Improving the Electricity Quality by Means of a Single-Phase Solid-State Transformer

: The paper describes the use of a single-phase three-stage solid-state transformer in networks with non-sinusoidal voltages in order to improve the quality of electricity. An active-inductive load was chosen as the load. The solid-state transformer was simulated by the Matlab / Simulink software. Its performance was analyzed and the parameters for optimal performance were speciﬁed. The voltage and current graphs on the load and their spectral analysis are given. Total harmonic distortion was evaluated for current and voltage. As a comparison, the operation of a classic transformer was simulated. Modeling shows that solid-state transformer copes with improving the quality of electricity better than a classical transformer. In addition to improving the quality of the load current, the solid-state transformer protects the consumer from overvoltage, voltage dips, and other transient phenomena, due to the accumulated supply of electricity in the capacitors of the DC-Bus.


Introduction
Transformers are widely used in power supply systems, carrying out AC voltage conversion and galvanic isolation. Recently, the use of smart grids has become more frequent. They differ from classical electric grids in that they include their own sources of energy generation and in critical situations are able to provide power to particularly responsible consumers. Large power plants and autonomous diesel-electric units, as well as high-capacity batteries, wind power stations, solar panels, hydrogen fuel cells, etc., can act as sources of electricity. The difficulty in using various sources in smart grids is the coordination of different voltage levels, which is exacerbated by the fact that the portion of the electricity is produced or stored in DC networks, and the other portion-in AC networks. A classic transformer provides direct conversion with very limited changes or improvements, so if there is any voltage asymmetry, voltage dips or frequency changes at the transformer input, the output voltage will have the same drawbacks. In addition, in order to work with direct current or alternating current networks of a different frequency, classical transformers require the use of additional equipment (inverters, rectifiers, frequency converters) [1,2].
These shortcomings can be eliminated by using solid-state transformers (SSTs) in smart power supply grids, which allow one to control the flow of electricity and improve its quality (reduce voltage dips and power surges, compensate reactive power without using any additional compensator). In addition, SSTs are smaller and make it easy to match direct and alternating currents of different voltage levels.
The single-stage SST topology uses an AC-AC full bridge converter which converts the low frequency AC input to a high-frequency one which is then stepped down using a high frequency (HF) transformer. The output of HF transformer is further converted to power frequency using another converter. The major disadvantage of the topology is the absence of a DC link which limits the functionality of the SST. The two-stage topology uses an AC-DC dual active bridge with a pulse-width modulation (PWM) inverter. The SST with two-stage topology avails a DC low-voltage link which can be used for the integration of distributed energy resources. This topology results in higher efficiency with a zero-voltage switching strategy. However, this type of converter suffers from the problem of high ripple current and the high sensitivity of active power flow on leakage inductance.
The three-stage SST topology comprises of a PWM rectifier, a DC-DC dual active bridge and a PWM inverter. This topology requires switching between two alternative control schemes for power flow in either direction. A more detailed comparison of various SST topologies is presented in [6,21,27,28]. It was the three-stage SST that became the most popular [28].

Results
Let us now evaluate how the three-stage SST will increase the quality of electricity with a high non-sinusoidality of the input voltage. The load is active-inductive in nature: R = 100 Ω, L = 1 mH.
Let us set the input voltage as Internal impedance is assumed to be 0.1 Ω and 20 µH. In the case of direct power supply from this voltage source, the current will repeat the form of voltage. The input non-sinusoidal voltage will create a non-sinusoidal load current, which will create additional losses resulting in economic damage. Usually, for the sake of safety, the source of electricity and the load are separated by galvanic isolation. This case will be considered further.

