Starting Pulse Vibration Torque Analysis of Aviation Variable Frequency Asynchronous Motor Based on Low-Frequency Step-Down Starting Methods

: The more electric aircraft provides 115 V / 360~800 Hz variable frequency power supply for the variable frequency asynchronous motor, and the motor operation characteristics change with the power frequency variation. It causes the starting pulse vibration torque with the low-frequency power supply (360 Hz) to increase greatly and the mechanical shock and fatigue damage. Therefore, this paper proposes step-down starting method with the low-frequency power supply. Based on the electromagnetic principles generated by the starting pulse vibration torque, this paper uses a novel method of simulation data ﬁtting to establish an approximate model of the starting pulse vibration torque. The parameter design formulas of the low-frequency step-down starting methods, including the reducing voltage, the series resistance, and the series inductance are proposed. The e ﬀ ectiveness of the di ﬀ erent methods are veriﬁed, and the performance is compared through the simulation. The experimental veriﬁcation of a small power asynchronous motor is completed. The simulation and experiment results show that the low-frequency step-down starting methods e ﬀ ectively reduce the starting peak torque, and also suppress the shock impact of starting current on the power supply.


Introduction
Regarding the asynchronous motor starting characteristic, the research and analysis contents pay more attention to issues such as the large starting current and the small starting torque [1,2]. In addition, when the asynchronous motor starts, there is the starting pulse vibration torque. It is transmitted to the mechanical system through the coupling of multiple physical domains and brings adverse effects for the mechanical system. The ref [3,4] mainly indicate that the starting pulse vibration torque effect of 50 Hz constant frequency asynchronous motor is transmitted to the mechanical system through the couplings of multiple physical domains, which leads to the bearing resonance and fracture. The ref [5] similarly describes that the impact of starting pulse vibration torque is transmitted to the mechanical system, which eventually damages and breaks the gearbox. Therefore, the starting pulse vibration torque brings the large damage to the mechanical system, which is the problem that cannot be ignored.
For the starting pulse vibration torque impact of asynchronous motors on the mechanical system, the mechanical system design is generally improved, and the mechanical system strength is increased to prevent the damage. The ref [6,7] reduce the starting pulse vibration torque by changing the motor structure, such as groove shape or the mechanical bearing stiffness. The ref [8] proposes a method by reducing the starting voltage to decrease the starting pulse vibration pulse. However, this method As seen from the mechanical characteristics of Figure 1, both the critical torque and the starting torque decrease with the increase of power supply frequency. It can be approximated as: where, Tst is the starting torque, Tem is the critical torque, p is the number of pole pairs, U1 is the power supply voltage, f1 is the power supply frequency, R1 is the stator resistance, Ll1 is the stator leakage inductance, R'2 is the rotor resistance, and L'l2 is the rotor leakage inductance. The critical torque is the approximately square descent as the power supply frequency rises, and the starting torque is the approximately cubic descent as the power supply frequency rises. Therefore, in the design of variable frequency asynchronous motor, it is necessary to provide an index of starting torque Tst and the critical torque Tem with the high-frequency power supply (f1 = f1H = 800 Hz). Generally expressed by the starting torque coefficient kst and the critical torque coefficient km, they are respectively defined as: where, TnH is the working torque with f1H, TstH is the starting torque with f1H, and TemH is the critical torque with f1H. According to the characteristics of Equations (1) and (2), it can be known that the realization conditions of kst in the Equation (3) are more rigorous than km. In the motor design, the motor starting with the loads needs to meet kst, and the motor starting with the light loads only needs to meet km.

Starting Pulse Vibration Torque of Variable Frequency Asynchronous Motor
In the mechanical design of asynchronous motors, it is necessary to analyze the maximum torque Tmax of shaft during the operation, and the Tmax generally appears as the asynchronous motor starts. It may be the critical torque Tem or the peak torque caused by the starting pulse vibration torque, which is defined by the Tstm.
For the asynchronous motor with the traditional constant frequency power supply, the Tstm is usually less than the Tem. The starting process of 400 Hz aviation constant frequency asynchronous motor is shown in Figure 2a. Even if Tstm is larger than the Tem, it is only necessary to appropriately increase the design safety factor, and the starting pulse vibration torque influence may not be considered. However, for meeting the mechanical characteristic requirement with the power supply frequency change, such as the Formula (3), the Tmax caused by the motor design parameters during the starting is no longer the Tem, for the asynchronous motor with the variable frequency asynchronous motor. The Tmax is the Tstm caused by the starting pulse vibration torque, as shown in Figure 2b. As seen from the mechanical characteristics of Figure 1, both the critical torque and the starting torque decrease with the increase of power supply frequency. It can be approximated as: where, T st is the starting torque, T em is the critical torque, p is the number of pole pairs, U 1 is the power supply voltage, f 1 is the power supply frequency, R 1 is the stator resistance, L l1 is the stator leakage inductance, R' 2 is the rotor resistance, and L' l2 is the rotor leakage inductance. The critical torque is the approximately square descent as the power supply frequency rises, and the starting torque is the approximately cubic descent as the power supply frequency rises. Therefore, in the design of variable frequency asynchronous motor, it is necessary to provide an index of starting torque T st and the critical torque T em with the high-frequency power supply (f 1 = f 1H = 800 Hz). Generally expressed by the starting torque coefficient k st and the critical torque coefficient k m , they are respectively defined as: where, T nH is the working torque with f 1H , T stH is the starting torque with f 1H , and T emH is the critical torque with f 1H . According to the characteristics of Equations (1) and (2), it can be known that the realization conditions of k st in the Equation (3) are more rigorous than k m . In the motor design, the motor starting with the loads needs to meet k st , and the motor starting with the light loads only needs to meet k m .

