Aiming at the fact that the rotor winding inter-turn weak faults can hardly be detected due to the strong electromagnetic coupling effect in the excitation system, an interval observer based on current residual is designed. Firstly, the mechanism of the inter-turn short circuit of the rotor winding in the excitation system is modeled under the premise of stable working conditions, and electromagnetic decoupling and system simplification are carried out through Park Transform. An interval observer is designed based on the current residual in the two-phase coordinate system, and the sensitive and stable conditions of the observer is preset. The fault diagnosis process based on the interval observer is formulated, and the observer gain matrix is convexly optimized by linear matrix inequality. The numerical simulation and experimental results show that the inter-turn short circuit weak fault is hardly detected directly through the current signal, but the fault is quickly and accurately diagnosed through the residual internal observer. Compared with the traditional fault diagnosis method based on excitation current, the diagnosis speed and accuracy are greatly improved, and the probability of misdiagnosis also decreases. This method provides a theoretical basis for weak fault identification of excitation systems, and is of great significance for the operation and maintenance of excitation systems.

In recent years, with the continuous promotion of infrastructure and urbanization in major emerging economies, the requirements for the working stability of the power supply system under the condition of high-power and long-distance transmission have gradually increased [

Rotor winding inter-turn short circuit is a common fault form in excitation system, and is widely identified through the current signal [

In recent years, the state observer has been widely used in the field of fault diagnosis due to the advantages of high precision and high robustness [

In this paper, a residual interval observer is proposed to transfer the state discrimination basis from the traditional state domain to the residual domain, so that the state signal is more sensitive to fault occurrence and the fault state discrimination is more reliable. Then the advantages of the residual interval observer is discussed from the aspect of accuracy and detection time. Aiming at the coupling characteristic of the excitation system, the electromagnetic decoupling is carried out using Park transform. The model is built in

The excitation system consists of the rotor and stator, and the excitation process between the rotor and stator is shown in

In _{A}, _{A} and _{A} are voltages, currents and magnetic potentials at the A-terminal of the stator, _{B}, _{B} and _{B} are voltages, currents and magnetic potentials at the B-terminal of the stator, _{C}, _{C} and _{C} are voltages, currents and magnetic potentials at C-terminal of the stator. _{a}, _{a} and _{a} are voltages, currents and magnetic potentials at the a-terminal of the rotor, _{b}, _{b}, _{b} are the voltages, currents and magnetic potentials at the b-terminal of the rotor, _{c}, _{c}, _{c} are the voltages, currents and magnetic potentials at the c-terminal of the rotor. _{s} is the stator resistance, and _{r} is the rotor resistance. The current and magnetic potential changes caused by the other external interference are ignored, and the stator and rotor voltages in the excitation system can be expressed as

When a short-circuit fault occurs in the excitation system, the excitation magnetic potential changes, the excitation current increases, and the loss in the system increases with the local temperature at the short-circuit point. The fault can be regarded as adding a short circuit in the system, as shown in

Here the short circuit is set as d, then another fault circuit equation needs to be added, and the matrix increases by one order, which can be expressed as

where

where _{d}, _{q} show

where

To improve the performance of weak fault detection, a residual interval observer is designed to distinguish the fault by generating residuals.

The upper and lower bound functions in the observer are constructed as

where ^{+} = max{0,^{−} = ^{+}−^{+} = max{0, ^{−} = ^{+}−

where

The influence of electromagnetic interference on the observer can be measured by _{1} performance and _{1} performance and

where the interference d is a bounded function,

The observer needs to have certain disturbance robustness to reduce the influence of external disturbance. The robustness of the observer is defined by Lyapunov function, as shown in the following formula:

where _{d} is the systematic error when

Then the designed observer can be considered to be robust. In

Therefore,

Similarly,

When there is no fault in the system,

To improve the diagnostic sensitivity of the observer, the Lyapunov function shown in the following formula is constructed:

where _{2} > 0, _{f} is the systematic error when

It can be considered that the system is stable and sensitive, and weak faults can be therefore detected.

The gain matrix is optimized by linear matrix inequality (LMI), and the Metzler conditions are given in LMI.

The optimal value of the gain matrix is solved by the following algorithm, and then the fault diagnosis of the motor is realized. On the premise of satisfying the constraint

where

To verify the performance of the proposed fault detection scheme, the generator excitation system is simulated in Matlab/Simulink by using the model in

System parameter | Numerical value | Unit |
---|---|---|

Rotation speed | 1600 | r/min |

Stator inductance | 0.0397 | H |

Rotor inductance | 0.0397 | H |

Mutual inductance | 0.0374 | H |

Stator resistance | 0.114 | Ω |

Rotor resistance | 0.146 | Ω |

Leakage coefficient | 0.122 |

The external disturbance of the system is set as sinusoidal function

The currents of the excitation system before and after the short-circuit fault occurs are shown in

It can be seen from the comparison of

As can be seen from

It can be seen from

It can be seen from

The short-circuit coefficient is then changed, and set as

As can be seen from

As can be seen from

To further verify the correctness of the mathematical model of rotor winding short-circuit fault of excitation system based on the residual interval observer, the current characteristics are studied in the experiment. The corresponding experimental platform is built as shown in

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

Disc diameter (mm) | 120 |

Disc length (mm) | 10 |

Rotor eccentric displacement (mm) | 0.5 |

Number of bearing rolling elements | 8 |

Diameter of bearing inner race (mm) | 30 |

Diameter of bearing outer ring (mm) | 62 |

Shaft diameter (mm) | 30 |

The shaft length (mm) | 860 |

In

It can be seen from

It can be seen from

In this paper, a residual interval observer is designed for the diagnosis of the short-circuit fault of rotor winding aiming at problem that the weak faults can hardly be detected in time. In stable working conditions, the electromagnetic decoupling is carried out through modeling and coordinate transformation, and the current residual of the monitoring system is proposed to improve the diagnosis accuracy. Theoretical and experimental studies show that it is difficult to identify the weak fault only by observing the excitation current signal, but rapid fault detection can be realized when the residual interval observer is applied. When the number of short-circuit turns increases, the detection speed is faster, and no false alarm is found to affect the weak fault detection. Under the premise of stable working conditions and sinusoidal external interference, the residual interval observer brings a more precise weak fault detection, and the detection speed is also faster. The residual interval observer proposed in this paper provide important theoretical and technical basis for the operation and maintenance of excitation system. Unstable working conditions and irregular external interference may lead to fluctuations in observed residuals and even false alarms, and it needs to be optimized in the future works.

The authors would like to thank the financial supports from National Science Foundation of China (Grant No. 51777121).

The authors declare that they have no conflicts of interest to report regarding the present study.

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