The effective transmission distance of a magnetic coupling resonance (MCR) wireless power transfer (WPT) system is an essential index of wireless power transfer. Existing systems often suffer from short transmission distances, low power, and low efficiency. In this paper, a method is proposed for improving the parameters of wireless power transfer systems to enhance the performance of the systems. The main parameters affecting the output power and transmission efficiency are determined by analyzing the MCR WPT system with SS-type topology. In addition, the multi-objective ant lion optimizer is combined with tent chaotic mapping to generate the location information of the initial population by using the distribution and randomness of tent chaotic mapping, which increases the diversity of the people and improves the convergence speed and global search capability of the algorithm to achieve multi-objective parameter optimization, and the optimized model is also analyzed. Experiments show that the optimized MCR WPT system has improved output power and transmission efficiency at a longer distance. The optimal transmission distance of the system is about 0.2 m with a maximum output power of 129.3 W, and the axial offset stability of the system is enhanced. Finally, the effectiveness of the improved model is verified by building a prototype system. It provides a valuable reference for the research of improving wireless power transfer.
Since the publication of the research results on wireless energy transmission technology by the MIT research team in 2007, the research and development of magnetically coupled resonant wireless energy transmission technology has been intensified.1 Subsequently, wireless energy transmission technology has entered a rapid development stage, and the related theoretical research, innovative experiments, and application promotion have made great progress.2 As a contactless power transfer (CPT) technology, wireless energy transfer technology can transfer energy from the power source to electrical devices through space, free from the limitations of traditional tangible media.3
Several research teams at home and abroad have studied wireless energy transmission technology in recent years. In 2014, Huang et al.4 proposed using an intermediate coil system to improve the efficiency of wireless power transfer (WPT). The coupled mode theory was applied to obtain an expression for the efficiency of the intermediate WPT system. By optimizing the key parameters of the system, the efficiency of the system was improved, and a magnetic resonance coupled intermediate WPT system was designed. In 2015, Zhao et al.5 proposed a WPT system model with a three-dimensional emitter (3DT WPT). By using electronic control methods, the efficiency formula was derived and analyzed, and the key parameters of the system were identified. The power transmission characteristics of the 3DT-WPT were demonstrated through the analysis of key parameters, and the analysis results were well verified through experiments. In 2015, Huang et al.6 proposed a method to adjust the working frequency and load resistance by solving the system equivalent equation to solve the problem of low efficiency caused by resonant frequency drift. When resonance frequency drift occurs, the WPT system can operate in a quasi-resonant state, and a WPT system based on magnetic resonance coupling was designed. In 2017, Jiang et al.7 analyzed a non-resonant converter with resonant energy storage and a resonant inverter with resonant power storage, compensation networks, and selective resonant circuits in wireless energy transmission systems. In addition, key issues such as zero-voltage switching, zero-voltage derivative switching, and total harmonic distortion were discussed. In 2019, Elnaggar et al.8 proposed wireless power transmission through a dielectric loaded multimode split cavity resonator (SCR). Due to the complexity of the structure, a circuit based approach was adopted to study the system performance. The results indicate that, unlike traditional inductive resonant coupling, this configuration provides the possibility of controlling transmission impedance and improving the power and efficiency of the system. In 2021, Xue et al.9 analyzed the effect of equivalent load and mutual inductance changes on the system by modeling the LCC-S topology using two-port theory. In 2022, Zhu et al.10 modeled the LCCL-S compensation structure and realized the difference in voltage gain without additional components and observed that the system remained in a resonant state. In 2022, Wen et al.11 proposed a series-parallel-series-parallel topology without energy transfer to address the problems of low power transfer efficiency and low output power in the traditional magnetically coupled topology, and through theoretical analysis, modeling simulation, and experimental verification, the rationality of the proposed structure and the correctness of the simulation parameters design method were proved. In addition, the thermal analysis of the coupled resonant coil of the wireless charging system for electric vehicles12 was carried out in terms of coil temperature distribution and other aspects, and a structure that facilitates coil heat dissipation was proposed. In 2022, Ren and Niu13 proposed a magnetoelectric WPT (ME-WPT) system with a new miniature ME-WPT receiver and a spiral coil-based transmitter. It enabled the size of the system to be reduced while providing DC magnetic bias. In 2023, Chen et al.14 proposed a switchable hybrid topology wireless charging system based on an integrated coil structure to achieve a high efficiency of 90.6% at an air gap of 20 cm when delivering 288 W to the load. In 2023, Zhu et al.15 designed an anti-misalignment printed circuit board (PCB) coil to improve the quality factor of the coil while ensuring uniformity of the magnetic field strength in the region of interest, and the effective power transfer area of the system was significantly expanded. In order to better integrate the magnetic coupling resonance (MCR) WPT system with engineering practice, improving its output power and transmission efficiency is one of the current hotspots of research.