Modeling a Circuit on a Classic Transformer
The model of a single-phase classical transformer implemented in Simulink is shown in Figure 1. Parameters of the classical transformer are as follows: • The total harmonic distortion (THD) of voltage U1(t) is 18.04%. The total harmonic distortion of input current THDI1 = 8.25%. The difference in values is that the primary winding of the transformer has a reactance and smoothens the high-frequency voltage ripples. In the secondary winding, THDU2 = 11.37%, THDI2 = 8.25%. Graphs of the input voltage and currents are presented in Figure 2a, where as the output voltage and current-in Figure 2b.  Let us evaluate the operation of the system during short-term power failure. The time of absence of voltage is three periods. The input current and voltage are shown in Figure 3a, the output current and voltage from a classic transformer are shown in Figure 3b. As can be seen from the The total harmonic distortion (THD) of voltage U 1 (t) is 18.04%. The total harmonic distortion of input current THD I1 = 8.25%. The difference in values is that the primary winding of the transformer has a reactance and smoothens the high-frequency voltage ripples. In the secondary winding, THD U2 = 11.37%, THD I2 = 8.25%. Graphs of the input voltage and currents are presented in Figure 2a, where as the output voltage and current-in Figure 2b. Parameters of the classical transformer are as follows: • The total harmonic distortion (THD) of voltage U1(t) is 18.04%. The total harmonic distortion of input current THDI1 = 8.25%. The difference in values is that the primary winding of the transformer has a reactance and smoothens the high-frequency voltage ripples. In the secondary winding, THDU2 = 11.37%, THDI2 = 8.25%. Graphs of the input voltage and currents are presented in Figure 2a, where as the output voltage and current-in Figure 2b.  Let us evaluate the operation of the system during short-term power failure. The time of absence of voltage is three periods. The input current and voltage are shown in Figure 3a, the output current and voltage from a classic transformer are shown in Figure 3b. As can be seen from the Let us evaluate the operation of the system during short-term power failure. The time of absence of voltage is three periods. The input current and voltage are shown in Figure 3a, the output current and voltage from a classic transformer are shown in Figure 3b. As can be seen from the graphs, with the disappearance of the voltage on the primary winding, the voltage on the secondary winding will also disappear. graphs, with the disappearance of the voltage on the primary winding, the voltage on the secondary winding will also disappear.

Modeling of the Circuit with a Single-Phase SST
The single-phase SST model implemented in Simulink is shown in Figure 4. The voltage source U1 has an active-inductive nature of the internal resistance R1. Voltage is supplied to a controllable bridge rectifier assembled with V1-V4 thyristors. In order to prevent the distortion of the input voltage due to strong distortions of the consumed current in the thyristor rectifier, it is possible to put a filter-compensating device at the SST input. The rectified voltage is smoothed by the capacitor C and then goes to the dual active bridge, consisting of an inverter based on insulated-gate bipolar transistor (IGBT) T1-T4, a high-frequency linear transformer and a rectifier based on diodes D1-D4. The resulting voltage is smoothed by the capacitor C2 and fed to the full-bridge converter, which converts to alternating voltage from direct voltage using PWM modulation. The main disadvantage of a single-phase SST as compared to a three-phase SST is that the rectified voltage after the first rectifier has a high ripple rate, i.e., the bulk capacitor must have a higher capacity in order for the SST to perform properly. Given the high voltage and large capacitance, bulk capacitors are large and expensive, which adversely affect the economic prospects of single-phase SSTs. In addition, the main load of any transformer is active-inductive; therefore, the inductance of the high frequency transformer in combination with the load inductance can create an oscillating circuit with capacitors, thereby creating unnecessary losses for heating and possible overcurrent and overvoltage.
SST was used with a small power (500 W) for the clarity of its work. In the case of a low-impedance load, the load inductance is usually large, which stretches the transients in time.

Modeling of the Circuit with a Single-Phase SST
The single-phase SST model implemented in Simulink is shown in Figure 4.
Designs 2020, 4, x FOR PEER REVIEW 5 of 10 graphs, with the disappearance of the voltage on the primary winding, the voltage on the secondary winding will also disappear.

