# Adaptive Droop Control for Microgrids Based on the Synergetic Control of Multi-Agent Systems

^{*}

## Abstract

**:**

## 1. Introduction

- Distributed synergetic control is used to design the droop parameters adaptively, in which each DG only requires the local and neighbor’s information.
- The general synergetic control algorithm considering the time-delays in communication network is proposed to adjust the initial frequency ${\omega}_{0}$ and voltage ${V}_{0}$ in droop control adaptively, which are used to compensate the frequency and voltage drops, respectively. Therefore, the system frequency and voltage are always at the expected value.
- The improved control strategy can effectively reduce the effects of the disturbance on the control precision and stability of the communication.
- Under the proposed control, the MG system has the globally asymptotic stability which has been verified by the direct Lyapunov method. Therefore, the effect of droop coefficients on stability in traditional and improved controls has been eliminated.

## 2. Dynamic Model of VSC-Based DG

_{Ni}[10], which is equivalent to $\frac{{P}_{1}}{{P}_{N1}}=\frac{{P}_{2}}{{P}_{N2}}=\cdots =\frac{{P}_{n}}{{P}_{Nn}}$, where P

_{N}is the rated active power.

## 3. Adaptive Droop Control Based on MAS

#### 3.1. Graph Theorem

**V**, and the associated adjacency matrix $A=\left[{a}_{ij}\right]\in {R}^{N\times N}$. In this paper, the communication network is assumed to be time-invariant, and

**A**is constant. In $G$, the edge $\left({v}_{j},{v}_{i}\right)$ means that node i receives the information from node j, and $\left({v}_{i},{v}_{i}\right)$ denotes the edge from node i to itself, which is usually neglected. ${a}_{ij}$ is the weight of edge $\left({v}_{j},{v}_{i}\right)$, and ${a}_{ij}>0$, if $\left({v}_{j},{v}_{i}\right)\in \epsilon $, which means that node j is a neighbor of node i; otherwise ${a}_{ij}=0$. In a diagraph, the set of neighbors of node i is denoted as ${N}_{i}=\left\{{v}_{j}|\left({v}_{j},{v}_{i}\right)\in \epsilon \right\}$. In the MG, because DGs exchange information through a communication bus, the non-directed diagraph is considered, which means that node i not only receives the information from node j, and also sends the corresponding information to node j at the same time. Usually, the Laplacian matrix of the digraph is used to express the communication relation defined as $L=\left[{l}_{ij}\right]\u03f5{R}^{n\times n}$, where ${l}_{ij}=-{a}_{ij}$ if $i\ne j$, and ${l}_{ii}=0$. In this paper, the weight of each edge is 1, the Laplacian matrix of the test MG is:

#### 3.2. Active Power Control

- (1)
- $V(0)=0$;
- (2)
- $V(x)>0$, for all $x\ne 0$;
- (3)
- $V(x)\to \infty $ as $\Vert x\Vert \to \infty $;
- (4)
- $\dot{V}(x)<0$ for all $x\ne 0$.

#### 3.3. Active Power-Frequency Droop Control

#### 3.4. Reactive Power-Voltage Droop Control

#### 3.5. Performance with Disturbance in Communication Network

## 4. Simulation and Results

^{k}when k is odd.

#### 4.1. Case Study I: Simulation without Time-Delays and Disturbance

_{2}connects to the grid at t = 2 s. Figure 9 and Figure 10 depicts the results of the proposed control and the traditional control, respectively.

#### 4.2. Case Study II: Simulation with Time-Delays

#### 4.3. Case Study 3: Simulation with Time-Delays and Disturbance

_{j}to DG

_{i}, where ${\delta}_{\omega j}=1.25\mathrm{sin}(2\pi 500t)$ and ${\delta}_{Pj}=50\mathrm{sin}(2\pi 500t)$ are the disturbances for frequency and active power, respectively. The time-delays is also 0.5 s. The simulation results are illustrated in Figure 12.

## 5. Analysis and Discussion

_{2}connects to the grid at t = 2 s due to the constant value of ${\omega}_{oi}$. Meanwhile, in Figure 9a, we know that all DGs work to the expected frequency after a regulation time of about 0.6 s. Therefore, the synergetic control can keep the system frequency near the expected value, and prevent the disturbances while the loads change. At the same time, the active power allocation among DGs is in inverse proportion to the droop coefficients under the operation of synergetic control without leaders, which is the same with that in traditional droop control, as illustrated in Figure 9b and Figure 10b.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

