-The present paper proposes a sliding mode control with fixed switching frequency for three-phase three-leg voltage source inverter based four-wire shunt active power filter. The aim is to improve phase current waveform, neutral current mitigation, and reactive power compensation in electric power distribution system. The performed sliding mode for active filter current control is formulated using elementary differential geometry. The discrete control vector is deduced from the sliding surface accessibility using the Lyapunov stability. The problem of the switching frequency is addressed by considering hysteresis comparators for the switched signals generation. Through this method, a variable hysteresis band has been established as a function of the sliding mode equivalent control and a predefined switching frequency in order to keep this band constant. The proposed control has been verified with computer simulation which showed satisfactory results.

The present paper deals with the sliding mode control of a three-phase four-wire shunt active filter SAF, to improve phase-current waveform, neutral current mitigation and reactive power compensation in electric power distribution system. The sliding mode is formulated using elementary differential geometry, then the control vector is deduced from the sliding surface accessibility using the Lyapunov stability. The algorithm used to establish the current references for the sliding mode controller is based on the instantaneous real and imaginary power theory for four-wire system. It will be seen that this method permits to synthesis the control vector with simple manner, and finally, the obtained simulation results confirm that the above objectives are satisfied.

The coil iron nucleus cylindrical is a nonlinear electro radio in which the moving of the nucleus in a sense or in other causes change in inductance and can reach extreme values at the superposition of nucleus and coil centers. The variation of the inductance and the degree of freedom of movement of the nucleus can lead to a device with electromechanical conversion The aim of this paper is the determination and visualization of self inductance and mutual of the (C.I.C.C) based on geometric dimensions and the displacement of the nucleus.

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