Backstepping controllers are obtained for distributed hybrid photovoltaic (PV) power supplies of telecommunication equipment. Grid-connected PV-based power supply units may contain dc-dc buck-boost converters linked to single-phase inverters. This distributed energy resource operated within the selfconsumption concept can aid in the peak-shaving strategy of ac smart grids. New backstepping control laws are obtained for the single-phase inverter and for the buck-boost converter feeding a telecom equipment/battery while sourcing the PV excess power to the smart grid or to grid supply the telecom system. The backstepping approach is robust and able to cope with the grid nonlinearity and uncertainties providing dc input current and voltage controllers for the buck-boost converter to track the PV panel maximum power point, regulating the PV output dc voltage to extract maximum power; unity power factor sinusoidal ac smart grid inverter currents and constant dc-link voltages suited for telecom equipment; and inverter bidirectional power transfer. Experimental results are obtained from a lab setup controlled by one inexpensive dsPIC running the sampling, the backstepping and modulator algorithms. Results show the controllers guarantee maximum power transfer to the telecom equipment/ac grid, ensuring steady dc-link voltage while absorbing/injecting low harmonic distortion current into the smart grid.

For three-phase four-wire circuits, two compensation criteria have been established: one based on the instantaneous value concept and the other on the average value concept. Thus, according to the instantaneous value concept the non instantaneous power current is reduced, without altering the instantaneous active power. According to the average value concept, the nonactive average-current is reduced, without altering the average power. When the zero-sequence voltage component exists, both compensation types would not enable the zero-sequence (neutral) source current elimination. Then, two approaches are marked in this paper. The first one is for eliminating the non instantaneous power current or the nonactive average-current but the neutral current can still flow. The second one for eliminating the modified non instantaneous power current or the modified nonactive average-current, thus the neutral current component is compensated. According to recent recommendations in this work three-phase systems are considered as four-conductor systems. Experimental results are obtained to confirm the theoretical properties and to show the compensator performance.Index Terms-Active power-line conditioner, compensation, instantaneous power theory.

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The control strategy derived from the instantaneous reactive power theory is one of the most commonly used in the Active Power Filters (APFs). For the last decades other formulations have been developed in order to achieve compensation objectives different to the proposed in the original one. Nevertheless, all of them can be only applied to three-phase systems, i. e.: in those formulations frameworks, they can not be used to obtain the control strategy for a polyphase system. This paper presents a new approach which can be applied to n wire systems. The powers and currents expressions derived from the formulations presented up now can be obtain applying this new approach. In this paper, the original p-q and the modified p-q formulation expressions are obtain in the new approach framework.