## 2 System Framework of Distribution System with DGs and BESSs  
The specific architecture proposed in this study is shown in Figure 1. Distributed generations convert renewable energy into electricity and integrate to the distribution system. There are several BESSs such as electric vehicles and batteries, which can be used for voltage/frequency regulation. The BESSs can interact with the control center through the communication network. The owner of BESSs can get profit by providing voltage/frequency regulation service [31; 32; 33; 34; 35; 36]. The cost-benefit of a Smarter Network Storage project of 6 MW/10 MWh-BESSs in Great Britain has been investigated in [34]. Total social cost, such as battery cells, construction, and operating costs, is \(\epsilon\)7,402,284 (average value). The social benefit streams from BESSs like frequency response, arbitrage and carbon abatement can get \(\epsilon\)9,731,525 (average value). Comparing the costs and benefits, the profit can be taken by BESSs as \(\epsilon\)2,329,241, i.e., 31.5% of the cost.  
In the structure, control center collects status information of BESSs through the communication network. To achieve the coordinated control of the BESSs, it is necessary to know the energy storage status. As show in Figure 2, status information includes the upper limit state of charge (\(SOC_{\text{max}}\)), the lower limit state of charge (\(SOC_{\text{min}}\)), the location information, the capacity of the energy storage device, and the connection status.  
Figure 1: Battery energy storage systems (BESS) coordination control architecture model.  
Status information is consisted by information matrix \(H\), and we use the matrix representation of the characteristics of the BESS model. Specific steps are as follows:  
The control center obtains the distance according to the position information of BESSs, and then formulates the distance matrix of Formula (1).  
\[D=[d_{1},d_{2},\dots,d_{n}]^{\mathrm{T}} \tag{1}\]  
where \(n\) indicates the number of the nodes in the distribution systems.  
The control center formulates energy capacity matrix of Formula (2) according to the capacity of the BESSs.  
\[E=[E_{1},E_{2},\dots,E_{n}]^{\mathrm{T}} \tag{2}\]  
The SOC limit is formulated as matrix of Formula (3) and Formula (4) according to the upper and lower limits of the current state of the BESSs.  
\[SOC_{\mathrm{max}}=[SOC_{\mathrm{max1}},SOC_{\mathrm{max2}},\dots,SOC_{ \mathrm{max}}]^{\mathrm{T}} \tag{3}\]  
\[SOC_{\mathrm{min}}=[SOC_{\mathrm{min1}},SOC_{\mathrm{min2}},\dots,SOC_{ \mathrm{min}}]^{\mathrm{T}} \tag{4}\]  
Control center formulates SOC matrix of (5) according to the current SOC of the BESSs.  
\[SOC=[SOC_{1},SOC_{2},\dots,SOC_{n}]^{\mathrm{T}} \tag{5}\]  
Finally, the information matrix \(H\) can be formulated as:  
\[H=[D,SOC_{\mathrm{max}},SOC_{\mathrm{min}},SOC,E] \tag{6}\]  
After developing the information matrix \(H\), the control center optimizes the coordinated control according to the proposed algorithm, and sends the commands of the charging or discharging power to BESSs. BESSs receive commands from the control center, and then complete the corresponding operations. In the charging and discharging operation, the regulation power is completed by all the BESSs of each node. As a result, SOC of a single BESS will not be too high or too low.