I. Introduction
During recent years, modular converters have been attracting increasing interest in industry [1]. Due to its simplicity, the traditional centralized control has been adopted for modular converters in many industrial applications as well as in academic research. However, since the central controller executes the whole control algorithm, high CPU computation speed and high communication bandwidth are usually required [2], [3]. Besides, the modularity of the modular converter can be limited by the centralized control [4]. In order to overcome these drawbacks, distributed control architectures are being pursued for modular converters. Much of the literature investigating such an approach has focused on the modular multilevel converter (MMC) for high-voltage applications, such as high-voltage direct current transmission [4]–[7] , wind power [8], and photovoltaics [9]. In these applications, considering the large number of submodules and high potential difference between the submodules, optical fiber and high-speed communication technology are usually adopted. Another focus is on parallel-connected converters, such as ac/dc converters [10]–[14]. To improve the performance of the distributed control system for modular converters, research has also been conducted on fault-tolerant designs [7], [8], [13], timing constraints analysis [6] , and analysis of noncharacteristic harmonic components owing to synchronization error [15].