**1. Introduction**

Model predictive control (MPC) has become an attractive alternative for controlling power electronic applications, such as motor drives and power converters [1]. There are two main categories of MPC: (1) continuous MPC (CMPC), in which output is generated and delivered to a modulator, and (2) finite-set MPC (FS-MPC), which can control a finite number of feasible switching states using a predefined cost function [2–5]. Among the two types, FS-MPC is preferable, owing to its many advantages, such as the fast dynamic response, intuitive appeal, inclusion of constraints and nonlinearities, and easy implementation. However, an important drawback of the original method is its variable switching frequency and large current ripples, which requires the use of large passive filter components [2,6].

Numerous studies aiming to improve the performance of classical FS-MPC for both power converters and motor drives have been performed. To reduce current ripples and alleviate harmonic distortion, an attempt was made in [7,8] to increase the prediction horizon of FS-MPC. Although good performance was achieved, intensive experimentation is still necessary for determination of correct weighting factors and control horizons [8], which is computationally demanding [9]. A deadbeat solution was suggested in Reference [10] for a two-level voltage-source inverter, which allows the computational load of FS-MPC to be reduced by reducing the complete enumeration for the whole

voltage vectors. Although this solution helped to address the problem of computational intensity, the large torque ripples could not be eliminated.

FS-MPC based on discrete space vector modulation (DSVM) was proposed in References [11,12] to reduce current ripples and guarantee a constant switching frequency. The main advantage of DSVM is that it allows the number of degrees of freedom to be increased by synthesizing various virtual voltage vectors in the space vector diagram [12]. Similarly to classical FS-PTC, the optimal voltage vector is selected to minimize the objective error in the respective cost function, and is applied to the inverter using space vector modulation (SVM). Nevertheless, the main issue associated with the DSVM approach is its high computational burden, owing to a large lookup table that holds the initialized virtual voltage vectors. To solve this problem, deadbeat control was utilized to consider a limited number of virtual voltage vectors, regardless of their number [13]. In this way, the calculation time was significantly reduced, making the method suitable for realistic applications.

Although two-level inverters (2L inverters) are extensively used for power converters and motor drives for generation of voltage vectors applied to terminals [14], they su ffer from some issues. Two-level inverters require a very high switching frequency; hence, a higher harmonic current distortion is generated, owing to the limitation of voltage levels. In addition, the maximal DC link voltage is constrained due to the rating of the semiconductors. Therefore, multilevel inverters (ML inverters) have been considered an attractive solution capable of solving the above-mentioned problems and synthesizing output voltages with several discrete levels. Three-level inverters (3L inverters), such as neutral-point clamped (NPC) and T-type inverters, are the most prominent topologies of ML inverters. Compared with 2L inverters, the number of degrees of freedom for obtaining the voltage vectors is higher, which yields better current quality and better control. Despite the advantages of 3L inverters, neutral-point voltage balancing seriously a ffects their control performance [15], causing higher ripples and distortion of stator currents. Hence, 3L inverters require high-rated capacitors, owing to their unequal voltage distribution, which, in turn, results in a higher voltage stress on the semiconductor switches.

It is worth mentioning it is complicated to include a NPC voltage balance variable in the cost function when implementing DBC. Thus, an algorithm for the DC link capacitor voltage balance should be separately applied for proper 3L inverter operation [16–20]. For example, in Reference [16], a calculated zero-voltage sequence was used for neutral-point balancing, while in Reference [18], the time-o ffset injection method was used for the same purpose. In Reference [20], a deadbeat model of predictive control combined with the discrete space vector modulation method was used for grid-connected systems using T-type 3L inverters. Two cost functions were used: one for selecting the optimal voltage, and another for the compensated voltage o ffset, because the neutral-point voltage problem of 3L inverters cannot be included as a variable in the cost function, due to the use of DBC method. The optimal voltage vectors were then synthesized using the SVM method for the entire sampling duration. Nevertheless, the use of two cost functions increased the computational burden of the control system.

This paper proposes a simplified control method for balancing the neutral point in the FS-MPC with the DSVM and DBC of grid-connected systems. Therefore, unlike the approach in Reference [20], the proposed method does not require additional cost functions for balancing the capacitance voltage. The proposed method led to a significant reduction in computation time while maintaining the current quality performance. This method was simulated and experimentally verified on a grid-connected, three-level T-type voltage source inverter.
