# Modified Dragonfly Optimisation for Distributed Energy Mix in Distribution Networks

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## Abstract

**:**

## 1. Introduction

## 2. Proposed Optimization Model and Strategies for DER Mix

#### 2.1. Wind Power Modeling

#### 2.2. Fuel Cell Modeling

#### 2.3. Load Demand

#### 2.4. Proposed Two-Stage Optimization Model

#### 2.4.1. Stage-I

#### Network Energy Loss Minimization

#### Bus Voltage Variation Minimization

#### Minimization of Load Profile Variation

#### Minimization of System Energy Spillage

#### Minimization of Conversion Losses of BESS and Control Variables

#### 2.4.2. Stage-II

Algorithm 1 Pseudo Codes for optimal operations of dispatchable DERs in stage-II. |

Require: Obtain the sub-optimal allocation of multiple DERs suggested by the Stage-I, and deploy in the model, i.e., Objective Function ${O}_{b{j}_{\mathit{2}}}\mathit{\left(}h\mathit{\right)}$ Equation (15)set h = 0while h ≤ 24 doh = h + 1 Obtain the the total power produce by WTs (${P}_{G}^{h}$) using Equation (2) and total demand of system (${P}_{D}^{h}$) using Equation (4) at hth hour Determine the lower and upper limits of dispatchable DERs i.e., BESS by [$\underline{{P}_{li{m}_{j}}^{h}}$, $\overline{{P}_{li{m}_{j}}^{h}}$] using Equations (17) and (18). if${P}_{G}^{h}$ > ${P}_{D}^{h}$ thenObtain the optimal power outputs of dispatchable DERs, ${P}_{C}^{BESS}h$, for the minimization of objective function ${O}_{b{j}_{\mathit{2}}}^{h}$ by controlling the power outputs of energy storage [$\underline{{P}_{li{m}_{j}}^{h}}$: 10 kW: 0 kW ]. elseObtain the optimal power outputs of dispatchable DERs, ${P}_{C}^{BESS}\mathit{\left(}h\mathit{\right)}$, for the minimization of objective function ${O}_{b{j}_{\mathit{2}}}^{h}$ by controlling its power outputs between [0 kW: 10 KW: $\overline{{P}_{li{m}_{j}}^{h}}$]. end ifCalculate the swarm fitness as per the new upgraded dragonfly position while considering the boundaries limitation.Execute power flow calculation and obtain the objective functions of I-stage optimization at hour h deploying BESS dispatch.end whilereturn Objective Function ${O}_{b{j}_{\mathit{2}}}^{h}$ for I-stage optimization for fitness values |

## 3. Proposed Dragon Fly Algorithm

#### 3.1. Standard Variant of Dragon Fly Algorithm

**Separation (${\mathit{S}}_{\mathit{a}}$)**: this function refer to a characteristics that helps dragonfly to avoid collision with near by flies of the swarm;**Alignment (${\mathit{A}}_{\mathit{a}}$)**: this function refer to a characteristics that helps dragonfly to match its flying velocity to that of other flies in the swarm;**Cohesion (${\mathit{C}}_{\mathit{a}}$)**: refers the that tendency of dragonfly individuals that attract them towards the centre of mass in the vicinity.

**Attraction (${\mathit{F}}_{\mathit{a}}$)**to food source and the

**Distraction (${\mathit{E}}_{\mathit{a}}$)**to an enemy is determine as:

#### 3.2. Improved Dragon Fly Algorithm

**(1) Observed limitation I:**It is analyzed that conventional DA, most often converges to a suboptimal results when tested to a complex engineering problem. It could be due to the unguided updates caused by the factors like inertia weight coefficient (w). As similar to the limitation observed in PSO, w may divert the solution in a particular direction that may or may not have the potential solution.

**Suggested improvement I:**In order to overcome this limitation of standard DA, the step vector ($\mathsf{\Delta}x$) is further multiplied by a random variable, $rnd$, scaled between 0 to 1. This will help in entering a random element into the mechanism and creates a probable global solution. Therefore, now the position vector will be upgraded as:

**(2) Observed limitation II:**In the standard DA to enhance the randomness and to execute exploration of the dragonfly. Levy flight mechanism is deployed to seek the domain by the random walk, as described in the Equation (23). It is found that during the execution of standard DA for engineering problems that deploying current position with levy flight may stag the solution, as this mechanism may keep the solution near the best find location that may or may not be the global position.

