Modeling and simulation of single-phase boost APFC converter with bidirectional switch in front

0 Introduction

The traditional single-phase boost APFC circuit has been widely used in power factor correction circuits, but this solution requires an independent uncontrolled rectifier bridge, and the boost inductor placed at the rear needs to solve the problem of DC bias magnetic resistance, and the location of the boost inductor is not conducive to the integration of the entire power circuit. These have caused people to rethink the traditional single-phase boost APFC circuit, and it is envisioned that the entire power circuit can be easily integrated by utilizing its mature control ideas and ready-made control circuits. In recent years, great progress has been made in this regard, and a variety of circuit topologies have been proposed. Among them, the single-phase boost APFC converter circuit with a bidirectional switch in front has attracted people's attention due to its unique performance.

1 Circuit structure of single-phase boost APFC converter with bidirectional switch in front

The circuit of the single-phase boost APFC converter with a bidirectional switch in front is shown in Figure 1. The input part consists of an AC voltage source VS and a filter capacitor C1. The bidirectional switch S1 and the inductor L complete the power factor correction function, where the bidirectional switch S1 consists of D5, D6, D7, D8 and V1. The rectifier part consists of D1, D2, D3, and D4, C2 plays the role of energy storage and output filtering, and R is the load.

Figure 1 Main circuit of a single-phase boost APFC converter with a bidirectional switch in front

2 Analysis of the working state of the single-phase boost APFC converter circuit with bidirectional switch in front

The following will analyze the operation process of the single-phase boost APFC converter circuit with a bidirectional switch in front. In the continuous conduction mode, corresponding to a high-frequency cycle of the switch tube, the current iL flowing through the inductor L, the voltage Vds applied to the two ends of the switch tube V1 and the waveform of the output current i0 are shown in Figure 2. The equivalent circuit corresponding to each period of time is shown in Figure 3. Among them, working state 1 and working state 2 are the conditions during the positive half cycle of the power frequency, and working state 3 and working state 4 are the conditions during the negative half cycle of the power frequency. The latter two states are just the repetition of the former two states in the negative half cycle. For the convenience of analysis, the conduction voltage drop of each diode and switch tube is regarded as zero. D1, D2, D3, D4, D5, D6, D7, and D8 in the equivalent circuit only represent the path through which the current flows. C2 is regarded as large enough to ensure that the output voltage is constant. C2 is very small and can be ignored.

(a) Waveform of one positive half cycle

(b) Negative half cycle waveform

Figure 2 Waveforms of iL, Vds, and i0 during switching of the converter circuit

Figure 3 Equivalent circuits in various working states

2.1 Working state when VS is in the positive half cycle

Working state 1 (t1

Working state 2 (t2

(1)

(2)

2.2 Working state when VS is in the negative half cycle

Working state 3 (t4

Working state 4 (t5

(3)

(4)

3 Small signal modeling of single-phase boost APFC converter circuit with bidirectional switch in front

For the single-phase boost APFC converter circuit with a bidirectional switch in front, in the CCM working mode, since the last two states are just the repetition of the first two states in the negative half cycle, the following analysis is based on the two states in the positive half cycle. In order to solve the static operating point of the converter, it is necessary to eliminate the high-frequency switching components of each variable in the converter, and the average value method is usually adopted. Under the condition of satisfying the low frequency assumption and small ripple assumption, the average value of the variables inductor current i(t), capacitor voltage v(t) and input voltage vs(t) in the switching period Ts is defined as :

(5)

(6)

(7)

To simplify the analysis, the active switch elements and diodes are considered as ideal elements. Then, each switching cycle of the converter in CCM mode has two working states. The differential equations (1), (2), (3), and (4) for the inductor voltage and capacitor current can be listed respectively. Then, by combining equations (5), (6), and (7), the average values ​​of the inductor voltage and capacitor current in one switching cycle can be obtained respectively. Further, a set of nonlinear average variable state equations (8) and (9) for the converter can be derived.

(8)

(9)

(8) and (9) are a set of nonlinear state equations. Each average variable and control variable d(t) contains both DC components and low-frequency small signal components. When the circuit satisfies the small signal assumption, the AC small signal state equations of the inductor and capacitor can be separated into (10) and (11).

(10)

(11)

The actual working state of the converter is to work near the static working point and change according to the linear law. However, the AC small signal state equation composed of equations (10) and (11) is still a nonlinear state equation, so the nonlinear equation needs to be linearized. Since all except and in equations (10) and (11) are linear terms, and these two product terms are much smaller than other terms, if they are omitted, it will not introduce too much error to the analysis. The linearized AC small signal state equations are (12) and (13).

