# Welfare Maximization-Based Distributed Demand Response for Islanded Multi-Microgrid Networks Using Diffusion Strategy

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## Abstract

**:**

## 1. Introduction

- 1)
- In existing studies, distributed DR is implemented on grid-connected microgrids which requires market price signals and a central aggregator. However, market prices are not available for islanded microgrids. Thus, existing methods cannot be applied for islanded microgrids. Therefore, we have proposed a distributed DR which is not dependent on market price and can be implemented for islanded microgrids.
- 2)
- In existing studies, distributed DR is applied to only single microgrids. We have proposed a distributed DR for a multi-microgrid system, which is more suitable for islanded microgrids to reduce load shedding by sharing power.
- 3)
- Diffusion strategy is utilized in the proposed method; hence, the convergence time is reduced in comparison with conventionally used distributed methods, thus making it more suitable for re-optimization during system contingencies.

## 2. Proposed Operation Method and System Model

#### 2.1. System Model

#### 2.2. Welafare Function

#### 2.3. Diffusion Strategy

_{ij}is the entry of adjacent matrix A and n

_{i}and n

_{j}are the number of neighboring nodes of agent i and j.

## 3. Problem Formulation

#### 3.1. Local Optmization

#### 3.2. Distributed Demand Response

#### 3.2.1. Information Sharing

Algorithm 1: Information Sharing |

Algorithm 2: Distributed demand response |

#### 3.2.2. Optimal Power Allocation

## 4. Numerical Simulations

#### 4.1. Input Data

#### 4.2. Local Optimization Results

#### 4.3. Distributed Demand Response Results

#### 4.3.1. Case 1: Information Sharing

#### 4.3.2. Case 1: Optimal Power Allocation

#### 4.3.3. Case 2: Information Sharing

#### 4.3.4. Case 2: Optimal Power Allocation

## 5. Discussion and Analysis

#### 5.1. Effect of Distributed Demand Response on the Network

#### 5.2. Convergence Analysis

#### 5.3. Implementation Complexity and Practical Implementation

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclatures

Indices | |

t | Index to time, running from t to T |

g | Set of generations, running from g to G |

i | Set of microgrids, running from i to I |

Variables and Parameters | |

${W}_{g,t}(\cdot )$ | Welfare function |

${C}_{g,t}^{DG}$ | Per-unit generation cost of DG unit g at t |

${C}_{g}^{SU}$ | Start-up cost of DG unit g at t |

${C}_{g}^{SD}$ | Shut-down cost of DG unit g at t |

${C}^{P}$ | Penalty cost for load shedding |

${C}^{inc}$ | Incentive price for showing surplus power |

${P}_{t}^{RDG}$ | Forecasted output of RGD at t |

${P}^{B\_Cap}$ | Capacity of BESS |

${P}^{Load}$ | Forecasted load at t |

${P}_{g}^{\mathrm{min}}$ | Minimum generation limit of DG unit g |

${P}_{g}^{\mathrm{max}}$ | Maximum generation limit of DG unit g |

$SO{C}_{\mathrm{min}}^{B}$ | Minimum State of charge of BESS |

$SO{C}_{\mathrm{max}}^{B}$ | Maximum State of charge of BESS |

${L}^{B+}$ | Charging loss of BESS |

${L}^{B-}$ | Discharging loss of BESS |

${u}_{g,t}$ | On/Off status of DG unit g at t |

${y}_{g,t}$ | Start-up status of DG unit g at t |

${z}_{g,t}$ | Shut-down status of DG unit g at t |

${P}_{g}^{\mathrm{min}}$ | Generation amount of DG unit g at t |

${P}_{t}^{B+}$ | Power charged to BESS at t |

${P}_{t}^{B-}$ | Power discharged from BESS at t |

$SO{C}_{t}^{B}$ | State of charge of BESS at t |

${P}_{t}^{sur}$ | Surplus amount of power at time t |

${P}_{t}^{short}$ | Shortage amount of power at time t |

${P}_{t}^{sur\_total}$ | Total surplus power of the network at t |

${P}_{t}^{short\_total}$ | Total shortage power of the network at t |

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**Figure 2.**(

**a**) Graphical representation of welfare functions; (

**b**) marginal benefit for different power consumptions.

**Figure 7.**Local optimization results for all MGs in the network: (

**a**) MG1; (

**b**) MG2; (

**c**) MG3; (

**d**) MG4; (

**e**) MG5.

**Figure 8.**Information sharing (case 1): (

**a**) shortage power information; (

**b**) surplus power information.

**Figure 10.**Information sharing (Case 2): (

**a**) shortage power information; (

**b**) surplus power information.

Parameters | MG1 | MG2 | MG3 | MG4 | MG5 |
---|---|---|---|---|---|

Operation Cost (KRW) | 76 | 88 | 85 | 74 | 82 |

Star-up Cost (KRW) | 200 | 195 | 192 | 187 | 185 |

Shut-down Cost (KRW) | 180 | 175 | 172 | 167 | 165 |

Minimum (kW) | 0 | 0 | 0 | 0 | 0 |

Maximum (kW) | 180 | 390 | 570 | 880 | 820 |

Parameters | MG1 | MG2 | MG3 | MG4 | MG5 |
---|---|---|---|---|---|

Capacity (kWh) | 50 | 100 | 150 | 180 | 230 |

Initial Charge (%) | 30 | 0 | 0 | 0 | 0 |

Charging loss (%) | 5 | 5 | 5 | 4 | 4 |

Discharging loss (kW) | 5 | 5 | 5 | 4 | 4 |

t | MG1 | MG2 | MG3 | MG4 | MG5 | t | MG1 | MG2 | MG3 | MG4 | MG5 |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0 | 109.737 | 0 | 234 | 0 | 13 | 2 | −115 | −38 | 136 | 0 |

