IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 6, JUNE 2009 2259 Small-Signal Model-Based Control Strategy for Balancing Individual DC Capacitor Voltages in Cascade Multilevel Inverter-Based STATCOM Yu Liu, Student Member, IEEE, Alex Q. Huang, Fellow, IEEE, Wenchao Song, Student Member, IEEE, Subhashish Bhattacharya, Member, IEEE, and Guojun Tan, Member, IEEE Abstract—This paper presents a new feedback control strategy for balancing individual dc capacitor voltages in a three-phase cascade multilevel inverter-based static synchronous compensator. The design of the control strategy is based on the detailed small- signal model. The key part of the proposed controller is a compen- sator to cancel the variation parts in the model. The controller can balance individual dc capacitor voltages when H-bridges run with different switching patterns and have parameter variations. It has two advantages: 1) the controller can work well in all operation modes (the capacitive mode, the inductive mode, and the standby mode) and 2) the impact of the individual dc voltage controller on the voltage quality is small. Simulation results and experimental results verify the performance of the controller. Index Terms—Multilevel converters, reactive power, static syn- chronous compensator (STATCOM), voltage balancing. I. I NTRODUCTION T HE static synchronous compensator (STATCOM) is a flexible ac transmission system device, which is connected as a shunt to the power system, for generating or absorbing reactive power [1]. A STATCOM works in the capacitive mode if it injects reactive power to the power system. It works in the inductive mode if it absorbs reactive power from the system. If no reactive power exchanges between a STATCOM and the system, the STATCOM works in the standby mode. STATCOM can be utilized to regulate voltage, control power factor, and stabilize power flow [2]. Compared with a conventional static VAr compensator, the STATCOM has advantages such as fast speed, compact footprint, and small harmonics [1], [3]. Increased attention has been paid to multilevel inverters for STATCOM in medium-voltage network, since it is hard to use single power semiconductor switch directly in medium- voltage networks [4]–[11]. Cascade multilevel inverters that are Manuscript received April 29, 2008; revised July 30, 2008 and October 26, 2008. First published March 16, 2009; current version published June 3, 2009. Y. Liu, A. Q. Huang, W. Song, and S. Bhattacharya are with the National Science Foundation’s Engineering Research Center for Future Renewable Electric Energy Delivery and Management (FREEDM) Systems, Department of Electrical Engineering, North Carolina State University, Raleigh, NC 27695 USA (e-mail: yliu8@ncsu.edu). G. Tan is with the China University of Mining and Technology, Xuzhou 221008, China (e-mail: gjtan@cumt.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2009.2017101 based on the connection of several H-bridges are very popular among the existing topologies of multilevel inverters due to their modularization and extensibility [9], [12]. One of main disadvantages of the cascade multilevel inverter in the application of STATCOM is the imbalance of the dc capacitor voltages [13], [14]. The imbalance is caused by: 1) different switching patterns for different H-bridges [7], [15]; 2) parameter variations of active and passive components inside H-bridges; and 3) the control resolution [16]. The imbalance of dc capacitor voltages will degrade the quality of the voltage output; in severe cases, this could lead to the complete collapse of the power-conversion system [11]. Moreover, it will cause excessive voltages across the devices and an imbalance of switching losses [16]. An adequate control strategy for avoiding the imbalance of dc capacitor voltages must meet four requirements: 1) It can balance voltages when the STATCOM works in the capacitive mode, the inductive mode, and the standby mode; 2) its impact on voltage quality is as small as possible; 3) it can balance voltages when components of H-bridges have parameter vari- ations; and 4) it can balance voltages when H-bridges switch with different switching patterns. The methods presented in [3] and [8] balance the voltages by swapping switching patterns. Due to no feedback control, they may not meet requirement 3). The feedback control strategies presented in [5], [6], [16]–[18] reshape the output voltages of H-bridges based on the feedback signals of the dc capacitor voltages. Thus, they meet the requirement 3) and 4). However, [5], [6], [16]–[18] did not show if the control strategies work in different operating modes. Moreover, the impacts on voltage qualities were not analyzed. The modeling of the multilevel converter benefits the design of control systems [19], [20]. This paper proposes a new feedback control strategy for balancing individual dc capacitor voltages based on the detailed small-signal model. The small- signal model leads us to find out an efficient way for reshaping the voltage to achieve the control aim. The transfer function for an individual dc capacitor voltage derived from the small-signal model shows that the gain of the transfer function is time- variant. By introducing a compensator into the control loop to cancel the variation of gain, the controller works well in the whole operation region: the capacitive mode, the inductive mode, and the standby mode. 0278-0046/$25.00 © 2009 IEEE