Simplified V/f Control Algorithm for Reduction of Current Fluctuations in Variable-Speed Operation of Induction Motors

: This paper introduces a straightforward control strategy aimed at the reduction of current fluctuations within the low-frequency domain of open-loop V/f control in induction motor drives. Traditional control techniques necessitate the addition of a current compensator based on motor parameters and the use of digital filters such as band-pass or high-pass filters. These methods, however, rely on precise motor parameters and involve complex filter design and implementation. The proposed control is capable of suppressing current fluctuations without controlling the slip of the induction motor. The proposed control strategy generates the forced rotation angle and command input voltage using the V/f block and outputs the d-axis voltage using a proportional integral controller to keep the d-axis current constant at zero. The difference between the command input voltage and the d-axis voltage is applied as the q-axis voltage and then applied through SVPWM. In order to verify the effectiveness of the proposed control, the proposed control is implemented and analyzed using power simulation based on the results of the analysis of the causes of current fluctuations in the induction motor. Finally, the effect of suppressing current fluctuations of the induction motor is verified through experimental results. In the 10~19 Hz range, where the conventional V/f control method resulted in current fluctuation rates exceeding 10% and peaking at 113.3% at 13 Hz, the proposed method suppressed the fluctuation rate to below 8.6% across all frequencies. This paper validates the effectiveness of the proposed control strategy through these results.


