# Load Concentration Factor Based Analytical Method for Optimal Placement of Multiple Distribution Generators for Loss Minimization and Voltage Profile Improvement

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## Abstract

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## 1. Introduction

- Load concentration factor as a method of choosing optimal location.
- Generalized analytical expressions for “N” DGs with improved mathematical representation in comparison to [35].
- Exhaustive method of finding operational power factor for DG operation.

## 2. Problem Formulation

#### 2.1. Distribution System Power Losses

#### 2.2. Methodological Steps

- Optimal location selection;
- Simultaneous optimal sizing.

## 3. Optimal Location Selection

#### 3.1. Basic Idea Behind Loss Reduction with DGs

#### 3.2. Types of Buses

_{i}” is defined as the set of the directly connected buses to bus “i” and bus “i” itself. For the bus itself, the line length is zero, hence the line loss. Loaded buses are the load carrying buses. For a bus without any load, a zero load can be considered in order to get generalized definitions and mathematical expressions. For the IEEE 37 node system given in [37], all the buses except 1, 3, 4, 6, 7, 8, 12, 16, 18, 25, 29 and 34 are categorized as loaded buses. For bus 22; 21, 23 and 24 are directly connected buses and set “$C22$” will be given as {21, 23, 24}. Similarly, for bus 10, “$C10$” will be given as {8}.

#### 3.3. Load Concentration Factor (LCF)

#### 3.4. Selecting the Optimal Locations

#### 3.5. Selection of Optimal Locations in the Systems Under Study

## 4. Simultaneous Optimal Sizing

#### 4.1. Analytical Expressions

#### 4.2. Operational Power Factor

#### 4.3. Algorithm for Optimal Sizes Calculation

- Enter the base case network.
- Enter the desired number of DGs to be placed.
- Run base case load flow and calculate losses using Equation (1).
- For all the buses in a region, calculate the $LC{F}_{i}$ and arrange the buses in descending order with respect to this.
- Choose “N” buses for placing “N” DGs. The initial set of bus numbers will contain the bus(es) with highest LCF in each region.
- Based on input data in step (4), find the optimal size of DGs using the expression given in Equation (11).
- Calculate operational power factor of DG using exhaustive method.
- Stop if:
- The sum of power of DGs to be installed is less than the total power demand plus losses.
- The bus voltages are within a permissible limit.
- The lines are not overloaded.

Else, look for new locations by using these steps.- Try to change only one bus in the region from the set of bus numbers chosen in step (4) i.e., for placing n DGs, $(n-1)$ buses will remain the same.
- The most suitable candidate for the changed bus will be the one which has the least difference in LCF from the LCF of a previously selected bus, while staying in the same region.
- In case of a clash between any two or more regions for the selection of the second highest LCF bus, priority will be given to the bus which carries the highest load.

Go to step (6) - Place sized DGs in the system and calculate losses using Equation (1).
- To check for better sizes, optimal sizes in nearest proximity can also be checked.
- To check for even better solutions, the next candidate buses in the list of LCF can also be checked, but experiments showed that this leads to zero or negligible improvements.

## 5. Comparative Studies

#### 5.1. Loss Sensitivity Factor

#### 5.2. Improved Analytical Method

#### 5.3. Exhaustive Load Flow Method

## 6. Results

#### 6.1. Experiments/Use Cases

#### 6.2. Operational Power Factor Test Results

#### 6.3. Active Power Loss Minimization Results

#### 6.3.1. 37 Bus System

#### 6.3.2. 119 Bus System

#### 6.4. Voltage Profile Improvement Results

## 7. Conclusions

## Author Contributions

## Conflicts of Interest

## Abbreviations

CLPF | Combined Load Power Factor |

DSPF | DIgSILENT PowerFactory |

ELF | Exhaustive Load Flow |

IA | Improved Analytical |

LSF | Loss Sensitivity Factor |

LCF | Load Concentration Factor |

MM | Mohsin’s Method |

pf | Power Factor |

VPI | Voltage Profile Improvement |

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Parameters | 37 Node System | 119 Node System |
---|---|---|

Active Power Demand | 4.98 MW | 22.71 MW |

Reactive Power Demand | 1.35 MVar | 17.04 MVar |

Active Power Loss without DGs | 281.77 kW | 1440.89 kW |

Min Voltage in Network | 0.878 p.u | 0.869 p.u |

Max Voltage in Network | 1.000 p.u | 1.000 p.u |

Case | Method | Installed DG Schedule (MW) | DG (MW) | Ploss (kW) | Loss Red (%) | Time (s) | ||||
---|---|---|---|---|---|---|---|---|---|---|

