Solid State Transformers: Concepts, Classiﬁcation, and Control

: Increase in global energy demand and constraints from fossil fuels have encouraged a growing share of renewable energy resources in the utility grid. Accordingly, an increased penetration of direct current (DC) power sources and loads (e.g., solar photovoltaics and electric vehicles) as well as the necessity for active power ﬂow control has been witnessed in the power distribution networks. Passive transformers are susceptible to DC offset and possess no controllability when employed in smart grids. Solid state transformers (SSTs) are identiﬁed as a potential solution to modernize and harmonize alternating current (AC) and DC electrical networks and as suitable solutions in applications such as traction, electric ships, and aerospace industry. This paper provides a complete overview on SST: concepts, topologies, classiﬁcation, power converters, material selection, and key aspects for design criteria and control schemes proposed in the literature. It also proposes a simple terminology to identify and homogenize the large number of deﬁnitions and structures currently reported in the literature.


Introduction
Passive transformers have been indispensable components in electrical power systems since Zipenowsky et al. demonstrated the first commercial transformer in 1885 [1,2]. Later, Tesla proposed the application of transformers for an electrical distribution system in 1888 [3]. Even though passive transformers can achieve voltage regulation through tap changers, solid state transformers (SSTs), also known as power electronic transformers (PETs), are capable of compensating voltage sags and harmonic distortion, interconnecting asynchronous networks, interfacing DC and AC port(s), compensating reactive power, regulating voltage magnitude, isolating disturbances from source and load or vice versa, and eliminating the use of mechanical actuators or tap changers. These features make SST a very attractive solution to replace passive low frequency transformers (LFTs) in several applications [4]. However, SSTs should not explicitly be implied as a complete replacement of LFTs as they may not be feasible in certain applications (e.g., special transformers such as instrument expand at a compound annual growth rate (CAGR) of 21.7% from 2019 to 2027 with Europe being projected to lead the market with a CAGR of 23.4% [36]. Thus, the growing adaptation of SSTs in academia and industry point SST as a next revolutionary step in the power electronics community.
In this work, an overview of SST is presented, discussing and classifying its concepts, topologies, and applications. The paper is organized as follows: Section 2 introduces the SST architectures and proposes a terminology for a simple classification. Section 3 presents the composition of SSTs using the proposed SST nomenclature. In Section 4, an overview on various classifications and sub-classifications of SSTs are reported. Section 5 details available power converter topologies for interfacing MV and LV side of the SST along with a brief review on the modulation schemes. Section 6 reviews the constructive aspects of SSTs in terms of semiconductor selection and design criteria of a medium frequency transformer (MFT). In Section 7, control schemes for the most relevant SST applications are reviewed. Section 8 presents safety and protection issues for SSTs. Finally, brief concluding remarks and future trends are presented in Section 9.

SST Architecture
The architecture of SSTs has been classified based on number of power conversion stages and electrical features that compose it, as first proposed by Lothar Heinemann et al. in [12] and illustrated in Figure 1. This classification was adopted by Xu She et al. in [37] with the single stage without DC-link being referred as type A, two stages with LV DC-link as type B, two stages with HV (or MV) DC-link as type C, and three stages with MV and LV DC-link as type D. However, considering the current state of the art on SSTs, this classification is not wide enough and several of the reported SST topologies are not covered by this classification. Thus, a simple and intuitive terminology for a universal classification of SSTs is proposed in this work. The terminology is based on the three key characteristics that define an SST i.e., connection to MV or HV at least in one port, MF isolation stage, and control of input/output electrical variables, being sufficiently general to include any kind of SST.  Figure 2 shows the proposed definition of two different groups of power conversion stages, for simplicity named as solid state transformer block (SST block ) and solid state transformer isolated block (SST i-block ), which can be considered as the building blocks for any SST. Thereby, the SST i-block corresponds to an isolated power conversion unit with connection to MV or HV levels while the SST block corresponds to a non-isolated power conversion unit, which ports can be indistinctly connected to LV and/or MV range. The SST i-block by itself satisfies the three key characteristics to be termed as an SST. Therefore, SST i-block represents the simplest form of an SST, i.e., a single stage SST. Single stage SSTs have a single port available at the primary and at the secondary side of the MFT. Accordingly, various single stage SSTs can be sub-classified as: single primary single secondary (SPSS) AC AC SST, SPSS AC DC SST, SPSS DC AC SST, and SPSS DC DC SST as shown in Figure 2a-d, where the symbol stands for the identification of the galvanic isolation. Thereby, SST block can be considered as extension stages of SST i-block to form different configurations of SSTs. Two-stage SST can be constructed using one SST i-block and one SST block . This interconnection generates a coupling link, which will be considered as a port only if it is intended for external interconnection; otherwise, it is just considered as an energy link. Thereby, based on the placement of the SST i-block , an additional port can be created either at the primary side of MFT for back-end SST i-block or at the secondary side of the MFT for front-end SST i-block . Accordingly, SST topology in Figure 1b,c can be defined as dual primary single secondary (DPSS) AC/DC AC SST and single primary dual secondary (SPDS) AC DC/AC SST, respectively. Authors in [16] presented an isolated front-end SST configuration with an AC link and reduced complexity and volume for MV converters, which is presented in Figure 3a. Although this topology is not contained into the classification presented in the literature (see Figure 1), based on the proposed terminology, it is defined as SPDS AC AC/DC SST. Supposing that the AC link is not intended for external interconnection, then the topology should be named as SPSS AC AC/DC SST. This clarifies that the SST is intended only for one AC input port and one DC output port, having an AC interlink after the SST i-block . Likewise, a three-stage SST such as Figure 1d is formed using one SST i-block and two SST block forming a dual primary dual secondary (DPDS) AC/DC DC/AC SST. Furthermore, authors in [38] proposed a three-stage SST named as a bidirectional intelligent semiconductor transformer as shown in Figure 3b, aimed for smart distribution systems and microgrids. Using the proposed terminology, this can be referred as a single primary triple secondary (SPTS) AC DC/DC/AC SST.
Thereby, an SST with any number of stages can be easily classified. Interconnection of two or more SST i-block will be considered as interconnection of separate SSTs, unless all the SST i-block and SST block are controlled as a single unit, without independent control for each block. In that case, the terminology remains unchanged and the symbol shall denote the number of SST i-block within the SST.
The concept presented in Figure 2 has assumed only one input and one output port per SST i-block , i.e., SISO SST i-block . Nevertheless, as presented in Figure 4, the concept can be extended for SST i-block (s) with multiple input multiple output (MIMO) ports. Thereby, MIMO blocks can interface an arbitrary number of m-input(s) and supply energy to n-output ports. Notice that the voltage ports for MIMO SST i-block in Figure 4a-d share the same nature (i.e., AC or DC). It is also possible to construct a MIMO SST i-block with voltage ports of different nature (i.e., AC and DC) defined as hybrid-port MIMO SST i-block and is shown in Figure 4e-thus completing the generality of the proposed terminology.   Figure 5 shows the different levels of integration to understand the composition of an SST. As it was previously discussed, generation of different SST architectures can be achieved using the combination of the defined SST i-block and SST block . The definition of these architectures have been made in a system level of integration. In order to further identify and classify the different topologies of SSTs proposed in the literature, it is required to look into the proposed SST i-block and SST block presented in Figure 2 and establish some definitions regarding its construction. Figure 5 defines the three different levels of integration. Firstly, the concept of integrated power modules (IPM) [40] is used, which is defined as the smallest self-contained power electronic unit. Thus, an IPM (also known as power electronics building block (PEBB)), defined as a module integration level, is composed of semiconductor devices, gate drivers, sensors, protections, power supplies, communication ports, passive elements, and the required circuitry to create one module. A typical example of an IPM would be one leg of a power converter. When an IPM is used to create an SST, it will be named as solid state transformer integrated power modules (SST IPM ). Likewise, and as shown in Figure 5, the interconnection of SST IPM forms a so called solid state transformer cell (SST cell ), if an MFT is used within the interconnection, they form a solid state transformer isolated cell (SST i-cell ). This represents the next level of integration, namely power converter integration level. Finally, the interconnection of one or more SST cell (or SST i-cell ) defines a SST block (or SST i-block ). Thus, the complexity of a SST block (or SST i-block ) is defined by the number of SST IPM in each SST cell (or SST i-cell ) and the number of SST cell (or SST i-cell ) in each the SST block (or SST i-block ).