2 | 0 | 12 | 37.1053 | 223 | 57.4167 | 14 | 53 | −124 | −64 | 146 | 6 |

3 | 0 | 120 | 0 | 186 | 86 | 15 | 0 | −167 | −96 | 149 | 19 |

4 | 0 | 138 | 0 | 122 | 42 | 16 | −49 | −189 | −83 | 65 | 25 |

5 | −1 | 135 | 0 | 119 | 19 | 17 | −47.5 | −178 | −18.5 | 93 | 0 |

6 | 0 | 116 | 0 | 90 | 0 | 18 | −81 | −133 | 0 | 119 | 0 |

7 | −90 | 84 | −39 | 45 | 0 | 19 | −104 | −4 | 0 | 137 | 0 |

8 | −74 | 13 | −100 | 91 | 0 | 20 | 13 | 162 | 36 | 128 | 48 |

9 | −78 | 0 | −83 | 97 | 17.2517 | 21 | 52 | 188 | 36 | 236 | 66 |

10 | −91.1 | −100 | −126 | 132 | 62 | 22 | 43 | 149 | 66 | 282 | 112 |

11 | 7.36842 | −180 | −64 | 101 | 11 | 23 | 36 | 155 | 46 | 262 | 92 |

12 | 50 | −171 | −109 | 111 | 21 | 24 | 30 | 134 | 91 | 257 | 107 |

MG | w | Shortage (kW) | Power Allocated (kW) |
---|---|---|---|

1 | 85 | 91 | 50.5 |

2 | 98 | 100 | 83 |

3 | 89 | 126 | 60.5 |

MG | w | Shortage (kW) | Power Allocated (kW) |
---|---|---|---|

1 | 93 | 47.5 | 43.5 |

2 | 88 | 178 | 31 |

3 | 84 | 18.5 | 18.5 |

t | MG1 | MG2 | MG3 | MG4 | MG5 | t | MG1 | MG2 | MG3 | MG4 | MG5 |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0 | 0 | 0 | 0 | 0 | 13 | 0 | 99.98 | 38 | 0 | 0 |

2 | 0 | 0 | 0 | 0 | 0 | 14 | 0 | 124 | 64 | 0 | 0 |

3 | 0 | 0 | 0 | 0 | 0 | 15 | 0 | 97.74 | 70.24 | 0 | 0 |

4 | 0 | 0 | 0 | 0 | 0 | 16 | 17.5 | 45 | 27.5 | 0 | 0 |

5 | 0 | 0 | 0 | 0 | 0 | 17 | 44 | 30.44 | 18.5 | 0 | 0 |

6 | 1 | 0 | 0 | 0 | 0 | 18 | 53.25 | 65.75 | 0 | 0 | 0 |

7 | 90 | 0 | 39 | 0 | 0 | 19 | 104 | 4 | 0 | 0 | 0 |

8 | 45.74 | 0 | 58.24 | 0 | 0 | 20 | 0 | 0 | 0 | 0 | 0 |

9 | 54.62 | 0 | 59.62 | 0 | 0 | 21 | 0 | 0 | 0 | 0 | 0 |

10 | 42.16 | 87.16 | 64.07 | 0 | 0 | 22 | 0 | 0 | 0 | 0 | 0 |

11 | 0 | 64 | 55.36 | 0 | 0 | 23 | 0 | 0 | 0 | 0 | 0 |

12 | 0 | 102.2 | 79.74 | 0 | 0 | 24 | 0 | 0 | 0 | 0 | 0 |

Parameters | Case 1 | Case 2 | ||
---|---|---|---|---|

Consensus Algorithm | Proposed Method | Consensus Algorithm | Proposed Method | |

Number of iterations | 72 | 8 | 91 | 10 |

Reduction of iterations (%) | 0 | 88.8 | 0 | 89.01 |

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## Share and Cite

**MDPI and ACS Style**

Ali, H.; Hussain, A.; Bui, V.-H.; Jeon, J.; Kim, H.-M.
Welfare Maximization-Based Distributed Demand Response for Islanded Multi-Microgrid Networks Using Diffusion Strategy. *Energies* **2019**, *12*, 3701.
https://doi.org/10.3390/en12193701

**AMA Style**

Ali H, Hussain A, Bui V-H, Jeon J, Kim H-M.
Welfare Maximization-Based Distributed Demand Response for Islanded Multi-Microgrid Networks Using Diffusion Strategy. *Energies*. 2019; 12(19):3701.
https://doi.org/10.3390/en12193701

**Chicago/Turabian Style**

Ali, Haesum, Akhtar Hussain, Van-Hai Bui, Jinhong Jeon, and Hak-Man Kim.
2019. "Welfare Maximization-Based Distributed Demand Response for Islanded Multi-Microgrid Networks Using Diffusion Strategy" *Energies* 12, no. 19: 3701.
https://doi.org/10.3390/en12193701