SINGLE-phase PFC rectifier are widely employed in industry,

1 High Static Gain Single-phase PFC Based on a Hybrid Boost Converter Marcello C. Maccarini, Member, IEEE, Samir A. Mussa, Member, IEEE, and Ivo Barbi, Fellow, IEEE, Abstract In this paper a single-phase unity power factor rectifier, based on a hybrid boost converter, resulting from the integration of a conventional dc-dc boost converter and a switched capacitor voltage doubler, is proposed, analyzed, designed and tested in the laboratory. The high power rectifier is controlled by two feedback loops, with the same control strategy employed in the conventional boost based rectifier The average output dc voltage is regulated by a slow response outer loop, while a faster inner-current loop shapes the input current to maintain a high power factor at the input. The main feature of the proposed rectifier is its ability to output a dc voltage larger than the double of the peak value of the input line voltage, while subjecting the power switches the half of the dc bus voltage, what contributes to reduce cost and to increase efficiency and power density. Experimental data were obtained from a laboratory prototype with an input voltage of 220 Vrms, line frequency of 60 Hz, output voltage of 800 Vdc, load power of 1000 W, and switching frequency of 50 khz. The efficiency of the prototype, measured in the laboratory was 96.5% for full load and 97% for half load. Index Terms ac-dc converter, switched-capacitor, high static gain PFC, rectifier, PFC, boost. I. INTRODUCTION SINGLE-phase PFC rectifier are widely employed in industry, commercial and domestic equipment, being used generally in electronic devices that require a DC power supply. These converters, isolated and non-isolated, are well known and have been many research topics over the years [1] [4]. Among the several topologies existing for this purpose, the best known is the conventional boost PFC rectifier. The main advantages of boost PFC are robustness, reliability, simple control, the low current harmonic distortion and unity power factor. This converter is commonly used in universal power supplies for many applications. However, for applications where are necessary high static gain, this converter becomes inappropriate because the losses in the components limits the maximum static gain of the converter. Furthermore, the blocking voltage of semiconductors is the same of output voltage, thus for high output voltage, the semiconductors are subjected to high voltage stresses. Among some of the applications for PFC rectifiers with high gain are: x-ray devices for industry and medicine, HVDC system insulation testing, electrostatic precipitators, etc [5]. A converter studied for this purpose was developed by the Cockcroft-Walton voltage multiplier (CW-VM) [6]. This converter is already used for many years as rectifier, but in applications with very low current without power factor correction, as is shown in [5]. Some variations of CW-VM are presents in [7], [8], where these topologies have high voltage gain and power factor correction. Nevertheless, these topologies start getting complex by the high number of switches and control. For many years, the switched-capacitor (SC) converters have been a very important research. The main characteristic of SC converters is the absence of magnetic elements, thus being composed only of capacitors and switches, reducing the size compared to other converters. Another characteristic is the low voltage stress in semiconductors and their behavior is described by simple equivalent circuits [9], [10], this has contributed to the increase the research in SC converters. This type of converter has been widely used in applications of dc-dc converters not isolated, with high static gain [11] [14]. Nevertheless, recently [15], [16], started using switching capacitor principle to AC-AC static conversion, obtaining promising results for AC-AC application. In this paper, is proposed a new single-phase PFC rectifier topologies with sinusoidal input currents, controlled output voltage and high static gain based in known single-phase PFC rectifier and switched-capacitor (SC) converters. The others important characteristic of new converter are: reduction of voltages stress at switches - half of output voltage, and mainly the use of control techniques well known to provide unity power factor - including use of IC common in industrial applications. The principle of operation, quantitative analysis, control modeling, design example and experimental results of the new converter are reported herein. II. SINGLE-PHASE PFC HYBRID BOOST CONVERTER AND PRINCIPLE OF OPERATION A. Genesis of the Single-phase PFC Hybrid Boost Converter The Fig. 1 shows the single-phase PFC boost converter that has been applied in industry for many years and being heavily researched. This converter was presented firstly in [1], [2], the main characteristics are a unity power factor and low harmonic line current. The disadvantage of this converter is for applications that require high voltage gains, since the switches are subjected to the same output voltage and switches losses limit the maximum gain of the converter. A CC-CC hybrid boost converter is proposed in [17], [18] and the topology is presented in Fig. 2. In this topology, the gain of the output voltage is twice that in the conventional boost converter and the voltage across the switches is half of the output voltage. Further advantage is that the number of levels can be extended, increasing static gain without raise the losses in the switches. The proposed single-phase PFC hybrid boost converter is presented in Fig. 3, this converter is a combination from the conventional single-phase PFC boost converter and the CC-CC

