*3.1. Improved AFE Rectifier Control*

As can be deduced from the voltage equation of the AFE rectifier, i.e., Equation (3), the three-phase AC voltage and current values continuously change as time progresses. Therefore, it is difficult to ensure stable control over the rectifier. To control the rectifier in a simple, yet accurate manner, it is necessary to convert the coordinates of the three-phase AC power supply to a given standard axis in order to convert the voltage equation of the AFE rectifier to that with a stable DC value. In particular, by changing the coordinate system using such a conversion, the three-phase AC levels, which continuously change over time, can be converted to two DC values d-q, which are easy to control. These converted values can then be used to control the AFE rectifier [22,33].

Figure 12 shows the structure of a phase angle detector that uses the PLL method rather than the existing zero crossing technique to find the phase angle in an AFE rectifier. The PLL phase angle detector converts the voltage of the three-phase AC power supply to a value on the d-q axis in a synchronous rotating coordinate system. These values can then be used to find voltages *ed*, *eq*, which are DC voltages, and therefore, easy to control. In our study, *ed* is arbitrarily set to be the active power, while *eq* is set to be the reactive power. Then, the value of the reactive power *eq* can be controlled to ensure that it is 0.

**Figure 12.** Block diagram of a phase detector using the PLL method.

Figure 13 shows the relationship between the q-axis voltage of the synchronous rotating coordinate system and voltage phase angle for controlling *eq* so that it is zero. In Equation (7), *Ps* is the active power supplied by the power supply.

> 2 -

*edid* + *eqiq* <sup>=</sup> <sup>3</sup> 2

*edid* (7)

*Ps* <sup>=</sup> *eaia* <sup>+</sup> *ebib* <sup>+</sup> *ecic* <sup>=</sup> <sup>3</sup>

**Figure 13.** Imaginary phase angle, which is the same as the actual phase angle.

Thus, the power supply current is only affected by *ed*, which indicates the voltage value on the d-axis, whereas the current value on the q-axis current does not have any effect on it. Therefore, the supplied current can be given by *Ps* = <sup>3</sup> <sup>2</sup> *edid*. If the active power values are set on the d-axis, and the q-axis voltage is controlled so that it is 0, the actual phase angle θ becomes the same as the imaginary phase angle θˆ as shown in Figure 13. Consequently, the phase angle θ can be accurately determined.

To find the actual phase angle θ, Equations (8) and (9) can first be solved by performing a coordinate conversion on the three-phase *ea*, *eb*,*ec* voltages of the AC power supply so that *ea*, *eb*,*ec* transform into voltages on the α − β axis of the static coordinate system, as shown in Figure 14.

$$e\_{\alpha} = E \cos \theta \tag{8}$$

$$
\epsilon\_{\beta} = E \sin \theta \tag{9}
$$

where, *E* is the peak value of the input AC phase voltage, and θ is the phase angle between *a* and the α-axis.

**Figure 14.** Conversion to input voltage's coordinate axis.

The values that have been converted to the static coordinate system with the α − β axis are then converted to a synchronous rotating coordinate system with a *d* − *q* axis using Equation (10). This is shown in Figure 15.

$$
\begin{bmatrix}
\varepsilon\_d \\
\varepsilon\_q
\end{bmatrix} = \begin{bmatrix}
\cos\theta & \sin\theta \\
\end{bmatrix} \begin{bmatrix}
\varepsilon\_\alpha \\
\varepsilon\_\beta
\end{bmatrix} \tag{10}
$$

**Figure 15.** Coordinate conversion to a synchronous rotating coordinate system.

If the phase angle is the imaginary phase angle θˆ rather than the actual phase angle θ, the voltage values on the *d* − *q* axis of the synchronous rotating coordinate system can be expressed using Equation (11) as follows.

$$
\begin{bmatrix}
\varepsilon\_d \\
\varepsilon\_\theta
\end{bmatrix} = \begin{bmatrix}
\cos\hat{\theta} & \sin\hat{\theta} \\
\end{bmatrix} \begin{bmatrix}
\varepsilon\_\alpha \\
\varepsilon\_\beta
\end{bmatrix}.\tag{11}
$$

