Electromechanical coupling dynamic characteristics of differential speed regulation system considering inverter harmonics under variable operating conditions

The differential speed regulation system driven by inverters, motors and differential gear trains is a complex electromechanical system that achieves speed regulation and energy savings efficiently and economically. In this paper, the complete drive trains dynamic model of the differential speed regulation system with the inverter power supply-motor-differential gearbox-load is established. The inverter power supply considers constant voltage to frequency ratio control, sinusoidal pulse width modulation and inverter, the motors are modeled based on the equivalent circuit method, and the differential gear trains consider a lateral-torsional model with time-varying meshing stiffness and damping. The dynamic properties of the system are analyzed and compared with the variable frequency drive model considering inverter power supply and the direct drive model using ideal power supply under variable operation conditions. The results show that the variable frequency drive model varies more smoothly in the time domain and contains additional harmonic components in the frequency domain resulting from the coupling of the inverter triangle carrier frequency to the fundamental frequency of the power supply than the direct drive model. It also shows that the variable frequency drive model is a more realistic and rational model than the direct drive model. The complex coupling relationship can be seen in the inverter power supply-motor-differential gearbox-load system, where both inverter harmonics and mechanical meshing force harmonics are found in the dynamic response of the motor’s electromagnetic torque, rotor speed; the inverter harmonics are also reflected in the mechanical meshing force harmonics.


I. INTRODUCTION
Variable speed drive (VSD) is a device that regulates the speed and rotational torque of mechanical equipment. The application of variable speed drives can increase productivity and save energy for pumps, fans, compressors, and other large industrial equipment [1][2][3]. The main forms of variable speed drives used in the industrial sector are hydraulic coupling speed regulation, mechanical speed regulation, and electrical speed regulation. The hydraulic coupling speed regulation is based on the principle of changing the speed difference between the active and driven shafts by changing the amount of oil in the coupling. Mechanical speed regulation mainly refers to the use of belts or gearboxes, both have some disadvantages, such as the use of gearboxes cannot achieve step-less speed regulation, the use of belts can achieve step-less speed regulation, but the accuracy cannot be maintained; most of the industrial power source for three-phase induction motors, electrical speed regulation methods are generally frequency control. The efficiency and accuracy of variable frequency drives are high, but the cost of the equipment and its maintenance is also expensive, especially when driving high-power motors with variable frequency drives. The differential characteristics of planetary differential gearboxes [4] combined with variable frequency drive energy-saving principle [5], high-power motors drive the gear ring constant speed operation, low-power motors for frequency control indirect drive carrier can achieve low equipment and maintenance costs, high efficiency to achieve differential speed regulation energy saving. With the emphasis on energy saving and consumption reduction, power plants and oil and gas transmission enterprises to the original fixed speed equipment to implement frequency conversion is a major trend [6][7][8].