Module Integration Level
At the module integration level, an SST IPM can take any form. Commonly, commercially available integrated power modules are used to create a SST IPM . Thereby, an SST IPM could be a half bridge phase leg, matrix converter phase leg [41], or a multi-level converter phase leg or a cascaded H-bridge (CHB) or modular multilevel converter (MMC) phase leg as shown in Figure 6. Figure 6. Topological equivalent of SST IPM at module-level: (a) Half bridge phase leg [40], (b) Matrix converter phase leg [41], (c) Matrix converter phase leg using reversed blocking-IGBT [41], (d) Neutral point clamped converter phase leg [42,43], (e) Flying capacitor phase leg [44], (f) Cascaded H-bridge phase leg [45,46], and (g) Modular multilevel converter phase leg [47].

Converter Integration Level: SISO Configuration-I
Standard and non-standard power electronics converters can be used at the converter level integration. This integration leads to the construction of SST block and SST i-block , which are further explored in this section.
A SST block is composed of either a single SST cell , i.e., a single power converter, as shown in Figure 7a, or it can be formed by using multiple units SST cell . Typically, interconnection of several SST cell are required to handle the high levels of voltage or current present at the terminals of an SST. Series interconnection helps to achieve high voltage levels with LV semiconductors. Similarly, parallel interconnection is suitable for handling high current levels. Accordingly, three different interconnections can be highlighted: input series output series (ISOS), input series output parallel (ISOP), and input parallel output parallel (IPOP) connection, as depicted in Figure 7b-d. A topological equivalent model of SST cell is shown in Figure 7e. Similarly, an SST i-cell is formed using one MFT only and its topological equivalent model is shown in Figure 7f. It is composed of an MFT placed in-between primary side and/or secondary side SST cell (s) (only one SST cell is required). A reactive high frequency network is usually present at the primary and secondary side of the MFT to control energy transfer, create resonance, and allow soft-switching operation on SST cell [50,51]. The MFT not only provides galvanic isolation but also produces large voltage and current transfer ratios with high efficiency.
An SST i-block is composed of either a single SST i-cell or using multiple SST i-cell connected in ISOS or ISOP configuration as shown in Figure 7a-c. Notice that an SST i-block formed using a single SST i-cell has a single and centralized MFT [4,52], while an SST i-block formed using multiple SST i-cell possesses several distributed MFTs [53,54]. The MFT implemented in an SST i-cell (see Figure 7f) can have several configurations, as shown in Figure 8a-f. These different MFT configurations can be used in the same manner to create an SST i-cell as presented in Figure 9.  [4], (b) three phase transformer [49], (c) single phase multi-winding transformer [55], (d) three phase multi-winding transformer [56], (e) split winding transformer [57], and (f) scott transformer [16].

Converter Integration Level: SISO Configuration-II
A single SST i-cell can be combined with additional SST cell (s) to extend the stages at the cell-level as shown in Figure 10a-c. Additionally, multiple units of multi-stage SST cell can be interconnected in ISOP or ISOS configuration to distribute the voltage or current burden as shown in Figure 10d,e respectively. It is noteworthy that the multi-stage SST i-block as shown in Figure 3 has a common DC-link unlike multi-stage SST i-cell as in Figure 10d,e that has multiple isolated and independent DC ports. Figure 10. Stage extension at cell level and formation of SST i-block using multi-stage SST cell [54,58]: (a) two-stage SST cell , (b) two-stage SST cell , (c) three-stage SST cell , (d) two-stage SST cell in ISOP configuration, and (e) three-stage SST cell in ISOS configuration.

Converter Integration Level: MIMO Configuration
MIMO SST i-block is composed of multiple units of either SST i-cell or multi-stage SST cell which are interconnected to create multiple input and/or output ports to achieve additional degree of freedom in terms of power routing. A three port MIMO SST i-block formed using SST i-cell and multi-stage SST cell is shown in Figure 11a,b. Furthermore, Figure 11c shows a hybrid-port MIMO SST topology.

