Journal of Engineering Science and Technology
Special Issue on Applied Engineering and Sciences, October (2014) 30 - 38
© School of Engineering, Taylor’s University

STUDY OF MATRIX CONVERTER BASED UNIFIEDPOWER FLOW CONTROLLER APPLIED PI-D CONTROLLER
K. MOTOYAMA1,*, T. HANAMOTO1, H. YAMADA1,N. F. MAILAH2, M. NORHISAM2
1

Department of Biological Functions and Engineering, Graduate School of Life Scienceand Systems, Engineering, Kyushu Institute of Technology, Kyushu 804-8550, Japan2
Department of Electrical & Electronic, Faculty of Engineering, University Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia*Corresponding Author: motoyama-kaichi@edu.life.kyutech.ac.jp

Abstract
In this paper, the Unified Power Flow Controller (UPFC) using a matrix converter
is studied. It is an adaptation of an approximate differentiation type PI-Dcontroller. By setting appropriately the values of the gain controller, it is possible
to stabilise the power of the transmission line by controlling the UPFC by a matrix
converter. The matrix converter is a power conversion circuit that can convert anarbitrary phase and amplitude of the AC power directly to AC power. The
principle of creating a switching pattern that adopts a Direct Duty ratio Pulse
Width Modulation (DDPWM) scheme. The UPFC is a stationary device to adjust
the grid voltage for controlling the power flow is inserted into the power system,
and controls the transmission power according to the load variations. This isintended to stabilise the power system. Verification is done by simulation using
MATLAB/Simulink for the validity of this proposed method.
Keywords: Matrix converter, Unified power flow controller, Direct duty ratio PWM,
Approximate differentiation PI-D controller.

1. Introduction
In recent years, highly reliable and stable power supply system is achieved
international, especially in Japan. With the entry of Independent Power Producer(IPP), the introduction of small-scale distributed power using natural energy IPP
and deregulation of power, there is a possibility that the power flow iscomplicated and the power transmission system is overloaded locally.

30

Study on Matrix Converter based Unified Power Flow Controller Applied . . . . 31

Nomenclatures,lMD
MN,MXn,,, ∗,,

Duty ratio value in each switching pattern
Differential gain value
Integral gain value
Proportional gain value
Time constantMedium Input voltage, V
Minimum Input voltage, VModulation rate in each of the axis
Maximum Input voltage, VPercentage of  for Time period, sTime period, sA-phase output terminal
Switching period, sIntegration of the output voltage
A-phase output voltage command
Averaged value of Input voltage in each phase

As transmission control system uses power electronics technology to avoid theseproblems. Therefore, to achieve effective use of the existing power transmission
system, the Flexible AC Transmission System (FACTS) concept has been proposed[1, 2]. The UPFC acts as one of FACTS devices, thereby improving stability andstrain transmission power control by adjusting the phase and amplitude of theelectric lines [3].
However, problems such as the loss of conversion and small capacity of thepower converter that compensates for the power stage must be resolved. So, thematrix converter is adapted as a power converter [4]. Matrix converter is able toconvert the AC power to AC power directly. Comparing with the back to backconverter, which connected converter and inverter with a electrolytic capacitor,
there is a merit of improving conversion efficiency and miniaturisation is possible
because electrolytic capacitors are not required [5-8].
We use the direct duty ratio pulse width modulation (DDPWM) [9]. DDPWM
synthesize the duty ratio value directly from the desired output voltage and havesome advantages that relatively easy implementation and decrease the switchingloss compared some other switching methods. To accommodate fast changes in
the load as the controller and performs stabilisation, the approximate
differentiation type PI-D controller with a low pass filter is designed. The
simulation results using MATLAB/Simulink have shown the validity of theproposed methods.

2. Proposed Method
The stabilisation of the power system by UPFC when the load current is varied is
as shown in Fig. 1.

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Fig. 1. Diagram of a Power System Inserted the UPFC.
The load is to simulate a location that requires power plants, homes andbuildings. The variety of the current supplied to the load must be always stable,
but demands for power with time. A method of keeping a stable power of Bus 3 isproposed where even the value of the load is changing rapidly, the UPFC can giveout a fast response, by adjusting the power of Bus 4.
The need of security of the power of the UPFC is because there is a need toconvert alternating current to direct power to security department. So, the matrix
converter had been adapted. Its advantage is that it can be miniaturised andconversion efficiency is improved when using the matrix converter.
A block diagram of an electric power system is inserted the UPFC is shown inFig. 2. Switching pattern is created by using DDPWM scheme.
Transmission line
current (Bus3)
iu
iv
iw