Introduction
In response to the escalating concerns about climate change and its potentially devastating effects, regulations are being fortified on a global scale.This international cooperative effort aims to not only mitigate the impacts of climate change but also stabilize the global climate system.As a direct consequence of these strengthened regulations, there has been a surge in research activities focusing on electrification systems in the industrial sector [1][2][3].This research is pivotal in transitioning towards more sustainable and energy-efficient industrial practices.Among the various components of these electrification systems, induction motors stand out as a representative example among AC motors.
The characteristics of induction motors make them particularly useful in many industrial fields [4][5][6][7][8][9].One of the key features of induction motors is their ability to operate at a constant speed without the need for a separate drive for operation.This simplifies the motor design and reduces the complexity of the motor control systems.However, while the ability to operate at a constant speed can be advantageous in certain applications, it also presents a challenge.Specifically, when induction motors operate at a constant speed under varying loads, it can result in significant energy loss.This is because the motor may be operating at a higher speed than necessary for the given load, leading to unnecessary energy consumption.To address this issue, drives are applied to induction motors to enable variable-speed operation [10][11][12][13][14].By allowing the motor speed to vary according to the load, these drives can significantly improve the energy efficiency of the system.Therefore, the research and development of these drives and their integration into induction motors is an active area of research, driven by the global push towards energy efficiency and sustainability.
In situations where a high degree of dynamic performance is necessitated, closed-loop control methodologies such as field-oriented control (FOC) or direct-torque control (DTC) are predominantly employed [15][16][17][18][19].These control methodologies are highly effective in optimizing the performance metrics of induction motors, ensuring stability under a wide array of load conditions.They achieve this by continuously monitoring the system's output and adjusting the input accordingly, thereby maintaining a desired system behavior.However, the implementation of such sophisticated control strategies requires a drive system that encompasses high-performance micro-controller units (MCU), a variety of sensors, and passive components.These elements, while integral to the functionality of the control system, contribute to an increase in the overall cost of the system.This cost factor can be a significant deterrent in certain applications, particularly those that are cost-sensitive.
To circumvent issues such as cost escalations, open-loop control is often preferred over closed-loop control in certain applications.In an open-loop system, the control action is independent of the output.This means that the system does not adjust itself based on the output, which simplifies the control mechanism.A representative example of an open-loop control method is V/f control.This method is particularly advantageous as it significantly reduces implementation costs because it does not necessitate the use of sensors and high-performance MCUs [20][21][22][23][24].This makes V/f control a cost-effective solution for controlling induction motors.
V/f control finds its application in systems such as pumps and fans, where the load torque is proportional to the square of the operating frequency [25].This relationship between load torque and operating frequency makes V/f control an ideal choice for these applications.However, in light-load and low-speed environments, V/f control can lead to continuous vibrations.These vibrations can cause seriously distorted output currents, leading to thermal damage due to overcurrent in the motor and potential damage to the power semiconductors in the drive [26].This is a significant concern as it can lead to system failure and costly repairs.
The vibration stability of V/f control was evaluated by providing global convergence stability conditions.These conditions are in relation to motor parameters, operating slip, and synchronous frequency.The evaluation was based on small-signal linearization and pole-position evaluation using the frequency-voltage plane or the torque-frequency plane [27][28][29][30].This evaluation provides valuable insights into the stability of the system under various operating conditions and can guide the design of more stable and reliable control systems.
The conventional solution to suppress vibration, a common issue in the operation of induction motors, is to apply active damping technology.This technology is fundamentally based on current feedback, a method that uses the motor's current to adjust its operation and reduce vibrations.This approach has been widely adopted due to its effectiveness and simplicity.
In reference [29], a specific implementation of this solution is discussed.Here, two proportional integral (PI) controls are used.These controls take the current magnitude and angle as input.Based on these inputs, the controls adjust the amplitude and frequency of the stator voltage.This adjustment allows the motor to operate more smoothly, reducing vibrations and improving overall performance.A similar PI approach is implemented in [30].In this case, the differential current, which is the difference between the actual and desired current, influences the amplitude of the stator voltage.By adjusting the stator voltage based on the differential current, the system can effectively control the motor's operation, leading to improved performance and reduced vibrations.
In [8], the direct-axis current is filtered with a band-pass filter (BPF).This filter allows only a specific range of frequencies to pass through, effectively filtering out unwanted noise and fluctuations.At low speeds, the output of the BPF alters the amplitude of the stator voltage, while at high speeds, it changes the frequency.This dynamic adjustment of the stator voltage helps to maintain stable motor operation across a wide range of speeds.
In [31], both the direct-axis current and quadrature-axis current are sent to a BPF.The filtered values are then used to adjust the frequency of the stator voltage.This method allows for precise control of the stator voltage frequency, leading to improved motor performance.In [32], the same scheme as [31] is used, but a high-pass filter (HPF) is used instead of a BPF.The HPF allows only frequencies higher than a certain cutoff frequency to pass through.This can be particularly useful in applications where it is necessary to eliminate low-frequency noise and fluctuations.
In [33], various strategies are tested.The HPF is applied to the quadrature-axis current and used to modify the direct-axis voltage, an HPF is applied to the direct-axis current and used to modify the quadrature-axis voltage, and finally, an HPF is applied to the direct-axis current and used to modify the voltage frequency.These various strategies provide valuable insights into the effectiveness of different control methods and can guide the development of more effective and efficient motor control systems.
All of these methods share a common foundation in that they are built upon the concept of compensation control.This type of control is fundamentally based on the parameters of the induction motor, such as its electrical and mechanical characteristics.By adjusting the control inputs based on these parameters, compensation control can effectively manage the operation of the motor and mitigate any undesirable behaviors.However, these methods also involve the use of BPFs and HPFs.These filters are used to process the motor's current and voltage signals, filtering out unwanted noise and fluctuations.While these filters can significantly improve the performance of the control system, they also add a level of complexity to the control algorithms.
This complexity can lead to an increase in computational time, particularly when complex mathematical formulas are involved.This increase in computational time presents a significant challenge when attempting to implement these control methods with low-cost MCUs.These MCUs typically have low clock speeds and limited storage spaces, making them ill-suited for complex computations.As a result, the implementation of these control methods on low-cost MCUs can be a challenging task.
In light of these challenges, this paper proposes a simplified V/f control that can be readily applied in low-cost MCUs.The primary objective of this control strategy is to mitigate the current fluctuations that occur at low operating frequencies.These fluctuations are commonly observed within the variable speed range of induction motors and can lead to unstable motor operation and reduced performance.By effectively mitigating these current fluctuations, the proposed V/f control presents a cost-effective solution for enhancing the performance and reliability of induction motors.This is particularly beneficial in low-frequency operations, where current fluctuations can be particularly problematic.
The simplicity of the proposed control strategy also means that it can be easily implemented on low-cost MCUs, making it a practical solution for a wide range of applications.In conclusion, while traditional control methods based on compensation control and the use of BPFs and HPFs can be effective, they also present challenges in terms of computational complexity and implementation on low-cost MCUs.The proposed V/f control addresses these challenges by offering a simplified and cost-effective solution that enhances the performance and reliability of induction motors, particularly in low-frequency operations.