Nowadays, severe electromechanical coupling effects are often observed in large rotating machines driven by asynchronous motors and controlled by inverters under variable speed drives, generating additional fluctuating drive torque components under transient and steady-state operating conditions [9]. The inverter-generated variable frequency power supply acts directly as an input to the motor, which acts as a power source for the gearbox, while the torque of the gearbox input shaft is also a load on the motor, with the three components interacting with each other. Many scholars at home and abroad have studied the dynamic characteristics of motor-gearbox electromechanical coupling: Khabou [10] established a coupled dynamics model of motor-gear pair-pump and analyzed the dynamic response of the gear pair in terms of vibration displacement, dynamic meshing force and transmission error when the system is in the motor start-up phase and subjected to periodic fluctuating load. Bai [12] established a non-linear dynamics model for a multi-motor gear system and investigated its dynamic characteristics, considering the effects of motor rotational inertia, mounting errors and time-varying meshing stiffness. The above models consider the mechanical and torsional characteristics of the motor but do not consider the electromagnetic effects of the motor, inverter harmonics, and variations in operating conditions. Szolc [9] studied the electromechanical coupling characteristics of an asynchronous motor and rotating machine drive system, and determined the electromagnetic stiffness and damping coefficients of the electromechanical system using the analytical method. Yi [13] established a model of an induction motor based on an equivalent circuit and a dynamics model of a multi-stage gear drive and analyzed the influence of the electromagnetic characteristics of the motor on the natural characteristics and dynamic response of the drive system. Bai [11,14] considered the effects of magnetic saturation of induction motor and machine slotting, and established the magnetic permeability network model of induction motor, combined with the lumpedparameter model of planetary gear, to analyze the dynamics of the electromechanical coupled system under load saltations and voltage transients. Liu [15] combined the lumped-parametric model of the sun gear and planetary gear with the finite element model of the ring and planetary carrier to propose a hybrid mechanical model to study the dynamic characteristics of the electromechanical coupling under the known dynamic electromagnetic torque excitation of the motor. Shu [16] established a model of the electromechanical coupling dynamics of a multi-source drive system which included the gear system, the load and the drive motors, and investigated the effect of different loads on the synchronization characteristics of the system. The above-mentioned papers modelled the electromechanical coupling between motor and gearbox, but oversimplified the supply voltage at the motor input and did not consider the influence of the inverter.
With the development of variable frequency speed regulation technology, Song-Manguelle [17] found that fluctuations in electromagnetic torque caused by high harmonic voltages generated during the operation of inverters are one of the main causes of failures in mechanical equipment, and pointed out that the frequency of fluctuating torque has a more significant impact on failures than the magnitude of fluctuations. Feese [18] found that excessive vibration and failure of the coupling and motor shaft of the fan system under variable frequency drive was caused by the interaction between the electrical PWM inverter and the mechanical modes. Itoh [19] compared between V/f control and position-sensorless vector control method, showed that V/f control is the best choice for simple variable-speed applications such as fan or pumps and is especially effective in the high-speed range. Lysenko [20] took constant voltage to frequency ratio control into account and simulated a real three-phase inverter-induction motor-centrifugal pump. Han [21] established an electromechanical coupling model in openloop voltage to frequency control mode and calculated and analyzed the effect of factors such as multi-stage inverters on fatigue life. Song-Manguelle [22] considered pulsewidth modulation, inverters, while simplifying a dynamic mechanical load to a variable frequency drive containing harmonics, and investigated the interaction between electrical and mechanical harmonics. The above studies show that inverters have an important influence on the drive system when studying the dynamic characteristics of electromechanical coupling.
In the dynamic characteristics analysis method, most scholars [12][13][14][15][16][17][18][19][20][21][22] mainly focus on the dynamics of electromechanical inter-coupling of systems in the steady state, and some scholars also study the dynamic characteristics of electromechanics under transient conditions for some electrical systems with transients [11] or sudden changes in mechanical loads [10,23]. However, for differential speed regulation systems, it is very basic and common for the variable frequency drive to produce smooth changes in the mechanical load. Therefore, it is necessary to carry out transient analysis of the start-up and speed regulation stages in addition to the study of the steady state characteristics of the differential speed regulation system. Some of the above-mentioned scholars [10][11][12][13][14][15][16] have studied the dynamic characteristics of motor-gear system coupling, while others [17][18][19][20][21][22] have analyzed the dynamic characteristics of inverter-motor coupling or invertermotor-pump coupling. These studies only consider part of the electromechanical drive system and do not provide a complete reflection of the overall coupling dynamic characteristics of the electromechanical coupling system. To solve the above issues, the complete drive trains dynamic model of the differential speed regulation system with the inverter power supply-motor-gearbox-load is established in this paper, which includes the fan-pump load, the differential planetary gear lateral-torsional model, the motor equivalent circuit model, and the inverter model. The differential gear lateral-torsional model considers the timevarying meshing stiffness in generalized angular coordinates and damping, the motor equivalent circuit model considers the voltage equation, the magnetic chain equation, and the electromagnetic torque equation, and the inverter power supply model considers constant voltage to frequency (V/f) ratio control, sine pulse width modulation (SPWM) and inverter harmonics. The dynamics of the differential speed regulation system are investigated in the start-up, steady-state and speed regulation stages.