uvw

ip

Mp×

PIDpq

＊LPF =

Active power reference

Vp

D

LPF

Mu

pq
uvw

LPF

Mv
Mw

PI×iq
Mq
Reactive power reference

Fig. 2. Diagram of Controller Block.
In order to obtain the robustness of the UPFC system and high-speed
response, its control is performed by using the model of instantaneous power pq.
First, the pq converts the three-phase alternating current, which is the output of
the matrix converter and is considered as an instantaneous reactive current andinstantaneous active current. Then, by adding the line voltage, it is considered as
instantaneous reactive power and instantaneous active power.
To give a command value for the power to perform the PI-D control, controlof the current is done by making an inverse transformation pq. Finally, it isconverted into three-phase alternating current again, to determine the duty ratioby using this value.

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Study on Matrix Converter based Unified Power Flow Controller Applied . . . . 33

PID controller is employed to the proposed system because it is widely used inmany industrial applications to obtain the desired response. Simple PI typecontroller and its controller gains design method was proposed by authors [7], but
in some cases more robust against the load change is demanded so PID typecontroller was also considered [8]. In this paper, an approximate differentiation
type PI-D controller is composed of the PI controller and this controller and low
pass filter is applied to the differential. By setting the appropriate gain value forthe control unit to control the UPFC, it is possible to stabilise the grid.

3. Direct Duty Ratio PWM (DDPWM)
The method of DDPWM is shown below. For this paper, only one out of the threephases is shown here. Two other phases are also determined in a similar manner.
First, as shown in Fig. 3, the phases have been divided into intermediate phase,the minimum phase voltage of the power supply. The intermediate phase is theswitching pattern II whereas the value of the switching pattern I is positive if thevalue is negative. Using these phases to create a switching pattern, whenswitching is done, the result is as shown in Fig. 4, when the switching pattern is atI. The switching period TS is divided into T1 and T2. T1 is defined as n = T1/TS
here. Divided into TA1, TA2, TA3, TA4 in switching cycle further, switching of theinput voltage MN, MX, MX, MD is performed to output in each section. Figure 5
shows the output voltage at this time.
Input voltage

Ⅱ ⅡⅠ Ⅰ ⅡⅡⅠ ⅠⅡ ⅡⅠ ⅠMXMDMNFig. 3. MX, MD, MN and Switching Pattern I, II.
10MXMNMXMD

Fig. 4. Output A-Phase Switching
State in Switching Pattern-I.

Fig. 5. Output A-Phase Voltage
Synthesis in Switching Pattern-I.

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where  is the average voltage. Section TA1 to TA4 can be obtained in thenext section as in Eqs. (1).
        !  "      !  "   ! "   ########################################################################################

    ! "   #################################################################################################### "Here, the section of each of the TA1 ~ TA4 is in a very small range, the voltage
may be a constant in the interval. Therefore, the integral value of the output
voltage of the switching period  between TS is given by Eq. (2).
%&$  ( )' * +   +  " , +  -###########################################."Equations (1) and (2) wherein the average value of the voltage  is asshown in Eq. (3).
 %&$  ( # )     '*!-+-!

," +,##################/"Therefore, by using the voltage command value  0 and n the maximum
phase of the input voltage, intermediate phase and the minimum phase, the dutyratio of 1 for A-phase is determined by the following equation. Therefore, byusing the voltage command value  0 and n the maximum phase of the input
voltage, intermediate phase and the minimum phase, the duty ratio of 1 for Aphase is determined by Eq. (4).
 



*!

-+-!

,

 ∗ !

,"#################################################2"

It is possible in the same manner, to determine the duty ratio even in switchingpattern II. Equation (5) shows the switching pattern corresponding to Figs. 6 and 7.

Fig. 6. Output A-phase Switching Statein Switching Pattern-II.

Fig. 7. Output A-Phase Voltage
Synthesis in Switching Pattern-II.

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Study on Matrix Converter based Unified Power Flow Controller Applied . . . . 35

  453#############################################################################################(5)∗ 6789678:8"

8;678968:78

Accordingly, the switching pattern for each duty ratio 1 of the A-phase isdetermined by Eq. (6).
 ∗ ! ,##########=>??@AⅠ########################################6"  <  ∗ * !   - + - ! , !   , !   - + #######=>??@AⅡ*! ,! -+ -4. Approximate Differentiation Type PI-D Controller

2000

1540

1500

1520
power[VA]

power[VA]

It is designed to approximate differentiation type PI-D controller in this study, it
has been used a simple PI controller first. The gain values have been determinedby trial and error, and these were KP = 10, KI = 100. Instantaneous reactive andactive power are as shown in Fig. 8. The enlarged view is also shown in Fig. 9.
The command value of the instantaneous active power is 1500 [VA] and of theinstantaneous reactive power is 0 [VA].

