# Study on a novel high-efficiency bridgeless PFC converter.

1. IntroductionA great number of harmonic currents, which are caused by nonlinear loads connected to grid, are main pollution sources of power system and important factors in the safe operation of the grid. In order to reduce the harmonic pollution, the active power filter (APF) and power factor correction (PFC) are required, which are applied to control the harmonic and reactive current generated from rectifier loads. PFC converter can realize the AC input current control and DC output voltage control at the same frequency and phase with AC voltage, and thus it is widely used in server power [1-8], charger, UPS, and so on. Traditional PFC converter includes a front-end bridge rectifier, which increases conduction loss and greatly affects the efficiency of the PFC converter. Moreover, more serious loss is generated under low input voltage and light load particularly [5, 9-13].

In order to improve efficiency of the traditional PFC converter, an effective method named as bridgeless PFC technology without front-end bridge rectifier is proposed [3, 14, 15]. Then the bridgeless PFC converter is proposed in [1-18], which uses two switches instead of the uncontrolled diodes. When AC input voltage is in positive half-cycle, the front bridge leg of the converter operations, while AC input voltage is in negative half-cycle, the rear bridge leg operations. The papers report that the bridgeless PFC converter adopts the same two DC-DC converters to implement the power conversion for positive and negative half-cycle of AC input voltage, respectively. Another bridgeless PFC converter makes the input voltage greater than zero at first and then obtains steady output voltage through the DCDC converter. All of these bridgeless PFC converters have a higher cost, require complex topology, and may lead to serious electromagnetic inference (EMI) [3, 13-18].

In this paper, we research a novel Pseudo-Boost converter, which has bipolar-gain characteristic; that is, no matter if the input voltage is positive or negative, the output voltage is always positive, and the converter also has the same characteristic as the traditional Boost converter. Although the converter has a resonant branch, the difference from the traditional resonant converter is that the voltage transfer ratio is not relevant to the resonant branch parameters and switching frequency; it only depends on the switching duty cycle. Based on the Bipolar-Gain Pseudo-Boost converter, a bridgeless Bipolar-Gain Pseudo-Boost PFC converter in continuous conduction mode (CCM) is investigated. The converter adopts one bidirectional controllable switch and two fast-recovery diodes instead of bridge rectifier, and the zero-current switching of the fast-recovery diodes is achieved. Therefore, the efficiency of the converter is improved. Meanwhile, the one-cycle control technology is adopted to control the Bipolar-Gain Pseudo-Boost PFC converter.

2. Operation Principle of Bipolar-Gain Pseudo-Boost Converter

The topology of the Bipolar-Gain Pseudo-Boost converter consists of switch S, two recovery diodes [D.sub.1] and [D.sub.2], resonant capacitor [C.sub.r], and resonant inductor [L.sub.r], as in Figure 1. When the input voltage is positive or negative, the output voltage of traditional Boost converter is the corresponding polarity. Compared with the traditional one, the output voltage of Bipolar-Gain Pseudo-Boost converter is just positive; that is, the Bipolar-Gain Pseudo-Boost has bipolar-gain characteristic. To simplify the analysis of the operation of the BipolarGain Pseudo-Boost converter, the following assumptions are made.

(a) All of the switches, diodes, inductors, and capacitors are ideal.

(b) Output capacitor [C.sub.0] is large enough to make the output voltage keep constant in a switching cycle.

(c) Resonant inductor [L.sub.r] and resonant capacitor [C.sub.r] are much smaller than the inductor L and output capacitor [C.sub.0], respectively.

(d) The converter operates in CCM.

2.1. Positive Input Voltage. The operation modes of BipolarGain Pseudo-Boost converter operate in CCM with positive input voltage (Figure 2). The corresponding key waveforms of the converter are shown in Figure 3. At the beginning of each switching cycle, the resonant inductor current [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is zero and the initial value of resonant capacitor voltage [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] exists.

