*2.3. AFE Rectification Method in Large-Scale Electric Propulsion Systems*

The AFE rectifier uses semiconductor-based technologies, such as Insulated Gate Bipolar Transistor (IGBTs), Integrated Gate Commutated Thyristor (IGCTs), and Metal Oxide Semiconductor Field Effect Transistor (MOSFETs), among others, which can turn power semiconductor elements off and on as required. Based on the control style of the semiconductor element, power conversion may be realized automatically. In particular, a fixed DC output voltage can be maintained even if the load changes. Thus far, AFE rectifiers have been primarily used in small- to mid-sized electric propulsion systems on ships owing to the limited capacities of the power semiconductor elements in these rectifiers [42].

The AFE rectifier must continuously measure the supply voltage to control the rectifier. As shown in Figure 7, the error of phase angle, which is crucial for the control of the rectifier, occurs momentarily due to the deterioration of the voltage quality, such as harmonics and noise included in the supply voltage.

**Figure 7.** An example of phase angle error.

As shown in Figure 8, the form of the AFE rectifier is the same as that of an inverter that converts DC current to AC current. The AFE rectifier consists of a total of three units and six power semiconductor switches. In addition, it includes an inductor that controls the input current of the power supply, as well as a capacitor that maintains a fixed DC output voltage.

**Figure 8.** Block diagram of an AFE rectifier.

Equation (3) is the voltage equation of the AFE rectifier.

$$
\sigma\_{\text{abc}} = R i\_{\text{abc}} + L \frac{d i\_{\text{abc}}}{dt} + V\_{\text{abc}} \tag{3}
$$

where, *eabc* is the three-phase power supply voltage, *iabc* is the phase current, and *Vabc* is the input side voltage of the rectifier.

The AFE rectifier controls the level and phase of the AC input current, *is*, while performing the power conversion. The AFE rectifier must control the level of the voltage that is applied to the inductor on the input side. In particular, *is* is controlled by controlling the input voltage of the rectifier, i.e., *Vrec*. Figure 9 shows the equivalent circuit for an AFE rectifier. The voltage *VL* that is applied to the inductor can be obtained using Equations (4) and (5).

$$
\sigma\_s = V\_{\text{Rec}} + V\_L \tag{4}
$$

$$V\_L = \,\,\omega \,\mathrm{Li}\_s\,\tag{5}$$

where, *es* is the AC input to the power supply, *VL* is the inductor voltage, and *Vrec* is the rectifier input voltage.

**Figure 9.** Equivalent circuit of the AFE equivalent circuit.

In order to control the AFE rectifier, it is necessary to find the d-q axis coordinate and current reference values that are in phase with the power supply voltage. To find these values, it is necessary to find the phase angle θ. In the conventional AFE rectifiers, the zero-crossing technique is used to find the phase angle θ for control. The zero-crossing technique involves measuring the power supply voltage and finding the 0 values that occur at each half cycle to estimate the current phase angle θ. Figure 10 shows the block diagram of a phase angle detector that uses the zero-crossing technique.

**Figure 10.** Phase angle detector using the zero-crossing technique.

In particular, to find the phase angle, the moment when the power supply voltage changes from negative to positive can be set as the standard angle 0◦, as depicted in Figure 11 Alternatively, the three-phase AC power supply values can be converted to a static coordinate system to find the phase angle directly, as given by Equation (6).

$$\theta = \tan^{-1}(\frac{\mathcal{e}\_{\alpha}}{\mathcal{e}\_{\beta}}) \tag{6}$$

**Figure 11.** Relationship between the power supply voltage and phase angle in the case of the zero-crossing technique.

One advantage of the zero-crossing technique is that it can be used to find the phase angle in a simple manner. However, in some cases, some zero points are missed during the phase detection step, and consequently, its estimation speed is slow. Furthermore, another disadvantage of the zero-crossing technique is that estimation errors occur when noise due to harmonics or voltage notching occurs. Therefore, in this study, we created an AFE rectifier control circuit that uses the PLL method to accurately find the phase angle.

#### **3. Large-Scale Electric Propulsion System Using an Improved AFE Rectifier**

With the recent development of high-capacity power semiconductor elements, which can be used in large-scale electric propulsion systems, it has become theoretically possible for AFE rectifiers, which, thus far, were primarily used in small- to mid-sized electric propulsion systems on ships, to be used in large-scale electric propulsion systems.