When converting a multi-objective problem into a single-objective problem, only one optimal solution can be generally obtained. In contrast, the multi-objective solution method based on the Pareto idea16 allows us to obtain several optimal solutions simultaneously. Therefore, it is applied to several practical problems. Grisales-Ramírez and Osorio17 provided a method for formulating combinatorial optimization problems that allow the inclusion of complex cost functions as well as multi-objective optimization problems. Shen et al.18 proposed a multi-objective immune optimization-based path plan for welding robots. Biswas et al.19 developed a workflow for joint optimization of multiple material functions using multi-objective Bayesian optimization. Among them, the Ant Lion Optimizer (ALO)20 was proposed by scholar Mirjalili in 2015, which has the advantages of fewer adjustment parameters and high optimization-seeking ability. In 2016, Mirjalili proposed Multi-Objective Ant Lion Optimization (MOALO),21 which uses the dominant relationship among individuals in the population to find the optimal solution set, and proved that the algorithm outperforms some classical multi-objective algorithms. Due to the superiority of this algorithm, it has been rapidly applied to several fields. Yingzhou et al.22 used the ant lion algorithm to optimize the core parameters of the prediction model and applied it to the life prediction of lithium batteries, which effectively improved the accuracy and robustness of the prediction of the remaining life of lithium-ion batteries. Yingming et al.23 used the ant lion algorithm to solve the wind power cluster energy storage capacity allocation optimization problem, analyzed the influence of the unit cost and lifetime of energy storage batteries on the optimization results, and verified the effectiveness of the proposed algorithm and model. Changqiang and Kexin24 used the improved ant lion algorithm for the 3D trajectory of Unmanned Aerial Vehicle (UAV) to achieve online local replanning optimization in the trajectory problem. In the optimization algorithm, the performance of the algorithm can be improved by improving the population initialization. Huang et al.25 used a quantum particle swarm optimization algorithm with tent chaotic mapping to make the root mean square error and average relative error of the sample test set smaller, reduce the time complexity of modeling, and improve the performance of engine fault diagnosis.
The current MCR WPT system has the problems of short transmission distance, low power, low efficiency, etc. The existing studies are mainly conducted on a single factor of efficiency or power, and the comprehensive performance of the system is poor. Based on the above-mentioned research, the equivalent system model is constructed in this paper, and the system’s power and efficiency are analyzed using MATLAB software. The system’s parameters are optimized using tent chaotic mapping, an improved multi-objective ant lion optimization, to achieve improvement in the transmission distance of the system and to enhance the stability of the system.
II. WIRELESS POWER TRANSFER SYSTEM CHARACTERISTICS
MCR WPT systems cannot be fully coupled during transmission due to a certain distance between coils, resulting in a lot of reactive power during energy transmission. Attaching a compensation network to the circuit can effectively reduce the system’s reactive power and reduce the reactive power loss of the line. Among them, SS-type topology has the advantages of high efficiency, simplified design, flexibility, and anti-interference in wireless power transfer, which makes it a common and effective topology choice for various wireless power transfer application scenarios. Therefore, SS-type topology is used for analysis and optimization in this paper.
