Predictive Control Formulation for Achieving a Reduced Finite Control Set in Flying Capacitor Converters Ricardo P. Aguilera and Daniel E. Quevedo Abstract— Multilevel Converters (MCs) have emerged as a promising alternative to traditional two level converters. These topologies present a better output voltage quality due to the reduction of the voltage steps by increasing the voltage number levels. Within the MC family, flying capacitor converters present a special attraction due to the easy way to increase output voltage levels by adding cells. Recently model predictive control algorithms have reached a special interest in MCs applications. In particular, finite control set predictive control algorithms applied to flying capacitor converters have shown that it is possible to achieve a good performance in the control of capacitor voltages and output current. For that purpose, at each sample time the controller explores all the switching states and determines the optimal one to be applied. However, the number of switching states grow exponentially in relation to the number of cells. This increases the time that the algorithm takes to find the optimal switching state. In this paper we present an off- line strategy to reduce the number of switching states to be explored in a finite control set predictive algorithm by using only those which produce that the system state point towards to the reference. Moreover, a sampling period design is presented to guarantee that the system state remains inside of a positive invariant set. I. I NTRODUCTION Multilevel converters (MCs) have emerged as an important technology in many industrial applications. The main reason for this is that MCs are able to operate at far higher power levels and also provide output voltage and currents with lower distortion than their two level counterparts [1]. In particular, flying capacitor converters (FCCs) have at- tracted significant attention [2] because of its special feature such as to have a unique dc-link voltage, easy way to increase the output voltage levels by adding cells and when an internal fault occurs, currents decay quickly, since the associated capacitors seek voltage balance [3]. However, a balancing of the capacitor voltages is required in FCCs to achieve a uniform distribution of the transistor blocking voltage [4]. Recently, predictive control strategies [5] have been ap- plied to power converters and multilevel converters in par- ticular, see e.g. [6]–[10]. Advantages of using predictive control, when compared to traditional PWM methods, derive from the fact that changing operating conditions are explic- itly accounted for. In [8], a model predictive control (MPC) strategy for FCCs is presented. The goal of this work is to control not only the output current but also the capacitor voltages and the current spectrum. For that propose, a cost The authors are with the School of Electrical Engineering & Computer Science, The University of Newcastle, NSW 2308, Australia; e-mails: ricardo.aguilera@studentmail.newcastle.edu.au, dquevedo@ieee.org function which takes into account the system state error is define. Moreover, a notch filter is applied to the error of the current in order to obtain a control of its spectrum. Finally, the controller minimizes this cost function by exploring a finite control set of switches to determine the optimal action to be applied. The elements of this control set depend on an exponential way of the number of cells. Thus, if the number of cells grows the controller will take a long time to find the optimal switching action to be applied. This hinders its use in many practical applications. In [11], a hybrid model of a boost converter is presented. Here, the power system the converter is analyzed taking into account its nature, which presents discrete inputs (switching action) and continuous outputs (currents and voltages). In addition, a safe spherical boundary space around the ref- erence point is presented. To guarantee the stability of the system by keeping the system state inside of this set, the maximum allowed radius of this sphere is subject to, for all system states inside of this region exist a discrete input which generates that the system state points inwards to the reference point. This paper presents a constraint finite control state MPC algorithm, which presents a reduction in the switching states to be explored. This reduction is based on the analysis of the continuous model of the converter choosing those switching states which yield that the system state points towards to the desired operating point. This analysis is carried out off-line, so it does not imply an extra effort in the implementation for the controller. Furthermore, a sampling period design is presented in order to define an admissible error in the system. Finally, this analysis allows one to establish an invariant set when the reference is constant, that means when the FCC is used as a dc-dc converter. The remainder of this paper is organized as follows: In Section II we develop the continuous and discrete model for a generalized n-cell FCC considered for the proposed strategy. Section III gives a brief of MPC algorithm applied to an FCC. In Section IV we present our proposed constraint finite control set Predictive Control strategy. Section V presents a specific design study and Section VI draws conclusions. II. FLYING CAPACITOR CONVERTER In this section we describe the flying capacitor topology in more detail and develop a model for the system. Figure 1 shows a topology of a generalized single phase n-cell flying capacitor converter. Here it is possible to see how the cells are interconnected in a cascade way. As it was Proceedings of the European Control Conference 2009 • Budapest, Hungary, August 23–26, 2009 WeA14.4 ISBN 978-963-311-369-1 © Copyright EUCA 2009 3955