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# Optimal design and analysis of wireless power transfer system with converter circuit

- Xiu Zhang
^{1, 2}, - Xin Zhang
^{1, 2}Email authorView ORCID ID profile, - Changmeng Zhang
^{1, 2}, - Shengwei Yao
^{1, 2}, - Hao Qi
^{1, 2}and - Yunyun Xu
^{1, 2}

**2017**:27

https://doi.org/10.1186/s13638-017-0813-7

© The Author(s). 2017

**Received:**2 November 2016**Accepted:**26 January 2017**Published:**6 February 2017

## Abstract

Wireless power transfer (WPT) technology has many applications by virtue of its intrinsic safety and convenience characteristics. This is particularly so when the WPT systems are used in conjunction with implanted medical devices, as they can greatly reduce the pain of patients and their financial burdens. In previous researches, the optimal system mainly focuses on the design of the coils which includes the transmitter coil and the receiver coil. In this paper, the WPT system will be optimized to include also the power source circuit and the load circuit, in addition to the coils, as an integral system. A simple circuit which converts the DC source into AC excitation as the feeding circuit is included in the WPT system. In this convert circuit, there are two inductors which can be formed by coils. In the WPT system, the two coils in the convert circuit are transmitter coils. In addition, the receiver coil should be optimized. Thus, the WPT system is constructed by the three coils. In this paper, the parameters in the convert circuit are considered along with the coil parameters in the optimization study.

## Keywords

- Convert circuit
- Finite element method
- Optimization method
- Power source circuit
- Wireless power transfer

## 1 Introduction

Wireless power transfer (WPT) system has a great application potential, because of the development of the electronic devices. Comparing with the traditional method of power transfer using magnetic inductive coupling in achieving wireless and efficient near-field power transfer, there are increasing number of researchers that focus on the magnetic resonant coupling method [1–3].

Since 1960s, the implanted medical devices for various functions gradually have permeated into people’s lives, such as pacemaker, deep brain stimulator, and nerve stimulator, which reduce the patients’ pain and effectively prolong their life. Although the industry of the implanted medical devices is in a rapid development, it also faces some problems, such as the battery life. In order to guarantee the normal work of the implanted devices, patients must regularly detect the remaining capacity of the battery. A new battery must replace the exhausted battery through surgery which not only increase the patients’ economic burden but also bring the patients’ physical trauma.

To seek more efficient and durable power supply way, therefore, become one of the key technologies of the implanted medical devices. After entering the end of the twentieth century, to realize the wireless charging for implanted medical devices provides a safe and reliable method to solve the supply problem. Thus WPT technology receives more and more attentions from the researchers in biomedical engineering [4–7].

In 2007, the MIT research team proposed the “WiTricity” system using the magnetic resonant coupling [8, 9]. In the WPT system, it is composed of two coil systems, one is a transmitter coil which is connected to a source to generate a shifting magnetic field, and the other one is a receiver coil which keeps away from the transmitter coil without a wire. The excitation of the WPT system should be a sinusoidal function. In practice, the sinusoidal function is obtained by a convert circuit which connects to a DC source.

Generally, power transfer efficiency is as the objective function under some constrains, such as the volume of the receiver coil or the power transfer distance. According to the application background, sometimes, the power transfer efficiency and the maximum power transfer are both as the objective functions [13]. Under this condition, the multi-objective optimization method [14, 15] can be used to design the WPT system. In this paper, the power transfer efficiency is chosen as the objective function. The WPT model is formulated as a constrained optimization problem. It is a simulation-based optimization problem with mixed discrete-continuous variables. Metaheuristic approaches are generally appropriate and hence commonly used for solving such optimization problems.

In this paper, a simple convert circuit is used to convert a DC source into an AC source. This circuit is applied into the WPT system for implanted medical devices. Thus, the system can be optimized and analyzed as a whole. A differential evolution (DE) algorithm is used to analyze the model. It is simple to implement, easy to use, and computationally fast.

## 2 Convert circuit as feeding circuit

*R*

_{1}, capacitors

*C*

_{1},

*C*

_{2}, and

*C*

_{3}, inductors

*L*

_{1}and

*L*

_{2}, together with a bipolar junction transistor (BJT)

*T*.

*R*

_{1}is used to limit the amplitude of the current flowing into the BJT to guarantee its proper operation; the capacitors

*C*

_{1}and

*C*

_{3}are assist components to ensure that the circuit gives more stable output voltage and current; the characteristic of power switch of BJT is used to carry out the conversion from DC to AC. When the excitation in the feeding circuit is a DC voltage, the output voltage and current in

*L*

_{2}are shown in Fig. 3a and b respectively. It can be seen that the output voltage and current are both a sinusoidal function.

