# Voltage Frequency Ratio Control Method of the Cycloconverter Based on the GSO Algorithm

Authors: Zhengwang Xu; Jiaqi Yu
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

In order to keep the flux constant when the asynchronous motor is running under load, especially under light load, a Glowworm swarm optimization (GSO) algorithm is proposed to control the voltage frequency ratio of the cycloconverter. Based on the analysis of the two variable control theory of the voltage frequency ratio of the cycloconverter and the working principle of the cycloconverter, the self-control method of the voltage frequency ratio of the cycloconverter by adaptive fuzzy backstepping sliding mode is proposed. In the control process, GSO and BFA are integrated to optimize the control process of the controller, and an adaptive selection strategy is adopted to ensure the adaptive step size of the firefly and improve the accuracy of the GSO algorithm. The experimental results show that when the optimal voltage-frequency ratio is switched between the online continuous frequency control strategy and the frequency range is small enough, the motor speed is stable, the speed regulation process is stable, and the motor is always in the state of high force index. It shows that the control method has a fast convergence speed and a good control effect on the voltage frequency ratio of the ring converter of the experimental motor, and it can keep the flux constant under light load.


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## Body

## 1. Introduction

The frequency control technology can be divided into AC-AC frequency conversion and AC-DC-AC frequency conversion, which have advantages and disadvantages [1]. The AC-AC frequency conversion is the direct conversion of a frequency of alternating current into an adjustable frequency of the alternating current. The AC-DC-AC frequency conversion is to convert alternating current into direct current first and then convert direct current into adjustable frequency alternating current, which belongs to indirect frequency conversion. Compared with the AC-DC-AC converter, the advantages of the AC-AC frequency conversion are as follows: only one time of the converter is needed, its efficiency is high, a four-quadrant operation can be easily realized, and the low-frequency output waveform is close to the sine wave.When the cycloconverter drives the asynchronous motor, it often chooses the motor with the larger capacity to guarantee the load capacity. However, the motor’s working condition in the actual operation is complex and changeable, often in the light load operation state. The light load operation of the motor makes the motor inefficient and uneconomical. At the same time, the power factor of the motor is also low, the proportion of reactive power consumption is large, and the loss of electric energy increases [2, 3]. However, the traditional voltage frequency coordinated control method, such as constant voltage frequency ratio control, mainly considers the problem of keeping the flux constant of the asynchronous motor; does not consider the specific working conditions of the motor, such as load characteristics and voltage level; and does not make the working conditions of the cycloconverter and asynchronous motor better match, resulting in the low power index of asynchronous motor, for example, the power factor and efficiency are low, which cannot achieve the purpose of energy saving [4]. Therefore, in order to save electric energy and improve the power index of the motor, it is necessary to find the optimal voltage frequency combination [5].At present, many scholars have carried out research in various directions in this field and made some achievements. Du et al. [6] studied the real-time conversion strategy of the AC inverter under bivariate control. The linearization improvement of the cosine intersection method is implemented, which can continuously change the amplitude and frequency of the reference voltage in real time and achieve the effect of real-time continuous frequency conversion control. The MATLAB platform is used to build a simulation model and obtain the output voltage and current waveform. This method can realize the real-time frequency control of the AC frequency converter, but it is difficult to control the voltage frequency ratio. Lei et al. [7] built a simplified model of the AC-AC inverter based on the dynamic phasor method. They switched the function builder dynamic phasor method model and only considered the fundamental frequency component of the device to realize the simplification process of the AC-AC inverter model. This model can retain the dynamic characteristics of the AC frequency converter and significantly shorten the simulation time. However, it is difficult to reasonably control the voltage frequency ratio of the device. Xie et al. [8] studied the control method of the AC converter with DC bus parallel and small capacity switching capacitor. Based on the analysis of the circuit structure and capacitance parameters of the converter, the voltage output of the converter when the DC bus is six-pulse voltage is studied, the control method with the highest voltage change efficiency is obtained, and the ideal model of the converter with small capacitance is deduced. This method reduces the electrolytic capacitor capacity of the converter. However, the voltage change efficiency is basically the same as that of the original converter, but it still fails to achieve effective control of the voltage frequency ratio.In this study, in order to achieve the optimal control effect of the AC frequency converter’s voltage frequency ratio, the Glowworm swarm optimization (GSO) algorithm was introduced, which originated in 2005. A new swarm optimization algorithm was presented by the Indian scholars Krishnanand and Ghose [9] at the IEEE Swarm Intelligence Conference. In 2009, Yang [10], a Cambridge scholar, proposed a firefly algorithm (FA) based on the luminescent behavior of fireflies in nature. Since the two kinds of FAs were put forward, scholars in various countries have studied, improved, and applied them [11, 12]. The GSO algorithm has been successfully applied in clustering analysis, signal source location, pattern recognition, robot path planning, multimode function optimization, combination optimization, social science, and other fields [13].Of course, the GSO algorithm, as a kind of guided stochastic heuristic search algorithm, also has some disadvantages, such as low precision, slow convergence in the later stage, easy fall into local optimum, and high dependence on the initial solution distribution, especially in the face of more complex multimode function optimization or large-scale complex problem-solving. Given the above shortcomings, some scholars at home and abroad have conducted relevant research and made many improvements. To some extent, the improvements have significantly improved the optimization performance of the GSO algorithm. However, due to the short time of the algorithm, there is still much work to be done in further optimization, application, and basic theoretical analysis [14–16].In this study, based on the improved GSO algorithm, the voltage frequency ratio self-control method of the cycloconverter is proposed to achieve the optimal self-control of the voltage frequency ratio of the cycloconverter, which can be widely used in the control of various motors and other devices [17, 18].


## 2. Methods

### 2.1. Design Process

The overall design idea of the proposed method is shown in Figure1.Figure 1
Overall design flow of the proposed method.As shown in Figure1, before designing the voltage-frequency ratio control method of the AC-AC converter, the working principle of the AC-AC converter and the bivariate control theory of the voltage-frequency ratio of the converter are first analyzed. Then, according to the adaptive fuzzy backstepping sliding mode control method, the voltage-frequency ratio autonomous controller is designed. Then, the GSO-BFA algorithm was used to optimize the controller parameters in the adaptive fuzzy backward sliding mode. After the initial solution set was generated by the GSO algorithm, the BFA algorithm was used to obtain the exact solution to improve the accuracy of the GSO algorithm. Finally, the optimized parameters are combined with the improved GSO algorithm to obtain the optimal autonomous control method of the voltage conversion ratio [19].