Starting Pulse Vibration Torque of Variable Frequency Asynchronous Motor
In the mechanical design of asynchronous motors, it is necessary to analyze the maximum torque T max of shaft during the operation, and the T max generally appears as the asynchronous motor starts. It may be the critical torque T em or the peak torque caused by the starting pulse vibration torque, which is defined by the T stm .
For the asynchronous motor with the traditional constant frequency power supply, the T stm is usually less than the T em . The starting process of 400 Hz aviation constant frequency asynchronous motor is shown in Figure 2a. Even if T stm is larger than the T em , it is only necessary to appropriately increase the design safety factor, and the starting pulse vibration torque influence may not be considered. However, for meeting the mechanical characteristic requirement with the power supply frequency change, such as the Formula (3), the T max caused by the motor design parameters during the starting Energies 2020, 13, 1337 4 of 18 is no longer the T em , for the asynchronous motor with the variable frequency asynchronous motor. The T max is the T stm caused by the starting pulse vibration torque, as shown in Figure 2b.
Energies 2020, 13, x FOR PEER REVIEW 4 of 19 The relationship between the Tstm caused by the starting pulse vibration torque and the power supply frequency f1 during the variable frequency asynchronous motor starting is shown in Figure  2c. It can be seen that the Tstm is already larger than the Tem with the f1H = 800 Hz, and the Tstm is significantly larger than the Tem with the f1L = 360 Hz. Obviously, the Tmax of mechanical shaft formed by the Tstm with the low-frequency power supply is very large, which has a great effect on the fatigue strength of mechanical shaft.

Starting Pulse Vibration Torque Model
The principle of starting pulse vibration torque of asynchronous motor is that the stator and rotor magnetic fields cannot be synchronized immediately, forming electromagnetic pulse vibration torque, due to the transient process existence in the stator and rotor circuits during the starting.

Transient Characteristics of Starting Current and Torque
The voltage balance formula of asynchronous motor in the α-β two-phase stationary coordinate system is: The relationship between the T stm caused by the starting pulse vibration torque and the power supply frequency f 1 during the variable frequency asynchronous motor starting is shown in Figure 2c. It can be seen that the T stm is already larger than the T em with the f 1H = 800 Hz, and the T stm is significantly larger than the T em with the f 1L = 360 Hz. Obviously, the T max of mechanical shaft formed by the T stm with the low-frequency power supply is very large, which has a great effect on the fatigue strength of mechanical shaft.

Starting Pulse Vibration Torque Model
The principle of starting pulse vibration torque of asynchronous motor is that the stator and rotor magnetic fields cannot be synchronized immediately, forming electromagnetic pulse vibration torque, due to the transient process existence in the stator and rotor circuits during the starting.

Transient Characteristics of Starting Current and Torque
The voltage balance formula of asynchronous motor in the α-β two-phase stationary coordinate system is: where, R 1 and R 2 are the stator and rotor resistances, respectively, L s and L r are the stator and rotor winding self-inductances, respectively, and L m is the mutual inductance between the stator and rotor windings.
The stator and rotor current expressions can be obtained as: The transfer function in the Equation (6) is: In the Formulas (5) and (7), T 1 and T 2 can be expressed as T 1 = L s /R 1 and T 2 = L r /R 2 . Figure 3a is the current waveform caused by the transient process of Equations (5)- (7). The stator currents i α1 , i β1 are the AC current with the frequency f 1 superimposed on the DC current transient process, and the rotor currents i α2 ,i β2 are AC current with the slip frequency f s superimposed on the DC current transient process.
, R1 and R2 are the stator and rotor resistances, respectively, Ls and Lr are the stator and rotor ng self-inductances, respectively, and Lm is the mutual inductance between the stator and rotor ngs. he stator and rotor current expressions can be obtained as: he transfer function in the Equation (6) n the Formulas (5) and (7), T1 and T2 can be expressed as T1 = Ls/R1 and T2 = Lr/R2. igure 3a is the current waveform caused by the transient process of Equations (5)~(7). The stator ts 1 i α , 1 i β are the AC current with the frequency f1 superimposed on the DC current transient ss, and the rotor currents 2 i α , 2 i β are AC current with the slip frequency fs superimposed on the rrent transient process.
ince the stator and rotor currents exist in the DC transient process, the starting torque includes lse vibration torque shown in Figure 3b, which can be expressed as:

Basic Principle of Starting Torque
Obviously, the cause of pulse vibration torque is that the power is suddenly applied to t and rotor windings generates the transient currents containing the AC and DC components is expressed as: These currents generate the magnetic potential in the motor air gap, as shown in Figure   (1) Fss: the rotating magnetic potential on the stator with the synchronous speed (ω1) gene the stator currents 1 Since the stator and rotor currents exist in the DC transient process, the starting torque includes the pulse vibration torque shown in Figure 3b, which can be expressed as: It consists of average torque T st and the pulse vibration torque T st during the starting operation. The peak torque caused by pulse vibration torque is: Energies 2020, 13, 1337 6 of 18

Basic Principle of Starting Torque
Obviously, the cause of pulse vibration torque is that the power is suddenly applied to the stator and rotor windings generates the transient currents containing the AC and DC components [22]. If it is expressed as: (1) F ss : the rotating magnetic potential on the stator with the synchronous speed (ω 1 ) generated by the stator currents i α1 , i β1 of frequency f 1 .
(2) F 0s : the static magnetic potential on the stator with the speed of zero caused by the DC component of stator currents i α10 ,i β10 .
(3) F 0r : the rotating magnetic potential on the rotor with the synchronous speed (ω m ) generated by the DC component of rotor currents i α20 ,i β20 . (4) F sr : the rotating magnetic potential on the rotor with the synchronous speed (ω 1 = ω s + ω m ) generated by the rotor current i α2 ,i β2 of frequency f s .
These currents generate the magnetic potential in the motor air gap, as shown in Figure 4.

Basic Principle of Starting Torque
Obviously, the cause of pulse vibration torque is that the power is suddenly applied to the stator and rotor windings generates the transient currents containing the AC and DC components [22]. If it is expressed as: These currents generate the magnetic potential in the motor air gap, as shown in Figure 4.
(1) Fss: the rotating magnetic potential on the stator with the synchronous speed (ω1) generated by the stator currents 1 (2) F0s: the static magnetic potential on the stator with the speed of zero caused by the DC component of stator currents 10 i α , 10 i β .
(3) F0r: the rotating magnetic potential on the rotor with the synchronous speed (ωm) generated by the DC component of rotor currents 20 i α , 20 i β .
(4) Fsr: the rotating magnetic potential on the rotor with the synchronous speed (ω1 = ωs + ωm) generated by the rotor current 2 i α , 2 i β of frequency fs.  The four kinds of magnetic potentials interact to generate the electromagnetic torque shown in Figure 3b. The F ss and F sr interact to produce the average electromagnetic torque T st in Equation (8), the F 0r and F sr with the f 1 interact to produce the pulse vibration torque T st , the F ss and F 0r with the f s interact to produce the pulse vibration torque T st2 , and the F 0s and F 0r with the fm interact to produce the pulse vibration torque T st3 , which is the relatively complicated transient process.
Obviously, if the analytical formula of pulse vibration torque is derived according to Formulas (5)-(8), it will be very complicated and inconvenient for the engineering design and application.

Approximate Model of Starting Peak Torque
For the research on the starting pulse vibration torque, it analyzes the T max of motor design, that is, the torque shock of mechanical device caused by the starting pulse vibration torque. Therefore, the starting peak torque T stm is taken as the research target, which requires a model that can express the law of T stm and is convenient for the engineering design and application.
For the torque characteristic of Equation (8) from t = 0 to ∆t, the T st generated by the interaction between F ss and F sr is usually described by the Formula (1) at the t = 0, and the starting current I st can be expressed as: Energies 2020, 13, 1337 7 of 18 where, the stator current and rotor current are approximately equal during the starting. They are proportional to the power supply voltage U 1 , and the starting torque T st is proportional to the starting current I 2 st . For the T st , the same method is applied. Since T stm only appears at the motor starting moment, the magnitude of DC component i α10 ,i β10 ,i α20 ,i β20 should be determined by the U 1 suddenly applied to the windings. It is close to the initial value of transition process, which is approximately proportional to U 1 . It can be seen that the F 0s and F 0r magnitudes are approximately proportional to U 1 . According to the Formula (11), it can also be approximately proportional to I st . If the magnetic potential phase effect is ignored, the T st can also be assumed to be proportional to I 2 st , the T stm with the different f 1 is approximately assumed to be: According to Formula (12), when 360~800 Hz aviation power supply is applied, the coefficient C st is inversely proportional to the power frequency f 1 . However, the motor operates in magnetic saturation state with the low frequency, and in weak magnetic state with the high frequency. The relationship between C st and f 1 is complex and nonlinear. The nonlinear relationship between the coefficient C tms of Formula (13) and is more complicated.
The 7.5 kW variable frequency asynchronous motor is taken as an example, the approximate law of T stm is analyzed by the simulation to verify the feasibility of Formula (13). The parameters of aviation variable frequency asynchronous motor are shown in Table 1. Table 1. Parameters of variable frequency asynchronous motor.