*L*

_{1},

*L*

_{2}, and

*C*

_{2}. The frequency can be calculated by

Specifications of the convert circuit

Parameters | Values |
---|---|

| 5 V |

| 0.1 μH |

| 0.2 μH |

| 5.1 kΩ |

| 220 nF |

| 1 nF |

| 459 pF |

According to (1), the frequency of the convert circuit is 13.56 MHz after the values of inductance and capacitance are substituted. The voltage and current in *L*
_{2} are shown in Fig. 3. It can be seen that the output voltage in *L*
_{2} becomes a sinusoidal function with 5-V amplitude from the DC source. The sinusoidal current in *L*
_{2} can generate a shifting electromagnetic field which is a key medium in the WPT system.

## 3 Analysis methods

### 3.1 Analysis procedure

*L*

_{2}. Then an optimization method is designed with the above results as the restrict conditions. As a whole, finally, the WPT system is optimized according to the determined initial parameters of the receiver coil.

### 3.2 Initial analysis

*C*

_{1}and

*C*

_{3}are analyzed. Figure 5a presents the current in

*L*

_{2}varied with

*C*

_{1}and Fig. 5b presents the current in L2 varied with

*C*

_{3}.

It can be seen that, the output current in *L*
_{2} reaches the maximum value when *C*
_{1} is about 4 pF as shown in Fig. 5a. In Fig. 5b, it indicates that the value of *C*
_{3} has no effect on the output current in *L*
_{2}. Its role is just to ensure that the BJT circuit has a relative high voltage gain.

*R*

_{1}also impacts output current in

*L*

_{2}as shown in Fig. 6. It can be seen that the output current in

*L*

_{2}will reach the maximum value when

*R*

_{1}is about 3 kOhm.

*L*

_{1}and

*L*

_{2}, the frequency of the feeding circuit is fixed. Then the output currents in

*L*

_{2}are obtained by varying with the values of

*L*

_{1}and

*L*

_{2}as shown in Fig. 7. It can be seen that the output current will reach its maximum when the values of the two inductors are chosen correctly.

### 3.3 Optimization method

where *x*
_{
r1}, *x*
_{
r2}, and *x*
_{
r3} are the solutions; v_{
i
} is called the mutant vector; and u_{
i
} is a candidate solution. Equations (3) and (4) are, respectively, the mutation operation and crossover operation in DE.

- (1)
DE algorithm is applied several times to tackle our problem. In the first trial, random initialization is used, while in the following trials, we embed the best found solution in previous trials into the initial population. In this way, DE starts in a good position in the subsequent trials.

- (2)
Solution revisiting happens when a heuristic algorithm converges to global/local optima. In preventing revisiting and saving simulation time, we use a non-revisiting scheme [20]. This scheme stores all solutions in a binary space-partitioning tree structure. This scheme requires more computer memory than an algorithm without this scheme; however, saving simulation time is more important than memory consumption in our case.

With the above two techniques, we expect that a good solution can be found.

### 3.4 Three-coil wireless power transfer system with the feeding circuit and load circuit

*L*

_{1}and

*L*

_{2}are combined as the transmitter coil while the coil

*L*

_{3}is the receiver coil.

*M*is the mutual inductance between the two coils.

where *r* is the radius of the circular coil. From the above equation, it can be seen that *H* can be maximized when \( r=\sqrt{2} x \). Therefore, the outer diameter of the transmitter coil can be chosen from \( {D}_{T\_ out}=2\sqrt{2} d \) where *d* is the power transfer distance.

In order to obtain a sensible design, the size of the receiver coil should be determined initially. In this research, it is assumed that the WPT system is designed for use in implanted medical devices. The size of the receiver coil, therefore, should be as small as possible. The frequency is chosen to be 13.56 MHz. Based on the above analysis, the WPT system as shown in Fig. 8 is optimized as an integrated system.

where *P*
_{Load} and *P*
_{Source} are the power in the load and the source respectively; *I*
_{Receiver} and *I*
_{Transmitter} are the currents in the receiver coil and the transmitter coil. The relationship of the power transfer distance and the diameter of the transmitter coil are the constraint condition.

## 4 Results

Specifications of the transmitter coil and the receiver coil

Parameters | Values | ||
---|---|---|---|

Transmitter coil | Coil | Number of turns | 1 |

Number of strands | 4 | ||

Diameter of coil | 64 mm | ||

Diameter of wire | 3 mm | ||

Coil | Number of turns | 2 | |

Diameter of coil | 64 mm | ||

Diameter of wire | 3 mm | ||

Number of strands | 4 | ||

Receiver coil | Number of turns | 5 | |

Diameter of coil | 10 mm | ||

Diameter of wire | 1 mm |

According to (1), the change of *C*
_{2} will determine the frequency of the output current in *L*
_{2}. The optimal results in Table 2 are based on the 13.56 MHz. The power transfer efficiency curve varied with different frequencies through changes in the value of *C*
_{2} is shown in Fig. 9. The power transfer efficiency achieves the maximum value (about 30%) when the frequency is 13.56 MHz.