### 2.2. Working Principle of the Cycloconverter

The cycloconverter modulates the trigger angle of the thyristor according to the law of sine, selectively connects some segments of the grid voltage, and splices them to output the AC sine voltage with adjustable amplitude and frequency. In essence, a cycloconverter is composed of a dual converter (i.e., forward and reverse group converter with reverse parallel connection). Through time control of its trigger pulse, the dual converter will generate the AC output voltage.The basic principle of the cycloconverter is analyzed by taking the single cycloconverter circuit as an example. As shown in Figure2, according to the positive and negative directions of the current flowing through the thyristor, the thyristors of each phase can be divided into forward and reverse groups. The first section u0>0, i0<0, is the reverse group inverter; the current in the second section is zero crossing, which is not a circulation dead zone; the third section u0>0, i0>0, is the forward group rectifier; the fourth section u0<0, i0>0, is the forward group inverter; the current in the fifth section is zero crossing, which is not a circulation dead zone; and the sixth section u0<0, i0<0, is reverse group rectifier. Because the output voltage waveform is spliced by intercepting the segments of the grid voltage, the more segments of the grid voltage are spliced in an output cycle, the closer the output voltage waveform is to the sine wave. The higher the frequency of the output voltage of the cycloconverter, the less the number of voltage segments contained in an output cycle, which will cause waveform distortion and harmonic increase. The resulting current waveform distortion will produce torque ripple. The output frequency of a cycloconverter is usually lower than 1/2 to 1/3 of the power frequency of the power grid. When the output frequency is above 1/3 of grid frequency because there are fewer voltage segments in an output cycle (e.g., there are eight voltage segments in an output cycle with dichotomy frequency), adding or reducing one voltage segment in each output cycle will seriously change the size of the output frequency, and the corresponding output frequency level difference is also large [20]. When the output frequency is lower than 1/3 of the grid frequency because there are many voltage segments in an output cycle (e.g., there are 56 voltage segments in an output cycle of decanter frequency), which is closer to the reference voltage waveform, then adding or reducing one voltage segment in an output cycle has a very small impact on the output frequency, and the corresponding output frequency changes. The level difference is also very small, so the output frequency can change in a very small range [21, 22]. In the macrostatistical sense, the output frequency can change continuously. This provides the possibility for research on the online continuous frequency conversion control strategy of the cycloconverter in the low-frequency band (the quintuple frequency) [23].Figure 2
Schematic diagram of the single intersection AC frequency conversion.


### 2.3. Design of Voltage Frequency Ratio Autonomous Controller of Cycloconverter Based on Adaptive Fuzzy Backstepping Sliding Mode

According to the working principle of the cycloconverter, the equivalent mathematical model is constructed as follows:(1)x1=x2,x2=Amx1+Bmx2+Cmu+f,andPa=x1. In the previous equation, f is the total amount of parameter perturbation, f=ΔAx1+ΔBx1+ΔCu+d.For the above two-order pressure control system, the sliding surface is designed as follows:(2)z1=c1+x2+ddt+λ2∫0tx1−xp∗dz.The stable term is defined asα1=c2z1, z2=z1+α1, V1=1/2z12, and V2=V1+1/2σ2, where σ=k1z1+z2. The upper bound F of external interference is estimated and defined as V3=V2+1/2γF2.The adaptive backstepping sliding mode controller and control law are designed according to the generalized conditions of reaching the sliding mode surface as shown in equations (3) and (4), and the exponential approach law is selected to approach the sliding mode surface:(3)u=c1+c2Cm−1−k1c1x2−k1x2−ke−2k1λe−λ2k1e−c1+c2Amx1−c1+c2Bmx2−c1+c2f^−x2−c1c2x2−e−2λ+c2e−2λc2+λ2e−λ2c2e−hσ+βsgnσ,(4)f^=c1+2γσ,where e=x1−xp∗,F=F∗−F^,h,β is the normal number. When equations (3) and (4) are introduced into V3, we can get the following equation:(5)V3=z1z2−c2z12+σ−hσ+βsgnσ=z1z2−c2z12−hσ2−hβσ=−zTQz−hβσ≤0,where Q=c2+hk12hk1−0.5hk1−0.5h.The appropriateh,c2,k1 is taken to make Q>0; that is, Q is a positive definite matrix. In addition, the saturation substitution method is used to weaken the chattering using the boundary layer as follows:(6)sats,ϕ=1,s>ϕ,sϕs≤ϕ,−1s<−ϕ,where ϕ is the thickness of the boundary layer and is the normal number.V3≤0 shows that the existence and stability of the sliding mode are asymptotically stable.A fuzzy controller is designed for the mainu of the control variable as follows:(7)uβ=1,β≤−1,2β3+9β2+7β+36β2+9β+6,−1<β≤−0.5,2β3+3β2−7β6β2+3β+3,0.5<β≤0,2β3−3β2−7β6β2−3β+3,0<β≤0.5,2β3−9β2−7β−36β2−9β+6,0.5<β≤1,−1,β>1.


