04075867

8/13/2019 04075867

http://slidepdf.com/reader/full/04075867 1/6

Multi-Machine Power System Stabilization Control

by Robust Decentralized Controller Based on

Optimal Sequential Design

Yoshitaka Miyazato1 Student Member, IEEE, Tomonobu Senjyu1, Member, IEEE, Ryo Kuninaka1, Member, IEEE,

Naomitsu Urasaki1, Member, IEEE, Toshihisa Funabashi2, Senior Member, IEEE and Hideomi Sekine1.

Abstract— This paper proposes a robust decentralized con-troller based on optimal sequential design. The proposed con-troller can directly consider the inter-area oscillation mode ondesign phase. Further, the sequential procedure is applied todesign for robust controllers in consideration of other controllers.The best design sequence of the controller is decided by using the

condition number. The effectiveness of the proposed controlleris demonstrated by comparing it with conventional controllers.Damping of many oscillations for a multi-machine power system

is demonstrated through simulations, which considered a threeline-to-ground fault for power system disturbance.

Index Terms— robust decentralized control, multi-machinestabilization, sequential manner, condition number.

I. INTRODUCTION

IN recent years, electric power systems have become huge

and complicated. Many oscillations are inherent in large

interconnected power systems. The present economic and

environmental factors increasingly put stress on the existing

transmission systems. As a result, damping of many modes

(0.2-4.0Hz) tends to degrade with increasing maximum power

transfer across tie-lines, exciting the low frequency oscilla-

tions. To correspond to these oscillations, various electricpower system stability improvements have been researched

[1-3]. For improving the dynamic stability of power systems,

utilization of supplementary excitation control signal, Power

System Stabilizer (PSS), has received much attention. For

PSS controller design, demonstrations of H ∞-based design

techniques to power system models have been reported in

the literature to guarantee stable and robust operation of the

systems [4-6].

On the other hand, from a practical viewpoint, the im-

portance of decentralized controllers has been recognized.

Indeed the decentralized control method has been researched

for multi-machine power systems [7-12]. In the design of

decentralized controllers in multi-machine power systems,it is important to consider the influence of the inter-area

oscillations. The controller designed in consideration of the

influence of the inter-area oscillations can control not only its

region but also the entire electric power system. Therefore, the

controller has good control and can improve the stability; this

(1) Yoshitaka Miyazato, Tomonobu Senjyu, Ryo Kuninaka, NaomitsuUrasaki, and Hideomi Sekine are with the Department of Electrical andElectronics Engineering, Faculty of Engineering, University of the Ryukyus,E-mail:[email protected]. (2) Toshihisa Funabashi is with theMeidensha Corporation, E-mail:[email protected].

is seen in comparing the controller designed using a model

whose multi-machine system is factorized to single-machine

infinite-bus system and out of consideration of the influence

of the inter-area oscillations, with the controller designed in

consideration of the influence of the inter-area oscillations.

Previous studies [13-15] have examined excitation decentral-

ized controller for designed multi-machine power systems. To

stabilize the entire electric power system, the state feedback

controller is designed. However, in the decentralized controller

designed by deleting non-corner element of the centralized

controller [15], stability in the entire electric power system is

not guaranteed for large disturbances, and the analysis is not

done.

In the reported works above, it is shown that when a decen-

tralized controller in consideration of the inter-area oscillation

is designed individually, a nominal plant was always targeted

and each controller designed without regard to each other.

Therefore, when two or more controllers were designed, there

was a possibility of having contradictory control operations

for the newly designed controller without considering existing

controllers. The controller designed in consideration of the

influence of the inter-area oscillations can make the entire

electric power system steady by its small contribution of

control. The controller output can be curbed by designing a

decentralized controller in consideration of the existence of

each controller, and it leads to the improvement in robustness

[16]. Moreover, many decentralized controllers designed have

state feedback controls. The output feedback control system

based on the observation output is necessary to implement in

the practical electric power system.

This paper proposes a robust decentralized controller based

on optimal sequential design. The proposed controller can

directly consider the inter-area oscillation on the design phase.

The method of sequential procedure is applied to design in

consideration of other controllers. The best design sequenceof the controller is decided by using the condition number

evaluation for the method of sequential design. Therefore, the

damping performance and the robustness performance in the

entire electric power system can be improved. In the study

of the effectiveness of the sequential design we undertook

eigen value analysis. Simulations in time-domain for the

electric power system of a multi-machine model was done by

comparing a conventional controller and an optional sequential

procedure designed controller, with the proposed controller.

