# Harmonic Distortion Minimization in Power Grids with Wind and Electric Vehicles

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## Abstract

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## 1. Introduction

- To develop a three-phase unbalanced distribution system model required for harmonic power flow (HPF) studies. The model is used to study the impact of EVs on voltage and current THDs in distribution system with varying degree of penetration. The same model is used to demonstrate that careful dispatch of WGs can help to reduce the harmonic distortions caused by the EVs.
- To develop optimal harmonic power flow (OHPF) model that utilizes previous HPF model as constraints and WGs as decision variables, and solution method based on GA. The model is then used to find optimal dispatch WGs that will reduce the voltage or current THDs in the distribution circuit with varying penetration level of the EVs.

## 2. Modeling

#### 2.1. Harmonic Power Flow (HPF) Model

#### 2.2. Optimal Harmonic Power Flow (OHPF) Model

## 3. Solution Approach

## 4. Impact of EV Penetration on THD

## 5. Reduction of Voltage and Current THDs

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Conceptual diagram depicting cancellation of harmonic from electric vehicles (EVs) by wind generators (WGs) at distribution feeder level.

**Figure 2.**Circuit connection showing the branch currents and nodal voltages used for modeling the harmonic power flow.

**Figure 3.**The developed interface between the harmonic power flow (HPF) model in OpenDSS and Optimization model in MATLAB.

**Figure 4.**Flowchart of the solution algorithm where a Genetic Algorithm (GA)-based optimization algorithm is built in MATLAB and a harmonic power flow model is built in OpenDSS.

Harmonic Order | Magnitude (%) | Angle (°) | Harmonic Order | Magnitude (%) | Angle (°) |
---|---|---|---|---|---|

1 | 100 | −26 | 11 | 9 | −67 |

5 | 25 | −94 | 13 | 5 | −46 |

7 | 17 | −67 |

**Table 2.**Wind Generator Current Harmonic Content (in p.u. based on 100 MVA) [19].

Harmonic Order | Mag. (p.u.) | Harmonic Order | Mag. (p.u.) | Harmonic Order | Mag. (p.u.) |
---|---|---|---|---|---|

2 | 0.000183 | 6 | 7.33 $\times {10}^{-5}$ | 13 | 7.33 $\times {10}^{-5}$ |

3 | 0.000147 | 7 | 0.00033 | 25 | 3.67 $\times {10}^{-5}$ |

4 | 0.00011 | 8 | 3.67 $\times {10}^{-5}$ | 45 | 3.67 $\times {10}^{-5}$ |

5 | 0.00077 | 11 | 0.000293 | 47 | 0.00011 |

Case Studies | Branch | THD ${\mathit{V}}_{\mathit{ab}}(\%)$ | THD ${\mathit{V}}_{\mathit{bc}}(\%)$ | THD ${\mathit{V}}_{\mathit{ca}}(\%)$ |
---|---|---|---|---|

Case 1 (EV) | 844–846 | 4.62 | 4.64 | 4.14 |

828–830 | 2.73 | 2.77 | 2.52 | |

808–806 | 0.09 | 0.09 | 0.08 | |

834–860 | 4.58 | 4.60 | 4.11 | |

Case 2 (EV + 1WG) | 844–846 | 3.81 | 4.06 | 3.74 |

828–830 | 2.60 | 2.71 | 2.53 | |

808–806 | 0.11 | 0.11 | 0.10 | |

834–860 | 3.78 | 4.03 | 3.71 | |

Case 3 (EV + 3WGs) | 844–846 | 3.99 | 4.58 | 4.13 |

828–830 | 2.96 | 3.39 | 3.11 | |

808–806 | 0.13 | 0.14 | 0.14 | |

834–860 | 3.95 | 4.54 | 4.09 |

Case Studies | Branch | THD ${\mathit{I}}_{\mathit{a}}(\%)$ | THD ${\mathit{I}}_{\mathit{b}}(\%)$ | THD ${\mathit{I}}_{\mathit{c}}(\%)$ |
---|---|---|---|---|

Case 1 (EV) | 844–846 | 25.75 | 24.20 | 23.19 |

828–830 | 8.04 | 7.22 | 6.16 | |

808–806 | 5.50 | 6.46 | 6.31 | |

834–860 | 6.41 | 3.43 | 6.09 | |

Case 2 (EV + 1WG) | 844–846 | 2.81 | 2.90 | 2.59 |

828–830 | 3.49 | 3.81 | 3.92 | |

808–806 | 4.42 | 4.29 | 4.14 | |

834–860 | 4.41 | 3.55 | 4.37 | |

Case 3 (EV + 3WGs) | 844–846 | 2.04 | 2.05 | 1.77 |

828–830 | 2.31 | 2.32 | 2.23 | |

808–806 | 2.14 | 2.33 | 2.35 | |

834–860 | 3.35 | 3.53 | 3.79 |

Case Studies | Branch | THD ${\mathit{I}}_{\mathit{a}}(\%)$ | THD ${\mathit{I}}_{\mathit{b}}(\%)$ | THD ${\mathit{I}}_{\mathit{c}}(\%)$ |
---|---|---|---|---|