Modeling of the Circuit with a Single-Phase SST
The single-phase SST model implemented in Simulink is shown in Figure 4. The voltage source U1 has an active-inductive nature of the internal resistance R1. Voltage is supplied to a controllable bridge rectifier assembled with V1-V4 thyristors. In order to prevent the distortion of the input voltage due to strong distortions of the consumed current in the thyristor rectifier, it is possible to put a filter-compensating device at the SST input. The rectified voltage is smoothed by the capacitor C and then goes to the dual active bridge, consisting of an inverter based on insulated-gate bipolar transistor (IGBT) T1-T4, a high-frequency linear transformer and a rectifier based on diodes D1-D4. The resulting voltage is smoothed by the capacitor C2 and fed to the full-bridge converter, which converts to alternating voltage from direct voltage using PWM modulation. The main disadvantage of a single-phase SST as compared to a three-phase SST is that the rectified voltage after the first rectifier has a high ripple rate, i.e., the bulk capacitor must have a higher capacity in order for the SST to perform properly. Given the high voltage and large capacitance, bulk capacitors are large and expensive, which adversely affect the economic prospects of single-phase SSTs. In addition, the main load of any transformer is active-inductive; therefore, the inductance of the high frequency transformer in combination with the load inductance can create an oscillating circuit with capacitors, thereby creating unnecessary losses for heating and possible overcurrent and overvoltage.
SST was used with a small power (500 W) for the clarity of its work. In the case of a low-impedance load, the load inductance is usually large, which stretches the transients in time. The voltage source U1 has an active-inductive nature of the internal resistance R1. Voltage is supplied to a controllable bridge rectifier assembled with V1-V4 thyristors. In order to prevent the distortion of the input voltage due to strong distortions of the consumed current in the thyristor rectifier, it is possible to put a filter-compensating device at the SST input. The rectified voltage is smoothed by the capacitor C and then goes to the dual active bridge, consisting of an inverter based on insulated-gate bipolar transistor (IGBT) T1-T4, a high-frequency linear transformer and a rectifier based on diodes D1-D4. The resulting voltage is smoothed by the capacitor C2 and fed to the full-bridge converter, which converts to alternating voltage from direct voltage using PWM modulation. The main disadvantage of a single-phase SST as compared to a three-phase SST is that the rectified voltage after the first rectifier has a high ripple rate, i.e., the bulk capacitor must have a higher capacity in order for the SST to perform properly. Given the high voltage and large capacitance, bulk capacitors are large and expensive, which adversely affect the economic prospects of single-phase SSTs. In addition, the main load of any transformer is active-inductive; therefore, the inductance of the high frequency transformer in combination with the load inductance can create an oscillating circuit with capacitors, thereby creating unnecessary losses for heating and possible overcurrent and overvoltage.
SST was used with a small power (500 W) for the clarity of its work. In the case of a low-impedance load, the load inductance is usually large, which stretches the transients in time. Despite the fact that the SST can be divided into relatively simple blocks, which are studied quite well, the design of the SST is complicated by the fact that the SST does not work regardless of the load. Therefore, ensuring the coordinated operation of the entire complex is the main obstacle to the widespread use of SSTs, and it Designs 2020, 4, 35 6 of 10 is necessary to design a device for the given parameters. To assess the quality of electricity, we can do this with an easily scalable model.
Consider the operation of a single-phase SST. The SST parameters are as follows: • Let us analyze the values of the output current and voltage with SST: THD U2 = 77.03%, THD I2 = 2.48%. As one can see, the THD current is much better than when using a classic transformer. We can further improve the quality of the voltage by using harmonic filters, including passive ones. This issue will not be considered, and in the future, only the SST will be considered in the article without the use of input and output filters so that the comparison of SST and a classical transformer is fair and does not depend on the type and parameters of low-pass filters. The cost of passive filters is not high, so installing a filter will not greatly affect the total cost of work.
Waveform of the voltage and currents on the load are presented in Figure 5a. A comparison of the average output voltage with the SST and the non-sinusoidal input is shown in Figure 5b. The THD of the average voltage value is 1.7% and is associated with the fact that due to small ripples during voltage rectification, distortion occurs during the formation of PWM modulation owing to the fact that the amplitude of the modulated signal varies within insignificant limits.
Designs 2020, 4, x FOR PEER REVIEW 6 of 10 Despite the fact that the SST can be divided into relatively simple blocks, which are studied quite well, the design of the SST is complicated by the fact that the SST does not work regardless of the load. Therefore, ensuring the coordinated operation of the entire complex is the main obstacle to the widespread use of SSTs, and it is necessary to design a device for the given parameters. To assess the quality of electricity, we can do this with an easily scalable model. Consider the operation of a single-phase SST. The SST parameters are as follows: • Let us analyze the values of the output current and voltage with SST: THDU2 = 77.03%, THDI2 = 2.48%. As one can see, the THD current is much better than when using a classic transformer. We can further improve the quality of the voltage by using harmonic filters, including passive ones. This issue will not be considered, and in the future, only the SST will be considered in the article without the use of input and output filters so that the comparison of SST and a classical transformer is fair and does not depend on the type and parameters of low-pass filters. The cost of passive filters is not high, so installing a filter will not greatly affect the total cost of work.
Waveform of the voltage and currents on the load are presented in Figure 5a. A comparison of the average output voltage with the SST and the non-sinusoidal input is shown in Figure 5b. The THD of the average voltage value is 1.7% and is associated with the fact that due to small ripples during voltage rectification, distortion occurs during the formation of PWM modulation owing to the fact that the amplitude of the modulated signal varies within insignificant limits.  Figure 5b shows that the first wave of the output voltage has a smaller value than the subsequent ones, which is due to the accumulation of energy in the SST reactive elements. The same elements make SST less sensitive to sharp and high-speed surges both in the direction of increase and decrease. The harmonic composition of the load voltage is shown in Figure 6a, and the harmonic composition of the load current is shown in Figure 6b.  Figure 5b shows that the first wave of the output voltage has a smaller value than the subsequent ones, which is due to the accumulation of energy in the SST reactive elements. The same elements make SST less sensitive to sharp and high-speed surges both in the direction of increase and decrease. The harmonic composition of the load voltage is shown in Figure 6a, and the harmonic composition of the load current is shown in Figure 6b. The output voltage is modulated by means of a PWM Generator (2-Level), which generated pulses for a PWM-controlled 2-Level converter, using a carrier-based two-level PWM method. A sine wave with a frequency of 1000 Hz is supplied to the HF transformer. The carrier frequency of wiring the inverter of the second stage is 20 kHz. The PWM on the primary winding of the HF transformer and voltage on the secondary winding are shown in Figure 7. As can be seen, the voltage on the secondary winding is close to a sinusoid. In addition to improving the quality of the current at the load, SST protects the consumer from overvoltage, voltage dips, and other transient phenomena due to the accumulated supply of electricity in reactive elements. Moreover, SST makes possible to connect DC sources with varying voltage (solar panels, wind power plants and other types of non-traditional power supply) to the network. It enables to achieve the flexibility and reliability of power supply, especially in local or independent smart grids or in systems with low power availability.
