Bidirectional Single-phase Solid-State Transformer
using Multi Cell for Volume Reduction of High
Voltage Capacitor
Jun-ichi Itoh, Kazuki Aoyagi and Toshiki Nakanishi
Department of Electrical Engineering
Nagaoka University of Technology
Niigata, Japan
itoh@vos.nagaokaut.ac.jp
Abstract— This paper proposes a simple circuit configuration
and a control strategy of Solid-State Transformer (SST). In the
proposed circuit, it is possible to reduce the volume of heat sinks
and passive components by using low voltage switching device
with low loss characteristic and high frequency operation.
Moreover, the circuit employed with the proposed control
strategy operates stably even when the ripple voltage is large.
Besides, the bidirectional operation of the proposed circuit is also
confirmed by simulation. From the simulation result, thecapacitance in each cell of the primary side (high voltage side)
can be minimized to only 3 μF for 10-kVA system. Moreover, aminiature model with three cells is tested to confirm thefundamental operation of the proposed circuit. As a results, thesinusoidal waveform of the input current is obtained without thelarge distortion. the total harmonic distortion (THD) of the input
current is 2.55%. In addition, it is confirmed that the primaryside capacitor voltage of each cell is kept constant without thebalance control.
Keywords—Solid-State Transformer; Power factor correction
converter; LLC resonant converter; High-frequency transformerI.

INTRODUCTION

Recently, a smart-grid has attracted attention due to anincrease of renewable energy [1]. In particular, a DC
distribution system in the smart-grid has been actively
researched in order to achieve the energy-saving of the datacenter and the large building [2-3]. In the conventional
distribution system, the AC-DC converter is required to eachsystem, whereas in the DC distribution system, the AC-DC
converter is not required. Thus, the volume of the DC
distribution system is reduced [4].
Moreover, in the conventional distribution system,transformers are utilized to achieve the step-down from the gridvoltage of several kilovolts to the distribution voltage ofseveral hundred volts [5]. However, the conventionaltransformers are bulky and heavy because the transformers
operate at the low grid frequency (50 Hz or 60 Hz).
As one of the solutions to reduce the volume and the weightof the transformer, Solid-State Transformer (SST) has been
researched actively [6-8]. SST simultaneously achieves theinsolation and the step-down function by using high frequency
transformer. Most of all, by applying SST, it is possible tosignificantly reduce the system volume compared to theconventional transformer because the transformer in SST
operates at the frequency of several ten-kHz. To sum up, SST
has following advantages [9]:Reduced size and weight of systemPower factor correction

Harmonic suppression

Active/ Reactive power control

In the medium voltage SST, it is possible to construct thecell converters with the multilevel topology, which contributes
to the reduction of the rating voltage of the switching device.
Thus, the switching devices with the low ON-state resistanceand the high speed switching are applied. Moreover, theinductor volume can also be reduced [10].
However, the number of switching device is greatly
increased in the multilevel topology. In particular, the control
becomes complicate because the gate signal is increased with
the increase of switching device [11]. Furthermore, in theconventional SST, a bulky capacitor at the DC link with a large
capacitance is required in order to maintain the constantcapacitor voltage in each cell [12-13]. This capacitor restricts
the volume reduction.
In this paper, first of all, a simple circuit configuration of
the single-phase SST is proposed. The proposed circuit can
reduce the number of the switching devices compared to theconventional circuit. It contributes to the simplification of thesystem. Moreover, the converter volume can be reduced byapplying the multi-cell topology with the small capacitors.
Second, the control strategy is proposed under the condition of
the large ripple voltage in each primary-side capacitor. Third,
the bidirectional operations of SST under the condition of thestable state and the circuit behavior at the sudden change of theload are confirmed by simulation. Finally, the proposed SST istested by using a miniature model with three cells and thevoltage of 200 V as the input voltage.

Cell No.1
Sing. PWM Rec.

Dual Active Bridge (DAB) Converter

Vout
vin
a

b
Cell No. 2

Cell No. m

Fig. 1. Circuit configuration of conventional single-phase SST.