(1) Mode 1 [[t.sub.0] ~ [t.sub.1]] as shown in Figures 2(a) and 3, at t = [t.sub.0], the switch S is turned on. The voltage across the inductor L is equal to input voltage [v.sub.in], which makes inductor current increase linearly. The resonant capacitor voltage [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] makes diode [D.sub.1] turn on, and the reverse voltage across [D.sub.2] makes it turn off. Resonant capacitor voltage [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and resonant inductor current [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are given as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)

where [Z.sub.n] = [square root of ([L.sub.r]/[C.sub.r])], [[omega].sub.r] = 1/[square root of ([L.sub.r][C.sub.r])].

(2) Mode 2 [[t.sub.1] ~ [t.sub.2]]: as shown in Figures 2(b) and 3, at t = [t.sub.1] = [t.sub.0] + [T.sub.r]/2, resonant inductor current [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is equal to zero and diode [D.sub.1] gets zero-current turn-off, where [T.sub.r] = 2[pi]/[[omega].sub.r] is the resonant period. At this moment, the resonant capacitor is equal to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Due to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the diode [D.sub.2] is still turned off with reverse voltage [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The voltage across diode [D.sub.1] is equal to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], while the voltage across diode [D.sub.2] is equal to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

(3) Mode 3 [[t.sub.2] ~ [t.sub.3]]: as shown in Figures 2(c) and 3, at t = [t.sub.2], the switch S is turned off. Because the inductor current [i.sub.L] does not change suddenly, the diode [D.sub.2] is turned on to provide the path for the inductor current [i.sub.L]. The diode [D.sub.1] is reversely biased and the voltage across it is equal to -[v.sub.c], and the inductor L is then discharged and capacitor C0 is charged. As [L.sub.r] [much less than] L, [L.sub.r] can be ignored. So during [t.sub.2] ~ [t.sub.3], the resonant capacitor voltage can be expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)

When the resonant capacitor voltage rises to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the converter begins to enter the next switch cycle.

2.2. Negative Input Voltage. Figure 4 shows the operation modes of Bipolar-Gain Pseudo-Boost converter operated in CCM with negative input voltage. The corresponding key waveforms of the converter are shown in Figure 5. At the beginning of each switching cycle, the resonant inductor current [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is zero and the initial value of resonant capacitor voltage [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

(1) Mode 4 [[t.sub.4] ~ [t.sub.5]]: as shown in Figures 4(a) and 5, at t = [t.sub.4], the switch S is turned on. The voltage across the inductor L is equal to input voltage -[v.sub.in], which makes inductor current decrease linearly. The diode [D.sub.2] is turned on by the opposite voltage [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and the diode [D.sub.1] is reversely biased. The resonant branch begins to resonate; the resonant capacitor voltage [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and resonant inductor current [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are given as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (3)

where [Z.sub.n] = [square root of ([L.sub.r]/[C.sub.r])], [w.sub.r] = 1/[square root of ([L.sub.r][C.sub.r])].

(2) Mode 5 [[t.sub.5] ~ [t.sub.6]]: as shown in Figures 4(b) and 5, at t = [t.sub.5], the resonant inductor current [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is equal to zero and diode [D.sub.2] gets zero-current turn-off, where [t.sub.5] - [t.sub.4] = [T.sub.r]/2 and [T.sub.r] = 2[pi]/[[omega].sub.r] is the resonant period. The resonant capacitor is equal to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the diode [D.sub.1] is still reversely biased, and the voltage across it is equal to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The voltage across diode D2 is equal to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

(3) Mode 6 [[t.sub.6] ~ [t.sub.7]]: as shown in Figures 4(c) and 5, at t = [t.sub.6], the switch S is turned off. Because the inductor current [i.sub.L] does not change suddenly, the diode [D.sub.1] is turned on to provide the path for the inductor current [i.sub.L]. The diode [D.sub.2] is reversely biased, and the inductor L is then discharged and capacitor C0 is charged. During [t.sub.6] ~ [t.sub.7], the resonant capacitor voltage can be given as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)

When the resonant capacitor voltage decreases to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the converter begins to enter the next switch cycle.