Parameters
Value Firstly, the power supply of asynchronous motor is set to different frequencies, then it changes the U 1 at each frequency f 1 . The basic motor parameters are obtained by the Ansoft simulation. The motor parameters are set in Simulink simulation for the motor model. The voltage and frequency of supply power are also changed, the I st and T stm are obtained through the dynamic characteristic simulation. The data relation between the I st and T stm is fitted according to the Formula (13). The fitting results are shown in Table 2 and the characteristics obtained are shown in Figure 5. Firstly, the power supply of asynchronous motor is set to different frequencies, then it changes the U1 at each frequency f1. The basic motor parameters are obtained by the Ansoft simulation. The motor parameters are set in Simulink simulation for the motor model. The voltage and frequency of supply power are also changed, the Ist and Tstm are obtained through the dynamic characteristic simulation. The data relation between the Ist and Tstm is fitted according to the Formula (13). The fitting results are shown in Table 2 and the characteristics obtained are shown in Figure 5.  The similarity of fitted results is analyzed by using the total sum square (TSS) and the residual sum square (RSS) [24]. The calculated goodness of fit is above 0.98. Therefore, the Tstm description of motor is feasible.

Low-frequency Step-Down Starting Method
As can be seen from Figure 2c, the variable frequency asynchronous motor has the maximum of Tstm with the low-frequency (360 Hz) power supply, and the mechanical damage is the greatest. Therefore, the Tstm with the low frequency is the research target.

Principle of Low-frequency Step-Down Starting
From the Equation (3), it can be seen that the kst and km of aviation variable frequency asynchronous motor are proposed for the f1H power supply. The kst and km have a large margin with the low-frequency f1L power supply, that is, the Tst and Tem are greater than the design requirements. Therefore, if the power supply voltage is appropriately reduced with the low frequency, Tstm can be effectively reduced on the premise of meeting the Tst and Tem requirements.
The frequency of variable frequency power supply is divided into the high-frequency band and the low-frequency band. The high-frequency band is started with the rated voltage UN, and the lowfrequency band is started with the low voltage UA. The fA is the boundary between the two frequency bands. The starting voltage Ust is selected as follows: when f1 ≥ fA, Ust = UN; when f1 < fA, Ust = UA. The Tstm characteristic is shown in Figure 6. The similarity of fitted results is analyzed by using the total sum square (TSS) and the residual sum square (RSS) [24]. The calculated goodness of fit is above 0.98. Therefore, the T stm description of motor is feasible.

Low-Frequency Step-Down Starting Method
As can be seen from Figure 2c, the variable frequency asynchronous motor has the maximum of T stm with the low-frequency (360 Hz) power supply, and the mechanical damage is the greatest. Therefore, the T stm with the low frequency is the research target.

Principle of Low-Frequency Step-Down Starting
From the Equation (3), it can be seen that the k st and k m of aviation variable frequency asynchronous motor are proposed for the f 1H power supply. The k st and k m have a large margin with the low-frequency f 1L power supply, that is, the T st and T em are greater than the design requirements. Therefore, if the power supply voltage is appropriately reduced with the low frequency, T stm can be effectively reduced on the premise of meeting the T st and T em requirements.
The frequency of variable frequency power supply is divided into the high-frequency band and the low-frequency band. The high-frequency band is started with the rated voltage U N , and the low-frequency band is started with the low voltage U A . The f A is the boundary between the two frequency bands. The starting voltage U st is selected as follows: when f 1 ≥ f A , U st = U N ; when f 1 < f A , U st = U A . The T stm characteristic is shown in Figure 6. The selection principle of frequency boundary fA and the step-down voltage UA is given according to Figure 6. The design principle of step-down starting: (1) Principle I: The power supply voltage UA must ensure that kst and km meet the design requirements with the power frequency fA. If the working torque is TnA, the starting torque TstA ≥ kstTnA, and the critical torque TemA ≥ kmTnA; (2) Principle II: The TstmL with the power supply frequency f1L and the voltage UA is equal to the TstmA with the power supply frequency f1A and the voltage UN, that is, the maximum Tstm is the lowest in the entire frequency range. For the low-frequency step-down starting shown in Figure 6, the voltage reduction, the series resistance and the series inductance can be adopted. The selection principle of frequency boundary f A and the step-down voltage U A is given according to Figure 6. The design principle of step-down starting: (1) Principle I: The power supply voltage U A must ensure that k st and k m meet the design requirements with the power frequency f A . If the working torque is T nA , the starting torque T stA ≥ k st T nA , and the critical torque T emA ≥ k m T nA ; Energies 2020, 13, 1337 9 of 18 (2) Principle II: The T stmL with the power supply frequency f 1L and the voltage U A is equal to the T stmA with the power supply frequency f 1A and the voltage U N , that is, the maximum T stm is the lowest in the entire frequency range.
For the low-frequency step-down starting shown in Figure 6, the voltage reduction, the series resistance and the series inductance can be adopted.

