# An Overview of Flexible Current Control Strategies Applied to LVRT Capability for Grid-Connected Inverters

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## Abstract

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## 1. Introduction

## 2. LVRT Considerations

#### 2.1. Voltage Sags

#### 2.2. Grid Code Requirements

#### 2.3. Voltage Support Strategies and Secondary Objectives

## 3. System Description

#### 3.1. Grid-Connected Inverter

#### 3.2. Control Loops

## 4. Flexible Current Control Algorithms

#### 4.1. Basic Formulation

#### 4.2. Fundamental Concepts of Flexible Control

- Instantaneous Active Reactive Control (IARC);
- Instantaneously Controlled Positive-Sequence (ICPS);
- Positive-Negative-Sequence Compensation (PNSC);
- Average Active-Reactive Control (AARC);
- Balanced Positive-Sequence Control (BPSC).

## 5. Current State of Art

## 6. Design of an LVRT Flexible Current Algorithm

#### 6.1. Scalar Factor Definition

#### 6.2. Injected Powers

#### 6.3. Voltage Support Strategy

#### 6.4. System Restrictions

#### 6.4.1. Maximum Current Limitation

#### 6.4.2. Maximum Voltage Limitation

#### 6.4.3. Maximum DC-Link Voltage

#### 6.5. Secondary Objectives

#### 6.6. Summary

## 7. Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Voltage Support Simulations (

**a**) Mode I: maximization of the positive sequence voltage; (

**b**) Mode II: minimization of the negative sequence voltage; (

**c**) Mode III: combination of Mode I and Mode II; and (

**d**) ${\sigma}_{i}$ for each voltage support model.

Control Strategy | Year | Flexible | Restrictions | Secondary Objectives | Control Features | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Over Current Control ${}^{1}$ | Over Voltage Control ${}^{2}$ | Deals with Power Curtailment ${}^{3}$ | Osc. Control ${}^{4}$ | ${\mathit{v}}_{\mathit{dc}}$ Osc. Control | Injection ${}^{5}$ | Grid Impedance ${}^{6}$ | RCI-GC ${}^{7}$ | Complexity | ||||||

${\stackrel{\sim}{P}}_{2\omega}$ | ${\stackrel{\sim}{Q}}_{2\omega}$ | P | Q | ${R}_{g}$ | ${X}_{g}$ | |||||||||