SST Classification Based on Voltage Levels
According to the key characteristics of an SST [13], at least one port of the SST has to be connected to MV, either AC or DC. Thus, regarding its voltage levels, the following classifications can be defined: (a) MV/LV configuration and (b) HV/MV configuration.  Figure 13a shows the MV/LV SST configuration, a low frequency (LF) MV input is interfaced at the primary side port of the SST which is processed either using a single SST cell or multiple SST cells . The primary side SST cell (s), which may also possess an MV DC-link, increases the frequency to provide medium frequency (MF) voltage to the primary side of the MFT, which, besides providing isolation, reduces the voltage magnitude. Depending on the power electronics structure and application, a frequency range of 1 kHz to several hundred kHz can be implemented. Similarly, the secondary side SST cell (s) provides LVAC and/or LVDC output. An extensive assessment of MV and LV voltage level standards is presented in [12]. Most of the publications related to SSTs are reported for MV/LV voltage levels, being an attractive and economically viable solution to interface electrical systems to medium voltage levels mainly in modern traction and smart grid technologies [48,49].
In addition, in Figure 13b, typical applications of SSTs adopted in high voltage (HV) levels such as offshore wind turbines for HVDC/MVAC configuration are reported in [59,61,62]. For this application, the lower weight/volume ratio of SSTs compared to passive transformers is a key feature which makes SST economically attractive. Moreover, authors in [60] have emphasized this benefits in HV/MV distribution grid highlighting faster replacement and cost for transporting SST using truck as compared to railways for a standard HV transformer.
Furthermore, the definition of medium voltage is wide and may be interpreted differently based on different national and/or international grid codes [63]. Table 1 depicts the voltage ranges defined in the IEC 60038 [64]. German standard BDEW 2008 defines the MV range for distributed energy resources (DER) connected to MV network ranging from 1 kV to 66 kV [65] and, in France, the medium voltage level could be referred to HVA range (>1 kV to <50 kV) as voltage levels below 1 kV are defined as low voltage in [66].

SST Classification Based on Control of Isolation Stage
SSTs can be classified based on control of the SST i-cell (or isolation stage) namely [67,68]: (a) Decoupled control of isolation stage and (b) Coupled control of isolation stage.

Decoupled Control of Isolation Stage
In this type of control, the primary and secondary side SST cell as shown in Figure 7f are controlled independently without utilizing the MFT's reactive network placed at the primary and/or secondary side of the MFT. The transformer acts as a passive element and transforms voltage appearing across its primary winding. In fact, the earliest proposal of Moonshik Kang et al. in [11] demonstrated voltage regulation using this approach. The phase shift angle (φ), which is the phase difference between the switching signals of the primary and secondary side SST cell , is set to zero. In addition, authors highlighted that no energy storage element was utilized. Similarly, a decoupled control of isolation stage is reported in [4,52].

Coupled Control of Isolation Stage
The coupled control of isolation stage utilizes primary and secondary side SST cell along with the reactive network as shown in Figure 7f. Reactive network is required, which is used for energy transfer, achieving current shaping and soft switching [50]. Two different circuits are reported [67,68] namely: (a) Non-resonant circuits and (b) Resonant circuits.

Isolation Stage Based on Non-Resonant Circuits
The concept of non-resonant based energy transfer can be associated with the principle of dual active bridge (DAB) which was first introduced by De Doncker et al. in 1991 [69] for high power density isolated DC/DC conversion as highlighted in Figure 14a. The reactive network consists of a series connected leakage inductance connected to the MFT, which is utilized for temporary energy storage allowing to control a phase shift angle (φ) between input and output voltages. It is also possible to achieve non-resonant based isolated DC/DC conversion using isolated push-pull topology [70] or using current doubler topology as reported in [71]. An extensive classification of isolated DC/DC converters with their topologies and modulations is detailed by Florian Krismer in [50].
Authors in [72] presented an isolated AC/AC stage as shown in Figure 14b. The control of this topology is based on principle of DAB; authors refer to it as an AC/AC DAB for SST and demonstrated energy transfer, voltage regulation, and soft switching using the non-zero leakage inductance. Furthermore, the author in [73] highlights the limitations to achieve zero voltage switching (ZVS) in AC/AC DAB as it requires additional auxiliary circuits to extend the ZVS range.
Authors in [68] presented a soft switching SST formed using an isolated AC/AC stage constructed using current source bridges and operating as a DAB. This topology utilizes transformer magnetizing inductance instead of the leakage inductance for energy transfer, and this topology is referred to as dynamic current converter or dyna C in [74] and is shown in Figure 14c. Authors in [75] highlighted several complex manufacturing issues in adopting a three phase isolated DC/DC DAB in SSTs as the three phase transformer requires symmetrical leakage inductances. In addition, optimizing performance using advanced modulation schemes such as those based on triangular or trapezoidal waveforms may not be feasible for a three-phase DAB. Therefore, single phase isolated DC/DC DAB stages are the most commonly adopted topology in multi-cell SSTs.
Falcones et al. in [76] adopted multiple active bridge (MAB) in SST, namely quad active bridge (QAB), as shown in Figure 14d aimed to integrate distributed generation and energy storage systems. Furthermore, Costa et al. in [77] highlights the benefits of MAB as they are reported to preserve the advantages of DAB and offer an additional advantage of reduced number of transformers and modules. Extensive details of various multi-port isolated DC/DC converters are found in [78].

Isolation Stage Based on Resonance Circuits
The concept of resonant converters was first proposed by Schwarz in 1970 [79]. The primary side reactive high frequency network is usually composed of leakage inductance with a combination of series and/or parallel inductor and/or capacitor to form: series resonant converter (SRC), parallel resonant converter (PRC), hybrid series-parallel LCC and LLC type to achieve medium frequency isolated DC/DC transformation [68], and this is shown in Figure 15a-d. A bidirectional power flow in resonant converters can be achieved using active devices in the secondary bridge and controlling the phase angle (φ) between the input and output voltages [68,80]. An example of coupled control in isolation stage using resonant circuits can be seen in [38], which utilizes an LLC based isolated AC/DC power conversion stage as shown in Figure 15e. Isolated DC/DC conversion using SRC in discontinuous-conduction mode is reported to provide a well regulated power over a wide loading range with minimal sensors [19]. In addition, the half-cycle discontinuous-conduction mode (HC-DCM) SRC has received more attention in SST due to higher power density, efficiency, and possibility to implement soft switching methods [81]. Unlike DAB, the performance of SRC depends of the accuracy of the resonance frequency of the circuit, which might change as passive components age or load changes worsening its performance. Thus, DAB has emerged as a preferred choice over SRC especially for SSTs in distributed systems [55]. Therefore, the selection of isolation stage based on resonance or non-resonance circuit depends on the application.