## 5 Conclusions

Wireless power transfer technology has a great application potential in implanted medical devices. Different from the previous research, in this paper, the optimization design for the WPT system not only includes the coil system but also considers the influence of the power source. In order to simplify the system, a simple feeding circuit is applied in the WPT system to convert a DC source into an AC source. The property of this feeding circuit is firstly analyzed, and the relationship between the parameters in the circuit is concluded in this paper. Then the optimization method is applied to optimize and design the WPT system as a whole. The results indicate that this method can obtain the optimal performance of the WPT system.

## Declarations

### Acknowledgements

This research was supported by the Natural Science Foundation of China (61601329, 61603275) and the Applied Basic Research Program of Tianjin (15JCYBJC52300, 15JCYBJC51500).

### Competing interests

The authors declare that they have no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

## References

- N Tesla, The transmission of electrical energy without wires as a means for furthering peace. Electrical World and Engineer
**1**, 21–21 (1905)Google Scholar - SYR Hui, W Zhong, CK Lee, A critical review of recent progress in mid-range wireless power transfer. IEEE Trans. Power Electronic
**29**(9), 4500–4511 (2014)View ArticleGoogle Scholar - W Brown, The history of power transmission by radio waves. IEEE Transactions on Microwave Theory and Techniques
**32**(9), 1230–1242 (1984)View ArticleGoogle Scholar - AK RamRakhyani, S Mirabbasi, M Chiao, Design and optimization of resonance-based efficient wireless power delivery systems for biomedical implants. IEEE Transactions on Biomedical Circuits and Systems
**5**(1), 48–63 (2011)View ArticleGoogle Scholar - Z Yang, W Liu, E Basham, Inductor modeling in wireless links for implantable electronics. IEEE Transactions on Magnetics
**43**(10), 3851–3860 (2007)View ArticleGoogle Scholar - Q Xu, H Wang, Z Gao, Z Mao, J He, M Sun, A novel mat-based system for position-varying wireless power transfer to biomedical implants. IEEE Transactions on Magnetics
**49**(8), 4774–4779 (2013)View ArticleGoogle Scholar - C Liu, Y Guo, H Sun, S Xiao, Design and safety considerations of an implantable rectenna for far-field wireless power transfer. IEEE Transactions on Antennas and Propagation
**62**(11), 5798–5806 (2014)MathSciNetView ArticleGoogle Scholar - A Kurs, A Karalis, R Moffatt, JD Joannopoulos, P Fisher, M Soljacic, Wireless power transfer via strongly coupled magnetic resonances. Science
**317**(5834), 83–86 (2007)MathSciNetView ArticleGoogle Scholar - A Karalis, JD Joannopoulos, M Soljacic, Efficient wireless non-radiative mid-range energy transfer. Annals of Physics
**323**, 34–48 (2008)View ArticleGoogle Scholar - Z Xiu, HL Li, SL Ho, WN Fu, A hybrid optimal design strategy of wireless magnetic-resonant charger for deep brain stimulation devices. IEEE Trans. Magn.
**49**(5), 2145–2148 (2013)View ArticleGoogle Scholar - SR Khan, GS Choi, Optimization of planar strongly coupled wireless power transfer system for biomedical applications. Microwave and Optical Technology Letters
**58**(8), 1861–1866 (2016)View ArticleGoogle Scholar - Z Xiu, SL Ho, WN Fu, Analysis and optimization of magnetically coupled resonators for wireless power transfer. IEEE Trans. Magn.
**48**(11), 4511–4513 (2012)View ArticleGoogle Scholar - S Barmada, M Raugi, M Tucci, A multi-objective optimization algorithm based on self-organizing maps applied to wireless power transfer systems. International Journal of Numerical Modelling: Electronic Networks Devices & Fields (2016)Google Scholar
- Z Wu, X Xia, B Wang, Improving building energy efficiency by multiobjective neighborhood field optimization. Energy and Buildings
**87**, 45–56 (2014)View ArticleGoogle Scholar - Z Wu, TWS Chow, Binary neighbourhood field optimization for unit commitment problems. IET Generation, Transmission & Distribution
**7**(3), 298–308 (2013)View ArticleGoogle Scholar - [online available] http://skory.gylcomp.hu/kapcs/kapcs.html. Accessed 1 Feb 2017.
- JP Cukovic, B Klopcic, M Petrun, B Polajzer, D Dolinar, Optimization of resistance spot welding transformer windings using analytical successive approximation and differential evolution. IEEE Transactions on Magnetics
**50**(4), 1–4 (2014)View ArticleGoogle Scholar - X Zhang, Z Xin, SL Ho, WN Fu, Designing loudspeaker by ensemble of composite differential evolution ingredients. IEEE Transactions on Magnetics
**50**(11), 1–4 (2014)Google Scholar - GC Tenaglia, L Lebensztajn, A multiobjective approach of differential evolution optimization applied to electromagnetic problems. IEEE Transactions on Magnetics
**50**(2), 625–628 (2014)View ArticleGoogle Scholar - SY Yuen, CK Chow, A genetic algorithm that adaptively mutates and never revisits. IEEE Transactions on Evolutionary Computation
**13**(2), 454–472 (2009)View ArticleGoogle Scholar