A. Characterization of SS-type systems
The equivalent circuit of SS-type topology is shown in Fig. 1, where US is the output voltage of the power supply, RS is the internal resistance of the power supply, M is the mutual inductance between the transmitter and receiver coils, LP and LS are the equivalent mutual inductances of the transmitter and receiver coils, respectively, CP and CS are the external series tuning capacitors of the transmitter and receiver coils, respectively, R1 and R2 are the equivalent loss resistances of the transmitter and receiver coils, respectively, and RL is the load resistance.
B. The relationship between the system’s multi-parameters and power output and transmission efficiency
The simulation parameters in this paper are selected as US = 24 V, f = 20 kHz, RS = 1 Ω, RL = 20 Ω, R1 = 0.2 Ω, R2 = 0.2 Ω, r1 = r2 = 0.075 m, and n1 = n2 = 15. The effects on the MCR WPT system’s output power and transmission efficiency are investigated by single- and multi-parameter analysis of the system. The effect of load resistance and coil distance of the magnetically coupled resonant system on the load output power and system transmission efficiency is investigated by using the system load resistance and coil distance as variables.
Figure 2(a) shows the graph of the system’s output power with the coil distance and load size. The experimental results show that the output power of the system PL increases and then decreases with the transmission distance, reaching a larger value of about 140 W at about 0.08–0.12 m. When the transmission distance is 0.2 m, the output power is below 70 W.
Figure 2(b) shows the graph of the system’s transmission efficiency with the coil distance and load size. The system’s transmission efficiency η tends to decrease with the transmission distance first. When the transmission distance is close, the transmission efficiency is higher at this time, generally reaching more than 80%. When the coils are about 0.1 m apart, the transmission efficiency is between 40% and 60%. When the transmission distance is 0.2 m, the system’s efficiency drops significantly, and the transmission efficiency is almost zero.
To further analyze the effect of the operating frequency of the magnetically coupled resonant system on the output power and transmission efficiency, the system was analyzed in the operating frequency range of 1–500 kHz by fixing the distances of the transmitter and receiver coils at 0.1 and 0.2 m, respectively.
Figure 3(a) shows the graph of power vs frequency for a transmission distance of 0.1 m. When the transmission distance of the system is 0.1 m, the system reaches the maximum output power in the frequency range of 50–100 kHz, and the maximum output power is about 137 W. After that, the system’s output power decreases as the frequency increases. Figure 3(b) shows the graph of power vs frequency for a transmission distance of 0.2 m. When the transmission distance of the system is 0.2 m, the system reaches the maximum output power after 300 kHz, and the maximum output power is about 130 W. After that, the system’s output power decreases with the increase in frequency.
The larger the load RL, the greater the operating frequency f required to achieve the maximum output power PL of the system.
Figure 4(a) shows a plot of efficiency vs frequency for a transmission distance of 0.1 m. In all cases, the system achieves more than 50% transmission efficiency at 0.1 m and above 100 kHz. Figure 4(b) shows the efficiency vs frequency for a transmission distance of 0.2 m. The system requires a larger operating frequency for a higher transmission efficiency at 0.2 m.
The overall transmission efficiency η of the system increases with the increase in frequency f and decreases with the increase in load resistance RL.
From the above-mentioned analysis, it can be seen that the transmission distance of the system, the operating frequency of the system, and the value of the load resistance all have a considerable impact on the final output power and transmission efficiency, after which the determined values of the three parameters need to be obtained to improve the system.
III. TENT CHAOTIC MAPPING FOR MULTI-OBJECTIVE ANT LION OPTIMIZATION IMPROVEMENT
The previous analysis of the system concluded that many factors affect the system’s final output power and transmission efficiency. The main influencing factors in this system are the transmission distance, the operating frequency of the system, and the load resistance value. To obtain the optimal matching values of these three parameters, this article intends to introduce artificial intelligence optimization algorithms to obtain the optimal values of system parameters.