### 2.4. Adaptive GSO-BFA Algorithm

In this study, the GSO-BFA algorithm is used to optimize the parameters of the controller in the adaptive fuzzy backstepping sliding mode and realize the voltage frequency ratio autonomous control of the cycloconverter. The initial solution set is generated by the GSO algorithm, and the BFA algorithm is used for an accurate solution. By describing the three operators of pheromone update, the firefly individual movement, and dynamic decision domain update, the algorithm is iteratively optimized. By introducing the concept of adaptive step size into the pheromone update operator, the GSO algorithm can ensure that the whole solution set cannot be fully optimized due to the too large or too small step size between firefly individuals. Although the larger step size can avoid precocity in the initial optimization process and improve the global optimization ability of the algorithm, it will reduce the optimization accuracy in the later stage of the algorithm. If the step size is small, it will reduce the optimization speed but improve the solution accuracy at the same time. In this study, the adaptive adjustment method for the step size of the fluorescent factor is adopted to dynamically adjust the step size. Then, there is the following equation:(8)si=smax−smin∗x1−xextdmax+smin,where Xi is the position of the i-th firefly, Xext is the position of the firefly with the highest concentration of fluorescein, and dmax is the maximum distance between the firefly with the highest concentration of fluorescein and all other fireflies.This scheme can not only prevent the algorithm from converging prematurely and falling into the local optimal solution at the initial stage of the algorithm but also promote the initial solution of the algorithm to traverse the optimization range. In the later stage, when the integrated algorithm performs accurate calculations, the optimization accuracy of the algorithm will not be reduced due to the large fluorescent factor. At the same time, the chemotaxis (flipping and swimming) operator in the bacterial foraging algorithm is modified to adopt Gaussian mutation, that is, to add a random disturbance term obeying Gaussian distribution to the current bacterial individualXi′=x1,x2,…,xm as follows:(9)Xi′=Xi+Xi×N0,1.In the previous equation,N0,1 adhere to the Gaussian distribution with a mean value of 0 and a mean square deviation of 1.By adding the random disturbance term of Gaussian distribution in equation (9), the current bacterial population is disturbed so that some individuals in the population can jump out of the local optimal solution. If the fitness of the optimal solution after replacement is larger than that before replacement, then the solution after replacement is better than that before replacement, and the equivalent replacement with probability is carried out. This kind of permutation increases the possibility of jumping out of the local optimal interval and makes equivalent optimization in a larger interval, thus enhancing the optimization ability of the integrated algorithm [24, 25].According to equation (2), parameters c1 and λ of the sliding surface are unknown. The values of these two parameters are related to each other and affect the transient dynamic characteristics of the system. In order to get a better dynamic response, the adaptive GSO-BFA algorithm is used to optimize the above parameters. In order to obtain satisfactory dynamic characteristics, ITAE is used as the objective function for parameter selection. In order to avoid the excessive control amount, the square term of control input is added to the objective function. In order to shorten the rise time, the relevant term with the rise time is introduced [26]. In order to avoid position overshoot, the penalty term related to the absolute value of the error is introduced when the system error e≤0. Equation (10) is selected as the optimal index for parameter selection as follows:(10)J=∫0∞w1et+w2u2t+w4etdt+w3tre≤0,J=∫0∞w1et+w2u2tdt+w3tre>0.λ=72.219. The parameters of the sliding surface are c1∈0,500, λ∈0,100. After 100 iterations, the optimized parameters are c1=381.276, λ=72.219. The design parameter is taken as h=60.


### 2.5. Improved GSO Algorithm

#### 2.5.1. Adaptive Selection Strategy

The parameters of the controller in the adaptive fuzzy backstepping sliding mode are optimized by the GSO-BFA algorithm, and the optimized parameters are combined with the improved GSO algorithm to find the optimal autonomous control method of the voltage frequency ratio [27, 28].In the initial GSO algorithm, the step size is fixed, easily leading to the algorithm falling into the local optimal solution. Therefore, the step size is constantly adjusted according to the results of each iteration to find the global optimal value quickly and accurately. For example, in the early stage of the algorithm iteration, the step size change needs to be larger, which can speed up the iteration speed. In the late stage of the iteration, the step size needs to be very small to accurately find the local optimal value. Therefore, the GSO algorithm and the optimal path of voltage frequency ratio of the AC-AC frequency conversion are coevoluted to find the optimal step length for each individual.Firstly, each individual randomly assigns the AC frequency ratio and step size in a suitable range, the affinity of each AC frequency ratio is calculated according to the iteration of the algorithm, and the affinity is calculated as follows:(11)AγiG=fxiG−fxiG+1fxiG+1,iffxiG+1<fxiG,0,other.In each iteration, a certain percentage of the voltage frequency ratio of the AC-AC frequency conversion is interfered with by some other factors, and the voltage frequency ratio of AC-AC frequency conversion is updated as follows:(12)αkG+1=αk+QG,ifQ+k≤M,υQ+k−Motherwise.According to the integer sequence decoding of the second half of the individual, we can get the processing machines of each process.Q31 is processed by the first machine, Q11 is processed by the third machine, and so on.The sequence code of operation processing is combined with the part code of machine selection to get the whole individual. The first half of the individual represents the operation code, and the second half represents the machine code, whereM=2∗NP,Q=0.2∗NP,k=1,2,…,2∗NP.According to a random probability, the step parameter is selected in the antibody, and the step parameter is updated according to the following equation:(13)γiG+1=πiG+1,ifPi≤Pc,θi,otherwise,where i=1,2,…,NP, Pi is Rand, Pc is the preset inoculation probability, πiG+1 is selected from αkG+1, and the selected strategy is roulette; k=1,2,…,2∗NP, and θi is selected from γi1.


#### 2.5.2. Flowchart of the Improved GSO Algorithm

The chart of the improved GSO algorithm is shown in Figure3.Figure 3
Flowchart of the improved GSO algorithm.Analyzing the flowchart of the improved GSO algorithm in Figure3, we can see that the initialization parameters and greedy coding strategy generate n individuals x and the number of iterations Tmax. Set the number of iterations of initial value t = 1. Update the fluorescein. Calculate the individual N (t) that is brighter than oneself within the strategy radius of individual i. Select an individual that is brighter than oneself for the wheel plug. Update the position of individual i. Judge that x is the rest of nonindividual I and x∈Nt; if it is another Pox crossover and if there is no domain insertion or reverse order arrangement, the two results will be output, respectively. Update the position of individual x. Update the decision radius and fitness value. Calculate the affinity. Update the AC frequency ratio. Update the step length. If the number of iterations does not have T<Tmax, the maximum brightness and the optimal position will be output. If T<Tmax, repeat the above result until T<Tmax.


## 2.1. Design Process

The overall design idea of the proposed method is shown in Figure1.Figure 1
Overall design flow of the proposed method.As shown in Figure1, before designing the voltage-frequency ratio control method of the AC-AC converter, the working principle of the AC-AC converter and the bivariate control theory of the voltage-frequency ratio of the converter are first analyzed. Then, according to the adaptive fuzzy backstepping sliding mode control method, the voltage-frequency ratio autonomous controller is designed. Then, the GSO-BFA algorithm was used to optimize the controller parameters in the adaptive fuzzy backward sliding mode. After the initial solution set was generated by the GSO algorithm, the BFA algorithm was used to obtain the exact solution to improve the accuracy of the GSO algorithm. Finally, the optimized parameters are combined with the improved GSO algorithm to obtain the optimal autonomous control method of the voltage conversion ratio [19].