Dynamic Equations of the Stator Current of an Induction Motor
The stator current dynamic characteristic equation of an induction motor can be expressed in the form .
x = Ax + Bu as follows [8]: where σ is 1 − (L m 2 /L s L r ), L s , L r , and L m are stator, rotor, and mutual inductances, R s is stator resistance, ω e is electrical angular velocity of the stator, i ds and i qs are the d-axis and q-axis stator currents, λ dr and λ qr are the d-axis and q-axis rotor fluxes, and v ds and v qs are the d-axis and q-axis stator voltages in the synchronous reference frame.For FOC and DTC, the λ qr is 0 and the λ dr is the same as the λ r , and they are maintained constant.In general V/f control, it is not possible to control the transient-state operation of the induction motor because the input voltage and operating frequency of the induction motor are controlled proportionally.Therefore, the dynamic equation in the steady state (d/dt = 0) of V/f control can be expressed as follows: The command values of v * ds and v * qs for general V/f control using Equations ( 3) and (4) can be expressed as follows: where the superscript * indicates the command value, V qs,max = ω * b L s i * ds is the maximum value of v qs , ω b is the base frequency, and ω * e is the frequency command value of the stator.In [8], a current compensator was added based on the above equation and proposed as follows: where k 1 and k 2 are the gains of the dynamic compensator and τ is a time constant of a low-pass filter circuit.This control method is effective in suppressing current fluctuations, but the formula is complex and the problem is that the selection of gain values depends on the parameters of the induction motor.The simplified V/f control based on dynamic current proposed in this paper can be expressed as follows: where k p and k i are the proportional and integral gains of the PI controller for i ds .v * s is the command value of the stator input voltage, e(t) is the difference between the command value of i * ds and the feedback value of i ds , and s is the Laplace operator.Compared to conventional V/f control, the proposed method allows for reduced computation time on the MCUs by utilizing simplified equations.

Proposed Control for Current Fluctuation Suppression
Figure 1 shows the control block diagram for current fluctuation suppression in an induction motor based on the proposed Equations ( 9) and (10).Controlling i ds to remain constant ensures that the air gap flux is maintained at a steady level, allowing for the suppression of current fluctuations during transient states.
When the command frequency f * s is applied to the V/f curve block, a forced rotation angle θ* and command input voltage are outputted.By measuring the phase currents of the two-phase stator of the inverter and performing dq transformation based on the forced rotation angle, i ds is calculated.Together with i * ds = 0, it is controlled via a PI controller.The output value of the d-axis PI controller becomes v * ds .v * qs is calculated by taking the square root of the difference between the squared v * s and the squared v * ds .v * ds and v * qs are converted into input phase voltages v a , v b , and v c through dq-to-abc transformation using the forced rotation angle and input into SVPWM (space vector pulse width modulation).
using the forced rotation angle and input into SVPWM (space vector pulse width modulation).
The proposed control strategy is designed with a specific objective in mind to maintain the d-axis current at zero.This is a critical aspect of the control strategy as it simplifies the control process and reduces the need for complex calculations.By keeping the d-axis current at zero, the need for precise tracking of the slip and rotor angle is eliminated.This is a significant advantage as tracking these parameters accurately can be challenging and prone to errors.Therefore, by eliminating the need for tracking, the control strategy becomes more robust and less susceptible to inaccuracies.

