# A Strategic and Significant Method for the Optimal Placement of Phasor Measurement Unit for Power System Network

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Fundamental Optimal PMU Placement Modelling

#### 2.2. Observability Analysis Using PMUs

- A bus with installed PMU is observed directly.
- A bus adjacent to PMU installed bus can be observed through Ohm’s law.
- If only one bus is unobservable, and rest of the incident buses are observed so the remaining one will be measured by KCL and KVL.

#### 2.3. IEEE-Networks Data

#### 2.4. Proposed Method

## 3. Results and Discussion

#### Effect of Channel Limit and Single PMUs Malfunction

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**(

**a**). Observability rule 1. Modelling; (

**b**). Observability rule 2. Modelling; (

**c**). Observability rule 3 modelling (ZIB).

**Figure 3.**Flow chart of removing the pure transit for the optimum placement of phasor measurement unit (PMU).

**Figure 4.**Interconnected IEEE-14 bus network [25].

**Table 1.**Attributes of the network system [13].

IEEE-Bus Network | No. of Connected Lines | Maximum Lines Connected to a Bus | Maximum Degrees of Bus |
---|---|---|---|

9-bus | 9 | 3 | 4 |

14-bus | 20 | 5 | 4 |

24-bus | 38 | 5 | 9 |

30-bus | 41 | 7 | 6 |

39-bus | 46 | 5 | 16 |

57-bus | 80 | 6 | 9 |

118-bus | 186 | 12 | 49 |

**Table 2.**Characteristics of buses [13].

Test System | Generator Buses | Load Buses | Reference Buses | Pure Transit Nodes |
---|---|---|---|---|

9-bus | 3 | 3 | 1 | 3 |

14-bus | 5 | 8 | 1 | 1 |

24-bus | 11 | 13 | 1 | 4 |

30-bus | 6 | 24 | 1 | 6 |

39-bus | 10 | 20 | 1 | 10 |

57-bus | 7 | 45 | 1 | 14 |

118-bus | 54 | 78 | 1 | 10 |

Test Cases | No. of PMUs ${\mathit{N}}_{\mathit{P}\mathit{M}\mathit{U}}$ | Locations of PMUs | Location of ZIBs in Placement Set | Location of ZIBs in Test-Cases | CPU Time in Seconds (s) |
---|---|---|---|---|---|

9-bus network | 3 | 4, 7, 9 | 4 | 4, 6, 8 | 0.31105 |

14-bus network | 4 | 8, 3, 5, 11 | - | 7 | 0.21095 |

24-bus network | 7 | 1, 7, 22, 10, 9, 15, 14 | - | 11, 12, 17, 24 | 0.7826 |

30-bus network | 7 | 1, 5, 16, 13, 10, 15, 19 | - | 6, 9, 22, 25, 27, 28 | 1.405 |

39-bus network | 13 | 2, 13, 15, 17, 19, 22, 24, 26, 34, 36, 37, 38, 39 | 2, 13, 17, 19, 22 | 2, 5, 6, 10, 11, 13, 14, 17, 19, 22 | 3.22 |

57-bus network | 14 | 2, 10, 13, 17, 19, 16, 24, 29, 30, 32, 38, 50, 54, 56 | 24 | 7, 11, 21, 22, 24, 26, 34, 36, 37, 39, 40, 45, 46, 48 | 6.218 |

118-bus network | 39 | 2, 117, 7, 14, 11, 10, 19, 36, 29, 115, 17, 21, 43, 37, 32, 25, 59, 53, 62, 58, 41, 57, 73, 46, 110, 105, 49, 70, 118, 78, 80, 95, 100, 102, 93, 91, 82, 89, 84 | 37 | 5, 9, 30, 37, 38, 63, 64, 68, 71, 81 | 21.4111 |

Test Cases | ${\mathit{N}}_{\mathit{P}\mathit{M}\mathit{U}}$ | Locations of PMUs | Location of ZIBs in Test-Cases | CPU Time in Seconds (s) |
---|---|---|---|---|

9-bus network | 2 | 2, 5 | 4, 6, 8 | 0.006 |

14-bus network | 2 | 2, 9 | 7 | 0.02132 |

24-bus network | 6 | 2, 3, 7, 10, 16 21 | 11, 12, 17, 24 | 0.2324 |

30-bus network | 5 | 2, 3, 10, 12, 19 | 6, 9, 22, 25, 27, 28 | 0.3567 |

39-bus network | 7 | 1, 3, 16, 20, 23, 25, 29 | 2, 5, 6, 10, 11, 13, 14, 17, 19, 22 | 0.5334 |

57-bus network | 10 | 1, 13, 19, 29, 30, 32, 38, 51, 54, 56 | 7, 11, 21, 22, 24, 26, 34, 36, 37, 39, 40, 45, 46, 48 | 0.8455 |

118-bus network | 29 | 1, 12, 13, 19, 21, 25, 29, 32, 36, 41, 43, 46, 49, 53, 57, 59, 62, 70, 73,78, 80, 82, 85, 90, 92, 95, 101, 105, 110, 115, 118 | 5, 9, 30, 37, 38, 63, 64, 68, 71, 81 | 1.0232 |

