# Multi-Objective Optimization of LCC-S-Compensated IPT System for Improving Misalignment Tolerance
## 3 Multi-Objective Optimization of Compensation Parameters
### Implementation of MOPSO
It can be observed that the Pareto front changes in a consistent trend, but different fitness function values are obtained, that is to say, the objective function is sensitive to the range of load, and the influence on misalignment tolerance capability can be significantly reduced by a narrow load range. In order to obtain the appropriate anti-misalignment effect, the optimization results of loads ranging from 90 to 100 \(\Omega\) were studied. From Figure 8, the voltage ripple and inductance current stresses cannot be optimized at the same time, and they are negatively correlated, while the ratio between the reactive power and active power has no positive or negative correlation with the two objects. Hence, it is more reasonable to take it as an important reference factor in the whole multi-objective optimization process. This paper takes minimum voltage ripple as the highest priority, considering both the reactive power and electrical element stress. Therefore, the reasonable solution point C that reflects trade-offs among the key objectives were selected from the Pareto front. The four compensation parameters obtained corresponding to point C were \(L_{\text{P1}}=206.51\)\(\mu\)H, \(C_{\text{P1}}=33.64\) nF, \(C_{\text{P2}}=692.13\) nF and \(C_{\text{S}}=11.82\) nF. The output voltage, input impedance angle, current stresses on inductors and voltage stresses over capacitors varying with the coupling coefficient and load are shown in Figure 9. As with the CCO type, the voltage defining fluctuation with the Case C compensations were indicated to be able to be maintained under 10.45% when the coupling coefficient varied from 0.5 to 0.25. The maximum current and voltage stress were 4.18 A and 375.26 V, respectively, which were both within the acceptable range for the compensation components. The impedance is inductive within the full coupling range, which can fulfill the ZVS requirement for the system. From Figure 9c, it can be seen that the transmitting coil current of the proposed scheme was negatively correlated with the coupling coefficient, indicating that the current of the transmitting coil tracked and compensated the coupling coefficient's influence on the output voltage. Figure 7: Main electrical values of CCO-type IPT system in case B: (**a**) output current; (**b**) input impedance angle; (**c**) current stresses on inductor and coils; (**d**) voltage stresses over capacitors. Based on the above analysis, the LCC-S-based IPT systems can enhance different misalignment-tolerant capabilities with compensating parameter optimization, which is realized at the cost of introducing extra reactive power. Moreover, it can also be observed in Figures 6, 7 and 9 that the optimized curve was approximately a parabola with different gradients and a coupling turning point, and the key features of the output profile are parametrically dependent. Meanwhile, the value of parameters affecting the efficiency and cost also needs to be considered. Possessing the smallest volatility of only around 10%, Case A and Case C had the best power transfer stability. Nevertheless, the introduction of more electric stresses on passive elements resulted in lower system efficiency. Notwithstanding, the robustness of power transfer and the high degree of design freedom are favorable in low-power applications. With small device stresses, Case B could provide a 30% current output fluctuation, which is more suitable for electrical devices with high requirements of both power and efficiency, such as stationary electric vehicle wireless charging. Case C illustrates that, after parameter optimization, the CVO-type IPT system could not meet the stable output demand in the scenario of large offset and wide load simultaneously. Therefore, if the load changes over a wide range, extra impedance matching circuits may need to be added between the rectifier and the actual load.