## 2.2. Working Principle of the Cycloconverter

The cycloconverter modulates the trigger angle of the thyristor according to the law of sine, selectively connects some segments of the grid voltage, and splices them to output the AC sine voltage with adjustable amplitude and frequency. In essence, a cycloconverter is composed of a dual converter (i.e., forward and reverse group converter with reverse parallel connection). Through time control of its trigger pulse, the dual converter will generate the AC output voltage.The basic principle of the cycloconverter is analyzed by taking the single cycloconverter circuit as an example. As shown in Figure2, according to the positive and negative directions of the current flowing through the thyristor, the thyristors of each phase can be divided into forward and reverse groups. The first section u0>0, i0<0, is the reverse group inverter; the current in the second section is zero crossing, which is not a circulation dead zone; the third section u0>0, i0>0, is the forward group rectifier; the fourth section u0<0, i0>0, is the forward group inverter; the current in the fifth section is zero crossing, which is not a circulation dead zone; and the sixth section u0<0, i0<0, is reverse group rectifier. Because the output voltage waveform is spliced by intercepting the segments of the grid voltage, the more segments of the grid voltage are spliced in an output cycle, the closer the output voltage waveform is to the sine wave. The higher the frequency of the output voltage of the cycloconverter, the less the number of voltage segments contained in an output cycle, which will cause waveform distortion and harmonic increase. The resulting current waveform distortion will produce torque ripple. The output frequency of a cycloconverter is usually lower than 1/2 to 1/3 of the power frequency of the power grid. When the output frequency is above 1/3 of grid frequency because there are fewer voltage segments in an output cycle (e.g., there are eight voltage segments in an output cycle with dichotomy frequency), adding or reducing one voltage segment in each output cycle will seriously change the size of the output frequency, and the corresponding output frequency level difference is also large [20]. When the output frequency is lower than 1/3 of the grid frequency because there are many voltage segments in an output cycle (e.g., there are 56 voltage segments in an output cycle of decanter frequency), which is closer to the reference voltage waveform, then adding or reducing one voltage segment in an output cycle has a very small impact on the output frequency, and the corresponding output frequency changes. The level difference is also very small, so the output frequency can change in a very small range [21, 22]. In the macrostatistical sense, the output frequency can change continuously. This provides the possibility for research on the online continuous frequency conversion control strategy of the cycloconverter in the low-frequency band (the quintuple frequency) [23].Figure 2
Schematic diagram of the single intersection AC frequency conversion.


## 2.3. Design of Voltage Frequency Ratio Autonomous Controller of Cycloconverter Based on Adaptive Fuzzy Backstepping Sliding Mode

According to the working principle of the cycloconverter, the equivalent mathematical model is constructed as follows:(1)x1=x2,x2=Amx1+Bmx2+Cmu+f,andPa=x1. In the previous equation, f is the total amount of parameter perturbation, f=ΔAx1+ΔBx1+ΔCu+d.For the above two-order pressure control system, the sliding surface is designed as follows:(2)z1=c1+x2+ddt+λ2∫0tx1−xp∗dz.The stable term is defined asα1=c2z1, z2=z1+α1, V1=1/2z12, and V2=V1+1/2σ2, where σ=k1z1+z2. The upper bound F of external interference is estimated and defined as V3=V2+1/2γF2.The adaptive backstepping sliding mode controller and control law are designed according to the generalized conditions of reaching the sliding mode surface as shown in equations (3) and (4), and the exponential approach law is selected to approach the sliding mode surface:(3)u=c1+c2Cm−1−k1c1x2−k1x2−ke−2k1λe−λ2k1e−c1+c2Amx1−c1+c2Bmx2−c1+c2f^−x2−c1c2x2−e−2λ+c2e−2λc2+λ2e−λ2c2e−hσ+βsgnσ,(4)f^=c1+2γσ,where e=x1−xp∗,F=F∗−F^,h,β is the normal number. When equations (3) and (4) are introduced into V3, we can get the following equation:(5)V3=z1z2−c2z12+σ−hσ+βsgnσ=z1z2−c2z12−hσ2−hβσ=−zTQz−hβσ≤0,where Q=c2+hk12hk1−0.5hk1−0.5h.The appropriateh,c2,k1 is taken to make Q>0; that is, Q is a positive definite matrix. In addition, the saturation substitution method is used to weaken the chattering using the boundary layer as follows:(6)sats,ϕ=1,s>ϕ,sϕs≤ϕ,−1s<−ϕ,where ϕ is the thickness of the boundary layer and is the normal number.V3≤0 shows that the existence and stability of the sliding mode are asymptotically stable.A fuzzy controller is designed for the mainu of the control variable as follows:(7)uβ=1,β≤−1,2β3+9β2+7β+36β2+9β+6,−1<β≤−0.5,2β3+3β2−7β6β2+3β+3,0.5<β≤0,2β3−3β2−7β6β2−3β+3,0<β≤0.5,2β3−9β2−7β−36β2−9β+6,0.5<β≤1,−1,β>1.


