**1. Introduction**

Low-voltage and high-current generation systems with currents higher than 10,000 A are widely used in ships, electrolytic plating, and industrial fields. Considering the integration of motor and power electronics technology, the synchronous generation system has developed rapidly from high power density, high reliability, and high fault tolerance points of view [1]. In the present study, a three-phase rectifier module is used to generate direct current (DC) through a confluence plate, based on a permanent magne<sup>t</sup> synchronous motor with only half-turn coil per phase. In order to ensure that the integrated DC generation system generates high quality electrical power, the present study focuses on the control strategy of this system

The control strategy of three-phase rectifier circuits has been extensively studied by many researchers. Thomas A.F. first proposed the hysteresis current control; in [2,3] this control method was adopted in the current inner loop. It is also proven that the disadvantage of this method is that the switching frequency changes as the load current changes. In other words, this method cannot guarantee a fixed switching frequency in a power cycle. This causes additional stress on the switching device and reduces the service life of the device. Kalman proposed the dead-beat control theory, which is a control method based on circuit equations. In [4], an improved implementation of the deadbeat current controller was considered that is aimed at two purposes: The minimization of the small-signal response delay and the optimization of the large-signal step response. This method cancels the zero with the pole by using state feedback and configures another pole at the origin [5]. However, studies showed that this method has major drawbacks, including a high real-time requirement for calculating the pulse width and the sensitivity of system stability to the circuit parameters and weaknesses. Although the aforementioned drawbacks can be resolved by employing a complicated algorithm and a current observer, a large error will be generated. Zadeh L.A. proposed the fuzzy control based on fuzzy reasoning, which mimics the human mindset and controls a model where it is di fficult to establish an accurate mathematical expression. In [6], a modified zero-voltage switching pulse width-modulation inverter with a digital signal processor-based proportional integral derivative-like fuzzy controller was implemented. The switches of the inverter achieved a soft-switching feature that largely reduced switching losses and improved the converting e fficiency. The disadvantage of this control strategy is that it only relies on the experience and attempt to design the controller. There is no systematic method of analyzing and designing the controller. The cycle is long and the precision is low. Once the adaptive limit is exceeded, this method will no longer be applicable [7]. Tokuo Ohnishi proposed the direct power control method. The proposed control method indirectly controls the output current through the direct control of active and reactive power. Moreover, this method establishes the voltage and the current double closed-loop model, according to the AC voltage and instantaneous power to select the output state corresponding to the switch table. In [8], a direct power control using the natural switching surface was proposed; the proposed control considered the output voltage when selecting the switching states. Therefore, the proposed control does not need an outer voltage control loop and can highly improve the dynamic performance of the DC output voltage. The advantages of this method are the high-power factor, the high e fficiency factor, and the ability to be used in a wide variety of applications [9,10]. However, due to the limitation of the current loop, it easily generates harmonic distortion in the input current, thereby reducing the power factor.

Lyapunov proposed the stability criterion control theory, which initially constructs a scalar energy-like function for the system and then designs the controller under the premise that the change in time of this function is negative [11]. This method was introduced into the rectifier control of a three-phase pulse with modulation (PWM) by Hasan K. [12]. He utilized the Lyapunov algorithm to control the three-phase rectifier system. This algorithm has the advantage that the system's stability is not interfered with by large signals and is independent of circuit parameters. At present, the application of the Lyapunov algorithm to control PWM rectifiers is concentrated on grid voltage rectification [13,14] where there is a mutual coupling phenomenon between the obtained control variables, which cannot guarantee the long-term stable operation of the system. This study first proposes the application of the Lyapunov algorithm to a multiple three-phase permanent magne<sup>t</sup> in the synchronous generator system. It is expected that the system with the proposed control scheme can provide a reasonable transient response, unified power factor control, reduced harmonics on the AC side and an increase in the reliability of the generation system. In order to ensure the stable operation of the system, the proposed method decouples the control variables in a simple way.