(12)

(13)

According to equations (12) and (13), a more intuitive AC small signal equivalent circuit model can be established to facilitate the analysis of the small signal characteristics of the converter, as shown in Figure 5:

Figure 4 AC small signal equivalent model of a single-phase boost APFC converter with a bidirectional switch in front in CCD mode

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4 Simulation Analysis of Single-Phase Boost APFC Converter with Bidirectional Switch in Front

The converter circuit is simulated using Simulink 6.0 simulation software in MATLAB 7.1, assuming the following parameter settings: Vs = 220V, primary inductance L = 1 × 10-3H, primary filter capacitor C1 = 3.3μF, output energy storage capacitor C2 = 200 ~ 5000μF, the operating frequency of the switch tube is fS = 50KHz, and the load R = 20 ~ 140Ω. The following discusses the impact of changes in energy storage capacitor C2 and load R on power factor (PF) and output ripple voltage (Vpp).

4.1 Effect of parameter changes on circuit power factor (PF)

Parameter changes will affect the power factor (PF) of the circuit. Taking the bridge arm parallel capacitor C2 and the load R as variables, the PF value of the circuit is simulated and the results are shown in Table 1:

Table 1 Simulation results of power factor with output side parallel capacitance value and load changes

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When the capacitor C2 is 500uF, 1000uF, 1500uF, 2000uF, and 2500uF respectively, 7 sets of data are taken correspondingly when the load is in the range of 20Ω to 140Ω. The cubic polynomial interpolation is performed on each PF value using MATLAB software, and the variation curve after interpolation is shown in Figure 5.

Figure 5 PF interpolation curve of power factor changing with output side parallel capacitance value and load

As can be seen from Figure 5, for a certain value of capacitance, the change of load has a great influence on the power factor. When 40Ω≤R≤60Ω, the power factor achieves a larger value.

4.2 Effect of parameter changes on the output ripple voltage (Vpp) of the circuit

The change of parameters will also affect the output ripple voltage (Vpp) of the circuit. Taking the bridge arm parallel capacitor C2 and the load R as variables, the output ripple voltage value of the circuit obtained by simulation is shown in Table 2.

Table 2 Simulation results of output ripple voltage as output side parallel capacitance value and load change

When the capacitor C2 is 500uF, 1000uF, 1500uF, 2000uF, and 2500uF respectively, 7 sets of data are taken correspondingly in the load range of 20Ω to 140Ω. The output ripple voltage (Vpp) is interpolated with cubic polynomial using MATLAB software, and the change curve after interpolation is shown in Figure 6.

Figure 6 PF interpolation curve of power factor changing with output side parallel capacitance value and load

As can be seen from Figure 6, the ripple voltage value decreases with the increase of load resistance. The larger the load resistance, the smaller the ripple and the smoother the output voltage. In practical applications, both design requirements and costs must be taken into account. Generally speaking, the output voltage ripple (Vpp) is no more than 20V under full load to meet the requirements. At this time, factors such as cost and capacitor volume should be considered as much as possible, so C2 can be taken as 1500uF.

In summary, if the output ripple voltage VPP is required to be within 20V, the capacitance is not too large, and the power factor is given priority, combined with factors such as volume and economy, the optimal parameters of the circuit are: C2 is about 1500uF, and R is 40Ω≤R≤60Ω.

4.3 Example simulation of optimal parameter case

The following simulation is performed for the optimal parameter case, and the parameter settings are as follows: Vs="220V", primary inductance L=1×10-3H, primary filter capacitor C1=3.3μF, output energy storage capacitor C2=1500μF, operating frequency of the switch tube is fS=50KHz, and load R=50Ω.

The simulation results are as follows:

After the system enters steady state, the input voltage and current waveforms are shown in Figure 7. It can be seen that the converter input current tracks the input voltage waveform very well. For ease of comparison, the AC voltage Vs amplitude in the figure is 1/20 of the original, each grid represents 20 volts, and the unit of current is ampere.

Figure 7 Input voltage and current waveform

The power factor curve is shown in FIG8 . It can be seen from the figure that before 0.15 seconds, the circuit is in an unstable state and the power factor has a large jump. After 0.15 seconds, the circuit enters a stable state and the power factor can reach above 0.95.

Figure 8 Power factor curve

The output voltage waveform is shown in Figure 9. It can be seen from the figure that the average output voltage is about 400V. After magnification, it can be seen that the peak-to-peak value of the ripple voltage is 15V. The capacitor voltage of this circuit is well limited within a certain range, and the withstand voltage of the energy storage capacitor is greatly reduced, ensuring the output characteristics of the circuit.

Figure 9 Output voltage waveform

5 Conclusion

The single-phase boost APFC converter circuit with a bidirectional switch placed in front of the rectifier bridge has placed the bidirectional switch in front of the rectifier bridge, which effectively solves the problem of DC bias magnetism of the boost inductor placed in the rear of the traditional single-phase boost APFC converter circuit, and is also convenient for circuit integration. By optimizing the circuit parameter configuration, a very high power factor can be achieved, and the output voltage is stable, the output ripple voltage is low, and good output characteristics can be obtained. This paper has found a better parameter configuration range through simulation, which has important guiding significance for practical applications.