# Research on Cascaded Single Phase PFC Based on Predictive PI Control

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Structure of Cascaded Single Phase PFC System

_{s}is the AC side current, L

_{s}is the filter inductor, C

_{s}is the filter capacitor, L is the boost inductor, and i

_{L}is the current flowing through the inductor L. C

_{i}and R

_{i}(i = 1, 2 … N) are the capacitors and DC loads. On the DC side, v

_{dc1}, v

_{dc2}… v

_{dcN}are the voltages across the capacitors’ side of the H-bridge. The DC load R

_{i}is used to replace the PFC post stage converter, where i is the serial connection unit number.

- (1)
- The common duty cycle control strategy is adopted, and the difference of switching function caused by CPS-SPWM is ignored, that is, m
_{1}≈ m_{2}≈ … ≈ m_{i}; and - (2)
- The capacitance and resistance of the DC side are the same, which are C and R, respectively.

_{s}/Nv

_{dc}, v

_{dc}= v

_{dc}

_{1}= v

_{dc}

_{2}⋯ = v

_{dc}

_{N}.

## 3. Design of Cascade Single Phase PFC Control System

_{dci}is the sum of N capacitor voltages. First, the given value of the voltage loop is compared with the average value of the capacitor voltage obtained by sampling, and the voltage error value is used as the input of the second-order notch filter. The secondary voltage ripple is filtered to improve the bandwidth of the voltage loop. The filtered signal is controlled by predictive PI to eliminate the negative modulation and improve the dynamic performance and anti-interference ability of the system. The maximum value of the current reference value of the appreciating inductor is obtained by multiplying the output signal of the predictive PI control by the scale factor. Then, the maximum value is multiplied by the sinusoidal value of the phase information of the power grid voltage processed by the phase locked loop, and the result is taken as the given value of the current loop. The current error is obtained by comparing the collected boost inductor current with the current reference value. The current error is adjusted by the PI controller, and then compared with triangular wave to obtain the control value. The obtained control quantity is input into the DPWM module to generate pulse, which can control the power switch after passing through the driving circuit [21,22].

#### 3.1. Predictive PI Control

_{c}(s) of the predictive PI controller is composed of G

_{c}

_{1}(s) and G

_{c}

_{2}(s). Among them, G

_{c}

_{1}(s) plays a traditional PI control function, G

_{c}

_{2}(s) plays a predictive role, and G

_{c}

_{2}(s) is composed of G

_{c}

_{2}

_{a}(s) and G

_{c}

_{2}

_{b}(s). G

_{P}(s) is the transfer function of the controlled object.

_{c}

_{1}(s) is a traditional PI controller, which is the main control part of the predictive PI control strategy. In a certain range, G

_{c}

_{1}(s) reacts to the internal and external disturbances and real-time parameter changes of the system to ensure the robustness of the whole control strategy. G

_{c}

_{2}(s) is the predictive part of the predictive PI control strategy, which means that the controller outputs the predictive value at a certain time in [t−τ, t], so that the controller and the controlled object can be combined to determine the current optimal value by rolling optimization, and the bad influence of the pure delay link on the control system can also be reduced.

_{P}in Equation (16) is the delay time variable parameter of the control process. It is necessary to further identify and fit the system using the identification of the second-order under-damped self regulating plant. For the transfer function (17):

#### 3.1.1. The Determination of Parameter K

#### 3.1.2. Determination of Parameters T and τ

^{∗}(t) can be expressed as Equation (23). Measure the values of y

^{∗}(t

_{1}) and y

^{∗}(t

_{2}) corresponding to t

_{1}and t

_{2}on the response curve of the transfer function G(s), and then calculate the value of T and τ according to Equations (24) and (25).

_{0}is the actual output value of PI, x

_{1}is the predicted value of PI, e is the absolute error between the predicted value x

_{1}and the actual value x

_{0}, and e

_{ss}is the relative error between the predicted value x

_{1}and the actual value x

_{0}. It can be seen that the predicted value x

_{1}tracked the actual value x

_{0}well. In steady state, the absolute error and relative error are very small. At 0.25 s, the system load changes, the absolute error and relative error fluctuate, but after 0.04 s adjustment, it is stable.

#### 3.2. Current Inner Loop Control

_{im}(s) is the transfer function of current power level, and G

_{ci}(s) is the PI control.

_{pi}is the gain of current controller, which can be obtained by Equation (27). K

_{ii}is the current loop integration coefficient and T

_{ic}is the current loop integration time constant, which can be obtained by Equation (28). f

_{c}is the shear frequency, so the phase margin of the current loop near the shear frequency should be large enough. f

_{d}is the compensation zero of the current loop controller.