Relationship between Rotor Moment of Inertia and Electromagnetic Torque of Induction Motor
The electromagnetic torque equation of the induction motor in the dq-axis coordinate system can be expressed as follows.The proposed control strategy is designed with a specific objective in mind to maintain the d-axis current at zero.This is a critical aspect of the control strategy as it simplifies the control process and reduces the need for complex calculations.By keeping the d-axis current at zero, the need for precise tracking of the slip and rotor angle is eliminated.This is a significant advantage as tracking these parameters accurately can be challenging and prone to errors.Therefore, by eliminating the need for tracking, the control strategy be-comes more robust and less susceptible to inaccuracies.

Relationship between Rotor Moment of Inertia and Electromagnetic Torque of Induction Motor
The electromagnetic torque equation of the induction motor in the dq-axis coordinate system can be expressed as follows.
The electromagnetic torque equation of induction motors considering the mechanical load can be expressed as follows: where J is the rotor moment of inertia, and ω m is the mechanical angular velocity.From Equations ( 11) and (12), it becomes evident that the electromagnetic torque of the induction motor is susceptible to variations contingent on the value of J, which symbolizes the rotor moment of inertia.This highlights the pivotal role that J assumes in modulating system dynamics, potentially instigating oscillations in performance metrics.Consequently, to conduct an exhaustive exploration of this phenomenon, a pair of induction motors, characterized by identical electrical parameters but divergent moments of inertia, were judiciously selected, as expounded in Table 1.The induction motor was modeled and the effectiveness of the proposed control was validated using PSIM 10, a simulation package that excels in interpreting power electronics and motor control circuits.Figure 2 represents the three line-to-line voltages v ab , v bc , and v ca , three-phase currents i a , i b , and i c , d-axis and q-axis currents i d and i q , speed n, and electromagnetic torque T e when a 44 V, 12 Hz three-phase sinusoidal line-to-line voltage is applied to models A and B, which have different rotor moments of inertia.In the case of Model A, the average root-mean-square (RMS) value of the three-phase current is 3.11 A, and it can be confirmed that there is no variation in each phase current.Since there is no fluctuation in the three-phase current, i d is −4.35A and i q is 6.45 A, remaining stable along with the DC components.The magnitude of the d-axis current and q-axis current is determined by the position of the rotor, which is tracked based on slip.These currents serve a vital role in the operation of the motor and their values can significantly affect the electromagnetic torque performance of the motor.When compared to Model A, it can be observed that in Model B, the maximum value of the three-phase current increases up to 8.35 A, indicating approximately 2.25 times greater current fluctuations.The peak-to-peak values of the d-axis and q-axis currents are 5.47 A and 8.05 A, respectively, indicating significant pulsations.Consequently, the peak-to-peak values of the speed and electromagnetic torque are 7.1 rpm and 4.62 Nm, respectively, confirming the occurrence of ripple.As a result, the d-axis and q-axis currents become unstable, ultimately leading to pulsations in the speed and electromagnetic torque.These phenomena eventually manifest as vibrations, thereby inducing instability in the motor drive system.
As shown in Figure 3a, when a line-to-line voltage proportional to the frequency is applied, the peak-to-peak value of the phase current, as depicted in Figure 3b, increases from 8 Hz to 16 Hz, with the highest point observed at 12 Hz.To examine the fluctuation rate for each frequency, the formulas for the current fluctuation rate i fluctuation in Figure 3c and speed fluctuation n fluctuation rate in Figure 3d can be expressed as follows: where i abnormal is the abnormal current, i normal is the normal current or no-load current, n max and n min are the maximum and minimum speeds of the motor, respectively, and n avg is for the average speed of the motor.The frequency range in which current fluctuation occurs is from 8 Hz to 16 Hz, and the point with the highest current fluctuation rate is at 12 Hz, where the peak-to-peak value of the phase current is 16.8 A, accounting for 90.72%.In terms of the speed fluctuation rate, the highest point is 11.31% at 10 Hz. and nmin are the maximum and minimum speeds of the motor, respectively, and navg is for the average speed of the motor.
The frequency range in which current fluctuation occurs is from 8 Hz to 16 Hz, and the point with the highest current fluctuation rate is at 12 Hz, where the peak-to-peak value of the phase current is 16.8 A, accounting for 90.72%.In terms of the speed fluctuation rate, the highest point is 11.31% at 10 Hz.