Techniques | Test-Cases | ||||||
---|---|---|---|---|---|---|---|

9-Bus | 14-Bus | 24-Bus | 30-Bus | 39-Bus | 57-Bus | 118-Bus | |

Proposed work | 2 | 2 | 6 | 5 | 7 | 10 | 29 |

Genetic algorithm [14] | N/A | 3 | 8 | 7 | N/A | 12 | 29 |

Dual search [4], [15] | N/A | 3 | N/A | N/A | N/A | N/A | 29 |

Tabu search [16] | N/A | 3 | N/A | N/A | N/A | 13 | N/A |

Particle swarm optimization [17] | N/A | 3 | N/A | 7 | N/A | 11 | 28 |

Binary search algorithm [8] | N/A | 3 | 6 | 7 | 8 | N/A | N/A |

Binary particle swarm optimization [18] | N/A | 3 | 8 | 10 | 8 | 11 | N/A |

Greedy algorithm [19] | N/A | 3 | N/A | 7 | 8 | 11 | N/A |

Branch and Bound algorithm [7] | N/A | 3 | N/A | 7 | 9 | 12 | 29 |

Test Cases | ${\mathit{N}}_{\mathit{P}\mathit{M}\mathit{U}}$ Proposed Work | Existing Techniques | |||
---|---|---|---|---|---|

Location of PMUs | [12] | [23] | [24] | ||

9-bus network | 6 | 1, 2, 3, 6, 8, 9 | N/A | 6 | N/A |

14-bus network | 9 | 2, 4, 5, 6, 7, 8, 9, 10, 13 | 9 | 9 | 9 |

24-bus network | 13 | 1, 4, 6, 7, 8, 10, 11,13, 14, 15, 17, 20, 21 | 14 | 14 | N/A |

30-bus network | 19 | 2, 3, 6, 7, 8, 9, 10, 12, 13, 15, 16, 19, 22, 23, 24, 25, 26, 27, 29 | 21 | N/A | 20 |

39-bus network | 28 | 2, 3, 5, 6, 8, 9, 10, 12, 13, 15, 16, 19, 20, 22, 23, 25, 28, 29, 30, 31, 32, 33,34, 35, 36, 37, 38, 39 | 28 | N/A | N/A |

57-bus network | 33 | 1, 3, 4, 6, 9, 11, 12, 13, 14, 17, 19, 20, 22, 24, 26, 28, 29, 30, 32, 33, 34, 36, 37, 38, 39, 41, 44, 47, 48, 50, 51, 53, 56 | 33 | N/A | 33 |

118-bus network | 68 | 2, 3, 5, 6, 9, 10, 11, 12, 15, 17, 19, 21, 22, 24, 25, 27, 29, 30, 31, 32, 34, 35, | 68 | N/A | 69 |

37, 40, 42, 43, 45, 46, 49, 51, 52, 54, 56, 57, 59, 61, 62, 64, 66, 68, 70, 71,73, | |||||

75, 76, 77, 79, 80, 83, 85, 86, 87, 89, 90, 92, 94, 96, 100, 101, 105, 106, 108, | |||||

110, 111, 112, 114, 116, 117 |

Test-Cases | Channel Limits, $\mathit{L}$ | Proposed Work ${\mathit{N}}_{\mathit{P}\mathit{M}\mathit{U}}$ | Existing Techniques | |||
---|---|---|---|---|---|---|

[12] | [26] | [27] | [28] | |||

9-bus network | 2 | 5 | N/A | N/A | N/A | N/A |

3 | 4 | N/A | N/A | N/A | N/A | |

4 | 3 | N/A | N/A | N/A | N/A | |

14-bus network | 2 | 7 | 7 | 7 | 7 | 7 |

3 | 5 | 5 | 5 | 5 | 5 | |

4 | 4 | 4 | 4 | 4 | 4 | |

5 | 3 | 4 | 4 | 4 | 4 | |

24-bus network | 2 | 12 | 12 | N/A | N/A | N/A |

3 | 8 | 8 | N/A | N/A | N/A | |

4 | 7 | 7 | N/A | N/A | N/A | |

5 | 6 | 7 | N/A | N/A | N/A | |

30-bus network | 2 | 15 | 15 | 15 | 15 | 15 |

3 | 10 | 11 | 11 | 11 | 11 | |

4 | 9 | 10 | 10 | 10 | 10 | |

5 | 9 | 10 | 10 | 10 | 10 | |

39-bus network | 2 | 19 | 21 | N/A | N/A | N/A |

3 | 14 | 14 | N/A | N/A | N/A | |

4 | 13 | 13 | N/A | N/A | N/A | |

5 | 13 | 13 | N/A | N/A | N/A | |

57-bus network | 2 | 29 | 29 | 29 | 29 | 29 |

3 | 19 | 19 | 19 | 19 | 19 | |

4 | 17 | 17 | 17 | 17 | 17 | |

5 | 17 | 17 | 17 | 17 | 17 | |

118-bus network | 2 | 63 | N/A | N/A | N/A | N/A |

3 | 42 | N/A | N/A | N/A | N/A | |

4 | 36 | N/A | N/A | N/A | N/A | |

5 | 36 | N/A | N/A | N/A | N/A |

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**MDPI and ACS Style**

Baba, M.; Nor, N.B.M.; Aman.Sheikh, M.; Irfan, M.; Tahir, M.
A Strategic and Significant Method for the Optimal Placement of Phasor Measurement Unit for Power System Network. *Symmetry* **2020**, *12*, 1174.
https://doi.org/10.3390/sym12071174

**AMA Style**

Baba M, Nor NBM, Aman.Sheikh M, Irfan M, Tahir M.
A Strategic and Significant Method for the Optimal Placement of Phasor Measurement Unit for Power System Network. *Symmetry*. 2020; 12(7):1174.
https://doi.org/10.3390/sym12071174

**Chicago/Turabian Style**

Baba, Maveeya, Nursyarizal B. M. Nor, M. Aman.Sheikh, Muhammad Irfan, and Mohammad Tahir.
2020. "A Strategic and Significant Method for the Optimal Placement of Phasor Measurement Unit for Power System Network" *Symmetry* 12, no. 7: 1174.
https://doi.org/10.3390/sym12071174