SST Classification Based on Modular Structure
Kolar et al. in [49] presented three degrees of freedom in terms of modularity defined based on: direction of power flow, connection to 3-phase system, and connection to the MV voltage levels. A similar concept is extended to the proposed SST concept (see Figure 2) and is defined as: (a) modularization based on direction of power flow (P-axis), (b) modularization based on voltage/current levels (V-axis), and (c) modularization based on phase interconnection (ψ-axis).
Modularization in the direction of power flow is achieved by adding SST block (s) to create additional power stages such as two-stage or three-stage SSTs, thereby obtaining additional degrees of freedom in control and interfacing ports e.g., the presence of a DC-link for decoupling the low frequency and high frequency side [49]. Figure 16 shows the degree of modularization along the P-axis. Notice that the SST i-block (or SST block ) along the P-axis alone are formed using single SST i-cell (or SST cell ) only.  Modularization based on voltage/current levels is defined based on no. of SST cell (or SST i-cell ) per power stage (see Section 3.2) and can be sub-classified as: (a) non-modular SSTs, (b) hybrid-cell SSTs, and (c) fully modular multi-cell SSTs as shown in Figure 17. Figure 17b highlights a hybrid-cell SPDS SST with an SST i-block formed using multiple units of SST i-cell and a SST block formed using single unit of SST cell and its placement on the PV-plane is highlighted.  Modularization based on phase interconnection is achieved in n-phase AC systems either in the electric circuit using single phase SST cell to n-phases by replicating it symmetrically or in the magnetic circuit using single phase MFT. Modularization in the ψ-axis can be sub-classified as: (a) non-modular SST, (b) semi-phase modular SST, and (c) fully phase modular SST, and is shown in Figure 18.

Phase interconnection
Non-modular Semi-phase modular Fully phase modular Modularity achieves scalability and redundancy. Therefore, it is crucial for SST as it ensures system reliability and simplifies mass production consequently, achieving lower production costs. The three-dimensional (PVψ-plane) for previous research works is illustrated in Figure 19. A comparative review of functional capabilities of previous SST topologies is found in [82]. The following sub-sections present a review of previous publications for these sub-classifications. EPRI [20] ABB [10] FREEDM Gen I [15] Fully modular multi-cell TIPS [56] Dyna C [74] ETH [33] BIST [38] P E T T

[ 5 8 ]
Semi-phase modular  [7] and demonstrated phase modulation using single phase matrix converters for a 3 kVA transformer. Authors in [11] presented a similar topology for a single phase 10 kVA, 240/246 V electronic transformer along with a multilevel approach. Authors in [84] proposed symmetric modulation scheme to achieve soft transitions for this topology. Similarly, the earliest proposed SPSS AC DC SST as shown in Figure 2b was presented by authors in [85] using a phase control methodology aimed for Uninterruptible Power Supplies (UPS) systems. Recently, authors in [57] highlighted single stage SPSS AC AC SST for a 7.2 kV input and reported a few limitations such as absence of DC-link which may require an increased size of filters consequently, affecting the input power factor.
Furthermore, authors in [86] demonstrated a two-stage DPSS AC/DC AC SST as illustrated in Figure 1b to address power quality issues such as: power factor correction, voltage regulation, voltage sag and swell elimination, and voltage flicker reduction. Typically, this configuration of SST can be employed in MVDC based electric ships or in DC collectors for large scale PV plant [29,[87][88][89]. Additionally, authors in [4] presented a two-stage SPDS AC DC/AC SST as shown in Figure 1c aimed at four-wire power distribution networks utilizing MMC for SST and reported that the topology had a reduced footprint and elements in the SST validating through a dynamic model and decoupled control system. The author in [90] reported the feasibility and advantages of a three-stage DPDS AC/DC DC/AC SST as shown in Figure 1d Figure 20a; the cells are interconnected in an ISOP configuration to form a 10 kVA 7.2 kV/120 V SST. Similarly, authors in [58] presented a PET aimed for traction as shown in Figure 20b and these both can be classified as fully modular SST. The SST presented as a patent by Sudhoff et al. in [10] can be defined as a hybrid cell modular SST as shown in Figure 20c. Authors in [92] report utilizing phase shedding technique i.e., activating or deactivating SST cell (s) based on system operating point could improve efficiency but is detrimental to system reliability as it increases the thermal stress. Therefore, authors propose a power routing concept to implement active thermal control through unevenly loaded SST cells to enhance system efficiency and increase the SST cell lifetime. Furthermore, authors in [53] presented a 1 MVA 10 kV/400V hybrid-phase modular SST and have highlighted the suitability of HC-DCM SRC in isolated DC/DC module for phase-modular SSTs as they are reported to achieve high operating efficiency. Authors have also highlighted its limitations such as inability to control the power flow and further proposed mitigation strategies to overcome propagation of single phase power fluctuation through HC-DCM SRC due to dynamic coupling in the DC/DC stage.
Authors in [55] reviewed phase modular SSTs as shown in Figure 22 and presented an inter-phase modular SST topology as shown in Figure 22d. Authors claim a better fault management capability in inter-phase modular topologies as compared to phase modular topology (see Figure 22c). To implement redundancy, a phase modular configuration would need three additional SST i-cell (one from each phase) as compared to inter-phase modular SST which would need only one additional SST i-cell .

Power Converter Topologies and Modulation Schemes
Power converter (s), embedded in the SST cell (s), are a key element for the operation of an SST. They synthesize the required voltage and currents, modulating and demodulating high frequency AC voltages across the MFT windings. Power converters, augmented with suitable control systems, are also required to eliminate low frequency signals in the MFT which otherwise would saturate its magnetic core. This section details various power converter topologies suitable for SST applications, which are classified based on the voltage operating range, namely: (1) MV side SST cell (s) and (2) LV side SST cell (s).

