A Study on Efficient Electric Propulsion System

1. Electric propulsion system

The general electric propulsion system used in electric propulsion ships is shown in [Fig. 1].

[Fig. 1]

General electric propulsion system.

The electric propulsion system consists of a source unit that supplies three-phase power, a rectifier stage that converts AC to DC, an inverter stage that controls the AC motor for propulsion, and a propulsion motor.

2. AFE Rectifier

The AFE rectifier converts the power of the rectifier by controlling the phase and magnitude of the AC input current, and adjusts the input current by controlling the rectifier input voltage. The rectifier input voltage controls the frequency, voltage, and phase, but the frequency must be the same as that of the power supply’s voltage, so that the voltage and the phase are controlled.

That is, when the magnitude of the phase angle increases and the input voltage increases, the magnitude of the input current should increase as well. In this way, the device operates in the rectification mode while maintaining an excellent power factor.

[Fig. 2] shows a three-phase AFE rectifier. The rectifier is composed of six switches in three stages, and a capacitor is installed on the direct current (DC) side, to maintain a constant DC output voltage despite sudden voltage fluctuations. To control the magnitude of the rectifier’s input current during power conversion, an inductor is installed on the power output side. The AC power sources e_a, e_b, e_c maintain a three-phase equilibrium.

[Fig. 2]

Circuit diagram of AFE rectifier.

When the switches of the upper and lower parts are turned on simultaneously, dv/dt increases rapidly and damages the switch; therefore, when the switches are operated, the delay time is set such that the two switches are turned on and off.

The voltage equation of the rectifier is

where e_a, e_b and e_c are the supply voltages of the a, b, and c phases, respectively, i_a, i_b, i_c are the phase currents, while V_a, V_b, V_c are the rectifier input voltages.

2. Direct torque control

The direct torque control method calculates the torque and the stator flux by measuring the voltage and current values in the motor. In addition, the torque error and the magnetic flux error are, respectively, provided to a hysteresis controller by comparing them with the command values of the magnetic flux and torque at every cycle. The output of the hysteresis controller is used as an input to a look-up table of voltage vectors, where a desired voltage vector is found and output.

Direct torque control is advantageous owing to its fast response and accuracy, because it independently controls the magnetic flux and the torque. In addition, control precision and the switching frequency may be varied by adjusting the hysteresis bandwidth using the errors of the magnetic flux and torque as inputs. The control structure is very simple in the digital form, and the dynamic characteristics of the torque only weakly affect the parameter variation of the motor rotor, while affording computational efficiency.

However, there are disadvantages in that the switching frequency is variable, and many ripples may occur in the torque and speed values. The control characteristics may deteriorate when the torque command is changed in the low-speed range and during start-up.

The stator flux can be expressed by Equation (6), using the voltage equation of the induction motor in the three-phase stationary coordinate system:

If the value of the stator magnetic flux is obtained from Equation (6), it is incorporated into Equation (7):

Here, V_dc is the DC link voltage.

In Equation (7), because the stator resistance value is very small, if we assume that the voltage drop R_s i_s is very small compared with the first equation and ignore it, the stator flux becomes proportional to the magnitude of the stator voltage and can be considered as a vector in the same direction.

The above relationship is captured by Equation (8), as follows:

• where Δt is the sampling period.

In other words, the stator flux moves in the same direction as the stator voltage vector v_s. When v_s is an effective vector, λ_s moves at a constant rate with the output voltage vector of the inverter, and when it is an ineffective vector, it moves at a very low speed. Accordingly, the rotational speed of the magnetic flux is controlled by the ratio of the effective and ineffective vectors of the inverter output voltage vector.

<Table 1> lists the voltage vectors selected when the stator magnetic flux is in the n-th sector.

<Table 1>

Selected vector and definition

The magnetic flux and the torque selection direction of the motor are determined according to the eight voltage vectors that are output by the inverter, and by the current magnetic flux vector. The switching vector is selected by considering the magnitude of the magnetic flux and its direction.