## 2.4. Adaptive GSO-BFA Algorithm

In this study, the GSO-BFA algorithm is used to optimize the parameters of the controller in the adaptive fuzzy backstepping sliding mode and realize the voltage frequency ratio autonomous control of the cycloconverter. The initial solution set is generated by the GSO algorithm, and the BFA algorithm is used for an accurate solution. By describing the three operators of pheromone update, the firefly individual movement, and dynamic decision domain update, the algorithm is iteratively optimized. By introducing the concept of adaptive step size into the pheromone update operator, the GSO algorithm can ensure that the whole solution set cannot be fully optimized due to the too large or too small step size between firefly individuals. Although the larger step size can avoid precocity in the initial optimization process and improve the global optimization ability of the algorithm, it will reduce the optimization accuracy in the later stage of the algorithm. If the step size is small, it will reduce the optimization speed but improve the solution accuracy at the same time. In this study, the adaptive adjustment method for the step size of the fluorescent factor is adopted to dynamically adjust the step size. Then, there is the following equation:(8)si=smax−smin∗x1−xextdmax+smin,where Xi is the position of the i-th firefly, Xext is the position of the firefly with the highest concentration of fluorescein, and dmax is the maximum distance between the firefly with the highest concentration of fluorescein and all other fireflies.This scheme can not only prevent the algorithm from converging prematurely and falling into the local optimal solution at the initial stage of the algorithm but also promote the initial solution of the algorithm to traverse the optimization range. In the later stage, when the integrated algorithm performs accurate calculations, the optimization accuracy of the algorithm will not be reduced due to the large fluorescent factor. At the same time, the chemotaxis (flipping and swimming) operator in the bacterial foraging algorithm is modified to adopt Gaussian mutation, that is, to add a random disturbance term obeying Gaussian distribution to the current bacterial individualXi′=x1,x2,…,xm as follows:(9)Xi′=Xi+Xi×N0,1.In the previous equation,N0,1 adhere to the Gaussian distribution with a mean value of 0 and a mean square deviation of 1.By adding the random disturbance term of Gaussian distribution in equation (9), the current bacterial population is disturbed so that some individuals in the population can jump out of the local optimal solution. If the fitness of the optimal solution after replacement is larger than that before replacement, then the solution after replacement is better than that before replacement, and the equivalent replacement with probability is carried out. This kind of permutation increases the possibility of jumping out of the local optimal interval and makes equivalent optimization in a larger interval, thus enhancing the optimization ability of the integrated algorithm [24, 25].According to equation (2), parameters c1 and λ of the sliding surface are unknown. The values of these two parameters are related to each other and affect the transient dynamic characteristics of the system. In order to get a better dynamic response, the adaptive GSO-BFA algorithm is used to optimize the above parameters. In order to obtain satisfactory dynamic characteristics, ITAE is used as the objective function for parameter selection. In order to avoid the excessive control amount, the square term of control input is added to the objective function. In order to shorten the rise time, the relevant term with the rise time is introduced [26]. In order to avoid position overshoot, the penalty term related to the absolute value of the error is introduced when the system error e≤0. Equation (10) is selected as the optimal index for parameter selection as follows:(10)J=∫0∞w1et+w2u2t+w4etdt+w3tre≤0,J=∫0∞w1et+w2u2tdt+w3tre>0.λ=72.219. The parameters of the sliding surface are c1∈0,500, λ∈0,100. After 100 iterations, the optimized parameters are c1=381.276, λ=72.219. The design parameter is taken as h=60.


## 2.5. Improved GSO Algorithm

### 2.5.1. Adaptive Selection Strategy

The parameters of the controller in the adaptive fuzzy backstepping sliding mode are optimized by the GSO-BFA algorithm, and the optimized parameters are combined with the improved GSO algorithm to find the optimal autonomous control method of the voltage frequency ratio [27, 28].In the initial GSO algorithm, the step size is fixed, easily leading to the algorithm falling into the local optimal solution. Therefore, the step size is constantly adjusted according to the results of each iteration to find the global optimal value quickly and accurately. For example, in the early stage of the algorithm iteration, the step size change needs to be larger, which can speed up the iteration speed. In the late stage of the iteration, the step size needs to be very small to accurately find the local optimal value. Therefore, the GSO algorithm and the optimal path of voltage frequency ratio of the AC-AC frequency conversion are coevoluted to find the optimal step length for each individual.Firstly, each individual randomly assigns the AC frequency ratio and step size in a suitable range, the affinity of each AC frequency ratio is calculated according to the iteration of the algorithm, and the affinity is calculated as follows:(11)AγiG=fxiG−fxiG+1fxiG+1,iffxiG+1<fxiG,0,other.In each iteration, a certain percentage of the voltage frequency ratio of the AC-AC frequency conversion is interfered with by some other factors, and the voltage frequency ratio of AC-AC frequency conversion is updated as follows:(12)αkG+1=αk+QG,ifQ+k≤M,υQ+k−Motherwise.According to the integer sequence decoding of the second half of the individual, we can get the processing machines of each process.Q31 is processed by the first machine, Q11 is processed by the third machine, and so on.The sequence code of operation processing is combined with the part code of machine selection to get the whole individual. The first half of the individual represents the operation code, and the second half represents the machine code, whereM=2∗NP,Q=0.2∗NP,k=1,2,…,2∗NP.According to a random probability, the step parameter is selected in the antibody, and the step parameter is updated according to the following equation:(13)γiG+1=πiG+1,ifPi≤Pc,θi,otherwise,where i=1,2,…,NP, Pi is Rand, Pc is the preset inoculation probability, πiG+1 is selected from αkG+1, and the selected strategy is roulette; k=1,2,…,2∗NP, and θi is selected from γi1.


### 2.5.2. Flowchart of the Improved GSO Algorithm

The chart of the improved GSO algorithm is shown in Figure3.Figure 3
Flowchart of the improved GSO algorithm.Analyzing the flowchart of the improved GSO algorithm in Figure3, we can see that the initialization parameters and greedy coding strategy generate n individuals x and the number of iterations Tmax. Set the number of iterations of initial value t = 1. Update the fluorescein. Calculate the individual N (t) that is brighter than oneself within the strategy radius of individual i. Select an individual that is brighter than oneself for the wheel plug. Update the position of individual i. Judge that x is the rest of nonindividual I and x∈Nt; if it is another Pox crossover and if there is no domain insertion or reverse order arrangement, the two results will be output, respectively. Update the position of individual x. Update the decision radius and fitness value. Calculate the affinity. Update the AC frequency ratio. Update the step length. If the number of iterations does not have T<Tmax, the maximum brightness and the optimal position will be output. If T<Tmax, repeat the above result until T<Tmax.


## 2.5.1. Adaptive Selection Strategy

The parameters of the controller in the adaptive fuzzy backstepping sliding mode are optimized by the GSO-BFA algorithm, and the optimized parameters are combined with the improved GSO algorithm to find the optimal autonomous control method of the voltage frequency ratio [27, 28].In the initial GSO algorithm, the step size is fixed, easily leading to the algorithm falling into the local optimal solution. Therefore, the step size is constantly adjusted according to the results of each iteration to find the global optimal value quickly and accurately. For example, in the early stage of the algorithm iteration, the step size change needs to be larger, which can speed up the iteration speed. In the late stage of the iteration, the step size needs to be very small to accurately find the local optimal value. Therefore, the GSO algorithm and the optimal path of voltage frequency ratio of the AC-AC frequency conversion are coevoluted to find the optimal step length for each individual.Firstly, each individual randomly assigns the AC frequency ratio and step size in a suitable range, the affinity of each AC frequency ratio is calculated according to the iteration of the algorithm, and the affinity is calculated as follows:(11)AγiG=fxiG−fxiG+1fxiG+1,iffxiG+1<fxiG,0,other.In each iteration, a certain percentage of the voltage frequency ratio of the AC-AC frequency conversion is interfered with by some other factors, and the voltage frequency ratio of AC-AC frequency conversion is updated as follows:(12)αkG+1=αk+QG,ifQ+k≤M,υQ+k−Motherwise.According to the integer sequence decoding of the second half of the individual, we can get the processing machines of each process.Q31 is processed by the first machine, Q11 is processed by the third machine, and so on.The sequence code of operation processing is combined with the part code of machine selection to get the whole individual. The first half of the individual represents the operation code, and the second half represents the machine code, whereM=2∗NP,Q=0.2∗NP,k=1,2,…,2∗NP.According to a random probability, the step parameter is selected in the antibody, and the step parameter is updated according to the following equation:(13)γiG+1=πiG+1,ifPi≤Pc,θi,otherwise,where i=1,2,…,NP, Pi is Rand, Pc is the preset inoculation probability, πiG+1 is selected from αkG+1, and the selected strategy is roulette; k=1,2,…,2∗NP, and θi is selected from γi1.