MV (or HV) Side SST cell (s)
There are four different methodologies reported in the literature [19,32,48,90] which are used to interface the MV voltage level, namely: (a) series connected LV semiconductor devices, (b) wide band gap based semiconductor devices, (c) multilevel converters, and (d) multi-cell approach. The present available rating for LV-IGBT is around 1700 V. A possible means to interface MV levels using a two-level bridge structure (Figure 6a) and LV semiconductor devices is by series connection of LV devices; however, dynamic voltage balancing is a challenging task [48]. Furthermore, additional snubber circuits make this approach less attractive as compared with other solutions.
Recently, with the availability of wideband gap semiconductor devices such as the 15-kV/10A SiC MOSFET and the 15-kV/20A SiC IGBTs [95], it is possible to adopt two-level bridge structures for lower MV levels; however, for higher MV levels, there may still be a need to connect these devices in series. Authors in [95] have carried out an analysis for series connected SiC IGBTs and SiC MOSFETs on the MV side for a DAB, the series connected 10-kV SiC MOSFET displays very low power dissipation up to 50 kHz switching frequency as compared to the 15-kV SiC IGBT; however, additional snubber circuits are required for making this approach due to lower voltage blocking capability.
The NPC topology is generally adopted as three levels ( Figure 6d) and practically feasible up to five levels [13]. At higher output voltage levels, there may be challenges in capacitor voltage balance and also a requirement of several series connected diodes resulting in higher conduction losses. Gabriel Ortiz in [32] has presented a detailed design of a power-cell using isolated a DC/DC converter comprised of an NPC half bridge leg on the MV side and full bridge on the LV side for 2 kV/400 V transformation. Krishna Mainali et al. in [56] have demonstrated a DPDS AC/DC DC/AC SST with the MV side formed by three-level NPC in a back-to-back configuration using 15-kV SiC switches for power substation application.
The FC is in principle similar to the NPC; the main difference is that the clamping diodes are replaced by flying capacitors [98]. A large number of capacitors allows voltage ride through during short outages and voltage sags. For a higher number of voltage levels, FC converters require a large amount of storage capacitor and the system tends to be bulky and expensive. Even though the NPC and FC can be adopted in modular SSTs, but they are not modular and scalable for high voltage levels.
The CHB is a type of multilevel converter which is modular and formed by a series connection of H-bridge cells wherein each H-bridge cell is connected to an individual DC source. Authors in [99] have analyzed modular power converters utilized in SSTs, i.e., CHB and MMC, and highlight that, in a CHB configuration with no DC voltage to supply, its cells have limited performance in terms of reactive power and harmonic compensation and usually the cells' capacitor voltage in such configurations are maintained close to a target average voltage. Most of the SST configurations adopting CHB topologies are either in fully phase modular configuration [54] or hybrid cell modular configuration [94,100].
Authors in [94] have presented a qualitative comparison for a CHB cascaded with a dual active bridge (DAB) and quad active bridge (QAB); authors report a cost savings in semiconductors alone of US $2350.08 for using QAB instead of DAB. However, QAB presents higher control complexities. Furthermore, authors in [100] present an startup procedure for CHB based hybrid-phase modular three stage SST. A distinctive feature of CHB topology is its inability to provide a common MVDC and/or LVDC port [19].
Finally, the MMC is a recent multilevel converter topology [47]. Unlike CHB, MMC requires no individual DC voltage supply; instead, it uses floating capacitors for energy transfer and is modular in nature. An MMC could be a better candidate as compared to the other multilevel converter topology on the MV (or HV) side due to its robust and modular nature whilst obtaining an improved power quality [4,[101][102][103][104].

LV Side SST cell (s)
This group of converters usually interface the load end and are connected to the secondary winding of the MFT. Direct matrix or indirect matrix converters may be adopted without series connected semiconductor devices for AC/AC conversion. As for the DC-link based converters, the secondary bridge is mostly a 2-level full bridge or half bridge configuration. Furthermore, the back-end inverter can either be a 2-level or a 3-level NPC voltage source inverter based on the application. In addition, the back-end inverter is capable of interfacing four wire AC output using four leg converters. Authors in [105,106] have presented extensive details on four-leg converters and its control.

Modulation Schemes
It is essential to understand available modulation schemes for the SST cell configurations discussed in the above sub-section. One of the earliest reviews on matrix converters can be traced to Wheeler et al. [107] in 2002 and similar reviews on AC/AC conversion and control are found in [108,109]. A review on control and modulation for matrix converters is explained in detail in [41,110]. Furthermore, authors in [111] have detailed various modulation techniques for multilevel converters.
Additionally, the most commonly adopted modulation scheme in a DAB is a single phase shift (SPS) modulation or rectangular modulation which operates the DAB at a constant frequency and a fixed duty cycle of primary (D1) and secondary side SST cell (D2) as 50%. The power flow in this technique is established by controlling the phase shift angle (φ) between the primary and secondary bridges, which, in turn, controls the voltage induced across the leakage inductance, thereby achieving power control from leading to lagging bridge [50,89,112]. Although this technique is simpler and achieves high power flow along with high dynamics, it has limited soft-switching range and possesses a large transformer root mean square (RMS) current. To reduce the semiconductor turn off losses, Schibli in [112] discussed a trapezoidal and triangular current modulation scheme. In a trapezoidal modulation scheme, a blanking time is added to the switching cycle whereby four switches can achieve soft-switching. There are two switches on the MV side and two on the LV side consequently, reducing the switching losses and achieving slightly higher efficiency. However, it is unable to operate when the secondary SST cell voltage is zero, i.e., for no-load condition and is not suitable for low loading conditions. In addition, it possesses an unsymmetrical share of losses on the half bridge for unequal voltage levels. In case of triangular modulation, which is a special case of trapezoidal modulation, one of the voltage edges of the primary and secondary is overlapped thereby, achieving a triangular current and the possibility for six switches to achieve soft switching capability [89]-thus making it as a lowest switching losses modulation of the hard switching methods. The author in [112] has also proposed a combined modulation scheme by switching rectangular, trapezoidal, and triangular modulation schemes according to operating conditions. Authors in [113] discussed a generalized modeling and optimization for the first three modulation schemes. Furthermore, authors in [114] have graphically illustrated the zero current switching (ZCS) and zero voltage switching (ZVS) boundary regions for all four of the current modulation schemes. Authors in [115] have carried out a comparative evaluation for these modulation techniques for DAB and SRC applications.
To increase efficiency, authors in [116] discussed an extended phase shift (EPS) modulation scheme aiming to expand regulating range of power transmission, reduce high transformer RMS currents, and to reduce circulating current. Authors in [117] proposed a dual phase shift (DPS) modulation aimed to reduce reactive power and output capacitance similarly, and authors in [118] discussed DPS to achieve wide voltage operating range. In case of EPS, one of the bridges generates two-level square waveforms while the other bridge generates three level waveform by regulating the duty cycles in contrast to the DPS which utilizes three level waveform for both of the bridges [119]. EPS and DPS offer two degrees of freedom in case of EPS either D1 or D2 and φ, while, in DPS, the intra-phase shift D1 and D2 are equal and controlled with φ. Furthermore, to expand the operating range for wide loading conditions, authors in [120] discussed a triple phase shift (TPS) modulation with three degrees of freedom i.e., D1, D2 being unequal as compared to DPS and also a control on φ. Authors in [121] have presented a composite TPS control scheme to operate ZVS at no load and achieve low RMS current and reducing core losses at low loading conditions. Authors in [122] provided a comprehensive overview of SPS, EPS, DPS, and TPS for isolated DC/DC converters operating on non-resonant and resonant principles and authors have also discussed their respective soft-switching characterization and range. Furthermore, in order to reduce computational complexities involving offline and online calculations, authors in [123,124] proposed a fundamental-optimal strategy based on fundamental component analysis and fundamental duty modulation.

