# The Voltage Balance Control Strategy of Static Var Generators DC-Side Capacitors Based on Fuzzy-PI Adaptive Cascaded H-Bridge

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. SVG Mathematical Model

#### Cascaded SVG Primary Circuit Topology

_{d}and reactive component d

_{q}of the typical duty cycle can be obtained, the common duty cycle dα can be obtained through DQ inverse transformation, and finally, the drive signal of each H-bridge switch transistor can be obtained through the carrier phase-shift PWM modulation.

## 3. SVG Control Strategy Based on the DQ Coordinate System

#### 3.1. Cascaded SVG Primary Circuit Topology

_{i}is theoretically derived. The active component d

_{d}of the typical duty cycle is superimposed to generate a new active duty cycle d

_{i}′, which controls the DC-side voltage balance. In the DC side capacitor voltage control section, n active-duty cycle corrections are generated by n−1 DC-side voltage balance feedback loops, and the control structure is simplified. On the basis of PI control, fuzzy control is introduced to greatly improve the speed and accuracy of voltage balancing.

#### 3.2. DC Side Voltage Balance Control Mechanism

_{d}of each H-bridge module is constant, and the DC side voltage is proportional to the equivalent resistance:

_{1}, R

_{2}, R

_{3}, and the resistance values are R

_{1}> R

_{2}> R

_{3}, and d is the public duty cycle [20]. It can be known from (4) that the vector relationship in Figure 5, can be represented by Udc1, Udc2, and Udc3. Ucd and Ucq are the active and reactive components of the AC side voltage, respectively, which can be written as follows:

_{P}and K

_{I}are the parameters of the PI controller, respectively, and their expressions are as follows:

#### 3.3. Fuzzy-PI Controller

#### 3.3.1. Fuzzy-PI Controller

_{E}and K

_{EC}. The scale factors are K

_{up}and K

_{ui}. Different values of the quantization factor and scale factor will affect the dynamic performance of the fuzzy controller.

_{P}and K

_{I}are the parameters of the PI controller, ΔK

_{P}and ΔK

_{I}are the adjustment quantities generated by the fuzzy control, and K

_{P}’ and K

_{I}’ are the adjusted PI parameters.

#### 3.3.2. Domain of Discourse and Membership Function

_{up}and K

_{ui}all obey the distribution of the triangular membership function curve.

#### 3.3.3. Establishment of the Fuzzy Rule Base

_{P}and K

_{I}are different. When designing fuzzy rules, K

_{P}and K

_{I}should follow the following principles:

- (1)
- When the error E is too large, the response speed of the system will be slow, and K
_{P}should take a more significant value; at the same time, to ensure that the system does not have integral saturation and limit the necessary action, K_{I}should take a smaller value. - (2)
- When the error E is around medium size, K
_{P}should take a small value, and K_{I}should take a significant discount to ensure the system response speed and control overshoot. - (3)
- When the error E is too small, to avoid excessive error in the steady-state operation of the system and affect the control effect, K
_{P}and K_{I}should take larger values.

#### 3.3.4. Fuzzy Inference and Defuzzification

_{P}is Ci and ΔK

_{I}is Di

_{P}, and ΔK

_{I}, respectively. Because the actual control quantity must be an exact value, the result obtained by fuzzy inference is still an undefined quantity, which needs to be de-fuzzified. In fuzzy control, defuzzification usually adopts the area centroid method, and its reasoning formula is as follows:

_{up}and K

_{ui}to obtain the values of ΔK

_{P}and ΔK

_{I}; only the same value can be accepted and recognized by the system to achieve the control effect. Therefore, the PI parameters adjusted by the fuzzy controller can be expressed as:

## 4. Simulation and Analysis

_{1}is changed from 100 Ω to 50 Ω at 1 s, the instantaneous voltage fluctuates violently. The adaptive voltage balance control strategy based on fuzzy PI begins to work. After a short voltage imbalance, the voltage recovers after 0.1 s to a state of equilibrium. This shows that the voltage balance control strategy can exert a good control effect when the system has a sudden voltage imbalance.

## 5. Conclusions

- (1)
- Compared with the traditional PI control, this paper is based on the fuzzy PI control voltage balance strategy, which significantly improves the response speed and accuracy of the DC-side voltage balance controller.
- (2)
- The overall system current DQ decoupling controls the output of the public active-duty cycle and reactive duty cycle, and the voltage balance controller increases the duty cycle correction on the common active-duty cycle component to achieve the effect of voltage balance.
- (3)
- While ensuring the constant voltage of the DC side, the DC side voltage balance controller does not have a coupling effect with the dual closed-loop control of the system, and the control structure is simple and easy to implement.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 10.**Current DQ decoupled double closed-loop control. (

**a**) When the equivalent resistance on the DC side is inconsistent, the voltage cannot be balanced. (

**b**) When the equivalent resistance on the DC side is consistent, the voltage can be balanced.

**Figure 16.**Voltage balancing control strategy tracks the situation as the reference voltage changes.

EC | NB | NM | NS | ZE | PS | PM | PB | |
---|---|---|---|---|---|---|---|---|

E | ||||||||

NB | PB | PB | PM | PM | PS | ZE | ZE | |

NM | PB | PB | PM | PS | PS | ZE | NS | |

NS | PM | PM | PM | PS | ZE | NS | NS | |

ZE | PM | PM | PS | ZE | NS | NM | NM | |

PS | PS | PS | ZE | NS | NS | NM | NM | |

PM | PS | ZE | NS | NM | NM | NM | NB | |

PB | ZE | ZE | NM | NM | NM | NB | NB |

EC | NB | NM | NS | ZE | PS | PM | PB | |
---|---|---|---|---|---|---|---|---|

E | ||||||||

NB | NB | NB | NM | NM | NS | ZE | ZE | |

NM | NB | NB | NM | NS | NS | ZE | ZE | |

NS | NB | PM | NS | NS | ZE | PS | PS | |

ZE | NM | NM | NS | ZE | PS | PM | PM | |

PS | NM | NM | ZE | PS | PS | PM | NM | |

PM | ZE | ZE | PS | PS | PM | NM | PB | |

PB | ZE | ZE | PS | PM | NM | PB | PB |

Parameter | Quantity | Symbol |
---|---|---|

power voltage | 220 | V |

Number of H-bridges | 3 | piece |

grid frequency | 50 | HZ |

Filter inductor | 5 | mH |

DC side capacitance | 10,000 | μF |

DC side reference voltage | 500 | V |

DC side equivalent resistance | 50/100/150 | Ω |

DC side equivalent resistance | 220 | V |

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**MDPI and ACS Style**

Gong, R.; Feng, Y.
The Voltage Balance Control Strategy of Static Var Generators DC-Side Capacitors Based on Fuzzy-PI Adaptive Cascaded H-Bridge. *Electronics* **2023**, *12*, 39.
https://doi.org/10.3390/electronics12010039

**AMA Style**

Gong R, Feng Y.
The Voltage Balance Control Strategy of Static Var Generators DC-Side Capacitors Based on Fuzzy-PI Adaptive Cascaded H-Bridge. *Electronics*. 2023; 12(1):39.
https://doi.org/10.3390/electronics12010039

**Chicago/Turabian Style**

Gong, Renxi, and Yuan Feng.
2023. "The Voltage Balance Control Strategy of Static Var Generators DC-Side Capacitors Based on Fuzzy-PI Adaptive Cascaded H-Bridge" *Electronics* 12, no. 1: 39.
https://doi.org/10.3390/electronics12010039