As shown in Figure 1, the shaft generation system comprises the Shaft Generator, Shaft Generator Drive (SGD), and Shaft Generator Management System. The Shaft Generator transmits the power generated by the torque of the propulsion engine to the ship's power system through the SGD. The Shaft Generator Management System communicates data with the Engine Control System (ECS) and the ship's power management system, and delivers commands to the SGD regarding active and reactive power.

Figure 1: 
Consist of Shaft Generator System for Vessel

The shaft generator is mechanically coupled with the propulsion engine's shaft, resulting in the rotor of the shaft generator rotating at the same rotational speed as the propulsion engine. The output frequency is determined as shown in Equation (1), where rpm represents the revolutions per minute of the shaft generator, f denotes frequency, and P indicates the number of poles [10].

Additionally, the output voltage of the shaft generator is determined according to Equation (2), where E represents the voltage, N is the number of turns, Φ denotes the flux, and Kw is the winding coefficient [10].

As can be seen from Equation (2), the number of turns and the winding coefficient in the output voltage equation of the shaft generator are constants determined during the manufacturing of the generator. As per Equation (1), the frequency varies with the rotational speed of the shaft generator. Therefore, the only adjustable parameter for controlling the output voltage is the magnitude of the flux. In the case of synchronous generators with exciters, the output voltage can be regulated by varying the flux magnitude. However, for induction or permanent magnet type shaft generators, the flux magnitude cannot be separately adjusted, so the output voltage is determined by the rotational speed of the shaft.

The shaft generator drive primarily consists of a rectifier section and an inverter section in Figure 2. The rectifier section converts the power input from the shaft generator into direct current (DC) using either a diode rectifier or an Active Rectifier. If the system operates on DC, the Shaft Generator Drive (SGD) is composed solely of the rectifier section. In cases where the system is alternating current (AC), an inverter section is additionally included. This inverter section adjusts the output to match the voltage and frequency of the ship's power system through the switching of power semiconductors.

Figure 2: 
Concept DWG. for Shaft Generator Drive

A diode rectifier primarily serves the purpose of rectifying current and, therefore, cannot regulate the magnitude of the direct current (DC) link voltage. The magnitude of the DC link voltage is determined by the size of the input voltage. Equation (3) represents the DC link voltage for a 6-Pulse rectifier, where Vdc is the DC link voltage and Vll is the input line-to-line voltage.

The Active Rectifier utilizes active components such as IGBTs (Insulated Gate Bipolar Transistors), IGCTs (Integrated Gate-Commutated Thyristors), or MOSFETs (Metal-Oxide-Semiconductor Field-Effect Transistors), instead of diode elements, allowing for direct control of the output voltage through switching [11]. The drive's DC link voltage is measured and compared with a reference voltage. By directly controlling the switching elements, the DC link voltage can be maintained at the desired level. Figure 3 illustrates the configuration of an Active Rectifier.

Figure 3: 
Consist of Acitve Rectifier

Based on Equations (1) and (2), a model of a permanent magnet type shaft generator, whose voltage and frequency vary with changes in the speed of the propulsion engine, was developed. This model takes the rotational speed of the propulsion engine as input and outputs three-phase voltage and frequency. It was constructed using the Matlab function block and libraries in Matlab Simulink, as illustrated in Figure 4.

Figure 4: 
Consist of Simplified PM type Shaft Generator

The output frequency is given by Equation (4), where rpm curr represents the real-time input parameter, and rated rpm refers to the rated revolutions per minute.

The instantaneous maximum of the three-phase voltage, denoted as Vmax , is given by Equation (5).

The magnitude of the three-phase voltage is expressed as per Equations (6), (7), and (8).

The parameters for this model and the Shaft Generator are as presented in Table 1.

Figure 5 illustrates the control block diagram for a three-phase active rectifier. The system measures the output voltage and current of the shaft generator, as well as the voltage at the DC link. It then controls the switching elements through a control system that follows the command voltage set point for the DC link.

Figure 5: 
Control block diagram for three phase active rectifier

The relationship between the output voltage of the shaft generator and the input voltage of the converter is given by Equation (9).

This relationship is transformed into a two-phase direct current component on the dq-axis, and when organized according to the three-phase balanced condition for the converter input voltage, it results in Equations (10) and (11).

