# A Parameter-Free Method for Estimating the Stator Resistance of a Wound Rotor Synchronous Machine

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## Abstract

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## 1. Introduction

- Direct measurement methods;
- Model-based estimation methods;
- Signal injection-based methods.

## 2. Flux Estimation

## 3. Effect of Stator Resistance Mismatch on the Estimated Flux

## 4. Simulation and Method Explanation

#### 4.1. Estimated Flux

#### 4.2. Estimation of Stator Resistance

#### 4.3. Kalman Filter Estimator

## 5. Experimental Results

#### 5.1. Flux Estimation

#### 5.2. Stator Resistance Estimation

#### 5.3. The Effect of a Sudden Change in Load

#### 5.4. Estimation of Resistance by Kalman Observer

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

WRSM | Wound Rotor Synchronous Machine |

DTC | Direct Torque Control |

MPC | Model Predictive Control |

${R}_{s}$ | Stator resistance |

${v}_{s}$ | Stator voltage |

${i}_{s}$ | Stator current |

${\psi}_{s}$ | Stator flux |

LPF | Low-Pass Filter |

${\omega}_{c}$ | Cutoff frequency of the LPF |

$Mag$ | Gain error produced by LPF |

$\phi $ | Phase error produced by LPF |

${\omega}_{e}$ | Synchronous angular frequency |

${\widehat{R}}_{s}$ | Initial resistance |

${\tilde{R}}_{s}$ | Error value of the resistance |

${\widehat{\psi}}_{s}$ | Estimated flux |

${\tilde{\psi}}_{s}$ | Error part of the estimated flux |

EKF | Extended Kalman Filter |

${v}_{d}$ | Voltages in the d axis |

${v}_{q}$ | Voltages in the q axis |

${i}_{e}$ | Rotor excitation current |

${L}_{d}$ | Stator inductance on the d axis |

${L}_{q}$ | Stator inductance on the q axis |

M | Mutual inductance between the rotor and the stator |

## References

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**Figure 3.**Simulation results: Flux ${\psi}_{d}$ as a function of ${i}_{d}$ in the case of ${R}_{s}$ mismatch.

**Figure 4.**Simulation results: Flux ${\psi}_{q}$ as a function of ${i}_{q}$ in the case of ${R}_{s}$ mismatch.

**Figure 5.**Simulation results: Flux ${\psi}_{q}$ as a function of ${i}_{d}$ in the case of ${R}_{s}$ mismatch.

**Figure 6.**Simulation results: Flux ${\psi}_{q}$ as a function of a sinusoidal variation of ${i}_{d}$ in the case of ${R}_{s}$ mismatch.

**Figure 7.**Algorithm of the proposed estimator (subscript ’p’ represents the variable in the previous time step).

**Figure 9.**Simulation results: Estimated ${R}_{s}$, estimated flux ${\psi}_{q}$, and with a sinusoidal signal injection on ${i}_{d}$.

**Figure 10.**Simulation results: Estimated ${R}_{s}$, estimated flux ${\psi}_{q}$, and with a sinusoidal signal injection on ${i}_{d}$.

**Figure 14.**Simulation results: Estimated resistance by Kalman observer when errors in the parameters are added.

**Figure 16.**Estimated flux with a sinusoidal signal injection on ${i}_{d}$ for different values of ${R}_{s}$.

**Figure 17.**Estimated resistance when the initial value was about 10 times smaller than the actual value.

**Figure 18.**Estimated resistance when the initial value was about 10 times bigger than the actual value.

**Figure 21.**Experimental estimated resistance with Kalman observer while there are errors in the parameters.

Parameter | Symbol | Value |
---|---|---|

Stator resistance | ${R}_{s}$ | 20 m$\mathrm{\Omega}$ |

d-axis inductance | ${L}_{d}$ | 80 $\mathsf{\mu}$H |

q-axis inductance | ${L}_{q}$ | 80 $\mathsf{\mu}$H |

Mutual inductance between rotor and stator | M | 3 mH |

Number of pole pairs | ${N}_{p}$ | 6 |

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## Share and Cite

**MDPI and ACS Style**

Haghgooei, P.; Jamshidpour, E.; Corne, A.; Takorabet, N.; Khaburi, D.A.; Baghli, L.; Nahid-Mobarakeh, B.
A Parameter-Free Method for Estimating the Stator Resistance of a Wound Rotor Synchronous Machine. *World Electr. Veh. J.* **2023**, *14*, 65.
https://doi.org/10.3390/wevj14030065

**AMA Style**

Haghgooei P, Jamshidpour E, Corne A, Takorabet N, Khaburi DA, Baghli L, Nahid-Mobarakeh B.
A Parameter-Free Method for Estimating the Stator Resistance of a Wound Rotor Synchronous Machine. *World Electric Vehicle Journal*. 2023; 14(3):65.
https://doi.org/10.3390/wevj14030065

**Chicago/Turabian Style**

Haghgooei, Peyman, Ehsan Jamshidpour, Adrien Corne, Noureddine Takorabet, Davood Arab Khaburi, Lotfi Baghli, and Babak Nahid-Mobarakeh.
2023. "A Parameter-Free Method for Estimating the Stator Resistance of a Wound Rotor Synchronous Machine" *World Electric Vehicle Journal* 14, no. 3: 65.
https://doi.org/10.3390/wevj14030065