# Transition Control from Dual to Single Motor to Prevent Speed Reduction during an Open-Circuit Fault in a DC Power System

Ayumi Obitsu, Keiichiro Kondo, Kantaro Yoshimoto, Satoshi Yazaki, Osamu

Kammoto, Hirotaka Sugawara, Takuya Shimotsu

► To cite this version:

Ayumi Obitsu, Keiichiro Kondo, Kantaro Yoshimoto, Satoshi Yazaki, Osamu Kammoto, et al. Transition Control from Dual to Single Motor to Prevent Speed Reduction during an Open-Circuit Fault in a DC Power System. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0123. hal-05097429

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# Transition Control from Dual to Single Motor to Prevent Speed Reduction during an Open-Circuit Fault in a DC Power System

Ayumi OBITSU*, Keiichiro KONDO*, Kantaro YOSHIMOTO**, Satoshi YAZAKI†, Osamu KAMMOTO††, Hirotaka SUGAWARA††, Takuya SHIMOTSU†

* WASEDA UNIVASITY, 3-4-1 Okubo, Shinjuku-ku, Tokyo, Japan

** TOKYO DENKI UNIVERSITY, 5 Senju Asahicho, Adachi-ku, Tokyo, Japan

††IHI, 1 Shin-nakahara-cho, Isogo-ku, Yokohama-shi, Kanagawa-ken, Japan

† IHI, 3-2-1 Daikanyama, Akishima-shi, Tokyo, Japan

Tel.: +81 / 80.1307.6794.

E-Mail: marcher18@fuji.waseda.jp

## Keywords

«Fault-tolerant control», «More-Electric Aircraft», «Multi-machine system», «Control of drive», «Reliability».

## Abstract

This study examined a tandem motor system for more electric aircraft (MEA). A method was proposed that, during a single motor's power loss, continuously outputs the necessary torque to maintain speed and suppress speed reduction compared with standard controls, achieved by directly modulating torque command distribution based on overmodulation detection.

## Introduction

Many studies on the fault-tolerant control of multiplexed systems have focused on motor faults. This study examined a single power source failure scenario, which resulted in a circuit breaker disconnection between the converter and smoothing capacitor. We aimed to adapt the system to a fuel electric pump that maintained the desired speed to feed fuel into the combustion chamber. The goal was to quickly switch to only healthy parts of the system during an open-circuit fault in a DC power system, thereby maintaining the rotational speed.

Previous studies on the long-term operation after losing the power supply include a study on switching to an emergency backup power supply [8] and another study that aimed to continue operation for a long time without a backup power supply by using the energy of the smoothing capacitor and kinetic energy [9]. However, this study assumed a multiplexed system. Therefore, a method that quickly detected voltage drops in the smoothing capacitor and shifted the control to maintain speed using only the healthy parts was

deemed more suitable than these previous approaches.

This study was aimed at aircraft fuel pumps. We proposed a method using the pulse width modulation (PWM) overmodulation to detect power loss and immediately switch to operations. with only the healthy system. Typically, one system manages automatic speed regulation (ASR) by, distributing torque commands equally across systems. Upon power supply loss, the faulty system ceases to output torque, resulting in speed reduction. In response, the ASR increases the total torque command to ensure that a healthy system alone can recover and maintain its speed. Using overmodulation, we directly detected and responded to deficiencies in voltage or torque output, thereby shifting the torque distribution to only healthy systems. This direct adjustment, which was performed using an automatic current regulator (ACR) control time constant, facilitated quicker transitions compared to ASR, thereby minimizing speed reduction during switching. Further, simulated experiments confirmed that the proposed control method effectively reduced speed loss compared with basic controls. Furthermore, these experiments also investigated the relationship between the low-voltage protection conditions and the extent of speed reduction.

