# Multi-Objective Optimization of LCC-S-Compensated IPT System for Improving Misalignment Tolerance
## 3 Multi-Objective Optimization of Compensation Parameters
### Implementation of MOPSO
Solution B has the smaller current stresses and reactive power, but the greater fluctuation of output current. For the solutions with \(f_{\text{IRO}}\) greater than B, the output fluctuation of the system would worsen, which deviates from the anti-misalignment characteristic pursued and will not be considered. The Pareto front enables decision makers to select the best compromise or near-best solution that reflects trade-offs among key objectives. Therefore, reasonable compensation parameters can be selected based on the compromise method to meet different design requirements for the IPT system. Specific to the CCO-type compensation network, after optimization, solution point A, which had the lowest fitness function value for the output current fluctuation, and point B, which had trade-offs of the three optimization objectives, were selected for comparison. The obtained four compensation parameters corresponding to point A were \(L_{\text{P1}}=147.6\) uH, \(C_{\text{P1}}=41.87\) nF, \(C_{\text{P2}}=214.88\) nFand \(C_{\text{S}}=8.77\) nF, while for point B, they were \(L_{\text{P1}}=217.43\) uH, \(C_{\text{P1}}=36.61\) nF, \(C_{\text{P2}}=47.36\) nF and \(C_{\text{S}}=13.02\) nF. With the optimized four parameters, the load current versus coupling coefficient and load can be obtained, as shown in Figures 6a and 7a. With the parameters at point A, the minimum load current, 0.87 A, was achieved when \(k\) and \(R_{\text{O}}\) were 0.25 and 100 \(\Omega\), respectively. The maximum load current was 1.08 A when \(k\) and \(R_{\text{O}}\) were 0.36 and 50 \(\Omega\). Therefore, the output current fluctuation range of the compensation topology was less than 10.8%. Similarly, with the parameters at point B, the output current fluctuation of 29.67% was obtained. Simultaneously, the inverter no longer has a tremendous current when two coils seriously misalign, which protects the power supply. From Figures 6 and 7, it can be seen that the input impedance angles of the two IPT systems remained at a positive value, which ensured the ZVS operation of the inverter switches. However, it can be observed that, generally, the phase angle of Case A was greater than that of Case B as they tried to reduce the output fluctuations. In Case A, the vital objective function is minimizing the current variation and a balanced trade-off of the  
Figure 5: The optimal solutions of the CCO-type IPT system. (**a**) 3D diagram; (**b**) 2D diagram. Figure 6: Main electrical values of CCO-type IPT system in case A: (**a**) output current; (**b**) input impedance angle; (**c**) current stresses on inductor and coils; (**d**) voltage stresses over capacitors. three optimization objectives is better reflected in Case B. Furthermore, it can be seen from Figure 6 that although group A parameters could obtain the characteristics of remarkable stable current output, the maximum current on the compensation inductor \(L_{\text{P1}}\) and the maximum voltage over \(C_{\text{P1}}\) reached 6.37 A and 412.89 V when \(k=0.25\) and \(R_{\text{O}}=100\)\(\Omega\). Coils and switches with high current tolerance are needed. This can be explained by the large amount of reactive power introduced into the IPT system. For Case B, although the current stresses on \(L_{\text{P1}}\) and the voltage stresses over compensation capacitors were relatively small, a nearly 30% fluctuation in the output current appeared. For the new CVO-type compensation network, the output voltage results derived by the proposed method were seriously affected by the load range. Taking 100 \(\Omega\) as the maximum load, for the minimum range of 50, 70 and 90 \(\Omega\) load, respectively, the best solutions among multiple optimized solutions were ultimately selected. Under different load ranges, the comparison diagram of multi-objective Pareto solutions for the system is shown in Figure 8, where \(f_{\text{URO}}\) represents the first objective function; namely, output current fluctuation.