Analysis and Design of a PFC AC-DC Converter with Electrical Isolation

Abstract

This study presents a single-phase power factor correction AC-DC converter that operates in discontinuous conduction mode. This converter uses the pulse-width modulation technique to achieve almost unity power factor and low total harmonic distortion of input current for universal input voltage $90V_{rms}$ to $264V_{rms}$) applications. The converter has a simple structure and electrical isolation. The magnetizing-inductor energy of the transformer can be recycled to the output without an additional third winding. The steady-state analysis of voltage gain and boundary operating conditions are discussed in detail. Finally, experimental results are shown to verify the performance of the proposed converter.

I. INTRODUCTION

DC power sources are widely used in industrial products and consumer electronics, such as battery chargers, DC power supplies, uninterruptible power supplies, inverters, and instruments. Thus, AC–DC power conversion is an important consideration. Diode-bridge or thyristor rectifiers can realize AC–DC power conversion, but such rectifiers will result in power pollution, including pulsating input current, low power factor, and high total harmonic distortion of input current(THDi). Several power factor correction (PFC) AC–DC converters have been investigated to address these issues. These converters possess non-isolated and isolated topologies. Non-isolated topologies include the boost [1]-[4], buck [5]-[7], buck-boost [8]-[10], Cuk [11], SEPIC [12], [13], and ZETA types [14]. These converters are operated in continuous conduction mode and discontinuous conduction mode (DCM) for different output-power applications. Isolated topologies include forward [15]-[17] and flyback types [18]-[20]. The forward types achieve low output voltage ripple and high THDi. Nevertheless, this converter requires the third winding to recycle the magnetizing-inductor energy of the transformer. The flyback types are shown in Fig. 1(a). This converter achieves high power factor and low THDi. Moreover, flyback types have a simple structure and low cost but have low efficiency because of the transformer leakage inductor. The clamping method is presented in [21], [22] to recycle leakage inductor energy. However, this method makes the power circuit complicated.

Fig. 1.(a) Conventional single-phase AC–DC flyback converter and (b) proposed single-phase AC–DC converter.

We propose a single-phase PFC AC–DC converter, as shown in Fig. 1(b). The proposed converter circuit configuration is very simple. The configuration includes only a set of input filter Lf–Cf, a diode-bridge rectifier, a transformer Tr, an inductor L1, an output diode Do, and an output capacitor Co. The proposed converter does not have the transformer leakage inductor issue associated with the flyback converter. Moreover, transformer magnetizinginductor energy can be recycled to the output without an additional third winding. This converter is operated in DCM by using the pulse–width modulation technique to achieve high power factor and low THDi for universal input-voltage applications.

 

II. OPERATING PRINCIPLES

The equivalent circuit of the proposed converter is shown in Fig. 2. The transformer is modeled as a magnetizing inductor Lm and an ideal transformer. Some key waveforms in a half line-source period are shown in Fig. 3. The operating principle is analyzed as 0 < ωt < π, where ω is the line angular frequency, because of the symmetrical characteristics of the single-phase system.

Fig. 2.Equivalent circuit of proposed converter.

Fig. 3.Key waveforms of the proposed converter for 0<ωt<π.

Mode 1, [kTs, tk1]: S1 is switched on. The current- flow path is shown in Fig. 4(a). The line source energy is transferred to the magnetizing inductor Lm of the transformer and the inductor L1. Thus, the currents iLm and iL1 are increased linearly. Given that magnetizing inductor Lm is significantly larger than inductor L1, the magnetizing-inductor current iLm becomes lower than inductor current iL1. The energy stored in magnetizing inductor Lm is the residual magnetism of the transformer. The energy stored in output capacitor Co is discharged to load R. This mode ends when S1 is switched off.

Fig. 4.Current flow path of the proposed converter for 0<ωt<π.

Mode 2, [tk1, tk2]: S1 is switched off. The current-flow path is shown in Fig. 4(b). The energies stored in magnetizing inductor Lm and inductor L1 are released to output capacitor Co and load R. The currents iLm and iL1 are decreased linearly. This mode ends when the currents iLm and iL1 are equal to zero. Therefore, the transformer residual magnetism can be released to empty during each switching period.

