By harnessing solar power, solar photovoltaic (PV) system helps to reduce reliance on fossil fuels, mitigate climate change, and contribute to a cleaner and more sustainable energy combination^1,2. The integration of PV systems into the electrical grid has gained significant momentum in recent years due to the growing emphasis on renewable energy sources^3,4,5. As PV installations continue to expand, there is a need for efficient and reliable power conversion technologies to maximize the utilization of solar energy^6,7. In this context, solid-state transformers (SSTs) offer promising solutions for PV system integration, enabling improved power quality, increased energy efficiency, and enhanced grid stability⁸. An SST for PV refers to the application of SST technology specifically tailored for photovoltaic power conversion and integration^9,10. It serves as an interface between PV arrays and the grid, transforming and controlling the power generated by the solar panels to match the requirements of the grid or local loads^11,12. Unlike traditional transformers, SSTs utilize advanced power electronic components and control algorithms to provide a range of functionalities and benefits for solar PV systems¹³. One of the key advantages of SSTs in solar PV applications is their ability to enhance power quality. SSTs can actively compensate for voltage fluctuations, harmonics, and other grid disturbances, ensuring stable and reliable power supply^14,15,16. This capability is crucial for PV systems as they are subject to variations in solar irradiation and fluctuating power outputs¹⁷. By regulating voltage levels and compensating for power quality issues, SSTs enable solar PV systems to operate at maximum efficiency and minimize the impact on the grid¹⁸. Another significant advantage of SSTs in PV application is their ability to optimize energy utilization and increase overall system efficiency^19,20,21. SSTs can employ advanced control algorithms to track the maximum power point of the PV panels, allowing for optimal energy extraction under varying solar conditions²². Additionally, SSTs can enable bidirectional power flow, facilitating grid interaction and energy storage integration, such as battery systems. This flexibility in power flow management contributes to higher energy conversion efficiency and improved system performance²³. Moreover, SSTs for solar PV can enhance grid stability and enable the seamless integration of solar PV systems into existing distribution networks. By advanced control capabilities, SSTs can provide grid support functions such as reactive power compensation, voltage regulation, and fault detection^24,25. These features help mitigate grid fluctuations caused by intermittent solar PV generation and ensure a smooth and reliable integration of solar PV source into the grid²⁶. Furthermore, SSTs offer compact and lightweight designs, allowing for easier installation and reduced space requirements compared to traditional transformers²⁷. This is particularly beneficial for PV installations where space constraints are often a concern. The compact size of SSTs also enables their integration within the PV system itself, reducing the need for additional external components and simplifying the overall system architecture²⁸. In conclusion, SSTs for PV applications represent an innovative and efficient solution for integrating photovoltaic systems into the electrical grid. They provide enhanced power quality, increased energy efficiency, and improved grid stability²⁹. As SST technology continues to advance, we can expect to see wider adoption of SSTs in PV installations, contributing to the continued growth and development of renewable energy³⁰. Advanced semiconductor materials and power electronic components are used for.

building SST³¹. To regulate the flow of electric power, they use high-frequency switching devices such as insulated gate bipolar transistors (IGBTs) or silicon carbide (SiC) MOSFETs. In contrast to traditional transformers, which rely on magnetic cores and copper windings, SSTs employ power electronics to transform and regulate electrical energy³². The key advantages of SSTs are their superior control, flexibility, and efficiency as compared to traditional transformers. Following are a few highlights and advantages: Voltage Regulation: SSTs can actively regulate voltage levels, allowing for improved power flow management and optimization. This allows for more efficient use of renewable energy sources, such as solar and wind, whose output is frequently variable³³. Improved Power Quality: SSTs may actively adjust for power quality concerns such as harmonics, voltage sags, and swells. SSTs may also offer reactive power assistance, which improves the stability of the grid and dependability. Smart Grid integration: Advanced communication and monitoring capabilities may also be added to SSTs. This facilitates real-time monitoring, fault detection, and grid management by allowing for smooth integration with smart grid systems³⁴. Compact and Lightweight Design: SSTs have a lower footprint and weight than standard transformers, making them easier to install and move. This is especially useful in cities or for adapting existing electrical infrastructure³⁵. Energy Efficiency: SSTs are more efficient than traditional transformers, particularly under fluctuating load situations. Their capacity to actively manage power flow and eliminate losses helps in reduction of total energy consumption³⁶.