## 2.5.2. Flowchart of the Improved GSO Algorithm

The chart of the improved GSO algorithm is shown in Figure3.Figure 3
Flowchart of the improved GSO algorithm.Analyzing the flowchart of the improved GSO algorithm in Figure3, we can see that the initialization parameters and greedy coding strategy generate n individuals x and the number of iterations Tmax. Set the number of iterations of initial value t = 1. Update the fluorescein. Calculate the individual N (t) that is brighter than oneself within the strategy radius of individual i. Select an individual that is brighter than oneself for the wheel plug. Update the position of individual i. Judge that x is the rest of nonindividual I and x∈Nt; if it is another Pox crossover and if there is no domain insertion or reverse order arrangement, the two results will be output, respectively. Update the position of individual x. Update the decision radius and fitness value. Calculate the affinity. Update the AC frequency ratio. Update the step length. If the number of iterations does not have T<Tmax, the maximum brightness and the optimal position will be output. If T<Tmax, repeat the above result until T<Tmax.


## 3. Experimental Results

In the experiment, 1LA7-113M-4AA three-phase asynchronous motor and magnetic powder brake are used as the loading system. JN338 type torque speed sensor is installed on the on-load system, and the collected speed and torque data are fed back to the JN338 torque and speed measuring instrument connected with the sensor, through which the speed, torque, and output power can be directly read out. At the same time, the upper computer is also equipped with software matching the instrument, which can not only read the speed and torque, but also directly give the change of speed and torque waveform. When the load is needed, only the excitation current of the magnetic powder brake needs to be increased, and the change of the load torque is reflected in the torque and speed measuring instrument. Then, for the three-phase asynchronous motor, the load system is used to determine the optimal voltage frequency ratio of the cycloconverter under different frequencies and loads [29].The test object is a three-phase asynchronous motor of 1LA7-113M-4AA. Its specific parameters are as follows: rated power is 4 KW, rated speed is 1440 r/min,UN = 380 V, fN = 50 NfHz, IN = 8.4 A, r1 = 5.25 Ω, r2′ = 2.3 Ω, rm = 5.7 Ω, l1 = 0.02 H, l2′ = 0.02 H, lm = 0.433 H, TN = 27 N·m, and J = 0.011 Kgm2.According to the main circuit of the six-pulse dual-variable cycloconverter and the actual circuit structure, a simulation model of the six-pulse cycloconverter is built under the environment of MATLAB/Simulink 7.0, as shown in Figure4.Figure 4
Simulation model of the speed regulation system of the six-pulse cycloconverter.Figure4 shows that the simulation model of the six-pulse cycloconverter is mainly composed of the modules: six-phase power module, thyristor circuit module, three-phase asynchronous motor module, measurement module, harmonic analysis module, display module, trigger S function module, and load torque S module.


### 3.1. Experiment of the Optimal Voltage Frequency Ratio at Six-Frequency Division

Under the experimental platform, the experiment is conducted on the three-phase asynchronous motor in six-frequency division (8.3 Hz) under the load of 3.4 N·m by the proposed method. At this time, the output voltage of the cycloconverter of the motor is 53.5 V (the optimal voltage corresponding to the load of 3.4 N·m in six-frequency division is 53.5 V). The output voltage waveform, current waveform, and speed waveform of the optimal voltage frequency ratio of the cycloconverter in the experimental motor under the control of the method in this study are shown in Figures5–7, respectively.Figure 5
Experimental trend of output voltage with the optimal voltage frequency ratio of the six-frequency division (F = 8.3 Hz).Figure 6
Experimental trend of the optimal voltage frequency ratio current of the six-frequency division (F = 8.3 Hz).Figure 7
Experimental trend of the optimal voltage frequency ratio speed of frequency division (F = 8.3 Hz).It can be seen from the experimental output trend chart of the six-frequency optimal voltage frequency ratio control of the experimental motor cycloconverter controlled by the proposed method that the symmetry and sinusoidal degree of the output voltage waveform of the six-pulse cycloconverter are also very good, the current waveform can also pass through the zero smoothly, and there is no dead zone in the current conversion process. The motor speed is very stable, and the vibration is very small. According to these experimental results, the output voltage waveform, current waveform, and motor speed of the real motor six-frequency cycloconverter under the control of the method in this paper are better, which shows that the control method in this study can effectively control the voltage frequency ratio of the cycloconverter, so that the motor speed is stable and the vibration is very small.


