## 5 Experimental Results
Initially (t \(<\) 10 s), the power of all the PV-sources were almost the same (=118 W) and all batteries were charging with the same power (=44 W) to maintain balanced SoCs. At t = 10 s the PV-source of M3 was switched OFF. This forced the battery of M3 to switch from charging to discharging state in order to contribute power to the load requirement, which needs to be kept at a minimum in order to limit the divergence of the battery module SoC. Therefore, the voltage contribution of M3 was set to the minimum (17 V). To compensate for this, the voltage contributions of M1 and M2 were increased delivering more power to the bus/load and less power (44 W \(\downarrow\)30 W) to charge their batteries but keeping the bus voltage at the reference level (75 V although a small dip is visible). When another PV-source (PV1) is switched OFF (t = 12.5 s), the voltage contribution of M2 increases to the maximum (36 V) to maximize its power share to the load and minimize the charging power of its battery module (30 W \(\downarrow\)9 W), allowing the modules without their PV source (M1 and M3) to minimize their power contribution to the load. The last PV-source (PV2) to be switched off was M2 at t = 16 s which means all the three battery modules were discharging, therefore the voltage/power contributions of all the modules were the same, to have same discharge power and maintain balanced SoCs. The second part of this test consisted of switching ON the PV sources in the same order. It can be seen that the voltage contribution of each module changes in a similar way as in the previous steps, which is consistent with  
Figure 11: Managing battery charge balancing under unbalanced power from PVs. the aim of minimizing as much as possible the power imbalance of the batteries while delivering a constant bus voltage to the load. The third test, shown in Figure 13, evaluated the capability of the MMPC to reduce the charge imbalance of the battery modules. As it required a long time to obtain a noticeable change in the SoC of the battery modules when using their real capacity, the capacity used in the SoC estimator in this test was reduced by a factor of 10. The test started with the following imbalance in the SoC of the battery modules 62% (M1), 52% (M2) and 42% (M3). In order to reduce this SoC imbalance, while the three PV sources provide balanced power (t \(<\) 11 s), the MMPC management strategy defines the voltage contribution of the PMs according to the SoC of their battery modules. M1 contributed with the highest voltage to the bus (28 V) according to its battery SoC, while M2 contributed with (25 V) and M3, which has the lowest SoC, contributed with (21 V). As a result, the charging power of M1 battery module was the minimum (33 W) while the charging power for M3 battery was the maximum (49.6 W). The charging power of M3's battery was (40 W). At t = 11 s, a simulated step change in the irradiance has been applied to the PV-source of M1 that caused a power increase from 120 W to 160 W, while the PV power of M2 and M3 remained the same. In order to have the fastest reduction of battery imbalance, the voltage contribution of M1 increased to its maximum (36 V) while the voltage contribution of M2 and M3 decreased to 22.5 V and to its minimum (17 V) respectively. Most of the increase of the PV power of M1 was directed to the bus/load allowing M2 and M3 to decrease their power contribution to the bus/load, which results in an increase of their battery charging powers: This will reduce the differences among the batteries SOCs. The test continued by having the load absorbing several power peak surges (600 W and 900 W at 32 s \(<\) t \(<\) 34 s and 38 s \(<\) t \(<\) 41 s), which required power to be supplied by the batteries and PVs. Available PV powers were equal. To further reduce the SoC imbalance, the voltage contribution to the bus and the discharging power of M1's battery was larger compared to M2 and M3. The test concluded with a sudden reduction of the power of all three PVs (t = 48 s).