# Consensus Control for Reactive Power Sharing Using an Adaptive Virtual Impedance Approach

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Background

#### 2.1. Modeling of AC Electrical Network of a Microgrid

#### 2.2. Modeling of the Communication Network of the Microgrid

#### 2.2.1. A Graph Theory Approach

**Definitions:**

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

#### 2.2.2. Communication Topology

## 3. Assumptions and Methods

#### 3.1. Proposed Communication Topology

#### 3.2. Mathematical Model of the Proposed Control Method

#### 3.2.1. Primary Control

#### Droop Control

#### Virtual Impedance Control

#### Outer Voltage and Inner Current Dual Loop Control

#### 3.2.2. Secondary Control

#### Reactive Power Sharing

#### Adaptive Virtual Impedance Control

#### Consensus Control

#### Theorems and Lemmas

**Theorem**

**1.**

**Theorem**

**2.**

**Theorem**

**3.**

**Lemma**

**1.**

**Proof of**

**Lemma 1.**

**Lemma**

**2.**

**Lemma**

**3.**

**Lemma**

**4.**

**Proof of**

**Lemma 4.**

**Lemma**

**5.**

**Proof of**

**Lemma 5.**

#### Reactive Power Sharing Based on Consensus Control

**leaderless consensus control algorithm**. In the case of

**leader-followers consensus control**, a DG unit is selected to be a leader and other DG units as its followers [34,36,37]. Thus, Equation (29) can be rewritten to describe this leader-follower structure, as

#### Stability Analysis of Consensus Control

#### Overall Control

## 4. Results and Discussion

#### 4.1. Case Study

#### 4.1.1. Case 1: Primary Control Alone

#### 4.1.2. Case 2: Leaderless Consensus Control with Ring Communication Topology

#### 4.1.3. Case 3: Leader-Followers Consensus Control with Ring Communication Topology

#### 4.1.4. Case 4: Leaderless Consensus Control with Complete Communication Topology

#### 4.1.5. Case 5: Leaderless Consensus Control with Triangle Mesh Communication Topology

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**An example of six distributed generator (DG) units connected based on ring communication topology.

Feeder Line between | Length | Resistance | Inductance |
---|---|---|---|

DGs 1 & 2 | 1 km | 0.642 $\mathsf{\Omega}$ | 0.22 m$\mathrm{H}$ |

DGs 1 & 3 | 1.5 km | 0.963 $\mathsf{\Omega}$ | 0.33 m$\mathrm{H}$ |

DGs 2 & 4 | 2 km | 1.284 $\mathsf{\Omega}$ | 0.44 m$\mathrm{H}$ |

DGs 3 & 5 | 2 km | 1.284 $\mathsf{\Omega}$ | 0.44 m$\mathrm{H}$ |

DGs 4 & 6 | 1.5 km | 0.963 $\mathsf{\Omega}$ | 0.33 m$\mathrm{H}$ |

DGs 5 & 6 | 1 km | 0.642 $\mathsf{\Omega}$ | 0.22 m$\mathrm{H}$ |

DG Component | Parameters | Values | DG Component | Parameters | Values |
---|---|---|---|---|---|

LC Filter | ${L}_{f}$ | 4 $\mathrm{mH}$ | Virtual Impedance | ${R}_{vi}$ | 0.01 $\mathsf{\Omega}$ |

${C}_{f}$ | 100 $\mathsf{\mu}\mathrm{F}$ | ${X}_{vi}$ | 0.5 $\mathrm{mH}$ | ||

Droop Control | ${\omega}_{ni}$ | $2\mathsf{\pi}\xb760$ rad/sec | Outer Voltage Loop | ${k}_{pv}$ | 1.8 |

${V}_{ni}$ | 311 $\mathrm{V}$ (220 ${V}_{rms}$) | ${k}_{iv}$ | 10 | ||

${k}_{pi}$ | 5 × 10^{−5} | Inner Current Loop | ${k}_{pi}$ | 1.8 | |

${k}_{qi}$ | 7 × 10^{−4} | ${k}_{ii}$ | 10 | ||

DC sources | ${V}_{dc}$ | $700\text{}\mathrm{V}$ | PWM Generator | ${f}_{sw}$ | 10k Hz |

Constant Power Load | Load Location | Operation Time | Active Power | Reactive Power |

Load 1 | DG 1 | All time | 5 kW | 3 kVar |

Load 3 | DG 4 | From 0 to 2 s | 5 kW | 5 kVar |

Load 4 | DG 5 | From 3 to 4 s | 4 kW | 5 kVar |

Constant Impedance Load | Load Location | Operation Time | Resistance | Inductance |

Load 2 | DG 3 | From 1 to 4 s | 10 $\mathsf{\Omega}$ | 27 m$\mathrm{H}$ |

Load 5 | DG 6 | All time | 15 $\mathsf{\Omega}$ | 40.5 m$\mathrm{H}$ |

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**MDPI and ACS Style**

Alsafran, A.S.; Daniels, M.W.
Consensus Control for Reactive Power Sharing Using an Adaptive Virtual Impedance Approach. *Energies* **2020**, *13*, 2026.
https://doi.org/10.3390/en13082026

**AMA Style**

Alsafran AS, Daniels MW.
Consensus Control for Reactive Power Sharing Using an Adaptive Virtual Impedance Approach. *Energies*. 2020; 13(8):2026.
https://doi.org/10.3390/en13082026

**Chicago/Turabian Style**

Alsafran, Ahmed S., and Malcolm W. Daniels.
2020. "Consensus Control for Reactive Power Sharing Using an Adaptive Virtual Impedance Approach" *Energies* 13, no. 8: 2026.
https://doi.org/10.3390/en13082026