# Nonlinear Modeling and Control Strategy Based on Type-II T-S Fuzzy in Bi-Directional DC-AC Converter

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Mathematical Modeling of Dual-Buck Bi-Directional Converter

_{g}is the voltage at the grid terminal and U

_{in}is the DC bus voltage. The circuit is topologically equivalent to a collection of two buck circuits: U

_{in}passes through the regulator filter capacitor C

_{d}, diodes D

_{1}, inductor L

_{1}and power switches S

_{1}and S

_{4}to form the first buck circuit, and diodes D

_{2}, inductor L

_{2}and power switches S

_{2}and S

_{3}to form the other buck circuit. S

_{1}and S

_{2}are high-frequency MOS power switches and S

_{3}and S

_{4}are two industrial-frequency (50 Hz) power switches that can be designed as zero-current switches. In addition, the operation modes of the bi-directional converter can be categorized into rectifier and inverter. The bi-directional converter judges the operation mode according to the bus voltage state, achieving bi-directional flow of power and power factor correction in the rectifier mode and reliable grid-connected operation in the inverter mode. When the converter is in rectifier mode, it is divided into four modes, as shown in Table 1, in a complete industrial frequency sinusoidal waveform. The circuit is symmetrical and equivalent to a dual-boost circuit under positive and negative half-cycle of AC voltage input. Its boost equivalent circuit for positive half-cycle is shown in Figure 2b. When the converter is in inverter mode, it is divided into four modes, as shown in Table 2. With the grid operating at positive and negative voltage half-cycles, the circuit loop is symmetrical and equivalent to a buck circuit. The buck equivalent circuit for positive half-cycle is shown in Figure 2c.

_{L}and the circuit output voltage u

_{o}(U

_{d}in rectifier and u

_{g}in inverter) are used as state vectors.

#### 2.2. Nonlinear Inductor Modeling

#### 2.3. Type-II T-S Fuzzy Modeling

_{L}is ${i}_{L}\in [{I}_{L\mathrm{min}},{I}_{L\mathrm{max}}]$.

## 3. Control Strategy for Dual-Buck Bi-Directional Converter

#### 3.1. Type-II T-S Fuzzy Controller Design

^{i}:

- Rule
^{1}: if i_{L}= I_{Lmin}, then

- Rule
^{2}: if i_{L}= I_{Lmax}, then

_{1}is the control parameter when the current is set to the minimum value under the fuzzy rule, and K

_{2}is the control parameter of the system when the inductor current increases to a certain degree and the inductor change tends to level off. When the system runs, the inductor current in the circuit is between the set maximum and minimum values, through the membership function of type-II T-S fuzzy, to determine the current value; the size of the weights of each sub-controller, at this point, the circuit control parameters are:

_{o}is U

_{d}and u

_{i}is u

_{g}) is:

_{o}is u

_{g}and u

_{i}is U

_{d}), the algorithmic expression is:

#### 3.2. Voltage Outer Loop Design

_{g}is a sinusoidal AC current with frequency 50 Hz and amplitude Gu

_{g}. The instantaneous input power at the grid side of the converter is:

_{o}is the output power. For the secondary ripple of the system at 100 Hz, the controller of the voltage loop is designed to traverse a frequency of 1/10 twice the industrial frequency: fc = 10 Hz. Equation (26) can then be obtained.

_{up}= 0.0169 and K

_{ui}= 1.0619 can be obtained, and in order to be applied to the digital embedded system, the incremental PI controller is discretized with Equation (27):

## 4. Results

#### 4.1. Simulation Analysis

#### 4.2. Experimental Validation

_{g}, host computer, voltage regulator, dual-buck bi-directional converter, DC source, electronic load to simulate half-load, full-load, and non-linear loads, and an oscilloscope for observing and recording experimental results.