3. The Steady-State Analysis of Bipolar-Gain Pseudo-Boost Converter

There are four state variables in Bipolar-Gain Pseudo-Boost converter. One is the energy storage state variable ([v.sub.c], [i.sub.L]), in which the natural frequency is much lower than the switching frequency. The other one is the resonant state variables [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], in which the natural frequency is close to the switching frequency. According to the generalized state space averaging (GSSA) approach, the GSSA equation of the converter can be established, which chooses [v.sub.c], [i.sub.L] as state variables. Based on the GSSA equation, the steady-state characteristic can be analyzed.

3.1. Positive Input Voltage. For positive input voltage, from Figures 2(a) and 2(b), when the switch S is turned on, the state differential equations are

L [[di.sub.L]/dt] = [v.sub.in],

[C.sub.0][[dv.sub.c]/dt] = - [[v.sub.c]/R]. (5)

From Figure 2(c), when the switch S is turned off, the corresponding state differential equations are

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)

The above analysis shows that the resonant capacitor voltage satisfies (2) when the switch S is turned off. From Figure 3, at the end of switching cycle, the resonant capacitor voltage is equal to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; meanwhile, the integration of the resonant capacitor voltage is zero.

The matrix representation of the state variables is x = [[[i.sub.L] [v.sub.c]].sup.T]; according to (5) and (6), the state space equation is

[??] = [A.sub.i]X + [B.sub.i]u, i = 1, 2, (7)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (8)

According to GSSA approach, for positive input voltage, the GSSA equation of the Bipolar-Gain Pseudo-Boost converter can be obtained as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (9)

where d is the transient state switching duty cycle.

The equation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is founded at steady state because L [much greater than] [L.sub.r], so L + [L.sub.r] [approximately equal to] L. From (9), there are

[v.sub.in] = (1-D) [v.sub.c], [I.sub.L] = [[v.sub.c]/R(1-D)], (10)

where D is the steady state switching duty cycle and [I.sub.L] is the steady state inductor current.

3.2. Negative Input Voltage. For negative input voltage, from Figure 4(a), when the switch S is turned on, the state differential equations are

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (11)

From Figure 4(b), when the switch S is turned on, the corresponding state differential equations are

L [[di.sub.L]/dt] = [v.sub.in],

[C.sub.0][[dv.sub.c]/dt] = - [[v.sub.c]/R]. (12)

From Figure 4(c), when the switch S is turned off, the corresponding state differential equations are

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (13)

According to the above analysis, it can be seen that the resonant capacitor voltage satisfies (4) when the switch S is turned off. From Figure 5, at the end of switching cycle, the resonant capacitor voltage is equal to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; thus, the integration of the resonant capacitor voltage is-[v.sub.c] in the time.

The matrix representation of the state variables is x = [[[i.sub.L] [v.sub.c]].sup.T]; according (11), (12), and (13), the state space equation is

[??] = [A.sub.i]x + [B.sub.i]u, i = 1, 2, 3, (14)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (15)

Therefore, for negative input voltage, the GSSA equation of the Bipolar-Gain Pseudo-Boost converter can be obtained as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (16)

The equation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is founded at steady state because L [much greater than] [L.sub.r], so L + [L.sub.r] [approximately equal to] L. From (16), there are

[v.sub.in] = (l-D) [v.sub.c], [I.sub.L] = [[v.sub.c]]/R(1-D)]. (17)

According to (10) and (17), no matter if the input voltage is positive or negative, the voltage transfer ratios of Bipolar-Gain Pseudo-Boost converter keep the same. The converter has the same Boost characteristic as the traditional Boost converter. In addition, the voltage transfer ratio does not rely on the resonant branch parameters and switching frequency, which is determined only by the switching duty cycle.

4. The Implementation of Bridgeless Bipolar-Gain Pseudo-Boost Converter

The voltage transfer ratio of traditional DC-DC converter is unipolar, which means that it only makes positive and negative input voltage transfer to positive output voltage. However, the PFC converter belongs to AC-DC converter, which makes AC input voltage transfer to DC output voltage. Hence, the traditional DC-DC converter cannot be used as PFC converter. To realize PFC, the most direct way is combining a front-end bridge rectifier with a DC-DC converter. Assume that the voltage transfer ratio of DC-DC converter is bipolar; that is, no matter if the input voltage is positive or negative, the output voltage is always positive. This DC-DC converter can realize AC-DC transformation, which eliminates the bridge of traditional AC-DC converter and improves the efficiency of the converter.

