Combination of Input/Output Control using Matrix
Converter for Islanded Operation for AC generator
Jun-ichi Itoh

Takuya Kataoka, Hiroki Takahashi

Dept. of Electrical Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
itoh@vos.nagaokaut.ac.jp

Dept. of Electrical Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
takuya_kataoka@stn.nagaokaut.ac.jp

Abstract—This paper proposes a control method of a matrix
converter in a micro grid system to obtain stable islanded
operation. The islanded operation using a matrix converter needs
a voltage feedback control to assume the matrix converter as aconstant voltage power supply for the load. On the other hand,
the islanded operation also requires a generator current control
with a feedback to determine provided power. However, whenthe matrix converter is applied two feedback controls on thegenerator side and the load side, the interference between bothcontrols occurs and the matrix converter becomes unstable. Thisinstability occurs due to difference of instantaneous active powers
between the generator side and the load side; therefore, the active
power is determined by the voltage source converter only. The
active current which is needed to control the filter capacitor
voltage should be converted to the generator current commandas an active power command. Thereby, the proposed control
method avoids the interference, and achieves a stable islanded
operation. In addition, the proposed control also offers a constant
three-phase voltage to the load even if the load power is lightbecause of a compensation of a reactive current into the filter
capacitor. As a result, the proposed control method achieves
stable islanded operation and unity displacement power factor of
the load side. The load current THD (Total harmonic distortion)is 1.4%, and the filter capacitor voltage THD is 1.5%. In theexperiment, the load voltage is a sinusoidal waveform of 200 V.
In addition, the load voltage THD is 4.56%. Therefore, it isconfirmed that the proposed control method achieves stable
operation without the interference. This paper confirms validityof the proposed control in the islanded operation by simulationand fundamental experiment.

bio-diesel engine generator, and so on [4]. Lately, it also has
been considered to apply a matrix converter to a micro grid
system and distributed generation system. In these applications,the generator is commonly connected as an input voltage
source of matrix converters [5-6]. In addition, micro gird
systems consist of distributed generators and loads in small
area such as a remote island which cannot interconnect
commercial grid. Thereby, matrix converters in the micro gridneed a capability of an islanded operation to continue
delivering power from the generator to the load [7].
However, a matrix converter in an islanded operation has aproblem. In this application, matrix converters need a voltage
feedback control to guarantee reliability as a constant voltage
power supply for the load. On the other hand, the matrix
converter also requires a generator current control with afeedback to determine provided power. Due to these two
feedback controls, the interference between both controls
occurs and leads to instability of the matrix converter [8]. The
instability is triggered because instantaneous active powers of
the input and output sides are determined by both controls
independently. However, a matrix converter does not haveenergy storages; therefore, a matrix converter becomes
unstable because of the difference between both instantaneous
active powers. However, solutions for this issue have beenreported rarely.

Recently, a matrix converter, which directly converts AC
power supply voltage into AC voltage of variable amplitudeand frequency without large energy storage such as electrolytic
capacitor, has been actively studied [1-3]. A matrix converter
has advantages over a conventional BTB (back to back) system
which is composed of a PWM rectifier and a PWM inverter on
the following aspects; size reduction, light-weight, long-lifeand high efficiency power supplies. These indexes are very
important for renewable energy systems

Previous studies regarding the island operation using amatrix converter have been discussed in [6] and [8]. In pastwork, a matrix converter is connected to a generator and a
motor [8]. This work achieves controls of a generator current
and an output voltage in the islanded operation. However, thegenerator should be used in high speed region only because thehigh voltage side of a matrix converter is connected to thegenerator. In addition, the terminal voltage of the generator andthe input current are unstable due to a filter resonance between
the synchronous reactance of the generator and the input
capacitor. Thereby, the control is more complex due tosuppressing control for the filter resonance. On the other hand,a matrix converter for a distributed generation achieves
islanded operation [6]. This work achieves the islanded
operation at rated power. However, this work does not confirm
the operation in area of light load.

Matrix converters can be applied in generation systems,
such as a wind turbine generators, micro-hydro power plant,

In this paper, in order to solve problem about the instability,
a control method for the islanded operation in a matrix

Keywords—islanded operation; matrix converter; micro grid

I. INTRODUCTION

converter is proposed. The proposed method has two feedback
controls for the filter capacitor voltage and the generator
current. However, the instability is avoided because theproposed method combines these feedback controls and only
the generator current control determines the active power of theconverter. As a result, the interference is not triggered and astable islanded operation obtained. In addition, the proposed
control compensates an effect of a reactive current into thefilter capacitor and offers a constant three-phase voltage to theload even when the load power is light. In this paper, thestability of islanded operation is evaluated in simulation andfundamental experiment.

vgen
Sru
Srv

ilaod

Srw

igen

U
V
W

Ssu

R
G S
Generator T

Ssv
Ssw
Stu

vc

Stv
Stw

Matrix converter

II. CIRCUIT CONFIGURATION AND CONTROL STRATEGY
A. Circuit configuration
Fig.1 shows a circuit diagram of an interface converter
between a generator and a load using a matrix converter. In thissystem, a low voltage side of the matrix converter is connectedto the generator, and high voltage side is connected to the load.
By this connection, the generator is utilized in wide speed
region though the opposite connection restricts the generator
operation in high speed region only. A matrix converter
requires LC filter in the load side to eliminate harmonic current
due to switching operation.
B. Virtual AC-DC-AC conveter control method
In order to simplify the control techniques, a virtual ACDC-AC conversion technique which has been discussed in [9]is referred.
Fig.2 shows an equivalent circuit of the matrix converter in
Fig.1 using an AC-DC-AC converter, which is based on thevirtual AC-DC-AC conversion technique. In Fig.1 and Fig.2,
the input voltage is represented as t[vr,vs,vt] and the output
voltage is represented as t[vu,vv,vw]. Sxy represents the switching
function of the switches, when Sxy is turned on, Sxy =1 andwhen Sxy is turned off, Sxy =0. According to the virtual AC-DCAC conversion theory, the PWM pattern for the matrix
converter can be converted by the following equation.

 S ruS
 rv
 S rw

S su
S sv
S sw

S tu   S up

S tv    S vp
S tw   S wp

S un  S
S vn   rp
S
S wn   rn

S sp
S sn

S tp 
(1)
S tn 

As a result, control performance of the matrix converter isexactly same as the AC-DC-AC converter because therelationship between input voltage and the output voltage is thesame. It should be noted that the relationship between input
current and output current is also the same. Thus, the switchingpulses of the matrix converter are generated easily because theproposed control method can considered with a voltage source
converter and a current source inverter.
C. Control strategy of islanded operaiton
Fig.3 shows a PWM pulse generator based on the virtual
AC-DC-AC conversion technique. This diagram combines
switching pulses generated by a virtual converter and a virtual
inverter controls and synthesizes switching pulses of the matrix

Load

LC filter

Fig. 1. Interface converter between a generator and a load using matrix
convertervgen
Srp SspStp

Swp Svp Sup

ilaod

igen

U
V
W

R
S
Generator T

G

Srn

Ssn

Stn

Load

vc
Swn Svn Sun

LC filter
Voltage Sorce Converter Current Sorce Inverter
Fig. 2. Equivalent circuit using AC-DC-AC converter. This circuit isused based on the virtual AC-DC-AC conversion technique in order
to simplify the control techniques.

converter according to (1). The voltage source converter
control is fed input voltage command vr*, vs*, vt* from thegenerator current control. Similarly, the current source inverter
control is fed output current command iu*, iv*, iw* from thefilter capacitor voltage control on the load side. Then, thevirtual converter is applied discontinuous PWM method for
improvement of a voltage transfer ratio. In contrast, the virtual
inverter uses single leg modulation [9].
Fig.4 shows the proposed control block diagram for theislanded operation. The proposed control method is based on dq frame because the d-q frame defines the d-axis as a reactive
component and the q-axis as an active component although thegenerator frequency is different from the grid frequency.
Thereby, the active power is simply controlled on the d-q
frame.
Fig.4(a) shows a control block diagram of the generator
current control. This control is for determining the
instantaneous active power from the generator and this control
uses a feedback controller as well as a voltage source converter
due to applying the virtual AC-DC-AC conversion technique.
Then, gen is a rotor angle of the generator, ir, is, it are detectedvalue of three phase generator current, vr*, vs*, vt* are input
voltage command for the voltage source converter, and Pload* isactive power command from the filter capacitor voltage control
on the load side. fe is back-emf constant of generator. gen isdetermined by integrating the generator rotation speed gen. An
ACR (Auto current regulator) block has a PI regulator in order
to control the generator current idgen, iqgen. In the case, the d-axis
generator current command idgen* is always fixed to 0 p.u. forachieving unity input displacement power factor. Furthermore,
the q-axis current iqgen* is calculated by the active power anddetected q-axis induced voltage of the generator.
Fig.4(b) shows control block diagram of the filter capacitor
voltage control on the load side. This control is for the islanded
operation which assumes the matrix converter as a constantvoltage power supply to the load. This control employs a
feedback controller as well as a current source inverter due toapplying the virtual AC-DC-AC conversion technique. Then,vu, vv, vw are detected filter capacitor voltage, iu*, iv*, iw* are
output current command for the current source inverter, andload* is phase angle of the load current. In order to supply thegenerator power to the load as well as a grid, load* isdetermined by integrating the grid frequency. An AVR (Autovoltage regulator) block has a PI regulator in order to control
the load voltage. In the case, the d-axis load voltage command
vdload* is always fixed to 0 p.u. for achieving unity output
displacement power factor. On the other hand, output of the qaxis AVR is not used in the current source inverter and the qaxis current command iqload* is set to 1. This is to avoid theinterference of the active power between the generator current
control and the filter capacitor control and the principle is asfollowing.
The active current command iqload* is needed to control the
q-axis voltage of the filter capacitor vqload. However, if thecurrent source inverter is fed the active current command iqload*from the feedback controller, the feedback controls of thegenerator side and the load side determine each required active
power independently. This is because the generator current
control decides the input voltage command with referring thegenerator current and the filter capacitor voltage control
decides the output current command with referring the filter
capacitor voltage, which is equivalent to determine theinstantaneous power. Thus, because of the difference between
both required instantaneous active powers, the matrix converter
becomes unstable. In order to avoid the interference, the active
current command of the current source inverter should be fed
with an open loop as shown in Fig.4(b), which does notcontribute to the active power. As a result, the active power isdetermined by the voltage source converter only and a stableislanded operation is achieved.
In contrast, a reactive power does not exist in DC link.
Thereby, the power transmitted between the generator and theload through the matrix converter is only active component, asshown in Fig.2. Hence, the active current which is needed tocontrol the filter capacitor voltage should be converted to thegenerator current command as an active power command.
Therefore, Fig. 4 uses the active power command Pload*.
Moreover, the output of the d-axis AVR adjusts the output
power factor of the matrix converter because the d-axis current
command of the current source inverter affects the reactive
current. Thus using the output of the d-axis AVR is equivalent
to compensation of the reactive current caused by the filter
capacitor and this compensation contributes to supplying a
constant voltage to the connected load at the light load area in
the islanded operation.

vr*,vs*,vt*

Voltage source
converter control

iu*,iv*,iw*

Current source
inverter control

6PWM
9Composition
6
SwitchingEq.(1)
pulse

Fig. 3. Switching pulse generator

idgen*=0
Pload* iqgen*



 ACR

ACR

idgen 3dq
iqgen

Kg=1/vgen_rated
vdgen*Kg

Kg

vqgen*

vr*,vs*,vt*dq
3

ir,is,it

gen
vqgen

1
s

gen

fe

(a) Generator current control

KL=1/(-iload_rated)idload* dq iu*,iv*,iw*KLiqload*=1 3
AVR
Pload*
×






AVR

vqload*vdload 3

vu,vv,vwdq

load*

vqload(b) Filter capacitor voltage control on the load side

Fig. 4. Control block diagram for islanded operation. This diagram isseparated into the generator current control and the filter capacitor
voltage control on the load side. This control obtains stability forislanded operation without interference between the feedback
controls on the generator and the load sides.

III. SIMULATION RESULTThe simulation parameters are as follows, the generator
induced voltage is 100V (line to line), the frequency of agenerator is 50Hz, the switching frequency is 10 kHz, and thecut-off frequency of LC filter is 1 kHz. Note that the simulation
is running in a RL load condition.
Fig.5 shows the generator side and the load side waveformin steady state with the interference between the generator
current and the filter capacitor voltage controls. In thissimulation, the generator current control and the filter capacitor
voltage control work independently. The load resister is 26.6 
and the load inductor is 2.55 mH (3%). This simulation
confirms unstable islanded operation without the proposed
control method. In this simulation, the active powers of thegenerator side and load side are independently determined byboth controls As a result, the load current and the filter
capacitor voltage is not sinusoidal waveform and thesewaveforms have distortion. Thereby, the operation of thematrix converter is instability.

Generator terminal voltage (phase) [V]

100

100

0

Generator terminal voltage (phase) [V]

0

-100
30

-100
20

Generator current [A]0Generator current [A]0-30

Load side filter capacitor voltage (phase) [V]

300

-20
200

0

Load side filter capacitor voltage (phase) [V]

0

-300
10

-200
10

Load current [A]0Load current [A]0-10

10 [ms/div]

Fig.5. Simulation results of the islanded operation without proposed
control. This waveform is unstable due to the interference.

100

Generator terminal voltage (phase) [V]-10

Fig.6. Simulation results of the islanded operation with proposed control
in steady state at rated power.

100

0

0

-100

-100

25
20

250
200

20

Generator current [A]0Load side filter capacitor voltage (phase) [V]

-20
250
200

0

0

-200
-250

-200
-250

10

Generator terminal voltage (phase) [V]Generator current [A]

0
-20
-25

10 [ms/div]

10

Load current [A]

0

0

-10

-10

Load power fluctuation(0.1 p.u. to 1p.u.)

Load side filter capacitor voltage (phase) [V]

20 [ms/div]

Load current [A]Load power fluctuation(1 p.u. to 0.1 p.u.)

20 [ms/div]

Fig.7. Simulation results of a load fluctuation under the islanded
operation. The load power is changed from 0.1 p.u. to 1 p.u.

Fig.8. Simulation results of a load fluctuation under the islanded
operation. The load power is changed from 1 p.u. to 0.1 p.u.

Fig.6 shows the generator side and the load side waveform
in a steady state with the proposed control method. The load
resister is 26.6  and the load inductor is 2.55 mH (3%). In
addition the matrix converter outputs 1.5kW (1p.u.). As a result,the film capacitor phase voltage is sinusoidal wave and thisRMS voltage value is 115 V (line to line voltage is 200 V.).
The generator current THD (Total Harmonics Distortion) is
0.8%, the load current THD is 1.4%, and the film capacitor
voltage THD is 1.5%. The proposed control method achieves
unity displacement power factor of the generator side and theload side. These results lead to a conclusion that the proposed
control obtains the stable islanded operation.

varied, the output voltage is maintained to a constant voltage of
115 V except a transient state regardless the load power. This isbecause of the compensation of the reactive current caused by
the filter capacitor. Thereby, the validity of the proposed
control method is confirmed.

Fig.7 and Fig.8 show the generator side and the load side
waveform in a load fluctuation by changing a load resister.
In Fig.7, the load resister value is changed to 266  from
26.6. The output power of the matrix converter changes to
0.15 kW (0.1p.u.) from 1.5kW (1p.u.). In Fig.8, the load
resister value is changed to 26.6  from 266. The output
power of the matrix converter changes to 1.5 kW (1p.u.) from
0.15kW (0.1p.u.). As results, although the output power is

IV. EXPERIMENTAL RESULTS
Table 1 shows experimental parameters. The proposed
method is based on a virtual AC-DC-AC conversion technique.
Therefore, the parameters of ACR and AVR are designed aswell as conventional design methods in a voltage source
inverter and a current source converter. Fig.9 shows a circuit
diagram of the matrix converter in an experiment. In Fig.9, amagnetic contactor is added to separate the grid connected
operation and the islanded operation. The generator is replacedwith a three-phase voltage source of 100 V and input inductors
in order to simplify the experiment.

A. Grid connected operation
In the grid connection operation, an open loop control isapplied to the grid side of the matrix converter. The q-axis
input current command iqgen* is fed by an open-loop control
instead of Pload* and the d-axis output current command idload*
is set to zero. Additionally, in order to connect the grid, themagnetic contactor is closed.

TABLE I.
Gnerator voltage

100 Vrms

Grid voltage

Generator frequency

50 Hz

Grid frequency

50 Hz

Input L

3.0 mH(3.5%)

Kp(ACR)

1.38 p.u.

Ti(ACR)

21.1 ms

Filter L(%Z)
Filter C(%Y)
Dampng resister(Damping Factor)

2.2 mH(2.6%)
4.5mF(3.8%)
47 (0.24)

Kp(AVR)

0.05 p.u.

Output power

1.5 kW

Ti(AVR)

4.67msCarrier frequency

10 kW

Fig.10. shows the input and the output waveform in thegrid connected test. The generator current and the grid current
are sinusoidal waveform with the THD of 4.88% and 8.65%,
respectively. In addition, the matrix converter operates in theunity displacement power factor on the generator and the gridsides because idgen* and idload* are zero. As a result, it isconfirmed that the matrix converter achieved stable operationin grid connected operation.
B. Islanded operation
In the islanded operation, the proposed control method isapplied to the matrix converter in order to obtain a stable
operation without the interference. By opening the magnetic
contactor, the matrix converter is separated from the grid.
Fig.11 shows the input and the output waveform in theislanded operation when a load resister Rload is 32.5  (1.22
p.u.). In this case, the matrix converter outputs approximately
1-kW power (0.66p.u.). The load voltage is sinusoidal
waveform of 200 V owing to the filter capacitor voltage
control. In Fig. 11, the generator current THD is 4.94%, theload voltage THD is 4.56%. In addition, the displacement
power factors on the generator side and the grid side are unity.
As a result, it is confirmed that the proposed control method
achieves a stable operation and a load voltage control without
the interference.
Fig.12 shows the input and output waveform in theislanded operation when a load resister Rload is 75  (2.81
p.u.), which is lower power than Fig. 11. The matrix converter
outputs approximately 0.5-kW power (0.33p.u.). By the
proposed method, the load voltage becomes a sinusoidal
waveform of 200 V in the same manner as Fig. 12. However,
the generator current and the load voltage distortion containmore because the filter capacitor is small and the bandwidth of
the filter capacitor voltage control is limited. This will be
improved in the future by establishing a design method of the
PI controller and the LC filter. Therefore, the proposed
method achieves a stable operation without depending on aload power.
V. CONCLUSION
This paper discusses a control method for the islanded
operation using a matrix converter. In order to guarantee
reliability as a constant voltage power supply for the load, theload voltage control is applied. In addition, the generator
current to determining control to determine provided power isalso introduced. However, these two feedback controls may
cause unstable operation because of the interference between
both controls in terms of the active power. In order to solve thisproblem, this paper proposes a control which combines thegenerator current control and the load voltage control, and thegenerator current only decides the active power due to avoid

EXPERIMENTAL PARAMETER
200 Vrms

grid
vgen

Magnetic
Contactor

Sru
Srv

igen
R
S
Generator T

G

Srw
Ssu

U

Ssv

V

Ssw

W

Stu

iload

vc

Stv
Stw

Load
ResisterFig. 9. Experimental circuit diagram. The operation mode is switched by
the magnetic contactor.
Grid voltage(line to line) 250V/div

Grid current 5A/div

000
10ms/div
0
Generator voltage(line to line) 250V/div

Generator current 10A/div

Fig. 10. Experimental results of the grid connected test in steady state.
The generator supplies power to the grid through the matrix
converter.

interference of difference of instantaneous active powers
between the generator side and the load side. As a result, theproposed control method avoids the interference, and achieves
the stable operation of the islanded operation. In simulation
result, proposed control method achieves stable islanded
operation. The load current THD is 1.4%, and the film
capacitor voltage THD is 1.5% at rated load. In addition, inorder to compensate a reactive current into the filter capacitor,
the proposed method offers a constant three-phase voltage tothe load even when the load power is light. In the experiment,
it is confirmed that the proposed control method achieves thestable operation and the load voltage control without theinterference. Then, the generator current THD is 4.94%, theload voltage THD is 4.56%, and the load current THD is 4.94%.
From these results, the validity of the proposed control method
for the islanded operation is demonstrated.
In the future, usefulness of the proposed method will be
confirmed in the islanded operation when a nonlinear load suchas a diode rectifier is connected.
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Load voltage(line to line) 250V/div

Load current 5A/div

000
10ms/div
0
Generator voltage(line to line) 250V/div

Generator current 10A/div

Fig. 11. Experimental results of the islanded operation in steady statewith RLoad=37.5. The load voltage is sinusoidal waveform of 200
V.
Load voltage(line to line) 250V/div

Load current 2A/div

000
10ms/div
0
Generator voltage(line to line) 250V/div

Generator current 5A/div

Fig. 12. Experimental results of the islanded operation in steady statewith RLoad=75. The proposed method achieves stable operation
without depending on the load power