2 Fig. 1: Single-phase PFC Boost Converter. Fig. 2: Single-phase Hybrid Boost Converter. hybrid boost converter. Thus, the main characteristics of each converter were maintained, as the high voltage gain and low loss switches, unity power factor and low harmonic distortion. Also, in this converter the number of levels can be extended. However, the loss also limits the maximum voltage gain as the PFC boost converter. B. Principle of Operation The principle of operation of the proposed converter is analyzed for high-frequency (switching frequency) and lowfrequency (frequency of the line voltage). The main characteristics and waveforms for both analysed are shown following. To the high-frequency operation, the proposed converter presents two operating stages per switching period. And the operation is the same for each half of the line voltage. As shown in [9], switched-capacitor converters can be operate in three modes: complete charge (CC), partial charge (PC) and no charge (NC). For this converter is considered the partial charge (PC), because in no charge mode (NC) is necessary high capacitances capacitors or a very high switching frequency and the complete charge (CC) mode can be destructive to the converter. Therefore, the on resistance of switch and diodes resistance are considered in this analysis. The converter operated in continuous mode and the operating stages are described below. First Stage - This stage starts when switch S 1 is turned on. The current through L b begins to increase linearly. The capacitor C 1 begins to discharges, capacitor C 2 charges through diode D 2 and capacitor C 3 discharges during this stage. The C 1 and C 3 are transferring power to the load. This stage finishes when S 1 is turned off. This topological stage is shown in Fig. 4a. Second Stage - This stage starts when switch S 1 is turned off. The inductor current closes diode D 1 and charges capacitor C 1 through it. Capacitor C 2 begins discharge and capacitor C 3 charges through D 3. The C 1 and C 3 are transferring power to the load. This stage finishes when S 1 is turned on and another switching period starts from the first stage. This topological stage is shown in Fig. 4b. The voltage stresses at switch and diodes are clamped by voltage capacitors, therefore, half of output voltage. In Fig. 5 the main theoretical waveforms for switching frequency are presented. To the low-frequency analysis the PFC hybrid boost converter ensures the input current is sinusoidal and the unity power factor. The capacitors voltages are balanced and are half of the output voltage. The expected main theoretical waveforms for line voltage frequency are presented in Fig. 6. III. QUANTITATIVE ANALYSIS This section presents the quantitative analysis of the proposed converter. For this analysis, all components are considered ideal, as these losses have low influenced on the main results, however the maximum theoretical gain is limited as in conventional PFC boost converter and CC-CC hybrid boost converter. Considering a sinusoidal grid given by v in (ω in t) = V inpk sin(ω in t) (1) where V inpk is the peak voltage and ω in is the angular mains frequency (ω in = 2πf in ) For an angle of line voltage where the output voltage, line voltage and the capacitors voltages are constants (i.e., v o = V o, v in = V in and v C1 = V C1 ), the voltage across capacitor C1 can be expressed by (2) and the output voltage by (3). V C1 = V o = V in (1 D) 2 V in (1 D) For this converter, the duty cycle is expressed as (2) (3) D (θ) = 1 M sin (θ) (4) where θ = ω in t and M is the modulation index given by Fig. 3: Single-phase PFC Hybrid Boost Converter. M = 2 V in pk V o (5)

3 (a) Fig. 4: Topological stages: (a) first stage; (b) second stage. (b) Fig. 6: Low frequency theoretical waveforms of the proposed converter. diodes D 1, D 2 and D 3 is defined by (8). Fig. 5: High frequency theoretical waveforms of the proposed converter. Considering the input current sinusoidal and in phase with the line voltage, the peak of input current can be expressed by (6). Therefore, the average current in inductor is defined by (7). I Lbavg I inpk = 1 π π 0 = 2 P o V inpk (6) I inpk sin (θ) dθ (7) Analysing nodes b,c and d on Fig. 3, the average current in I D1avg = I D2avg = I D3avg = I o (8) Thus, the average current in the switch is I Savg = I Lbavg I D1avg (9) The expressions (III) and (10) define the inductor current ripple and output voltage ripple, respectively. I Lb (θ) = D S (θ) V inpk sin (θ) 2 L b f s V o = P o 2 π f in C o (10) These expressions are defined as for the PFC boost converter, where C o is expressed by

