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Finite set model predictive control to a shunt multilevel active filter

Hernaldo Saldías Molina (Laboratory of Electric Vehicles, Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile)
Juan Dixon Rojas (Laboratory of Electric Vehicles, Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile)
Luis Morán Tamayo (Department of Electrical Engineering, Universidad de Concepción, Concepción, Chile)



The purpose of this paper is to implement a finite set model predictive control algorithm to a shunt (or parallel), multilevel (cascaded H-bridge) active power filter (APF). Specifically, the purpose is to get a controller that could compensate the mains current and, at the same time, to control the voltages of its capacitors. This strategy avoids the use of multiple PWM carriers or another type of special modulator, and requires a relatively low processing power.


This paper is focussed in the application of the predictive controller to a single-phase parallel APF composed for two H-bridges connected in series. The same methodology can be applied to a three-phase APF. In the DC buses of each H-bridge, a floating capacitor was connected, whose voltage is regulated by the predictive controller. The controller is composed by, first, a model for the charge/discharge dynamics for each floating capacitor and a model for the output current of the APF; second, a cost function; and third, an optimization algorithm that is able to control all these variables at the same time, choosing in each sample period the best combination of firing pulses.


The controller can track the voltage references, compensate the current harmonics and compensate reactive power with an algorithm that evaluates only the three nearest voltage levels to the last voltage level applied in the inverter. This strategy decreases the number of calculations required by the predictive algorithm. This controller can be applied to the general case of a single-phase multilevel APF of N-levels and extend it to the three-phase case without major problems.

Research limitations/implications

The implemented controller, when the authors consider a constant sample time, gives a mains current with a Total Harmonic Distortion (THD-I) slightly greater in comparison with the base algorithm (that evaluates all the voltage levels). However, when the authors consider the processing times under the same processor, the implemented algorithm requires less time to get the optimal values, can get lower sampling times and then a best performance in terms of THD-I. To implement the controller in a three-phase APF, a faster Digital Signal Processor would be required.


The implemented solution uses a model for the charge/discharge of the capacitors and for the filter current that enable to operate the cascaded multilevel inverter with asymmetrical voltages while compensates the mains currents, with a predictive algorithm that requires a relatively low amount of calculations.



This work was financially supported by CONICYT though Project FONDECYT 1110592.


Saldías Molina, H., Dixon Rojas, J. and Morán Tamayo, L. (2015), "Finite set model predictive control to a shunt multilevel active filter", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 34 No. 1, pp. 279-300.



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