In this paper, utilizing DC-DC and dual active bridge converters, a novel high-voltage gain structure of an SST is presented. The proposed converter comprises three DC links with varying voltages. The first DC link is connected to a high voltage gain DC-DC converter, that offers benefits like high voltage gain, low peak voltage of diodes and power switch, and low input current ripple. This enables the reception of power from renewable energy sources like PV panels through a high voltage DC link. The second DC link is connected to an AC source through a rectifier, allowing for the utilization of both DC and AC sources. A HFT is employed to ensure galvanic isolation between the sources and the third DC link. The proposed topology is studied using analysis for operational modes, steady state behavior. Finally, an experimental prototype is built which is capable of delivering 620 W power to output load at a switching frequency of 50 kHz, and the experimental results are presented.

The proposed SST is depicted in Fig. 1. This converter includes two sections. The first section is DC-DC conversion, and the other section includes three dual active bridge (DAB) converters and a high frequency transformer (HFT). Also, the proposed converter has three DC links (DC link-1, DC link-2, and DC-link-3). The voltage of DC link-1 is obtained by boosting of a low voltage renewable energy source like PV panel. The voltage of DC link-2 is obtained by rectifying an AC voltage source. DC link-3 is used to provide the dc input voltage for an inverter which transfers energy to an AC load. The summation of output AC voltages of DAB converters is applied to the primary winding of the HFT. The DAB converter in the secondary side of the HFT can operate as a rectifier and obtain a DC voltage for DC link-3. Therefore, the are used for building SST¹⁵. To regulate the flow of electric power, they use high-frequency switching devices such as insulated gate bipolar transistors (IGBTs) or silicon carbide proposed SST provides two AC ports and one DC port, and, three DC link with different voltages. DC-DC conversion section includes one power switch (S), four diodes (D₁, D₂, D₃, and D₄), five capacitors (C₁, C₂, C₃, C₄, and C₅), one input inductor (L_in), and one coupled inductor. The turns ratio of the coupled inductor is defined as n = n₂/n₁. Each DAB converter has four switches. Also, the turns ratio of the HFT is presented as N = N₂/N₁. The PWM pulses of the power switches (S, S₁, S₂, S₃, S₄, Q₁, Q₂, Q₃, Q₄, S_o1, S_o2, S_o3, and S_o4), and main waveforms are depicted in Fig. 2. Based on this figure, the proposed SST operates in three main modes, and two transient modes. Because transient modes don’t affect steady-state analysis, only main operational modes are described in the subsequent subsections.

The proposed SST.

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The main waveforms.

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Operation modes

Mode 1 [t
₀
< t < t
₁

This mode starts when power switches S, S₁, S₄, Q₁, and Q₄ are tuned on. Power switches S₂, S₃, Q₂, and Q₃ are turned off during mode 1. Furthermore, the DAB converter in the secondary side of HFT operates as a rectifier and all switches of this DAB are turned off, and the current flows through anti-parallel diodes of switches S_o1~S_o4. The equivalent circuit of mode 1 is illustrated in Fig. 3 (a). As noted from this figure, the currents flowing through the switches S₁, S₄, Q₁, and Q₄ are equal. The voltage of DC link-3 is N(V_DC1+V_DC2). This mode ends at time instant, t = t₁, when diode D₄ is reverse biased.

Operational modes, (a) mode 1, (b) mode 2, and (c) mode3.

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Mode 2 [t
₁
< t < t
₂

At the start of mode 2, power switch S is turned off, and correspondingly, switches S₂, S₃, Q₂, and Q₃ are turned on. During this mode, L_in is discharged and its current is decreased. However, the voltage over L_m and L_k is positive and their currents are increasing. The standing voltages over switches S₁ and S₄ are equal to V_C5=V_DC1, and peak voltage across switches Q₁ and Q₄ are qual to V_C=V_DC2. The leakage energy of the coupled inductor is transferred to capacitor C₃ through diode D₂. Thus, the leakage energy is recycled during mode 2. The equivalent circuit of the converter during mode-2 is shown in Fig. 3 (b). Considering this figure, the following equations are obtained.

Mode 3 [t
₂
< t < t
₃

At time instant, t = t₂, diode D₁ is turned off and diode D₃ is forward biased. The state of other semiconductor switches is same as that in mode 2. Since, the diode D₄ is tuned off, therefore, the energy of solar PV source is not delivered to DC link-3. However, the stored energy of capacitor C₅ is transferred to output capacitor C_o through HFT windings. The configuration of this mode is depicted in Fig. 3 (c). During mode 3, the voltage across the capacitor C₄ is as.

