IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 19, NO. 4, OCTOBER 2004 1919 Nonlinear Control Strategies for Cascaded Multilevel STATCOMs Diego Soto, Member, IEEE, and Rubén Peña, Member, IEEE Abstract—Two internal nonlinear control strategies based on the feedback linearization technique for cascaded multilevel static compensators (STATCOMs) are presented. The strategies depend on the control capability of the converter output voltage and are suitable for line frequency-switched converters. The first strategy considers a STATCOM where the voltage is set independently of the dc link voltage. Fast reactive power control within subcycle time response is achieved. The second strategy is constrained to a voltage whose amplitude remains proportional to the dc link voltage. Despite this limitation, the proposed strategy allows full stabilization of the STATCOM dynamics and relatively fast control of the reactive current (within one cycle). This may be adequate for most STATCOM applications. Simulation results, using power system computer-aided design/electromagnetic transient program (PSCAD/EMTP), presented for both strategies confirm the ef- fectiveness of the control schemes to impose linear STATCOM dynamics. Preliminary experimental results from a five-level prototype are presented for a converter using fixed control angles. Index Terms—Flexible ac transmission systems (FACTS), multilevel converter, nonlinear control, static compensator (STATCOM), static var generator. I. INTRODUCTION T HE static compensator (STATCOM) is the modern ver- sion of the well-established reactive power compensator. Various experimental systems are already in service. Most of them use the multipulse converter topology [1]. Alternatively, multilevel converters can be used [2], thus eliminating the complex transformer array needed to suppress harmonics. In comparison with other multilevel converter topologies, the cascaded topology requires the least number of components (controlled and passive devices) and can be implemented in a modular fashion. Fig. 1 shows a three-phase, cascaded STATCOM using two H-bridge modules per phase and Fig. 2 shows its typical five-level “staircase” phase voltage wave- form, synthesized keeping the switching at line frequency. Pulse-width modulation PWM methods can be employed if higher switching frequency can be accommodated. However, the line-frequency-switched version remains of most interest in STATCOM implementations (to keep converter losses as low as possible). The main role of a STATCOMis to provide voltage support at critical points of a transmission system. This is accomplished Manuscript received June 24, 2003. Paper no. TPWRD-00311-2003. This work was supported by Fondecyt Chile under Contract 1010939. The authors are with the Department of Electrical Engineering, University of Magallanes, Punta Arenas, Chile (e-mail: dsoto@ona.fi.umag.cl). Digital Object Identifier 10.1109/TPWRD.2004.835394 by injecting reactive current into the line in according to a line voltage control scheme. This normally comprises a reactive cur- rent controller at the converter level (which is the subject of this work), and a line voltage controller at the transmission system level. In general, the reactive current injected by a STATCOM is proportional to the voltage difference between the STATCOM and the line. Therefore, adjusting the converter voltage can con- trol the reactive current. In general, the design and performance of the internal control system of a STATCOM depends on how its output voltage is controlled. In this context, depending on the switching pattern employed [1], converters can be classified as either directly or indirectly controlled. Each H-bridge module provides one control angle (e.g., and in Fig. 2), a degree of freedom per quarter-cycle. For an -module converter, one degree of freedom is used to set the amplitude of the fundamental whereas the others are normally used to cancel low-order harmonics. In this case, control an- gles; hence, switching pattern, vary with the voltage amplitude. A multilevel STATCOM using this switching strategy is able to exert direct control over the amplitude of its output voltage, within a certain range, independent of the dc link voltage, and is therefore categorized as a STATCOM with direct voltage con- trol capability. In converters where the switching losses are crucial and where a moderate number of H-bridge modules are used, commutation angles may be set to minimize harmonic dis- tortion (while maximizing the fundamental) and are therefore kept fixed, independent of the voltage amplitude needed. This restricts the voltage amplitude to remain proportional to the dc link voltage and only phase shifting of the switching pattern; hence, the output voltage is possible. In order to provide a controllable converter voltage, the dc voltage must vary accord- ingly. This is achieved by temporally shifting the switching pattern in order to partially charge or discharge the dc link ca- pacitor. A multilevel STATCOM using this switching strategy is then categorized as an indirectly controlled type. The performance of a reactive current control system in an in- directly controlled STATCOM depends on the capacitor voltage dynamics, which is relatively slow, because of the large capac- itor needed to reduce dc voltage ripple, and highly coupled to the STATCOM currents. This makes implementation of fast con- trol strategies difficult. In addition, STATCOM dynamic is non- linear and, therefore, the performance of a controller, typically designed on the basis of a linear approximation around an oper- ation condition, is optimal only in a small region. This limits the STATCOM performance outside the optimal region and, there- fore, a form of nonlinear compensation is needed [3]. In this context, the use of the feedback linearization approach [4] to 0885-8977/04$20.00 © 2004 IEEE