Constructive Aspects of SST
SSTs mainly consists of SST cell and MFT. This section provides a summary and discusses the available semiconductors to form SST IPM and also materials and design considerations to build MFT for an SST.

Semiconductor Devices for SST IPM
Power electronic converters are mainly composed of power semiconductor devices and passive energy storage elements such as inductors and capacitors. Solid state power devices are a key element in power converters and selection of these devices depends on the power converter topology adopted, which, in turn, depends on the voltage/power levels. The author in [125] presents the current state of the art in power semiconductor devices and lists the important parameters for selection of power devices, namely: (a) voltage ratings, (b) current ratings, (c) switching frequency, and (d) maximum junction temperature. In addition, a good semiconductor device should possess high blocking voltage, high current carrying capability, and low on-state losses. The majority of forced commuted power converters can be constructed using IGBT; however, MOSFETs are preferred for DC/DC converters because of their lower losses at higher frequencies. In addition, trends and progress in wide bandgap semiconductor devices, mainly SiC and GaN, have been reported in [126]. The critical electric field Ec is about 2 V/µm for Si material and Ec is around 300 V/µm for wideband gap semiconductor materials [125]. Authors in [127] have performed a loss evaluation for an isolated DC/DC converter using the latest trench gate Si-IGBT and SiC-MOSFET and reported an achievable efficiency of about 99% or higher for using SiC MOSFET, while a maximum achievable efficiency of 97.4% for using Si-IGBT. Authors in [126] also highlight the benefits of SiC unipolar switches such as SiC JFET for the voltage range 1.2-1.7 kV as it has ultra low on-state resistance as compared to Si-MOSFET and the dynamic losses are low for fast switching applications as compared to Si-IGBT. Furthermore, in applications such as aerospace and nuclear plants, power semiconductor devices may be susceptible to failure due to cosmic radiations and have to be derated for reliable operation. Authors in [128] reported that higher voltage SiC MOSFETs may require a derating of up to 45% to achieve a module failure rate of 100 FIT (failure rate in time), while, with lower voltage of 1.2-kV SiC MOSFETs, the derating may require only about 25% to achieve a similar failure rate.

Medium Frequency Transformer
Medium frequency transformers are key elements in SSTs. An MFT coupled with a power converter achieves low footprint and higher power density while enhancing its efficiency [49,129]. Higher power densities accompany higher loss density. Therefore, for a good design of high power MFTs, numerous parameters such as: core material and its geometry, winding material and configuration, insulation, and thermal management have to be carefully considered while designing an efficient MFT. It is also important to account for the magnetic and electric parasitic effects. An extensive analysis of a MFT design is reported in [130,131]. The above-mentioned parameters are interdependent and an efficient design would consider the trade-off among them. This could be solved using a multi-objective optimization approach to obtain a balanced design. Authors in [132] have considered a genetic algorithm based approach to minimize power loss, weight, and volume; similarly, authors in [133] present a statistical approach using Pareto-front analysis to obtain optimal set of values.

Core Material
The core material is typically a soft magnetic material which can be easily magnetized and demagnetized. Four features have to be considered for selection of a high performance magnetic material, namely: (a) low core losses, (b) high saturation flux density, (c) high continuous operating temperatures capability, and (d) high relative permeability.
There are five main types of soft magnetic materials [130], namely: (a) powdered iron, (b) silicon steel, (c) ferrite, (d) amorphous, and (e) nanocrystalline based cores. The powdered iron core possesses low relative permeability µ r and high specific core losses which makes it not suitable for high power medium frequency operation. For the remaining core materials, Table 2 summarizes and details the magnetic material properties [134]. An extensive review on design trade-offs based on magnetic material properties such as specific core losses, saturation flux density B sat , saturation magnetostriction λ s , and permeability µ r is found in [135]. It is worth noting that the Curie temperature is the theoretical thermal operational limit while the actual thermal limits are determined by lamination and coatings, which are the maximum working temperatures. From Table 2, silicon steel and nickel steel are typically used in conventional low frequency transformers. However, these have considerable losses at higher frequency, which makes them unsuitable for application in MFT. Advanced silicon steel displays a lower loss but presents reduced saturation flux density. Therefore, the remaining three soft magnetic materials: ferrite, amphorphous alloy, and nano-crystalline may be preferred for medium frequency and high power operation. Although ferrite cores have moderate power losses and high relative permeability, it possesses low saturation flux, requiring large transformer volume. Amorphous has a reasonable cost for cores and has high permeability and saturation flux density but possesses slightly higher losses than nanocrystalline cores. Commercially available amphorphous cores from Metglas, USA are extensively used. Nanocrystalline cores in the names of Vitroperm, Finemet, NanoPhy are available from manufacturers Hitachi, Japan; Vaacuumschuleze, Germany and IMPhY, France respectively; however, Finemet and Vitroperm are widely adopted. An extensive analysis on core selection is reported in [48,130,133,[136][137][138]. Furthermore, in case of MFT for DAB, a leakage inductance either of transformer or by adding a regular leakage layer is utilized. Authors in [51] recommend ferrite material for tape wound cores for DAB MFT, as transformers constructed using amorphous and nanocrystalline material even without a leakage layer presented three times higher core losses at maximum power transfer condition as compared to ferrite which showed negligible core losses.
Typical core losses are determined using loss separation method, empirical method, and the time domain approach, where the loss separation method accounts for eddy current losses, hysteresis losses, and anomalous losses. The time domain method uses a core loss separation method in the frequency domain. However, the most commonly adopted method is an empirical method using the Steinmetz loss equation [139].
Besides the core material, core geometry is also an important factor to decide the compact design, heat dissipation and achievable voltage transfer ratios for an MFT [37]. Four different core geometries are reported in the literature [130,140] namely: (a) core type, (b) shell type, (c) matrix type [37,141], and (d) co-axial winding type (CWT) [32] as shown in Figure 23. Figure 23. Transformer core geometries [130,140,141]: (a) core type, (b) shell type, (c) matrix type, and (d) CWT.