Equation (11) can be represented as Equations (12) and (13) on simplification. Furthermore, Equations (8) and (9) can be used to obtain the voltage values in the static coordinate system using the actual phase value, and if they are substituted in Equations (12) and (13), the resulting equations are Equations (14) and (15), respectively.

$$e\_d = e\_\alpha \cos \hat{\theta} + e\_\beta \sin \hat{\theta} \tag{12}$$

$$
\epsilon\_q = -\epsilon\_a \sin \theta + \epsilon\_\beta \cos \theta \tag{13}
$$

$$\mathcal{E}\_d = E(\cos\theta\cos\theta + \sin\theta\sin\theta) = E\cos(\theta - \theta) \tag{14}$$

$$\epsilon\_q = E(-\cos\theta\sin\hat{\theta} + \sin\theta\cos\hat{\theta}) = E\sin(\theta - \hat{\theta})\tag{15}$$

where, θ is the actual phase value between the α and *d* axes, whereas θˆ is the imaginary phase angle.

In Equation (15), if *q*-axis voltage value *eq* is adjusted to be 0, then θ = θˆ, and Equations (16) and (17) can be solved. Consequently, the imaginary phase angle θˆ can be controlled so that it matches the actual phase angle θ.

$$e\_d = E \cos(\theta - \hat{\theta}) = E \tag{16}$$

$$
\varepsilon\_q = E \sin(\theta - \theta) = 0.\tag{17}
$$

If the three-phase input current is converted to the *d* − *q* coordinate axis system based on the phase angle θ that is accurately obtained with the phase angle detector using the PLL control for the AFE rectifier, the DC equivalent values of the AC current can be obtained. Thus, it is possible to use a proportional integral controller to obtain an AFE rectifier with excellent control performance. Equations (18) and (19) represent the voltage equation in the synchronous rotating coordinate system with the *d* − *q* axes.

$$
\sigma\_d = R i\_d + L \frac{d i\_d}{d t} - \omega L i\_q + V\_d \tag{18}
$$

$$\varepsilon\_{\eta} = R i\_{\eta} + L \frac{d i\_{\eta}}{dt} - \alpha L i\_{d} + V\_{\eta}. \tag{19}$$

As is clear from Equations (18) and (19), there are speed electromotive and counter-electromotive force components that represent a disturbance in the current control. In particular, these components act as mutual interference components in the current control so that changes in the d-axis current affect the q-axis current and vice-versa. Therefore, in order to obtain good control characteristics when current control is performed in a synchronous rotating coordinate system, it is necessary to design a current controller that includes feed-forward compensation for the counter-electromotive and speed electromotive forces as indicated in Figure 16. If a feed-forward controller is included, the output voltage of a proportional integral current controller in a synchronous rotating coordinate system can be expressed as Equations (20) and (21).

$$
\varepsilon\_d^\* = \varepsilon\_{d-fb}^\* + \varepsilon\_{d-ff}^\* \tag{20}
$$

$$
\varepsilon\_q^\* = \varepsilon\_{q-fb}^\* + \varepsilon\_{q-ff}^\* \tag{21}
$$

**Figure 16.** Current controller in the AFE rectifier that compensates for the counter-electromotive force.

## *3.2. Controlling the Propulsion Motor Speed of a Large-Scale Electric Propulsion System Using the Improved AFE Rectifier*

In this study, we used an indirect vector control technique to control the propulsion motor speed of a large-scale electric propulsion system. The indirect vector control technique uses flux current, torque current, and electric motor constant in the synchronous rotating coordinate system to calculate the slip reference angular speed. The integral value of this added to the rotor speed is considered as the flux angle. For high-performance torque and flux control, the stator current that is provided to the motor is divided into different components that match each of the components that are orthogonal to the standard flux [38,43].

In Figure 17, the α − β axis is fixed to the stator, while the d–q axis rotates at the synchronous angular speed ωθ. The rotating axis is matched to the d axis, while the slip angle (θ*sl*) to the rotor axis is maintained as the axis rotates. Therefore, the stator current supplied to the electric motor is divided into the flux component current *ids* and torque component current *iqs*, which can be used to perform high-quality torque and flux control.

