# A Novel Adaptive Model Predictive Control Based Three-Phase Inverter Current Control Method
## 1 Introduction  
Model Predictive Control (MPC) is recently regarded as one of the most promising control methods in controlling power converters, due to its predictive effect and robustness [1]. The fundamental idea of MPC is to predict the optimal controls of next step(s) to minimize the cost function based on the model of the object under control as well as a set of constraints. During normal operation, the accuracy of predicted model parameters can be improved online, resulting in enhanced control accuracy and better adaptability [2]. This feature is highly attractive when the operating conditions varies frequently. In recent years, MPC has been successfully used in grid-tie converters for renewable energy systems, where it delivers improved dynamic performances, robustness and system stability [3; 4; 5; 6; 7; 8]. In most of existing applications of MPC for power converters, the control command of next period is directly selected from a finite set of switching states according to the cost function, namely finite-control-set MPC (FCS-MPC) [9; 10; 11; 12]. While in some other approaches, the output variables, such as the current or voltage references, are continuous values, and these methods are known as continuous control set MPC (CCS-MPC) [13; 14]. Applications of FCS-MPC have attracted much attention because of several advantages, such as fast transient response, simple implementation, and so on. Up to now, most MPC based control methods for power converters are of this type. In [15], a FCS-MPC on three-phase voltage source inverter is proposed to select an optimal switching state for next step to minimize the error and guarantee control accuracy. Experimental results show that the proposed method controls the load currents effectively with a better dynamic response comparing to conventional linear control methods. In addition, this method is simple and easy for DSP implementation. Paper [16] proposes a FCS-MPC on controlling the flying capacitor voltage and the grid current of the Packed-U-Cells inverter. The eight available switching states are evaluated everyperiod and the optimal one is selected according to a cost function. Experimental results validate the good dynamic performance in controlling the grid-connected system. Paper [17] proposes a FCS-MPC based control method for four-leg indirect matrix converters to minimize the instantaneous reactive input power. A significant advantage of this method is the reduction of control strategy complexity. However, FCS-MPC is not suitable in the cases when the optimal switching state cannot be directly selected or there are considerably number of switching states. The three major drawbacks of FCS-MPC are: (i) High computational burden due to evaluation of all the switching states; (ii) low control accuracy due to limited switching states; (iii) model dependency [13]. Paper [13] has validated that CCS-MPC based methods have better performance and reduced computational burden in power electronic system applications. In this paper, a CCS-MPC based control method for grid-connected photovoltaic (PV) systems. The proposed method is applied to control the power exchange between PV and grid, while achieving the unit power factor. It is verified to have good dynamic performance. In [18], a CCS-MPC method is applied in controlling of permanent magnet synchronous machines. Experimental results prove the effectiveness of the proposed method in such applications. However, for above mentioned approaches, the performance of the control largely depends on the accuracy of the model parameters. An inherent steady-state error cannot be eliminated during the control process since there is no adaptation on the parameters. Paper [19] analyzes the influence of model error on the accuracy of MPC for current control in a three-phase inverter. It has been confirmed that the mismatch of prediction inductance can cause steady-state error in inverter current. Limited research works have been conducted in improving the model accuracy.