[Fig. 3] is a conceptual diagram of the direct torque control, showing the switching vector and the magnetic flux vector.

[Fig. 3]

Conceptual diagram of the direct torque control method.

[Fig. 4] shows the trajectory of the rotating magnetic flux according to the selection of the switching vector in the hysteresis band. The magnetic flux rotates while drawing the trajectory of a pulsating circle, as shown in [Fig. 4].

[Fig. 4]

Trajectories of the reference λs* with xT= 1 and stator flux λs

Equation (9) describes the hysteresis band of the magnetic flux:

The selection of the magnetic flux vector is not only related to the magnitude within the hysteresis band, but also to the direction of rotation.

For example, when the magnetic flux rotates clockwise, v₆ is selected when the magnetic flux contacts the lower limit of the hysteresis band, while v₅ is selected when it contacts the upper limit of the hysteresis band.

Similarly, when rotating counterclockwise, v₂ and v₃ are selected. When the magnetic flux is determined, the torque is determined using Equation (10):

When the torque value T_e reaches the setpoint T_e^*, T_e should decrease as slowly as possible to reduce the switching frequency of the inverter. That is, it is better to use an ineffective vector among the switching vectors of the inverter. The torque can be divided into two categories, according to the direction of the rotation.

$$ T_e{}^{\text{*}}-\Delta T_e\le T_e\le T_e{}^{\text{*}}$$

• when λ_s rotates clockwise

$$ T_e{}^{\text{*}}\le T_e\le T_e{}^{\text{*}}+\Delta T_e$$

• when λ_s rotates counterclockwise

Assuming that λ_s rotates clockwise, when T_e touches T_e^*, an invalid vector is selected to stop the effective vector and reduce T_e.

Conversely, when T_e touches T_e^* - Δ T_e an effective vector for rotating the magnetic flux in the clockwise direction is selected.

To calculate the optimal voltage vector from <Table 2>, it is necessary to know the position information of the stator flux linkage. This positional information can be obtained from the values of the α axes and β axes of the stator flux linkage in the stationary coordinate system using Equations (11a), (11b) and (11c), as follows:

Here, v_αs, v_βs, i_αs, i_βs are the measured stator currents and voltages, respectively

<Table 2>

Optimum switching voltage vector look-up table

Therefore, the torque can be expressed as Equation (12), as follows:

[Fig. 5(a)] shows the magnetic flux hysteresis controller. In the case of the stator magnetic flux, because the magnitude of the magnetic flux is always positive, the comparator output Δ|λ_s| consists of two steps (1,-1). That is, when the stator flux error is larger than the positive hysteresis band H_F, it becomes Δ|λ_s| = 1, and when the stator flux error is smaller than the negative hysteresis band -H_F, it becomes Δ |λ_s| = -1.

[Fig. 5]

Characteristics of torque and flux hysteresis comparator.

[Fig. 5(b)] shows the torque hysteresis controller used in the inverter of the direct torque control method. In general, unlike a magnetic flux hysteresis comparator, output Δ T_e is in three stages (-1, 0, 1) so that both forward and reverse torque commands can be followed.

<Table 2> shows the lookup table of the optimal switching voltage vector based on the characteristics of the magnetic flux and torque hysteresis comparator.

3. Sensorless speed control by current error compensation

If Equation (13) is shown as a differential equation with respect to the current, Equation (14) is obtained, as follows:

• Here, p is a differential operator.

If Equation (13) is shown as a differential equation with respect to current, Equation (14) is obtained.

• Here, $$ D=L_s{L}_r-L_m^2$$

The generated torque and rotational speed of the motor are expressed by Equations (15) and (16), respectively, as follows:

• Here, $$ p{\lambda }_{\alpha s}=v_{\alpha s}-R_s{i}_{\alpha s}$$
• 　　　$$ p{\lambda }_{\beta s}=v_{\beta s}-R_s{i}_{\beta s}$$

P is the number of poles, J and B are friction coefficient and the moment of inertia, respectively, and T_L is the load torque.

