## 1 Introduction  
A recent increase in applications of high voltage systems and equipment in industrial fields has revealed limitations of two-level rectifiers [1; 2; 3; 4]. To resolve the drawbacks of the two-level rectifiers, many multi-level rectifiers have been studied to increase the voltage levels of rectifiers as compared to the two-level rectifiers because of the increased number of switches existing in each phase [5; 6; 7; 8; 9; 10; 11]. This circuit structural feature allows multiple switches to distribute stresses. In addition, due to the increased levels, input current waveforms have a lower total harmonic distortion (THD) than the two-level rectifiers, yielding improved current characteristics without increasing the filter size. Furthermore, the reduced THD eliminates the need for higher switching frequencies, which can increase efficiency more than the two-level rectifiers. Three-phase three-level neutral point clamped (NP) rectifiers have four switches and two clamping diodes per phase, and two additional DC capacitors, in which capacitor voltages should be balanced and three-phase input currents should be synthesized in a sinusoidal form [12; 13; 14]. The unbalance of capacitor voltages not only reduces control performance, but also increases stresses on the switches, which can increase the probability of the rectifier failing. Therefore, various control methods for controlling both the input current and the capacitor voltage of the three-phase three-level NP rectifiers have been studied [15; 16; 17; 18; 19]. Predictive control methods, which select an optimal switching state minimizing a cost function to satisfy rectifier performance, have also been investigated to control the NP rectifier [20; 21; 22; 23]. So as to simultaneously fulfil the sinusoidal input current generation and the NP voltage balancing, a cost function for the NP rectifiers consists of two terms for the input current and the capacitor voltage, which are adjusted by a weighting factor that determines a control ratio between two terms. It is burdensome to empirically redesign the weighting factor in cases that parameters or control conditions change. Thus, this paper addresses a predictive control method which can eliminate this hassle.  
In this paper, a predictive control method with offset voltage injection for achieving neutral point (NP) voltage balance of three-phase three-level neutral point clamped (NP) rectifiers is proposed. The proposed algorithm does not use a weighting factor as the cost function of the conventional approach. Instead, the proposed method individually develops an offset voltage which is decided by the difference between the upper capacitor voltage and lower capacitor voltage, in addition to produce a reference voltage which is used to control the three-phase sinusoidal input currents. Then, the offset voltage, which is injected to the reference voltage in the proposed scheme, can successfully reduce the difference between the two capacitor voltages. Consequently, the proposed algorithm using the offset voltage injection can control the input currents and retain the balance of the NP voltage. Validity of the proposed method is verified through simulations and experiments.