The multi-objective ant lion optimization has fewer adjustment parameters, high convergence accuracy, good robustness, and global optimality. The method first uses the storage space to store the currently obtained non-dominant Pareto optimal solutions. Then it uses the roulette wheel mechanism to select the solution and guide the ant lion toward the region of the multi-objective search space. This paper uses its fitness function for the SS-type equivalent circuit model to find the optimal solution.
A. Population initialization through tent chaotic mapping
The original multi-objective ant lion algorithm starts its execution by randomly generating the initial position information of the ant lion population. The ant lion population generated in this way is not diverse enough, and for dealing with complex functions, it may cause the algorithm to eventually fall to an optimal local solution, affecting its convergence accuracy.
Chaotic mapping is a complex nonlinear dynamical system, and its properties of randomness, reversibility, sensitivity, and disorder make it a tool in multi-objective optimization.
The tent chaotic mapping function optimizes the multi-objective ant lion optimization, and the data generated by the tent mapping are used as the location information of the initial ant lion population. The search diversity of the ant lion population is preserved so that individual ant lions can jump out of the optimal local solution in the search process, and the convergence speed and global search ability of the ant lion optimizer are improved.
B. Multi-objective ant lion optimization flow
The multi-objective ant lion algorithm mainly includes the following roles: ants, ant lions, and elite ant lions. The specific hunting process of the ant lion is the optimization process of the algorithm. First, the ant represents the attempt to solve, and it begins to move. The ant lion randomly excavates a conical sand pit trap on the sand and waits for the ant to fall into the trap. Then, the ant lion will prey on the ant that falls into the trap, and the ant lion that preys on the ant represents the local optimal solution. After the predation, the ant lion will dig a new trap and wait for the next ant to enter the next cycle. Each time the ant lion updates, it will select the elite ant lion according to the fitness value and take it as the local optimal solution. By continuously iterating, it finds a more optimal solution near the local optimal solution and finally obtains a more accurate global optimal solution.
The multi-objective ant lion optimization has the following parts:
Random initialization of the population:
The improved multi-objective ant lion optimization population initialization is obtained by tent chaotic mapping after determining the constraints, as shown in Eq. (6).
Ants’ random walk:The definition equation of ant random wandering is Xi = [0, cumsum [2r(1) − 1], …, cumsum [2r(t) − 1], …, cumsum [2r(T) − 1]], where cumsum is the cumulative numerical function, t and T are the current and maximum number of iterations, respectively, r(t) is 0 or 1, and v is a random number within [0, 1], defined as(7)To ensure that the paths traveled by the ants are maintained within the upper and lower bounds, their travel paths are normalized and defined aswhere bi and ai are the upper and lower bounds of the i-th variable, respectively, and and are the upper and lower bounds of the t-th generation of variables, respectively.(8)
Roulette wheel selection:The ant lion selected by roulette and the upper and lower bounds jointly determine the wandering boundary of ants, and the expression iswhere and are the upper and lower bounds of the variable at the t-th generation, respectively. is the position of the s-th ant lion. During the random wandering of the ants, the ant lion will dig traps to catch the ants, which can be abstracted as the ants keep approaching the ant lion. The process is defined as follows:(9)where I is the contraction bound and k increases stepwise with the number of iterations t. The expressions are(10)(11)
- Ant lion predation: In the process of capturing ants, if the ant lion captures successfully, it becomes a new elite ant lion. The expression of the process iswhere is the position of the s-th ant lion in the t-th generation, is the position of the i-th ant in the t-th generation, and and are the fitness functions.(12)
Selection of elite ant lions:The ant lion with the highest fitness in each generation is considered the elite ant lion, and one ant lion is randomly selected by roulette to decide the wandering path of the ants jointly, and the expression of the process iswhere is the random wandering of ants selected by the t-th generation of roulette and is the random wandering of ants around the t-th generation of elite ant lion selection.(13)
Reconstruction trapAn external archive is used in the multi-objective ant lion optimization algorithm to store the Pareto non-dominated solution set, and to obtain more diverse solutions, the distribution of solutions in the external archive is judged using a niche technology,(14)Pi is used to define the probability of selecting a solution in the archive. When the archive is full, the solution with the densest neighbors is removed from the archive to accommodate the new solution. The process expression is(15)
Here, Di is used to define the probability of removing a solution from the archive, c is a constant greater than 1, and Ni is the number of nearby solutions of the i-th solution. Within a fixed radius, the more the other neighboring solutions exist around the solution, the lower the probability that the solution will be archived. When the archive is full, the more the other solutions exist around the solution, the higher the probability of being removed.
