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Citation information: DOI 10.1109/TIA.2018.2801838, IEEE Transactions on Industry Applications IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS 1 Model Predictive Direct Current Control of Permanent Magnet Synchronous Generator based on Flexible Lyapunov Function Considering Converter Dead Time Tin Bariˇ sa, ˇ Sandor Ileˇ s, Damir Sumina, Jadranko Matuˇ sko University of Zagreb, Faculty of Electrical Engineering and Computing, Unska 3, 10000 Zagreb, Croatia tin.barisa@fer.hr, sandor.iles@fer.hr damir.sumina@fer.hr, jadranko.matusko@fer.hr Abstract—This paper proposes a dual-mode model predictive direct current control (MP-DCC) of a permanent magnet syn- chronous generator (PMSG). The proposed algorithm is capable of minimizing switching losses in a two-level synchronous gener- ator side converter (SGSC). A new prediction model which takes the converter dead time into consideration when choosing the optimal switching state is introduced. The proposed prediction model provides a more accurate state prediction ensuring that the states of the system stay inside the control invariant set in the steady state even in the case of a significant converter dead time. To guarantee recursive feasibility and closed-loop stability a flexible control Lyapunov function (CLF) is employed as an optimization problem constraint which enables the minimization of switching losses both during transients and in the steady state. The influence of the converter dead time on the performance of the proposed algorithm is considered, and accordingly, a control invariant set is determined. Simulation results show that stator currents are kept within the control invariant set if dead time is taken into account in the prediction model. Furthermore, the proposed algorithm is implemented in a digital control system and experimentally verified on a 375 kW interior PMSG. Experimental results verify that the proposed control algorithm provides a successful flying start of the PMSG, and show that the application of the flexible CLF results in lower switching frequency, but also higher current ripple. By adjusting the upper bound of the control invariant set a desired trade-off between the low stator current ripple and the minimization of switching losses can be achieved. Index Terms—AC generators, converters, current control, permanent magnet generators, predictive control, wind power generation I. I NTRODUCTION Recently, model predictive control (MPC) has been increas- ingly applied in the control of power converters and electrical machines. Compared to the standard control structure based on proportional-integral (PI) or hysteresis controllers, the MPC is based on the prediction of future system states by employing a discrete-time system model. At each sampling instant an optimization problem is solved and the optimal control input is applied to the system while taking the constraints on the control input and system states into account. As to power converters, there are two main types of MPC algorithms, one in which a modulator-based scheme such as pulse-width modulation (PWM) is used (e.g. a continuous control set - CCS) and another, in which the power converter is treated as a discrete system with a finite number of voltage vectors (e.g. a finite control set - FCS) [1]. The latter has recently received close attention. In FCS-MPC algorithms the pulse- width modulation (PWM) is omitted and the switches of a power converter are directly actuated [2], as in the case of the direct torque control (DTC) [3]. Compared to CCS-MPC algorithms, FCS-MPC algorithms generally result in better dynamic performance along with lower switching frequency. However, if the sampling time of the algorithm is not suffi- ciently short, a larger current ripple is produced in the steady state compared to the CCS-MPC algorithms. In the case of the prediction horizon of one step, FCS-MPC algorithms are generally not computationally intensive and can be solved on standard digital signal processors (DSPs). However, as the prediction horizon increases, the computational burden exponentially rises. Recently, a permanent magnet synchronous generator (PMSG) has been widely used in wind energy conversion sys- tems (WECSs) including a full-scale back-to-back converter [4]–[6]. A typical back-to-back converter consists of a power grid side converter (PGSC), a DC-link and a synchronous generator side converter (SGSC). In several papers, FCS-MPC algorithms have been applied to control a PMSG used in WECSs. FCS-MPC has been applied to control a four-level converter [7] and a three-level-boost converter along with a neutral point clamped (NPC) converter [8]. In order to enhance the low-voltage ride-through capability of the three-level-boost and NPC converter the FCS-MPC has been proposed in [9]. In numerous papers, FCS-MPC algorithms were applied for the control of a permanent magnet synchronous motor (PMSM). Depending on the controlled variable, algorithms such as the model predictive direct speed control (MP-DSC) [10], the model predictive direct current control (MP-DCC) [11] and the model predictive direct torque control (MP-DTC) [12], [13] have been developed. Depending on the objective function, MP-DTC algorithms can be used to achieve different control objectives. In [14], [15] MP-DTC algorithms which reduce the torque ripple have been reported. On the other hand, MP-DTC algorithms which minimize switching losses have been proposed in [16],