Flatness-Based Voltage-Oriented Control of Three-Phase PWM Rectiﬁers J. Dannehl, F.W. Fuchs Institute of Power Electronics and Electrical Drives, Christian-Albrechts-University of Kiel, D-24143 Kiel, Germany, Phone: +49 (0) 431-880-6107, Email: jda@tf.uni-kiel.de Abstract— Flatness-based control is applied to the three- phase PWM-rectiﬁer in synchronous reference frame. The DC-link voltage and reactive current are shown to be ﬂat outputs of the full-order system. Two different approaches are presented. At ﬁrst the DC-link voltage is controlled directly. The second employs inner current loops. Feed forward design based on system ﬂatness is shown and discussed. In many applications the DC-link voltage and reactive current are controlled to constant values. In this case the direct ﬂatness-based approach offers no advan- tages compared to conventional voltage-oriented PI-control whereas the second approach outperforms it with respect to the obtained control dynamic. Keywords— Converter control, Non-linear control. I. I NTRODUCTION Three-phase grid-connected PWM rectiﬁers are often applied in regenerative energy systems and in adjustable speed drives when regenerative braking is required. Be- sides power regeneration they offer the control of the power factor as well as the DC-link voltage while emitting less current harmonics to the grid compared to passive diode rectiﬁer bridges. A cascaded control structure with an outer DC-link voltage control and inner current control loops are commonly used. For L-ﬁlter grid connections the current control is mostly done with PI controllers in line voltage-oriented coordinates [1]. For many applications this so-called voltage-oriented con- trol (VOC) is suitable and well working but for special applications research still goes on. Line voltage distor- tions like harmonics and unsymmetries for example are challenging the control. As PI controller can not reject sinusoidal disturbances additional control concepts are often necessary in order to meet the standards. Stability problems due to interactions with the fundamental VOC can occur, especially in weak grid conditions [2]. An- other issue which often requires additional concepts is the resonance damping if LCL-ﬁlters are used as grid connection. The different control subsystems are mostly designed separately and interactions are often neglected. As the conventional VOC is a cascaded control it requires different time constants of the different loops. Therefore the DC link control bandwidth is limited. Furthermore the outer loop is tuned assuming the DC link voltage near to its constant reference. The inherited nonlinearity can lead to instability if the voltage variations are too high. An approache for minimizing the DC capacitance is presented in [3]. When PWM rectiﬁers with reduced DC capacitance are used, a load step will cause a DC- link voltage dip. The smaller the capacitance the faster the controller has to react. In this case the time constants are getting closer to each other and the DC link voltage variations get higher. Stability problems may arise. The application of nonlinear control strategies does not require different time constants of the DC link and current dynamics and the control design can be done for the full- order system without linearization around the constant DC voltage reference. Because of these reasons a faster control can be achieved which can be used for reducing the DC link capacitances. In [4], [5] and [6] the applica- tion of feedback linearization [7] for the PWM rectiﬁer control yields faster control or smaller DC capacitors, respectively. Other nonlinear methods like Sliding Mode Control [8], passivity-based control [9] or the direct Lyapunov method [10] are also applied to the PWM rectiﬁer control in order to improve the performance [11] [12] [10]. Another nonlinear method is the ﬂatness-based control (FBC) [13] [14] which is successfully applied to motor control applications [15] [16] [17]. Recently, FBC is applied to the three-phase PWM rectiﬁer [18] and [19] in order to achieve a higher control dynamic. In [18] the PWM rectiﬁer was shown to be ﬂat with the reactive current and the stored system energy as ﬂat outputs. In [19] the experimental validation is shown. The stored energy depends on the active and reactive currents as well as the DC link voltage. For the ﬂatness-based control the reference trajectories of the ﬂat outputs have to be derived. As the basic control objective is the control of the DC link voltage and the reactive power in terms of the reactive current the above choice requires calculations in order to formulate the reference trajectories of the ﬂat outputs. In particular, the trajectory of the active current component has to be derived. Because the application in [19] is a D-STATCOM without DC load the active current is zero is steady state. Therefore the stored system energy is mostly related to the DC link voltage and the reactive current. But for transients the trajectory of the active current has to be derived which remains unclear from [19]. For other applications like adjustable speed drives with regenerative braking or distributed energy generation the active current is mostly nonzero and time varying. In this paper the the DC link voltage and the reactive current are shown to be ﬂat outputs itself. Its references