# 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 |

## References

- Singh, D.; Singh, D.; Verma, K. GA based energy loss minimization approach for optimal sizing & placement of distributed generation. Int. J. Knowl. Based Intell. Eng. Syst.
**2008**, 12, 147–156. [Google Scholar] - Georgilakis, P.; Hatziargyriou, N. Optimal distributed generation placement in power distribution networks: Models, methods, and future research. IEEE Trans. Power Syst.
**2013**, 28, 3420–3428. [Google Scholar] [CrossRef] - Taylor, M.; Daniel, K.; Ilas, A.; So, E. Renewable Power Generation Costs in 2014; International Renewable Energy Agency: Masdar City, Abu Dhabi, UAE, 2015. [Google Scholar]
- Li, W.; Joos, G.; Belanger, J. Real-time simulation of a wind turbine generator coupled with a battery supercapacitor energy storage system. IEEE Trans. Ind. Electron.
**2010**, 57, 1137–1145. [Google Scholar] [CrossRef] - Pigazo, A.; Liserre, M.; Mastromauro, R.; Moreno, V.; Dell’Aquila, A. Wavelet-based islanding detection in grid-connected PV systems. IEEE Trans. Ind. Electron.
**2009**, 56, 4445–4455. [Google Scholar] [CrossRef] - Yao, W.; Chen, M.; Matas, J.; Guerrero, J.; Ming Qian, Z. Design and analysis of the droop control method for parallel inverters considering the impact of the complex impedance on the power sharing. IEEE Trans. Ind. Electron.
**2011**, 58, 576–588. [Google Scholar] [CrossRef] - Guerrero, J.M.; Vasquez, J.C.; Matas, J.; de Vicuna, L.G.; Castilla, M. Hierarchical control of droop-controlled AC and DC microgrids—A general approach toward standardization. IEEE Trans. Ind. Electron.
**2010**, 58, 158–172. [Google Scholar] [CrossRef] - Guerrero, J.; Matas, J.; de Vicuna, L.G.; Castilla, M.; Miret, J. Decentralized control for parallel operation of distributed generation inverters using resistive output impedance. IEEE Trans. Ind. Electron.
**2007**, 54, 994–1004. [Google Scholar] [CrossRef] - Hung, D.Q.; Mithulananthan, N.; Bansal, R. Analytical strategies for renewable distributed generation integration considering energy loss minimization. Appl. Energy
**2013**, 105, 75–85. [Google Scholar] [CrossRef] - Atwa, Y.; El-Saadany, E.; Salama, M.; Seethapathy, R. Optimal renewable resources mix for distribution system energy loss minimization. IEEE Trans. Power Syst.
**2010**, 25, 360–370. [Google Scholar] [CrossRef] - Antonova, G.; Nardi, M.; Scott, A.; Pesin, M. Distributed generation and its impact on power grids and microgrids protection. In Proceedings of the 2012 65th Annual Conference for Protective Relay Engineers, College Station, TX, USA, 2–5 April 2012; pp. 152–161.
- Standard EN 50160. Voltage Characteristics of Public Distribution Systems; CENELEC: Brussels, Belgium, 2010. [Google Scholar]
- Liu, Y.; Bebic, J.; Kroposki, B.; De Bedout, J.; Ren, W. Distribution system voltage performance analysis for high-penetration PV. In Proceedings of the IEEE Energy 2030 Conference, ENERGY 2008, Atlanta, GA, USA, 17–18 November 2008; pp. 1–8.
- Moradi, M.; Abedini, M. A combination of genetic algorithm and particle swarm optimization for optimal {DG} location and sizing in distribution systems. Int. J. Electr. Power Energy Syst.
**2012**, 34, 66–74. [Google Scholar] [CrossRef] - Mithulananthan, N.; Oo, T.; Phu, L.V. Distributed generator placement in power distribution system using genetic algorithm to reduce losses. Thammasat Int. J. Sci. Technol.
**2004**, 9, 55–62. [Google Scholar] - Singh, D.; Singh, D.; Verma, K. GA based optimal sizing & placement of distributed generation for loss minimization. Int. J. Intell. Technol.
**2007**, 2, 263–269. [Google Scholar] - De Souza, B.; de Albuquerque, J. Optimal placement of distributed generators networks using evolutionary programming. In Proceedings of the Transmission Distribution Conference and Exposition: Latin America, Caracas, Venezuela, 15–18 August 2006; pp. 1–6.
- El-Zonkoly, A. Optimal placement of multi-distributed generation units including different load models using particle swarm optimisation. IET Gen. Transm. Distrib.
**2011**, 5, 760–771. [Google Scholar] [CrossRef] - Bouhouras, A.S.; Sgouras, K.I.; Gkaidatzis, P.A.; Labridis, D.P. Optimal active and reactive nodal power requirements towards loss minimization under reverse power flow constraint defining DG type. Int. J. Electr. Power Energy Syst.
**2016**, 78, 445–454. [Google Scholar] [CrossRef] - Wang, C.; Nehrir, M. Analytical approaches for optimal placement of distributed generation sources in power systems. IEEE Trans. Power Syst.
**2004**, 19, 2068–2076. [Google Scholar] [CrossRef] - Ziari, I.; Ledwich, G.; Ghosh, A.; Cornforth, D.; Wishart, M. Optimal allocation and sizing of DGs in distribution networks. In Proceedings of the 2010 IEEE Power and Energy Society General Meeting, Minneapolis, MN, USA, 25–29 July 2010; pp. 1–8.
- Lee, S.H.; Park, J.W. Selection of optimal location and size of multiple distributed generations by using Kalman filter algorithm. IEEE Trans. Power Syst.