## Assumed system configuration

In this study, we assumed a system with n sets of power supplies, converter, inverters, and PMSMs connected in tandem. Fig 1 illustrates the system configuration for two sets (n = 2), where
Motor A ($M_A$) and Motor B ($M_B$) are connected in tandem, each powered by its own converter, inverter and power supply. Additionally, a load ($L$) is connected to the motors, and a capacitor ($C$) is connected to the DC side of the inverter. Under normal conditions, the system is driven by the combined torque of the two motors ($M_A$ and $M_B$). This study explores the implications of a power supply failure, specifically focusing on scenarios where the failure of one power supply ($G_A$) triggered the circuit breaker between the converter and the smoothing capacitor, consequently causing the motor ($M_A$) corresponding to $G_A$ to lose power supply.

# Control system

## Basic control

A block diagram of the control system is shown in Fig. 2. In this study, only one motor performed ASR to calculate the necessary total torque $T_{e\_SUM}^*$, and the torque command value given to each motor ($T_e^*$) was the equally distributed share of $T_{e\_SUM}^*$. Specifically, if the number of motors was $n$, the torque distribution block shown in Fig. 2 was $1/n$. The system assumed to use PMSMs. However, to facilitate ease of control, the maximum torque per ampere (MTPA) strategy was not employed, and $i_d^* = 0$.

$$ T_{e\_SUM}^* = K_{pASR} (\omega_{rm}^* - \omega_{rm}) + K_{iASR} \int (\omega_{rm}^* - \omega_{rm}) dt \quad (1) \\ T_e^* = \frac{T_{e\_SUM}^*}{n} \quad (2) $$

In (1), $\omega_{rm}$ and $\omega_{rm}^*$ rad/s are the actual and commanded angular velocities of the motor, respectively, and $K_{pASR}$ and $K_{iASR}$ are the proportional and integral gains of the ASR, respectively. In (2), $T_e^*$ is provided a torque command to each motor. When the power supply fails and the circuit breaker opens, the smoothing capacitor is the only source of energy for the inverter motor system. If the control continued after failure, the failed system receives a torque command of $T_{e\_SUM}^*/n$, which briefly produces the commanded torque using the energy of the capacitor. However, as the DC link voltage declines, the PWM enters an overmodulated state, thereby reducing the actual voltage and torque output and causing the speed to drop. As the speed decreases, the ASR increases the total torque $T_{e\_SUM}^*$, thereby enhancing the torque output

<figure><img src="image_2.png" /><figcaption>Fig. 1. Assumed system diagram</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. control block diagram</figcaption></figure>

from the healthy system to maintain the set speed. The total torque command, when all systems are healthy, is defined as $T_{e\_SUM0}^*$. If $m$ systems fail, the command is adjusted as shown in (3).

$$ T_{e\_SUM}^* = \frac{n}{n-m} T_{e\_SUM0}^* \quad (3) $$

Healthy systems output $1/n$ of the torque from (3), whereas faulty systems receive the same command, but output no torque. Although motor performance may change due to factors such as overheating, this study assumes that motors not experiencing failure can output torque according to the commanded values.

## Proposed control - Torque distribution change by overmodulation judgment

### Torque distribution when judging overmodulation

This study aimed to switch to driving only the healthy parts of the system while maintaining the speed in case of a power supply failure. Therefore, quick detection of voltage drops in the DC link that prevent the output of the commanded voltage
<figure><img src="image_4.png" /><figcaption>Fig. 3. Flowchart for overmodulation region determination</figcaption></figure>

is crucial for switching to a healthy system. As mentioned previously, in the PWM overmodulation region, the commanded torque cannot be the output. Thus, when overmodulation is detected, the torque distribution is adjusted to the zero-torque command ($T_{ef}^*$) for the overmodulated system and $T_{eh}^*$ for the healthy system.

$$T_{eh}^* = \frac{T_{e\_SUM}^*}{n-m} \qquad (4)$$

Considering that it is highly unlikely that all power sources will fail simultaneously, we have $n \neq m$. Furthermore, assuming that each motor connected in tandem can independently output $T_{e\_SUM0}^*$, adjustments to the torque distribution, as described in (4) upon the detection of overmodulation allows any system to follow the commanded torque. Consequently, speed is maintained. In basic control, the ASR adjusts $T_{e\_SUM}^* = \frac{n}{n-m} T_{e\_SUM0}^*$, assigning a torque of $\frac{1}{n-m} T_{e\_SUM0}^*$ to all the motors. Conversely, the proposed control adjusted the torque distribution upon overmodulation and immediately changed the torque of the healthy motors to $\frac{1}{n-m} T_{e\_SUM0}^*$. Therefore, whereas the basic control uses an ASR response, the proposed control adopted an ACR response, quickly switching to only a healthy system to effectively suppress speed reduction.