In the case of using other modeling parameters (load power, voltage levels, load power factor, etc.) SST will work similarly. When using other parameters of the load and the transformer, conclusions about improving the quality of electricity are reached. For example, for a load of 5 kW, the THD of a classic transformer will be 7.42% versus 2.39% for an SST.
Let us see how the SST behaves in the event that the voltage disappears for a short time. We take into account that there are no sources of electricity on the DC side, i.e., transient processes at the time of voltage shutdown will occur solely due to the accumulated energy in the reactive elements of the SST. Graphs of voltage and currents on the load are presented in Figure 8a. A comparison of the average output voltage with the SST and the non-sinusoidal input is shown in Figure 8b. Figure 8b shows that for three periods there was no voltage at the input of the SST, and the output voltage did not equal zero. The minimum value of the voltage at the SST output corresponds to the period following the moment the power was restored, which corresponds to the fourth period. The output voltage is modulated by means of a PWM Generator (2-Level), which generated pulses for a PWM-controlled 2-Level converter, using a carrier-based two-level PWM method. A sine wave with a frequency of 1000 Hz is supplied to the HF transformer. The carrier frequency of wiring the inverter of the second stage is 20 kHz. The PWM on the primary winding of the HF transformer and voltage on the secondary winding are shown in Figure 7. As can be seen, the voltage on the secondary winding is close to a sinusoid. The output voltage is modulated by means of a PWM Generator (2-Level), which generated pulses for a PWM-controlled 2-Level converter, using a carrier-based two-level PWM method. A sine wave with a frequency of 1000 Hz is supplied to the HF transformer. The carrier frequency of wiring the inverter of the second stage is 20 kHz. The PWM on the primary winding of the HF transformer and voltage on the secondary winding are shown in Figure 7. As can be seen, the voltage on the secondary winding is close to a sinusoid. In addition to improving the quality of the current at the load, SST protects the consumer from overvoltage, voltage dips, and other transient phenomena due to the accumulated supply of electricity in reactive elements. Moreover, SST makes possible to connect DC sources with varying voltage (solar panels, wind power plants and other types of non-traditional power supply) to the network. It enables to achieve the flexibility and reliability of power supply, especially in local or independent smart grids or in systems with low power availability.
In the case of using other modeling parameters (load power, voltage levels, load power factor, etc.) SST will work similarly. When using other parameters of the load and the transformer, conclusions about improving the quality of electricity are reached. For example, for a load of 5 kW, the THD of a classic transformer will be 7.42% versus 2.39% for an SST.
Let us see how the SST behaves in the event that the voltage disappears for a short time. We take into account that there are no sources of electricity on the DC side, i.e., transient processes at the time of voltage shutdown will occur solely due to the accumulated energy in the reactive elements of the SST. Graphs of voltage and currents on the load are presented in Figure 8a. A comparison of the average output voltage with the SST and the non-sinusoidal input is shown in Figure 8b. Figure 8b shows that for three periods there was no voltage at the input of the SST, and the output voltage did not equal zero. The minimum value of the voltage at the SST output corresponds to the period following the moment the power was restored, which corresponds to the fourth period. In addition to improving the quality of the current at the load, SST protects the consumer from overvoltage, voltage dips, and other transient phenomena due to the accumulated supply of electricity in reactive elements. Moreover, SST makes possible to connect DC sources with varying voltage (solar panels, wind power plants and other types of non-traditional power supply) to the network. It enables to achieve the flexibility and reliability of power supply, especially in local or independent smart grids or in systems with low power availability.
In the case of using other modeling parameters (load power, voltage levels, load power factor, etc.) SST will work similarly. When using other parameters of the load and the transformer, conclusions about improving the quality of electricity are reached. For example, for a load of 5 kW, the THD of a classic transformer will be 7.42% versus 2.39% for an SST.
Let us see how the SST behaves in the event that the voltage disappears for a short time. We take into account that there are no sources of electricity on the DC side, i.e., transient processes at the time of voltage shutdown will occur solely due to the accumulated energy in the reactive elements of the SST. Graphs of voltage and currents on the load are presented in Figure 8a. A comparison of the average output voltage with the SST and the non-sinusoidal input is shown in Figure 8b. Figure 8b shows that for three periods there was no voltage at the input of the SST, and the output voltage did not equal zero. The minimum value of the voltage at the SST output corresponds to the period following the moment the power was restored, which corresponds to the fourth period. The maximum subsidence voltage is 17.91%. In the second period, after power was restored, the voltage at the SST output stabilized. Thereby, we can conclude that the use of SST ensured the reliable operation of the load during the introduction/withdrawal of additional capacities with the provision of high power quality. An additional element can be a rechargeable battery (less often a solar panel, a wind generator, a fuel cell), which, together with the SST, will act as an uninterruptible power supply for a predetermined time. However, the battery does not have to be connected to the SST direct current line. If necessary, the battery can be put into operation in the event of a mains failure. Input time can be calculated in a few tenths of a second, which is satisfactory for both electromagnetic switches and solid-state switches.
Designs 2020, 4, x FOR PEER REVIEW 8 of 10 The maximum subsidence voltage is 17.91%. In the second period, after power was restored, the voltage at the SST output stabilized. Thereby, we can conclude that the use of SST ensured the reliable operation of the load during the introduction/withdrawal of additional capacities with the provision of high power quality. An additional element can be a rechargeable battery (less often a solar panel, a wind generator, a fuel cell), which, together with the SST, will act as an uninterruptible power supply for a predetermined time. However, the battery does not have to be connected to the SST direct current line. If necessary, the battery can be put into operation in the event of a mains failure. Input time can be calculated in a few tenths of a second, which is satisfactory for both electromagnetic switches and solid-state switches.

