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Harmonic current suppression method of virtual DC motor based on fuzzy sliding mode

  • Lisha Shang EMAIL logo , Yajuan Jia , Liming Zheng and Gaoshang Xie
Published/Copyright: December 31, 2023
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Open Physics
From the journal Open Physics Volume 21 Issue 1

Abstract

In the operation of power grid, the low frequency subharmonics in power lines are easy to cause harmonic current problems. A harmonic current suppression method is constructed based on fuzzy sliding mode and virtual DC motor (VDC). First, the adaptive linear network is introduced to compare and analyze the output value and the actual value in the power line, and the possible harmonic current is obtained, which is detected and discretized. After that, this study adopts Fuzzy sliding mode control (FSMC) strategy for VDC, uses FSMC to participate in on-off control of VDC, and then realizes the suppression of harmonic current in VDC ports. In addition, the model also uses the circuit superposition theorem and the amount of harmonic data to be compensated by FSMC. The whole method uses VDC control technology to ensure the voltage stability of DC bus and load side when the load changes. In this physical experiment, harmonic current generated by load disturbance is eliminated by reducing DC harmonic voltage, so as to achieve the suppression of DC port harmonic current. Experimental results show that the third and fifth harmonics in power lines can be eliminated by this method to a large extent. Therefore, the proposed method can accurately detect and eliminate the harmonic current caused by sudden load change, and then realize the suppression of VDC harmonic current.

Keywords: fuzzy sliding mode control; VDC; harmonic current suppression; ADALINE; voltage stability

1 Introduction

With the vigorous promotion of distributed power generation such as photovoltaic, wind power, and energy storage, and the increasing proportion of DC load in power terminals, DC microgrid has begun to attract people’s attention and achieved great development [1]. However, in the DC microgrid, all distributed power supplies, energy storage devices, and loads are connected to the DC bus through the power electronic converter, which lacks inertia and damping [2]. When the load power in DC microgrid fluctuates, the instantaneous voltage impulse and fluctuation have a great impact on the DC bus voltage, which is not conducive to the stable operation of DC microgrid [3]. virtual DC motor (VDC) is a new technology which can control DC bus voltage smoothly and stably with the development of virtual synchronous machine (VSM). VDC technology can ensure the dynamic stability of the power grid system, and its realization premise is that the voltage and current of the power grid do not exist in harmonics, otherwise it is difficult to achieve the stable output of the load voltage by stabilizing the DC voltage. However, the interface between the VDC and the power line generally has low-order harmonics, which will cause the same frequency harmonics to enter the grid current. Therefore, the stability of power grid is closely related to harmonic content. For the power grid harmonic suppression methods, many scholars have made a discussion. Currently, most foreign scholars use multiple rectifiers, proportional resonance and other methods to suppress harmonic current. Although some research results on harmonic current suppression have been obtained, these methods generally have problems such as poor harmonic current suppression effect and unchanged operation [4,5]. Fuzzy sliding mode control (FSMC) is a control method combining fuzzy control (FC) and sliding mode control (SMC), which is mainly used to control complex objects effectively in uncertain environment. FSMC system has the advantages of high efficiency and robustness for uncertain nonlinear systems. To solve the above problems, this study tries to combine FSMC with VDC technology to ensure the stability of DC voltage and load side voltage during power generation. The innovations of this research are as follows: (1) Adaptive linear network (ADALINE) is introduced into VDC technology to detect harmonics. (2) Adopt FSMC control strategy, use FSMC to participate in on-off control VDC, and then realize the suppression of harmonic current at VDC ports. The disturbance of nonlinear load is compensated by fuzzy sliding mode method to keep the current and voltage constant. The aim of this study is to promote the rapid development of VDC and provide guarantee for the stable operation of power grid.

2 Related work

VDC technology is mainly applied to improve the stability of DC side voltage. In recent years, many scholars have discussed this issue. Liu et al. [6] suggested a commutation deviation correction method on the bias of VDC technology. This method aimed to reach optimal current commutation. In addition, a DC bus electrical reconstructor is proposed to remove the waveform distortion’s effect. The test proved the availability of the method for sensorless high-accuracy error correction and optimal current commutation of DC motors. Zhao et al. [7] observed that the necessary condition for efficient operation of brushless current motor was to achieve accurate commutation signal. Therefore, this experiment proposed a new method based on virtual zero-line voltage. This method could show higher compensation accuracy and faster compensation speed without current sensor. At last, the method’s availability was tested on the 80WBLDC motor. Yang et al. [8] carried out research on high-speed brushless DC motor. The experiment aimed to explore the driving method of wireless sensor based on virtual third harmonic back EMF. An envelope of virtual third harmonic back EMF based on oversampling point technique was proposed experimentally. In addition, this study also constructed a new method to suppress negative effects. All the theories proposed in the experiment had been verified on the 60,000 rpm BLDC drive platform. To enhance the inertia of the DC microgrid, Zhi et al. [9] proposed a VDC combining the state of charge and the distributed energy storage system. This method balanced power consumption and state of charge by adding the charging and discharging power and state of charge of each energy storage unit to the armature resistance. Finally, the experiment verified that the improved VDC can enhance the DC bus voltage’s transient steadiness by testing the DC microgrid. Yan et al. [10] found that when the traditional Vienna rectifier was connected to the interface of the electric vehicle charger, it had high requirements for voltage stability. Therefore, it was proposed to apply virtual synchronous motor to Vienna rectifier to improve the adaptability of power grid to large-scale access of electric vehicles. The model built in the experiment could improve the inertia and damping at the interface, and ensured that the vehicle could realize fast charging while improving the stability of the power grid.

