# Adaptive Phasor Estimation Algorithm Based on a Least Squares Method

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## Abstract

**:**

## 1. Introduction

## 2. Proposed Phasor Estimation Algorithm

#### 2.1. Basic Least Squares Model

#### 2.2. Time Constant Calculation

#### 2.3. Adaptive Least Squares Model

## 3. Case Studies

#### 3.1. Computer-Generated Signals

#### 3.2. EMTP Simulation Signals

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## References

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**Figure 7.**Test results for fault distance: 10%, fault inception angle: 0°: (

**a**) Estimated RMS values; (

**b**) errors.

**Figure 8.**Test results for fault distance: 50%, fault inception angle: 0°: (

**a**) Estimated RMS values; (

**b**) errors.

**Figure 9.**Test results for fault distance: 90%, fault inception angle: 0°. (

**a**) Estimated RMS values; (

**b**) errors.

**Figure 10.**Test results for fault distance: 10%, fault inception angle: 90°: (

**a**) Estimated RMS values; (

**b**) errors.

**Figure 11.**Test results for fault distance: 50%, fault inception angle: 90°. (

**a**) Estimated RMS values; (

**b**) errors.

**Figure 12.**Test results for fault distance: 90%, fault inception angle: 90°. (

**a**) Estimated RMS values; (

**b**) errors.

Sequence | Parameter | Value | Units |
---|---|---|---|

Positive & Negative | R_{1}, R_{2} | 0.0419 | Ω/km |

L_{1}, L_{2} | 0.8799 | mH/km | |

C_{1}, C_{2} | 0.0128 | μF/km | |

Zero | R_{0} | 0.2294 | Ω/km |

L_{0} | 2.6666 | mH/km | |

C_{0} | 0.0043 | μF/km |

Sequence | Source 1 | Source 2 | ||
---|---|---|---|---|

S [GVA] | X/R | R [GVA] | X/R | |

Positive & Negative | 5.0 | 10.7 | 2.1 | 7.4 |

Zero | 11.5 | 5.1 | 6.3 | 4.9 |

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**MDPI and ACS Style**

Kim, W.-J.; Nam, S.-R.; Kang, S.-H.
Adaptive Phasor Estimation Algorithm Based on a Least Squares Method. *Energies* **2019**, *12*, 1387.
https://doi.org/10.3390/en12071387

**AMA Style**

Kim W-J, Nam S-R, Kang S-H.
Adaptive Phasor Estimation Algorithm Based on a Least Squares Method. *Energies*. 2019; 12(7):1387.
https://doi.org/10.3390/en12071387

**Chicago/Turabian Style**

Kim, Woo-Joong, Soon-Ryul Nam, and Sang-Hee Kang.
2019. "Adaptive Phasor Estimation Algorithm Based on a Least Squares Method" *Energies* 12, no. 7: 1387.
https://doi.org/10.3390/en12071387