# Optimal Siting and Sizing of Distributed Generators by Strawberry Plant Propagation Algorithm

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## Abstract

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## 1. Introduction

- Type 1:
- Injects active power into the system;
- Type 2:
- Injects both active and reactive power into the system;
- Type 3:
- Injects active power but absorbs reactive power;
- Type 4:
- Injects reactive power only.

## 2. Power Loss Reduction and Cost Analysis Formulation

#### 2.1. Power Loss Reduction

#### 2.2. Cost Analysis

## 3. Optimization Using Strawberry Plant Propagation Algorithm

#### Optimal Placement of DGs Using SPPA

- Take network input from user and read system data.
- Initialize the algorithm parameters ($iter$, $ite{r}_{max}$, population size $ns$, network size, DG type, and variable I to store the results of each iteration).
- Calculate P, Q, V, ${P}_{loss}$, and ${Q}_{loss}$.
- Rank nodes with respect to power losses in descending order.
- Randomly, the number of runners, ${n}_{r}$ (i.e., DG Size) generated by a solution should be proportional to its fitness, given as:$${n}_{r}=\left[{n}_{max}{N}_{i}r\right]$$
- Distance covered (Loss) by each runner—i.e., $d{x}_{j}^{i}$—will be given as:$$d{x}_{j}^{i}=2(1-{N}_{i})(r-0.5)$$
- The placement of DG is performed through an equation, given as:$${Y}_{j}={x}_{j}+({b}_{j}-{a}_{j})d{x}_{j}^{i}$$The ${Y}_{j}$ values are then adjusted to ensure that new points generated are within the bounds ${a}_{j}$ and ${b}_{j}$; the distance calculated will be used to update the solution i based on the bounds in ${x}_{j}$.
- Calculate ${P}_{loss}$ and ${Q}_{loss}$.
- Compare if ${P}_{loss}$ is less than the previous iteration.
- Update the results stored in variable I (step 2).
- Else existing placement of DG will be remaining stored in variable I.
- Check if $iter=ite{r}_{max}$, then go to step 13; otherwise, go to step 3.
- Print results, the global optima is found.

## 4. Results and Discussion

#### 4.1. 33-Node System

#### 4.2. 69-Node System

#### 4.3. Results Comparison with Other Optimization Techniques

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Technique | Optimal Size (kW) | Optimal Location | ${\mathit{P}}_{\mathit{Injected}}$ (kW) | ${\mathit{P}}_{\mathit{Loss}}$ (kW) | $\mathit{PLR}$ (%) | ${\mathit{V}}_{\mathit{min}}$ (pu) | Ref. |
---|---|---|---|---|---|---|---|

BFOA | 779, 880, 1083 | 14, 25, 30 | 2742 | 73.53 | 65.1 | – | [27] |

WOA | 1072.8, 772.5, 856.7 | 30, 25, 13 | 2702 | 73.75 | 65.1 | 0.97 | [31] |

PPBIL& PSO | 403, 524, 642 | 12, 15, 31 | 1569 | 91.5 | 56.6 | 0.96 | [36] |

DSCA-SOCP | 801, 1091, 1053 | 13, 24, 30 | 2945 | 72.8 | 65.5 | – | [37] |

SPSO | 640, 740, 420 | 16, 30, 32 | 1800 | 74 | 64.5 | 0.97 | [42] |

ALO | 850, 1191 | 13, 30 | 2041 | 82.6 | 60.8 | 0.97 | [43] |

FPA | 1039, 1086 | 12, 30 | 2125 | 89.2 | 57.7 | 0.97 | [44] |

GA | 1323, 867 | 30, 13 | 2190 | 81.75 | 61.1 | 0.97 | [45] |

IHHO | 775.5, 1080.8, 1066.7 | 14, 24, 30 | 2923 | 72.8 | 65.5 | – | [46] |

GAMS | 770, 1096, 1065 | 14, 24, 30 | 2931 | 72.8 | 65.5 | – | [47] |

CBGA-VSA | 801, 1091, 1053 | 13, 24, 30 | 2945 | 72.8 | 65.5 | 0.97 | [48] |

SPPA | 1270, 2225 | 3, 6 | 3495 | 63.74 | 69.4 | 0.99 | Proposed |

Technique | Optimal Size (kW) | Optimal Location | ${\mathit{P}}_{\mathit{Injected}}$ (kW) | ${\mathit{P}}_{\mathit{Loss}}$ (kW) | $\mathit{PLR}$ (%) | ${\mathit{V}}_{\mathit{min}}$ (pu) | Ref. |
---|---|---|---|---|---|---|---|

WOA | 489, 476, 1680 | 11, 18, 61 | 2645 | 69.72 | 69 | 0.98 | [31] |

PPBIL& PSO | 178, 1053, 420 | 26, 61, 66 | 1651 | 86.9 | 64.1 | 0.96 | [36] |

DSCA-SOCP | 526, 380, 1719 | 11, 18, 61 | 2625 | 69.41 | 69.2 | – | [37] |

SPSO | 1360, 520 | 61, 64 | 1880 | 81 | 64 | 0.98 | [42] |

ALO | 538, 1700 | 17, 61 | 2238 | 70.75 | 68.6 | 0.98 | [43] |

FPA | 463, 1771 | 17, 61 | 2234 | 71.7 | 68.1 | 0.97 | [44] |

IHHO | 527.2, 382.5, 1719.4 | 11, 17, 61 | 2629.1 | 69.41 | 69.2 | – | [46] |

GAMS | 813, 1444, 289 | 12, 61, 64 | 2546 | 72.09 | 68 | – | [47] |

CBGA-VSA | 526, 380, 1719 | 11, 18, 61 | 2625 | 69.41 | 69.2 | 0.98 | [48] |

PSO | 1293, 673, 868 | 61, 17, 50 | 2834 | 87.48 | 61.1 | 0.98 | [49] |

SPPA | 42.8, 995, 102.1, 1768 | 57, 7, 6, 58 | 2907.9 | 46.89 | 79.2 | 0.98 | Proposed |

