# Low Current Ripple Parameter-Free MPCC of Grid-Connected Inverters for PV Systems
## 1 Introduction
When current gradient renewal is installed during one sampling period, the system control performance will deteriorate, and the grid-connected current will not meet national requirements. Simultaneously, Ref. [19] predicted the future current using the LaGrange interpolation algorithm rather than the slope change, avoiding the problem of stagnation. Gradually, diverse parameter-free MPC strategies have attracted significant attention in inverter control. These methods can be categorized into three types: ideal model-based, current gradient-based, and ultralocal model-based methods [20; 21]. Ultralocal model-based predictive control is more reliable than the other two methods because it breaks away from the renewal stagnation of the look-up table [22]. Meanwhile, the optimal voltage vector (VV) has been chosen from eight basic VVs in conventional MPCC. The number of candidate VVs is limited, and the switching state of the inverter stays the same during one period. Consequently, the current changes greatly, resulting in large current pulsation. In order to further improve the quality of grid-connected currents without increasing the hardware burden, virtual voltage vectors (VVVs) have been widely applied [23; 24; 25]. In essence, the active VVs take advantage of devised composition principle to generate several VVVs, which equips the grid with diverse amplitudes and angles compared to active VVs. Undoubtedly, the finite control set can be extensively expanded by synthesizing VVVs, and more candidate VVs can be prepared for rolling optimization in the cost function. The number of recursive operations in MPCs has also increased. Ref. [26] reduced the number of candidate vectors to three by pre-selecting them before performing the rolling optimization. Specifically, according to the position of the calculated reference VV in the space vector diagram, the three nearest VVs are selected in a small triangle for evaluation. Similarly, by introducing three auxiliary lines into the space vector diagram, three relatively suitable virtual voltage vectors are calculated in [27]. Although the number of iterations in the MPC is significantly reduced in [26; 27], the sensitivity of the parameters is increased, owing to the dead-beat properties. The design logic is too complex in these methods. Until now, such MPCC is still absent for GCI control, where both strong robustness and satisfactory quality of grid-connected current are taken into consideration. Therefore, for the sake of parameter-free control with reduced current ripples, this paper conceivesan improved MPCC based on the ultralocal model. The main contributions are listed as follows: (1) A linear extended state observer (LESO) is designed to estimate the unknown part of system, so that the future grid current can be predicted accurately by building the ultralocal model. Only the sampling information is required instead of inverter parameters. This method successfully circumvents the complicated tuning work and the existence of abnormal data. (2) This paper establishes a synthesis mechanism of VVVs, based on which, a space distribution of 38 new vectors is built. Furthermore, the triangle candidate strategy is conducted to filter the optimal control set, followed the steps of hypotenuse selection and right-angle side selection. In this manner, the candidate VVs can be reduced to 7. It means that the quality of grid-connected current is greatly improved, and the calculation burden is significantly alleviated. (3) The problem of the delay due to the calculation time in the MPCC strategy has been solved by one-step delay compensation, so that the grid-connected current ripple is further reduced. This paper expounds the research of the proposed parameter-free MPCC relying on the following parts. In Section 2, the model of GCI is constructed in detail. Then, in Section 3, the proposed parameter-free MPCC is elaborated, including the LESO, optimization strategy for VV selection, and delay compensation. Thereafter, experimental results are exhibited in Section 4.