8651-4244-0178-X/06/$20.00 ©2006 IEEE PSCE 2006

8/13/2019 04075867


Table 1. System constants (base of machine unit).Generator1

M = 8!$D = 2!$x

d = 0.4!$xd = 1.7!$

xq = 1.7!$T

do = 4.97!$T A = 0.3!$T G = 2.0!$

K A = 50!$K G = 20!%

Generator2

M = 8!$D = 2!$x

d = 0.4!$xd = 1.7!$

xq = 1.7!$T

do = 5.86!$T A = 0.3!$T G = 2.0!$

K A

= 50!$

K G

= 20!%Generator3

M = 8!$D = 2!$x

d = 0.4!$xd = 1.7!$

xq = 1.7!$T

do = 6.86!$T A = 0.3!$T G = 2.0!$

K A = 50!$K G = 20!%

Generator4

M = 8!$D = 0!$x

d = 0.32!$xd = 1.67!$

xq = 1.55!$T

do = 8.14!$T A = 0.3!$T G = 2.0!$

K A = 50!$K G = 20!%

Transmission linesZ l1 = Z l2 = Z l3 = j 0.19,Z l4 = Z l5 = Z l6 = j 2.09.

TransformerX = 14 %

Table 2. Conventional PSS parameters.

K s = 1.0, T w = 4.0, T 1 = 0.025, T 2 = 0.138,T 3 = 0.019, T 4 = 0.136, T 5 = 0.190.

II . POWER SYSTEM MODELS

In this paper, we consider a multi-machine power system

as shown in Fig. 1. Here, G4 represents a large-scale system.

In this power system, the synchronous generator is equipped

with an automatic voltage regulator (AVR), a power system

stabilizer (PSS) and a governor (GOV). Fig. 2(a), (b), and (c)

show the block diagrams of AVR, PSS, and, GOV respectively.

This paper adopts ∆P e input type PSS as shown in Fig. 2(b),

where ∆P e is the deviation of electrical power output of the

synchronous generator, and U PSS is the PSS output that is

used as a stabilization auxiliary signal for the AVR. This kindof control system is called conventional PSS in this paper.

The parameters of these controllers (AVR, PSS, and GOV)

are decided on a trial and error basis so that they result in better

control performance at nominal conditions. Table 1 shows the

system constants utilized in this study, while Table 2 shows

the parameters of conventional PSS.

III. µ-SYNTHESIS

In this section, an overview of µ-synthesis is described

for the robust control method. The µ-synthesis takes into

account the perturbation structure by model uncertainty, which

is expressed as a diagonal matrix. Fig. 3 shows the general

µ-synthesis problem where, if T zw(s) and ∆(s) are stable,

a necessary and sufficient condition for the stability of thesystem for all model errors satisfying eq. (1) is given by eq.

(2):

σmax(∆j( jω )) ≤ 1, ω ∈ R (1)

µ∆(T zw( jω)) < 1, ω ∈ R. (2)

µ∆ is called structure singular value (SSV), and the relation-

ship between µ∆ and maximum singular value σmax is

µ∆(T zw( jω)) ≤ σmax(T zw( jω)). (3)

G1

Bus1

Bus4

Bus7

Load 1

G3

Bus3

Bus6

Bus9

Load 3

G2

Bus2

Bus5

Bus8

Load 2

G4

1000MVA 1000MVA 1000MVA

10000MVA

line1 line2 line3

line4 line5 line6

Bus10 Bus11

Fig. 1. 4-machine 11bus power system.

++

e fd0 5.0 p.u.

−5.0 p.u.

∆e fd

Upss

1+T S

++ A

K A−∆V t e fd

(a) Automatic voltage regulator(AVR)

T w s1+T w s 1+T 1 s

1+T 2 s1+T 3 s

1+T 4 s1+T 5 s

−∆Pe UpssK s 1

gain washout filter phase compensation 0.1 p.u.

-0.1 p.u.

(b) Power system stabilizer(PSS)

++−∆ω

1+T SG

K G

∆Pm

Pmo

Pm

1.2

0.8

Pmo

Pmo

(c) Governor(GOV)

Fig. 2. Block diagram of the controllers.

When we use a diagonal matrix D(s) as a scaling matrix, eq.

(3) is extended to

µ∆(T zw( jω)) ≤ σmax(D−1( jω)T zw( jω)D( jω)). (4)

A sufficient requirement for eq. (2) is

σmax(D−1( jω)T zw( jω)D( jω)) < 1, ω ∈ R. (5)

By solving the robust stability problem we obtain the con-

troller K that stabilizes the system in Fig. 3 if all model

errors satisfy eq. (5). The controller K is calculated by using

µ-toolbox in MATLAB.

866

8/13/2019 04075867


∆

P

K

w z

d e

∆

P

:

:

K

d

:

:

e :

Perturbations

General plant

Controller

Disturbance

Output from plant

T zw

Fig. 3. Generalized µ-synthesis problem.