## 4. System Experimental Analysis

#### 4.1. System Steady-State Experimental Analysis

_{AO}is the bus voltage at the AC side of the system; and i

_{s}is the bus current at the AC side of the system and i

_{L}is the current of boost inductor L. Figure 11 is the system switching cycle waveform. T

_{s}is the normal switching cycle of each switch, and T

_{cs}is the switching period of each switch after carrier phase-shifting modulation.

#### 4.2. System Dynamic Experimental Analysis

_{dc1}is the voltage of the output capacitor C

_{1}, and i

_{L}is the current of boost inductor L. It shows the load from 144 Ω changed to 72 Ω. The response of output voltage and input current was obtained. After the system was put into operation, when the load changed abruptly from 144 Ω to 72 Ω, it can be seen from Figure 12a that under the conventional PI double loop control, the output voltage overshoot was large, and reached a new stable state after about 0.15 s adjustment; after 0.05 s adjustment, the output current reached a new stable state. It can be seen from Figure 12b that under predictive PI control, the output voltage overshoot was relatively small and reached a new stable state after about 0.075 s adjustment; the output current reached a new stable state after 0.05 s of adjustment. Through the previous comparison, it can be seen that the system adopted predictive PI control; in the case of load mutation, the overshoot was small, and the dynamic performance was significantly improved.

_{dc1}is the voltage of the output capacitor C

_{1}, and i

_{L}is the current of boost inductor L. It shows the load from 72 Ω changed to 144 Ω. The response of output voltage and input current was obtained. After the system was put into operation, when the load changed abruptly from 72 Ω to 144 Ω, it can be seen from Figure 13a that under the conventional PI double loop control, the output voltage overshoot was large, and it reached a new stable state after about 0.15 s of adjustment; After 0.1 s adjustment, the output current reached a new stable state. It can be seen from Figure 13b that under predictive PI control, the output voltage overshoot was relatively small and reached a new stable state after about 0.075 s of adjustment; the output current reached a new stable state after 0.05 s of adjustment. Through the previous comparison, it can be seen that the system adopted predictive PI control; in the case of load mutation, the overshoot was small, and the dynamic performance was significantly improved.

## 5. Conclusions

- (1)
- The cascaded multilevel structure can effectively improve the system power density of the charger, reduce the voltage drop borne by a single switch, and improve the power factor of the system output.
- (2)
- The carrier phase shift control strategy was adopted to greatly increase the system switching frequency to reduce the burden of each switch and reduce the switching loss.
- (3)
- Predictive PI control was adopted in the voltage loop to effectively improve the dynamic stability of the system.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 5.**The open-loop Bode diagram of the outer voltage loop: (

**a**) Open loop Bode diagram of voltage loop before compensation and (

**b**) open loop Bode diagram of compensated voltage loop.

**Figure 8.**The open-loop Bode diagram of the inner current loop: (

**a**) Open loop Bode diagram of current loop before compensation; (

**b**) Open loop Bode diagram of compensated current loop.

**Figure 12.**Output voltage and input current response to load change from 144 Ω to 72 Ω: (

**a**) Traditional double loop PI control; (

**b**) predictive PI control.

**Figure 13.**Output voltage and input current response to load change from 72 Ω to 144 Ω: (

**a**) Traditional double loop PI control; (

**b**) predictive PI control.

Component | Model |
---|---|

Switch tube | EPC2032 |

Isolator | ISOW7840 |

Driver | LMG1205 |

Driver power supply | TPS60150 |

Current sensor | ACS723 |

DSP | TMS320F28069 |

FPGA | AL3S10NG88 |

Parameter | Values |
---|---|

Main inductance | 5 μH |

Filter inductance | 8 μH |

Filter capacitor | 620 nF |

Unit bus capacitance | 1800 μF |

Unit resistive load | 12 Ω |

Switching frequency | 60 kHz |

AC side phase voltage | 220 V |

DC side voltage | 360 V |

Rated power | 2 kW |

Power density | 1500 W/in^{3} |

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**MDPI and ACS Style**

Shi, G.; Qian, Y.
Research on Cascaded Single Phase PFC Based on Predictive PI Control. *World Electr. Veh. J.* **2022**, *13*, 48.
https://doi.org/10.3390/wevj13030048

**AMA Style**

Shi G, Qian Y.
Research on Cascaded Single Phase PFC Based on Predictive PI Control. *World Electric Vehicle Journal*. 2022; 13(3):48.
https://doi.org/10.3390/wevj13030048

**Chicago/Turabian Style**

Shi, Guoping, and Yece Qian.
2022. "Research on Cascaded Single Phase PFC Based on Predictive PI Control" *World Electric Vehicle Journal* 13, no. 3: 48.
https://doi.org/10.3390/wevj13030048