Fig.2 Circuit configuration of proposed single-phase SST.
II.

CIRCUIT CONFIGURATION OF CONVENTIONAL SST AND
PROPOSED SST

Figure 1 shows the circuit configuration of the conventional
single-phase SST [14-15]. The conventional SST includes the
PWM rectifier and the isolated DC-DC converter with the highfrequency transformer. In the conventional SST, the input sideand the output side are isolated by the high frequency
transformer of the dual active bridge (DAB) converter. Thus,
the volume of the system is reduced because the low frequency
transformer is not required. However, the number of switch
increases greatly with the number of cell.
Figure 2 shows the circuit configuration of the proposed
single-phase SST. In the proposed SST, the rectifier isconnected to the all cell converter. Moreover, the rectifier
obtains DC voltage by only switching polarity. In the rectifier,the switching device with high rating voltage are required.
However, it is possible to use the switch with the slower
switching speed because these switches are operated at only the
low frequency (50 Hz or 60 Hz). The cell converter includes aboost converter and a half bridge LLC resonant converter as
one cell. The boost converter control the input current tosinusoidal waveform with the unity power factor. In addition,

Table I. Comparison of switching device between
conventional SST and proposed SST.

the input voltage is shared equally because the grid side of thecell converter is connected in series. Thus, the voltage per cellis reduced. As a result, it is possible to use the switching of low
voltage rating. In the LLC resonant converter, the volume oftransformer is reduced because the transformer operates at highfrequency.
Table I shows the comparison of the switch number
between the conventional SST and the proposed SST. Note thatthe number of cell is calculated by the rated voltage of theswitch. As shown in table I, the proposed SST can reduce thenumber of switch about 2/3 compared to that in theconventional SST. The reason is because the proposed SST
uses only one rectifier for each cell.
A. PFC circuit (Boost converter)
The boost converter corrects the power factor of the gridside because the boost inductor current is controlled into fullwave rectified waveform same as general PFC circuit. The
boost inductor Lb in the PFC circuit is given by (1).

Lb =2Vin …………………………………………(1)4 f eq ΔI Lb

where, ΔILb is the ripple current of the inductor current, feq isthe equivalent switching frequency of the output voltage Veq.
Then, the equivalent switching frequency feq is given by (2).

f eq = m × f sw …………………………………………(2)where m is the number of cell, fsw is the switchingfrequency of the PFC.
As observed in (2), the equivalent switching frequency feq
is proportional to the number of cell. On the other words, theequivalent frequency becomes higher by increasing thenumber of cells. As a result, it is possible to reduce the volumeof the boost inductor Lb because the ripple current decreases.
In the proposed SST, the turn ratio of transformer isdesigned by (3) because the operation mode always becomes
the boost operation with respect of the primary side voltage.
N=

N1
2Vin
……………………………………(3)≥N 2 2mλVout

where λ is the modulation index of the boost converter.
B. LLC resonant converter
In the half-bridge LLC resonant converter, the zero current
switching (ZCS) is achieved by using the series resonancebetween the leakage inductance Ls of the high frequency
transformer and the capacitor Cs at the turn-on switching andthe turn-off switching. Thus, the switching loss is greatly
reduced.
Furthermore, the leakage inductance is designed to be

N2
N1

1
Vin

negligibly smaller than the excitation inductance. Then, theswitching frequency fo of LLC is given by (4), i.e. theresonance frequency, and the duty ratio of the switch is set to50%.
1…………………………………………(4)fo =2π Ls Cs
III.

