## 3 Coordinated Control Scheme for the Energy Router
### Power-Based Current Tracking Control for Self-Energy Storage System  
The self-energy storage system consists of a battery unit and a supercapacitor, because the combination of their characteristics has complementary advantages for stabilizing the DC bus voltage [33]. As shown in Figure 3, the battery and supercapacitor are connected to the DC bus through bidirectional DC/DC converters.  
Compared to the method to control charging or discharging currents directly, the indirect method works better to maintain the instantaneous power balance by controlling the charging or discharging power [34]. In order to maintain the system power balance, the following equation must be satisfied,  
\[\frac{1}{2}C_{\mathrm{dc}}\frac{du_{\mathrm{dc}}^{2}}{dt}=P_{\mathrm{DG}}+P_{ \mathrm{bat}}+P_{\mathrm{sc}}-P_{\mathrm{ac}} \tag{9}\]  
where \(C_{\mathrm{dc}}\) is the capacitance of the DC bus capacitor, \(u_{\mathrm{dc}}\) is the DC bus voltage, \(P_{\mathrm{DG}}\) is the output power of the DGs, \(P_{\mathrm{bat}}\) and \(P_{\mathrm{sc}}\) are the charging or discharging power of the battery and the supercapacitor, and \(P_{\mathrm{ac}}\) is the active power fed to the AC bus through the main converter. Following equation is derived when the DC bus voltage is constant,  
\[P_{\mathrm{ac}}=P_{\mathrm{DG}}+P_{\mathrm{bat}}+P_{\mathrm{sc}} \tag{10}\]  
In view of the working characteristics of battery and supercapacitor, the battery is responsible for most of the charging or discharging power, while the supercapacitor is used to improve the transient characteristics of the DC bus voltage.  
Current tracking control is used to regulate the charging or discharging currents of the battery and supercapacitor. The following equation describes the relationship between voltage and current of the battery or supercapacitor,  
\[L\frac{di_{\mathrm{s}}}{dt}=u_{\mathrm{s}}-u_{\mathrm{m}} \tag{11}\]  
where \(i_{\mathrm{s}}\) is the charging or discharging current, \(u_{\mathrm{s}}\) is the output voltage, \(u_{\mathrm{m}}\) is the modulation voltage of the DC/DC converter. On the basis of Equation (11), \(u_{\mathrm{mref}}\) can be derived as,  
\[u_{\mathrm{mref}}=u_{\mathrm{s}}+(k_{p}+\frac{k_{i}}{s})(i_{\mathrm{sref}}-i_ {\mathrm{s}}) \tag{12}\]  
Then modulation signals of the DC/DC converter are gotten,  
\[m_{\mathrm{d}}=\frac{u_{\mathrm{mref}}}{u_{\mathrm{dc}}} \tag{13}\]  
Based upon above analysis, the control scheme of the charging or discharging process of the self-energy storage system is formulated. As shown in Figure 6, a power-based current tracking control method is adopted by the DC/DC converters to achieve instantaneous power balance in the energy router. The square of the error between the referenced voltage \(u_{\mathrm{dcref}}\) and the actual voltage \(u_{\mathrm{dc}}\) of the DC bus is used by PI regulator to derive the power \(P_{\mathrm{sc}}\), which needs to be provided by supercapacitor. The power \(P_{\mathrm{bat}}\), which needs to be provided by the battery, will be calculated by the fuzzy logic controller described in the following section. The calculated charging or discharging power divided by output voltage is the reference current. Subsequently, the output currents of the battery and supercapacitor will track the reference currents \(i_{\mathrm{s1 ref}}\) and \(i_{\mathrm{s2 ref}}\) through the PI regulators.  
Then the modulation signals \(m_{\text{d1}}\) and \(m_{\text{d2}}\) can be derived to control the DC/DC converters of the battery and supercapacitor.