# Distributed Economic Power Dispatch and Bus Voltage Control for Droop-Controlled DC Microgrids

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## Abstract

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## 1. Introduction

## 2. Problem Formulation

#### 2.1. Conventional Droop Control Method in DC Microgrids

#### 2.2. Proposed Optimal Bus Voltage Control

## 3. Distributed Consensus-Based EPD and ABVO Algorithms

#### 3.1. Graph Theory Review

#### 3.2. Distributed Consensus Algorithm

#### 3.3. Distributed Consensus-Based EPD Algorithm

_{i}$\underset{\xaf}{{\lambda}_{i}}+{b}_{i}$.

#### 3.4. Distributed Consensus-Based ABVO Algorithm

#### 3.5. Algorithm Implementation

## 4. Simulation Studies

#### 4.1. Algorithm Convergence Test

#### 4.2. Performance Comparison with and without the Proposed Algorithm

#### 4.3. Time-Varying Load Demand Test

#### 4.4. Performance Comparison with a Distributed Cooperative Control Strategy

#### 4.5. Algorithm Robustness Test

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Proposed distributed optimal bus voltage control for droop-controlled DC microgrids. EPD, economic power dispatch; ABVO, average bus voltage observation.

**Figure 6.**Convergence test of the EPD and ABVO algorithms for a DC microgrid with 5 DGs. (

**a**) Incremental cost of the DGs in each iteration; (

**b**) EPD of the DGs in each iteration; (

**c**) observed average bus voltage of the DGs in each iteration.

**Figure 7.**Convergence test of the EPD and ABVO algorithms for a larger DC microgrid with 20 DGs. (

**a**) Incremental cost of the DGs in each iteration; (

**b**) EPD of the DGs in each iteration; (

**c**) observed average bus voltage of the DGs in each iteration.

**Figure 8.**Convergence test of the EPD and ABVO algorithms for a larger DC microgrid with 20 DGs when two DGs reached their rated power. (

**a**) Incremental cost of the DGs in each iteration; (

**b**) EPD of the DGs in each iteration.

**Figure 9.**Convergence test of the EPD algorithm for a DC microgrid with 20 DGs when the communication network among agents is designed with different topologies. (

**a**) Each agent communicates with its six adjacent neighbors; (

**b**) each agent communicates with its eight adjacent neighbors; (

**c**) each agent communicates with its ten adjacent neighbors.

**Figure 10.**Comparative studies of a DC microgrid before and after the proposed control strategy was applied. (

**a**) Generated power of each DG. (

**b**) Incremental cost of each DG. (

**c**) Total generation cost of all the DGs. (

**d**) Average bus voltage of the microgrid.

**Figure 11.**Performance of the proposed control strategy with time-varying load demand. (

**a**) Generated power of each DG. (

**b**) Incremental cost of each DG. (

**c**) Total generated power of all the DGs. (

**d**) Average bus voltage of the microgrid.

**Figure 12.**Comparative studies between the proposed control strategy and distributed cooperative control. (

**a**) Generated power of each DG with the proposed control strategy. (

**b**) Generated power of each DG with the conventional distributed cooperative control. (

**c**) Total generation cost of all the DGs. (

**d**) Average bus voltage of the microgrid.

**Figure 13.**Performance of the proposed control strategy with a DG turned off. (

**a**) Generated power of each DG. (

**b**) Incremental cost of each DG. (

**c**) Total generation cost of all the DGs. (

**d**) Average bus voltage of the microgrid.

**Figure 14.**Performance of the proposed control strategy with an agent loss. (

**a**) Generated power of each DG. (

**b**) Incremental cost of each DG. (

**c**) Total generation cost of all the DGs. (

**d**) Average bus voltage of the microgrid.

DG and Agent Index | Neighboring Agents | ${\mathit{a}}_{\mathit{i}}$ $\mathbf{\$}/{\mathbf{kW}}^{2}\mathbf{h}$ | ${\mathit{b}}_{\mathit{i}}$ $\mathbf{\$}/\mathbf{kWh}$ | ${\mathit{c}}_{\mathit{i}}$ $\mathbf{\$}/\mathbf{h}$ | ${\mathit{m}}_{\mathit{i}}$ V/A | Range kW |
---|---|---|---|---|---|---|

1 | 2,3 | 0.0001 | 0.042 | 0.25 | 0.1533 | [0, 60] |

2 | 1,4 | 0.0001 | 0.05 | 0.42 | 0.7667 | [0, 12] |

3 | 1,4,5 | 0.0001 | 0.044 | 0.35 | 0.2410 | [0, 40] |

4 | 2,3,5 | 0.0001 | 0.048 | 0.45 | 0.3213 | [0, 30] |

5 | 3,4 | 0.0001 | 0.047 | 0.33 | 0.0640 | [0, 20] |

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## Share and Cite

**MDPI and ACS Style**

Cheng, Z.; Li, Z.; Liang, J.; Gao, J.; Si, J.; Li, S. Distributed Economic Power Dispatch and Bus Voltage Control for Droop-Controlled DC Microgrids. *Energies* **2019**, *12*, 1400.
https://doi.org/10.3390/en12071400

**AMA Style**

Cheng Z, Li Z, Liang J, Gao J, Si J, Li S. Distributed Economic Power Dispatch and Bus Voltage Control for Droop-Controlled DC Microgrids. *Energies*. 2019; 12(7):1400.
https://doi.org/10.3390/en12071400

**Chicago/Turabian Style**

Cheng, Zhiping, Zhongwen Li, Jing Liang, Jinfeng Gao, Jikai Si, and Shuhui Li. 2019. "Distributed Economic Power Dispatch and Bus Voltage Control for Droop-Controlled DC Microgrids" *Energies* 12, no. 7: 1400.
https://doi.org/10.3390/en12071400