CONTROL BLOCK FOR PROPOSED SST

Figure 3 shows the control block diagram of the proposed
circuit. The proposed control includes a voltage control (AVR)
for the output voltage Vout and a current control (ACR) for theboost inductor current. The balance control of the primary side
capacitor voltage Vdc1 is not required, and this becomes one of
the advantages of this control. In particular, when the capacitor
voltage in the cell of the primary side is imbalance due to theuneven of the capacitances or the transient phenomenon of theload, the output voltage of each cell is increased or decreased
according to the capacitor voltage of the primary side.
Consequently, the capacitor voltage in the primary side isnaturally corrected. As a result, the balance control for the highvoltage capacitor is not required. Thus, the voltage
management in the high-voltage side is not required. In
addition, the proposed control system is simple because the
AVR and the ACR are achieved by only the switches of PFC(Spfc).
A. Input current control and Output DC voltage control
In the input current control, the boost inductor current is
controlled into full wave rectified waveform in order to correct
the power factor of the grid side. Hence, the inductor current
command value IL* is given by (5).

I L* = I amp sin(ωt ) ……………………………………(5)where Iamp is the output of the AVR. IL* is generated by themultiplication of Iamp and the full wave rectified waveform withsame phase as the input voltage.
On the other hand, in the output voltage control, the output
voltage is always regulated to the voltage command by using
PI controller. Note that the response of the AVR is sufficiently
lower than the ACR in order to avoid the interference between
the AVR and the ACR. In the proposed SST, the single-phase

1
m

1
Vc1

1
Vcm

Fig. 3. Control block diagrams of proposed circuit.

Table II. Switching mode of LLC resonant converter and rectifier at power running and regeneration.

power fluctuation occurs as a disturbance due to the use of thesmall-value capacitor at the primary side. As a resolution, theband elimination filter (BEF), which eliminates the voltage
harmonics at 100 Hz, is applied to the voltage detection.
Consequently, the AVR can control the average value of theoutput voltage despite the high fluctuation of the capacitor
voltage at the primary side. Therefore, the design of the
proposed control system becomes simple.

Table III. Simulation conditions.

In the triangular wave comparator, the gate signal for PFC
is generated by phase shifted carrier. Thus, the input voltage isequally divided because the switching timing is different. In
addition, it is possible to use the switching device with low
voltage rating. Note that the ripple current is reduced because
the inductor voltage is reduced by the series connection in the
PFC converter. Then, the phase shift angle θ is given by (6).

θ=2k
π ( k = 0, 1, , m − 1 )…………………………(6)m

B. Switching of power runnnig mode and regeneration mode
Table II shows the switching mode at the power runningand the regeneration. In the power running, the switch ofrectifier (Sa ~ Sd) is always OFF, whereas the switch of LLC
resonant converter (Sllc11, Sllc12) is operated. In constrast, in theregeneration, the LLC resonant converter side is always OFF,whereas rectifier side is operated.
IV.

SIMULATION RESULT

A. Bidirectional operation of SST
Table III shows simulation conditions. The 6.6-kV grid isadopted as the input power source and the power rating of thesystem is 10-kVA. Then, it is assumed that the switching
device with 3.3 kV voltage rating is applied to the proposed
circuit.
Figure 4 shows the bidirectional operation waveforms of
the proposed SST in the simulation when the primary side
capacitor is 3 µF and the number of cells is six. The
bidirectional operation is confirmed to in the proposed circuit.
Moreover, the sinusoidal waveform of the input current isobtained without any large distortion in both operations.
In the input side, it is also confirmed that the unity power
factor between the input voltage and the input current isobtained. The low input current THD of 1.71% is obtained. In
the output sum voltage of each cell, it is confirmed that the
waveform is seven-level staircase voltage. Furthermore, theequivalent switching frequency feq is 60 kHz.