Simulation Results Using PWM Inverter
The control block diagram proposed in Figure 1 was implemented in the PSIM simulation circuit as shown in Figure 4a.The induction motor model with parameters of Model B was connected to the output terminals of a three-phase inverter.The switching frequency of the six IGBTs inside the inverter was set to 8 kHz, and the control interrupt period was set to 0.125 ms, which is the inverse of the switching frequency.All blocks in

Simulation Results Using PWM Inverter
The control block diagram proposed in Figure 1 was implemented in the PSIM simulation circuit as shown in Figure 4a.The induction motor model with parameters of Model B was connected to the output terminals of a three-phase inverter.The switching frequency of the six IGBTs inside the inverter was set to 8 kHz, and the control interrupt period was set to 0.125 ms, which is the inverse of the switching frequency.All blocks in the simulation circuit operate synchronously with the interrupt period.When the command frequency is input to the frequency ramp, a reference frequency with a slope of 6 Hz per second is outputted.According to the traditional V/f curve, where the command frequency R_Freq is input to the V/f generator, the output phase voltage Vs and frequency Fout are produced.These values are inputted into the Forced Rotating Angle Generator to produce the forced electrical rotation angle FRA.The FRA is utilized as the angle for abc-to-dq transformation and dq-to-abc transformation.In the proposed control block, the PI controller is configured to maintain a constant d-axis feedback current id_P, calculated from the abc-to-dq transformation using the measured two-phase currents.The output of the PI controller is the d-axis voltage vd.The q-axis voltage is calculated as the square root of the difference between the square of vs and the square of vd.The outputted vd and vq are transformed back to phase voltages va, vb, and vc through abc-to-dq transformation and then inputted to the SVPWM block.The three outputs of the SVPWM block are transformed into six PWM waveforms through comparators and fed into the gate inputs of the six IGBTs inside the inverter.
Figure 4b,c presents a comparison of the output characteristics of Model B at the frequencies of 11 Hz and 12 Hz applied to a PWM inverter.When the proposed control is not applied, unstable fluctuations occur in phase current i a_without , d-axis current i ds_without , electromagnetic torque T e_without , and speed n without .Compared to the results without the proposed control, the proposed control shows stable output characteristics in phase current i a_with , d-axis current i ds_with , electromagnetic torque T e_with , and speed n with .Figure 5 represents a comparative analysis of simulations without and with the proposed control applied to a PWM inverter, depending on the frequency.In Figure 5a, without the proposed control, the current fluctuation rate is over 10% in the 8~20 Hz range, and the maximum current fluctuation rate is 166.48% at 15 Hz.When the proposed control Figure 5 represents a comparative analysis of simulations without and with the proposed control applied to a PWM inverter, depending on the frequency.In Figure 5a, without the proposed control, the current fluctuation rate is over 10% in the 8~20 Hz range, and the maximum current fluctuation rate is 166.48% at 15 Hz.When the proposed control is applied, it can be confirmed that the current fluctuation rate is attenuated to 1.5~3.6% in all frequency ranges.Figure 5b is a curve comparing the speed fluctuation rate.The existing control increased up to a maximum of 20.7% at 10 Hz, but in the case of the proposed control, it was confirmed to be within 0.35% in all frequency ranges.

Experimental Results
Figure 6 illustrates the experimental setup for measuring the current fluctuation rate to validate the effectiveness of the proposed control.The phase current was measured Figure 5c is a curve comparing the current reduction rate without and with the proposed control.The formula for the current reduction rate is as follows: where i without is the peak-to-peak value of the phase current when the proposed control is not applied, and i with represents the peak-to-peak value of the phase current when the proposed control is applied.The current fluctuation reduction is achieved in the range of 8 Hz to 20 Hz, and the frequency with the largest reduction rate is 15 Hz, which is 196.84%.In other frequency ranges, it means that there is no current fluctuation.Figure 5d shows the results of the harmonic analysis of electromagnetic torque at 11 Hz and 12 Hz.For 11 Hz, the highest electromagnetic torque magnitude is 3.25992 Nm at 3 Hz, and for 12 Hz, it is 4.10676 Nm at 4 Hz.When the proposed control is applied, it can be confirmed that the operation is stable as no magnitude occurs in all frequency ranges of the harmonic analysis results of 11 Hz and 12 Hz.These values ultimately cause vibration and noise in the induction motor, leading to system instability.

