# Optimization Design of Planar Circle Coil for Limited-Size Wireless Power Transfer System
## 4 Simulations and Analysis
### Comparison with Traditional Design and Single-Objective Optimization  
After verifying the reliability of the optimization process, this part compares the design results of traditional design [12; 13], single-objective optimization (Maximize _M/R_ to improve efficiency) [18], and multi-objective optimization. Since the optimal solution of multi-objective optimization is the Pareto front data set, it isn't easy to compare with a single optimization result. At the same time, different design methods will inevitably have different coils parameters; obviously the coils parameters cannot be used as independent variables. After noting that there is an approximately linear relationship between the multi-objective results and the circuit frequency, this paper finally takes the frequency as the abscissa to screen the appropriate Pareto front points and compares the \(\eta\) and \(K\) of different designs when \(R_{L}=5\ \Omega\), \(R_{L}=50\ \Omega\), and \(R_{L}=100\ \Omega\), respectively.  
Figure 12 illustrates that while the load is the same, both traditional and single-objective optimization designs maintain a high degree of system efficiency over the fre  
Figure 11: Efficiency \(\eta\), voltage modulus gain \(K\) of Pareto front and Multisim.  
Figure 10: Multisim simulation model of S-S compensation.  
quency range. The main reason is that both take a sizeable mutual inductance \(M\) as the design indicator, so the system will eventually work in the over-coupling state. In this situation, the system's PTE can be guaranteed, but it will inevitably lead to lower system PT. However, multi-objective optimization can balance this problem nicely. Taking \(R_{L}\) = 50 \(\Omega\) as an example, the traditional design's maximum efficiency and voltage gain in the given frequency band are 98.10% and 0.86. The efficiency and voltage modulus gain for multi-objective optimization are 95.24% and 5.01 at 483,279 Hz. The system achieves 5.83 times voltage gain at the cost of 2.87% efficiency, which means the TP will increase 34 times, and the final system PTE of 95.24% is still within the acceptable engineering range. Compared with the \(M\)/\(R\) single-objective optimization of PTE design, the multi-objective optimization can improve the TP 12.8 times under the cost of 3% TPE, which makes sense for input voltage-constrained systems.  
Figure 12: Efficiency \(\eta\), voltage modulus gain \(K\) of traditional design, single-objective optimization, and multi-objective optimization. (**a**) The load resistance \(R_{L}\) = 5 \(\Omega\). (**b**) The load resistance \(R_{L}\) = 50 \(\Omega\). (**c**) The load resistance \(R_{L}\) = 100 \(\Omega\).  
It can also be obtained from Figure 12 that the smaller the load resistance \(R_{L}\), the better the multi-objective optimization effect. The main reason is that the load resistance doesn't connect with the optimization target in traditional design and single-objective optimization. When the load resistance is low, the secondary side's voltage sharing capability is decreased, and the power consumed on the coils is increased, so the PTE and TP of the system reduce at the same time. Meanwhile, it is obvious from Figure 12a-c that the two optimization results are better than the traditional design at some point. As a result, it's critical to optimize parameters in the design stage based on the desired design objectives.  
Figure 13 depicts the Pareto front curves optimized under different load resistance. Obviously, the larger the load, the more likely it is to obtain and maintain the ideal PTE and TP simultaneously. As a result, a careful selection of load resistance during the system design stage can help to improve system performance.