No DG | Total Real Load = 4.977 MW | - | 281.77 | - | - | |||||

4 DGs | LSF | Bus | 25 | 2 | 7 | 37 | 7.5 | 150.465 | 46.60 | 35.34 |

Size | 2.5 | 5 | 0 | 0 | ||||||

IA | Bus | 5 | 19 | 24 | 33 | 3.23 | 37.798 | 86.52 | 18.32 | |

Size | 0.67 | 1.05 | 0.51 | 1 | ||||||

ELF | Bus | 11 | 13 | 22 | 32 | 4.5 | 10.318 | 96.33 | 117.44 | |

Size | 0.5 | 1.5 | 1 | 1.5 | ||||||

MM | Bus | 12 | 18 | 22 | 32 | 3.5 | 11.479 | 95.92 | 12.54 | |

Size | 0.6 | 0.6 | 0.9 | 1.4 |

Case | Method | Installed DG Schedule (MW) | DG (MW) | Ploss (kW) | Loss Red (%) | Time (s) | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

No DG | Total Real Load = 22.71 MW | - | 1440.89 | - | - | ||||||

5 DGs | LSF | Bus | 52 | 69 | 83 | 95 | 114 | 15.5 | 490.73 | 65.94 | 619.01 |

Size | 3.5 | 3 | 2.5 | 3 | 3.5 | ||||||

IA | Bus | 53 | 77 | 82 | 112 | 116 | 12.1 | 345.24 | 76.04 | 106.59 | |

Size | 3.6 | 3.1 | 1.7 | 2.4 | 1.3 | ||||||

ELF | Bus | 52 | 74 | 83 | 100 | 114 | 14 | 270.9 | 81.20 | 3077.71 | |

Size | 3.5 | 3 | 2.5 | 1.5 | 3.5 | ||||||

MM | Bus | 43 | 52 | 74 | 82 | 115 | 12.8 | 305.2 | 78.82 | 42.95 | |

Size | 0.4 | 3.3 | 2.9 | 2.8 | 3.4 |

Case | Method | Installed DG Schedule (MW) | DG (MW) | Ploss (kW) | Loss Red (%) | Time (s) | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

No DG | Total Real Load = 22.71 MW | - | 1440.89 | - | - | ||||||

5 DGs | LSF | Bus | 46 | 52 | 82 | 95 | 114 | 14 | 568.48 | 60.55 | 649.12 |

Size | 1 | 3.5 | 3 | 3 | 3.5 | ||||||

IA | Bus | 53 | 74 | 82 | 112 | 117 | 12.3 | 409.9 | 71.55 | 109.67 | |

Size | 3.7 | 2.7 | 1.8 | 2.4 | 1.7 | ||||||

ELF | Bus | 52 | 75 | 83 | 100 | 114 | 14 | 341.28 | 76.31 | 3107.33 | |

Size | 3.5 | 3 | 2.5 | 1.5 | 3.5 | ||||||

MM | Bus | 43 | 52 | 74 | 82 | 115 | 13 | 375.96 | 73.91 | 44.28 | |

Size | 0.4 | 3.3 | 3 | 2.8 | 3.5 |

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**MDPI and ACS Style**

Shahzad, M.; Ahmad, I.; Gawlik, W.; Palensky, P. Load Concentration Factor Based Analytical Method for Optimal Placement of Multiple Distribution Generators for Loss Minimization and Voltage Profile Improvement. *Energies* **2016**, *9*, 287.
https://doi.org/10.3390/en9040287

**AMA Style**

Shahzad M, Ahmad I, Gawlik W, Palensky P. Load Concentration Factor Based Analytical Method for Optimal Placement of Multiple Distribution Generators for Loss Minimization and Voltage Profile Improvement. *Energies*. 2016; 9(4):287.
https://doi.org/10.3390/en9040287

**Chicago/Turabian Style**

Shahzad, Mohsin, Ishtiaq Ahmad, Wolfgang Gawlik, and Peter Palensky. 2016. "Load Concentration Factor Based Analytical Method for Optimal Placement of Multiple Distribution Generators for Loss Minimization and Voltage Profile Improvement" *Energies* 9, no. 4: 287.
https://doi.org/10.3390/en9040287