The rest of the paper is structured as follows: Section 2 presents the differential planetary gear lateral-torsional model and the load model; Section 3 presents the motor equivalent circuit model; Section 4 presents the inverter power supply model; Section 5 investigates the dynamic characteristics and parameter effects of differential speed regulation systems under variable frequency drive and direct drive during start-up, steady-state and speed regulation stages. Finally, Section 6 gives the conclusions and recommendations of the study.
II. Model of the differential planetary differential gear system and load This paper investigates the dynamic characteristics of the electromechanical coupling of a differential speed regulation system for fans or pumps, the composition of which is shown in Fig. 1. The power system mainly includes the three-phase power supply and inverter power supply containing V/f control, SPWM and inverter. The motor part consists of a main motor providing the main power and two auxiliary lowpower motors for speed regulation in order to balance the forces on the system. The mechanical system is composed of 2K-H type planetary differential gears and fixed shaft gears for the synthesis of power and motion to achieve a certain range of speed regulation. The electrical section is connected as shown in the imaginary line. The main motor does not need to go through the inverter as the auxiliary motor is driven by a variable frequency drive. The mechanical part is connected as shown in a straight line. The main motor drives the ring directly through the connecting shaft, the two auxiliary motors drive the external gears through the connecting shaft and then indirectly drive the carrier through the fixed gears system, the sun gear is connected to the load by a shaft, which acts as an output to increase the speed and reduce the torque. When the system needs speed regulation, the speed of the main motor is kept constant and the speed of the two low-power motors is adjusted synchronously to achieve the final speed regulation requirement at the load side. Angular displacement is chosen as the generalized coordinate in the dynamical model of the gears system. In this section, the lateral-torsional dynamics of a planetary differential gears system are developed. In Fig. 2 x -axis is in the radial direction and the pi y -axis is in the tangential direction. The angular displacement of each gear is measured in the corresponding coordinate system, In this paper, the equations of motion of the planetary differential system are derived using Newton's laws in the non-inertial system. In the planetary gear section, as the sun gear, planetary gears and ring translation vibrations are all associated with the rotation of the carrier, the translational vibration acceleration of the planetary gears' components should contain not only the translational acceleration but also the centripetal accelerations, the Coriolis accelerations and the tangential accelerations of the carrier. For example, the position of the sun gear is s s s r x i y j   , and the translational acceleration of the sun gear is In the planetary differential system, since the speed of the carrier is not very high, the Coriolis acceleration 2 c s y can be neglected. Considering that there is a variable speed process in the differential system, the tangential acceleration of the carrier c s x   , c s y   is taken into account, so the translational vibration acceleration of the sun gear is VOLUME XX, 2017   [11] . In the fixed-axis gear section, the translational vibration acceleration of the fixedaxis gears contains only the translational acceleration, e.g., the position of gear 1 is 1 The equation of motion of the sun gear is as follows: The equation of motion of the ring is as follows: The equations of motion of the components of the fixed shaft gears are as follows: 1 The remaining equations for fixed shaft gear dynamics can be found in Ref. 13 which is not described here [13].