**Figure 17.** Indirect vector control.

In the case of rotator flux-based indirect vector control, the rotator flux is controlled to ensure that it only exists as a d-axis component. Therefore, Equation (22) is valid.

$$
\lambda\_{qr} = \rho \lambda\_{qr} = 0 \tag{22}
$$

As can be deduced from Equation (23), the torque is proportional to *iqs*. Therefore, *iqs* can be considered as the torque component current. Furthermore, when flux control is constant, the rotator flux can be controlled via *ids*. Therefore, *ids* can be considered as the flux component.

$$T\_{\varepsilon} = \frac{3}{2} \frac{P}{2} \frac{L\_{\text{m}}}{L\_{\text{r}}} \lambda\_{dr} i\_{qs} \tag{23}$$

Thus, when *ids* is constant, the slip relational equation can be expressed as Equation (24).

$$
\omega\_{sl} = \frac{R\_r}{L\_r} \frac{i\_{qs}}{i\_{ds}} \tag{24}
$$

The position of the rotator flux can be obtained as the integral value of the sum of the electric motor speed and slip reference angular speed, as shown in Equation (25) below.

$$
\theta\_{\ell} = \int (\omega\_{\ell} + \omega\_{sl}) dt\tag{25}
$$

#### **4. Methodology**

In the present study, several different large-scale electric propulsion systems were modeled using the DFE rectifier, phase shifting transformer, conventional AFE rectifier, and improved AFE rectifier. A comparative analysis was performed on the operating characteristic results that were obtained for the large-scale electric propulsion system with the improved AFE rectifier and conventional DFE and AFE rectifiers in Figure 18. The modeled large-scale electric propulsion system is the same as the electric propulsion systems that are installed and used in current LNG tankers. The propulsion motor parameters are listed in Table 3. Figure 19 is a graph showing the oscillation of the output voltage of the generator due to the load variation during the actual operation of the ship. Thus, in order to verify the effectiveness of the proposed AFE rectifier, an arbitrary waveform was inserted into the output of the generator during the simulation.

**Figure 18.** Flowchart of comparison analysis with each rectifier.

**Table 3.** Propulsion of large-scale electric propulsion ships applied to simulations electric motor parameters.


**Figure 19.** The hunting of the output voltage of generator due to load variation in the actual operation of the ship.

To compare the characteristics of the large-scale electric propulsion systems based on their rectification method, systems were developed that used the improved AFE rectifier in Figure 20 as well as one that used an existing 24-pulse rectifier in Figure 21 with a phase shifting transformer. The improved AFE rectifier and power semiconductor in the inverter used the same IGBT module. The primary specifications of the power semiconductor are listed in Table 4 [44].

**Figure 20.** Overall block diagram of the electric propulsion system with the improved AFE rectifier.

**Table 4.** Semiconductor model and specification for IGBT power used in AFE rectifier.

**Figure 21.** Overall block diagram of the electric propulsion system with a 24-pulse rectifier that employs a phase shifting transformer.

In order to verify the robustness of the proposed AFE rectifier control, an irregular waveform was arbitrarily generated by inserting instantaneous zero-point noise, harmonics, etc. in the output power voltage of the generator during the simulation.

In Figure 20, the phase angle that is needed to control the proposed improved AFE rectifier was obtained using a phase angle detector with a PLL controller, as shown in Figure 22. The q-axis voltage, which is the reactive power component that is converted to a synchronous rotating coordinate system, was controlled always to be 0, so that the phase angle would match the actual phase angle during phase angle determination.

**Figure 22.** Phase angle detector with a PLL controller.

The current controller for the AFE rectifier is shown in Figure 23. In particular, the output of the DC link was compared with the reference voltage value in real time using the current controller used for controlling the AFE rectifier. Furthermore, the error was controlled by the proportional integral controller, and the feed-forward compensation technique was used to remove the mutual interference components of the counter electromotive and speed electromotive forces.

**Figure 23.** Current controller for the AFE rectifier.

In addition, the inverter used the indirect vector technique to control the speed and torque of the propulsion motor. This indirect vector control is depicted in Figure 24. Simulations of the modeled circuits were performed to compare speed response characteristics of the propulsion motor, DC output voltage waveforms of the DC link, input side harmonic output characteristics of the power supply, and heat loss in the inverter switching element, among others based on the changes in the rectification method of the simulated large-scale electric propulsion system.

**Figure 24.** Block diagram of the indirect vector control for propulsion motor speed.