FSMC is a control method, which combines FC and SMC. It is mainly applied to effectively control complex objects in uncertain environment. FSMC has the advantages of both FC and SMC, and has good robustness to external interference. In recent years, many researchers in the field of scientific research have begun to study this. Qu et al. [11] proposed a FSCM for wireless sensor networks, aiming at the problem that wireless sensor networks are vulnerable to congestion. This method was able to adaptively balance the queue length of the blocking node buffer, thus reducing external interference. A large number of results indicated that the constructed model had higher convergence speed and higher throughput, and could adapt to the change in queue length. To further enhance the network bandwidth utilization of networked control systems, Wang et al. [12] established a new FSMC. The sliding surface could ensure the accessibility by synthesizing SMC laws. In addition, to guarantee the asymptotic steadiness of sliding module mechanics, the necessary and sufficient conditions were established by using convex optimization theory and Lyapunov method. The final checking results verified the feasibility of this method. Wu et al. [13] proposed a new backstepping FSMC and applied it to the trajectory tracking process of differential wheel mobile robot under external interference. This technology could eliminate the attitude deviation of mobile robot by backstepping control technology. The dynamic SMC could track the speed of the driving wheel. FC could adjust the switch adaptively to alleviate the chattering problem. Results indicated that the proposed model had better precision. Lan et al. [14] proposed a FSMC based on fuzzy switch gain adjustment to improve the anti-interference ability of controllable excitation linear synchronous motor. The proposed method introduced an integral term to remove the steady-state error of the system, and used fuzzy logic to eliminate the unknown interference of the system. It was obviously that this method could improve the dynamic performance of the system and had strong practicability. Wang et al. [15] designed a model to solve the problem of poor tracking accuracy of welding robot. The controller could effectively identify the external disturbance signal and dynamic uncertainty signal, and then suppressed the chattering phenomenon of the model. The method’s good robustness was verified.

To sum up, VDC technology and FSMC have many research results in their respective fields. However, the method of combining the two to ensure the DC stability in the power generation process is still worth exploring at present. Therefore, the FSMC is introduced into the virtual DC generator technology in this research, and the disturbance of nonlinear load is compensated by the FSMC, so as to keep the current and voltage of the power line constant. The experiment aims to provide guarantee for the stable operation of the power grid.

3 Research on harmonic current suppression model of VDC based on fuzzy sliding mode

3.1 VDC control principle

The control method of VDC is relative to the algorithm of VSM. It mainly simulates the motion equation and electromagnetic equation of VSM through reasonable control strategy. Based on the simulation, virtual inertia and virtual damping are introduced. At the same time, frequency modulation and excitation control are introduced to form closed-loop regulation, so that the output of three-phase inverter has better performance [16,17]. The VDC can make the power electronic converter of the DC microgrid have inertia, and can efficiently suppress the voltage fluctuation of the DC bus. The system concept diagram of virtual motor is shown in Figure 1. PV refers to photovoltaic power generation module; L is the equivalent inductance at the grid side; R denotes the equivalent resistance at the grid side; u a , u b , and u c are the output voltage at the inverter side; u ga , u gb , and u gc denote the three-phase voltage of the power grid; i Lg , i Lb , and i Lc represent the output current at the inverter side; and u dc represents the DC voltage output by the PV.

Figure 1 Conceptual structure diagram of virtual motor.
Figure 1

Conceptual structure diagram of virtual motor.

Currently, the research of VDC is mostly about the stability analysis and parameter design of the motor equation. The current and voltage of DC bus and its load are easy to fluctuate under the conditions of power generation and transformation, and its power quality will be reduced. To show the inertia and damping characteristics of the VDC itself [18], and to improve the power quality, the experiment added the mechanical and electromotive force balance equations in the process of restricting its change. The VDC takes the synchronous generator as the reference object, and obtains its specific formula by combining the active-frequency and reactive power-voltage equation as follows [19]:

(1) P m − P e ω = J d ω d t + D Δ ω ,

(2) Δ ω = ω − ω ′ ,

(3) U = U 0 + D q ( Q 0 − Q ) ,

where P m and P e are the mechanical and electromagnetic power of the VDC; ω and ω ′ are the single angular frequency of the power grid; J is the moment of inertia; D is the damping coefficient; Q 0 , Q , and D q are given and measured quantities and voltage sag coefficients under reactive power; U 0 and U are the rated value of voltage and the calculation amount.

