## 4 Test and Result Analysis
### Result Analysis  
The voltage fluctuation curves before and after voltage regulation are shown in Figures 10 and 11 respectively. Each curve in Figures 10 and 11 each curve represents the voltage status of a node during the 24 h.  
According to the voltage sensitivity coefficient, nodes number of 1-4 and 19-25 have small sensitivity coefficient and therefore voltage deviation is small in these nodes. It is can be seen from Figure 11 that during the period of 9:15-11:00 and 12:30-13:10, the grid is in an overvoltage state because of the large output of PV generation and low load consumption. During the time of 18:30-22:00, the grid is in an undervoltage state. The peak and valley of voltage are 1.13573 and 0.88816 p.u., respectively. The result after voltage regulation is shown in Figure 11. The proposed algorithm regulates the voltage fluctuations within he permission range by coordinated control of BESSs charging and discharging. The maximum voltage deviation shown in Figure 11 is 0.09895 p.u. Figure 8: State of charge (SOC) curve of a BESS. Figure 9: Daily load and photovoltaic power curves. Figure 12 shows the power system frequency deviation curve regulated by the proposed algorithm. Dashed and solid curves indicate the frequency before and after regulation, respectively. During the period of 6:40-7:05 and 11:45-12:15 frequency exceeds the lower limit, 9:35-10:30 and 12:10-12:45 frequency exceeds the upper limit. Actually, the net load (load-PV) that, shown in Figure 9, is in a high load state during 6:40-7:05 and 11:45-12:15, and in a low load state during the period of 9:35-10:30 and 12:10-12:45. In addition, the fluctuation of PV is intense during this period, the frequency fluctuation is consistent with the trend of the daily net load curve. After the regulation, the frequency of the power distribution system is within the normal range. Figure 11: Voltage curve after voltage regulation. Figure 10: Voltage curve before voltage regulation. Because of the different sensitivity coefficients of each node, the variation of the SOC of BESS for all the nodes are different. Nodes numbering 1-4 and 19-25 have small sensitivity coefficient, therefore these nodes are selected as the candidate nodes for frequency regulation. The gaps between voltage regulation and frequency regulation are evenly distributed to the BESSs of the candidate nodes. Therefore, SOC variation of candidate nodes BESSs fluctuate greatly. In order to show the dynamic analysis of our proposed coordinated control algorithm, we take a time point of 9:27:30, which is shown with black dot in Figures 10-12. At this time point, the voltage fluctuation of Node 18 is the largest which reached 1.109 p.u., and the frequency deviation of distribution network reached 0.3402 Hz. Both of the voltage and frequency exceed the permissible range, which are needed to be regulated. According to the calculation of Sections 3.2 and 3.3, the required power for the voltage and frequency regulation are 1065.68 kW and 2902.68 kW, respectively. As the power required for frequency regulation is larger than the required for voltage regulation, the total power of 2902.68 kW was chose, and the difference part of 1837 kW was allocated to the nodes with lower voltage sensitivity coefficient according to Section 3.4. After regulating, the frequency deviation of the distribution network reduced to 0.153 Hz, and the voltage of Node 18 reduced to 1.06 p.u., the frequency fluctuation reduced 55.03% and the voltage reduced 15.32%, both of them are within a permissible range. In [PERSON]'s algorithm, the BESSs are operated in a sequential order for the voltage and frequency regulation, and total power of 3968.36 kW will be charged. The proposed coordinated control algorithm is compared with [PERSON] algorithm [29]. Figure 13 shows the total number of BESSs charging and discharging cycles, and Figure 14 shows the total BESS charging and discharging power. The number of charging cycles of [PERSON] algorithm is 2312 and the number of discharges cycles is 7130.