Winding Material and Arrangement
Typical choice of a winding material is copper or aluminum due to low electrical resistance. However, winding material selection is influenced by transformer short circuit current due to their melting points and an extensive discussion on selection of winding material is found in [142]. In addition, losses such as skin and proximity effects are dominant at higher frequencies. The skin depth for circular cross-sectional conductors is reduced at higher frequencies. Thus, this limits possibility of circular shaped conductors. Therefore, litz wire or foil conductors are preferred for a MFT. Additionally, the use of litz or foil conductors depends on the design trade-offs such as window dimensions, window utilization, or the window fill factor and number of turns, as litz wires are reported to have low window utilization factor, requiring more window area. Optimal design considerations for the choice of winding material are presented in [143]. In addition, frequency of operation for a litz wire depends on the number of strands and the strand gauge [144]. Based on the resistance reduction factor for litz and solid conductors, there is an optimal frequency of operation and cross over frequency for which the performance of litz wire is better than the typically achieved by solid wires. Usually, it is above 10-20 kHz [145]. Furthermore, to reduce the winding losses with large number of layers, it is suggested to interleave the high and low voltage winding [146]. Authors in [147] argue that interleaving can be avoided with an effective design.

Insulation and Thermal Considerations
High thermal conductivity and high dielectric factor accompanied with tolerance to partial discharges is a typical requirement for the selection of a good insulation material. Air is preferred for cooling. Usually, in a highly compact and dry-type transformer, epoxy is used as dielectric material where air is insufficient for handling high voltage levels [37]. Nomex paper for windings and mineral oil as a coolant and primary insulation material are adopted in [148].
Authors in [149] have avoided oil as an insulating medium citing environmental and safety reasons. Alternatively, application of biodegradable oils in transformers is a current challenge in the industry. Among the biodegradable oils, silicone oil or ester type are predicted to benefit in the future to reduce the footprint of biodegradable oil-based transformers [150]. Mica tape is recommended as insulation for windings in [149]; moreover, authors have demonstrated thermal analysis and cooling design considering hot spots for a water-cooled MFT in SSTs. Authors in [151] realized a high frequency transformer with an achieved power density of 75 kW/kg and report performance of cooling system influences the power density and performance of a transformer [152]. Furthermore, due to reduced volume of an MFT, galvanic insulation becomes an issue restricting its volume/size. Therefore, careful selection of insulation material is needed and a few typical insulation materials along with their essential properties as reported in [153] are highlighted in Table 3. Table 3. Properties of insulation materials reported in [153].

Applications of SST and Control Techniques
Various different applications of SSTs have been detailed in the Introduction. A majority of applications benefit from their reduced volume and weight. Authors in [154] report a 75% weight reduction and 40% size reduction with a single phase 13.8 kV/ 270 V SST. Furthermore, authors in [33] provide a comprehensive discussion on volume, weight, and cost of SST vs. a conventional transformer and report about half the losses and one third of weight and volume reduction for SSTs as compared to conventional transformers in AC/DC applications. Authors in [155] realized an MVAC/LVDC SST cell with a power density of 24.6 W/in 3 . In addition, utilization of SSTs in an application is decided by the total cost of ownership (TCO). Authors in [156,157] have presented computation of TCO incorporating environmental costs such as carbon footprint of the transformer. Authors in [17] report a probable price of an AC/AC SST to be at least 10 to 25 times higher than that of an equally rated LFT. Moreover, authors present an extensive assessment of applicability of SSTs in distribution grids based on different applications. Furthermore, authors in [158] present various market drivers which affect the commercialization of SSTs for different SST applications. This section reviews the control loops and functionality of SST applied in some important applications.

Wind Turbines
The benefits of flexibility and controllability of SST are exploited for wind turbine applications. Xu She et al. in [159] have proposed the application of SSTs in the wind energy system to suppress voltage fluctuations caused by intermittent nature of wind energy without requiring additional reactive power compensator. Typically, a three-stage DPDS AC/DC DC/AC SST architecture is most commonly proposed for wind turbines.
In Figure 24, a three stage DPDS AC/DC DC/AC SST is adopted for grid integration of a doubly fed induction generator (DFIG) based wind turbine in [160]. Variable speed operation of DFIG is ensured by a rotor side control, which enables sub-synchronous or super synchronous modes. Authors developed control loops based on their power stages: Control loop for the front end SST block is defined as machine interfacing control to maintain 1 p.u. voltage at the stator terminals of the machine. The middle SST i-block utilizes coupled control using non-resonant circuits to maintain a constant LVDC voltage level whilst achieving a voltage transformation from 1.15 kV to 50 kV. Finally, the back-end SST block has two operating modes, wherein the normal mode meets grid requirements and ensures that the active power generated by a wind turbine is supplied to the grid. Additionally, during faulty mode, the control objective is set to meet the required reactive power.  Figure 24. Application of SST in wind turbines as highlighted in [160].