The member c is a composite member of the carrier and gear 4 and is subject to both the forces of the planetary gears on the carrier and the meshing forces of gear 7 and gear 3, with the following equations of motion:  is the support damping of the bearing to each member, 1 2 3 , , T T T is the input torque of the ring, gear 1 and gear 5 respectively, and also the load torque of the three motors, expressed as   The mechanical characteristics of the fan and pump loads are [24]: where  is the fan or pump speed, k is the fluid resistance torque coefficient, b is the viscous manufacturing resistance torque coefficient, c is the potential torque coefficient, a is the inertia torque coefficient, the steady state load torque is mainly determined by the fluid resistance torque of the fan/pump load, the expression is as follows: III. Model of the motor by the equivalent circuit method The motor acts as a hub connecting the power supply and mechanical part and in order to study the complete electromechanical coupling dynamic characteristics, it is necessary to model the electromagnetic dynamics of the motor. Currently, the most straightforward way to accurately model the motor is to use the finite element method for analysis, but when it comes to co-simulation with other systems, the finite element method becomes less practical. It is possible to decouple this by making reasonable assumptions and using a set of linear differential equations of the same order containing the voltage equation, the magnetic chain equation, and the electromagnetic torque equation to describe the electromagnetic dynamics of the motor [25] In this section, the Park transform is used to describe the motor by modeling the equivalent circuit in the motor rotating d-q coordinate system, the equivalent circuit is shown in Fig. 3 [26] .
where the subscripts d and q denote the d-axis quantities and q-axis quantities respectively, the subscripts s and r denote the stator and rotor quantities respectively, u, i, R is the voltage, current and resistance respectively, , r   are the rotor mechanical angular velocity and rotor electromagnetic angular velocity respectively, ѱ is the flux, and the equation for the flux of the stator and rotor is: Where , s r L L are the stator and rotor winding leakage inductance respectively and m L is the magnetizing inductance.
The generation of electromagnetic torque in a motor is essentially based on the interaction of magnetic flux and current and is given by the following equation : 1.5 ( ) ds qs e qs ds T is the electromagnetic torque and p is the number of poles in the motor.

IV. UNITS
As the auxiliary motor requires speed regulation, the auxiliary motor power supply needs to be regulated by an inverter. The principle is shown in Fig. 4, where the reference voltage and reference frequency required for system speed regulation is calculated through constant voltage to frequency (V/f) control, and the signal generated by sine pulse width modulation (SPWM) drives the inverter to generate the required inverter power to drive the motor and achieve speed regulation.  [19]. The voltage versus frequency of the auxiliary motor after considering the compensation voltage is as follows: Where N u is the rated voltage of the motor, N f is the rated frequency of the motor, 0 u is the voltage to compensate for the voltage drop of the stator resistance during starting. The operating curve of voltage and frequency is shown in Fig. 5. As can be seen from Fig. 5, below the rated frequency N f is V/f control, the flux basically remains the constant, above the rated frequency N f , the voltage does not increase with the frequency, for the constant power stage. The input to the SPWM is three sinusoidal reference voltages with a phase interval of 120 degrees. The triangular carrier signals u  are compared with the corresponding reference signals ref u to produce the gating signal for that phase, and the generation mechanism is shown in Fig. 6. The carrier signal is compared with the reference voltage , , a b c u u u to obtain 1 3 5 , , g g g ,respectively, and the nongetting 2 4 6 , , g g g of 1 3 5 , , g g g is taken, which together form the PWM waveform. The inverter consists of six power switching devices IGBTs [28], as shown in Fig. 7. The V/f control and SPWM output pulses are used to control the power switching devices IGBTs to turn on or off to adjust the output three-phase AC voltage and current magnitude, thus realizing the drive control of the load. Inverter model The inverted three-phase voltage after SPWM and inverter with the reference three-phase voltage is shown in Fig. 8. In this study, the dynamic model for the electromechanical coupled system consisting of inverter power supply, threephase asynchronous motors, differential planetary gear system and pump load is established. The dynamic characteristics of the coupled electromechanical system are analyzed under the conditions of start-up, steady-state, and speed regulation. The planetary differential gear system model considering time-varying meshing stiffness and damping was built in Matlab/Simulink by S-function. The gear model is connected with V/f control, SPWM generator, inverter and Asynchronous Machine in Matlab/Simulink, where the inverter generates the inverted voltage directly as an input to the motor, and the motor is connected to the gear system by electromagnetic torque and torque on the motor shaft with the following differential equations: where the subscript n=1,2,3 represents the main motor and the two auxiliary motors respectively, en T is the electromagnetic torque of the nth motor and n T is the load torque of the nth motor, for which the formula F is the coefficient of viscous friction and Mn  is the angle of rotation of the nth motor, as already given in Section 2.
The main parameters of the electromechanically coupled differential speed regulation system are as follows.

A. Start-up stage
In previous studies of electromechanical coupling, the influence of the inverter part was not considered and the power supply to the motor was simplified to an ideal threephase supply direct drive (DD). In the variable frequency drive (VFD), the voltage frequency of the starting process is gradually increased from 0 to the rated frequency. The ideal line voltage of the auxiliary motor is shown in Fig. 9(a) for both models of the variable frequency drive and the direct drive, where the amplitude and frequency of the voltage in the variable frequency drive are continuously increased under constant voltage to frequency ratio control (V/f), while the amplitude and frequency of the supply voltage in the direct drive are constant. Due to the inverter, the inverted line voltage is plotted against the ideal line voltage as shown in Fig. 9(b). The main motor starts under DD, the main motor starts under DD and the auxiliary motors are driven with VFD and DD. Driven by the drive voltage, the motor startup characteristics are shown in Fig. 10. As can be seen in Fig.  10(a), the electromagnetic torque of the auxiliary motor under VFD fluctuates more smoothly than DD until 0.2s, the time to reach the peak torque is shorter and the peak is lower than DD, as a result of the uniform rise in voltage and frequency of the supply using the VFD, but the presence of the inverter increases the harmonic content of the electromagnetic torque and makes it more volatile. The load torque of the motor is shown in Fig. 10(b). The load torque is the link between the gear system and the motor system, during the start-up process, the load torque on the motor shaft will produce shocks, and the shocks are produced earlier under VFD than DD, and the load torque vibration trend during the start-up process basically matches the electromagnetic torque. Fig. 10(c) shows the auxiliary motor speed. It can be seen that the motor speed takes less time to reach steady state with VFD than DD, and that there is a reduction and then increase in motor speed at 3.1s, which is related to the increase and then decrease in torque amplitude at 3.1s in Fig. 10(a) and Fig. 10(b). As can be seen in Fig.  10(d), the motor stator current is significantly lower than that of the DD during start-up, resulting in a smaller impact on the electrical network. From Fig. 10(a), (b) and (d) it can be seen that the amplitude of the electromagnetic torque, load torque and stator current keep growing steadily after violent fluctuations and reaches a steady state after 3s. This is caused by the fact that the main motor speed under DD is increasing as in Fig. 10(e) and the speed of the sun gear is increasing, resulting in the increasing system load torque as in Fig. 10(f) due to the load torque of the fan and pump being proportional to the square of the speed. During the start-up of the differential speed regulation system, the meshing forces between the fixed shaft gears and the planetary gears are shown in Fig. 11. Fig. 11(a) shows the meshing forces between gear 1 and gear 2 directly connected to the auxiliary motor, Fig. 11(b) shows the meshing forces between the sun gear and planetary gear 1, and Fig. 11(c) shows the meshing forces between the ring and planetary gear 1. These three meshing forces basically coincide with the overall trend in the start-up transient values, and the startup process before 1s shows that the system is preceded at peak and valley start-up values by VFD. During the period 1s-3s the meshing forces increase, this is due to the fact that the system speed is increasing and the load torque is rising, after 3s the VFD has a smaller peak compared to DD before reaching a steady state. After reaching a steady state, the time domain diagrams of the auxiliary motor supply line voltage for the two drive models are shown in Fig. 12(a), where the supply voltage in the VFD is the inverter voltage generated through the inverter and the supply voltage in the DD is the ideal sinusoidal voltage. The spectrum of the voltage is shown in Fig. 12(b), the power supply fundamental frequency 1 f is the dominant frequency, near 1 f the spectral characteristics of the two are basically the same, but at high frequencies, the ideal voltage approximates a smooth curve, the inverter voltage spectrum contains more harmonic components, which peaks at the modulation frequency meshing frequency harmonics and the inverter harmonic components. The motor stator current spectrum is shown in Fig. 13(d). The spectral characteristics are similar to those of the voltage spectrum in Fig. 12(b) but are smoother at higher frequencies than in Fig. 12(b), due to the electromagnetic effect of the motor, which attenuates the harmonic effects of the inverter. The above spectrum shows that the motor system is affected by the coupling of the gear mesh harmonics and the inverter harmonics, indicating that the relationship between the two should be fully considered when designing the system to avoid resonance between the two harmonics in close proximity. The gear meshing force at a steady state is shown in Fig.14. The peak meshing force at steady-state with variable frequency drive is slightly smaller than with direct drive, and no further difference can be seen in the meshing force timedomain diagram, which is analyzed in the meshing force spectrum below.

