IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 27, NO. 9, SEPTEMBER 2012 4071 Virtual-Flux-Based Voltage-Sensor-Less Power Control for Unbalanced Grid Conditions Jon Are Suul, Member, IEEE, Alvaro Luna, Member, IEEE, Pedro Rodr´ ıguez, Senior Member, IEEE, and Tore Undeland, Fellow, IEEE Abstract—This paper presents a virtual flux-based method for voltage-sensor-less power control of voltage source converters un- der unbalanced grid voltage conditions. The voltage-sensor-less grid synchronization is achieved by a method for virtual flux es- timation with inherent sequence separation in the stationary ref- erence frame. The estimated positive and negative sequence (PNS) virtual flux components are used as basis for calculating cur- rent references corresponding to the following objectives for con- trol of active and reactive powers under unbalanced conditions: 1) balanced positive sequence currents, 2) elimination of double- frequency active power oscillations, and 3) elimination of double- frequency reactive power oscillations. For simple implementation and flexible operation, the derived current references are synthe- sized into one generalized equation where the control objectives can be selected by real coefficients. Since the converter has a lim- ited current capability, a simple, generalized, method for current limitation is also presented with the purpose of maintaining the in- tended power flow characteristics during unbalanced grid faults. The proposed strategies for virtual flux-based voltage-sensor-less operation have been investigated by simulations and laboratory experiments, verifying the expected performance of active and re- active power control with different objectives. Index Terms—Control of active and reactive powers, three-phase voltage source converters, unbalanced grid voltage, virtual flux, voltage-sensor-less control. I. INTRODUCTION O VER the past decades, there has been a continuous growth in the use of three-phase voltage source converters (VSCs) for grid-connected power conversion systems [1], [2]. The es- tablished applications of VSCs cover a wide power range and include, among others, variable speed wind turbines and other Manuscript received September 26, 2011; revised December 28, 2011; accepted February 26, 2012. Date of current version May 15, 2012. This work was supported in part by the Project ENE2011-29041-C02-01 funded by the Spanish Ministry of Science and Innovation. Recommended for publication by Associate Editor V. Staudt. J. A. Suul was with the Department of Electric Power Engineering, Nor- wegian University of Science and Technology, 7491 Trondheim, Norway. He is now with SINTEF Energy Research, 7465 Trondheim, Norway (e-mail: jon.are.suul@elkraft.ntnu.no). A. Luna is with the Department of Electrical Engineering, Technical Univer- sity of Catalonia, 08034 Barcelona, Spain (e-mail: luna@ee.upc.edu). P. Rodr´ ıguez is with the Department of Electrical Engineering, Technical University of Catalonia, 08034 Barcelona, Spain, and also with the Electri- cal Engineering Division, Abengoa Research, E-41014 Seville, Spain (e-mail: prodriguez@ee.upc.edu). T. Undeland is with the Department of Electric Power Engineering, Norwe- gian University of Science and Technology, 7491 Trondheim, Norway (e-mail: Tore.Undeland@elkraft.ntnu.no). 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/TPEL.2012.2190301 distributed generation systems, regenerative loads, energy stor- age systems, high-voltage dc-transmission, and various types of compensation devices. In an increasing number of these appli- cations, the VSCs are required to be capable of operating during grid voltage disturbances [3]–[5]. The performance of control systems designed for balanced three-phase conditions will, how- ever, degenerate if the grid voltage becomes unbalanced [6]. One of the main challenges for unbalanced operation of three- phase VSCs is to achieve both fast and accurate grid synchro- nization. The simple and well-known synchronous reference frame (SRF) phase-locked loop (PLL) can, however, not achieve satisfactory operation during unbalanced conditions without sig- nificantly reducing the bandwidth, as demonstrated by the re- sults presented in [7]. As reviewed in [8], several solutions to overcome this problem have been suggested, for instance, by adding digital filters in the traditional SRF PLL structure, or by applying various techniques for separating PNS components in synchronous or stationary reference frames. The performance of the inner control loops, i.e., the current control loop in a traditional cascaded control structure, must also be ensured un- der unbalanced conditions. This is usually achieved by either implementing separate current controllers in the PNS SRFs or by applying current controllers designed for operating in the stationary reference frame [9]–[11]. With satisfactory performance of the current controllers, the operational characteristics of a converter under unbalanced con- ditions will mainly be influenced by the objectives and tech- niques used for calculating the current references. In early pub- lications related to control of VSCs during unbalanced con- ditions, the focus was mainly on avoiding second harmonic oscillations in the active power flow of the converter, and by that reducing or eliminating oscillations in the dc-link volt- age [9], [10], [12], [13]. In other cases, the priority has been to assure balanced sinusoidal currents from the converter, in- dependently of the grid voltage unbalance. With the increased use of VSCs in renewable energy systems and the emergence of grid codes requiring capability for delivering reactive power to the grid during voltage disturbances, other control objectives have become relevant [3], [14]. Several recent publications have, therefore, presented generalized discussions on how to derive current references corresponding to different objectives for con- trol of active and reactive powers during unbalanced conditions, as well as comparative studies investigating converter operation with various control objectives [5], [14]–[20]. The available studies of generalized and flexible power con- trol strategies for VSCs during unbalanced conditions are based on utilizing measured voltages to fulfill the specified control 0885-8993/$31.00 © 2012 IEEE