The flow chart of the multi-objective ant lion optimization is shown in Fig. 5.
IV. OPTIMIZATION OF MULTI-OBJECTIVE PARAMETERS BASED ON MULTI-OBJECTIVE ANT LION OPTIMIZATION
In this paper, an improved multi-objective ant lion optimization is used, and the design parameters are optimized based on the model established in the previous paper. Constraints and fitness functions are constructed first, and then the optimal parameters are solved for them.
A. Optimization of MCR WPT systems
The range of d is set at [0.2, 0.22] for the optimal transmission distance of the system to be within this range.
The above-mentioned constraints and fitness functions are written in MATLAB software for solving the system output power and transmission efficiency functions. The number of populations of the multi-objective ant lion optimization is set to 100, and the number of iterations is 100; finally, the Pareto optimal solution set is obtained. Figure 6 shows the Pareto front (PF) diagram. The circle icon indicates the Pareto optimal solution and returns the optimized f, RL, and d parameters, which is a three-dimensional array.
V. EXPERIMENT AND VALIDATION
A. Analysis of optimization results
The average value of the solution set is taken for multiple operations as [159 035.5213, 1.3026, 0.2050], that is, when the operating frequency is 159 035.5213 Hz, the load resistance is 1.3026 Ω, the transmission distance is 0.2050 m, and the system performance is optimal for the values of the two objectives under the solution set for the Pareto preference.
Figure 7(a) shows the power and efficiency variation in the system before optimization. The system can reach 60–138 W between 0.04 and 0.75 m transmission distance. The maximum transmitted power is achieved at 0.055 m, and the axial offset of the coil produces a large power difference. Figure 7(b) shows the power and efficiency variation in the optimized system. The system can reach 60–130 W between 0.145 and 0.285 m transmission distance. The maximum transmitted power is achieved at 0.205 m. The distance of the system maximum increased by 0.15 m, and the axial offset of the coil can produce a power difference compared to that before optimization, which has been significantly mitigated. The efficiency of the system, while maintaining the same nature as the original circuit, gradually decreases with the increase in the distance efficiency. When the system reaches the maximum output power, the efficiency is about 50%.
Through simulation experiments, it has been shown that the power and efficiency of the optimized system significantly decreased when the distance exceeds 0.1 m. The operating range of the system is relatively small, around 0.04 m, and the optimal output distance is relatively short. The optimized system has a larger working distance range, around 0.14 m, and the optimal output distance is even further. At the same time, when the system generates a small axial offset, there will be no significant power difference, which increases the stability of the system’s axial offset.
To verify the effectiveness of the improved optimization algorithm for the improved magnetic coupling model, the corresponding resonant circuit’s experimental platform is designed for verification.
B. Prototype platform construction
The selection of the experimental platform parameters is based on the system parameters obtained through dual parameter optimization of system frequency and load. The experiment selected a coil with a diameter of 0.15 m surrounded by copper wire with a diameter of 2.5 mm and an inductance of 220 μH. The number of turns is 15, and the resonant capacitor is selected as 33 μF. At this point, the resonant frequency is 159 kHz, and the power output voltage is 24 V.
The MCR WPT system’s experimental platform is shown in Fig. 8 (1: DC power supply, 2: signal generator, 3: digital oscilloscope, 4: spectrum analyzer, 5: voltage stabilizing circuit module, 6: digital frequency meter, 7: filtering circuit, 8: inverter circuit, 9: transmitting resonant coil, 10: receiving resonant coil, and 11: load).
