## 1 Introduction  
Recently, single-phase three-level neutral point clamped (NPC) converters have been addressed for various applications, especially in the interface of renewable energy sources and storage system because of its reduced total harmonic distortion (THD), lower device power losses, and lower electromagnetic interference (EMI) compared with two-level converters [1; 2; 3; 4; 5; 6; 7; 8]. Three-level NPC converters operated with model predictive control (MPC) methods, aided by fast and inexpensive microprocessors, are currently used to generate sinusoidal voltage and current [9; 10; 11; 12]. Furthermore, NPC converters must maintain the balance of two dc capacitor voltages to avoid deteriorating output performance [13; 14; 15; 16; 17; 18; 19; 20; 21]. Hence, the two main control objectives that three-level NPC converters need to be met for correct operation are regulated sinusoidal source current and capacitor voltages' balancing. MPC methods with multiple control objectives, as in the case of three-level NPC converters, commonly employ a cost function using weighting factors that consider proper pertinence and emphasis among control terms. The conventional MPC method determines a weighting factor that is mostly based on empirical procedures, although some research has been comprehensively explored to improve weighting factor selection work [22; 23; 24; 25; 26; 27]. Therefore, it should be noted that the weighting factor tuning works are not straightforward and practical for implementation. Several studies have been conducted to eliminate the weighting factors of the model predictive control methods [28; 29; 30]. In [28], the capacitor voltage control part of the MPC method for the T-type converters was eliminated from the cost function. Thus, the corresponding weighting factor can be removed because the cost function only consists of the current control terms. In this algorithm, the capacitor voltage adjustment is obtained by selecting an appropriate small vector and a corresponding switching state to reduce the neutral point (NP) voltage unbalance in advance. Although this method can successfully eliminate the weighting factor, the capacitor voltage balance can be limited in operating regions with high reference voltage magnitude, which does not employ the small vectors. In [29], the MPC method with a three-step control procedure was developed to eliminate weighting factors for the T-type converters. The first step selects N switching states with the smallest errors using a cost function that controls only the capacitor voltage. In the second step, the cost function that controls only real and reactive power terms is used to select K number of switching states that minimize power errors among the N number of switching states. In the last step, the cost function that controls the switching frequency is used to select one of the K switching states to minimize errors. Although the proposed method based on the three cascading processes can implement the model predictive control method without the weighting factor, computational burden and calculation times of this control method can be increased due to the additional repetition steps. In [30], a Lyapunov-based finite control-set MPC was presented to achieve weighting factors' elimination for the nested neutral- point-clamped converters but the complexity of this control scheme is high. Based on the deterministic approach and previous work [31; 32; 33], this paper presents an MPC control scheme using a novel cost function design using only one reference voltage to achieve the multiple control objectives for single-phase three-level NPC converters. The reference voltage is generated by using a difference-mode voltage term and a common-mode term to regulate the source current and capacitor voltages' balancing, respectively.