Voltage calculations

This section presents the calculation of voltage across the semiconductor switches, diodes and capacitors. Using volt-sec balance principle on input inductors, L_in and L_m, the expressions for V_C1 and V_C2 are obtained:

Substituting the value of V_c2 in (7), the expression for V_C3 is

Also, substituting the value of V_c3 in (9), the expression for V_C4 is

Substituting the values of V_c1, V_c2, V_c3 and V_c4 from (10), (11), (12) and (13) in (3), the simplified expression for V_c5

The voltage gain of DC-DC conversion section can be written as:

Furthermore, the ideal voltage gain is as follows:

The voltage of DC link-3 versus DC link-1 and DC link-2 can be expressed as:

The maximum blocking voltage over diodes D₁, D₂, and D₃ can be calculated during mode 1, when these diodes are reverse biased. The expressions for V_d1, V_d2 and V_d3 are

Power switch, S and diode, D₄ are turned off during mode 2. Thus, considering Fig. 3 (b), the maximum voltage across these elements can be obtained.

The normalized voltage stresses of semiconductors are presented by (24). Additionally, the variation of voltage gain, M_DC/DC and voltage stresses across the switches and diodes versus coupled inductor turns ratio and duty cycle of power switch S are depicted in Fig. 4 (a) and (b). Plotting these figures, the voltage stresses across semiconductor switches and diodes in the DC-DC conversion section are normalized with respect to DC link-1 voltage (V_dc1=V_C5).

Voltage analysis, (a) normalized voltage stress (Eq. (24)) versus n and D = 0.6, and (b) The 3d view of the voltage gain M_DC/DC.

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Finally, the voltage stresses of power switches included in DAB converters are calculated as (25).

Current calculations

The average current of input inductor L_in can be obtained versus current of DC link-1:

The maximum value of current flowing through L_in is equal to algebraic sum of average current and half of peak-to-peak ripple:

The average currents flowing through the diodes in DC-DC conversion section are equal to I_dc1. Based on the proposed SST’s configuration, the average current of power switch S is calculated as (28):

Therefore, considering the mean value, the peak current of switch S can be written as follows:

Considering the fact that, the average current of capacitors is zero, and using KCL, the average current of magnetizing inductance is obtained versus I_s and I_Lin.

Also, the maximum current of L_m is

The peak current or current stress of diode D₁ can be calculated during mode 2 operation, when the diode D₁ is forward biased and is given by

The peak current of diodes D₂, D₃, and D₄ are obtained as

This section presents the design consideration of the used components which are semiconductors, capacitors, and magnetic devices.

The semiconductor switches and diodes of DC-DC conversion section and power switches included in DAB converters are selected based on maximum standing voltage and pathing current. These values are presented in the previous subsections of Sect. 2.

The values of capacitors are calculated based on this assumption that; the ripple voltage is almost 2% of average voltage across the capacitor. Using the voltage and current in the pervious section, the minimum values of capacitors are attained as follows:

To achieve continuous conduction mode (CCM) of operation for DC-DC conversion section, which is suitable for renewable energy sources, the magnitude of ripples in inductor current is assumed to be lower than half of the average current. The minimum value of L_in and L_m is presented as (42) and (43).

The turns ratio of the coupled inductor (n = n₂/n₁) can be calculated based on Eq. (44):

The HFT is selected based on the maximum voltage applied across the primary and secondary windings (V_N1 and V_N2), maximum pathing current of windings (I_N1 and I_N2), turns ratio (N = N₂/N₁), and switching frequency (f_s) of the proposed SST.

The efficiency of the proposed SST is analyzed using calculation of elements losses. The total loss is presented in (45), which includes loss of power switches, diodes, capacitors, and magnetic devices.

In (45), (Delta P)are the total loss, (Delta {P_S}), (Delta {P_D}), (Delta {P_C}), and (Delta {P_{Magnetics}}) power switches, diodes, capacitors, and magnetic devices losses.

Total Loss of power switches consists conduction and switching losses:

(P_{{Loss}}^{S}), (P_{{Loss}}^{{{S_{1 – 4}}}}), (P_{{Loss}}^{{{Q_{1 – 4}}}}), and (P_{{Loss}}^{{{S_{o1 – o4}}}}) are defined as (47):

In (47), ({r_{on}})is the on-state resistance, t_s and t_r are the falling and raising times of the power switches.

Total Loss of diodes includes conduction and forward voltage losses:

Where ({r_{{D_i}}})is the internal resistance during on state, ({V_{{F_i}}})is the forward voltage of didoes.