[Fig. 6] shows the block diagram of the sensorless speed control mechanism of the induction motor, presented in this study

[Fig. 6]

Block diagram of the proposed current error compensation control system for induction motors.

The induction motor sensorless control system operates as follows:

⑴ The phase voltage applied in the previous control loop, the motor phase current of two phases, and the DC link voltage are measured.

⑵ By converting the voltage and current values into 3-phase/2-phase, the actual motor-generated torque and the magnitude and direction of the stator magnetic flux are calculated.

⑶ The magnitudes of the model flux and torque are calculated using the phase voltage and the speed-setting value applied to the numerical model.

⑷ After finding a sector by the stator magnetic flux direction obtained in (b), the optimal voltage vector is selected and output to the motor and model, so that the torque and magnitude of the magnetic flux of the actual motor approach the values of the numerical model.

⑸ Since the same voltage is applied to the both sides to match the magnetic flux and torque of the motor and the numerical model, the speed of the motor is also given by Equations (14) and (15).

1. Simulation

In the high-speed and low-speed ranges, the speed control algorithm of an induction motor with a sensor attached to a general rectifier and the sensorless speed control method of an induction motor based on the AFE converter and current error compensation presented in this paper is comparatived using PISM software. In the computer simulation, first, a load proportional to the speed square in the high-speed range (1,200 [rpm]) was applied, a step torque load was applied at 500 [rpm] in the low-speed range, and a forward/reverse operation was performed at 300 [rpm].

The system constants and parameters of the induction motor used in the computer simulation (<Table 3>).

<Table 3>

Parameters of induction motor.

[Fig. 7] shows the PSIM block diagram of the direct torque control method induction motor driving simulation using the proposed AFE converter and the current error compensation senseless control method.

[Fig. 7]

PSIM diagram of AFE converter and inverter.

2. Simulation of an induction motor with a sensor attached.

[Fig. 8] shows the speed response characteristics of the induction motor when the speed command is applied from 0[rpm] to 1,200[rpm].

[Fig. 8]

Response characteristics according to speed change (0→1,200[rpm]).

(a) shows the speed change of the motor, (b) shows the load change proportional to the speed square, and stable and stable control results are shown. (c) shows the input phase current in the steady state section, and the harmonic is 510 [%]. d) is the motor load current in the steady state section. (f) shows the input current and input voltage in the steady state section, and the power factor was 79.6 [%].

[Fig. 9] shows the response state when a load torque of 5 [N m] is applied during steady state operation at 500 [rpm].

[Fig. 9]

Response characteristics according to load torque change(500[rpm], 5[N·m]).

The motor speed change (a) and the torque change (b) before and after the application of the load torque reacted quickly. (c) shows the change in the phase current shape of the input stage before and after the application of the load torque, and the maximum load was increased from 7.2[A] to 8.9[A]. (d) shows the motor load current before and after the application of the load torque, and the current was stably controlled within 0.2 seconds.

[Fig. 10] shows the characteristics of the motor when the reverse speed command is applied at -300[rpm] while driving at 300[rpm]. (a) shows the speed change of the motor, and (b) shows the torque change before and after the application of the reverse speed command. Stable control results were shown when the reverse speed command was applied. (c) shows the change in the shape of the phase current at the input stage before and after applying the inversion command, and the current was stabilized within 0.2 seconds. (d) shows the motor load current before and after the reversal command, and according to the speed change, the load current was stably controlled within 0.2 seconds.

[Fig. 10]

Response characteristics according to speed change(300 → -300 [rpm]).