Experimental Results
Figure 6 illustrates the experimental setup for measuring the current fluctuation rate to validate the effectiveness of the proposed control.The phase current was measured using an oscilloscope according to the frequency in a no-load condition of a 746 W induction motor.The frequency range in which current fluctuations occur was confirmed as shown in Figure 7, increasing by 1 Hz from 10 Hz to 19 Hz.The area where current fluctuations occur is from 10 Hz to 19 Hz, and this frequency range can vary depending on the parameter changes due to the temperature of the motor and the change in inertial load due to the transient state of speed.Figure 8 demonstrates the stability of the phase current across frequencies when the proposed control is applied.(i) (j) Table 2 represents the fluctuation rate of the phase current when the phase current is selected as the normal current according to the frequency when FOC control is applied.In FOC control, the d-axis current is set based on the parameters of the induction motor.In this experiment, the peak-to-peak value of no-load current was derived as 8.57A using the auto-tuning function of the Yaskawa A1000 drive (Yaskawa, Fukuoka, Japan).Using Equation ( 13), it was confirmed that the current fluctuation was suppressed to within approximately 8% ± 0.6%.The presence of a current fluctuation rate is due to the difference caused by the limitations of ADC and operation control resolution due to the use of a lowcost MCU.However, this difference is not significant, and the results sufficiently validate the effectiveness of the proposed control.

Conclusions
This paper presents a novel, simplified, and highly effective control strategy specifically designed for suppressing current fluctuations in the low-frequency range of openloop V/f control in induction motor drives.The strategy is devised and involves applying the command frequency to the V/f curve block.This block, in turn, outputs two crucial parameters: the forced rotation angle and the command input voltage.
The inverter, a key component in the system, measures the phase current of the twophase stator.It then performs the dq transformation, a mathematical operation that is based on the stator's forced rotation angle.This transformation is used to calculate the daxis current, a critical parameter in the control of the motor.This calculated d-axis current is then regulated to zero using a PI controller.The output of this controller becomes the Table 2 represents the fluctuation rate of the phase current when the phase current is selected as the normal current according to the frequency when FOC control is applied.In FOC control, the d-axis current is set based on the parameters of the induction motor.In this experiment, the peak-to-peak value of no-load current was derived as 8.57A using the auto-tuning function of the Yaskawa A1000 drive (Yaskawa, Fukuoka, Japan).Using Equation ( 13), it was confirmed that the current fluctuation was suppressed to within approximately 8% ± 0.6%.The presence of a current fluctuation rate is due to the difference caused by the limitations of ADC and operation control resolution due to the use of a lowcost MCU.However, this difference is not significant, and the results sufficiently validate the effectiveness of the proposed control.

