## 3 Enabling Technologies for Smart and Resilient Grids
### Matrix Converter Applications in Solid State Transformers (SSTs)  
Solid state transformers (SSTs) are receiving increasing focus in academia with a number of distinct topologies and concepts emerging in recent years [23]. The use of  
Figure 4: Example of a matrix converter-based hybrid transformer, adapted from [21].  
Figure 5: Experimental results of matrix converter-based hybrid transformer (**a**) local power factor compensation, LV voltage and current (purple and blue respectively), MV voltage and current (yellow and green respectively). (**b**) Voltage sag compensation, LV voltage and current (purple and green respectively), MV voltage and current (yellow and blue respectively).  
high/medium frequency transformers enables new paradigms for power density and functionality of these devices. A different range of applications can benefit from the use of SSTs, from smart grids [24] to traction [25], aviation and naval applications [26].  
Figure 6 shows typical SST topologies in the replacement of conventional distribution transformers from medium voltage to low voltage.  
Applications in SGs can also be found in [27], where a grid forming SST with modular matrix converters and a medium frequency transformer operating in the 2 kHz range is proposed. The authors highlight the capability of voltage sag and swell mitigations and propose a modified space vector modulation that prevents the saturation of the transformer.  
In [28] a three-phase modular isolated matrix converter is proposed, where single phase matrix converters are coupled with medium frequency transformers operating in the range of 5 to 10 kHz, using suitable modulation and control strategies. The same authors also approach in [29] the problem of switching between the converter vectors under the effect of the leakage inductance of the transformer proposing a suitable commutation strategy.  
A solid state transformer using an indirect matrix converter-based topology is proposed in [30] where the authors devise a model predictive controller (MPC)-based controller with the aim of allowing a bidirectional power flow and mitigating power quality issues. However, the proposed topology is only suitable for LV to LV applications given the lack of modularity of the proposed topology.  
In [31] a matrix converter is used as a LV output stage of a SST where the input is composed of back to back VSCs. A modulation technique and a controller are proposed such that the output of the SST enables voltage swell and sag mitigation together with input power factor correction.  
To highlight potential modular topologies that employ matrix converters in the connection to the MV grid, two different topologies are displayed.  
The first one, in Figure 7, shows a SST topology proposed in [23] where a 3 \(\times\) 3 direct matrix converter is coupled trough a high frequency transformer to three single phase matrix converters so that it can be coupled in series at the input and in parallel at the output enabling the conversion from MV to LV.  
Figure 6: Representation of a two-stage and a four-stage solid state transformers (SST) topology using medium to high frequency transformers.  
A second SST topology is presented in Figure 8 and can be connected to the MV grid to generate LV nanogrids for both AC and DC power distribution networks as highlighted in [32]. A single-phase matrix converter is used to convert high AC voltages to low DC voltages by means of current doubler rectifiers (CDRs). The output of these CDRs can then be used to connect the AC LV bus through a VSC, or to connect DC distributed energy resources (DERs) as batteries (distributed energy storage systems--DESSs) and photovoltaics (PVs), among others.