3. Simulation using AFE method and sensorless method

[Fig. 11] shows the speed response characteristics of the induction motor when a load proportional to the speed square was applied, and a speed command was applied from 0 to 1,200 [rpm]. (a) shows the speed change of the motor, and the stable speed control results are shown. (b) shows the load change proportional to the s2peed square, with a load shape similar to the speed change in the transient state. (c) shows the input phase current in the steady state, with a stable waveform close to a sine wave. (d) shows the motor load current in the steady state. (e) shows the voltage of the DC link and stably maintains the regulated voltage suitable for the AFE characteristics. (f) shows the input current and input voltage in the steady state, and a high power factor, at 99.4[%].

[Fig. 11]

Response characteristics according to speed change (0→1,200[rpm]).

[Fig. 12] shows the response state when a load torque of 5 [N·m] was administered during operation at 500 [rpm]. (a) shows the speed change of the motor, with stable control after the load application. Panel (b) shows the torque change, before and after the load torque. (c) shows the change in the shape of the input phase, the phase current before and after the load torque, and the input current with a shape close to that of a sine wave after the load stabilization. (d) shows the motor load current before and after the application of the load torque, and the current was stably controlled within 0.3 seconds.

[Fig. 12]

Response characteristics according to load torque change(500[rpm], 5[N·m]).

[Fig. 13] shows the characteristics of the motor when a load proportional to the speed square was applied, and a reverse speed command was applied at –300 [rpm] while driving at 300 [rpm]. (a) shows the speed change of the motor, and shows stable control results after the reverse speed command was applied. (b) shows the torque change before and after the application of the reversing speed command. It can be seen that it appears in a form similar to the speed change of the motor. (c) shows the change in the phase current shape of the input stage before and after application of the inversion command, and the current stabilized after 0.2 seconds. (d) shows the motor load current before and after the reversal command, and the load current was stably controlled after 0.2 seconds according to the speed change. current in the steady state. (e) shows the voltage of the DC link and stably maintains the regulated voltage suitable for the AFE characteristics. (f) shows the input current and input voltage in the steady state, and a high power factor, at 99.4[%].

[Fig. 13]

Response characteristics according to speed change(300 → -300 [rpm]).

4. Review simulation results

When comparing [Fig. 8(a)], [Fig. 11(a)] and [Fig. 8(b)], [Fig. 11(b)] respectively, speed command is applied from 0[rpm] to 1,200[rpm], speed and torque are controlled stably. When comparing [Fig. 8(c)] and [Fig. 11(c)], the THD of the conventional method is 510[%] and presented method THD 7.97[%] shows a current waveform close to the sine wave, indicating that the input current is very good quality. When comparing [Fig. 8(d)] and [Fig. 11(d)], the maximum load current was about 10.5 [A] in the steady state section, and it was the same in both methods. In [Fig. 8(e)], the power factor was 79.6 [%], and in [Fig. 11(f)], it was found to be 99.4 [%] according to the characteristics of the AFE rectifier with improved power factor. In [Fig. 11(e)], a DC voltage of 400[V] can be obtained from an input current of AC 220[V] according to the characteristics of the AFE rectifier that can adjust the voltage.

When a load of 5 [N m] was applied while driving at 500 [rpm], comparing [Fig. 9(a)], [Fig. 12(a)] and [Fig. 9(b)], [Fig. 12(b)] showed stable speed and torque changes in both. In [Fig. 9(c)], [Fig. 9(d)] and [Fig. 12(c)], [Fig. 12(d)] after torque is applied, the input current and load current are stabilized after 0.15 seconds in the conventional method and after 0.2 seconds in the proposed method. At this time, the input current changes from 7.2[A] to 8.9[A] based on the maximum value. When a reverse command is applied during operation at 300[rpm], comparing [Fig. 10(a)], [Fig. 13(a)] and [Fig. 10(b)], [Fig. 13(b)] the speed and load were stabilized in 0.15 seconds in the conventional method, and the speed and load were stably controlled after 0.2 seconds in the proposed method. In [Fig. 10(c)], [Fig. 10(d)] and [Fig. 13(c)], [Fig. 13(d)] when the motor reverses, the input current and the load current are the same. The existing method stabilizes after 0.2 seconds and the proposed method after 0.25 seconds.