Case 4 (EV) | 844–846 | 50.26 | 38.70 | 37.75 |

828–830 | 11.02 | 9.52 | 6.98 | |

808–806 | 6.67 | 7.913 | 7.12 | |

834–860 | 14.89 | 7.62 | 12.96 | |

Case 5 (EV + 1WG) | 844–846 | 4.50 | 5.03 | 4.03 |

828–830 | 3.43 | 5.98 | 5.93 | |

808–806 | 10.91 | 9.00 | 6.46 | |

834–860 | 10.20 | 6.37 | 9.56 | |

Case 6 (EV + 3WGs) | 844–846 | 2.59 | 2.73 | 2.07 |

828–830 | 3.87 | 3.78 | 3.72 | |

808–806 | 3.72 | 3.99 | 3.96 | |

834–860 | 7.39 | 5.88 | 7.33 |

Case Studies | Branch | THD ${\mathit{V}}_{\mathit{ab}}(\%)$ | THD ${\mathit{V}}_{\mathit{bc}}(\%)$ | THD ${\mathit{V}}_{\mathit{ca}}(\%)$ |
---|---|---|---|---|

Case 4 (EV) | 844–846 | 9.61 | 9.54 | 7.82 |

828–830 | 5.38 | 5.57 | 4.62 | |

808–806 | 0.16 | 0.17 | 0.14 | |

834–860 | 9.54 | 9.46 | 7.76 | |

Case 5 (EV + 1WG) | 844–846 | 5.43 | 5.84 | 4.73 |

828–830 | 4.19 | 4.04 | 3.53 | |

808–806 | 0.18 | 0.18 | 0.15 | |

834–860 | 5.40 | 5.80 | 4.62 | |

Case 6 (EV + 3WGs) | 844–846 | 5.91 | 6.80 | 5.84 |

828–830 | 4.47 | 4.97 | 4.35 | |

808–806 | 0.19 | 0.20 | 0.19 | |

834–860 | 5.84 | 6.72 | 5.77 |

Branch | THD ${\mathit{V}}_{\mathit{ab}}(\%)$ | THD ${\mathit{V}}_{\mathit{bc}}(\%)$ | THD ${\mathit{V}}_{\mathit{ca}}(\%)$ |
---|---|---|---|

844–846 | 2.39 | 2.96 | 2.92 |

828–830 | 1.57 | 2.04 | 1.88 |

808–806 | 0.13 | 0.15 | 0.14 |

834–860 | 2.35 | 2.90 | 2.86 |

Node | WG (kW) | Node | WG (kW) | Node | WG (kW) | Node | WG (kW) | Node | WG (kW) |
---|---|---|---|---|---|---|---|---|---|

1 | 254.9 | 8 | 490.2 | 15 | 176.47 | 22 | 58.82 | 29 | 950.98 |

2 | 372.55 | 9 | 1205.8 | 16 | 352.94 | 23 | 264.7 | 30 | 2323.5 |

3 | 2450.98 | 10 | 950.98 | 17 | 88.24 | 24 | 617.55 | 31 | 1568.6 |

4 | 303.92 | 11 | 715.69 | 18 | 1568.83 | 25 | 245.1 | 32 | 2294.1 |

5 | 519.61 | 12 | 19.61 | 19 | 1833.33 | 26 | 2480.4 | 33 | 137.25 |

6 | 215.69 | 13 | 1450.9 | 20 | 833.33 | 27 | 1950.9 | 34 | 2490.2 |

7 | 1862.75 | 14 | 156.86 | 21 | 215.69 | 28 | 1382.3 |

Branch | THD ${\mathit{V}}_{\mathit{ab}}(\%)$ | THD ${\mathit{V}}_{\mathit{bc}}(\%)$ | THD ${\mathit{V}}_{\mathit{ca}}(\%)$ |
---|---|---|---|

844–846 | 3.72 | 4.04 | 3.73 |

828–830 | 1.59 | 1.43 | 1.51 |

808–806 | 0.24 | 0.28 | 0.26 |

834–860 | 3.66 | 3.97 | 3.68 |

Node | WG (kW) | Node | WG (kW) | Node | WG (kW) | Node | WG (kW) | Node | WG (kW) |
---|---|---|---|---|---|---|---|---|---|

1 | 2245.1 | 8 | 1813.73 | 15 | 1186.27 | 22 | 2235.29 | 29 | 2421.5 |

2 | 2264.7 | 9 | 2411.76 | 16 | 343.14 | 23 | 1196.08 | 30 | 2117.6 |

3 | 2137.25 | 10 | 2470.59 | 17 | 2450.98 | 24 | 617.65 | 31 | 323.53 |

4 | 1892.16 | 11 | 2460.78 | 18 | 1931.37 | 25 | 2215.69 | 32 | 990.2 |

5 | 2127.45 | 12 | 2303.92 | 19 | 1803.92 | 26 | 19.61 | 33 | 254.9 |

6 | 284.31 | 13 | 235.29 | 20 | 313.73 | 27 | 2245.1 | 34 | 196.8 |

7 | 1666.6 | 14 | 1529.41 | 21 | 156.86 | 28 | 1725.5 |

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## Share and Cite

**MDPI and ACS Style**

Misra, R.; Paudyal, S.; Ceylan, O.; Mandal, P. Harmonic Distortion Minimization in Power Grids with Wind and Electric Vehicles. *Energies* **2017**, *10*, 932.
https://doi.org/10.3390/en10070932

**AMA Style**

Misra R, Paudyal S, Ceylan O, Mandal P. Harmonic Distortion Minimization in Power Grids with Wind and Electric Vehicles. *Energies*. 2017; 10(7):932.
https://doi.org/10.3390/en10070932

**Chicago/Turabian Style**

Misra, Ritam, Sumit Paudyal, Oğuzhan Ceylan, and Paras Mandal. 2017. "Harmonic Distortion Minimization in Power Grids with Wind and Electric Vehicles" *Energies* 10, no. 7: 932.
https://doi.org/10.3390/en10070932