# Adaptive Linear Neural Network Approach for Three-Phase Four-Wire Active Power Filtering under Non-Ideal Grid and Unbalanced Load Scenarios

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## Abstract

**:**

## 1. Introduction

## 2. Circuit Connection of Shunt Active Power Filter in a Three-Phase Four-Wire System and Associated Control Algorithms

## 3. Design Concept and Operation of Enhanced-ADALINE Algorithm

#### 3.1. Working Principle of ADALINE Module

#### 3.2. Working Principle of HSF Synchronizer Module

#### 3.3. Integration of ADALINE, HSF, and Averaging Function for Generating Reference Current

## 4. Results and Discussion

#### 4.1. Scenario I: Balanced and Distorted Source Voltage

#### 4.2. Scenario II: Unbalanced and Sinusoidal Source Voltage

#### 4.3. Scenario III: Unbalanced and Distorted Source Voltage

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Shunt active power filter (SAPF) in a three-phase four-wire system: (

**a**) connection of power circuits and (

**b**) control algorithms applied.

**Figure 5.**Simulation model of SAPF in a three-phase four-wire system: (

**a**) connection of power circuits, and (

**b**) control algorithms that constituted the control system.

**Figure 6.**Non-ideal source voltages considered in this work: (

**a**) balanced and distorted (Scenario I), (

**b**) unbalanced and sinusoidal (Scenario II), and (

**c**) unbalanced and distorted (Scenario III).

**Figure 7.**Simulation result obtained under Scenario I, showing the magnitude (mean value) of fundamental load current extracted by the enhanced-ADALINE algorithm with and without integrating Averaging function: (

**a**) Load A and (

**b**) Load B.

**Figure 8.**Simulation results obtained under Scenario I for Load A, showing source voltage ${v}_{Sabc}$, load current ${i}_{Labc}$, injection current ${i}_{injabc}$, source current ${i}_{Sabc}$, and neutral current before and after mitigation, demonstrated by SAPF while applying the (

**a**) enhanced-ADALINE and (

**b**) STF-dq0 algorithms.

**Figure 9.**Simulation result obtained under Scenario I for Load A, showing the overall dc-link voltage ${V}_{dc}$, and individual voltage of each split capacitor ${V}_{dc1}$ and ${V}_{dc2}$, demonstrated by SAPF while applying the enhanced-ADALINE algorithm.

**Figure 10.**Simulation results obtained under Scenario I for Load B, showing source voltage ${v}_{Sabc}$, load current ${i}_{Labc}$, injection current ${i}_{injabc}$, source current ${i}_{Sabc}$, and neutral current before and after mitigation, demonstrated by SAPF while applying the (

**a**) enhanced-ADALINE and (

**b**) STF-dq0 algorithms.

**Figure 11.**Simulation result obtained under Scenario I for Load B, showing the overall dc-link voltage ${V}_{dc}$, and individual voltage of each split capacitor ${V}_{dc1}$ and ${V}_{dc2}$, demonstrated by SAPF while applying the enhanced-ADALINE algorithm.

**Figure 12.**Simulation result obtained under Scenario II, showing the magnitude (mean value) of fundamental load current extracted by the enhanced-ADALINE algorithm with and without integrating Averaging function: (

**a**) Load A and (

**b**) Load B.

**Figure 13.**Simulation results obtained under Scenario II for Load A, showing source voltage ${v}_{Sabc}$, load current ${i}_{Labc}$, injection current ${i}_{injabc}$, source current ${i}_{Sabc}$, and neutral current before and after mitigation, demonstrated by SAPF while applying the (

**a**) enhanced-ADALINE and (

**b**) STF-dq0 algorithms.

**Figure 14.**Simulation result obtained under Scenario II for Load A, showing the overall dc-link voltage ${V}_{dc}$, and individual voltage of each split capacitor ${V}_{dc1}$ and ${V}_{dc2}$, demonstrated by SAPF while applying the enhanced-ADALINE algorithm.