3.2 Research on harmonic detection method based on ADALINE neural network

ADALINE is a classical supervised learning algorithm, which is a form of neural network. It uses a gradient descent algorithm to adjust the weights to minimize output errors and find the best classification bounds. Adaline has a linear activation function that can be used to process linearly separable data. It can be viewed as an improved version of the perceptron algorithm because it uses continuous activation functions instead of simple step functions. By comparing the network output and the target output, the ADALINE method constantly adjusts the network weight to minimize the error between the network output and the target output. ADALINE algorithm has the characteristics of nonlinearity and nonlocality, and has strong ability to calculate large amounts of data. Therefore, it is suitable for signal detection, extraction, and noise reduction. In view of this, this study applies ADALINE neural network to detect harmonics. The harmonic detection process based on ADALINE network is shown in Figure 2. In Figure 2, the harmonic sine and cosine signals are generated by the coordinate rotation digital computer. The amplitude of direct flow and harmonic volume is regarded as the weight of ADALINE network, and LMS algorithm is used to update and adjust.

Figure 2 Harmonic detection method based on ADALINE. (a) D-axis current harmonic extraction and (b) Q-axis current harmonic extraction.
Figure 2

Harmonic detection method based on ADALINE. (a) D-axis current harmonic extraction and (b) Q-axis current harmonic extraction.

First, the current signal with harmonic ( n times) on both sides of the VDC is discretized to obtain Eq. (4) [20].

(4) y ( n ) = ∑ m = 0 M a m sin m N ω ̇ n + b m cos m N ω ̇ n ,

where the maximum number of spectral lines of the VDC is expressed by M , the number of cycles contained in the analysis window is described by N, the weight coefficients of the sine and cosine terms of the m -th harmonic are expressed by a m and b m , respectively, the number of certain frequency spectral lines is expressed by m , and m N and ω ̇ are the order and angular frequency of harmonics, respectively.

(5) y ( n ) = ∑ m = 0 M c m sin m N ω ̇ n + φ m ,

(6) c m = a m 2 + b m 2 ,

(7) φ m = arctan a m b m π + arctan a m b m ,

where c is the amplitude of harmonic signal, and φ is its phase angle. Determine the harmonic frequency ω ̇ = 2 π f and multiply by the number of harmonics. Select the input sine and cosine vectors through ADALINE neural network, and after cycling k times, the calculation formula of input vector x k can be obtained at the point n of the current signal with possible harmonics, as shown in Eq. (8).

(8) x k = sin 0 N ω ̇ n cos 0 N ω ̇ n sin 1 N ω ̇ n cos 1 N ω ̇ n ⋯ sin m N ω ̇ n cos m N ω ̇ n T .

When the harmonic frequency ω ̇ is a fixed value, the position of the current signal n point that may have harmonics is variable. The output weight vector is calculated by Eq. (9).

(9) w k = [ a 0 b 0 a 1 b 1 ⋯ a m b m ] .

ADALINE network output is as shown in Eq. (10).

(10) y k ( n ) = w k x k .

There is an error signal between the current signal that may have harmonics input by ADALINE network and the actual harmonic current signal, whose formula is expressed as follows:

(11) e k ( n ) = y ( n ) − y k ( n ) ,

where y k ( n ) represents the actual output harmonic current signal, and y ( n ) indicates a current signal that may have harmonics. Take the error signal e k ( n ) as the input, and modify the step size according to the minimum mean square root of the variable step size to obtain the corresponding error accuracy w k = ( a m , b m ) . Meanwhile, output a fine-tuning signal for the weight vector and calculate the step size of the weight vector based on signal overlap.

(12) Δ w k = μ k e k ( n ) x k ,

where μ represents the modified step size. Introduce learning rate γ s into step size, γ s > 0 . The new step length is μ k + 1 = α μ k + γ s ∥ P ¯ ∥ 2 e 2 ( k ) , wherein 0 < α < 1 . The calculation formula of smooth gradient vector P ¯ obtained from the above content is shown in Eq. (13).

(13) P ¯ ( k ) = β P ¯ ( k − 1 ) + ( 1 − β ) e k ( n ) x k ,

where 0 < β < 1 . β is a smoothing factor of approximately 1. Combined with formulas (5)–(7), the spectrum of the voltage and current signal to be measured for the VDC can be obtained.

3.3 Construction of harmonic current suppression model based on FSMC and VDC

FSMC is a kind of control method that combines FC and SMC. It is mainly used in uncertain environment for effective intelligent control of complex objects. This control method has strong independence and robustness against various disturbances. It has the advantages of the two control modes. The characteristic of FSMC is that it is adjusted by fuzzy logic in the approaching stage to control the function of the whole system. The core idea of SMC is to control the state quantity to move near the sliding mode. Therefore, the main content of the SMC is the ability to maintain the motion of the state variables near the sliding mode surface [5,20]. In recent years, the relevant theories of fuzzy logic control system have become increasingly mature. This experiment combines SMC with FC, designs sliding mode surface and uses fuzzy reasoning mechanism, and finally deblurring [21]. The significance of the above operation is to reduce the adverse effects of switching gain and symbol function in the original design controller, so as to achieve the purpose of optimization and improvement.

The experiment combines the harmonic detection of VDC and the theorem of circuit superposition to extract the h harmonic of the control when the VDC works stably [22]. After that, the experiment calculates the amount of data for harmonic compensation through the FSMC. Meanwhile, the harmonic current generated by load disturbance is eliminated by reducing the harmonic voltage. In the design process, the harmonic voltage of the VDC interface is set to 0, and the calculation formula of the terminal voltage is obtained through the load part of the harmonic equivalent circuit, as shown in Eq. (14) [23].

(14) V 0 ¯ = E 〈 δ − Z 0 I 〈 θ = E cos δ − Z 0 I cos θ + j ( E sin δ − Z 0 I sin θ ) ,

where E and I denote the voltage and current of DC bus, respectively, θ = 90 ° , Z 0 and δ , respectively, represent the phase difference between the equivalent impedance and the voltage and current sources, sin δ ≈ δ , and cos δ ≈ 1 .

The output of FSMC can realize the size control of variable u through FSMC rules. Finally, the stability condition s s ̇ < 0 can be satisfied. Assuming that the detected currents with harmonics i C a ⁎ , i C b ⁎ , and i C c ⁎ are current signals, the actual compensation currents are i C a , i C b , and i C c , respectively, i.e., the detected currents are tracked and controlled by SMC. Set the tracking error and change rate as e i and e c i , respectively, to obtain Eq. (15) [15].

(15) e i = i c i ⁎ − i c i e c i = d ( i c i ⁎ − i c i ) d t

where i = a , b , c . The sliding surface of SMC is defined in Eq. (16).

(16) S i = c i e i + d i e c i ,

where c i > 0 , d i > 0 , and i = a , b , c . Input ( s , s ̇ ) into the fuzzy controller, fuzzify it, and then obtain the fuzzy variable of the FSMC according to the FC rules. The final output is the fuzzy output variable after the de-blurring process is completed. Then, the explicit output of FSMC is obtained. Meanwhile, the fuzzy dataset is defined as: PB = positive large, PM = positive middle, PS = positive small, ZO = zero, NS = negative small, NM = negative middle, NB = negative large. Applying the fuzzy rule “If S is A and S is B, then u is C,” the structure of the FSMC is shown in Figure 3.

Figure 3 Fuzzy sliding mode controller.
Figure 3

Fuzzy sliding mode controller.

Therefore, the current amplitude and angular frequency of the harmonics to be cleared can be obtained by calculation. In addition, the given value of harmonic voltage and current can also be obtained through the combined transformation of voltage and coordinate. To sum up, the experiment uses FSMC to participate in the on-off control of VDC, and then realizes the suppression of harmonic current at the VDC port.

4 Performance verification of VDC harmonic current suppression model based on fuzzy sliding mode

To verify the performance of the harmonic current suppression model combining the FSMC and the VDC, the experiment is conducted in the power grid simulation laboratory of the Electric Power Research Institute of a provincial power company limited by the State Grid in the semi-physical simulation platform RTLAB. In the experiment, the data are collected and analyzed by the Audley data acquisition system DEWE5000 and the daily 3198 power quality analyzer. The experimental parameters are set as follows: the nonlinear load active power P ref is 200 W. The load reactive power Q ref is 0 kVar. Select the voltage source module in the RTLAB module, and its rated voltage is 220 V. The load resistance is 50 Ω, inductance is 20 mH, the capacitance is 1,500 µF, the sampling frequency is set to 6.4 kHz during measurement, and the voltage regulator is used for voltage control.

Figure 4 shows the convergence test results of ADALINE. As shown in Figure 4, when iteration is performed for 57 times, both Error and Loss values of ADALINE dropped to the lowest point, and the convergence of the model tended to be stable with the increase in iterations, indicating that ADALINE had good convergence performance.

Figure 4 Convergence performance of ADALINE. (a) Error and (b) loss.
Figure 4

Convergence performance of ADALINE. (a) Error and (b) loss.

To verify the effect of VDC on the circuit converter, the VDC is introduced into the control system of the circuit converter. Figure 5 shows the relationship between the amplitude and phase of the vibration before and after adding the VDC and the speed, namely, the Bode diagram. The curve in the figure shows that after adding the VDC, the range of its turning rate is greatly reduced. At this time, the network bandwidth will also decrease. In addition, the phase margin will also be greatly increased. The above situation shows that the first-order inertia of the VDC control link plays an important role in improving the performance of the overall converter.

Figure 5 Bode diagram before and after adding VDC.
Figure 5

Bode diagram before and after adding VDC.

To explore the influence of the control system of the VDC link on the steadiness of the overall converter control system, the experiment chooses to load the load side of the circuit once at a certain time after the output voltage is stable. The load resistance values are set to 1 and 10 Ω, respectively. The system response results of the simulation experiment are shown in Figure 6. In both cases, the addition of VDC increases the rise time of the original stable system, so the system’s response speed slows down. In addition, due to the disturbance of small load, the voltage fluctuation of the original control system is large. However, the system is relatively more stable after the introduction of VDC control technology, which verifies the effectiveness of virtual DC click to suppress the voltage fluctuations.

Figure 6 System corresponding diagram before and after adding VDC technology. (a) Switch 1 Ω resistance at load side and (b) Switch 10 Ω resistance at load side.
Figure 6

System corresponding diagram before and after adding VDC technology. (a) Switch 1 Ω resistance at load side and (b) Switch 10 Ω resistance at load side.

Subsequently, the experiment verifies the current tracking control error of the VDC method based on FSMC proposed in this study, and the results are shown in Figure 6. From Figure 7, it can be seen that the tracking error of the current in the power line without the method proposed in this study is relatively large, and the error is significantly reduced after the method proposed in this study is applied. Thus, it is verified that the method can efficiently prevent the buffeting of power lines in the case of load disturbance, thus improving the accuracy of current tracking control.

Figure 7 Current tracking error before and after using this method. (a) Tracking error before use and (b) tracking error after use.
Figure 7

Current tracking error before and after using this method. (a) Tracking error before use and (b) tracking error after use.

In the same power line, the suppression effect of harmonics in the current before and after the application of this method is analyzed. From Figure 8, it can be seen that when this method is not used, there are third and fifth harmonics in the power line. After applying this method, it can be clearly seen in Figure 8(b) that the third and fifth harmonics are almost completely eliminated. The harmonic condition is obviously improved, which verifies that the method proposed in this study has excellent harmonic current control effect. The proposed method can better control the power quality of power lines, effectively maintain the energy output of power equipment, and ensure the stable operation of power lines.

Figure 8 The harmonics before and after using this method. (a) Harmonic condition before use and (b) Harmonic condition after use.
Figure 8

The harmonics before and after using this method. (a) Harmonic condition before use and (b) Harmonic condition after use.

The results of the FSM harmonic current suppression method proposed in this study are shown in Figure 9 when there are third and fifth harmonics in the power line. From Figure 9, before the application of the method, the current waveform has vibration and shows irregular shape. After adopting the FSMC proposed in this study, the current waveform is relatively smooth and close to the standard sine wave. This shows that the third and fifth harmonics of the current in the power line have been successfully suppressed and attenuated. The harmonic suppression method of VDC based on FSMC constructed in this experiment has a small control delay, and can effectively achieve the suppression of harmonic current of power lines without static error.

Figure 9 Harmonic current suppression before and after using this method.
Figure 9

Harmonic current suppression before and after using this method.

Connect the nonlinear load in the experimental power line, and the experimental current waveform before and after the application of this method is shown in Figure 10. The current waveform connected to nonlinear load has serious distortion before applying the proposed method. After applying this method, the current waveform is obviously enhanced and the harmonics are reduced. The results show that the quality of current waveform has been significantly improved, and the method can efficiently suppress the disturbance of nonlinear load.

Figure 10 Nonlinear load suppression before and after using the proposed method.
Figure 10

Nonlinear load suppression before and after using the proposed method.

To further verify the dynamic response capability, the compensation effect under load change is taken as an indicator in the experiment. According to the results shown in Figure 11, in the case of load changes, the curve of compensation current is significantly more rounded after the application of this method. The overall curve has no deformation and is more stable. However, when this method is not applied, the current is seriously deformed. From the comparison of the two methods, it can be seen that this method can effectively compensate for the current when the load changes, achieving the experimental purpose.

Figure 11 Compensation effect under load variation. (a) Load current and (b) compensation current.
Figure 11

Compensation effect under load variation. (a) Load current and (b) compensation current.

5 Conclusion

Aiming at the low frequency harmonics of power lines in the process of power grid operation, this study proposes a harmonic current suppression method based on FSMC and VDC. This method uses VDC control technology to ensure the voltage stability of DC bus and load side in case of sudden load change, and incorporates fuzzy sliding mode technology into the original suppression method to calculate the amount of harmonic data to be compensated. Among them, ADALINE network is also used for discrete processing of current signals that may have harmonics in power lines. The results indicate that the voltage fluctuation of the control system is smaller and more stable when the load resistance is 1 and 10 Ω, respectively. The verification results of current tracking control error show that the suggested model can efficiently prevent buffeting of power lines in the case of load disturbance. In terms of harmonic elimination, the proposed method almost eliminates the third and fifth harmonics. It not only improves the quality of DC voltage, but also improves the power quality of power lines. And when the current waveform of nonlinear load is connected, the model improves the current waveform and reduces the harmonics, and improves the quality of the current waveform. Therefore, the proposed method can accurately detect and eliminate the harmonic current caused by sudden load change, effectively reduce the buffeting of power lines, and thus achieve the suppression of harmonic current of VDC without static error. The limitation of this study is that it fails to verify the complexity of FC, which can be used as the next research direction.

Acknowledgments

The authors are grateful for the reviewer’s valuable comments that improved the manuscript.

  1. Funding information: This work was supported by the Railway Intelligent Operation and Maintenance Engineering Research Center of Shaanxi Universities.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

  4. Data availability statement: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Received: 2023-06-25
Revised: 2023-10-16
Accepted: 2023-11-13
Published Online: 2023-12-31

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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  1. Regular Articles
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  3. Parametric simulation of stagnation point flow of motile microorganism hybrid nanofluid across a circular cylinder with sinusoidal radius
  4. Fractal-fractional advection–diffusion–reaction equations by Ritz approximation approach
  5. Behaviour and onset of low-dimensional chaos with a periodically varying loss in single-mode homogeneously broadened laser
  6. Ammonia gas-sensing behavior of uniform nanostructured PPy film prepared by simple-straightforward in situ chemical vapor oxidation
  7. Analysis of the working mechanism and detection sensitivity of a flash detector
  8. Flat and bent branes with inner structure in two-field mimetic gravity
  9. Heat transfer analysis of the MHD stagnation-point flow of third-grade fluid over a porous sheet with thermal radiation effect: An algorithmic approach
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  11. Bioconvection effect in the Carreau nanofluid with Cattaneo–Christov heat flux using stagnation point flow in the entropy generation: Micromachines level study
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  13. Analysis of sweeping jet and film composite cooling using the decoupled model
  14. Research on the influence of trapezoidal magnetization of bonded magnetic ring on cogging torque
  15. Tripartite entanglement and entanglement transfer in a hybrid cavity magnomechanical system
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  18. Multiple Lie symmetry solutions for effects of viscous on magnetohydrodynamic flow and heat transfer in non-Newtonian thin film
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  24. Controlling the physical field using the shape function technique
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  28. Research on WPD and DBSCAN-L-ISOMAP for circuit fault feature extraction
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  37. Effect of dysprosium on the radiation-shielding features of SiO2–PbO–B2O3 glasses
  38. Asymptotic formulations of anti-plane problems in pre-stressed compressible elastic laminates
  39. A study on soliton, lump solutions to a generalized (3+1)-dimensional Hirota--Satsuma--Ito equation
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https://doi.org/10.1515/phys-2023-0162
Keywords for this article
fuzzy sliding mode control; VDC; harmonic current suppression; ADALINE; voltage stability
Creative Commons
BY 4.0

Articles in the same Issue

  1. Regular Articles
  2. Dynamic properties of the attachment oscillator arising in the nanophysics
  3. Parametric simulation of stagnation point flow of motile microorganism hybrid nanofluid across a circular cylinder with sinusoidal radius
  4. Fractal-fractional advection–diffusion–reaction equations by Ritz approximation approach
  5. Behaviour and onset of low-dimensional chaos with a periodically varying loss in single-mode homogeneously broadened laser
  6. Ammonia gas-sensing behavior of uniform nanostructured PPy film prepared by simple-straightforward in situ chemical vapor oxidation
  7. Analysis of the working mechanism and detection sensitivity of a flash detector
  8. Flat and bent branes with inner structure in two-field mimetic gravity
  9. Heat transfer analysis of the MHD stagnation-point flow of third-grade fluid over a porous sheet with thermal radiation effect: An algorithmic approach
  10. Weighted survival functional entropy and its properties
  11. Bioconvection effect in the Carreau nanofluid with Cattaneo–Christov heat flux using stagnation point flow in the entropy generation: Micromachines level study
  12. Study on the impulse mechanism of optical films formed by laser plasma shock waves
  13. Analysis of sweeping jet and film composite cooling using the decoupled model
  14. Research on the influence of trapezoidal magnetization of bonded magnetic ring on cogging torque
  15. Tripartite entanglement and entanglement transfer in a hybrid cavity magnomechanical system
  16. Compounded Bell-G class of statistical models with applications to COVID-19 and actuarial data
  17. Degradation of Vibrio cholerae from drinking water by the underwater capillary discharge
  18. Multiple Lie symmetry solutions for effects of viscous on magnetohydrodynamic flow and heat transfer in non-Newtonian thin film
  19. Thermal characterization of heat source (sink) on hybridized (Cu–Ag/EG) nanofluid flow via solid stretchable sheet
  20. Optimizing condition monitoring of ball bearings: An integrated approach using decision tree and extreme learning machine for effective decision-making
  21. Study on the inter-porosity transfer rate and producing degree of matrix in fractured-porous gas reservoirs
  22. Interstellar radiation as a Maxwell field: Improved numerical scheme and application to the spectral energy density
  23. Numerical study of hybridized Williamson nanofluid flow with TC4 and Nichrome over an extending surface
  24. Controlling the physical field using the shape function technique
  25. Significance of heat and mass transport in peristaltic flow of Jeffrey material subject to chemical reaction and radiation phenomenon through a tapered channel
  26. Complex dynamics of a sub-quadratic Lorenz-like system
  27. Stability control in a helicoidal spin–orbit-coupled open Bose–Bose mixture
  28. Research on WPD and DBSCAN-L-ISOMAP for circuit fault feature extraction
  29. Simulation for formation process of atomic orbitals by the finite difference time domain method based on the eight-element Dirac equation
  30. A modified power-law model: Properties, estimation, and applications
  31. Bayesian and non-Bayesian estimation of dynamic cumulative residual Tsallis entropy for moment exponential distribution under progressive censored type II
  32. Computational analysis and biomechanical study of Oldroyd-B fluid with homogeneous and heterogeneous reactions through a vertical non-uniform channel
  33. Predictability of machine learning framework in cross-section data
  34. Chaotic characteristics and mixing performance of pseudoplastic fluids in a stirred tank
  35. Isomorphic shut form valuation for quantum field theory and biological population models
  36. Vibration sensitivity minimization of an ultra-stable optical reference cavity based on orthogonal experimental design
  37. Effect of dysprosium on the radiation-shielding features of SiO2–PbO–B2O3 glasses
  38. Asymptotic formulations of anti-plane problems in pre-stressed compressible elastic laminates
  39. A study on soliton, lump solutions to a generalized (3+1)-dimensional Hirota--Satsuma--Ito equation
  40. Tangential electrostatic field at metal surfaces
  41. Bioconvective gyrotactic microorganisms in third-grade nanofluid flow over a Riga surface with stratification: An approach to entropy minimization
  42. Infrared spectroscopy for ageing assessment of insulating oils via dielectric loss factor and interfacial tension
  43. Influence of cationic surfactants on the growth of gypsum crystals
  44. Study on instability mechanism of KCl/PHPA drilling waste fluid
  45. Analytical solutions of the extended Kadomtsev–Petviashvili equation in nonlinear media
  46. A novel compact highly sensitive non-invasive microwave antenna sensor for blood glucose monitoring
  47. Inspection of Couette and pressure-driven Poiseuille entropy-optimized dissipated flow in a suction/injection horizontal channel: Analytical solutions
  48. Conserved vectors and solutions of the two-dimensional potential KP equation
  49. The reciprocal linear effect, a new optical effect of the Sagnac type
  50. Optimal interatomic potentials using modified method of least squares: Optimal form of interatomic potentials
  51. The soliton solutions for stochastic Calogero–Bogoyavlenskii Schiff equation in plasma physics/fluid mechanics
  52. Research on absolute ranging technology of resampling phase comparison method based on FMCW
  53. Analysis of Cu and Zn contents in aluminum alloys by femtosecond laser-ablation spark-induced breakdown spectroscopy
  54. Nonsequential double ionization channels control of CO2 molecules with counter-rotating two-color circularly polarized laser field by laser wavelength
  55. Fractional-order modeling: Analysis of foam drainage and Fisher's equations
  56. Thermo-solutal Marangoni convective Darcy-Forchheimer bio-hybrid nanofluid flow over a permeable disk with activation energy: Analysis of interfacial nanolayer thickness
  57. Investigation on topology-optimized compressor piston by metal additive manufacturing technique: Analytical and numeric computational modeling using finite element analysis in ANSYS
  58. Breast cancer segmentation using a hybrid AttendSeg architecture combined with a gravitational clustering optimization algorithm using mathematical modelling
  59. On the localized and periodic solutions to the time-fractional Klein-Gordan equations: Optimal additive function method and new iterative method
  60. 3D thin-film nanofluid flow with heat transfer on an inclined disc by using HWCM