## Overmodulation judgment method

Overmodulation is determined using the flowchart shown in Fig. 3.

In this flowchart, $v_m^*$ represents the amplitude of the output voltage command value converted into the line voltage RMS value, as defined in (5).

$$v_m^* = \sqrt{v_d^* + v_q^*} \qquad (5)$$

Let the DC link voltage be denoted as $v_{DC}$. The maximum amplitude of the phase voltage on the AC side of the inverter ($v_{pa\_max}$) is half of $v_{DC}$.

$$v_{pa\_max} = \frac{1}{2} v_{DC} \qquad (6)$$

Consequently, the maximum RMS value of the line-to-line voltage ($v_{lr\_max}$) can be expressed using equation (7).

$$v_{lr\_max} = \frac{\sqrt{6}}{4} v_{DC} \qquad (7)$$

From this, it can be inferred that overmodulation occurs when the amplitude of the output voltage command $v_m^*$ exceeds $\sqrt{6}/4$ times $v_{DC}$. In this study, overmodulation is determined by utilizing the fact that it occurs when $v_m^*$ exceeds $\sqrt{6}/4$ times the $v_{DC}$.

The voltage command values for the d- and q-axes in the two-phase rotating (dq) coordinate system, $v_d^*$ and $v_q^*$, respectively, are expressed by (8). Further, $K_{pACR}$ and $K_{iACR}$ are the proportional and integral gains of ACR, respectively.

$$ \left\{ \begin{aligned} v_d^* &= Ri_d^* - \omega_{re}L_q i_q^* + K_{pdACR}(i_d^* - i_d) \\ &\quad + \int K_{idACR}(i_d^* - i_d) dt \\ v_q^* &= Ri_q^* + \omega_{re}L_d i_d^* + \omega_{re}\Psi_f \\ &\quad + K_{pqACR}(i_q^* - i_q) \\ &\quad + \int K_{iqACR}(i_q^* - i_q) dt \end{aligned} \right. \qquad (8) $$

The d- and q-axis current command values $i_d^*$ and $i_q^*$, respectively, were set such that $i_d^* = 0$ to simplify the control. Assuming operation in the constant torque region in this study, $i_q^*$ is directly proportional to the torque command value $T_e^*$, as expressed in (9).

$$i_q^* = \frac{T_e^*}{P_n \Psi_f} \qquad (9)$$

However, when overmodulation was detected and torque distribution was adjusted, the current command values for overmodulation judgment, $i_{dJ}^*$ and $i_{qJ}^*$, were employed instead of the actual current command values. This assumes that all the systems received equal torque command values.
$$ \begin{cases} i_{dJ}^* = 0 \\ i_{qJ}^* = \frac{1}{P_n \Psi_f} \frac{T_{e\_SUM}^*}{n} \end{cases} \quad (10) $$

The d- and q-axis voltage command values for the overmodulation judgment, $v_{dJ}^*$, and $v_{qJ}^*$, respectively, were calculated using (11) with $i_{dJ}^*$ and $i_{qJ}^*$.

$$ \begin{cases} v_{dJ}^* = Ri_{dJ}^* - \omega_{re}L_q i_{qJ}^* \\ v_{qJ}^* = Ri_{qJ}^* + \omega_{re}L_d i_{dJ}^* + \omega_{re}\Psi_f \end{cases} \quad (11) $$

We substitute $v_{dJ}^*$ and $v_{qJ}^*$ for $v_d^*$ and $v_q^*$, respectively, in (5) to calculate the overmodulation judgment voltage $v_{mJ}^*$. Subsequently, we used $v_{mJ}^*$ to determine whether overmodulation had occurred.

## Ideal speed maintenance condition by proposed method

### Minimum capacity required to maintain speed

With the torque output by one motor during basic control defined as $T_e$, the composite moment of inertia as $J$ kgm², the viscous friction coefficient as $b$ kgm/s, and the running resistance as $T_r$ Nm, the equation of motion is expressed as (12).

$$ J \frac{d}{dt} \omega_{rm} = nT_e - b\omega_{rm} - T_r \quad (12) $$

Therefore, the torque $T_{en}$ that one motor needs to output to maintain speed is defined by (13), considering that the acceleration is zero during constant-speed operation.

$$ T_{en} = \frac{b\omega_{rm} + T_r}{n} \quad (13) $$

As mentioned in the previous section, the d-axis current $i_d$ was set to 0 in this study. Thus, the q-axis current $i_{qn}$, which was required to output $T_{en}$, was calculated by substituting $T_{en}$ for $T_e^*$ in (9). The d- and q-axis voltages at that time, $v_{dn}$ and $v_{qn}$, respectively, can be obtained by substituting 0 for $i_d^*$ and $i_{qn}$ for $i_{qJ}^*$ in (11), assuming that there are no parameter errors or other discrepancies. The amplitude of the voltage converted to the line- voltage RMS value, denoted as $v_{mn}$, can be calculated by substituting them for $v_d^*$ and $v_q^*$ into (5). The DC link voltage $v_{DCl1}$ that can be output by PWM with a modulation ratio of 1.0 for $v_{mn}$ is expressed as (14).

$$ v_{DCl1} = \frac{v_{mn}}{\sqrt{6}/4} \quad (14) $$

The amplitude of the phase voltage $v_{aom}$ that can be output by PWM in the state of overmodulation

is expressed as (15) when the modulation ratio is $\alpha$.

$$ V_{aom} = \frac{V_{DC}}{2} \frac{2}{\pi} \left( \sqrt{1 - \frac{1}{\alpha^2}} + \alpha \arcsin\left(\frac{1}{\alpha}\right) \right) \quad (15) $$

According to (15), with a modulation ratio of $\alpha = 1.025$, the output voltage error was only 0.5%. Therefore, we hypothesized that the torque could be accurately produced up to this modulation ratio. When $v_{mn}$ is the specified command value, the DC link voltage $v_{DCom}$ that achieves this modulation ratio can be calculated by substituting $v_{DCom}$ for $v_{mn}$ in (14).

$$ v_{DCom} = \frac{V_{DCl1}}{1.025} \quad (16) $$

The proposed method detected overmodulation, adjusted the torque distribution in the next control cycle, and ensured that only a healthy system output the necessary torque. Theoretically, if a power-loss system can maintain the required torque during this period, no speed reduction occurs. If the conditions in (17) are satisfied, it is theoretically possible to generate the torque necessary to maintain speed. Thus, the system can switch to driving only a healthy system, without any reduction in speed. Notably, this assumes no loss in the inverter or other components. Equation (17) defines $C$ and $F$ as the capacitance of the smoothing capacitor and $\Delta t_c$ as the control period.

$$ \frac{1}{2} C(v_{DCl1}^2 - v_{DCom}^2) \geq T_{en} \omega_{rm}^* \Delta t_c \quad (17) $$

Therefore, the minimum smoothing capacitor capacitance $C_{min}$ that facilitates switching to driving only in a healthy system without causing speed reduction is the case wherein the equality sign in (17) holds.

$$ C_{min} = \frac{2T_{en}\omega_{rm}^*\Delta t_c}{v_{DCl1}^2 - v_{DCom}^2} \quad (18) $$

## Inverter gate off by low voltage protection

Inverters typically feature low-voltage protection that disables the gate signal if the DC input voltage drops below a set level for a specified period. When activated, this prevents voltage and torque output, leading to a speed reduction. In the proposed control, when overmodulation was detected, $T_{e\_SUM}^*$ was supplied only to the healthy side as a torque command value. Thus, if overmodulation was detected before the system was judged to have a low voltage, the speed reduction that causes low-voltage protection can be avoided. To achieve this, the judgment voltage for a low voltage must be
set below $v_{DCl1}$. In addition, the time $t_{lvl1}$ between the power loss and when $v_{DC}$ reaches $v_{DCl1}$ is defined in (19), where $v_{DCini}$ is the initial DC link voltage. Thus, setting the low-voltage judgment duration to at least $t_{lvl1}$, prevents the system from being judged as low voltage before a torque distribution change occurs, regardless of the judgment voltage.

$$t_{lvl1} = \frac{C(v_{DCini}^2 - v_{DCl1}^2)/2}{T_{en}\omega_{rm}^*} \quad (19)$$

## Experimental system

### Configuration of Experimental system setup

Fig. 4 illustrates the experimental system used for the simulation experiments of the two-set configuration shown in Fig. 1, which includes a DC regeneration power supply, motor-generator (MG) set with a PMSM (PM), induction motor (IM), and a no-fuse breaker (NFB). This study assumes a scenario where identical PMSMs are connected in tandem on the same axis. However, such motors were not available in our laboratory. Therefore, the PMSM simulated speed control as an $M_A$, while the IM simulated both the torque control and the load for $M_B$. Additionally, the standard rotation direction for both the PMSM and the IM is set such that each motor twists in opposite directions. To align the direction of the torque outputs, with the PMSM assuming the torque output of $M_A$ and the IM simulating the torque portion corresponding to $M_B$, the torque command sign for $T_{e\_IM}^*$ was reversed compared to $T_{e\_SUM}^*$. The torque command assigned to the IM in the experimental system was $T_{e\_IM-l}^*$, which was calculated by subtracting the load torque from $T_{e\_IM}$. The control block diagram of the simulated experiment is shown in Fig. 5. The details of the MG set ratings are presented in Tables 1 and 2, and the machine constants, simulated loads and smoothing capacitors are listed in Table 3.

In the simulated experiment, a machine angular velocity command of $\omega_{rm}^* = 160$ rad/s was set. The minimum capacitance of $C_{min} = 5.94$ $\mu F$, calculated using $J = J_m + J_l$ from (18), was smaller than that used in this experiment. In addition, $v_{DCl1} = 0.16$ V and $t_{lvl1} = 0.16$ s were obtained using (14) and (19) respectively. Setting the low-voltage judgment conditions below $v_{DCl1}$ and at least $t_{lvl1}$ theoretically allowed switching from a two-motor to a one-motor drive while maintaining speed. During the

<figure><img src="image_5.png" /><figcaption>Fig. 4. Simulated experiment system diagram</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5. Control block diagram in simulated experiment</figcaption></figure>

<table><caption>Table 1. Ratings of PM for Experiment</caption><tr><td>1.0[kW]</td><td>185[V]</td><td>3.70[A]</td></tr><tr><td>50[Hz]</td><td>2000[rpm]</td><td>8[poles]</td></tr></table>

<table><caption>Table 2. Ratings of IM for Experiment</caption><tr><td>2.2[kW]</td><td>200[V]</td><td>8.8[A]</td></tr><tr><td>50[Hz]</td><td>2860[rpm]</td><td>2[poles]</td></tr></table>

<table><caption>Table 3. Mechanical constants and smoothing capacitors</caption><tr><td>Actual moment of inertia J<sub>m</sub></td><td>0.00628[kgm<sup>2</sup>]</td></tr><tr><td>Actual running resistance T<sub>r</sub></td><td>0.530[Nm]</td></tr><tr><td>Simulated load moment of inertia J<sub>l</sub></td><td>0.00148[kgm<sup>2</sup>]</td></tr><tr><td>Viscous resistance of simulated load b<sub>l</sub></td><td>0.00819[kgm<sup>2</sup>]</td></tr><tr><td>Smooth capacitor capacitance C</td><td>1.32[mF]</td></tr></table>

tests, the low-voltage judgment voltage was varied at 95, 90, 80, and 70% of $v_{DCini} = 300$ V, with judgment times set at 5.0, 2.0, 0.5, 0.05, and 0.005 s.
<table><caption>Table 4. Low voltage judgment conditions and maximum deviation (Basic Control)</caption><thead><tr><th rowspan="2">Voltage<br/>[%]</th><th colspan="5">time [s]</th></tr><tr><th>5.0</th><th>2.0</th><th>0.5</th><th>0.05</th><th>0.005</th></tr></thead><tbody><tr><td>70</td><td>-2.58</td><td>-2.50</td><td>-2.58</td><td>-2.94</td><td>-3.15</td></tr><tr><td>80</td><td>-2.59</td><td>-2.51</td><td>-2.59</td><td>-3.16</td><td>-3.12</td></tr><tr><td>90</td><td>-2.63</td><td>-2.59</td><td>-2.61</td><td>-3.18</td><td>-3.05</td></tr><tr><td>95</td><td>-2.50</td><td>-2.57</td><td>-2.54</td><td>-3.20</td><td>-3.06</td></tr></tbody></table>

<table><caption>Table 5. Low voltage judgment conditions and square integral of deviation (Basic Control)</caption><thead><tr><th rowspan="2">Voltage<br/>[%]</th><th colspan="5">time [s]</th></tr><tr><th>5.0</th><th>2.0</th><th>0.5</th><th>0.05</th><th>0.005</th></tr></thead><tbody><tr><td>70</td><td>1.64</td><td>1.64</td><td>1.60</td><td>1.56</td><td>1.65</td></tr><tr><td>80</td><td>1.63</td><td>1.60</td><td>1.62</td><td>1.66</td><td>1.58</td></tr><tr><td>90</td><td>1.70</td><td>1.64</td><td>1.64</td><td>1.66</td><td>1.58</td></tr><tr><td>95</td><td>1.56</td><td>1.60</td><td>1.56</td><td>1.58</td><td>1.55</td></tr></tbody></table>

## Evaluation of speed fluctuation

Speed fluctuations were evaluated based on two criteria: the maximum deviation and integral of squared deviations, calculated using (20) and (21), respectively. Further, $t_1$ marked the time of power loss, and $t_2$ the indicated the point when the system stabilized after switching to control only the healthy motor.

$$ \max(\omega_{rm}^* - \omega_{rm}) \quad (20) $$

$$ \int_{t_1}^{t_2} (\omega_{rm}^* - \omega_{rm})^2 dt \quad (21) $$

## Experimental results

### Basic control

Tables 4 and 5 summarize the maximum deviations and integrals of the squared deviations under the basic control conditions. The results for the low-voltage conditions of 70% (5.0 s) and 95% (0.005 s) are shown in Fig. 6.

For the 70% (5.0 s) condition, following the power loss, the DC link voltage on the PM side reduced as the stored capacitor energy was used to produce torque. As $v_{DC\_PM}$ decreased, $T_{e\_PM}$ could not keep up with $T_{e\_PM}^*$. Consequently, the combined PM and IM torques became insufficient to maintain the speed, and the speed decreased. Thus, the ASR function increased the total torque command $T_{e\_SUM}^*$, boosting the torque of the IM, and thereby restoring the speed to match the command value. Eventually, $v_{DC\_PM}$

<table><caption>Table 6. Low voltage judgment conditions and maximum deviation (Proposed Control)</caption><thead><tr><th rowspan="2">Voltage<br/>[%]</th><th colspan="5">time [s]</th></tr><tr><th>5.0</th><th>2.0</th><th>0.5</th><th>0.05</th><th>0.005</th></tr></thead><tbody><tr><td>70</td><td>0.13</td><td>0.15</td><td>0.15</td><td>0.14</td><td>0.18</td></tr><tr><td>80</td><td>0.15</td><td>0.20</td><td>0.14</td><td>0.15</td><td>0.11</td></tr><tr><td>90</td><td>0.15</td><td>0.27</td><td>0.20</td><td>-0.25</td><td>-0.38</td></tr><tr><td>95</td><td>0.16</td><td>0.17</td><td>0.15</td><td>-0.30</td><td>-0.84</td></tr></tbody></table>

<table><caption>Table 7. Low voltage judgment conditions and square integral of deviation (Proposed Control)</caption><thead><tr><th rowspan="2">Voltage<br/>[%]</th><th colspan="5">time [s]</th></tr><tr><th>5.0</th><th>2.0</th><th>0.5</th><th>0.05</th><th>0.005</th></tr></thead><tbody><tr><td>70</td><td>0.006</td><td>0.005</td><td>0.006</td><td>0.004</td><td>0.007</td></tr><tr><td>80</td><td>0.004</td><td>0.008</td><td>0.005</td><td>0.004</td><td>0.005</td></tr><tr><td>90</td><td>0.005</td><td>0.010</td><td>0.006</td><td>0.006</td><td>0.008</td></tr><tr><td>95</td><td>0.006</td><td>0.006</td><td>0.007</td><td>0.007</td><td>0.032</td></tr></tbody></table>

stabilized at the line voltage amplitude of the PM, $\sqrt{2}\omega_{re}^*\Psi_f$.

Under the 95% (0.005 s) condition, $v_{DC\_PM}$ also decreased the post-power loss; however, the gate signal was turned off, while $T_{e\_PM}$ was still following its command. Consequently, the torque command of the IM had not increased at the time of the gate-off. This led to the total output torque being reduced to half, thereby causing a significant speed drop, which was greater than the speed reduction observed under the 70% (5.0 s) condition.

Table 4 indicates that longer judgment times (> 0.5 s) resulted in smaller maximum deviations than that in case of the shorter judgment times (< 0.05 s). This difference was attributed to the torque output from the IM when the gate signal was turned off. When the judgment times exceeded $t_{lvl1}$, the total torque output was prevented from dropping to half of $T_{e\_SUM0}^*$ at gate-off, which occurred with shorter judgment times. Consequently, even under basic control, exceeding $t_{lvl1}$ reduced the rate of deceleration and minimized the speed reduction (maximum deviation) compared to that under shorter judgment times. Table 5 indicates that the integrals of the squared deviations exhibited no clear correlation across all the low-voltage conditions. This was because, under strict conditions, large decelerations increased deviations but accelerated the switch to a single-motor drive. Conversely, under lenient conditions,
<figure><img src="image_7.png" /><figcaption>Fig. 6. Speed change at the DC voltage shutdown with Basic Control</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7. Speed change at the DC voltage shutdown with Proposed control</figcaption></figure>

smaller decelerations resulted in fewer deviations but delayed the transition.

## Proposed control

Tables 6 and 7 summarize the maximum deviations and the integrals of the squared

deviations under low-voltage judgment conditions, with results for the 70% (5.0 s) and 95% (0.005 s) conditions shown in Fig. 7.

In the 70% (5.0 s) scenario, similar to basic control, the PM's DC link voltage $v_{DC\_PM}$, dropped post-power loss, causing
overmodulation and a shift in torque distribution; the $T_{e\_PM}^*$ was set to zero and $T_{e\_IM}^*$ matched $T_{e\_SUM}^*$. In contrast to the basic control, this torque adjustment, conducted with the quick response of the ACR, enabled a swift transition to single-motor operation, significantly reducing speed fluctuations. Although $T_{e\_PM}$ did not drop to zero immediately, leading to a brief speed increase, the maximum deviation was still smaller than that in the basic control with a lower integral of the squared deviations.

Under the 95% (0.005 s) condition, $v_{DC\_PM}$ dropped after power loss, but the gate turned off before overmodulation was detected, thereby halving the torque output and reducing speed. Consequently, the ASR activated and increased $T_{e\_SUM}^*$. Even after the gate was turned off, the stored charge continued to discharge through the resistors and inductors on the DC side of the inverter, causing further voltage drops. Once overmodulation was detected, the torque distribution changed. However, $T_{e\_SUM}^*$ was already greater than $T_{e\_SUM0}^*$, leading to an increase in speed. Finally, the ASR adjusted $T_{e\_SUM}^*$ to match the speed command value.

Table 6 indicates that conditions with high low-voltage judgment voltage and short judgment time exhibited negative maximum deviations, indicating deceleration whereas, the others resulted in acceleration. In all conditions where the maximum deviation was negative, except for the 95% (0.005 s) scenario, the torque distribution and gate-off occurred almost simultaneously, resulting in less deceleration compared with the 95% (0.005 s) condition. Although the proposed control resulted in larger maximum deviations under the 95%-0.005 s condition, it still maintained smaller maximum deviations and integrals of squared deviations than the basic control, which relied on the ASR for transitioning to single-motor operation.

## Conclusion

In this study, we considered a scenario wherein one of the DC power supplied in a tandem-connected system failed and the circuit breaker opened, causing the motor to lose its power supply. To minimize the speed reduction and switch to operation with only a healthy system, we proposed a method that used overmodulation judgment to directly adjust the torque distribution. This approach facilitated the transition to operate solely with a healthy system based on the

response time constant of the ACR, rather than that of the ASR, thereby suppressing speed reduction. We also obtained the theoretical values of the smoothing capacitor capacity required to prevent speed reduction, as well as the relationship with low-voltage protection conditions. Simulated experiments confirmed that the proposed control method effectively reduced speed fluctuations.

## References

[1]. P. Wheeler: "Technology for the more and all electric aircraft of the future," 2016 IEEE International Conference on Automatica (ICA-ACCA), Curico, Chile, 2016, pp. 1-5

[2]. N. Nagel: "Actuation Challenges in the More Electric Aircraft: Overcoming Hurdles in the Electrification of Actuation Systems," in IEEE Electrification Magazine, Vol. 5, no. 4, pp. 38-45, Dec. 2017

[3]. H. Gao, Z. Zhang, Y. Liu, W. Huang and H. Xue, "Development and Analysis of Dual Three-Phase PMSM With Phase-Shifted Hybrid Winding for Aircraft Electric Propulsion Application," in IEEE Transactions on Transportation Electrification, vol. 10, no. 3, pp. 6497-6508, Sept. 2024

[4]. Y. Yang and G. Möhlenkamp: "Short Circuit Behavior of Dual Three-phase Permanent Magnet Synchronous Motors with Different Mutual Inductance in Electric Propulsion Application," 2022 24th European Conference on Power Electronics and Applications (EPE'22 ECCE Europe)

[5]. B. V. Ravi Kumar, K. Sivakumar, K. M. Reddy and S. Karunanidhi: "A new fault tolerant dual rotor BLDC drive for electro-mechanical actuator in more electric aircraft applications," 2017 IEEE Transportation Electrification Conference (ITEC-India), Pune, India, 2017, pp. 1-4

[6]. M. Villani, M. Tursini, G. Fabri and L. Castellini, "Multi-phase fault tolerant drives for aircraft applications," Electrical Systems for Aircraft, Railway and Ship Propulsion, Bologna, Italy, 2010, pp. 1-6

[7]. H. Kobayashi, ANishizawa, T. Iijima: "Development and Flight Demonstration of a Multiplexed Electric Motor System for Aeropropulsion ", Aerospace Technology Japan, Vol. 16, pp.115-122, 2017 (in Japanese)

[8]. Y. Qian, Y. Zhang, M. Chen, J. Sun, C. Du and Y. Wang: "Application of Solid State Transfer Switch in emergency power supply
vehicles," 2014 China International Conference
on Electricity Distribution (CICED), Shenzhen,
China, 2014

[9]. J.Heo, K.Matsuo, K.natori, K.Konodo: "Continuous Operation Control of PMSM with Compressor Loads of Air Conditioners in Case of DC Power Supply Loss", IEEJ, Vol., pp, 20 (in Japanese)