**2009**, 24, 1393–1400. [Google Scholar] - Khatod, D.; Pant, V.; Sharma, J. Evolutionary programming based optimal placement of renewable distributed generators. IEEE Trans. Power Syst.
**2013**, 28, 683–695. [Google Scholar] [CrossRef] - Liu, Z.; Wen, F.; Ledwich, G. Optimal siting and sizing of distributed generators in distribution systems considering uncertainties. IEEE Trans. Power Deliv.
**2011**, 26, 2541–2551. [Google Scholar] [CrossRef] - Kayal, P.; Kar, S.; Upadhyaya, A.; Chanda, C. Optimal sizing of multiple distributed generation units connected with distribution system using PSO technique. In Proceedings of the 2012 International Conference on Emerging Trends in Electrical Engineering and Energy Management, Chennai, India, 13–15 December 2012; pp. 229–234.
- Acharya, N.; Mahat, P.; Mithulananthan, N. An analytical approach for DG allocation in primary distribution network. Int. J. Electr. Power Energy Syst.
**2006**, 28, 669–678. [Google Scholar] [CrossRef] - Hung, D.Q.; Mithulananthan, N.; Bansal, R. Analytical expressions for DG allocation in primary distribution networks. IEEE Trans. Energy Convers.
**2010**, 25, 814–820. [Google Scholar] [CrossRef] - Hung, D.Q.; Mithulananthan, N. Multiple distributed generator placement in primary distribution networks for loss reduction. IEEE Trans. Ind. Electr.
**2013**, 60, 1700–1708. [Google Scholar] [CrossRef] - Kamel, R.; Kermanshahi, B. Optimal size and location of distributed generations for minimizing power losses in a primary distribution network. Sci. Iran. Trans. D Comput. Sci. Eng. Electr. Eng.
**2009**, 16, 137–144. [Google Scholar] - Viral, R.; Khatod, D. An analytical approach for sizing and siting of DGs in balanced radial distribution networks for loss minimization. Int. J. Electr. Power Energy Syst.
**2015**, 67, 191–201. [Google Scholar] [CrossRef] - Carpinelli, G.; Celli, G.; Pilo, F.; Russo, A. Embedded generation planning under uncertainty including power quality issues. Eur. Trans. Electr. Power
**2003**, 13, 381–389. [Google Scholar] [CrossRef] - Haesen, E.; Driesen, J.; Belmans, R. Robust planning methodology for integration of stochastic generators in distribution grids. IET Renew. Power Gen.
**2007**, 1, 25–32. [Google Scholar] [CrossRef] - Evangelopoulos, V.; Georgilakis, P. Optimal distributed generation placement under uncertainties based on point estimate method embedded genetic algorithm. IET Gen. Transm. Distrib.
**2014**, 8, 389–400. [Google Scholar] [CrossRef] - Singh, A.; Parida, S. Selection of load buses for DG placement based on loss reduction and voltage improvement sensitivity. In Proceedings of the 2011 International Conference on Power Engineering, Energy and Electrical Drives (POWERENG), Malaga, Spain, 11–13 May 2011; pp. 1–6.
- Shahzad, M.; Ullah, I.; Palensky, P.; Gawlik, W. Analytical approach for simultaneous optimal sizing and placement of multiple Distributed Generators in primary distribution networks. In Proceedings of the 2014 IEEE 23rd International Symposium on Industrial Electronics (ISIE), Istanbul, Turkey, 1–4 June 2014; pp. 2554–2559.
- Kothari, D.; Dhillon, J. Power System Optimization; Prentice-Hall: New Dehli, India, 2004. [Google Scholar]
- IEEE PES Distribution System Analysis Subcommittee’s Distribution Test Feeder Working Group. Available online: http://ewh.ieee.org/soc/pes/dsacom/testfeeders/ (accessed on 11 April 2016).
- Zhang, D.; Fu, Z.; Zhang, L. An improved TS algorithm for loss-minimum reconfiguration in large-scale distribution systems. Electr. Power Syst. Res.
**2007**, 77, 685–694. [Google Scholar] [CrossRef] - Hung, D.Q.; Mithulananthan, N. DG allocation in primary distribution systems considering loss reduction. In Handbook of Renewable Energy Technology; Chapter 23; World Scientific: Singapore, 2011; pp. 587–635. [Google Scholar]
- Ahmad, I.; Kazmi, J.H.; Shahzad, M.; Palensky, P. Co-simulation framework based on power system, AI and communication tools for evaluating smart grid applications. In Proceedings of the IEEE PES Innovative Smart Grid Technologies 2015 Asian Conference, Bangkok, Thailand, 3–6 November 2015.
- Latif, A.; Shahzad, M.; Palensky, P.; Gawlik, W. An alternate PowerFactory Matlab coupling approach. In Proceedings of the 2015 International Symposium on Smart Electric Distribution Systems and Technologies (EDST), Vienna, Austria, 8–11 September 2015; pp. 486–491.
- Siano, P.; Ochoa, L.; Harrison, G.; Piccolo, A. Assessing the strategic benefits of distributed generation ownership for DNOs. IET Gen. Transm. Distrib.
**2009**, 3, 225–236. [Google Scholar] [CrossRef] - Ackermann, T.; Andersson, G.; Söder, L. Distributed generation: A definition. Electr. Power Syst. Res.
**2001**, 57, 195–204. [Google Scholar] [CrossRef]

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