived as: di vi u d i u C rc (7) The ideal sliding dynamics could be obtained by replacing u with u eq ; that is: di vi ueq (8) d i ueq C r C Assume an equilibrium point exists in the sliding manifold; then, stability equation (9) could be derived from (8) when di =0 and o dv =0: I Vo (9) V R i According to perturbation theory and referring to (5), (8) and (9), the small signal of ideal sliding dynamics could be linearized on the equilibrium point. Decomposing the signal into AC and DC (capital letters denote DC, lowercase letters with the superscript "~" denote AC), it could be derived as: ~ ~ ~ ~ d( I i ) ( Vi vi ) ( Vo ) d( Vo ) { K ~ C ( ) Vo ~ ~ K ( K )[ Vref ( Vo )] K ( I i ) K3 ( K )[ Vref ~ ~ ~ ( Vo )] K3 ( I i ) ( Vi vi )} ( 0) ~ ~ ~ d( Vo ) ( I i ) d( Vo ) { K ~ C K ( K )[ Vref C( Vo o ) v ~ ~ ~ ( Vo )] K ( I i ) K3 ( K )[ Vref ( Vo )] ~ ~ ~ ( Vo ) K3 ( I i ) ( Vi vi )} RC Ignoring the DC items of (0), the signal could be written as: 6

7 ~ ~ ~ ~ ~ d i a i a a3 i a4 ~ ~ ~ ~ ~ d o 3 a i a v a i a4 ~ () d( ) ~ ~ ~ ~ i a3 i a3 a33 i a34 ~ d( v ) ~ ~ ~ ~ o a4 i a4 a43 i a44 where K K KC ( K ) K K3 ( K ) K3 a ; a ; a3 ; a4 ; Vo ( K K ) Vo [ KC ( K ) K ] Vo K3 a ; a ; a3 ; CRVi CRVi RC CRVi Vo ( K ) K3 a4 ; CRVi a3 ; a3 0; a33 0; a34 0; a 0; a ; a 0; a 0; The characteristic equation derived from () and () is: where s a a a a 3 4 a s a a a s bs cs ds e s s b a a c aa aa a3 a4 d a a a a a a a a e a3a4 a4a (4) (3) ( ) According the Routh-Hurwitz law, the judgment condition of stability could be written as follows: 7

8 4 s c e 3 s b d s s s 0 bc d b bcd b e d bc d e e 0 (5) The inequalities b 0, bc d 0, satisfied to guarantee the stability of the sliding system. bcd b e d >0, and e 0 must be The duty cycle D could be determined by u eq plus a feedforward v / v ; the result is as follows: u +( vi / )= KiC K ( Vref ) K3 ( Vref ) v D= eq o K[ K( Vref ) i ] K3 [ K( Vref ) i ] (6) According to equation (6), the program of calculation of switch-on time could be written. v_ref,ic,il,vi,,k,k,k,k3 denote V ref, ic, i, vi,, K, K, K, K 3. In equation (6), could be set to, and the period is half of the switch period value of DSP. The program is as follows: i o v_err=v_ref-; i_err=k*v_err-il; sigma_v_err+=v_err; sigma_i_err+=i_err; duty_delta=(k*ic+k*(v_err+i_err)+k3*(sigma_v_err+sigma_i_err))/; duty=period+period*duty_delta; 3. Experiment and Results The prototype of totem pole PFC is shown in Fig.. 8

9 Fig. Prototype of Totem Pole PFC The waveforms of input ltage and input current at different input conditions are shown in Fig. 3; it can be concluded that the higher the input ltage and output power, the better the input current. When the input ltage is 30 V and the power is kw, the RMS and peak-to-peak values of the current are 8.77 A and 9. A; when the input ltage is 5 V and the power is kw, the RMS and peak-to-peak values of the current are 9.04 A and 3.4 A. (a) Vi=30 V, P= kw (b) Vi=5 V, P= kw Fig. 3 Waveforms of input ltage and input current The test results for efficiency and power loss are shown in Fig. 4. As the switch frequency increases, the efficiency decreases, and power loss increases accordingly. At different switch frequencies, the peak efficiencies are 99.07% (50 khz), 98.79% (00 khz) and 98.48% (50 khz). 9

10 Efficiency(%) Hz Efficiency 00Hz Efficiency 50Hz Efficiency 50Hz Power oss 00Hz Power oss 50Hz Power oss Power(W) Power oss(w) Fig. 4 Efficiency and Power oss As shown in Fig. 5, when the load is more than half, the THD is below 4% regardless of whether the input ltage is 5 V or 30 V, and the minimum values are.8% (5 V) and.7% (30 V), respectively. The test result of the current THD is good and meets the standard of IEC V 5V THD(%) Power(W) Fig.5 THD of 5V and 30V respectively Conducted emissions have also been measured for this prototype using a IN-5A ISN by Com-Power. The result, compared to EN550A and EN550B, is shown in Fig. 6. Test ltage and power are 30 V and 00 W, respectively, and and N are the output and input terminals of the EMI tester. 0

11 Fig. 6 EMI Test Result 4. Conclusions A.4kW digital non-interleaved totem pole PFC with GaN HEMT is illustrated in this paper. Due to proposed advantages of the sliding mode control and GaN HEMT, the high-power prototype achieves better performances, such as efficiency, power loss, THD and EMI, than the traditional interleaved PFC based on the linear control and MOSFET. This means not only better performances but also lower cost and smaller lume. The cost of the totem pole PFC with GaN HEMT is not higher than the dual bridgeless PFC with MOSFET, owing to the fewer components and the lower filtering cost. It should be noted that GaN HEMT performs better than MOSFET only when operating in CCM, the advantages are not obvious when operating in either CRM or DCM. Acknowledgments This work was supported by the Science and Technology Projects of Guizhou Province of China (Grant No. 04H7050)