According to the steady state characteristic of Bipolar-Gain Pseudo-Boost converter, it is shown that the converter has bipolar-gain characteristic. So the Bipolar-Gain Pseudo-Boost converter can be used as PFC converter. From Figure 6, the bridgeless PFC converter can be achieved by using bidirectional switch [S.sub.1] combined with [S.sub.2] instead of controllable switching S of the Bipolar-Gain Pseudo-Boost converter. The converter has some advantages such as simple topology, high efficiency, and simple controlled circuit. Compared with the double bridge-leg bridgeless PFC converter researched in paper [3, 14-16], the converter has reduced the EMI due to common-grounded input and output. Compared with the bridgeless PFC converter proposed in paper [3, 13-17], the Bipolar-Gain Pseudo-Boost converter has improved the utilization ratio and reduced the costs.

From the preceding analysis, the achievement conditions of bridge Pseudo-Boost PFC converter are as follows.

(1) From Figures 3 and 5, a two-way switch is needed because the switch S should suffer positive and negative voltage.

(2) The choice of inductor L: to guarantee that the converter operates in CCM, the inductor L must satisfy

[[v.sub.inp,max]/L] [D.sub.max][T.sub.s] [less than or equal to] 2[I.sub.inp]. (18)

The input current effective value is [I.sub.inp] = [square root of (2)] [P.sub.0]/ [eta][v.sub.in,RMS], where [v.sub.in,RMS] is the input voltage effective value, [v.sub.inp,max] is the maximum input voltage peak value, [P.sub.0] is the output power, and [eta] is the efficiency of the converter. In addition, [D.sub.max] is the maximum duty cycle and [T.sub.s] is the switching cycle.

(3) The choice of resonant branch parameters: from (2), (4), and the operation figure, it can be obtained as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (19)

From (19), the choice of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] has nothing to do with resonant inductor [L.sub.r]. [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is too large to increase the switch voltage stress, so larger resonant [C.sub.r] and smaller switching period [T.sub.s] should be chosen with the condition that resonant capacitor [C.sub.r] is much smaller than output capacitor [C.sub.0]. However, the resonant capacitor [C.sub.r] is too small to result in zero-crossing distortion, and it must satisfy [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; moreover,

[D.sub.min][T.sub.s] > [[T.sub.r]/2], (20)

where the minimum duty cycle is [D.sub.min] = 1 - [v.sub.inp,max]/[v.sub.c], and the resonant period is [T.sub.r] = 2[pi][square root of ([L.sub.r][C.sub.r])]. Thus, a suitable resonant inductor [L.sub.r] should be chosen with respect to (19) when the resonant inductor [L.sub.r] is much smaller than the Boost inductor L.

5. One-Cycle Control Bridgeless Bipolar-Gain Pseudo-Boost Converter

Figure 7 is the principle scheme of bridgeless PseudoBoost PFC converter based on one-cycle control technology. The main circuit topology employs a bidirectional switch composed of [S.sub.1] and [S.sub.2]. Dotted part of Figure 7 is the one-cycle control circuit, which consists of an integrator with reset function, a comparator, a RS trigger, and a clock signal generator.

The output voltage [v.sub.c] is sampled in each period and compared with a reference voltage [V.sub.ref]. The compared result is compensated by PI regulator and then the modulation signal [v.sub.m] is obtained. At each clock pulse coming, the two-way switch is turned on. Meanwhile, the modulation signal [v.sub.m] begins to be integrated by the reset integrator. The difference values [v.sub.1] between [v.sub.m] and [R.sub.s] [absolute value of ([i.sub.L])] are compared with the output signal [v.sub.2] from reset integrator, when [v.sub.2] = [v.sub.1], and the output level of the comparator is flipped and the switch is turned off, while the reset integrator resets to zero until the next clock pulse arrives.