Furthermore, the total loss of capacitors and magnetic devices can be calculated using (49) and (50).

In (49) and (50), ({r_C}) and ({r_{{L_{in}}}}) are the ESR o capacitors and inductors. The average and peak values of currents flowing through the semiconductors included in DAB converters, current of capacitors in each mode, and RMS values of currents of all components, which are essential to calculate the power efficiency are listed in Table 1.

This section presents the experimental results of the proposed converter to verify the theoretical analysis. For this purpose, a prototype is built with 620 W output power. The parameters of the proposed converter are listed in Table 2. The presented topology can deliver power from two diverse power sources. One DC power source with voltage of 25 V is connected to the DC-DC converter. The coupled inductor turns ratio and duty cycle of power switch S is chosen as N = 1 and D = 0.6 to obtain an output voltage of 200 V at DC link-1. The DC-DC converter delivers a power of 200 W to DC link-1. Furthermore, an AC source with peak voltage of 110 V deliver 420 W to DC link-2 through a rectifier. After rectifying AC voltage, a 110 V DC voltage is obtained over DC link-2. Based on the configuration of the proposed converter, the summation of voltages of DC link-1 and 2, which is equal to V_N1=200 + 110 = 310 V is applied to the primary winding of the HFT. The turns ratio of the HFT is 2:1. Thus, the voltage of secondary winding and also voltage of DC link-3 is equal to 155 V. The DC-DC converter includes 4 power diodes for which ultra-fast recovery STTH30R04 diode is used.

The power switch of DC-DC converter and power switches of the DAB converters are silicon carbide power MOSFET C3M0065090D. To generate PWM pules for power switches, TI C2000 TMS320F28379D launchpad is used. along with GDA-2A4S1 which is an isolated gate driver. Input value of inductance, L_in is selected to be 300 µH, while the magnetizing inductance, L_m of the coupled inductor is 300 µH, and its leakage inductance equal to 3 µH. To implement the input and coupled inductors, ferrite EE 55/28/21 cores are utilized. Also, all used capacitors are aluminum electrolytic, and the values of capacitances of capacitors C₁ ~ C₄ are330 µF each, while for capacitor C5 (DC Link-1) the selected value is 680 µF, capacitance of C (DC Link-2) is 1500 µF, and the capacitance value of output capacitor (DC Link-3), C_o is 470 µF. Figure 5 (a) shows the voltage waveforms of the DC link-1, 2 and 3. The voltages of DC link-1, 2, and 3 are measured as 192 V, 108 V, and 150 V, respectively. The waveforms of voltages across the diodes D₁ ~ D₄ are depicted in Fig. 5 (b). Voltage of diodes D₁, D₃, and D₄ is almost 60 V, and voltage of diode D₂ is measured as 119 V. These values validate the relations given by (19)-(22). Between diodes, the maximum normalized standing voltage is related to diode D₂, which is 119 V/192 V = 0.61. Figure 5 (c) depicts voltages of capacitors C₁ ~ C₄. Voltage across the capacitor C₁ is measured to be 54 V, and voltage of capacitors C₂, C₃, and C₄ are obtained as 36 V, 70 V, and 35 V, respectively. These results confirm the mathematical equations presented in (10)-(14). Figure 5 (d) illustrate the voltage waveforms of the coupled inductor’s primary winding, HFT secondary winding, and power switch S. The maximum voltage appearing across windings n₁ and N₂ of the HFT are measured as 37 V and 150 V. The peak voltage across the power switch S is obtained to be 58 V. Therefore, the normalized voltage stress of this switch is equal to 58 V/ 119 V = 0.48. The input current of the DC-DC converter and leakage inductance of the HFT are shown in Fig. 5 (e). The average value of the input current i_Lin is obtained 8.4 A, and peak to peak value of this current is 1.8 A. This experimental result validates that due to low value of ripples in input current, the DC port is suitable for renewable sources. Due to the AC from, the average value of the pathing current from HFT is almost zero. Also, the maximum pathing current form primary side of the HFT is measured 4.5 A, and peak to peak value of this current is 8.5 A. The measured efficiency versus output power is presented in Fig. 5 (f). The efficiency of the proposed SST for variation of output power from 50 W to 620 W is obtained between 91.55% and 94.1%. The maximum efficiency is measured at P_o= 500 W, which is 94.1%. Also, at the rated power, the efficiency achieved is 93.81%. The DAB converters in the primary side of the HFT act like inverters. The PWM pulses of each leg in these inverters are complimentary with a dead band equal to 1 µs. The DAB converter in the secondary side of the HFT used as a rectifier. Therefore, it doesn’t need PWM pulses, and current paths though anti-parallel diode of power switches. The voltage across the power switches related to these three DAB converters are depicted in Fig. 6 (a)- (f). According to these figures, the maximum voltage across power switches S₁ ~ S₄ is equal to 192 V. Also, V_Q1~V_Q4 are measured to be 108 V, and V_So1~V_So4 are obtained as 150 V. Furthermore, considering Fig. 7, the effect of leakage inductance of the HFT is visible, which make spikes on the voltage waveforms of power switch S₁ ~ S₄, Q₁ ~ Q₄, and S_o1~S_o4. The experimental prototype is shown in Fig. 8. To measure the efficiency versus PV input, the ac voltage and output load (500 W) are considered constant. Then for different voltage values of DC source, the efficiency is measured. For this work, the dc voltage is set from 15 V to 25 V. For a constant value of output load, it is clear that, the power loss is reduced with increasing the input voltage. Therefore, with increasing input dc voltage, efficiency is increased, which can be seen in Fig. 7. The proposed control strategy is shown in Fig. 9. As can be seen, MPPT of PV can be obtained by DC-DC converter inside of the SST. In fact, one of the reasons of using high step-up DC-DC converter in the proposed SST is to track the MPP of renewable energy sources like PV panel. The voltage of DC link 1 and 2 (V_dc1 and V_dc2) are regulated by dual active bridge converters in the primary side of the HFT. To control of voltages of DC link 1 and 2, the DC links total voltage error (DCL TVE) is summed and DCL TVE is controlled by PI controller. The controlled signal is considered as the reference output power of dual active bridge in the secondary side of the HFT. Thus, the injected current to the PWM inverter can be controlled. Furthermore, the voltage of DC link-3 can be regulated by PWM inverter. Totally, the voltage regulation cannot be an unsolvable problem using a three stages SST. It should be noticed that, three stages SST has DC links in both primary and secondary sides of the HFT, and the proposed SST can be categorized as a three stages SST.