[64] | * | × | ✓ | × | × | ✓ | ✓ | ✓ | ✓ | ✓ | × | × | × | Low |

[67] | 2012 | ✓ | × | × | × | ✓ | × | ✓ | ✓ | × | × | ✓ | × | Low |

[68] | 2013 | ✓ | ∘ | ✓ | × | × | × | × | × | ✓ | × | ✓ | × | Low |

[23] | 2013 | ✓ | ✓ | × | × | ∘ | × | × | ✓ | ✓ | × | ✓ | × | Medium |

[69] | 2014 | ✓ | ✓ | ✓ | × | × | × | × | × | ✓ | × | ✓ | ✓ | Medium |

[70] | 2014 | ✓ | × | × | × | × | × | × | ✓ | × | ✓ | × | × | Low |

[71] | 2014 | × | ✓ | ✓ | × | × | × | - | × | ✓ | × | ✓ | ✓ | Low |

[21] | 2015 | ✓ | ✓ | × | ✓ | × | × | × | ✓ | ✓ | ✓ | ✓ | × | Low |

[18] | 2015 | × | ✓ | ✓ | × | × | × | ✓ | × | ✓ | × | ✓ | × | Medium |

[72] | 2015 | × | ✓ | ✓ | × | × | × | × | ✓ | ✓ | × | ✓ | × | Low |

[73] | 2016 | × | ✓ | × | ✓ | ∘ | × | × | ✓ | ✓ | × | × | ✓ | Low |

[74] | 2016 | × | × | × | × | ∘ | ∘ | ∘ | ✓ | ✓ | ✓ | ✓ | × | Low |

[19] | 2016 | ✓ | ✓ | × | × | ✓ | × | ✓ | ✓ | ✓ | × | × | × | Low |

[22] | 2017 | ✓ | ✓ | × | ✓ | ✓ | × | ✓ | ✓ | ✓ | × | × | × | Medium |

[75] | 2018 | ✓ | ✓ | ✓ | × | × | × | × | × | ✓ | × | ✓ | × | Low |

[34] | 2018 | ✓ | ✓ | × | × | ∘ | × | ∘ | ✓ | ✓ | × | × | ✓ | Medium |

[48] | 2018 | × | ✓ | ✓ | ✓ | ∘ | × | ∘ | ✓ | ✓ | ✓ | ✓ | × | High |

[41] | 2018 | × | ✓ | × | × | × | × | × | ✓ | ✓ | ✓ | ✓ | × | Low |

[47] | 2018 | ✓ | ✓ | ✓ | × | × | × | - | ✓ | ✓ | × | ✓ | ✓ | Low |

[76] | 2019 | ✓ | ✓ | × | × | ∘ | ∘ | ∘ | ✓ | ✓ | × | × | × | Medium |

[77] | 2019 | × | ✓ | × | × | × | × | × | ✓ | ✓ | ✓ | ✓ | × | Low |

[40] | 2020 | ✓ | ✓ | ✓ | × | ∘ | ∘ | ∘ | ✓ | ✓ | ✓ | ✓ | × | Medium |

[78] | 2020 | ✓ | ✓ | × | × | ✓ | × | ✓ | ✓ | ✓ | ✓ | ✓ | × | Low |

[79] | 2020 | ✓ | ✓ | × | × | ∘ | ∘ | ∘ | ✓ | ✓ | × | × | × | Medium |

[80] | 2020 | ✓ | ✓ | ✓ | × | ∘ | ∘ | × | ✓ | ✓ | × | ✓ | ✓ | Medium |

[65] | 2021 | ∘ | ✓ | × | × | ✓ | ∘ | ✓ | ✓ | ✓ | × | × | × | Low |

^{1}Over current control refers to the limitation of the maximum instantaneous phase current.

^{2}Over-voltage control refers to the limitation of the maximum instantaneous phase voltage at the PCC.

^{3}Power curtailment refers to the capability of the control to deal with the extra energy on the DC stage caused by the power curtailment.

^{4}Oscillation control describes if power oscillations are canceled or mitigated.

^{5}The table shows if the algorithm is able to inject active and/or reactive power during the voltage sag.

^{6}Grid impedance shows if the resistance or the inductance are considered in the control strategy.

^{7}RCI-GC refers to reactive current injection according to the grid code. * Although it was named as IARC by Rodriguez in 2007 [20], this strategy correspond to the power definition according to the Instantaneous Power Theory.

Mode | ${\mathit{k}}_{\mathit{p}}^{+}$ | ${\mathit{k}}_{\mathit{p}}^{-}$ | ${\mathit{k}}_{\mathit{q}}^{+}$ | ${\mathit{k}}_{\mathit{q}}^{-}$ | $\overline{\mathit{p}}$ | $\overline{\mathit{q}}$ | $\stackrel{\sim}{\mathbf{p}}$ | $\stackrel{\sim}{\mathbf{q}}$ | ||
---|---|---|---|---|---|---|---|---|---|---|

${\mathit{P}}^{*}$ | ${\mathit{Q}}^{*}$ | ${\mathit{P}}^{*}$ | ${\mathit{Q}}^{*}$ | |||||||

1 | 1 | 1 | 1 | 1 | ${P}^{*}$ | ${Q}^{*}$ | ✓ | 0 | 0 | ✓ |

2 | 1 | −1 | 1 | −1 | 0 | ✓ | ✓ | 0 | ||

3 | 1 | −1 | 1 | 1 | 0 | 0 | ✓ | ✓ | ||

4 | 1 | 1 | 1 | −1 | ✓ | ✓ | 0 | 0 |

Mode | Voltage Support | ${\mathit{k}}_{\mathit{p}}^{+}$ | ${\mathit{k}}_{\mathit{p}}^{-}$ | ${\mathit{k}}_{\mathit{q}}^{+}$ | ${\mathit{k}}_{\mathit{q}}^{-}$ |
---|---|---|---|---|---|

I | ${V}^{+}$↑ | 1 | 0 | 1 | 0 |

II | ${V}^{-}$↓ | 0 | 1 | 0 | 1 |

III | ${V}^{+}$↑ and ${V}^{-}$ ↓ | 1 | −1 | 1 | 1 |

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© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rincon, D.J.; Mantilla, M.A.; Rey, J.M.; Garnica, M.; Guilbert, D.
An Overview of Flexible Current Control Strategies Applied to LVRT Capability for Grid-Connected Inverters. *Energies* **2023**, *16*, 1052.
https://doi.org/10.3390/en16031052

**AMA Style**

Rincon DJ, Mantilla MA, Rey JM, Garnica M, Guilbert D.
An Overview of Flexible Current Control Strategies Applied to LVRT Capability for Grid-Connected Inverters. *Energies*. 2023; 16(3):1052.
https://doi.org/10.3390/en16031052

**Chicago/Turabian Style**

Rincon, David J., Maria A. Mantilla, Juan M. Rey, Miguel Garnica, and Damien Guilbert.
2023. "An Overview of Flexible Current Control Strategies Applied to LVRT Capability for Grid-Connected Inverters" *Energies* 16, no. 3: 1052.
https://doi.org/10.3390/en16031052