**Suggested improvement II:**In order to overcome this limitation and enhance the potential of DA the Equation (23) is rewritten [27,28] as:

Algorithm 2 Pseudocode code for IDA algorithm. |

Initialize the population of dragonflies, and set the values of required parameters i.e., max. iteration, various constrains (${c}_{\mathit{1}}$, ${c}_{\mathit{2}}$…) etc. Further, initiate the step vector $\mathsf{\Delta}x$.whilei< max. iteration doCalculate the fitness of each dragonfly with respect to its position.Upgrade the location of food source and enemy with respect to dragonfly.Calculate the value of ${S}_{a}$, ${A}_{a}$, ${C}_{a}$, ${F}_{a}$, and ${E}_{a}$ from the Equation (19).Upgrade the neighbouring radius.if The individual has at least one vicinity dragonfly thenUpgrade the velocity vector by Equation (26).Upgrade the position vector by Equation (27).elseUpgrade the position vector by Equation (27).end ifCalculate the swarm fitness as per the new upgraded dragonfly position while considering the boundaries limitation.end whileKeep the value of best solution |

## 4. Simulation Results

#### 4.1. Validation of Proposed Improvements in the Dragonfly Algorithm

#### 4.2. Case Studies of DER Mix

#### 4.2.1. DER Mix in 33-Bus Distribution Network

#### 4.2.2. DER Mix in 108-Bus Indian Distribution Network

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Comparison of convergence characteristics of DA, improvements, and IDA. (

**b**) Box plot of solution archived from IDA, DA, EHO, and PSO for power losses minimization in an ADN.

Parameter and Specification | Value |
---|---|

$\zeta $ ,$\gimel $ ,${T}_{Lvl}$ ,${P}_{dg}^{max}$ | 365, 90, 24, 2500 (kW) |

${\nu}_{c\_out}$, $\nu \left(r\right)$, ${\nu}_{c\_in}$ | 20, 15, 4 (m/s) |

$SO{C}^{max}$, $SO{C}^{min}$ | 100, 10 (%) |

${P}_{c}^{max}$, ${P}_{d}^{max}$ | 1000 (MW) each |

$B{s}^{max}$ | 50% of FC capacity & 6000 (kWh) |

Technique | Best * | Mean * | Worst * | SD |
---|---|---|---|---|

DA | 0.0721 | 0.0741 | 0.0793 | 0.00252 |

IDA | 0.0715 | 0.0730 | 0.0769 | 0.00239 |

Techniques | Optimal DG [Sizes in MW] Size | Power Loss in MW |
---|---|---|

TLBO [32] | [1.183]12; [1.191]28; [1.186]30 | 0.1246 |

GA [33] | [1.500]11; [0.423]29; [1.071]30 | 0.1063 |

PSO [33] | [1.177]08; [0.982]13; [0.830]32 | 0.1053 |

GA/PSO [33] | [0.925]11; [0.863]16; [1.200]32 | 0.1034 |

QOTLBO [32] | [1.083]13; [1.187]26; [1.199]30 | 0.1034 |

CMSO [5] | [0.756]14; [1.097]24; [1.066]30 | 0.0714 |

IDA | [0.754]15; [1.100]24; [1.072]31 | 0.0714 |

Case | 33-Bus Distribution Network | 108-Bus Indian Distribution Network |
---|---|---|

Base Case | NO DERs | NO DERs |

Case I | 3 WTs | 7 WTs |

Case II | 3 WTs & 1 BESSs | 7 WTs & 2 BESSs |

Case III | 2 WTs & 1 FCs | 5 WTs & 2 FCs |

**Table 5.**Optimal sites and sizes of mixed DERs in 33-bus test distribution system obtained by IDA two-stage optimization method.