Experimental waveforms, (a) voltage of DC links, (b) voltage of diodes D₁ ~ D₄, (c), voltage of capacitors C₁ ~ C₄, (d) voltage of power switch S, primary winding of the coupled inductor and secondary winding of the HFT, and (e) current waveform of input inductor L_in and primary winding of the HFT, and (f) the measured efficiency versus P_o.

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Experimental waveforms, (a) & (b) voltage of switches S₁ ~ S₄, (c) & (d) voltage of switches Q₁ ~ Q₄, (e) & (f) voltage of switches S_o1~S_o4.

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Experimental prototype.

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The efficiency curve versus PV input voltage.

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The proposed control method.

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Figure 10 illustrates the experimental control scheme for the solid-state transformer. In this scheme, the DC link voltages are regulated even when there are sudden changes in the PV and AC input sources. The corresponding experimental results are shown in Fig. 11, demonstrating the system’s performance under these varying input conditions. The proposed control method demonstrates the ability to effectively regulate the voltage of the DC links, even when there are fluctuations or variations in the input sources. This ensures stable performance and maintains the desired output despite changes in the input conditions, making the system more reliable and adaptable to dynamic operating environments. This capability is especially important for applications where input power may be inconsistent, such as in renewable energy systems, ensuring that the output remains steady and within the desired voltage range.

The experimental scheme for control of the proposed SST.

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The closed-loop experimental waveforms.

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In this article, a novel high-voltage gain topology of an SST is proposed. The converter presented consists of three DC links with different voltages. The first DC link is connected to a high voltage conversion ratio converter, offering advantages such as high voltage gain, low peak voltage of diodes and power switch, and low input current ripple. This allows power to be received from renewable energy sources like PV panels through a high voltage DC link. The second DC link is connected to an AC source via a rectifier, enabling the utilization of both DC and AC sources. Galvanic isolation between the sources and the third DC link is ensured through the use of an HFT. It should be noticed that, the third DC link is located in the output side of the converter. As a result, using HFT, the output port is isolated from input sources. The proposed topology is thoroughly surveyed by analysis of operational modes, steady state behavior, and efficiency Subsequently, an experimental prototype is built, capable of delivering 620 W of power to the output load at a switching frequency of 50 kHz, and the findings obtained from the experiments are showcased. The efficiency at rated power (P_o=620 W) is 93.81%. Also, the maximum efficiency is obtained at P_o= 500 W which is equal 94.10%.