# Decoupled MPC Power Balancing Strategy for Coupled Inductor Flying Capacitor DC-DC Converter
## 4 Experimental Verification
### Experimental Results  
The output voltage under Buck mode is set to 50 V. The experimental results of the proposed power balancing MPC strategy under Buck mode are shown in Figure 7. Due to the unequal inductance between the two phases, \(i_{\mathrm{a}}\) and \(i_{\mathrm{b}}\) are imbalanced. As can be seen in Figure 7a, before the proposed strategy put into operation, \(i_{\mathrm{a}}\) is 3 A and \(i_{\mathrm{b}}\) is 2 A. After the control strategy is put into operation, the current reaches a balanced state within 10 ms. Compared to the initial state, the two-phase current is balanced by 20%. Figure 7b shows the voltage curves of \(C_{\mathrm{fa}}\) and \(C_{\mathrm{fb}}\) when the power balancing control is in action. It can be seen that the FC voltage is unchanged. Figure 7c shows the response curve of FC voltage from an imbalanced to a balanced state. Due to the direct regulation of flying capacitor voltage, the voltage difference between \(C_{\mathrm{fa}}\) and \(C_{\mathrm{fb}}\) quickly changes from 10 V to 0 V within 5 ms, achieving a balanced control state.  
The input voltage under Boost mode is set to 50 V and the voltage on high voltage side is set to 60 V. The verification results are shown in Figure 8. Figure 8a shows that before the proposed strategy is put into operation, \(i_{\mathrm{a}}\) is 4 A and \(i_{\mathrm{b}}\) is 2.8 A. Due to the shoot-through state in Boost mode, the current change is more obvious than that in Buck mode, and it can  
Figure 6: Experimental platform.  
be seen that \(i_{\text{a}}\) and \(i_{\text{b}}\) achieve balancing state within 20 ms at 3 A. The maximum current balancing regulation reaches 33%. Figure 8b shows the output voltage and FC voltage curves. Because the FC voltage is related to the output voltage under Boost mode, \(u_{\text{o}}\), \(u_{\text{fa}}\) and \(u_{\text{fb}}\) finally remain at 60 V, 30 V, and 30 V, respectively, after a short fluctuation. Figure 8c shows the FC voltage control response curve. It can be seen that the voltage difference between \(C_{\text{fa}}\) and \(C_{\text{fb}}\) quickly changes from 10 V to 0 V less than 5 ms, achieving a balanced control state.  
The abrupt load changing results under Buck mode are shown in Figure 9. Figure 9a shows the loading results from 12 \(\Omega\) to 6 \(\Omega\). Due to the differences in inductance, the two-phase current has different response curves, increasing from 1.6 A to 3.2 A. After a short oscillation within 22 ms, the two-phase current reaches a new balancing state and the voltage of flying capacitor remains controllable. The abrupt unloading results are shown in Figure 9b. The load resistor is changed from 6 \(\Omega\) to 12 \(\Omega\). It can be seen that the current between phases can always remain balanced while the voltage of \(u_{\text{fa}}\) and \(u_{\text{fb}}\) is kept at 50 V.  
Figure 8: Experimental results under Boost mode. (**a**) Current balancing response curves. (**b**) FC voltage response curves with current balancing control. (**c**) FC voltage balancing response curves.  
Figure 7: Experimental results under Buck mode. (**a**) Current balance response curves. (**b**) FC voltage response curves with current balancing control. (**c**) FC voltage balancing response curves.  
The experimental results with load changing from 12 \(\Omega\) to 6 \(\Omega\) and from 6 \(\Omega\) to 12 \(\Omega\) under Boost mode are shown in Figure 10a,b. The inductance current increased from 1.5 A to 3 A under the loading condition and recovered to 1.5 A after unloading. It can be seen that both the current and voltage have favorable response performance: the current remains balanced and the FC voltage is controllable.  
According to the above experimental results, it can be concluded that the proposed MPC power balancing strategy has favorable power balance performance to control the coupled inductor FCDC with imbalanced coupled inductor and can achieve FC voltage control. It can quickly respond to load power demands, maintain current balancing control, and ensure system stability.