Mode 3, [tk2, (k+1)Ts]: S1 remains switched off. The current-flow path is shown in Fig. 4(c). The energies stored in magnetizing inductor Lm and inductor L1 are empty at t = tk2. The energy stored in output capacitor Co is discharged to load R. This mode ends when S1 is switched on at the beginning of the next switching period.

 

III. STEADY-STATE ANALYSIS

Given that the single-phase system is symmetrical, the following analysis is discussed for 0 < ωt < π. For simplicity, the effect of the input filter is neglected. The line voltage is given by

where Vrms and Vm are the root-mean-square value and line voltage amplitude, respectively. The line voltage is considered a piecewise constant during each switching period because switching frequency fs is larger than line frequency f1. If m is the switching number within [0, π/ω], then m is equal to fs/2f1. The following analysis is considered during switching period [kTs, (k+1)Ts], where k = 0, 1, ….., m-1. The magnetizing inductor Lm is ignored in the following analysis because it is significantly larger than inductor L1.

When S1 switched turned on, the voltage across inductor L1 is obtained as

where es(tk) is the input-voltage level during switching the period [kTs, (k+1)Ts], and the turns ratio of transformer n = N2/N1. Then,

The inductor current iL1 is given by

When t is equal to tk1, the peak value of inductor current iL1 is

where ton = tk1 – kTs = dTs.

When S1 is switched off, the voltage across inductor L1 is given by

Then,

By solving (7), we derive the inductor current iL1 as follows:

Given that iL1(tk2) = 0, the peak value of inductor current iL1 is

where tr,k = tk2 – tk1.

Using (5) and (9), time duration tr,k can be given by

A. Power Factor Correction

As shown in Fig. 3, the average value of unfiltered input current iN1 in one switching period Ts can be computed as

where iL1p is the inductor current peak value for each switching period. Substituting (1) and (5) into (11), we derive the following equation:

The average value of unfiltered input current iN1 is sinusoidal and in phase with the input voltage. Moreover, the harmonic components of current iN1 are distributed over the switching frequency multiples. The harmonic components are easily filtered out by using input filter Lf –Cf. The input filter cutoff frequency is significantly lower than the switching frequency.

B. Voltage Gain

From Fig. 3, the average value of the output-capacitor current ico during [kTs, (k+1)Ts] can be obtained as

Substituting (1), (5), and (10) into (13) yields

The average value of output–capacitor current ico during a half line-source period [0, π/ω] is written as follows:

Given that m is larger than 1, equation (15) is approximated as:

The output voltage differential equation is given by

The DC model equation is written as

where Vo and D are the DC quantities of vo and d, respectively.

The normalized inductor time constant is then defined as

Substituting (19) into (18), the voltage gain is derived as

C. Boundary Condition

The current iL1 must be zero in each switching period to ensure that the proposed converter is operated in DCM. From Fig. 3, time duration ts,k is obtained as

When the maximum value of ts,k is equal to Ts and |es| is equal to Vm, the proposed converter is operated in boundary conduction mode. Therefore, substituting ts,k = Ts and |es| = Vm into (21) can determine the boundary voltage gain as

Using (20) and (22), the curves of voltage gain and boundary voltage gain are shown in Fig. 5. When the voltage gain M is equal to its boundary voltage gain Mbc, the boundary normalized inductor time constant τL1B is given by

Fig. 5.Voltage gain and boundary voltage gain (under n = 0.5).

τL1B is plotted in Fig. 6. We can observe that the proposed converter is operated in DCM when τL1 < τL1B.

Fig. 6.Boundary operating condition.

