# Improved Control of Forest Microgrids with Hybrid Complementary Energy Storage
## 3 Hybrid Complementary Energy Storage System
### Improvement in Traditional Control of Batteries and Supercapacitors  
The reference current absorbed or released by the energy storage system is divided into a low frequency part and a high frequency part through the low pass filter (LPF). As batteries boast high energy density and large energy storage, they are used as long-term devices for power balance by absorbing or releasing low frequency power, while supercapacitors are utilized for suppressing high frequency disturbances.  
The power disturbances that lead the system to emergency mode always give rise to large change rates of DC voltage (d\(U_{\text{dc}}\)/d\(t\)). Therefore, d\(U_{\text{dc}}\)/d\(t\) can be utilized to adaptively modify the droop coefficient of the energy storage converter. When it exceeds the preset threshold \(C\), the droop coefficient \(k_{\text{i}}\) varies adaptively to improve the response speed, as shown in Equation (1).  
\[k_{\text{i}}=\left\{\begin{array}{ll}k_{\text{n\_i}}-m_{1}\big{(}\Big{|}\frac {\text{d}U_{\text{dc}}}{\text{d}t}\Big{|}^{m_{2}}&,\text{for}\Big{|}\frac{ \text{d}U_{\text{dc}}}{\text{d}t}\Big{|}\geq C\\ k_{\text{n\_i}}&,\text{for}\Big{|}\frac{\text{d}U_{\text{dc}}}{\text{d}t} \Big{|}<C\end{array}\right., \tag{1}\]  
where \(k_{\text{n\_i}}\) is the droop coefficient of the converter in the original control method. Constants \(m_{1}\) and \(m_{2}\) are based on the rated capacity of microgrid converter and the maximum allowable deviation of DC voltage. \(m_{1}\) is determined by the following Equations.  
\[m_{1}=\frac{k_{\text{n\_i}}-k_{\text{i\_min}}}{\big{(}\Big{|}\frac{\text{d}U_{ \text{dc}}}{\text{d}t}\Big{|}_{\text{max}}\big{)}^{m_{2}}}, \tag{2}\]  
\[k_{\text{i\_min}}=\frac{\Delta U_{\text{dc}}}{\Delta I_{\text{i\_max}}}, \tag{3}\]  
where \(k_{\text{i\_min}}\) is the minimum droop gain, the selection of which is to prevent the output power of the converter from exceeding its maximum limit. \(\Delta U_{\text{dc}}\) is the variation of DC voltage corresponding to the maximum current limit (\(\Delta I_{\text{i\_max}}\)) of the convertor, and is intended for setting the allowable voltage variation corresponding to a specific converter.  
The value of \(m_{1}\) depends on the output capacity of the converter represented by the maximum voltage change rate \(|\text{d}U_{\text{dc}}\)/d\(t\)\(t\)\(|_{\text{max}}\) and \(k_{\text{i\_min}}\). The power support capability of the energy storage converter increases in the same direction with \(m_{1}\). A small \(m_{1}\) may result in transient overshoot of DC voltage, while a large one may cause power oscillation of the system. Therefore, it is critical to select an appropriate \(m_{1}\). Similarly, a smaller \(m_{2}\) corresponds to smaller droop coefficient of the converter,which implies more power available at the instant of disturbance, providing reliable energy support for the system.  
The generation procedure of the reference value of the energy storage converter with an adaptive droop coefficient is shown in Figure 4. When the system operates steadily, the change rate of DC voltage is less than the set threshold \(C_{\text{i}}\). Therefore, the output of the comparator is 0, and the converter operates with the original droop coefficient. When the system is disturbed rapidly with large amplitudes, which leads the system to emergency mode, the change rate of DC voltage may exceed the set threshold. Under this circumstance, the output of the comparator is 1 and the dynamic droop coefficient of the converter is adopted, which smooths the DC voltage.