# A Hierarchical Coordinative Control Strategy for Solid State Transformer Based DC Microgrids
## 2 Overview of the SST-Based DC Microgrid System  
### Mathematical Model of the SST  
The topology of the solid state transformer used in this paper is shown in Figure 2. Compared with the traditional topology, a three-phase MMC is selected to replace the CHB as the input stage, and a CLLC resonant converter is used to replace the DAB converter as the isolation stage. As mentioned above, an MMC can reduce the number of power switching devices and high frequency transformers. Under the comparative conditions in the literature [22], an MMC can reduce the number of switching devices by 20% and the number of high-frequency transformers by 50%, in contrast to CHB. The CLLC resonant converter is a new type of structure, which has not been fully covered in the literature on SSTs. \(E_{a}\), \(E_{b}\), and \(E_{c}\) are the voltages of the three-phase distribution network; \(i_{a}\), \(i_{b}\), and \(i_{c}\) are the currents of distribution network; \(L_{s}\) and \(L_{a}\) represent the smoothing inductor on the grid side and the arm inductor of MMC, respectively; \(U_{a}\), \(U_{b}\), and \(U_{c}\) are the AC output voltages of MMC; \(C_{H}\) and \(C_{L}\) are the series HVDC link capacitor and parallel CLLC output capacitor, respectively; \(C_{s}\) represents the MMC submodule capacitor; \(N\) denotes the number of arm submodules of MMC, and the same number for the CLLC submodule; \(i_{o}\) and \(i_{L}\) represent output-stage load current and inductance current, respectively; and \(L_{f}\) and \(C_{f}\) represent the LC filter parameters. The topology of the SST-based DC microgrid is shown in Figure 3. In this system, the SST functions as an energy center to balance the power flow among the regional distribution network, DC microgrid, and the household LVAC load. The voltage level of the distribution network is 10 kV. The DC microgrid consists of photovoltaic (PV) power supply, energy storage system (ESS), and DC loads. It is connected to the distribution grid through the 700 V LVDC port of the SST. In synchronous rotating coordinates (d-q coordinates), the dynamic equations of the MMC can be described in Equation (1):  
\[\left\{ \begin{array}{l}\left(L_{s}+\frac{L_{q}}{2}\right)\frac{d_{i}}{dt}\!=\!E_ {d}\!-\!U_{d}\!+\!w\!\left(L_{s}+\frac{L_{q}}{2}\right)\!i_{q}\\ \left(L_{s}+\frac{L_{q}}{2}\right)\!\frac{d_{i}}{dt}\!=\!E_{q}\!-\!U_{q}\!-\!w \!\left(L_{s}+\frac{L_{q}}{2}\right)\!i_{d}\\ C_{He}\frac{dU_{He}}{dt}=\frac{3E_{q}i_{d}}{2U_{dc}}-\sum\limits_{i=1}^{N}i_ {1i}=\frac{3E_{q}i_{d}}{2U_{dc}}\!-\!i_{1}\end{array} \right. \tag{1}\]  
where \(E_{d}\) and \(E_{q}\) are the AC voltages of the distribution grid under d-q coordinates; \(i_{d}\) and \(i_{q}\) are the AC currents; \(U_{d}\) and \(U_{q}\) are the line-frequency output voltages of the MMC under d-q coordinates; \(\omega\) is the fundamental frequency; \(U_{dc}\) is the HVDC bus voltage; \(C_{He}\) is the equivalent shunt capacitor of the HVDC link; \(i_{1i}\) is the input current of the CLLC submodule \(i\); and \(i_{1}\) is the sum of the N submodule input currents of CLLC. The topology of a single submodule of the CLLC resonant converter is shown in Figure 4, where \(i_{dc}\) is the input current of the HVDC link; \(U_{dci}\) and \(U_{out}\) are the input and output DC voltages of the submodule; \(i_{1i}\) and \(i_{2i}\) are the input and output currents; \(i_{Lj}\) is the outlet current of submodule i, and  
Figure 3: Topology of a DC microgrid system. Figure 2: Topology of the solid state transformer (SST). is the outlet current of the overall input-series-output-parallel (ISOP) CLLC resonant converter; \(C_{r1}\), \(L_{r1}\) and \(C_{r2}\), \(L_{r2}\) are the resonant capacitors and inductors on the primary and secondary sides; \(L_{m}\) is the magnetic inductor, which can be integrated inside the HFT; \(n\) is the transformation ratio of the HFT; \(NC_{L}\) represents the equivalent parallel capacitance of the LVDC link; and \(i_{inv}\) and \(i_{mc}\) are the input currents of the output stage and local DC microgrid.