# Multi-Objective Optimization of LCC-S-Compensated IPT System for Improving Misalignment Tolerance
## 3 Multi-Objective Optimization of Compensation Parameters
### Implementation of MOPSO  
Four compensation parameters, \(L_{\text{P1}}\), \(C_{\text{P1}}\), \(C_{\text{P2}}\) and \(C_{\text{S1}}\), need to be optimized for the LCC-S compensation IPT system. Therefore, this is a four-dimensional optimization problem for the PSO algorithm. The velocity of each particle is constrained within the range [\(V_{\text{min}}\), \(V_{\text{max}}\)], and the values of the four different velocities are derived by the positive integers \(N_{\text{i}}\). The position is limited within the range [\(X_{\text{min}}\), \(X_{\text{max}}\)], which is determined by the component constraints. In order to describe the optimization process clearly, the flowchart of the MOPSO algorithm is shown in Figure 4. As shown in Figure 4, the MOPSO algorithm is divided into about seven steps: (1) initialization of parameters; (2) velocities and positions update; (3) calculation of fitness; (4) update of individual optimal position \(p_{\text{i-best}}\) (\(k\)); (5) update of archives; (6) update of global optimal vector \(g_{\text{best}}\) (\(k\)); (7) repeat steps (2) through (6) until the end of the loop condition is met. The desired output current \(I_{\text{RO}\text{,D}}\) was set to 1 A and the desired output voltage \(U_{\text{RO}\text{,D}}\) was set to 100 V. The basic setting of the MOPSO optimization process is listed in Table 2. The number of particles is \(N_{\text{P}}\) = 200, and the dimension of each particle is four, which corresponds to \(L_{\text{P1}}\), \(C_{\text{P1}}\), \(C_{\text{P2}}\) and \(C_{\text{S}}\). The range of compensated inductance is 10-1000 uH and the range of each compensated inductance capacitance is 0.1-800 nF. The repository size for each iteration is 200 to show more optimization results. The maximum number of iterations is limited to 200, so as not to prolong the simulation time. The maximum and minimum moving velocities of particles is limited by 1/200 of the range of each particle. In addition, the inertia factor \(w\) and learning factors \(c_{1}\), \(c_{2}\) take the empirical value, which are 0.7, 1.8, 1.8, respectively. In order to solve the nonlinear optimization problem proposed in this case, the MOPSO program was written in the MATLAB software. The time cost is about 74.9 s and is realized by a computer (Intel Core i7-9700: 3.00 GHz, RAM: 32 GB). For the CCO-type system, all the solutions successively generated in the archive after 200 iterations are shown in Figure 5a (3D diagram). In each iteration, the MOPSO algorithm performed non-dominated sorting and finally converged to the Pareto front. The optimization Pareto front of the output current fluctuation versus input impedance angle and current stresses of three inductors was obtained as shown in Figure 5b (2D diagram). According to the Pareto front, it is evident that different weight combinations of three objectives can lead to large variant results. In Figure 5, \(f_{\text{IRO}}\) represents the output current fluctuation function, which is the most important target. \(f_{\text{IL}}\) represents the second objective function, which is the sum of current stresses with respect to load and coupling coefficient. The color bar in the figure represents the sum of the ratio between the reactive power and active power in the LCT, which is the third objective function \(f_{\text{GPS}}\). From Figure 5, the output current ripple of solution A is the minimum, but the current stresses \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline \(w\) & 0.7 & \(N_{p}\) (Population) & 200 \\ \(c_{1}\) & 1.8 & \(T\) (Iterations) & 200 \\ \(c_{2}\) & 1.8 & \(R_{pp}\) (Repository) & 200 \\ \(L_{i}\) & 10–1000 \(\mu\)H & \(C_{j}\) & 0.1–800 nF \\ \(l_{\text{Lmax}}\) & 16 A & \(U_{\text{Cmax}}\) & 600 V \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The main parameters related to the MOPSO algorithm. Figure 4: Flowchart of the MOPSO algorithm. and reactive power is large.