4 Fig. 8: Blocks diagram of average current mode control technique. must to be fast. Analysing Fig. 4, is defined (12) and through it, the model transfer function of the input current is obtained, shown in (13). Fig. 7: Average current mode control technique applied in PFC converter. L di Lb(t) = D ( ) V in I Lbavg R L I Savg R S + dt + (1 D) ( ) (12) V in I Lbavg R L I D1avg R D V C1 C o = C 1 C 3 C 1 + C 3 (11) IV. MODELLING AND CONTROL STRATEGY A. Control Strategy The most common control strategy applied in PFC boost converter is average current-mode control [19]. This strategy is simple and has many years of research and several applications in industry. As shown in Fig. 7 [20], there are three control loops in this technique: the current loop, responsible for input current shape control; the line voltage feedforward loop, to compensate the line voltage variation; DC voltage loop, to regulate the output voltage and control the power flow of the line voltage to load. The Fig. 8 presented the block diagram of control strategy. The inner loop is of input current and should be the fastest to ensure the input current be sinusoidal and in phase with line voltage. The DC voltage loop controls the output voltage acting in the amplitude of input current reference. This is the outer loop and should be sufficient slow to minimize the maximum undulation on input current reference. The voltage feedforward loop is to compensate the line voltage variation. Is the slowest loop and is used a second-order low pass filter as controller. B. System Modeling To define the transfer function of the input current will be considered non idealities of the components, as shown in Fig. 4. These resistances are considered since it changes the frequency of pole of the transfer function. The input current model is based on small-signal average current modeling, for switching frequency, since it current loop V o V ILb (s) C1 + R S + V o R D D (s) = R o R o (13) sl b + R L For the transfer function of the output voltage, should be considered slower than input current loop and the frequency of the line voltage, to avoid input current distortion. The transfer function to output voltage is show in (14) and was obtained by the average values of variables accounted in one line voltage half-period. V o (s) I Lb (s) = π R o V inpk (14) 4 C o R o V o s + 8 V o V. DESIGN EXAMPLE AND EXPERIMENTAL RESULTS After analysis, a single-phase PFC hybrid boost converter was design according to the specifications given in Table I, in order to build a prototype to validation of this study. A. Determination of Passive Components To define the mains currents and voltages involved in the converter, the parameters of Table I were applied to the following equations. The average and rms current through inductor are I Lbavg I inpk = 1 π = 2 1000W 311V π 0 I Lbrms = 6.43A (15) 6.43 sin (θ) dθ = 4.09A (16) = 1000W 220V = 4.54A (17)

5 TABLE I MAIN SPECIFICATION Description Output Power (P o ) RMS Input Voltage (v in ) Output DC Voltage (V o ) Frequency of AC Voltage (f in ) Switching Frequency (f s ) Value 1kW 220V 800V 60Hz 50kHz The average output current is I o = P o V o (18) I o = 1000W = 1.25A (19) 800V The inductor is defined by maximum ripple in the input current for the worst case. For this converter is when the input voltage is maximum. Assuming I Lb% = 0.15 and θ = π/2, then the inductor is calculated from (1) L b = 0.2225 311V sin ( π ) /2 = 1.12mH (20) 2 0.15 4, 095A 50kHz The inductor was built with a core of Thornton IP-12 ferrite EE-55, with 99 turns with four 21AWG conductors in parallel, the effective inductance was 1.2mH and resistance was 0.2Ω. The capacitors voltages are V C1 = V C2 = V C3 = V o 2 (21) V C1 = V C2 = V C3 = 800V = 400V (22) 2 The capacitors C 1 and C 3 can be calculated with (10) and (11). Assuming V o% = 0.01 V o the capacitors are C o = 1000W 2 π 60Hz 800V 0.01 800V = 414.46µF (23) C 1 = C 3 = 828.93µF (24) Two 470µF/450V parallel-connected were chosen for each capacitor (C = 940µF ). The capacitor C 2 was chosen by the maximum rms current it supports. Due to the complexity of calculating the rms current of this capacitor, this current it was determined by simulating of the converter, thus two capacitors of 100µF/450V parallelconnected were used. B. Switches Voltage and Current Stresses The average current through D 1, D 2, D 3 and S are I D1avg = I D2avg = I D3avg = I o = 1, 25A (25) I Savg = I Lbavg I D1avg (26) (a) Fig. 9: Frequency response of inductor current loop: (a) G i (s); (b) open loop compensated. (a) Fig. 10: Frequency response of output voltage loop: (a) G v (s); (b) open loop compensated. I Savg = 4, 09A 1, 25A = 2.84A (27) The diodes reverse voltage and the maximum voltage across the off switch are V D1 = V D2 = V D3 = V S = V C1 = 400V (28) For the diodes D 1, D 2 and D 3 were employed SiC Schottky diodes SDT10S60 (Infineon, V RRM = 600V and I F = 10A ) and the switch was employed CoolMos SPP24N60C3 MOS- FET (Infineon, V DS = 650V and R DS(on) = 0.16Ω). C. Control System Design The UC3854 IC [21] was used for system current control. This IC accomplish average current model control for power factor correction, also provide over current protection and PWM modulator. The current compensator chosen is a proportional integrator controller with filter. Its cutoff frequency was established in 10kHz, the designed current controller transfer function is given by (29) and expression (30) represents the open-loop (b) (b)