C. Speed-down stage
When the system meets the process requirements, the speed needs to be reduced, keep the main motor speed constant, through the constant voltage to frequency ratio control of the auxiliary motor voltage and frequency smoothly reduced, VFD and DD ideal line voltage as shown in Fig. 16 (a), the voltage amplitude and frequency change abruptly with DD and transition smoothly with VFD. The inverter voltage and the ideal voltage in the VFD are shown in Fig. 16 The dynamic characteristics of the motor during speed regulation are shown in Fig.17. As can be seen in Fig. 17(a), under direct drive, the voltage amplitude and frequency change abruptly, resulting in a large shock to the auxiliary motor electromagnetic torque, and there are also large fluctuations in amplitude after the shock, while under variable frequency drive the motor electromagnetic torque changes more smoothly, and the time required to reach steady state is short, and the fluctuations under steady state are small. As the electromagnetic torque decreases, the rotor speed of the auxiliary motor Fig. 17(c) also decreases. The speed changes more evenly and the time required to reach the new steady state is longer and less volatile under VFD, the time required to reach the steady state is shorter but more volatile under DD. The trends in motor load torque Fig.17(b) and electromagnetic torque Fig.17(a) largely coincide, with the load torque containing more vibrations and harmonics due to the electromagnetic effect of the motor attenuating the harmonics and vibrations of the electromagnetic torque. As can be seen in Fig. 17(d) for the auxiliary motor stator current, direct changes in voltage amplitude and frequency under DD cause the stator current to surge, while slow changes in voltage amplitude and frequency under VFD cause the current to vary more gently. During the auxiliary motor for speed regulation, the main motor rotor speed is shown in Fig.17(e), due to the auxiliary motor speed regulation process caused a load shock change, resulting in the main motor rotor speed also a shock, after the shock the main motor speed is slightly higher, caused by the main motor load torque reduction after speed regulation, the electromagnetic torque of the main motor is shown in fig.  17(f), after speed regulation the electromagnetic torque is reduced, the power is reduced, to achieve the purpose of energy-saving. During speed regulation, the gear meshing force changes as shown in Fig. 18. As the speed decreases, corresponding to lower system load torque, the meshing force between the gears also decreases. Fig. 18(a) shows the meshing force between the fixed shaft gear 1 and gear 2. The gear meshing force varies relatively smoothly under VFD, with no obvious shocks, which is a similar trend to the electromagnetic torque Fig. 17(a) and the load torque Fig. 17(b) of the auxiliary e motor. Fig. 18(b) shows the meshing force between the sun gear and planetary gear 1. The meshing force decreases smoothly under VFD, while a sudden change in meshing force resulting in shock can occur under DD. When the system speed needs to be increased, similar to the speed-down stage, the main motor is kept constant and the variable frequency drive smoothly increases the voltage and frequency of the auxiliary motor through constant voltage to frequency ratio control, and the direct drive changes abruptly to the target frequency. The ideal line voltage under both drives is shown in Fig. 19(a), the inverter voltage and the ideal voltage under VFD is shown in Fig. 19(b). The dynamic characteristics of the motor during the speedup process are shown in Fig. 20. As can be seen in Fig. 20(a), the electromagnetic torque of the auxiliary motor changes smoothly under VFD, while a temporary shock is generated under DD due to sudden changes in frequency. Fig. 20(b) shows the load torque of the auxiliary motor, with a similar trend to the electromagnetic torque, but with greater amplitude of vibration than in Fig. 20(a), due to the electromagnetic effect of the motor as mentioned in several processes above. Fig. 20 (c) shows the rotor speed of the auxiliary motor. Under DD, the rotor speed of the auxiliary motor appears to decrease and then increase at around 6.05s, which is related to the sudden change