It is observed from the waveform of the capacitor voltage inthe primary-side cell that, the average voltage is shared equally
among all cells without the balance control and stays stably
even when the ripple voltage is large. In addition, the primaryside capacitor voltage includes the 10 kHz component of theswitching frequency of the PFC circuit and the 50 kHz
component of resonant frequency. However, it is not affect theoperation because these frequency components are less than
1% against the DC component. Moreover, the capacitor voltage
in the secondary side is regulated to the voltage command of
320 V. As a result, it is confirmed that the stable operation isachieved even when the primary side capacitor is small. On theother hand, the output voltage include the distortion by thesingle-phase power fluctuation. As a solution to reduce thedistortion, the large capacitance is applied at output side.
Finally, it is observed from the waveform of theregeneration operation that the input current is reversed against
the input voltage, i.e. the confirmation of the regeneration
operation. The low input current THD of 1.84% is alsoachieved. The other waveforms are same as the waveforms of
the power-running operation.
B. Transient operation
Figure 5 shows the transient operation when the stepchange of the load ratio occurs in 100% to 50%, and theswitching from power running to regeneration. Note that thecurrent source is connected to the output side in order toproduce the step change of the load power. The input current isdecreased by 48.3% at half the load power. In addition, theinput current is increased rapidly when the power running
operation is switched to the regeneration operation. The reason

(a) Power running(b) Regeneration
Fig. 4 Operation waveform of single-phase SST.
is that the command of the power flow changes in the step
response. In addition, the average voltage control of the
primary side capacitor is confirmed in each cell. Moreover, theoutput voltage is still regulated to the voltage command of 320
V. Consequently, the stability operation of the control system isconfirmed even when the load power changes suddenly.
V.

EXPRIMANTAL RESULTS

Table IV shows experimental conditions. In this experiment,
the fundamental operation is verified by using a miniaturemodel with the input voltage of 200 V when the number ofcells is three. In addition, the primary side capacitor is applied
the large capacitance.
Figure 6 shows the waveforms of the input voltage, theinput current, the output sum voltage of each cell and theoutput voltage. As shown in Figure 6, the operation of theminiature model without the large distortion is confirmed.
In the input side, it is confirmed that the unity power factor
between the input voltage and the input current is obtained assame as the simulation result. In particular, the input current
THD of 2.55% is obtained at the rated load.
The input voltage is equally divided to each cell because
the output sum voltage of each cell clearly becomes balanced
multilevel waveform. Furthermore, it is also confirmed that theequivalent switching frequency feq is 30 kHz. In the output
side, the step-down operation is achieved because the output
voltage is regulated stably to 50 V.
Figure 7 shows the primary side capacitor voltage of eachcell. It is observed that the average voltage of capacitor voltage
is kept constant. Moreover, the maximum value of the primaryside capacitor voltage also shows same value in each cell.
Thus, it is confirmed that, the primary side capacitor voltage isshared equally among all cells without the balance control.
Figure 8 shows the relationship of input current THD and
output power of the SST. It is confirmed that the input current

Fig. 5 Operation waveform at sudden change of load.
Table IV. Experimental conditions.

THD becomes larger when the output power of the SST is low.
The reason is that the low order harmonics component appears
remarkably with respect with the fundamental component
because the low input current occurs when the output power of
SST is low.
VI.

Input voltage vin [300 V/div]

Input Current iin [5 A/div]

10 ms

CONCLUSION

This paper proposed the simple circuit configuration andthe control strategy of the SST in order to reduce the system
volume. The bidirectional operation of the proposed circuit was
confirmed with six cells. In the capacitor voltage in the cell of
the primary side, the average voltage was shared equally andstably among all cells without the voltage balance control.
Moreover, the stability operation of the control system wasconfirmed even when the load power was suddenly changed. In
the experimental result, the fundamental operation was
confirmed as same as the simulation. The sinusoidal waveformof the input current was obtained without the large distortion.
Moreover, it was also confirmed that the unity power factor
between the input voltage and the input current was obtained.
Furthermore, the average voltage of primary side capacitor was
shared equally among all cells

Output sum voltage of each cell Veq [300 V/div]
Output voltage Vout [50 V/div]

Fig. 6. Operation waveform of miniature model SST.
Primary side capacitor voltage Vdc1 at Cell No. 1

Primary side capacitor voltage Vdc2 at Cell No. 2

In future, the operation with the small-value capacitor at the
primary side will be confirmed by experiment.

Primary side capacitor voltage Vdc3 at Cell No. 3

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