### Abstract

Grid-connected converters are an important class of power electronic systems. Many power and energy applications require grid-connected converters. To control grid-connected converters, precise information of the grid voltage frequency and phase are required. Gradient estimators can be very useful in this regard. They are suitable to estimate the frequency and phase of the grid voltage signal. Various gradient estimators are already available in the literature e.g. regression-based techniques. However, most of them are designed by using the instantaneous estimation error as the cost-function. This amplifies the effect of noise in the estimated parameters. To overcome this issue, an integral cost-function is considered in this paper. The integral cost-function tries to minimize the estimation error over the integration window leading to reduce the effect of noise in the estimated frequency and phase. Moreover, the cost-function uses tunable forgetting factor to give more importance to recent data. The proposed gradient estimator assumes the grid frequency to be constant. However, in practice the frequency is variable with known nominal value. To overcome this problem, a frequency estimation block is coupled with the gradient estimator. The frequency estimation block uses the idea of phase-based frequency estimation. Comparative numerical simulation and experimental studies are performed to demonstrate the suitability of the proposed technique over three other advanced techniques from the literature.

Original language | English |
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Article number | 9060880 |

Pages (from-to) | 70693 - 70702 |

Number of pages | 10 |

Journal | IEEE Access |

Volume | 8 |

DOIs | |

Publication status | Published - 8 Apr 2020 |

### Bibliographical note

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/### Keywords

- Gradient estimator
- frequency estimation
- phase estimation
- grid synchronization
- noise robust estimation
- single-phase system

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## Cite this

Ahmed, H., Salgado, I., Chairez, I., & Benbouzid, M. (2020). Robust Gradient Estimator for Unknown Frequency Estimation in Noisy Environment: Application to Grid-Synchronization.

*IEEE Access*,*8*, 70693 - 70702. [9060880]. https://doi.org/10.1109/ACCESS.2020.2986409