Wireless Distributed Control with Open-Phase
Fault-Tolerance for Delta-Connected ThreePhase Three-Wire Solid-State Transformers
Keita Ohata1, Koki Yamanokuchi1 and Jun-ichi Itoh1
1

Nagaoka University of Technology, Japan

Abstract— This paper proposes wireless distributed
control with a fault-tolerant for a solid-state transformer(SST) in single-wire open fault. A voltage imbalance occurs
at the input side of each cell in the SST when an open-phasefault occurs. The voltage imbalance causes overmodulation in
the power factor correction (PFC) converter. The proposed
method employs the current droop control as an autonomous
distributed control to achieve the voltage balance of each celland prevent overmodulation without communication among
each cell. The proposed method reduces the imbalance of the
input voltage among series-connected cells by up to 95%
compared to the control without the current droop control.
Moreover, continuous operation is achieved during singlewire open-phase faults.
Index Terms— Distributed control, Fault-tolerant, Solidstate transformer, Current droop control

I. INTRODUCTION
Power distribution systems in the DC grid have been
attracted to widespread renewable energies, such as
photovoltaic systems. A solid-state transformer (SST) is
the leading candidate for a replacement of a conventional
AC-DC converter, which consists of a line-frequency
transformer (LFT) and an AC-DC converter because the
SST has various functions and advantages such as
harmonic suppression, power flow control, anddownsizing [1]-[7]. Generally, Input-Series-OutputParallel (ISOP) configuration is used owing to a mediumvoltage-AC (MVAC) and increasing the output power [1],[3]-[7]. The large-capacity SST consists of tens tohundreds of cells. Thus, many signal wires are required forcentrally controlled SST. Moreover, if the centralized
controller fails, the SST cannot continue operation [8].
Hence, the redundancy of the control configuration in the
SST must be improved to introduce the SST as a part ofthe infrastructure equipment.
In order to improve the redundancy of the control
configuration, a distributed control is applied. A typical
distributed control scheme is a two-layer controller where
the local controllers have a droop-based distributed
controller, and the host controller has some additional
compensators [9]-[10]. Some key element technologies
have also been proposed to enhance the typical distributed
control, such as the high synchronization accuracy
technique [8], [11]-[13], cooperative control strategy withlow-bandwidth communications [14]-[17]. However,adopting these enhanced controls is insufficient to deal
with grid disturbances such as short circuits between line-

to-line, ground faults, and imbalanced grid conditions.
Some fault detection, localization, and tolerant controls areproposed [18]-[21]. However, these papers are targeted at
the centralized control. The fault-tolerance control for griddisturbances in distributed controllers has not been welldiscussed. This paper focuses on single-wire open-phasefaults in the distributed control.
Some open faults in the grid have been reported owing
to the disconnection of transformer wiring [22]. The
disconnection occurs by a strong wind or salty water. A
continuous operation is possible as a single-phaseconverter using a two-wire connection when the singlewire open-phase fault occurs. Thus, the system should
operate continuously as a single-phase converter in an
emergency. In three-wire delta-connected SST, the part ofthe connection of cells changes to a series connection when
the single-wire fault occurs. When the input current in eachphase is controlled independently, control interference
occurs among distributed controllers.
This paper proposes a distributed control with an openphase fault-tolerant control method for a delta-connected
three-phase three-wire SST with low-bandwidth wirelesscommunication. The current droop control in the proposed
method is adding a virtual admittance at the seriesconnected current source. The current droop control
reduces the input voltage imbalance among seriesconnected cells. The new contribution of this paper isachieving continuous operation without overmodulation
during open-phase faults in distributed controlled SSTs.
Furthermore, the voltage stress on switching devices isequalized. Therefore, it is expected to achieve easy systemmanagement when an open-phase fault occurs. As asecond benefit, the proposed method does not require highspeed wired communication.
This paper is organized as follows; first, the circuit
configuration of the proposed circuit and the proposed
distributed control scheme is described; next, thefundamental characteristics of the current droop control
are shown; moreover, the current droop parameter isdesigned for the single open-phase fault-tolerant
operation; at last, the proposed method is verified by the
7.2-kW six-cell prototype.
II. CIRCUIT CONFIGURATION
Figure 1 shows the proposed three-phase three-wire
SST with low-bandwidth wireless distributed control. The
SST is connected to a three-phase MVAC. A diode bridge

Lb
Cell

PFC converter

icell

L

Cell
Cell
Lline

3f
MV

Lb

vin

Local controller

Resonant DC-DC converter

S1

S3

Cdc

Cs Ls

S4

Cell
Cell
Lb

D5

D7

Cout

+

S2

Cell

Cf
Rf

Hi-Freq.
Trans.

icell

Lm

D6

D8

S1 ~ S4

Vdc

Vout

Vout

Local controller

Local controller

CellFig. 2: Configuration of cell converters.

Cell

Local controller
Fig. 1: Proposed three-phase three-wire solid-state transformers.

III. PROPOSED CONTROL SCHEME
Figure 3 shows the proposed control block diagram.
The controller of this system consists of a two-layer
structure: a host controller and local controllers. The hostcontroller transmits the input current command Iin* to each
local controller. The host controller also receives the statusof the cell converters from each local controller. The local
controller controls the input current iin based on thereceived command from the host controller throughwireless communication. The series-connected cells ineach phase are driven by phase-shifted carriers,
contributing to Lb miniaturization.

Iin-cell*Host controller

is connected to the input of each phase, and small-capacity
converters (cells) are connected in series at the rear of thediode bridge. The outputs of the cell converters areconnected to the DC bus in parallel.
Figure 2 shows the circuit diagram of the cell converter.
The cell converter consists of a PFC converter and aresonant DC-DC converter. The resonant DC-DC
converter utilizes the resonance between Ls and Cs in orderto perform soft switching. In the system, the resonant DCDC converter is driven at a constant switching frequency
without the output voltage control. As a result, the resonant
DC-DC converter performs a DC-DC transformer with aconstant voltage transfer ratio. Thus, the output powerfrom each phase fluctuates at twice the frequency of thegrid frequency. However, the fluctuation of the output
power from each phase has 120 degrees of phasedifferences among other phase cells. Hence the sum of theoutput power of the system is constant without any control
in the DC-DC converter. In other words, the DC-link
capacitors on the primary and secondary sides do not needto compensate for the fluctuation. For this reason, the small
capacitance of the DC link capacitor and the output
capacitor is accepted.

for PFC converters
At open-phase
Input current: ON
Yd LPFdroop control
OP
+
S1
Iin*
PI
+
+
S2
|sinqvin | iin-cell
|vin|
abs
Carrierfsw(PFC)
Phase
S1
detection

for Cell 1

DC busfor Cell 2

Cell

vin

StatusError flags,
Detection
values(Vout , Pout )S2Open-phasedetectionVin(peak)vcell-thPhase shifted
carrier fsw(PFC)

+
-

OP

S1

for Cell N

Host
controller

S2

for DC-DC converters
Phase shifted
carrier fsw(PFC)S3
S4Gate signal
fsw(DC DC ) const.
Duty 50% const.

Local controller U-V
Local controller V-W
Local controller W-U

Fig. 3 Proposed signal wireless distributed controller.

U-V cell

Luv

iuv
U
V
W

Cdc

Lvw
ivw

Cdc

+

U
V
W
Openphase

Lwu

iwu

Luv

+

Cdc

+

iuv
V-W cell
Lvw
ivw

Cdc

Cdc

+

+

W-U cell
Lwu
iwu

Cdc

+

Overlapped inductor
current path(a) Three-phase mode.
(b) W-phase open-phase mode.
Fig. 4. Current path of grid current.

A. Three-phase mode
Figure 4(a) shows the current path in a three-phase
operation. During three-phase, no control interferenceoccurs for current control because the current path of eachinductor is controlled independently.

IV. CHARACTERISTIC OF CURRENT DROOP CONTROLLER
In this section, the characteristics of the current droop
control are mentioned. This paper focuses on the voltage
and the current of each cell.
A. Current deviation
When the current droop control is applied during a Wphase open fault, the grid current igrid is given by (1) fromFig 5 (b), which is applied to the principle of superposition.

ii3
igrid = Yd vg + iuv + vw + wu
2
2
2

(1)

where Yd is virtual admittance, vg is grid voltage， and iuv,
ivw, iwu are the actuating value of the input current
controller in each local controller. When iuv, ivw, and iwu

V-W
cell

ivw

U-V
cell

vgrid
U-V
phase

iuv
U-V
cell

W-U
cell

iwu

igrid Y
d
vgrid
U-V
phase

iduv

Y
U-V d
cell

iuv idvw
Yd

V-W
cell

ivw
W-U
cell

iwu

idwu
(a) without current droop control.
(b) with current droop control.
Fig. 5 Equivalent circuit on the AC grid side at open W phase (in thecase of Fig.4(b)).

Input current deviation Iin [p.u.]

B. Single-wire open-phase mode
Figure 4(b) shows the current path when the W-phase
opens. The V-W and W-U cells are connected in series
between U and V-phases. In other words, inductors Lvw
and Lwu are connected in series. Local controllers control
inductor currents, respectively. Thus, interference among
current controllers occurs, as shown in Fig. 5(a). This
paper proposes open-phase fault-tolerant control by thecurrent droop control in order to prevent control
interference.
Figure 5(b) shows the equivalent circuit when thecurrent droop is implemented. The input current of eachcell is controlled by local controllers. Hence, the cell isequivalent to a current source. Note that the seriesconnected cells in each phase drive the same inductor Lb
using the phase-shifted carrier. Thus the equivalent circuit
is also the same when the number of cells increases. Whenthe current sources output different currents, control
interference occurs because the operation conflicts with
Kirchhoff's current law.
The current droop control is implemented to solve thisproblem. The droop control in this context means the
addition of virtual admittance in parallel with these current
sources. The current droop control is the duality relation
between the well-known droop control for parallel
connected power converters [9]-[10]. The interference
among the current controllers is suppressed by the virtual
current in the virtual admittance.

0.6

Over deviation(Iin > 0.25p.u.)

1 p.u. = 6 mS 0.5p.u.

0.5

0.4
0.3

0.2
0.1
0.0

Kcd

0.05p.u.

iv w = 0.0

Eq. (4)Vuv(peak) = 200 2 V
Ns = 4
Vdc = 100 V

-0.1
-0.2
-0.10

-0.05

0.00

0.05

0.10

Detection error of input current ivw [–]Fig. 6 Current deviation characteristics when the current droop gain
and the detection error of input current are changed.

have the detection errors iuv, ivw, and iwu, respectively,
each cell current ix is controlled to,ix = (1 −  ix )iin*(x=uv, vw or wu)(2),

where iin* is the input current command. Thus, (1) with
detection error of current is rearranged to(1 −  ivw )iin* (1 −  iwu )iin*
3
igrid = Yd vg + (1 −  iuv )iin* +
+
(3).
2
2
2
the input current iin at the series connected cells, VW-celland WU-cell, is given by,(1 +  ivw )iin* (1 +  iwu )iin*1
iin = Yd vg +
+
2
2
2

(4).

Figure 6 shows the input current deviation Iin. The
deviation is calculated from (4). The input current
detection ivw is changed from -10% to +10%, and thecurrent droop gain Kcd is changed from 0.05p.u. to 1.0p.u..
the DC bus voltage is set to 80 V. the current droop gain
Kcd and the input current deviation Iin are defined as:
K cd =Yd
Yload

I −I *
 I in = in * in
I in

(5),

(6),

where Iin* is the current command. Note that the winding
ratio of the transformer in the resonant DC-DC converter
Nsec/Npri is set to 2.0, and the DC-DC converter is driven
with constant frequency. As a result, the DC-link voltage
Vdc and the output voltage Vout always maintain a constantratio of 1:1 in the configuration. The input current
deviation Iin increases with the detection error of the input
current at VW-cell ivw. Moreover, the deviation Iin
increases with increasing the current droop gain Kcd. Thus,
the current droop gain Kcd should be as small as possible
to suppress the current deviation. The maximum gain of
current droop control is determined by the specification of
the allowable current deviation. For example, themaximum current deviation is specified as 25% of the140

B. Input voltage Imbalance120

The sums of input voltages of each phase seriesconnected cell Vvwcells(peak) and Vwucells(peak) are given by (7)and (8) from Fig. 5 (b) when the current droop control isapplied during a W-phase open fault,
Vvwcells ( peak ) =Vwucells ( peak ) =1 *1iin (1 +  ivw ) − (1 +  iwu ) + Vuv
2Yd
2

(7)

1 *
1
iin (1 +  iwu ) − (1 +  ivw ) + Vuv
2Yd
2

(8)

Figure 7 shows the peak value of the input voltage
calculated from (7) and (8). the input current detection ivw
is changed from -10% to +10%, and the current droop gain
Kcd is changed from 0.1p.u. to 0.5p.u.. when the VW- local
controller detects the input current with a negative
detection error, the VW-controller tries to increase theinput current compared to the WU-controller. Hence, theVvwcells(peak) increase and Vwucells(peak) decrease. In addition,
when Kcd is increased, the increasing detection error issmaller. Thus, the current droop gain Kcd should be as large
as possible to suppress the input voltage imbalance
between series-connected cells VW-cells and WU-cells.
The non-overmodulation condition determines theminimum current droop gain. The condition is obtained
from the peak input voltage of each cell Vin(peak) and the DC
link voltage Vdc. The non-overmodulation condition isexpressed by,Vin( peak )  Vdc(9).

Note that the Vin(peak) is given by,
Vin ( peak ) =Peak of input voltage
Vvwc ells(peak), Vwuc ells(peak) [V]command value, and an input current detection error of±10% is tolerated when Kcd is 0.4 p.u. or less.

Overmodulation(Vin_x(peak) > Vdc ) 0.1p.u.
0.1p.u.
Vwuc ells(peak)
Kcd
Kcd
Vvwc ells(peak)

100
80

0.5p.u.

60

0.5p.u.
Eq. (8)Eq. (7)40

ivw = 0.0

Vuv(peak) = 200 2 V
Iin *= 6 A
Ns = 4
Vdc = 100 V

20
0
-0.10

-0.05

0.00

< Spe cification >PphaseVdc
Iin(max)Ns(open)

2Ns

0.10

i_maxImax

Start
Input specification
Calc. of max. load admittance
Yload(max)Increasing Yd(Init. value: Yd= 0.01Yload(max))

Calc. Iin by (4)Calc. Vcells(pe ak) by (7),(8)Vin(peak) < Vdc at i_max?
(Over-modulation ?)YesIin < Iin(max) at i_max?

2Vgrid0.05

Detection error of input current ivw [-]Fig. 7. Input voltage characteristics of each series connected cellwhen the current droop gain and the detection error of input current
are changed.

No
Changing
specification
No(Allowable current deviation?)(10),

where Ns is the number of series-connected cells in eachcell, and Vgrid is the root mean square value of the gridvoltage between line-to-line. For example, Ns and Vout are
specified as 2 and 100 V, respectively. Then the minimum
Kcd must be at 0.14p.u. or more.
V. DESIGN OF CURRENT DROOP GAIN FOR OPEN-PHASE
FAULT-TOLERANT CONTROLThis section shows the design of the current droop gain
Kcd for the open-phase fault-tolerant operation based on
Section III. The design has been enhanced based on [23][24] to apply the open-phase failure. The stability of thecurrent droop control is decreased by the computation
delay and the PWM delay due to the digital control. The
effect has already been discussed in [24]. As a result, thecurrent droop control is stable in the region, which is
sufficiently lower than the current control bandwidth. In
this paper, the stable region is used. Hence, this paper
focuses on the design of the current droop gain for openphase fault-tolerant control.

Yes
Finish

Output: Yd

Fig.8. Design flowchart of current droop admittance Yd.

Figure 8 shows the design flowchart of the current droop
gain Kcd. The design requires the six specifications of the
SST as follows:
1) Rated power of cell Pcell
2) DC-link voltage Vdc
3) Maximum input current Iin(max)4) Number of series-connected cells during singlewire open-phase fault Ns(open)5) Allowable input current deviation Imax
6) Allowable detection error of input current imax
First, the maximum input admittance Yin_phase(max) of the
SST is calculated from the specifications. Second, the gain
Kd is set to 0.01Yin_phase(max) at the first time. Third, (4)calculates to derive the input current deviation Iin. In
addition, (7) and (8) calculate to derive the sums of input
voltages of each phase series-connected cell Vvwcells(peak)
and Vwucells(peak). Fourth, checking that the condition is nonovermodulated. When the condition is satisfied, thecurrent droop gain Kcd should be increased again. The trial

VI. EXPERIMENTAL RESULTS
Fig. 10 shows the experimental environment. A deltaconnected prototype SST consists of two cells in eachphase. Three local controllers independently control eachcell. The SST is connected to the three-phase three-wire
grid. An RC filter is provided at the input of the SST toremove switching frequency components in the input
current. The single-wire open-phase fault is emulated by
opening the magnet contactor. The open-phase fault is
automatically detected from a decrease in the input voltage.
A. Steady response during single-wire open-phase fault
Figure 11(a) shows the input voltage of each cell andinput current when the current droop control is not applied.
The modulation rate of VW-cells mvw is over 1.0. Thus,
The input current cannot be controlled sinusoidally.
Figure 11(b) shows the waveform when the current
droop control is applied with Kcd=0.05p.u. (Ycd=3mS). The
input voltage imbalance is 200 V, and overmodulation
occurs. Thus, the gain is not sufficient.
Figure 11(c) shows the waveform when the current
droop control is applied with Kcd=0.2p.u. (Ycd=12mS). The
input voltage imbalance is 40 V. Thus, the imbalance isreduced by 80% compared to Fig.11(b) condition.
Figure 12 shows the transient response from threephase to single-wire open-phase fault during W-phase
open fault. The input voltage imbalance between seriesconnected cells vin(VW-cell) and vin(WU-cell) is suppressed forabout three cycles. Note that a surge voltage occurs at the
SST input due to the wiring inductance from the open fault
point to the SST input. On the other hand, an absorber isgenerally installed to suppress the lightning surge voltage.
Thus, the surge voltage due to the open-phase fault is notapplied directly to the switching device.
B. Transient response from single-wire open-phasefault to Three-phase mode
Figure 12 shows the transient response from the threephase mode to the open-phase fault-tolerant mode. Each
local controller automatically changes the operation mode

Experimental condition

0.6

Input current deviation Iin [p.u.]

is repeated to obtain the minimum current droop gain Kcd
without over-modulation. Depending on the specificationof Imax and imax, the overmodulation and the current
deviation may not be satisfied at the same time. Then, thechanging specification is required. Note that when avoltage controller is added to the outer current controller,
the voltage controller compensates for the current
deviation. Then, there is no problem with the current
deviation. However, the additional output voltage droop
controller is needed to prevent voltage control interference
among parallel connected cells [15].
Figure 9 shows the operation area. The input current
deviation and the detection error of input current limit thearea. In Section VI, The gain design is verified at two
operation points, A (Overmodulation) and B (Desirable
operation).
Table I lists the design specification and the derived
value of the current droop gain Kcd. Kcd is set to 0.05p.u. or
0.2 p.u. The designed gain is used in Section VI.

0.5p.u.

1 p.u. = 6 mS

Over deviation(Iin > 0.25p.u.)

0.5
0.4

0.3
0.2

Kcd

B
A

0.1
0.0

0.05p.u.
+0.05p.u. step

-0.1

-0.2
-0.10

Range of assum ed error ivw = 0.0
i_max Vu v(p eak ) = 200 2 V

Overmodulation(Vin(peak) > Vdc )-0.05

Ns = 4
Vd c = 100 V

0.00

0.05

0.10

Detection error of input current ivw [–]Fig.9 Allowable operation area. The operation area is limited by
the input current deviation characteristics and the design flowchartof current droop gain.
TABLE IDESIGN SPECIFICATIONS AND EXPERIMENTAL CONDITIONS
Name

SymbolValue

Input voltage
Number of series connected cells
at single-wire open-phase fault

Vin

200 Vrms

Ns

4

7.2 kW
Output powerP(1.2 kW×6 cells)
100 V (Fig. 11)
Output voltage
Vout
150 V (Fig. 12, 13)
1:2
Wiring ratio of transformer
N1/ N2(Vout = Vdc)
3 mH
Boost inductance
Lb(%Z=2.8 %)1080 mF
DC-link capacitance
Cconv(H = 35 ms)
Resonant inductor
Ls
10 m
Resonant capacitor
Cs
0.45 mF
1080 mF
Output capacitanceCout(H = 35 ms)
Resonant frequency
fres
75 kHzSwitching freq. at PFC
fsw(PFC)
45 kHzSwitching freq. at res. DC-DC
fsw(DC-DC)
85 kHzMaximum input admittance
Yload(max)
60 mS
Detection error
ivw+5%of input current
iwu
0%
3 mS (A in Fig. 9)
Current droop admittanceYcd
12 mS (B in Fig. 9)
0.05 p.u. (A in Fig. 9)
Current droop gain
Kcd
0.2 p.u. (B in Fig. 9)
H: Unit capacitance constant of output capacitance based onconverter capacity
3 mH
Cell
Cell

U

Local ctrl.
CellV

4.4 mF
3W

3f 200 V W

MCCB
Open-phasesignalMagnetContactor

CellElectricload
CV 150Vor 100V

Local ctrl.
Cell
Cell

Host
controller

Local ctrl.

Fig. 10 Experimental environment. The SST is connected to a Threephase 3-wire grid. Each local controller outputs PWM signals using
phase-shifted carriers for series-connected cells.

00

Status of current droop control: H: Enable, L: Disable

0

Input voltage 200 V/div
VW cells Vvwcells

Status of current droop control: H: Enable, L: Disable

0

WU cells Vwucells

VW cells
Vvwcells

Input current
ivw, iwu 5 A/div0
1
0

WU cells Vwucells

Modulation index [-](Duty) mvw, mwu
1.0/div
mvw

Overmodulation occurs

mwu

4 ms/div(a) Without current droop control.

010Input current
iin(vw-cell),iin(wu-cell) : 10 A/div
Modulation index [-] mvw, mwu 1.0/div

10 ms/div

Fig. 12 Transient response from three-phase to W-phase open faulttolerant. vw is 0.05 (+5%), wu is 0 (+0%).
Status of current droop control: H: Enable, L: Disable

0

Status of current droop control: H: Enable, L: Disable

200 V
imbalanced

Input voltage 200 V/div000

WU cells Vwucells
VW cells Vvwcells010Overmodulation

VW cells
Vvwcells

0

Input current
iin(vw-cell),iin(wu-cell) : 10 A/div

Modulation index [-]mvw, mwu 1.0/div

WU cells Vwucells

4 ms/div

10

Input current
iin(vw-cell),iin(wu-cell) : 10A/div
Modulation index [-] mvw, mwu 1.0/div

10 ms/div(b) With current droop control Kcd=0.05p.u.(Yd=3 mS) (at A in Fig. 9).

Fig. 13 Transient response from W-phase open fault to three-phase
operation. vw is 0.05 (+5%), wu is 0 (+0%).

0

imbalance among series-connected cells. The proposedcurrent droop method reduced the voltage imbalance by up
to 95% compared to the case without the current droop
control.
In future work, the local controller will be installed ineach cell, not in each phase, in order to improve theredundancy.

Status of current droop control: H: Enable, L: Disable

40 V imbalanced

Input voltage 200 V/div

0

WU cells Vwucells
VW cells Vvwcells010Modulation index [-]mvw, mwu 1.0/div

Input current
iin(vw-cell),iin(wu-cell) : 10 A/div

4 ms/div(c) With current droop control Kcd=0.2p.u.(Yd=12 mS) (at B in Fig.9).
Fig.11 Input voltage and input current at steady state during W-phase
open fault. vw is 0.05 (+5%), wu is 0 (+0%).

to the fault-tolerant operation without communication
among cells.
Figure 13 shows that the single-wire open-phase fault isremoved, and the sum of input voltages of each phaseseries-connected cell is recovered to 200 V. Each slave
controller detects the recovered voltage, and the SST is
restored from the fault mode to the three-phase mode
quickly without the signal communication among local
controllers. After returning to the three-phase operation,
the input voltage and the input current are controlled to thesame phase as the input voltage in 20 ms, and the threephase function is restored.
VII. CONCLUSION
This paper proposed a single-wire open-phase faulttolerant method for a delta-connected three-phase threewire SST. The current droop control was employed toprevent the current control interference. The proposed
method prevented overmodulation due to the input voltage

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