P_{L} | the active power in the transmission line |

Q_{L} | the reactive power in the transmission line |

P_{i} | the active power of DG_{i} |

Q_{i} | the reactive power of DG_{i} |

V | amplitude voltage of the node |

$\delta $ | voltage phase of the node |

R | resistance of the transmission line |

X | reactance of the transmission line |

$\Delta \delta $ | power angle |

$\Delta V$ | voltage drop |

${\omega}_{i}$ | frequency of DG_{i} |

${V}_{di}^{*}$ | amplitude voltage in d-axis |

${V}_{qi}^{*}$ | amplitude voltage in q-axis |

${\omega}_{0i}$ | frequency when the active power is zero |

${V}_{0i}$ | voltage when there active power is zero |

m_{i} | droop coefficient in active power control |

n_{i} | droop coefficient in reactive power control |

${x}_{\omega}$ | frequency first derivative in Rad/s |

${x}_{v}$ | voltage first derivative in V/s |

${x}_{P}$ | active power first derivative in W/s |

${u}_{c\omega i}$ | control variables in frequency control |

${u}_{cvi}$ | control variables in voltage control |

${u}_{cPi}$ | control variables in active power control |

t_{d} | time-delays in communication |

${k}_{P1},{k}_{p2}$ | control gains in active power control |

${k}_{\omega 1}$, ${k}_{\omega 2},{k}_{\omega 3}$ | control gains in frequency control |

${k}_{v1}$, ${k}_{v2},$ ${k}_{v3}$ | control gains in voltage control |

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**Figure 9.**Simulation results without time-delays and disturbance. (

**a**) Frequency; (

**b**) active power of each DG; (

**c**) voltage; (

**d**) reactive power of each DG; (

**e**) adaptive ${\omega}_{oi}$; (

**f**) adaptive ${V}_{oi}$.

**Figure 10.**Simulation results with the traditional droop control. (

**a**) Frequency; (

**b**) active power of each DG; (

**c**) voltage; (

**d**) reactive power of each DG.

**Figure 12.**Simulation results with time-delays and disturbances. (

**a**) Active power; (

**b**) reactive power.

DGs | R_{c}_{1} = R_{c}_{2} = R_{c}_{3} = R_{c}_{4} | L_{c}_{1} = L_{c}_{2} = L_{c}_{3} = L_{c}_{4} | ||

0.2 Ω | 1 mH | |||

Lines | Line_{1} and Line_{3} | Line_{2} | ||

R_{Line}_{1} = R_{Line}_{3} | L_{Line}_{1} = L_{Line}_{3} | R_{Line}_{2} | L_{Line}_{2} | |

0.23 Ω | 0.318 mH | 0.35 Ω | 1.847 mH | |

Loads | Load_{1} | Load_{3} | ||

P_{1} (kW) | Q_{1} (kVar) | P_{3} (kW) | Q_{3} (kVar) | |

36 | 36 | 45.9 | 22.8 | |

Load_{2} | ||||

P_{2} (kW) | Q_{2} (kVar) | |||

36 | 36 |

Primary Control | m_{P1} = m_{P2} | n_{Q1} = n_{Q2} | m_{P3} = m_{P4} | n_{Q3} = n_{Q4} |

0.000094 | 0.0013 | 0.000125 | 0.0015 | |

${V}_{oi}$ | ${\omega}_{oi}$ | |||

330 V | 325.3 rad/s | |||

Control Gains | Frequency | ${k}_{\omega 1}$ | ${k}_{\omega 2}$ | ${k}_{\omega 3}$ |

50 | 0.8 | 800 | ||

Voltage | ${k}_{v1}$ | ${k}_{v2}$ | ${k}_{v3}$ | |

150 | 0.8 | 3 | ||

Active power | ${k}_{P1}$ | ${k}_{P2}$ | ||

500 | 0.8 |

Control Strategy [Reference] | Communication | Frequency Error | Voltage Error | System Stability | Active Power Allocation |
---|---|---|---|---|---|

Synergetic control | necessary | No | No | stable | proportional to the rated |

[17] | unnecessary | No | Yes | stable | proportional to the rated |

[21] | unnecessary | Yes | Yes | stable | nonlinear with the frequency |

[22] | unnecessary | No | Yes | SSS | proportional to the rated |

[24] | unnecessary | Yes | Yes | SSS | proportional to the rated |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Yu, Z.; Ai, Q.; He, X.; Piao, L.
Adaptive Droop Control for Microgrids Based on the Synergetic Control of Multi-Agent Systems. *Energies* **2016**, *9*, 1057.
https://doi.org/10.3390/en9121057

**AMA Style**

Yu Z, Ai Q, He X, Piao L.
Adaptive Droop Control for Microgrids Based on the Synergetic Control of Multi-Agent Systems. *Energies*. 2016; 9(12):1057.
https://doi.org/10.3390/en9121057

**Chicago/Turabian Style**

Yu, Zhiwen, Qian Ai, Xing He, and Longjian Piao.
2016. "Adaptive Droop Control for Microgrids Based on the Synergetic Control of Multi-Agent Systems" *Energies* 9, no. 12: 1057.
https://doi.org/10.3390/en9121057