International Electrical Engineering Journal (IEEJ) Vol. 3 (2012) No. 2, pp. 738-744 ISSN 2078-2365 Page 738 Vahid and Shoulaie, Capacitors Natural Voltage Balancing Mechanism Investigation in Flying Capacitor Multicell Converters Capacitors Natural Voltage Balancing Mechanism Investigation in Flying Capacitor Multicell Converters Vahid Dargahi and Abbas Shoulaie Department of Electrical Engineering, Iran University of Science and Technology, Tehran 16846, Iran vdargahi@elec.iust.ac.ir , shoulaie@iust.ac.ir Abstract—This paper presents an analytical analysis of flying capacitors voltage balancing process in flying capacitor multicell converters. The analysis is based upon renowned theory of Double Fourier series which leads to modeling and state-space representation of converters. State-space representation of converter can be utilized to investigate the transient and steady states of internal flying capacitors voltages. To provide verification, experimental results acquired from a laboratory prototype are compared against numerical solution of differential equations of converter state-space representation and simulation results. Keywords Flying Capacitor Multicell Converter, Double Fourier Series, Self balancing. I. INTRODUCTION As a consequence of reaching higher power and lack of its suitable ranged switches, multilevel converters popped up in 1975 and have been continuously developed in recent years due to the necessity of increase in power level of industrial applications especially high power applications such as high power AC motor drives, active power filters, reactive power compensation and FACTS devices. The main reason is the capability of these topologies to handle voltage/power in the range of kilovolts/megawatts as a result of recent developments in the area of high power semiconductors [1]-[5]. The concept of multilevel arises from acquiring a staircase output voltage waveform as voltage levels from input dc voltages by means of converter appropriate configuration and its proper switching pattern. This staircase voltage by its resemblance to sinusoidal voltage waveform leads to primitive advantages of utilizing switches with low-voltage ratings, higher power quality, lower total harmonic distortion, etc [1]- [5]. The term multilevel starts with the three-level converter introduced by Nabae et al. The Neutral Point Clamped (NPC) converter, presented in the early 80’s, is a standard topology in industry on its 3-level version. However, for a higher number of levels, this topology has some drawbacks such as: voltage balance of the dc-link capacitors and the number of clamping diodes [2]-[4]. Alternatives for the NPC converters are the multicell topologies. Different cells and approaches to interconnect them lead to many topologies which the most important ones are the Cascaded Multicell (CM) and the Flying Capacitor Multicell (FCM) accompanied by its sub-topology Stacked Multicell (SM) converters [2][3][5]. The FCM converter, and its derivative, the SM converter, have many advantageous properties for medium voltage applications, particularly the transformer-less operation and the ability to naturally maintain the flying capacitors voltages at their target operating levels. This substantial property is called natural balancing and allows the construction of such converters with a large number of voltage levels. Natural self- balancing of the flying capacitors voltages occurs without any feedback control. A necessary condition for this phenomenon is that average currents of the flying capacitors must be zero. As a result, each cell must be controlled with the same duty cycle and a regular phase shifted progression along the cells. Generally, an output RLC filter (balance booster circuit), tuned to the switching frequency or multiple of that, is suggested to be connected across the load in order to accelerate this self balancing process in the transient states [2][3][5]. The FCM converter uses a series connection of “cells” comprising a flying capacitor and its associated complimentary switch pair and produces a switched voltage that is the sum of the individual cell states [2][3][5]. Despite of mentioned appreciable advantages, multilevel converters possess some following main drawbacks: increased number of isolated dc voltages, clamping diodes, capacitors and of power semiconductor switches accompanied by their related gating and protection circuits which result in a sophisticated overall system [2][3][5]. As mentioned, voltage natural balancing mechanism is a fundamental principle in flying capacitor and stacked multicell converters which consents to construction of voltage levels at the converter output [8]-[11]. The main objective of this paper is to provide a mathematical model for flying capacitor multicell converters intended for investigation of transient and steady state of flying capacitors voltages accompanied by taking into account the effect of balance booster circuit.