### 3.2. Online Continuous Frequency Conversion Experiment of Optimal Voltage Frequency Ratio

The optimal voltage frequency ratio of the motor with different loads at each frequency is obtained by the experiment of the optimal voltage frequency ratio. Combined with the control method in this study, the experiment on the optimal voltage frequency ratio of the experimental motor cycloconverter under the control of the method is conducted. Taking the optimal voltage frequency ratio of the decadal frequency (5 Hz) with 2.6 N·m load and the decadal frequency (5.56 Hz) with 2.47 N·m load as an example, the online continuous frequency conversion experiment of the experimental motor cycloconverter controlled by the proposed method is studied.Figure8 is the motor speed when switching from 5.56 to 5 Hz, Figure 9 is the motor speed when switching from 5 to 5.56 Hz, and Figure 10 is the motor speed when switching from 5 to 5.56 Hz and then from 5.56 to 5 Hz.Figure 8
Test trend of motor speed when switching fromF = 5.56 to f = 5 Hz.Figure 9
Test trend of motor speed when switching fromF = 5 to f = 5.56 Hz.Figure 10
Test trend of motor speed whenf = 5 to f = 5.56 h switch each other.Figures8 and 9 show that, in the process of frequency switching from 5.56 to 5 Hz and from 5 to 5.56 Hz, the experimental motor under the control of the proposed method has stable speed, smooth switching transition, small vibration, and fast switching response. It shows that the control method in this study is good [30]. Under the condition of online continuous frequency conversion of the optimal voltage frequency ratio, the motor speed can still be controlled effectively and stably. When the voltage frequency is switched, the transition is smooth, the vibration is minimal, and the response speed is extremely fast.It can be seen from Figure10 that in the process of frequency switching from 5 Hz to 5.56 Hz and then from 5.56 Hz to 5 Hz, the motor speed control transition process controlled by the proposed method is very smooth and stable.It can be seen from the above that when the motor switches between 5 and 5.56 Hz, the speed regulation process of the motor is smooth and stable under the level difference of 0.5 Hz. Because the level difference of 0.5 Hz is already very small, it can be considered that the speed of the experimental motor under the control of the method in this study is continuously changing. It shows that, under the condition of online continuous frequency conversion, the control effect is optimal when the optimal voltage frequency ratio of the experimental motor is controlled by the method in this study.Then, any number of the optimal voltage frequency ratio controlled by the method in this study is given for an online continuous frequency conversion experiment, and the speed waveform of the experimental motor under the control of the method in this study is shown in Figure11. It can still be seen from Figure 11 that the optimal voltage frequency ratio of the experimental motor controlled by the method in this study is stable and the speed regulation is smooth and stable.Figure 11
Experimental trend of the optimal voltage frequency ratio’s online continuous frequency conversion and speed up.From the motor speed waveform obtained from the above experiments, when the online continuous frequency conversion control strategy for the optimal voltage frequency ratio of the experimental motor cycloconverter is controlled by the method in this study and when the frequency range is small enough to switch between each other, the motor speed is stable and the speed regulation process is smooth, which can make the motor always run in an economic state with high force index.In order to further verify the convergence of the control method in this study, the pressure input of a certain motor is selected, and the NURBS control method, AUV control method, and the control method in this study are respectively selected for experimental results’ comparison. Figure12 is the motor pressure tracking curve of the three control methods, and Table 1 is the motor pressure error of the three control methods.Figure 12
Pressure tracking control trend of three control methods.Table 1
Pressure error of three control methods.
Pressure error (MPa)Time (min)NURBS control methodAUV control methodControl method in this study1444210.5030004−4−4−45−1−0.506000It can be seen from the analysis of Figure12 and Table 1 that the convergence speed of the pressure control error curve and pressure tracking control curve of the experimental motor using the control method in this study is faster than that of the other two control methods, and the tracking of the input quantity can be recovered in a short time, which shows that the convergence number of the voltage frequency ratio of the experimental motor cycloconverter is faster and the control effect is good.


## 3.1. Experiment of the Optimal Voltage Frequency Ratio at Six-Frequency Division

Under the experimental platform, the experiment is conducted on the three-phase asynchronous motor in six-frequency division (8.3 Hz) under the load of 3.4 N·m by the proposed method. At this time, the output voltage of the cycloconverter of the motor is 53.5 V (the optimal voltage corresponding to the load of 3.4 N·m in six-frequency division is 53.5 V). The output voltage waveform, current waveform, and speed waveform of the optimal voltage frequency ratio of the cycloconverter in the experimental motor under the control of the method in this study are shown in Figures5–7, respectively.Figure 5
Experimental trend of output voltage with the optimal voltage frequency ratio of the six-frequency division (F = 8.3 Hz).Figure 6
Experimental trend of the optimal voltage frequency ratio current of the six-frequency division (F = 8.3 Hz).Figure 7
Experimental trend of the optimal voltage frequency ratio speed of frequency division (F = 8.3 Hz).It can be seen from the experimental output trend chart of the six-frequency optimal voltage frequency ratio control of the experimental motor cycloconverter controlled by the proposed method that the symmetry and sinusoidal degree of the output voltage waveform of the six-pulse cycloconverter are also very good, the current waveform can also pass through the zero smoothly, and there is no dead zone in the current conversion process. The motor speed is very stable, and the vibration is very small. According to these experimental results, the output voltage waveform, current waveform, and motor speed of the real motor six-frequency cycloconverter under the control of the method in this paper are better, which shows that the control method in this study can effectively control the voltage frequency ratio of the cycloconverter, so that the motor speed is stable and the vibration is very small.


