## 2 The Structure of Typical DC Microgrids and Traditional Control Strategies
### Improved Model Predictive Control of the Inner Current Control Loop  
Improved model predictive control (MPC) is proposed for the inner current loop of HESS. Based on the prediction of the future state satisfying the state and control constraints, the principle of MPC is to obtain the optimal switching states by minimizing the evaluation function. The design procedures of MPC are:  
1. Model the converters and identify all switching modes. Predict behaviors of the controlled variables (e.g., voltages, currents) under various switching modes. 2. Define the evaluation function according to the system model and control variables and obtain values of the predicted evaluation function. 3. Choose the optimal switching state corresponding to the minimized evaluation function. For HESS, the same internal current control strategy is used for battery and supercapacitor converters. Large-capacity HESS composed of n battery converters and a supercapacitor converter is shown in Figure 8. The \(i\)-th battery converter is taken as a typical example. In Figure 8, \(V_{dc}\) is the DC bus voltage, \(C_{bus}\) is the DC bus capacitance, \(I_{bat}\) and \(I_{sc}\) is the battery and supercapacitor currents. \(L_{1}\) and \(L_{i}\) are the first and \(i\)-th inductors of battery converters. \(L_{n+1}\) is the inductor of supercapacitor converter. SW\({}_{i}\), SW\({}_{i+1}\), SW\({}_{n}\) and SW\({}_{n+1}\)  
Figure 8: The topology of large-capacity HESS. represent the power switches of \(i\)-th battery converter and the supercapacitor converter. The states of the power switches are 0 (off) or 1 (on). When the conventional MPC is utilized, there are four complementary switching modes for the \(i\)-th battery converter and the supercapacitor converter, as shown in Table 1.  
In fact, for HESS Buck-Boost converters, only one power switch action is needed during charging and discharging periods, and the state of the other switch is 0 (off). Unfortunately, the states 0 of 2 switches in the Buck-Boost converter are not considered in Table 1, and complementary switching modes for HESS when traditional MPC is utilized could significantly increase switching losses. Consequently, it is necessary to consider that 2 switches in the Buck-Boost converter are both off, and non-complementary switching modes for HESS when improved MPC is utilized are shown in Table 2.  
As shown in Table 2, 9 switching modes of battery and supercapacitor converters are divided into 3 types. Type 1: \(\textbf{SW}_{i}\) and \(\textbf{SW}_{i+1}\) is in 1 and 0 states, respectively. The equivalent diagram of the battery converter is shown in Figure 8. \(T_{\text{i}}\) is the model-predicted sampling period. The discharging current is defined as positive, and the mathematical model and the discrete model of the battery converter in Figure 9 are shown as  
\[L_{1}\frac{\text{d}I_{\text{bat}}}{\text{d}t}=V_{\text{bat}}-V_{\text{dc}} \tag{31}\]  
\[I_{\text{bat}}(\text{k}+1)=I_{\text{bat}}(\text{k})+\frac{T_{\text{i}}}{L_{ \text{I}}}(V_{\text{bat}}-V_{\text{dc}}) \tag{32}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Switching Modes**} & \multicolumn{2}{c}{**Battery Converter**} & \multicolumn{2}{c}{**Supercapacitor Converter**} & \multicolumn{2}{c}{**Switches in on State**} \\ \cline{2-5}  & \(\textbf{SW}_{i}\) & \(\textbf{SW}_{i+1}\) & \(\textbf{SW}_{n+1}\) & \(\textbf{SW}_{n+2}\) & **n** \\ \hline
2 & 1 & 0 & 0 & 1 & 2 \\ \hline
3 & 1 & 0 & 0 & 0 & 1 \\ \hline
4 & 0 & 1 & 1 & 0 & 2 \\ \hline
5 & 0 & 1 & 0 & 1 & 2 \\ \hline
6 & 0 & 1 & 0 & 0 & 1 \\ \hline
7 & 0 & 0 & 1 & 0 & 1 \\ \hline
8 & 0 & 0 & 0 & 1 & 1 \\ \hline
9 & 1 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Non-complementary switching modes for HESS when improved MPC is utilized.