# Power Decoupling Method Based on the Diagonal Compensating Matrix for VSG-Controlled Parallel Inverters in the Microgrid

^{*}

## Abstract

**:**

## 1. Introduction

## 2. VSG Control Principle

_{dc}is the voltage of the DC source; Z

_{line}is the line impedance from DG to the point of common coupling (PCC); R

_{in}, L, and C denote the inductance internal resistance, the smoothing inductance, and the smoothing capacitance of the filter, respectively; v

_{o}and i

_{o}are the filter capacitor voltage and the inverter’s output current, respectively; i

_{c}denotes the filter capacitor current; P

_{set}and Q

_{set}represent the input mechanical power and reactive power reference of the inverter, respectively; and P

_{e}and Q

_{e}represent the active and reactive power output of the inverter, respectively. In this article, according to the instantaneous power theory, P

_{e}and Q

_{e}can be calculated as:

_{p}is the damping coefficient representing the function of damping winding, ω

_{ref}is the synchronization angular frequency of the power grid, and ω

_{N}is the rated angular frequency. During normal operation, the angular frequency reference ω

_{ref}is equal to ω

_{N}, which can implement the primary frequency modulation (PFM) of VSG. For the design of the active power loop of VSG, most existing researches on the design of the VSG active power loop are based on the PFM function.

_{q}is the droop coefficient of voltage, K is the reactive power regulation coefficient, and V

_{o}and V

_{ref}are effective values of the output voltage and rated voltage, respectively. The input command signal e

_{m}of the voltage loop can be obtained by combining the amplitude information E

_{m}generated by the reactive power loop and the phase information δ by the active power loop as:

## 3. Output Power Model of Microgrid

_{out}and the line impedance Z

_{line}. Suppose that the grid impedance is referred to as Z∠θ = R + jX. A single phase study is given below. The output power equation can be written as:

_{s}, δ

_{s}) can be expressed as:

## 4. Decoupling Control Method for VSG Control

#### 4.1. Control Principle

_{c}becomes

_{c}can be calculated as:

#### 4.2. Feasibility Analysis and Improvement Approach for Power Sharing

_{c}can be derived as:

_{p}of each inverter proportional to its capacity. For Q–V control, however, the output voltage of the inverter will be not same due to the existence of line voltage drop. This phenomenon affects the reactive power sharing. To overcome this problem, the PCC voltage is introduced as a consistent variable. Figure 5 shows the improved reactive power loop. The reactive power sharing can be ensured by making D

_{q}of each inverter proportional to its capacity.

## 5. Simulation Verification

#### 5.1. Verification of the Power Decoupling Performance

#### 5.2. Verification of the Power Sharing Performance

_{Line1}= 0.8 + j0.5 Ω, and another is Z

_{Line2}= 0.5 + j0.83 Ω.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 7.**(

**a**) The power output response to the frequency fluctuation; (

**b**) The power output response to the voltage amplitude fluctuation.

**Figure 9.**Output waveforms of VSG control to frequency deviation. (

**a**) Without decoupling link; (

**b**) With decoupling link; (

**c**) Output current of VSG1 with decoupling link.

**Figure 10.**Output waveforms of VSG control to voltage deviation. (

**a**) Without decoupling link; (

**b**) With decoupling link; (

**c**) Output current of VSG2 with decoupling link.

Parameters | Values | Parameters | Values |
---|---|---|---|

V_{dc} | 800 V | V_{pcc} | 220 V |

L | 2 mH | P_{set} | 10 kW |

C | 300 μF | Q_{set} | 5 kVar |

R_{in} | 0.05 Ω | J | 0.2 |

ω_{N} | 314 rad/s | D_{p} | 20 |

E_{s} | 235.7 V | D_{q} | 500 |

δ_{s} | 0.07 | K | 50 |

Parameters (VSG1) | Values | Parameters (VSG2) | Values |
---|---|---|---|

V_{dc} | 800 V | V_{dc} | 600 V |

L | 3 mH | L | 2 mH |

C | 400 μF | C | 300 μF |

R_{in} | 0.08 Ω | R_{in} | 0.05 Ω |

ω_{N} | 314 rad/s | ω_{N} | 314 rad/s |

E_{s} | 235.7 V | E_{s} | 230.1 V |

δ_{s} | 0.07 | δ_{s} | 0.05 |

V_{pcc} | 220 V | V_{pcc} | 220 V |

P_{set} | 10 kW | P_{set} | 5 kW |

Q_{set} | 5 kVar | Q_{set} | 5 kVar |

J | 0.15 | J | 0.2 |

D_{p} | 30 | D_{p} | 15 |

D_{q} | 600 | D_{q} | 300 |

K | 55 | K | 50 |

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**MDPI and ACS Style**

Li, B.; Zhou, L.
Power Decoupling Method Based on the Diagonal Compensating Matrix for VSG-Controlled Parallel Inverters in the Microgrid. *Energies* **2017**, *10*, 2159.
https://doi.org/10.3390/en10122159

**AMA Style**

Li B, Zhou L.
Power Decoupling Method Based on the Diagonal Compensating Matrix for VSG-Controlled Parallel Inverters in the Microgrid. *Energies*. 2017; 10(12):2159.
https://doi.org/10.3390/en10122159

**Chicago/Turabian Style**

Li, Bin, and Lin Zhou.
2017. "Power Decoupling Method Based on the Diagonal Compensating Matrix for VSG-Controlled Parallel Inverters in the Microgrid" *Energies* 10, no. 12: 2159.
https://doi.org/10.3390/en10122159