 

IV. SELECTIONS OF INDUCTOR AND CAPACITOR

A. Selection of Inductor L1

The appropriate τL1B is selected under the required voltage gain to ensure that the proposed converter is operated in DCM. The inductor L1 needs to satisfy the following inequality:

B. Selection of Output Capacitor Co

Using (14), the average value of output–capacitor current ico during one switching period is simplified as follows:

Substituting (18) into (25), output–capacitor current ico is expressed as

Therefore, the output voltage ripple in one switching period is given by

Then, the output voltage ripple function during time interval [0, π/ω] is obtained as

Using (28), the output voltage ripple during time interval [0, π/ω] is derived as

Thus,

Output capacitor Co must satisfy the following inequality to meet the following output voltage ripple percentage specification:

 

V. EXPERIMENTAL RESULTS

The prototype circuit is applied in the laboratory to demonstrate the performance of the proposed converter. Electrical specifications and circuit components are set as follows:

The voltage gain M is varied from 0.27 to 0.79 according to the electrical specifications. Substituting M = 0.79 and n = 0.5 into (22), the maximum duty ratio Dmax is derived as 0.61. Substituting Dmax = 0.61 into (23), τL1B is obtained as 0.038. Using (24), the inductor L1 is given by

The inductor L1 is 60 μH, and the core is EI-40. Thus, τL1 is equal to 0.03 at full load R = 100 Ω and is equal to 0.006 at light load R = 500 Ω. Substituting the two values of τL1 and n = 0.5 into (20), the operating area of the experimental prototype is shown in Fig. 7. The proposed converter is operating in DCM.

Fig. 7.Operating range of the prototype circuit.

Under the operating conditions Vrms = 90 V and R = 100 Ω, M and τL1 are derived as 0.79 and 0.03, respectively. Substituting M = 0.79, n = 0.5, and τL1 = 0.03 into (20), duty ratio D is obtained as 0.55. The ripple percentage of Vo is selected as 5%. From (31), the output capacitor inequality is given by

Thus, output capacitor Co is selected as 600 μF.

The control circuit is shown in Fig. 8. Figs. 9 and 10 show the experimental waveforms under Vrms = 115 V, Vo = 100 V, Po = 100 W and Vrms = 230 V, Vo = 100 V, Po = 100 W, respectively. In Figs. 9(a) and 10(a), we observe that input current is sinusoidal and is in phase with input voltage. The current waveforms of the transformer primary and secondary sides iN1 and iN2 are shown in Figs. 9(b) and 10(b), respectively. The waveforms are taken at the peak value of input voltage. The current iN2 drops to zero during each switching period, which indicates that the transformer residual magnetism is released to empty during each switching period. The currents iL1 and iDo are shown in Fig. 9(c) and 10(c), respectively. We observe that the proposed converter is operated in DCM. The waveform vS1 across the switch drain source is shown in Figs. 9(d) and 10(d). The measured efficiencies of the proposed converter and flyback converter are compared in Fig. 11. We observe that efficiency is improved in the proposed converter. The measured power factor and THDi are shown in Fig. 12. The measured power factor is higher than 0.96, whereas the measured THDi is lower than 5.8%.

Fig. 8.Control circuit of the proposed converter.

Fig. 9.Experimental waveforms at 115–Vrms line voltage: (a) es and is, (b) iN1 and iN2, (c) iL1 and iDo, (d) vS1.

Fig. 10.Experimental waveforms at 230–Vrms line voltage: (a) es and is, (b) iN1 and iN2, (c) iL1 and iDo, (d) vS1

Fig. 11.Measured efficiency for the proposed converter and conventional flyback converter.

Fig. 12.Measured results: (a) power factor and (b) THDi.

 

VI. CONCLUSIONS

The forward and flyback PFC AC–DC converters are efficient choices for electrical isolation because of their simple structure. However, the forward AC–DC converter cannot achieve high power factor and low THDi. Additionally, this converter requires a third winding to recycle transformer magnetizing inductor energy. The flyback AC–DC converter can achieve high power factor and low THDi. Nevertheless, the transformer leakage inductor results in low efficiency. Therefore, we present a single-phase AC–DC converter that has a simple structure and is operated in DCM to achieve high power factor and low THDi. A steady-state analysis is conducted. We implement a hardware circuit with simple control logic in the laboratory. The experimental results reveal the performance of the converters. The measured efficiencies reveal that the proposed converter exhibited higher efficiency than the conventional flyback converter.