  61. Numerical study of static pressure on the sonochemistry characteristics of the gas bubble under acoustic excitation
  62. Optimal auxiliary function method for analyzing nonlinear system of coupled Schrödinger–KdV equation with Caputo operator
  63. Analysis of magnetized micropolar fluid subjected to generalized heat-mass transfer theories
  64. Does the Mott problem extend to Geiger counters?
  65. Stability analysis, phase plane analysis, and isolated soliton solution to the LGH equation in mathematical physics
  66. Effects of Joule heating and reaction mechanisms on couple stress fluid flow with peristalsis in the presence of a porous material through an inclined channel
  67. Bayesian and E-Bayesian estimation based on constant-stress partially accelerated life testing for inverted Topp–Leone distribution
  68. Dynamical and physical characteristics of soliton solutions to the (2+1)-dimensional Konopelchenko–Dubrovsky system
  69. Study of fractional variable order COVID-19 environmental transformation model
  70. Sisko nanofluid flow through exponential stretching sheet with swimming of motile gyrotactic microorganisms: An application to nanoengineering
  71. Influence of the regularization scheme in the QCD phase diagram in the PNJL model
  72. Fixed-point theory and numerical analysis of an epidemic model with fractional calculus: Exploring dynamical behavior
  73. Computational analysis of reconstructing current and sag of three-phase overhead line based on the TMR sensor array
  74. Investigation of tripled sine-Gordon equation: Localized modes in multi-stacked long Josephson junctions
  75. High-sensitivity on-chip temperature sensor based on cascaded microring resonators
  76. Pathological study on uncertain numbers and proposed solutions for discrete fuzzy fractional order calculus
  77. Bifurcation, chaotic behavior, and traveling wave solution of stochastic coupled Konno–Oono equation with multiplicative noise in the Stratonovich sense
  78. Thermal radiation and heat generation on three-dimensional Casson fluid motion via porous stretching surface with variable thermal conductivity
  79. Numerical simulation and analysis of Airy's-type equation
  80. A homotopy perturbation method with Elzaki transformation for solving the fractional Biswas–Milovic model
  81. Heat transfer performance of magnetohydrodynamic multiphase nanofluid flow of Cu–Al2O3/H2O over a stretching cylinder
  82. ΛCDM and the principle of equivalence
  83. Axisymmetric stagnation-point flow of non-Newtonian nanomaterial and heat transport over a lubricated surface: Hybrid homotopy analysis method simulations
  84. HAM simulation for bioconvective magnetohydrodynamic flow of Walters-B fluid containing nanoparticles and microorganisms past a stretching sheet with velocity slip and convective conditions
  85. Coupled heat and mass transfer mathematical study for lubricated non-Newtonian nanomaterial conveying oblique stagnation point flow: A comparison of viscous and viscoelastic nanofluid model
  86. Power Topp–Leone exponential negative family of distributions with numerical illustrations to engineering and biological data
  87. Extracting solitary solutions of the nonlinear Kaup–Kupershmidt (KK) equation by analytical method
  88. A case study on the environmental and economic impact of photovoltaic systems in wastewater treatment plants
  89. Application of IoT network for marine wildlife surveillance
  90. Non-similar modeling and numerical simulations of microploar hybrid nanofluid adjacent to isothermal sphere
  91. Joint optimization of two-dimensional warranty period and maintenance strategy considering availability and cost constraints
  92. Numerical investigation of the flow characteristics involving dissipation and slip effects in a convectively nanofluid within a porous medium
  93. Spectral uncertainty analysis of grassland and its camouflage materials based on land-based hyperspectral images
  94. Application of low-altitude wind shear recognition algorithm and laser wind radar in aviation meteorological services
  95. Investigation of different structures of screw extruders on the flow in direct ink writing SiC slurry based on LBM
  96. Harmonic current suppression method of virtual DC motor based on fuzzy sliding mode
  97. Micropolar flow and heat transfer within a permeable channel using the successive linearization method
  98. Different lump k-soliton solutions to (2+1)-dimensional KdV system using Hirota binary Bell polynomials
  99. Investigation of nanomaterials in flow of non-Newtonian liquid toward a stretchable surface
  100. Weak beat frequency extraction method for photon Doppler signal with low signal-to-noise ratio
  101. Electrokinetic energy conversion of nanofluids in porous microtubes with Green’s function
  102. Examining the role of activation energy and convective boundary conditions in nanofluid behavior of Couette-Poiseuille flow
  103. Review Article
  104. Effects of stretching on phase transformation of PVDF and its copolymers: A review
  105. Special Issue on Transport phenomena and thermal analysis in micro/nano-scale structure surfaces - Part IV
  106. Prediction and monitoring model for farmland environmental system using soil sensor and neural network algorithm
  107. Special Issue on Advanced Topics on the Modelling and Assessment of Complicated Physical Phenomena - Part III
  108. Some standard and nonstandard finite difference schemes for a reaction–diffusion–chemotaxis model
  109. Special Issue on Advanced Energy Materials - Part II
  110. Rapid productivity prediction method for frac hits affected wells based on gas reservoir numerical simulation and probability method
  111. Special Issue on Novel Numerical and Analytical Techniques for Fractional Nonlinear Schrodinger Type - Part III
  112. Adomian decomposition method for solution of fourteenth order boundary value problems
  113. New soliton solutions of modified (3+1)-D Wazwaz–Benjamin–Bona–Mahony and (2+1)-D cubic Klein–Gordon equations using first integral method
  114. On traveling wave solutions to Manakov model with variable coefficients
  115. Rational approximation for solving Fredholm integro-differential equations by new algorithm
  116. Special Issue on Predicting pattern alterations in nature - Part I
  117. Modeling the monkeypox infection using the Mittag–Leffler kernel
  118. Spectral analysis of variable-order multi-terms fractional differential equations
  119. Special Issue on Nanomaterial utilization and structural optimization - Part I
  120. Heat treatment and tensile test of 3D-printed parts manufactured at different build orientations
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