**Figure 15.**Simulation results obtained under Scenario II for Load B, showing source voltage ${v}_{Sabc}$, load current ${i}_{Labc}$, injection current ${i}_{injabc}$, source current ${i}_{Sabc}$, and neutral current before and after mitigation, demonstrated by SAPF while applying the (

**a**) enhanced-ADALINE and (

**b**) STF-dq0 algorithms.

**Figure 16.**Simulation result obtained under Scenario II for Load B, showing the overall dc-link voltage ${V}_{dc}$, and individual voltage of each split capacitor ${V}_{dc1}$ and ${V}_{dc2}$, demonstrated by SAPF while applying the enhanced-ADALINE algorithm.

**Figure 17.**Simulation result obtained under Scenario III, showing the magnitude (mean value) of fundamental load current extracted by the enhanced-ADALINE algorithm with and without integrating Averaging function: (

**a**) Load A and (

**b**) Load B.

**Figure 18.**Simulation results obtained under Scenario III for Load A, showing source voltage ${v}_{Sabc}$, load current ${i}_{Labc}$, injection current ${i}_{injabc}$, source current ${i}_{Sabc}$, and neutral current before and after mitigation, demonstrated by SAPF while applying the (

**a**) enhanced-ADALINE and (

**b**) STF-dq0 algorithms.

**Figure 19.**Simulation result obtained under Scenario III for Load A, showing the overall dc-link voltage ${V}_{dc}$, and individual voltage of each split capacitor ${V}_{dc1}$ and ${V}_{dc2}$, demonstrated by SAPF while applying the enhanced-ADALINE algorithm.

**Figure 20.**Simulation results obtained under Scenario III for Load B, showing source voltage ${v}_{Sabc}$, load current ${i}_{Labc}$, injection current ${i}_{injabc}$, source current ${i}_{Sabc}$, and neutral current before and after mitigation, demonstrated by SAPF while applying the (

**a**) enhanced-ADALINE and (

**b**) STF-dq0 algorithms.

**Figure 21.**Simulation result obtained under Scenario III for Load B, showing the overall dc-link voltage ${V}_{dc}$, and individual voltage of each split capacitor ${V}_{dc1}$ and ${V}_{dc2}$, demonstrated by SAPF while applying the enhanced-ADALINE algorithm.

Load Configuration | Details | ||
---|---|---|---|

Load A: Three single-phase loads with a common neutral connected in parallel with a three-phase load (refer Figure 5a) | Phase a | Uncontrolled single-phase rectifier feeding: | 80 Ω resistor and 1500 μF capacitor in parallel |

Phase b | 20 Ω resistor and 50 mH inductor in series | ||

Phase c | 40 Ω resistor and 1100 μF capacitor in parallel | ||

Phase abc | Uncontrolled three-phase rectifier feeding: | 30 Ω resistor and 80 mH inductor in series | |

Load B: Three single-phase loads with a common neutral | Phase a | Uncontrolled single-phase rectifier feeding: | 20 Ω resistor and 50 mH inductor in series |

Phase b | 80 Ω resistor and 1500 μF capacitor in parallel | ||

Phase c | 40 Ω resistor and 80 mH inductor in series |

**Table 2.**Summary of performance parameters demonstrated by the enhanced-ADALINE and STF-dq0algorithms under Scenario I.

Performance Parameter | Load A | Load B | ||||
---|---|---|---|---|---|---|

Phase a | Phase b | Phase c | Phase a | Phase b | Phase c | |

Before installing SAPF | ||||||

THD (%) | 34.46 | 18.60 | 45.46 | 35.29 | 123.90 | 33.65 |

Phase difference (°) | 13.90 | 13.10 | 12.20 | 10.40 | 10.10 | 9.00 |

PF | 0.917 | 0.957 | 0.889 | 0.927 | 0.618 | 0.936 |

After installing SAPF (controlled by enhanced-ADALINE algorithm) | ||||||

THD (%) | 1.29 | 1.01 | 1.49 | 1.72 | 2.59 | 2.12 |

Phase difference (°) | 0.30 | 0.30 | 0.50 | 0.40 | 0.20 | 0.90 |

PF | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |

After installing SAPF (controlled by STF-dq0 algorithm) [22] | ||||||

THD (%) | 1.66 | 1.50 | 2.01 | 1.90 | 3.41 | 2.55 |

Phase difference (°) | 0.40 | 0.30 | 0.60 | 0.50 | 0.30 | 1.10 |

PF | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |

**Table 3.**Summary of performance parameters demonstrated by the enhanced-ADALINE and STF-dq0 algorithms under Scenario II.