1000
5000-500
01500
1480
1460

0.01

0.02
0.03
Time[sec]

0.04

Fig. 8. Instantaneous Power(KP=10, KI=100).

0.05

1440
00.01

0.02
0.03
Time[sec]

0.04

0.05

Fig. 9. Enlarged View
(KP=10, KI=100).

It has not been possible from Fig. 8, the instantaneous reactive power tofollow the command value. The instantaneous power takes long time to settle
the steady state when the load change occurs in 0.02 s from enlarged view.
Therefore, it is necessary to modify the controller and gain values to enhancestability; an approximate differentiation type PI-D controller is designed. By
using this controller, without differentiation settings directly, derivative action
is to function only on the control variables, and a low pass filter is applied tothe differential, thus rapid changes is seen stepwise and less sensitive to thenoise component it is strongly against. These gain values are determined by trial
and error again, and these were set to KP = 40, KI = 400, KD = 0.3, and time
constant is 0.12. Instantaneous active and reactive power is as shown in Fig. 10.
The enlarged view is also shown in Fig. 11. From Fig. 10, it is able to follow
the command value both instantaneous active and reactive power by using theapproximate differentiation type PI-D controller. It can be seen from theenlarged view; it is able to stably keep the active power even when the loadchange occurs. So this controller is adapted in this study.

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Fig. 10. Instantaneous Power(KP=40, KI=400, KD=0.3).

Fig. 11. Enlarged View
(KP=40, KI=400, KD=0.3).

5. Results and Discussions
These simulations according to the proposed method, is carried out by
MATLAB/Simulink, the simulation was performed by varying load conditions asshown in Table 1. The result is shown in the Figs. 12-17. The parameter of thecontrol block is shown in Table 2.
Table. 1. Value of RLC Load.
RLCloadvalue

Time [s]R[W]L[var]
C[var]

0~0.0220000.02~0.04
400200300

0.04~0.05
2000Table. 2. Parameter of Control Block.
Reference (active)
Value
Reference (reactive)
Value
KP
PI-D ControllerKI(active and reactive)KDl0.5[p.u.]
040
400
0.3
0.12

Figures 12 and 13 respectively indicates a modulation rate of the reactive
component and active component.

Fig. 12. Instantaneous Power(KP=10, KI=100).

Fig. 13. Enlarged View
(KP=10, KI=100).

Figures 14 and 15 show the voltage and current of Bus 4 which is the outputof the matrix converter. The voltage and current of Bus 3 is a system that is toundergo stabilisation is shown in Figs. 16 and 17.

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Study on Matrix Converter based Unified Power Flow Controller Applied . . . . 37

400

Voltage[V]Current[A]1000-200

-10
0200

0.01

0.02
0.03
Time[sec]

0.04

0.05

-400
0

0.04

0.05

1000-1000Fig. 16. Bus 3 Current.

0.02
0.03
Time[sec]

Fig. 15. Bus 4 Voltage.
Voltage[V]Fig. 14. Bus 4 Current.

0.01

0.01

0.02
0.03
Time[sec]

0.04

0.05

Fig. 17. Bus 3 Voltage.

It is found that the output of the matrix converter is changed from Fig. 14,
with varying value of the load. From Fig. 16, the power of the system that isintended to be stabilised when changing the value of the load is changed
momentarily. It can be seen that both the phase and amplitude is back to its
regulated value instantly. Having said that, it can be seen that in Figs. 14 and 16,changing the value of the load are controlled by the UPFC power of the system so
as to maintain a stable value. The instantaneous power of Bus3 is shown inFig. 18. It is found that the power of the system is stabilised by UPFC from thewaveform. Therefore, the gain value set from these results is appropriate and it
was possible to control the power of the system.

6. Conclusions
In this paper, it has been described that the UPFC can be used onto the PV
derivative type PI-D control using a matrix converter. The controller is designed
successfully from the simulation results that are built as a simulation model. Thesystem also revealed the effectiveness and feasibility of the PV derivative type PI-D
control of the UPFC matrix converter based as had been proposed. The simulation
results show the validity of the proposed controller. Furthermore, it can be studied
using the actual simulation for further understanding in the future.

power[VA]

1500
1000
500
000.010.02
0.03
Time[sec]

0.04

0.05

Fig. 18. Instantaneous Powers of Bus 3.

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Acknowledgement
This work was supported by JSPS KAKENHI Grant Number 24560336.

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