6 TABLE II COMPONENTS OF THE PROTOTYPE Description MOSFET Value SPP24N60C3 (Infineon) (Vds = 650V and Rds(on) = 0.16Ω) Diodes (D1, D2, D3 ) SDT10S60 (Infineon) (Vrrm = 600V and IF = 10A) Inductor 1, 2mH (core EE-55 4 x 21 AWG - 99 turns ) Capacitors (C1, C3 ) 470µF (each two in parallel) Electrolytic (EPCOS) Capacitors (C2 ) 100µF (each two in parallel) Electrolytic (EPCOS) Diode Bridge (DB1 ) KBU1008 (WTE) (VR = 800V and Io = 10A) Current Sensor LAH 55-NP (LEM) Circuit Integrated Controller UC3854AN (Texas) Fig. 11: Photograph of the prototype implemented in the laboratory. compensated current system model. In Fig. 9, the frequency response of current model and compensated model are presented. Ci (s) = 2.06 108 s + 2 π 72.34 s s + 2 π 3.28 106 Ti (s) = Gi (s) Ki Ci (s) GP W M (29) (30) The same controller type was chosen for voltage regulation. Its cutoff frequency was established in 4Hz and the transfer function is given by (31) and expression (32) represents the open-loop compensated voltage system model. In Fig. 10, the frequency response of voltage model and compensated model are presented. Cv (s) = 3.03 105 s + 2 π 48.23 s s + 2 π 1.46 104 Tv (s) = Gv (s) Kv Cv (s) GP W M (31) (32) D. Experimental Results The main components used in the prototype are presented in Table II. In Fig. 11 and 12, a photograph of prototype and the schematic of the implemented circuit are shown, respectively. The experimental waveforms obtained from this prototype are recorded while the converter was supplying 1000W to the load. Fig. 13a shows the line voltage vi n, input current iin and output voltage vo. Can be observed that the input current is sinusoidal, the converter operates with high power factor and output voltage vo was regulated close to 802V. Fig. 13b shows the voltage across capacitors C1, C2, C3 and output voltage. As expected, the voltages across capacitors are one-half of the output voltage, and are well balanced. Fig. 13c shows the voltage across diodes D1, D2, D3 and the switch S, showing that these voltages are one-half of output voltage, where the maximum value measured is 430V, including overvoltage. The current through the capacitors C1, C2 and C3 are presented in Fig. 13d, 13e and 13f, respectively. And these currents have the shape similar to that shown in Fig. 5, as expected. Also it is clear that the capacitor is operating in PC mode. A load disturbance, from 50% to 100% of the nominal load value, was applied to the converter, in order to check the system dynamic response and stability. Fig. 14 shows the line voltage vin, input current iin and the output voltage vo. As expected, the converter continued to operate normally, the input current remains a sinusoidal waveform, the output voltage present small oscillation and the system remained stable. The efficiency curve plotted in Fig. 15 show that for a wide load range the efficiency is higher than 96%. At rated power, the efficiency was 96.5%. The efficiency peak was 97% and occurred at 510W. The input power factor is close to one at rated power as shown in Fig. 16, but it drops considerably for low power. Nevertheless, it is possible to conclude that the converter had a satisfactory operation for a wide load values. VI. C ONCLUSION From the theoretical and experimental studies presented in this paper, we can draw the conclusions as follows. a) the hybrid cc-cc boost converter is appropriate to replace the conventional cc-cc boost converter in single-phase power factor correction applications; b) the well known control techniques, such as average current control used in the conventional PFC is also suitable for controlling the new converter; c) the well know dedicated IC, such as the UC3854, can equally be employed to control the proposed high power factor rectifier; d) with the proposed circuit, the voltage across the power semiconductor is the half of the load voltage;

7 Fig. 12: Schematic of the implemented circuit. (a) (b) (c) (d) (e) (f) Fig. 13: Steady state experimental waveforms: (a) input current (i in ), line voltage (v in ) and output voltage (v o ); (b) capacitors voltages(v C1, v C2, v C3 ) and output voltage(v o ); (c) switch voltage (v s ) and diodes voltages (v D1, v D2, v D3 ); (d) capacitor current (i C1 ); (e) capacitor current (i C2 ); (f) capacitor current (i C3 ).

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