Performance Parameter | Load A | Load B | ||||
---|---|---|---|---|---|---|

Phase a | Phase b | Phase c | Phase a | Phase b | Phase c | |

Before installing SAPF | ||||||

THD (%) | 33.36 | 15.77 | 45.29 | 25.99 | 118.27 | 23.46 |

Phase difference (°) | 9.20 | 11.20 | 5.60 | 15.60 | 9.80 | 13.80 |

PF | 0.936 | 0.968 | 0.906 | 0.932 | 0.636 | 0.945 |

After installing SAPF (controlled by enhanced-ADALINE algorithm) | ||||||

THD (%) | 0.88 | 0.98 | 1.38 | 2.19 | 2.63 | 2.31 |

Phase difference (°) | 0.10 | 0.60 | 0.50 | 1.20 | 0.40 | 0.80 |

PF | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |

After installing SAPF (controlled by STF-dq0 algorithm) [22] | ||||||

THD (%) | 1.19 | 1.49 | 1.85 | 1.94 | 2.83 | 2.14 |

Phase difference (°) | 0.10 | 0.80 | 0.70 | 1.40 | 0.40 | 0.80 |

PF | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |

**Table 4.**Summary of performance parameters demonstrated by the enhanced-ADALINE and STF-dq0 algorithms under Scenario III.

Performance Parameter | Load A | Load B | ||||
---|---|---|---|---|---|---|

Phase a | Phase b | Phase c | Phase a | Phase b | Phase c | |

Before installing SAPF | ||||||

THD (%) | 27.74 | 18.56 | 53.32 | 33.79 | 129.01 | 27.13 |

Phase difference (°) | 9.80 | 13.50 | 5.80 | 11.20 | 10.10 | 11.90 |

PF | 0.949 | 0.956 | 0.877 | 0.929 | 0.603 | 0.944 |

After installing SAPF (controlled by enhanced-ADALINE algorithm) | ||||||

THD (%) | 1.45 | 0.98 | 1.87 | 1.73 | 2.13 | 1.53 |

Phase difference (°) | 0.10 | 0.60 | 0.40 | 1.00 | 0.30 | 0.80 |

PF | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |

After installing SAPF (controlled by STF-dq0 algorithm) [22] | ||||||

THD (%) | 1.91 | 1.66 | 2.34 | 2.20 | 2.92 | 2.05 |

Phase difference (°) | 0.10 | 0.80 | 0.60 | 1.10 | 0.40 | 0.90 |

PF | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hoon, Y.; Mohd Radzi, M.A.; Al-Ogaili, A.S. Adaptive Linear Neural Network Approach for Three-Phase Four-Wire Active Power Filtering under Non-Ideal Grid and Unbalanced Load Scenarios. *Appl. Sci.* **2019**, *9*, 5304.
https://doi.org/10.3390/app9245304

**AMA Style**

Hoon Y, Mohd Radzi MA, Al-Ogaili AS. Adaptive Linear Neural Network Approach for Three-Phase Four-Wire Active Power Filtering under Non-Ideal Grid and Unbalanced Load Scenarios. *Applied Sciences*. 2019; 9(24):5304.
https://doi.org/10.3390/app9245304

**Chicago/Turabian Style**

Hoon, Yap, Mohd Amran Mohd Radzi, and Ali Saadon Al-Ogaili. 2019. "Adaptive Linear Neural Network Approach for Three-Phase Four-Wire Active Power Filtering under Non-Ideal Grid and Unbalanced Load Scenarios" *Applied Sciences* 9, no. 24: 5304.
https://doi.org/10.3390/app9245304