## 2 The Structure of Typical DC Microgrids and Traditional Control Strategies
### Designing a Secondary DC Bus Voltage Compensator in the Condition of Voltage Drops  
Droop control is used to achieve power distribution between n batteries, and DC bus voltage deviations are introduced. The accuracy of power distribution is also affected by voltage deviations. To solve the shortcomings of droop control, a voltage compensator based on active disturbance rejection control (ADRC) is derived. The presented DC bus voltage compensator includes a linear extended state observer and a linear state error feedback control. The linear extended state observer observes and compensates for the total disturbance of the system, the linear state error feedback controller scales the differences between the DC bus reference voltage and the voltage estimated by the linear extended state observer, and finally, the compensated DC bus voltage is obtained based on the high-frequency gain. The controlled object is written as follows:  
\[\dot{y}=ay+bu \tag{44}\]  
In (44), \(y=V_{dc}\), \(u=\Delta V_{dc}\) are the input and output of the controlled object. a is the controlled object gain, and b is the controller gain. a and b are unknown, and the assumption \(b_{0}\) (\(b_{0}>0\)) is introduced, (44) are written as  
\[\dot{y}=ay+(b-b_{0})u+b_{0}u \tag{45}\]  
Based on linear ADRC, the total disturbance \(f\) including internal disturbances and external disturbances is introduced and shown as  
\[f=ay+(b-b_{0})u \tag{46}\]  
Thus, based on (45), (46) is rewritten as  
\[\dot{y}=b_{0}u+f \tag{47}\]  
By introducing the state variable \(x_{1}=y\) and the expanded state variable \(x_{2}=f\), the state space of the controlled object is obtained and shown as  
\[\left\{ \begin{array}{l}\dot{x}_{1}=x_{2}+b_{0}u\\ \dot{x}_{2}=\dot{f}\\ y=x_{1}\end{array} \right. \tag{48}\]  
The linear expansion state observer is designed as follows:  
\[\left\{ \begin{array}{l}\dot{\hat{x}}_{1}=\beta_{1}(y-\hat{x}_{1})+\hat{x}_{ 2}+b_{0}u\\ \dot{\hat{x}}_{2}=\beta_{2}(y-\hat{x}_{1})\end{array} \right. \tag{49}\]  
In (49), \(\beta_{1}\) and \(\beta_{2}\) are the state observer gains. The linear ADRC is used to track each variable of the controlled object in real time, and the state feedback controller is designed as follows:  
\[u=\frac{1}{b_{0}}[k_{\mathrm{P}}(r-\ \hat{x}_{1})-\ \hat{x}_{2}] \tag{50}\]  
The DC bus voltage deviation after the parameter adjustment is expressed as  
\[\Delta V_{\mathrm{dc}i}=K_{1}v_{\mathrm{dc}f}-(K_{1}+K_{2})\overline{v}_{ \mathrm{dc}i} \tag{51}\]  
In (51), \(K_{1}\), \(K_{2}\) are shown as  
\[K_{1}=\frac{k_{\mathrm{P}}(s+\omega_{\mathrm{o}})^{2}}{b_{0}s(s+2\omega_{ \mathrm{o}})},\ K_{2}=\frac{{\omega_{\mathrm{o}}}^{2}}{b_{0}(s+2\omega_{ \mathrm{o}})}y\]Design Procedure of Proposed Control Strategies of n Parallel Battery Converters and the Supercapacitor Converter in DC Microgrids  
The coordinated control strategy of large-capacity HESS in DC microgrids is shown in Figure 12, and there are n + 1 Buck-Boost converters of HESS. Control strategies of n battery converters are the same. ADRC is utilized in outer voltage control loops, and improved MPC is employed in inner current control loops. Droop control is adopted to obtain power distribution between n battery converters, and the introduced DC bus voltage deviations are compensated for by a DC bus voltage compensator based on a linear ADRC. Compared with traditional observers, the voltage expansion state observer of ADRC control is not related to the system model and parameters, the disturbance immunity is enhanced, and voltage overshoots are significantly reduced. On the other side, in the MPC-based inner current control loop, the current response speed is accelerated and smaller switching losses are achieved. The low-pass filter (LPF) is adopted to obtain high-frequency power as the reference for the supercapacitor converter, ADRC is also utilized in the outer power control loop, and MPC is employed in the inner current control loop. The design procedure of n + 1 bidirectional Buck-Boost converters in HESS is shown as follows. 1.