Cases | DER Sites [Sizes (kW)] | DERP (%) | BESS Sites [Sizes (kWh)] | SDD (kW) | AEL (MWh) | Min./Mean Voltage (p.u.) | Conv. Loss (MWh) | Reduc. in TAEL (%) |
---|---|---|---|---|---|---|---|---|

Base | - | - | - | 1165.21 | 3493.27 | 0.899/0.940 | - | - |

Case I. (EHO) | $07{\left[500\right]}_{WT}$$10{\left[1250\right]}_{WT}$$32{\left[2000\right]}_{WT}$ | 47.67 | - | 1785.9 | 1821.0 | 0.956/0.975 | - | 47.67 |

Case I. (PSO) | $04{\left[500\right]}_{WT}$$11{\left[1500\right]}_{WT}$$31{\left[2000\right]}_{WT}$ | 67.29 | - | 1835.9 | 1782.7 | 0.956/0.975 | - | 48.96 |

Case I. (IDA) | $11{\left[850\right]}_{WT}$$27{\left[1250\right]}_{WT}$$32{\left[1250\right]}_{WT}$ | 56.36 | - | 1734.2 | 1750.5 | 0.935/0.966 | - | 50.04 |

Case II. (IDA) | $14{\left[1500\right]}_{WT}$$27{\left[500\right]}_{WT}$$31{\left[2000\right]}_{WT}$ | 67.29 | 10[5170] | 1386.4 | 1685.7 | 0.967/0.978 | 357.2 | 41.54 |

Case III. (IDA) | $27{\left[1876\right]}_{FC}$$11{\left[850\right]}_{W}T$$25{\left[500\right]}_{WT}$ | 54.28 | 874.60 | 967.9 | 1447.5 | 0.989/0.998 | 245.5 | 51.53 |

**Table 6.**Optimal sites and sizes of mixed DERs in 108-bus Indian distribution system obtained by IDA two-stage optimization method.

Cases | DER Sites [Sizes (kW)] | DERP (%) | BESS Sites [Sizes (kWh)] | SDD (kW) | AEL (MWh) | Min./Mean Volt. (p.u.) | Conv. Loss (MWh) | Reduc. in TAEL (%) |
---|---|---|---|---|---|---|---|---|

Base | - | - | - | 3780.6 | 10,996.91 | 0.876/0.95 | - | - |

Case I. | $27{\left[2250\right]}_{WT}$ $34{\left[1250\right]}_{WT}$ $42{\left[1500\right]}_{WT}$ $48{\left[850\right]}_{WT}$ $60{\left[2000\right]}_{WT}$ $85{\left[1500\right]}_{WT}$ $102{\left[2000\right]}_{WT}$ | 22.11 | - | 5712.2 | 6417.4 | 0.956/0.975 | - | 41.64 |

Case II. | $26{\left[1500\right]}_{WT}$ $32{\left[2250\right]}_{WT}$ $39{\left[1500\right]}_{WT}$ $60{\left[2250\right]}_{WT}$ $63{\left[1500\right]}_{WT}$ $93{\left[2250\right]}_{WT}$ $102{\left[2250\right]}_{WT}$ | 23.39 | 92[4756.9] 102[5337.3] | 5233.5 | 5810 | 0.961/0.978 | 1802.5 | 30.78 |

Case III. | $60{\left[2671.9\right]}_{FC}$ $102{\left[1841.9\right]}_{FC}$ $31{\left[1500\right]}_{WT}\phantom{\rule{0ex}{0ex}}$ $43{\left[1250\right]}_{WT}$ $46{\left[1500\right]}_{WT}$ $72{\left[500\right]}_{WT}$ $86{\left[1500\right]}_{WT}$ | 20.98 | 633.24; 800.1 | 4082.2 | 5806.4 | 0.956/0.975 | 1070.6 | 37.46 |

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**MDPI and ACS Style**

Singh, P.; Meena, N.K.; Yang, J.; Bishnoi, S.K.; Vega-Fuentes, E.; Lou, C.
Modified Dragonfly Optimisation for Distributed Energy Mix in Distribution Networks. *Energies* **2021**, *14*, 5690.
https://doi.org/10.3390/en14185690

**AMA Style**

Singh P, Meena NK, Yang J, Bishnoi SK, Vega-Fuentes E, Lou C.
Modified Dragonfly Optimisation for Distributed Energy Mix in Distribution Networks. *Energies*. 2021; 14(18):5690.
https://doi.org/10.3390/en14185690

**Chicago/Turabian Style**

Singh, Pushpendra, Nand Kishor Meena, Jin Yang, Shree Krishna Bishnoi, Eduardo Vega-Fuentes, and Chengwei Lou.
2021. "Modified Dragonfly Optimisation for Distributed Energy Mix in Distribution Networks" *Energies* 14, no. 18: 5690.
https://doi.org/10.3390/en14185690