## 3.2. Online Continuous Frequency Conversion Experiment of Optimal Voltage Frequency Ratio

The optimal voltage frequency ratio of the motor with different loads at each frequency is obtained by the experiment of the optimal voltage frequency ratio. Combined with the control method in this study, the experiment on the optimal voltage frequency ratio of the experimental motor cycloconverter under the control of the method is conducted. Taking the optimal voltage frequency ratio of the decadal frequency (5 Hz) with 2.6 N·m load and the decadal frequency (5.56 Hz) with 2.47 N·m load as an example, the online continuous frequency conversion experiment of the experimental motor cycloconverter controlled by the proposed method is studied.Figure8 is the motor speed when switching from 5.56 to 5 Hz, Figure 9 is the motor speed when switching from 5 to 5.56 Hz, and Figure 10 is the motor speed when switching from 5 to 5.56 Hz and then from 5.56 to 5 Hz.Figure 8
Test trend of motor speed when switching fromF = 5.56 to f = 5 Hz.Figure 9
Test trend of motor speed when switching fromF = 5 to f = 5.56 Hz.Figure 10
Test trend of motor speed whenf = 5 to f = 5.56 h switch each other.Figures8 and 9 show that, in the process of frequency switching from 5.56 to 5 Hz and from 5 to 5.56 Hz, the experimental motor under the control of the proposed method has stable speed, smooth switching transition, small vibration, and fast switching response. It shows that the control method in this study is good [30]. Under the condition of online continuous frequency conversion of the optimal voltage frequency ratio, the motor speed can still be controlled effectively and stably. When the voltage frequency is switched, the transition is smooth, the vibration is minimal, and the response speed is extremely fast.It can be seen from Figure10 that in the process of frequency switching from 5 Hz to 5.56 Hz and then from 5.56 Hz to 5 Hz, the motor speed control transition process controlled by the proposed method is very smooth and stable.It can be seen from the above that when the motor switches between 5 and 5.56 Hz, the speed regulation process of the motor is smooth and stable under the level difference of 0.5 Hz. Because the level difference of 0.5 Hz is already very small, it can be considered that the speed of the experimental motor under the control of the method in this study is continuously changing. It shows that, under the condition of online continuous frequency conversion, the control effect is optimal when the optimal voltage frequency ratio of the experimental motor is controlled by the method in this study.Then, any number of the optimal voltage frequency ratio controlled by the method in this study is given for an online continuous frequency conversion experiment, and the speed waveform of the experimental motor under the control of the method in this study is shown in Figure11. It can still be seen from Figure 11 that the optimal voltage frequency ratio of the experimental motor controlled by the method in this study is stable and the speed regulation is smooth and stable.Figure 11
Experimental trend of the optimal voltage frequency ratio’s online continuous frequency conversion and speed up.From the motor speed waveform obtained from the above experiments, when the online continuous frequency conversion control strategy for the optimal voltage frequency ratio of the experimental motor cycloconverter is controlled by the method in this study and when the frequency range is small enough to switch between each other, the motor speed is stable and the speed regulation process is smooth, which can make the motor always run in an economic state with high force index.In order to further verify the convergence of the control method in this study, the pressure input of a certain motor is selected, and the NURBS control method, AUV control method, and the control method in this study are respectively selected for experimental results’ comparison. Figure12 is the motor pressure tracking curve of the three control methods, and Table 1 is the motor pressure error of the three control methods.Figure 12
Pressure tracking control trend of three control methods.Table 1
Pressure error of three control methods.
Pressure error (MPa)Time (min)NURBS control methodAUV control methodControl method in this study1444210.5030004−4−4−45−1−0.506000It can be seen from the analysis of Figure12 and Table 1 that the convergence speed of the pressure control error curve and pressure tracking control curve of the experimental motor using the control method in this study is faster than that of the other two control methods, and the tracking of the input quantity can be recovered in a short time, which shows that the convergence number of the voltage frequency ratio of the experimental motor cycloconverter is faster and the control effect is good.


## 4. Discussion

According to the control process and results of the voltage frequency ratio autonomous control method based on the GSO algorithm, suggestions are given to enhance the control effect of the proposed method.In the experiment of speed regulation in this study, due to the limitation of experimental conditions and technology, there are still some shortcomings. Therefore, some improvements are put forward to make the voltage frequency of the cycloconverter better than the autonomous control method. In the online real-time continuous frequency control strategy, the fixed point frequency switching mode has certain hysteresis [31]. If real-time frequency switching can be realized, the response speed of the system frequency switching can be greatly improved. From the perspective of converter performance, a six-pulse cycloconverter can be developed into a twelve-pulse cycloconverter or matrix cycloconverter. In particular, the matrix cycloconverter adopts fully controlled devices with high efficiency and excellent electrical performance. In terms of control strategy, vector control and direct torque control can be further studied and utilized. The DSP chip can also be used for motor control to improve data processing ability and operation speed. At present, the speed control system of the cycloconverter built in the laboratory is still in the experimental stage. In the future, each module can be miniaturized and portable to realize productization and be applied to production practice.Based on the study of the GSO algorithm, this study proposes some improvements to the convergence speed of the GSO algorithm. However, there are still some problems in other aspects of the GSO algorithm, which need further research and improvement. (1) Parameter design of the algorithm: in the basic GSO algorithm, a few parameters need to be adjusted, but whether the selected parameters are appropriate will have a significant impact on the performance of the algorithm. At present, the selection of parameters in the GSO algorithm is mostly based on the experience value summed up by previous experiments without a considerable theoretical basis. In future research, the parameters of the algorithm can be studied from the theory and experiment, which makes the selection of parameters more reasonable and greatly improves the performance of the algorithm. (2) Global search of the algorithm: we only study the performance of the algorithm in terms of multimodal optimization, not the problem of finding global optimization. If the GSO algorithm can be well applied in finding the global optimization, it can greatly improve the practicability of the algorithm. (3) The optimization ability of the algorithm in the multidimensional space: the test functions used in this study are all in two-dimensional space. Of course, the optimization of fireflies can be carried out not only in two-dimensional space, but also in the multidimensional space. However, this study does not involve multidimensional space optimization. In the future, the optimization of algorithms in the multidimensional workspace can be studied [32].In addition, the optimal voltage frequency ratio control strategy of cycloconverter can adjust the different proportion or combination of stator phase voltage and stator angle frequency of asynchronous motor according to the working conditions of asynchronous motor (such as load size) on the premise of ensuring the speed regulation requirements of the asynchronous motor to make the active and reactive power of asynchronous motor close to the optimal coordination state and make the total loss of motor. In order to guarantee the optimal synthesis of power factor and efficiency of asynchronous motor, the force and energy index is optimized. The optimal voltage frequency ratio control strategy can also adjust and reduce the stator terminal voltage continuously under a certain frequency and a certain load according to the needs of artificial experience and actual working conditions and take the minimum stator current as the breakthrough point to find the optimal comprehensive point of power factor and efficiency within a certain range, that is, the optimal voltage frequency matching relationship. Then, according to the specific working conditions of the asynchronous motor, combined with the online continuous frequency control strategy, through the specific experiment of the six-pulse dual-variable cycloconverter to drive the asynchronous motor, it always runs in the economic state with a high-power factor and efficiency.


## 5. Conclusion

In order to keep the flux constant when the asynchronous motor is running under load, especially light load, this study proposes a new control method for the voltage-frequency ratio of AC converter based on the GSO algorithm to independently control the voltage-frequency ratio of AC converter. Based on the improved GSO algorithm, the optimal voltage-frequency ratio control of the loop converter is realized in the adaptive fuzzy backstepping sliding mode. The FA is used to iteratively optimize the descriptions of pheromone update, firefly individual motion, and dynamic decision domain update, which avoids the shortcoming of the algorithm falling into convergence early and failing to obtain the global optimal solution and improves the local and global optimization ability of the algorithm. As a result, through a large number of validated experimental data, the method in this study can, according to handing over the inverter online continuous variable frequency control method, realize the optimal voltage frequency ratio control, get the output voltage and current waveform, and speed torque waveform analysis, all demonstrating the validity and applicability of this method, to illustrate that the design results of the method can achieve the purpose of this study, It provides a theoretical basis for better control of voltage frequency ratio of AC converter.



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*Source: 3280622-2022-09-05.xml*