C. Test results
The load is adjusted to 1.3 Ω, and the power and efficiency are measured once at a distance interval of 0.01 m in the range of 0.01–0.3 m and calculated.
The dashed line in Fig. 9(b) shows the optimized theoretical efficiency curve, and the realization shows the experimental measurement result curve. The maximum output power is measured to be 129.3 W at about 0.20 m when the efficiency is 50%. The error of 0.205 m from the above-mentioned theoretical value is within a reasonable range.
As can be seen from the figure, the power and efficiency measurements of the system, which are basically in line with the theoretical values, verify the effectiveness of the algorithm. However, when the coil distance increases to 0.2 m, the power and efficiency drop slightly faster than the theoretical value. The reasons for this is that the coils are not perfectly aligned for transmission, the presence of media in the air, the heating of the circuit, etc. The error stays within an acceptable range.
Keeping the coil distance at 0.2 m and varying the load value in the range of 0.5–3 Ω, the power and efficiency are measured and calculated for every 0.1 Ω increase. Figure 10 shows the variation in system power vs efficiency when the load varies. When the resistance value is close to 1.2 Ω, the transmission efficiency is 50%, and the output power is 129.3 W. When the output power and transmission efficiency are most stable, the system performance is the best. Therefore, the physical experiment results are close to the optimized resistance value of 1.3026 Ω, and the error is within a reasonable range, which verifies the effectiveness of the algorithm.
This paper addresses the problems of insufficient output power and low transmission efficiency of the MCR WPT method and proposes a method for improving the parameters of the wireless power transfer system to solve the problem of limited transmission distance of the system by optimizing the circuit parameters. Transmission efficiency, output power, transmission distance, operating frequency, and load resistance are the main objects of the study. Based on Kirchhoff’s law, the MCR WPT system of SS-type topology is analyzed, and the tent chaotic mapping improved multi-objective ant lion optimizer is used to solve the optimal Pareto solution set for the system’s transmission efficiency and output power under reasonable constraints. Through experiments, it is proved that the optimization of the method can precisely achieve stability in efficiency and fast convergence, which verifies that the method can obtain the optimal solution set. Then by analyzing and comparing the efficacy curve relationship before and after the optimization, it can be seen that the optimized system is better than the original system in transmission distance and output stability. Finally, a prototype is built to verify the effectiveness of the algorithm. The method has some reference value for the study of wireless charging systems. Once the transmission distance, load size, and operating frequency are determined, the system power and efficiency can be studied more deeply by optimizing the coil structure, improving the inverter circuit, and designing the primary and secondary side circuits.
See the supplementary material for the complete experimental data of the studied physical system.
This work was sponsored in part by the National Natural Science Foundation of China, under Grant No. 61662005; by the 2021 Project of Scientific Research Basic Ability Improvement for Young and Middle-aged Teachers in Guangxi Universities, under Grant No. 2021KY0164; the Innovation Project of Guangxi Graduate Education, under Grant No. YCSW2023252; and by the Guangxi Key Laboratory of Power System Optimization and Energy Technology. This study was approved by the Guangxi University for Nationalities.
Conflict of Interest
The authors have no conflicts to disclose.
Chunming Wen: Conceptualization (equal); Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal). Jianheng Li: Conceptualization (equal); Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal). Bingxu Hou: Formal analysis (equal); Software (equal); Visualization (equal). Yikui Liao: Resources (equal); Validation (equal). Yaqiong Fan: Resources (equal); Validation (equal). Huanyu Guo: Conceptualization (equal); Methodology (equal). Jiarong Wu: Conceptualization (equal); Methodology (equal). Xiaohui Zhao: Resources (equal); Validation (equal). Yuanxiong Liang: Supervision (equal). Kairong Liang: Supervision (equal).
The data that support the findings of this study are available within the article and its supplementary material.