Conclusions
As a result of the simulation performed in Matlab/Simulink, the performance of a single-phase SST at an input non-sinusoidal voltage showed that the SST improves the quality of the load current, which can be controlled using total harmonic distortion. The results of modeling the converter circuit by means of 500W-SST and a classical transformer are compared. The analysis showed a worse performance of a classical transformer (THD is 8.25%) compared to SST (THD is 2.48%). When using other parameters of the load and the transformer, conclusions about improving the quality of electricity are reached. It is shown that with a voltage dip, the SST copes with changes in the input and can maintain the output voltage until the input voltage is stabilized, or wait for the introduction of alternative sources of electricity, for example, a battery.

Conclusions
As a result of the simulation performed in Matlab/Simulink, the performance of a single-phase SST at an input non-sinusoidal voltage showed that the SST improves the quality of the load current, which can be controlled using total harmonic distortion. The results of modeling the converter circuit by means of 500W-SST and a classical transformer are compared. The analysis showed a worse performance of a classical transformer (THD is 8.25%) compared to SST (THD is 2.48%). When using other parameters of the load and the transformer, conclusions about improving the quality of electricity are reached. It is shown that with a voltage dip, the SST copes with changes in the input and can maintain the output voltage until the input voltage is stabilized, or wait for the introduction of alternative sources of electricity, for example, a battery.