Design of Low-Frequency Voltage Reduction
The design method of voltage reduction with the low-frequency power supply is applied. Firstly, according to the design principle I, the reduced voltage U A should meet k st and k m at the frequency boundary point f A . If the design is applied based on the starting torque T stA = k st T nA , it is: It is arranged to obtain: Designed with the critical torque T emA = k m T nA in the Equation (3), U A should meet at the frequency point f A : It is arranged to obtain: According to the design principle II, the formula (13) is expressed as: In order to simplify the calculation, it is approximately (R 1 + R 2 ) 2 << 4π 2 f 2 A (L l1 + L l2 ) 2 and written as: Coupled, the (15) and (19) or (17) and (19), the f A and U A can be estimated.

Design of Low-Frequency Series Resistance
If the stator winding with the series resistance is used to reduce the power supply voltage for the low-frequency power supply, it is necessary to estimate the frequency boundary point f A and the series resistance R A .
Similarly, according to the design principle I, it is calculated by the starting torque T stA = k st T nA at the point f A , and the starting torque should satisfy: Energies 2020, 13, 1337 10 of 18 The total resistance value R = R 1 + R A + R' 2 should meet: However, it is calculated by the T em = k m T nA at the point f A , defines R 1 = R 1 + R A , and meets: The R 1 is: According to the design Principle II, the Equation (13) is: Due to the f A > f 1L , it is approximately (R 1 + R 2 ) 2 << 4π 2 f 2 A (L l1 + L l2 ) 2 , and written as: Coupled the (21) and (25) or (23) and (25), the f A and R A can be estimated.

Design of Low-Frequency Series Inductance
It reduces the power supply voltage of asynchronous motor by the series inductance. However, the voltage drop across the inductor is not only related to the starting current, but also to the frequency. Its characteristics are different from the series resistance. The frequency boundary point f A and the series resistance L A are estimated.
Similarly, according to the design principle I, it is calculated by the starting torque T stA = k st T nA at the point f A , and it should satisfy: The total inductance value L = L l1 + L A + L' l2 should meet: However, it is calculated by the T em = k m T nA at the point f A , and meets: It is expressed as: According to the design Principle II, the Equation (13) is: It is approximately (1/k stm − 1)(R 1 + R 2 ) 2 << 4π 2 f 2 A (L l1 + L l2 ) 2 , and written as: Coupled the (27) and (31) or (29) and (31), the f A and L A can be estimated.

Design Example of Low-Frequency Step-Down Starting
The variable frequency asynchronous motor shown in Table 1 is taken as an example, and the design methods of voltage reduction, the series resistance, and the series inductance are respectively applied. It is assumed that the constant power load is driven, and the motor starts with load at the same time for meeting k st the design requires k st = 1.2~1.4. Coupled with the (15) and (19), (21) and (25), (27) and (31), respectively. The simulation results are shown in Table 3. The starting peak torque characteristics of voltage reduction methods are shown in Figure 7.
It is expressed as: According to the design Principle II, the Equation (13) Coupled the (27) and (31) or (29) and (31), the fA and LA can be estimated.

Design Example of Low-frequency Step-Down Starting
The variable frequency asynchronous motor shown in Table 1 is taken as an example, and the design methods of voltage reduction, the series resistance, and the series inductance are respectively applied. It is assumed that the constant power load is driven, and the motor starts with load at the same time for meeting kst the design requires kst = 1.2~1.4. Coupled with the (15) and (19), (21) and (25), (27) and (31), respectively. The simulation results are shown in Table 3. Table 3. Design data of low-frequency step-down starting. The starting peak torque characteristics of voltage reduction methods are shown in Figure 7.  The motor starts with the rated voltage, and the peak torque T stm of power supply with f 1L (360 Hz) is 135.49 N·m. As can be seen from the data in the Table 3, it respectively reduces to 54%, 41% and 61% of the the peak torque T stm with 360 Hz power supply. The effect of series resistance is the best.

Control Parameters Voltage Reduction Series Resistance Series
The above mentioned design methods may not achieve the goal of principle II, since the approximate relationship is used and it is affected by magnetic saturation. If the gap between T stmL and T stmA is large, it needs to adjust appropriately. When T stmL is larger than T stmA , the voltage U A can be appropriately reduced, or the step-down resistor R A or inductance L A can be increased. At the same time, in order to ensure the requirement of k st , the frequency boundary point f A can be appropriately reduced.

Characteristics of Starting Peak Torque
The aviation variable frequency asynchronous motors apply three kinds of low-frequency step-down starting methods by the voltage reduction, the series resistance, and the series inductance. According to the characteristics of starting peak torque T stm shown in Figure 7, it has the following characteristics: (1) The series resistance method has the better suppression effect on the starting peak torque T stm , as shown in Figure 8a. When the power supply frequency f 1 decreases in the low-frequency stage, the voltage drop across the resistor R A increases due to the increase of starting current I st .
The voltage on the stator winding reduces to make T stm decrease effectively.
(2) The series inductance method has the poor suppression effect on the starting peak torque T stm , as shown in Figure 8a. When the power supply frequency f 1 decreases in the low-frequency stage, the impedance on the inductor L A decreases linearly. However, the starting current I st does not increase linearly. The voltage drop on the inductor L A reduces and the voltage on the stator winding increases, causing the larger low-frequency T stm . (3) The disadvantage of series resistance method is that it consumes the parts of power and causes the resistor heat. Therefore, it needs to be analyzed for the asynchronous motor that requires frequent starting. For the long-time work motor, the power consumed can be ignored since the starting time is short.
time, in order to ensure the requirement of kst, the frequency boundary point fA can be appropriately reduced.

Characteristics of Starting Peak Torque
The aviation variable frequency asynchronous motors apply three kinds of low-frequency stepdown starting methods by the voltage reduction, the series resistance, and the series inductance. According to the characteristics of starting peak torque Tstm shown in Figure 7, it has the following characteristics: (1) The series resistance method has the better suppression effect on the starting peak torque Tstm, as shown in Figure 8a. When the power supply frequency f1 decreases in the low-frequency stage, the voltage drop across the resistor RA increases due to the increase of starting current Ist.
The voltage on the stator winding reduces to make Tstm decrease effectively.
(2) The series inductance method has the poor suppression effect on the starting peak torque Tstm, as shown in Figure 8a. When the power supply frequency f1 decreases in the low-frequency stage, the impedance on the inductor LA decreases linearly. However, the starting current Ist does not increase linearly. The voltage drop on the inductor LA reduces and the voltage on the stator winding increases, causing the larger low-frequency Tstm. (3) The disadvantage of series resistance method is that it consumes the parts of power and causes the resistor heat. Therefore, it needs to be analyzed for the asynchronous motor that requires frequent starting. For the long-time work motor, the power consumed can be ignored since the starting time is short.

Characteristic Analysis of Starting Current
The surge current during the traditional asynchronous motor starting is always considered as an important factor affecting the power supply stability. The starting current of variable frequency asynchronous motor can be expressed as: As seen from Equation (32), the starting current I st is approximately inverse proportional to the power frequency f 1 . For the variable frequency asynchronous motor with the rated voltage, the starting current I st with the high-frequency (800 Hz) is 167.2A, and the starting current I st with low frequency (360 Hz) is 286.3A, as shown in Figure 8b.
The low-frequency step-down starting can also suppress the surge current I st during the starting. The starting current I st of step-down methods is shown in Figure 8b. The maximum is at the frequency boundary point with the rated voltage.
(1) The frequency boundary point of series resistance method is the highest, and the starting current is the smallest with the rated voltage, which is 214A. The frequency boundary point of series inductance method is the lowest, and the starting current is the largest, which is 243A. The voltage reduction method is center, and the current is 236A.
(2) For the starting current at the frequency f 1L , the series resistance method has the lowest voltage, and the starting current is also the lowest, which is 195A. The starting currents of voltage reduction and the series inductance are 212A and 216A, respectively. The effect of series resistance is the best.

Simulation Test and Analysis of Starting Process
The power supply frequency of variable frequency asynchronous motor is set with 400 Hz, and the load torque is 12.46 N·m, which is the rated torque. Three kinds of low-frequency step-down starting methods are used for the simulation test, and the normal power supply is restored after the starting at the 0.28 s. The characteristics of torque and phase current are shown in Figure 9.
The Table 4 shows the simulation data of starting process with the step-down voltage methods. The steady-state torque shown in Figure 9 is 12.46 N·m, the effective value of steady-state phase current is 35.15A, and the peak value is 49.7A. The ∆I Am of switching characteristics is the fluctuation value based on the steady-state peak current (49.7A), which can be seen from the data in Table 4: (1) The starting torque T stm of three methods is consistent with the characteristics of Figure 7.
The series resistance method is the smallest, and the starting torque T st is not a huge different.
(2) The starting current I st of three methods is consistent with the characteristics of Figure 8b, and series resistance method is the smallest. (3) After the step-down starting is completed, the normal power supply switching is restored, and the ∆T em , ∆I Am of series resistor method are the smallest.

Simulation Test and Analysis of Starting Process
The power supply frequency of variable frequency asynchronous motor is set with 400 Hz, and the load torque is 12.46 N·m, which is the rated torque. Three kinds of low-frequency step-down starting methods are used for the simulation test, and the normal power supply is restored after the starting at the 0.28 s. The characteristics of torque and phase current are shown in Figure 9. The Table 4 shows the simulation data of starting process with the step-down voltage methods. The steady-state torque shown in Figure 9 is 12.46 N·m, the effective value of steady-state phase current is 35.15A, and the peak value is 49.7A. The ∆IAm of switching characteristics is the fluctuation value based on the steady-state peak current (49.7A), which can be seen from the data in Table 4: (1) The starting torque Tstm of three methods is consistent with the characteristics of Figure 7. The series resistance method is the smallest, and the starting torque Tst is not a huge different.
(2) The starting current Ist of three methods is consistent with the characteristics of Figure 8b, and series resistance method is the smallest. (3) After the step-down starting is completed, the normal power supply switching is restored, and the ΔTem, ΔIAm of series resistor method are the smallest.

Experiment of Pump-Type Variable Frequency Asynchronous Motor
The 850 W pump-type variable frequency asynchronous motor with the narrow frequency conversion (360~600 Hz) is used to test the starting characteristics. The parameters of prototype are shown in Table 5. frequency power supply uses a capacity of 30 kVA. The output frequency of power supply can be adjusted in a wide range from 300~800 Hz, and the output voltage range is from 92.0~150.0 V. For the strating (stall) test, the prototype is placed on the torque bench and connected to the 30kVA power electronic variable frequency power supply and carried out the stall test with diffrernt frequncies, shown in Figure 10. It is approximately taken as the starting torque analysis. The straight line is the simulation characteristic with the motor design data, and the "*" is the experimental data. It can be seen that the experimental torque is significantly lower than the simulation value with the low frequency, and the reason is the low-frequency saturation factor.
Energies 2020, 13, x FOR PEER REVIEW 15 of 19 supply can be adjusted in a wide range from 300~800 Hz, and the output voltage range is from 92.0~150.0 V. For the strating (stall) test, the prototype is placed on the torque bench and connected to the 30kVA power electronic variable frequency power supply and carried out the stall test with diffrernt frequncies, shown in Figure 10. It is approximately taken as the starting torque analysis. The straight line is the simulation characteristic with the motor design data, and the "*" is the experimental data. It can be seen that the experimental torque is significantly lower than the simulation value with the low frequency, and the reason is the low-frequency saturation factor.
. Figure 10. The data comparison of simulation and experiment.
For the starting torque dynamic experiment, the prototype was placed on a loadable speed regulation test bench. The experimental equipments mainly include the 30KVA AC variable frequency power supply, the pump-type variable frequency asynchronous motor, the adjustable resistance box, and the digital oscilloscope. According to the series resistance design method of lowfrequency step-down starting, the series resistance is 2 Ω. The purpose of experiment is to verify the current and torque starting characteristics of variable frequency asynchronous motor with the direct starting and the series resistance starting. For the direct starting experiment, the AC variable frequency power supply is adjusted to the 115 V/400 Hz output, and directly connected to the variable frequency motor at a certain time, recording the current data through the oscilloscope. For the series resistance starting, the AC variable frequency power supply is also adjusted to the 115 V/400 Hz output, and connected the resistor of 2 Ω. The variable frequency motor is connected at a certain time, recording the current data through the oscilloscope.
The dynamic experiment of starting process can measure the three-phase voltage and current. The A-phase voltage and current waveforms are shown in Figure 11. Figure 11a-c shows the voltage waveforms with the direct starting and the series resistance starting. When the motor starts, the voltage drops the 3.5% and 5.2%, respectively. Figure 11b-d shows the current waveforms with the direct starting and the series resistance starting, and the peak current reaches 28.12A and 20.04A, respectively.
(a) For the starting torque dynamic experiment, the prototype was placed on a loadable speed regulation test bench. The experimental equipments mainly include the 30KVA AC variable frequency power supply, the pump-type variable frequency asynchronous motor, the adjustable resistance box, and the digital oscilloscope. According to the series resistance design method of low-frequency step-down starting, the series resistance is 2 Ω. The purpose of experiment is to verify the current and torque starting characteristics of variable frequency asynchronous motor with the direct starting and the series resistance starting. For the direct starting experiment, the AC variable frequency power supply is adjusted to the 115 V/400 Hz output, and directly connected to the variable frequency motor at a certain time, recording the current data through the oscilloscope. For the series resistance starting, the AC variable frequency power supply is also adjusted to the 115 V/400 Hz output, and connected the resistor of 2 Ω. The variable frequency motor is connected at a certain time, recording the current data through the oscilloscope.
The dynamic experiment of starting process can measure the three-phase voltage and current. The A-phase voltage and current waveforms are shown in Figure 11. Figure 11a-c shows the voltage waveforms with the direct starting and the series resistance starting. When the motor starts, the voltage drops the 3.5% and 5.2%, respectively. Figure 11b-d shows the current waveforms with the direct starting and the series resistance starting, and the peak current reaches 28.12A and 20.04A, respectively.
In order to obtain the approximate trend of stating pulse vibration torque, the rotor current is calculated by using Formula (6) and the dynamic torque is calculated by using Formula (9). Figure 12a-b shows the torque waveforms with the the direct starting and the series resistor starting.
The peak torque reaches 7.78 N·m and 4.21 N·m, respectively. The peak torque is 45.89% less than the peak torque with the direct starting.
Obviously, the data of A point and B point shown in Figure 10 can be expressed separately the change trend with the direct starting and the series resistance starting. The peak torque of experimental data is smaller than that of simulation, since the power supply exhibits the voltage transient drop effect during the starting. The dynamic experiment of starting process can measure the three-phase voltage and current. The A-phase voltage and current waveforms are shown in Figure 11. Figure 11a-c shows the voltage waveforms with the direct starting and the series resistance starting. When the motor starts, the voltage drops the 3.5% and 5.2%, respectively. Figure 11b-d shows the current waveforms with the direct starting and the series resistance starting, and the peak current reaches 28.12A and 20.04A, respectively. In order to obtain the approximate trend of stating pulse vibration torque, the rotor current is calculated by using Formula (6) and the dynamic torque is calculated by using Formula (9). Figure  12a-b shows the torque waveforms with the the direct starting and the series resistor starting. The peak torque reaches 7.78 N·m and 4.21 N·m, respectively. The peak torque is 45.89% less than the peak torque with the direct starting.
Obviously, the data of A point and B point shown in Figure 10 can be expressed separately the change trend with the direct starting and the series resistance starting. The peak torque of experimental data is smaller than that of simulation, since the power supply exhibits the voltage transient drop effect during the starting.

Conclusions
The strating pulse vibration torque of aviation variable frequency asynchronous motor is taken as the research object. The design methods of low-frequency step-down starting is proposed, which are the voltage reduction, the series resistance, and the series inductance according to a novel approximate model by the data fitting for peak torque generated by the starting pulse vibration torque. The paper also proposes the estimation algorithm of parameters and analyzes and compares the starting pulse vibration torque characteristics. The research and experiment results show that the low-frequency step-down starting can effectively reduce the pulse vibration torque and the surge current during the low-frequency starting. The series resistance method has the better effect on the peak torque caused by the starting pulse vibration torque and the starting current suppression, which is suitable for the variable frequency asynchronous motor drive system with the infrequent starting. The actual motor model establishment is worth considering in future research.
Author Contributions: Z.C. and Y.Z. formulated the research content of energy consumption characteristics based on more electric aircraft. Z.C. consulted the papers, derived formulas, modeled and simulated for the energy consumption characteristics of more electric aircraft actuation system and the traditional aircraft actuation system. N.W. enriched and supplemented the content of power loss. Z.C. and N.W. also modified the paper language.
Funding: This work was supported by the Aviation Nature Fund (2014ZC01002).

Conclusions
The strating pulse vibration torque of aviation variable frequency asynchronous motor is taken as the research object. The design methods of low-frequency step-down starting is proposed, which are the voltage reduction, the series resistance, and the series inductance according to a novel approximate model by the data fitting for peak torque generated by the starting pulse vibration torque. The paper also proposes the estimation algorithm of parameters and analyzes and compares the starting pulse vibration torque characteristics. The research and experiment results show that the low-frequency step-down starting can effectively reduce the pulse vibration torque and the surge current during the low-frequency starting. The series resistance method has the better effect on the peak torque caused by the starting pulse vibration torque and the starting current suppression, which is suitable for the variable frequency asynchronous motor drive system with the infrequent starting. The actual motor model establishment is worth considering in future research.