Conclusions
This paper presents a novel, simplified, and highly effective control strategy specifically designed for suppressing current fluctuations in the low-frequency range of open-loop V/f control in induction motor drives.The strategy is devised and involves applying the command frequency to the V/f curve block.This block, in turn, outputs two crucial parameters: the forced rotation angle and the command input voltage.
The inverter, a key component in the system, measures the phase current of the two-phase stator.It then performs the dq transformation, a mathematical operation that is based on the stator's forced rotation angle.This transformation is used to calculate the d-axis current, a critical parameter in the control of the motor.This calculated daxis current is then regulated to zero using a PI controller.The output of this controller becomes the d-axis command voltage.The output of this controller is designated as the d-axis command voltage, and the q-axis command voltage is determined by the difference between this command voltage and the command input voltage.This q-axis command voltage is then input to SVPWM through the αβ transformation.One of the significant advantages of this proposed method is that it does not require complex formulas to track the slip of the induction motor.This simplifies the control strategy and makes it more robust and easier to implement.The method has been proven to effectively suppress current fluctuations, enhancing the stability and performance of the motor.Experimental results provide strong evidence of the effectiveness of the proposed method.The results show that the proposed method reduces current fluctuation rates to below 8.6% across all frequencies in the 10~19 Hz range.This is a substantial improvement from the over 10% and up to 113.3% fluctuation rates observed without the proposed control.The simplicity of the proposed method, which does not require precise motor parameters or complex filter design and implementation, makes it a practical solution for enhancing the stability of induction motor drive systems.Furthermore, the proposed control, composed of simpler equations and devoid of digital filters, can reduce the computation time of the MCU, enabling the use of low-cost MCUs.This is a significant advantage in cost-sensitive applications.Future research will focus on suppressing current fluctuation rates under load conditions across all frequency ranges and further reducing current fluctuation rates.This will further enhance the performance and reliability of induction motor drive systems, contributing to the development of more efficient and sustainable industrial systems.

Figure 1 .
Figure 1.Control block diagram of the proposed V/f control.

Figure 1 .
Figure 1.Control block diagram of the proposed V/f control.

Figure 2 .
Figure 2. Comparison of output characteristics according to the rotor moment of inertia: (a) Model A; (b) Model B. When compared to Model A, it can be observed that in Model B, the maximum value of the three-phase current increases up to 8.35 A, indicating approximately 2.25 times

Figure 2 .
Figure 2. Comparison of output characteristics according to the rotor moment of inertia: (a) Model A; (b) Model B.

Figure 3 .
Figure 3. Output characteristics of the modeled induction motor according to frequency: (a) line-to-line voltage; (b) peak-to-peak value of phase current; (c) current fluctuation rate; (d) speed fluctuation rate.
Energies 2024, 17, x FOR PEER REVIEW 11 of 20 electromagnetic torque Te_without, and speed nwithout.Compared to the results without the proposed control, the proposed control shows stable output characteristics in phase current ia_with, d-axis current ids_with, electromagnetic torque Te_with, and speed nwith.

Figure 4 .
Figure 4. Simulation results of proposed control: (a) simulation circuit of Model B and inverter considering load; (b) output characteristics of the induction motor without and with proposed control at 11 Hz; (c) output characteristics of the induction motor without and with proposed control at 12 Hz.

Figure 5 .
Figure 5. Comparative analysis of the results depending on the presence or absence of the proposed control in the frequency range where current fluctuations occur: (a) current fluctuation rate; (b) speed fluctuation rate; (c) current reduction rate; (d) harmonic analysis of electromagnetic torque.

Energies 2024 ,
17,  x FOR PEER REVIEW 15 of 20 using an oscilloscope according to the frequency in a no-load condition of a 746 W induction motor.The frequency range in which current fluctuations occur was confirmed as shown in Figure7, increasing by 1 Hz from 10 Hz to 19 Hz.The area where current fluctuations occur is from 10 Hz to 19 Hz, and this frequency range can vary depending on the parameter changes due to the temperature of the motor and the change in inertial load due to the transient state of speed.Figure8demonstrates the stability of the phase current across frequencies when the proposed control is applied.

Energies 2024 ,
17,  x FOR PEER REVIEW 15 of 20 using an oscilloscope according to the frequency in a no-load condition of a 746 W induction motor.The frequency range in which current fluctuations occur was confirmed as shown in Figure7, increasing by 1 Hz from 10 Hz to 19 Hz.The area where current fluctuations occur is from 10 Hz to 19 Hz, and this frequency range can vary depending on the parameter changes due to the temperature of the motor and the change in inertial load due to the transient state of speed.Figure8demonstrates the stability of the phase current across frequencies when the proposed control is applied.

Table 1 .
Parameters of two induction motors with different rotor moments of inertia.

Table 2 .
Experimental results of current fluctuation rate depending on frequency without and with proposed control.

Table 2 .
Experimental results of current fluctuation rate depending on frequency without and with proposed control.