According to the principle of one-cycle control, it can be obtained that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (21)

where [v.sub.m] = [v.sub.c][R.sub.s]/[R.sub.e] and Re is the equivalent input resistor of the bridgeless Bipolar-Gain Pseudo-Boost PFC converter and [R.sub.s] is the sampling resistor of inductor current.

When (21) is applied at each switching cycle, the output voltage of the bridgeless Bipolar-Gain Pseudo-Boost PFC converter is steady; moreover, the input current that is [i.sub.L] will maintain sinusoidal, and thus the purpose of PFC is achieved.

6. Experiment Verification

In order to verify the accuracy of the theoretical analysis, a set of experiments are designed. According to (18)-(20), the parameters of experiment circuit are as follows: [P.sub.0] = 100 W, [v.sub.in,RMS] = 50 V, [v.sub.c] = 100 V, C = 470 [micro]F, [f.sub.line] = 50 Hz, f = 50 kHz, L = 2.5 mH, [L.sub.r] = 7.8 [micro]H, and Cr = 330 nF.

Figure 8 shows the input voltage, input current, and output voltage waveforms of bridgeless Bipolar-Gain Pseudo-Boost PFC converter with [P.sub.0] = 100 W. It can be observed from Figure 8 that the output voltage of the converter [v.sub.c] is constant and the input current in closely follows the input voltage [v.sub.in] to realize power factor correction.

Figure 9 shows the efficiency curve of bridgeless Pseudo-Boost PFC converter with [v.sub.c] = 100 V. It can be seen that the proposed converter has relatively high efficiency.

Figures 10(a) and 10(b) show the switch voltage, diode voltage, and inductor current waveforms for the positive input voltage and negative voltage. It is seen that the experiment waveforms are consistent with the theoretical analysis waveforms and the diodes [D.sub.1] and [D.sub.2] can realize zero-current switching.

The measured harmonic contents of the line current at 100 V AC input voltage are shown in Figure 11 together with the limits of IEC61000-3-2 class D standard. It is shown that the input current harmonics of proposed converter can meet the IEC61000-3-2 standard. In addition, Figure 12 illustrates the measured PF value at full load of the proposed converter as the function of input voltage.

7. Conclusion

In this paper, we research the Bipolar-Gain Pseudo-Boost converter, and the topology and operation principles in CCM and DC steady-state character of this converter are analyzed. Based on this topology, a novel bridgeless Bipolar-Gain Pseudo-Boost PFC converter is proposed. In addition, the implement condition of the bridgeless PFC and control technology of the converter is studied. The experiments show that the proposed converter is capable of achieving the PFC better, and zero-current switching of the fast recovery diode is achieved. Moreover, the reverse-recovery loss of the diode is reduced and the efficiency of the converter is improved.

http://dx.doi.org/10.1155/2014/514281

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

This work was supported by the Applied Basic Research Programs of Technology Department under Foundation of Sichuan Province of China (no. 2012JY0120/12209596), Technology Support Programs of Technology Department of Sichuan Province (no. 2013GZ0130), the Educational Commission of the Sichuan Province of China (no. 11ZA003/11209435), the Key Programs of Xihua University (no. Z1120940), and Key Laboratory of University Project of Sichuan Provincial (application promotion and solar technology integration).

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Cao Taiqiang, (1) Chen Zhangyong, (2) Wang Jun, (1) Sun Zhang, (1) Luo Qian, (3) and Zhang Fei (2)

(1) School of Electric Information, Xihua University, Chengdu 610039, China

(2) School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China

(3) Information Technology Branch, The Second Research Institute of General Administration of Civil Aviation of China, Chengdu 610042, China

Correspondence should be addressed to Cao Taiqiang; ctq815@163.com

Received 24 January 2014; Accepted 18 June 2014; Published 4 August 2014

Academic Editor: Gongnan Xie

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Title Annotation: | Research Article |
---|---|

Author: | Taiqiang, Cao; Zhangyong, Chen; Jun, Wang; Zhang, Sun; Qian, Luo; Fei, Zhang |

Publication: | Journal of Applied Mathematics |

Article Type: | Report |

Date: | Jan 1, 2014 |

Words: | 4366 |

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