726 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 21, NO. 2,APRIL 2006 Voltage Regulation With STATCOMs: Modeling, Control and Results Amit Jain, Member, IEEE, Karan Joshi, Student Member, IEEE, Aman Behal, Member, IEEE, and Ned Mohan, Fellow, IEEE Abstract—This paper presents system modeling and control design for fast load voltage regulation using static compensators (STATCOMs). The modeling strategy gives a clear representation of load voltage magnitude and STATCOM reactive current on an instantaneous basis. The particular coordinate transformation employed here also facilitates extraction of linearized system dynamics in conjunction with circuit simulators. It is rigorously shown that the control problem of load voltage regulation using reactive current is nonminimum phase. Linear and nonlinear con- trollers for the regulation problem are designed and compared via simulation results. Internal dynamics of the STATCOM are mod- eled using the same strategy. Lyapunov based adaptive controllers are designed for controlling the STATCOM reactive current while maintaining its dc bus voltage. Simulation results of the controlled STATCOM integrated with the load bus voltage controller are presented to show efficacy of the modeling and control design. Index Terms—Flicker mitigation, nonlinear control, power quality, static compensators (STATCOMs), system modeling, voltage regulation. I. INTRODUCTION I N A POWER distribution system, fast load voltage regula- tion is required to compensate for time varying loads such as electric arc furnaces, fluctuating output power of wind gener- ation systems, and transients on parallel connected loads (e.g., line start of induction motors) [1]–[3]. Reactive power sources are commonly used for load voltage regulation in the presence of disturbances. Due to their high control bandwidth, static com- pensators (STATCOMs), based on three phase pulse width mod- ulated voltage source converters, have been proposed for this application [4]–[7]. For effecting fast control, the STATCOM is usually modeled using the axis theory for balanced three phase systems, which allows definition of instantaneous reactive current and instantaneous magnitude of phase voltages (e.g., see [8]). Most literature on STATCOM control concentrates on control of STATCOMoutput current and dc bus voltage regulation for a given reactive current reference. This current reference is gen- erated from a PID controller that regulates the load bus voltage. Manuscript received April 23, 2004; revised November 23, 2004. Paper no. TPWRD-00203-2004. A. K. Jain is with Analog Power Design, Inc., Lakeville, MN 55044 USA (e-mail: akj@ece.umn.edu). K. Joshi and A. Behal are with the Electrical and Computer Engi- neering Department, Clarkson University, Potsdam, NY 13699 USA (e-mail: joshik@clarkson.edu; abehal@clarkson.edu). N. Mohan is with the Electrical and Computer Engineering Depart- ment, University of Minnesota, Minneapolis 55455-0213 USA (e-mail: mohan@ece.umn.edu). Digital Object Identifier 10.1109/TPWRD.2005.855489 Aside from experimental procedures like Ziegler and Nichols [9], to the authors’ knowledge, there is no standard procedure for designing a load voltage controller that ensures the required bandwidth and robustness to system variations. For example, in [10], state feedback control is designed utilizing linearized STATCOM dynamics for dc bus voltage regulation and tracking the reactive current to a reference that is generated via a PID controller. The effect of variation in the distribution system pa- rameters is studied only with regard to the internal dynamics of the STATCOM. In [4], the composite system (i.e., the distribu- tion system dynamics and the STATCOM dynamics) was con- sidered for regulation of load bus voltage and STATCOM dc bus voltage. For control design, a small signal model of the distribu- tion system was derived by transforming the equivalent system impedance to a frame rotating at the system synchronous fre- quency in steady state, thereby imposing a limitation on the dy- namic response. In this paper, a modeling strategy similar to that used for the field oriented control of three phase ac machines is used (i.e., the frequency of the transformation is not assumed to be con- stant). This gives a clearer representation of instantaneous load bus voltage magnitude and STATCOM reactive current without any restriction on the dynamics. This derived model is exact and can be used for control design using linear or nonlinear tech- niques. It is shown how circuit simulators with analog behav- ioral modeling capability can be used to extract linearized sys- temdynamics without the need for writing all state equations explicitly. As a first step, the system model is utilized to ad- dress the problem of bus voltage regulation with the STATCOM assumed to be a controlled reactive current source. It is rigor- ously shown that this control problem is nonminimum phase for certain operating conditions and thus has an inherent limitation on the achievable dynamic response; a physical explanation for this phenomena is also presented. Subsequently, linear and non- linear controllers are designed and their performance compared via simulation results. The next step involves controlling the STATCOM to behave as a reactive current source while main- taining its dc bus voltage. This problem is addressed by means of a Lyapunov based adaptive controller. The STATCOM con- trol rapidly regulates the reactive current to its reference (com- puted from the load bus voltage controller) and regulates the dc bus voltage via the real current absorbed by the STATCOM. The values of the parasitics used in the controller are obtained on-line via gradient based estimation schemes. The controlled STATCOM is then integrated with the distribution system model and the load bus voltage controller. Simulation results of the in- tegrated system show the efficacy of the strategy. 0885-8977/$20.00 © 2006 IEEE