_{3}and S

_{4}are off and S

_{1}and S

_{2}are in the positive and negative half-cycle of the high-frequency operation, respectively. When S

_{1}is on and S

_{2}is off, withstand-voltage switch U

_{S1}and diode U

_{D4}is 0. In the inverter state, as shown in Figure 13b,d,f, the switches S

_{1}and S

_{2}are working at high frequency to ensure the sinusoidalizing of the current, and S

_{3}and S

_{4}are switches under the control of the PWM frequency to form a connected circuit loop. When switches S

_{2}and S

_{3}are on and switches S

_{1}and S

_{4}are off, withstand-voltage switch U

_{S4}and diode U

_{D4}are 0, which is in accordance with the operation principle of the dual-buck bi-directional DC-AC circuits.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Converter circuit topology. (

**a**) Dual-buck bi-directional converter; (

**b**) positive half-circle rectifier equivalent circuit; (

**c**) positive half-circle inverter equivalent circuit.

**Figure 11.**Type-II T-S fuzzy single-cycle control waveform under different power. (

**a**) Light-load (200 W) rectified waveforms, THDi = 4.0%; (

**b**) half-load (500 W) rectified waveform, THDi = 2.2%; (

**c**,

**d**) full-load (1000 W) rectified/inverter waveform, THDi = 2.6%/THDi = 2.7%, respectively.

**Figure 13.**Rectifier/inverter grid-connected experiment steady state waveforms. (

**a**,

**b**) Driving waveforms of switchers; (

**c**,

**d**) withstand-voltage waveforms of the S

_{1}and S

_{4}; (

**e**,

**f**) corresponding D

_{1}and D

_{4}withstand-voltage waveforms.

u_{g} | Mode | S_{1} | S_{2} | S_{3} | S_{4} | D_{1} | D_{2} | D_{3} | D_{4} |
---|---|---|---|---|---|---|---|---|---|

>0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |

2 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | |

<0 | 3 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 |

4 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |

u_{g} | Mode | S_{1} | S_{2} | S_{3} | S_{4} | D_{1} | D_{2} | D_{3} | D_{4} |
---|---|---|---|---|---|---|---|---|---|

>0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |

2 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | |

<0 | 3 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |

4 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |

I (A) | L (mH) | I (A) | L (mH) | I (A) | L (mH) | I (A) | L (mH) |
---|---|---|---|---|---|---|---|

1 | 4.23 | 6 | 2.83 | 11 | 1.54 | 16 | 0.83 |

2 | 4.13 | 7 | 2.57 | 12 | 1.35 | 17 | 0.74 |

3 | 3.88 | 8 | 2.26 | 13 | 1.19 | 18 | 0.66 |

4 | 3.66 | 9 | 1.96 | 14 | 1.05 | 19 | 0.60 |

5 | 3.23 | 10 | 1.71 | 15 | 0.93 | 20 | 0.55 |

Parameters | Value |
---|---|

DC Voltage Reference | 380 V |

Grid Voltage | 220 V/50 Hz |

Switching Frequency | 40 kHz |

Rated Power | 1000 W |

Filter Capacitance | 1 mF |

Parameters | Value |
---|---|

DC Voltage Reference | 360 V |

Rated AC Voltage/Frequency | 220 V/50 Hz |

Rated Power | 1000 W |

Switching Frequency | 40 kHz |

Filter Inductance | 3 mH |

DC-Side Bus Capacitance | 1 mF/450 V |

Power Switch | MOSEFT SPW24N60C3 (Voltage Withstand: 650 V, Current Withstand: 24 A) |

Diode | STTH1212D (Reverse Breakdown Voltage Maximum: 1200 V, Current Withstand: 12 A) |

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**MDPI and ACS Style**

Chen, Z.; Huang, R.; Lin, Q.; Yu, X.; Dan, Z.
Nonlinear Modeling and Control Strategy Based on Type-II T-S Fuzzy in Bi-Directional DC-AC Converter. *Electronics* **2024**, *13*, 1684.
https://doi.org/10.3390/electronics13091684

**AMA Style**

Chen Z, Huang R, Lin Q, Yu X, Dan Z.
Nonlinear Modeling and Control Strategy Based on Type-II T-S Fuzzy in Bi-Directional DC-AC Converter. *Electronics*. 2024; 13(9):1684.
https://doi.org/10.3390/electronics13091684

**Chicago/Turabian Style**

Chen, Zhihua, Ruochen Huang, Qiongbin Lin, Xinhong Yu, and Zhimin Dan.
2024. "Nonlinear Modeling and Control Strategy Based on Type-II T-S Fuzzy in Bi-Directional DC-AC Converter" *Electronics* 13, no. 9: 1684.
https://doi.org/10.3390/electronics13091684