The PWM (Pulse Width Modulation) voltage command for the converter, which utilizes a PI (Proportional-Integral) current controller, is defined by Equations (12) and (13).

The d-axis current command with the applied PI voltage controller is given by Equation (14).

Based on the rated output, voltage, and DC command voltage of the shaft generator, an LCL filter was designed to reduce power noise and harmonics [12]. The related parameters are as presented in Table 2.

For comparison with the Active Rectifier, a Diode Rectifier was set up as shown in Figure 6, with an inductor and a capacitor applied on the load side.

Figure 6: 
Consist of Diode Rectifer

In the absence of a filter under full load, approximately 13% voltage ripple occurred. To reduce this to within 2%, an inductor and capacitor were designed based on the parameters listed in Table 3 [13].

To evaluate the control and output characteristics of the Active Rectifier in comparison with the Diode Rectifier, a simulation was conducted by linearly decreasing the speed of the shaft generator from 100% to 60% of its rated speed over a period of 10 seconds, as outlined in Table 4.

The voltage values input to both the Diode Rectifier and Active Rectifier were monitored in accordance with the SG rpm variation scenario. Figure 7 shows the SG voltage output at rated conditions, while Figure 8 displays the voltage output at 60% of the rated conditions.

Figure 7: 
3-Phase Voltage for SG at rated rpm

Figure 8: 
3-Phase Voltage for SG at 1080 rpm

As shown in Figures 7 and 8, it can be observed that the shaft generator (SG) outputs a voltage of 690V at its rated speed and 500V at 1080 rpm. This demonstrates that the output voltage varies in accordance with changes in speed.

Figure 9 presents a graph of the output frequency as it changes with the SG's rotational speed. It can be seen that the frequency also changes in proportion to the linear decrease in speed.

Figure 9: 
Voltage Ripple without LC Filter for DC Link

Figure 10 presents the DC Link graphs for both the Diode Rectifier and the Active Rectifier. In the case of the Diode Rectifier, as the three-phase input voltage decreases, the output voltage also decreases correspondingly. In contrast, the Active Rectifier continuously maintains the commanded voltage of 1000V.

Figure 10: 
DC Voltage for Diode Rectifier and Active Rectifier

Figure 11 shows a graph representing the DC Link output voltage ripple during the initial 0.1 to 0.2 seconds of the simulation when the rated voltage of the shaft generator is applied to the rectifier. The Diode Rectifier exhibits a voltage fluctuation between 919.7 and 938.5 [V], with a ripple rate of about 2.02%, while the Active Rectifier shows a voltage fluctuation between 994 and 1003 [V], resulting in a ripple rate of approximately 0.90%.

Figure 11: 
DC Voltage Ripple for Diode Rectifier and Active Rectifier at Rated Power

Figure 12 depicts the DC Link output voltage ripple during the period between 9.8 and 10.0 seconds in the simulation, when the rpm and output voltage of the shaft generator are reduced by 40% and applied to the rectifier. The Diode Rectifier shows a voltage fluctuation between 667.3 and 721.3 [V] with a ripple rate of about 7.78%, whereas the Active Rectifier exhibits a voltage fluctuation between 993.7 and 1002.9 [V], resulting in a ripple rate of approximately 0.92%. The ripple rate of the Diode Rectifier increases by 5.76% compared to the rated input voltage, while the Active Rectifier shows a minor increase of 0.02%, indicating negligible difference despite the input voltage variations.

Figure 12: 
DC Voltage Ripple for Diode Rectifier and Active Rectifier at 60% of Rated Power

Figure 13 presents a graph of the three-phase current of the shaft generator during the initial 0.1 to 0.15 seconds of the simulation. When the Diode Rectifier is used, distortion in the current waveform results in an output that is not a normal sine wave. However, with the Active Rectifier applied, the current waveform of the shaft generator is observed to be closely resembling a sine wave.

Figure 13: 
SG Line to Line Current for Diode Rectifier and Active Rectifier at Rated Power

Figure 14 illustrates a graph showing the output current waveform of the shaft generator at 60% of the rated revolutions per minute (rpm). Similar to the findings at the rated condition, it is observed that the current output waveform of the Diode Rectifier is not a stable sine wave.

Figure 14: 
SG Line to Line Current for Diode Rectifier and Active Rectifier at 60% of Rated Power