Traction
Gabriel Ortiz in [32] has presented a comprehensive discussion on application of SSTs in traction. Authors in [58] presented a fully-modular multi-cell AC DC SST as illustrated in Figure 25 and have adopted an ABB AC 800 PEC control platform. The front end converter has two control loops: an inner line current loop implemented with proportional resonant controllers in stationary reference frame and outer DC voltage control loop based on proportional integral controllers aiming to maintain constant voltage.

Energy Routing, Grid Interconnection, and Reactive Power
It is claimed in [15] that deployment of SSTs in distribution feeder could achieve a 1.4% of loss reduction, thereby SST could function as energy routers. In addition, Sixifo Falcones et al. in [57] have claimed that the application of SST in the envisioned future electricity grid could lead to a stable and optimal operation of distribution system using SST and secure COMM network.
Authors in [39] under a UNIFLEX project have discussed reactive power control for a three-port fully phase modular SST as illustrated in Figure 26 and presented a supervisory control to maintain reactive power between the three ports. Two methods are discussed to balance reactive power: (a) fuzzy logic control (FLC) method and (b) proportional reactive power (PRP) balancing method. The first method of FLC uses a set of pre-defined rules to govern reactive power of port 1 based on active powers of port 2 and port 3. The second method sets the reactive power on port 1 proportional to a limited value of active power on port 2. In addition, authors suggest a hybrid control scheme as FLC outperforms PRP under certain operating conditions and PRP displays better performance under certain other conditions.

Asynchronous Connections
SSTs are capable of interfacing asynchronous grids and loads; one such prototype constructed for asynchronous applications is highlighted in Figure 27 using an SPSS AC AC SST [161]. A 50 Hz grid supplies a load operating at 60 Hz using finite set model predictive control (MPC) with delay compensation. The predicted values are utilized in the pre-defined system cost function to obtain the most suitable switching state which achieves minimal cost. Similarly, authors in [54] for a fully phase modular SST highlight the advantages of finite control set MPC over traditional control techniques such as the ability to avoid cascaded control loops, easy inclusion of constraints, and fast transient response.

Safety and Protection of SST
There is a significant scope in domains of safety and protection for SSTs and very few articles address this issue. Even though SSTs have a complete control over the electrical parameters such as voltage and current, SSTs are susceptible to uncertain failures such as semiconductor failures, thermo-mechanical failures, measurement and control errors, short circuit or over-voltage, and lightning surges [162]. Although the presence of a DC-link decouples the LV and MV system, the external faults arising from MV and LV side should be addressed separately. Semiconductor devices have limited over-current handling capability and also are not equipped to handle over-voltages above their blocking capability, therefore requiring external protection schemes. Authors in [163] have discussed various faults and recommended a protection scheme employing disconnectors, breaker, fuse, and surge arrestors at the primary and secondary side of the SST. In addition, a pre-charging and bypass switch is added at the primary side to limit the inrush current. Similarly, authors in [164] propose a protection scheme employing a fast acting AC switch, fuse, and a metal oxide varistor on the input side, while an over-current and over/under voltage protection is implemented in a separate protection board to shutdown the PWM pulses. In addition, authors recommend adding fast acting switches at positive and negative terminals of DC ports. Authors in [153] report electro-magnetic interference (EMI) issues for SSTs employed in traction application due to high frequency switching and stray components and present solutions to overcome the issues of conducted EMI. Authors in [162] recommend and highlight the advantages of employing solid state circuit breakers and current limiters for the MV system. Furthermore, it is equally important to ensure grid stability while adopting SSTs; foreseeing high penetration of SSTs in electric grids, authors in [165] have highlighted potential instabilities in grids due to harmonic resonance and emphasized on a design criterion for an SST input filter to mitigate these instabilities.

Conclusions
This review summarized the most important contributions in control, topologies, constructive aspects, protections, power converter topologies, and applications of SSTs. The review also introduces a new methodology for the classification of SSTs, as an attempt to include some of the SST topologies which are not currently included in the reported classification schemes proposed in the literature. An extensive discussion on aspects related to the design and implementation of medium frequency transformers has also been included in this work.
In this paper, the main advantages of SSTs have been discussed and extensively analyzed and the performance of SSTs have been compared with that obtained using the legacy transformers. Solid state transformers can be used to provide reactive power compensation, harmonic distortion reduction, smart protection, fault ride through control, and interconnecting networks of different frequency and voltages. Selected applications of SSTs have also been discussed in this work, as, for instance, the utilization of SST in wind energy systems, traction and the utilization of SSTs for 4-leg distribution systems have also been presented, and its impact over future distribution networks have been also discussed in this work.
Considering the advantages of SSTs and the increasing interest in the power electronic community in this area of research, it is forecasted that more advances in the field of solid state transformer will be realized in the near future-for instance, integrating in large scale renewable energy resources to the distribution networks, gradual replacement of passive transformers by SSTs, smart grid, and microgrid applications, communications between SSTs and other elements in the grid, and the application of SSTs in the hybrid DC/AC grid (as, for instance, to integrate a large amount of solar panels to the AC grid and to enable efficient integration of electric vehicles and energy storage elements, such as batteries). In addition, this paper highlights further applications of SSTs in AC/DC systems such as rack level power supply for data centers, future shipboard power systems, and future aircraft power systems.
Although, as presented in this work, there is a large amount of literature regarding SSTs and its applications, it can be still considered as an unmatured technology. There are certain aspects which still remain under research, and certainly will be the focus of research in the following years, such as: (a) capability of real-time communication among different SSTs within a network: this is very important to ensure power system stability when the power system network is composed of SSTs and passive transformers, (b) control of hybrid (DC and AC) power flow in complex networks: when an SST has two or more ports, the capability of the SST to regulate the power share of DC and AC power flows within the SST is an important feature to optimize its use, which have not been reported so far, (c) four wire distribution networks: Although many reported works claim to apply the SST in distribution networks, few of them lead with unbalanced four-wire networks, which are the most common LV distribution networks. To deal with harmonics and unbalanced content at the output of the SST staying free of low frequency oscillations, the MFT is also a challenging topic which have not been reported, (d) modulations schemes and topologies of SSTs to achieve small footprint and high efficiency, (e) protections and reliability of SSTs, (f) fault ride through capability of SSTs, (g) new power electronics topologies considering advanced magnetic cores materials and power semiconductors, and (h) economical viability such as lifetime cost analysis of SSTs vs. conventional transformers.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Abbreviations
The following abbreviations are used in this manuscript: