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Optimal frequency control of an islanded microgrid has been a challenging issue in the research field of microgrids. Recently, fractional-order calculus theory and some related control methods have attempted to handle this issue. In this paper, a novel fractional-order model predictive control (FOMPC) method is proposed to achieve the optimal frequency control of an islanded microgrid by introducing a fractional-order integral cost function into model predictive control (MPC) algorithm. Firstly, a discrete state-space model is derived for the optimal frequency control problem of an islanded microgrid. Afterward, a fractional-order integral cost function is designed to guide the FOMPC algorithm to obtain optimal control law by borrowing the Grünwald-Letnikov (GL) definition of fractional order calculus. Six simulation studies have been carried out to illustrate the superiority of FOMPC to conventional MPC under dynamical load disturbances, perturbed system parameters and random dynamical power fluctuation of wind turbines.

This paper puts forward the ML-FEM coupled model for analyzing the transient behavior of stator ground fault in generators, which possesses the distinguished capability to accurately take account of not only the distributed capacitances of the stator windings to the ground, but a variety of generator nonlinearities. The numerical simulation of stator ground fault in generators, along with the related experiments, has been completed. The simulation and experiment results explicitly demonstrate that the ML-FEM coupled model is superior to the ML model presented previously, and more preferable for transient analysis of stator ground fault in generators. As paves the way to develop and improve the relay protection scheme against this type of fault.

Based on the multi-loop circuit method of calculating the inductance parameters of AC machine windings, a comprehensive and transient simulation model is established for various faults in the stator windings of a salient-pole synchronous generator. In term of different fault styles, the fault-associated matrix in the state equations is modified, and all of faults in stator windings including internal faults and ground faults can be simulated in this unified model. Simulation results are compared with those of experiments to verify the proposed method. Using the model to study the variation of current and voltage is conductive to analyze the features of faults, and design the relevant protection scheme.

Based on the multi-loop circuit method of AC machine a mathematic model is established for the large unit-connected generators, namely the outlet terminal of generators connected to a common busbar, and the transient zero-sequence current and voltage of these generators are simulated and analyzed at different grounding location. Further, making use of the wavelet transform sensitively detecting the singularity of signal, the properties of their value of wavelet transform are analyzed, and a selective transient protection is proposed according to the sign and value of the modulus maxima of wavelet transform. The results of simulation and experiment verify the new protection can correctly detect the generator with ground fault, and discriminate between the internal and external faults.

This paper puts forward a developed scheme against the deficiencies of the out-of-step protection based on the three-impedance element principle, which is widely applied at present. Compared with the original scheme, the developed scheme can predict the out-of-step caused by steady stability disruption or transient instability by using the least square method in advance and monitor the limit of steady stability. So the performance of the out of step protection is improved. The paper gives the whole developed protection scheme. The results of dynamic simulation experiments verify the scheme.

By analyzing the sensitivity and its influencing factors of stator earth-fault protection by injecting a 20 Hz signal, this paper puts forward an improved generator protection scheme based on the impedance angle and its mutation component. The simulation results verify this kind of protection scheme has higher reliability and sensitivity under generator neutral grounding through a distribution transformer with a secondary resistor and arc-extinguishing coil compared with the conventional criterion. Against different grounding modes, the sensitivity of the protection scheme is further improved by correspondingly adjusting the frequency of the injected signal.