Technique | ${\mathit{P}}_{\mathit{LOSS}}$ (kW) | ${\mathit{P}}_{\mathit{DG}}$ (kW) | ${\mathit{P}}_{\mathit{IN}}$ (kW) | ${\mathit{E}}_{\mathit{IN}}$ (kWh) | ${\mathit{K}}_{\mathit{EIN}}$ (kWh) | Cost Reduction | Ref. |
---|---|---|---|---|---|---|---|

BFOA | 73.53 | 2742 | 1046.5 | 9,167,603 | 1,672,171 | 73.1 | [27] |

WOA | 73.75 | 2702 | 1086.8 | 9,520,315 | 1,736,505 | 72.3 | [31] |

PPBIL& PSO | 91.5 | 1569 | 2237.5 | 19,600,500 | 3,575,131 | 42.9 | [36] |

DSCA-SOCP | 72.8 | 2945 | 842.8 | 7,382,799 | 1,346,623 | 78.5 | [37] |

SPSO | 74 | 1800 | 1989 | 17,423,640 | 3,178,072 | 49.3 | [42] |

ALO | 82.6 | 2041 | 1756.6 | 15,387,816 | 2,806,738 | 55.2 | [43] |

FPA | 89.2 | 2125 | 1679.2 | 14,709,792 | 2,683,066 | 57.2 | [44] |

GA | 81.75 | 2190 | 1606.7 | 14,075,130 | 2,567,304 | 59.0 | [45] |

IHHO | 72.79 | 2923 | 864.7 | 7,575,035 | 1,381,686 | 77.9 | [46] |

GAMS | 72.01 | 2931 | 856.0 | 7,498,648 | 1,367,753 | 78.1 | [47] |

CBGA-VSA | 72.09 | 2945 | 842.1 | 7,376,708 | 1,345,512 | 78.5 | [48] |

SPPA | 63.74 | 3495 | 251.7 | 2,205,242 | 402,236 | 93.5 | Proposed |

WITHOUT | 208.5 | 0 | 3923.5 | 34,369,503 | 6,268,997 |

Technique | ${\mathit{P}}_{\mathit{LOSS}}$ (kW) | ${\mathit{P}}_{\mathit{DG}}$ (kW) | ${\mathit{P}}_{\mathit{IN}}$ (kW) | ${\mathit{E}}_{\mathit{IN}}$ (kWh) | ${\mathit{K}}_{\mathit{EIN}}$ (kWh) | Cost Reduction | Ref. |
---|---|---|---|---|---|---|---|

WOA | 69.7 | 2645 | 1226.7 | 10,746,067 | 1,960,083 | 69.5 | [31] |

PPBIL& PSO | 86.9 | 2028 | 1860.9 | 16,301,484 | 2,973,391 | 53.8 | [36] |

DSCA-SOCP | 69.4 | 2625 | 1246.4 | 10,918,552 | 1,991,544 | 69.1 | [37] |

SPSO | 36 | 1880 | 1958 | 17,152,080 | 3,128,539 | 51.3 | [42] |

ALO | 70.8 | 2238 | 1634.8 | 14,320,410 | 2,612,048 | 59.4 | [43] |

FPA | 71.7 | 2234 | 1639.7 | 14,363,772 | 2,619,952 | 59.2 | [44] |

IHHO | 69.4 | 2629 | 1242.3 | 10,882,636 | 1,984,993 | 69.1 | [46] |

GAMS | 72.1 | 2546 | 1328.1 | 11,634,068 | 2,122,054 | 67.0 | [47] |

CBGA-VSA | 69.4 | 2625 | 1246.4 | 10,918,464 | 1,991,528 | 69.0 | [48] |

PSO | 87.5 | 2835 | 1054.5 | 9,237,245 | 1,684,873 | 73.8 | [49] |

SPPA | 46.9 | 2907 | 941.9 | 8,250,956 | 1,504,974 | 76.6 | Proposed |

WITHOUT | 225 | 0 | 4026.9 | 35,275,644 | 6,434,277 |

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**MDPI and ACS Style**

Shahzad, M.; Akram, W.; Arif, M.; Khan, U.; Ullah, B.
Optimal Siting and Sizing of Distributed Generators by Strawberry Plant Propagation Algorithm. *Energies* **2021**, *14*, 1744.
https://doi.org/10.3390/en14061744

**AMA Style**

Shahzad M, Akram W, Arif M, Khan U, Ullah B.
Optimal Siting and Sizing of Distributed Generators by Strawberry Plant Propagation Algorithm. *Energies*. 2021; 14(6):1744.
https://doi.org/10.3390/en14061744

**Chicago/Turabian Style**

Shahzad, Mohsin, Waseem Akram, Muhammad Arif, Uzair Khan, and Barkat Ullah.
2021. "Optimal Siting and Sizing of Distributed Generators by Strawberry Plant Propagation Algorithm" *Energies* 14, no. 6: 1744.
https://doi.org/10.3390/en14061744