## 3 Experimental Setup  
In this paper, the MCBC was experimentally verified to validate the theoretical operation of the proposed topology. The experimental setup consisting of two parts is illustrated in Figure 11, and circuit components are shown in more detail in Table 1. The first part is the designed MCBC, which consists of twelve switches, two diodes, one module balancing capacitor \(C_{\text{m}}\), and two multi-winding transformers. An IM 3533 LCR meter was used to measure the magnetizing and leakage inductances of two transformers. The second part is the available equipment such as power supply, voltage recorder, oscilloscope and DSP board. The voltage recorder (i.e., YOKOGAWA-GP10) was used to measure and record the voltage balancing process of eight cells, and the battery cell used Lithium-ion cell LIR17335-PCM C5264 RR (2/3 A 3.7 V 700 mAh). Gate driver voltage \(V_{\text{gs}}\) of the switches such as \(S_{11}\), \(S_{24}\), \(S_{\text{a1}}\), and \(S_{\text{b1}}\) is shown in Figure 12. Therein, the duty ratio (\(D\)) of signals to power switches in the intra-module balancers is 37.5%, and the duty ratio (\(D_{1}\)) of the signal to switches \(S_{\text{a1}}\), \(S_{\text{b1}}\) is 50% of one switching period where the \(S_{\text{a1}}\) and \(S_{\text{b1}}\) are complementary, and switching frequency of \(f\) and \(f_{1}\) are set for 40 kHz. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Parameter**} & \multicolumn{1}{c}{**Value**} \\ \hline \multicolumn{2}{c}{Twelve MOSFETs} & \multicolumn{1}{c}{IPP023N10N5} \\ \hline \multicolumn{2}{c}{Two diodes} & \multicolumn{1}{c}{DO-204 AC (DO-15)} \\ \hline \multicolumn{2}{c}{Core: EER2828N} \\ \cline{3-3} \multicolumn{2}{c}{} & \multicolumn{1}{c}{\(N_{1}\):\(N_{2}\) = 1:1} \\ \cline{3-3} \multicolumn{2}{c}{Two Transformers} & \multicolumn{1}{c}{\(L_{\text{m1}}\) = 1.88 mH; \(L_{\text{m2}}\) = 1.83 mH} \\ \cline{3-3} \multicolumn{2}{c}{Cell balancing circuit} & \multicolumn{1}{c}{(Four primary/One secondary windings)} & \multicolumn{1}{c}{\(L_{\text{h11}}\) = 1.87 uH; \(L_{\text{h12}}\) = 1.95 uH; \(L_{\text{h13}}\) = 3.39 uH; \(L_{\text{h14}}\) = 1.94 uH; \(L_{\text{h21}}\) = 2.30 uH; \(L_{\text{h22}}\) = 1.99 uH; \(L_{\text{h23}}\) = 2.00 uH; \(L_{\text{h24}}\) = 1.98 uH; \(L_{\text{h24}}\) = 1.98 uH; } \\ \cline{3-3} \multicolumn{2}{c}{Balancing capacitor} & \multicolumn{1}{c}{700 uF} \\ \cline{3-3} \multicolumn{2}{c}{} & \multicolumn{1}{c}{Gate driver} & \multicolumn{1}{c}{UCC27519A-Q1} \\ \hline \multirow{4}{*}{Battery string} & \multirow{4}{*}{Eight Lithium-ion cells} & Nominal capacity & 700 mAh \\ \cline{3-3} \cline{3-3} \multicolumn{2}{c}{} & \multicolumn{1}{c}{\(N_{1}\):\(N_{2}\):\(N_{3}\):\In this work, the experiment in three cases of initial different voltage arrangements of the cells is performed. The voltages of the cells are set as follows. Case 1: the voltages of eight cells are arranged in decreasing order from \(Cell_{11}\) (i.e., \(V_{\text{cell11}}\)) to \(Cell_{24}\) (i.e., \(V_{\text{cell24}}\)); Case 2: \(V_{\text{cell11}}>V_{\text{cell21}}>V_{\text{cell12}}>V_{\text{cell12}}>V_{ \text{cell122}}>V_{\text{cell13}}>V_{\text{cell23}}>V_{\text{cell14}}>V_{\text{cell 24}}\), and case 3: the initial voltage of the cells is set randomly, as shown in detail in Table 2.