in torque in Fig.  20(a)(b), compared to the smooth change in speed under VFD. Fig. 20(d) shows the stator current of the auxiliary motor. As can be seen in fig. 19, the voltage and frequency increase from low to high to the rated value under both drives, but the amplitude of the motor's stator current increases to a peak value larger than the rated value and then decreases to the rated value, which is the similar trend as the load torque of the auxiliary motor in Fig. 20(b). It shows that the stator current is not only influenced by the amplitude and frequency of the power supply, but also by the mechanical load. During the speed-up of the auxiliary motor, the main motor rotor speed, as shown in Fig. 20 (e), fluctuates temporarily and then drops slightly, as a result of the fluctuation and then rise of the main motor load torque during speed regulation as shown in Fig. 20   The meshing forces during the speed-up process are shown in Fig. (21). During the speed regulation process, the direct drive will have a large shock at around 6.05s and 6.15s for all three meshing forces, and then tends to stable, which coincides with the impact of the auxiliary motor electromagnetic torque, load torque, main motor rotor speed and electromagnetic torque, and it is the impact of the motor electromagnetic torque that causes the impact of the gear meshing forces. After the speed increase, the vibration amplitude of the three meshing forces is more intense than before the speed regulation, indicating that the choice of system speed is very important for the vibration characteristics of the electromechanically coupled system.

VI. Conclusions
In the dynamic analysis of electromechanical systems, it is important to accurately model the whole system and to analyze the dynamic characteristics of the steady state and transients for design improvement and health monitoring. In this paper, the electromechanical coupled system model with inverter power supply, three-phase induction motor, differential planetary gears and load is established. The differences of the dynamic characteristics of the electromechanical system under the variable frequency drive (VFD) model and the direct drive (DD) model are investigated, where the VFD model includes constant voltage to frequency ratio control, sinusoidal pulse width modulation (SPWM) and inverter, and the DD model is a simplified model considering an ideal power supply. The dynamic characteristics of the electromechanical coupling of the system during the start-up, steady-state, speed-down and speed-up stages are analyzed. With the VFD model, the drive voltage of the three-phase asynchronous motor is more complex and contains more harmonics due to the presence of the SPWM and inverter. In the start-up stage, the induction motor of the VFD model reaches steady state faster and fluctuates more smoothly than the DD model, but the electromagnetic torque under VFD model contains more harmonic components, and the time domain meshing forces of the gear system do not differ much, both vibrating first and then steadily increasing to steady state values. During the speed regulation stage, the frequency and voltage of the supply are uniformly changed under VFD model, making the process smooth and with relatively low shock vibration. Compared to DD model, the VFD model reflects the transient dynamic characteristics of the system in a more realistic and rational form. In the steady state stage, we can see from the auxiliary motor electromagnetic torque spectrum diagram that the motor is affected by the coupling of the inverter harmonics in the power supply section and the gear meshing harmonics in the mechanical section. The VFD model has a richer harmonic component than the DD model, which is reflected in the electromagnetic torque, motor rotor speed, stator current, and the gear meshing forces directly connected to the auxiliary motor. This indicates that the interaction between the carrier frequency and the fundamental frequency of the power supply section and the gear meshing frequency of the mechanical section should be fully considered when designing the planetary gear or selecting the inverter. A suitable speed should also be selected to avoid resonance due to the similarity of the harmonic frequencies of the two.