-1-1

S i n g u l a r V

a l u e s ( d B )

30

20

10

0

-10

-20

-30

-4010

-110

0-1-1

10-2 10

110

2

Frequency (rad/sec)

Fig. 4. Singular values plot for U pss2 → ∆P e2solid line : without controller,

broken line : with normal robust PSS.

IV. ROBUST D ECENTRALIZED C ONTROLLER BASED ON

OPTIMAL S EQUENTIAL D ESIGN

A. Sequential Design

The robust decentralized controller designed on multi-

machine power system by considering the model from anotherarea may be designed similarly for the entire electric powersystem. Generally, a decentralized controller is individuallydesigned by using a nominal model, that is, the controller isnever set up for the plant. However, the controller is designedby considering the influence of the inter-area oscillation in thestabilization of the entire electric power system. Therefore, itis important that aspects of the entire electric power systemare stabilized by a little amount of control operation by

considering each controller. In this paper, as noted above, µ-synthesis of controller is called sequential design robust PSS(without consideration of sequential procedure). Further, µ-synthesis of controller designed in the nominal plant model bywithout considering other machine controllers is called normalrobust PSS. The problem of the decentralized controller designthat does not consider other controllers is verified.

Fig. 4 shows the eigen value from U pss2 to ∆P e2. The solid

line is a nominal model and the broken line is the eigen valueof the model where G1 has normal robust PSS 1. It is observed

-1

S i n g u l a r

V a l u e s ( d B )

30

20

10

0

-10

-20

-30

-4010

-1

Frequency (rad/sec)

100

101

102

Fig. 5. Singular values plot for U pss1 → ∆P e1.

-1

S i n g u l a r V a l u e s ( d

B )

30

20

10

0

-10

-20

-30

-40-1

10-1

Frequency (rad/sec)

100

101

102-1-1

10-2

Fig. 6. Singular values plot for U pss3 → ∆P e3.

from Fig. 4 that the target frequency domain for the resonancepoint of the plant has clearly changed. From this result it can

be said that the influence of normal robust PSS 1 cannot bedisregarded when the controller of G2 is designed. Thus itis important to consider an existing controller by sequentialdesign.

B. Condition Number

The right-hand side vector of the simultaneous equationaffects the solution. The extent of this effect depends on theproperty of the coefficient matrix and can be quantitativelyshown by introducing the norm concept that shows the size of

the matrix and the vector. The condition number is defined ascond(A) = A A−1.

The condition number can evaluate the influence of solutiongiving the changes of the right-hand side vector.

C. Procedure for Controller Design by Condition Number

Because the controller previously designed cannot consider

the controller designed afterward in sequential design, it isnecessary to consider the controller design optimal procedure.

867

8/13/2019 04075867


Generally, the sequence of controller design starts with the

large order as the basis is the degree of influence. Then, it is

necessary to quantitatively evaluate the size of the influence

that each controller has on the controlled object. Robust

decentralized controller based on optimal sequential design

is proposed in this paper. We design a one-input, one-output

type controller. The electric power output deviation ∆P ei is

the input to the synchronous generators G1 ∼ G3 as shown

Fig. 1, while the supplementary signal U pssi to AVR of each

machine is the output.

The design procedure is based on the condition number

described in paragraph subsection IV B. The controller de-

signed sequentially by the µ-synthesis in consideration of

the condition number be called the optimal sequential design

robust PSS. In this paper, the optimal sequential design robust

PSS is designed for machines G1 ∼ G3 in the targeted electric

power system. The controller is sequentially designed based

on the order with large influence of each input controller U pssito each electric power output deviation ∆P e. The linearized

model of the electric power system can be regarded such that

the input to the plant is a right-hand side vector, while theelectric power output deviation is the solution. Therefore, the

condition number that influences the size from each input to

each output can be invoked.

Solving the matrix from each input of electric machine

U pssi to each electric power output deviation ∆P e invokes

the condition number of each control input. Thus three con-

dition numbers are solved such that U pss1−3 "* [∆P e1 ∆P e2∆P e3 ∆P e4]. The requested condition numbers are shown as

follows:

• cond(G1)=9.0818 !_105

• cond(G2)=2.9703 !_105

• cond(G3)=2.9702 !_105

The following statement can be observed from the resulting

calculation

cond(G1) > cond(G2) cond(G3). (6)

It can be confirmed that the largest is electric machine G1

input U pss1 to AVR. In the order of designing the controller,

normal robust PSS which inputs a supplementary signal to

AVRG1 is designed from the design policy of previously

designing from the controller with the largest influence. After

the control loop is closed, the subsequent controller considers

an existing controller as having been designed. Therefore, in

this paper, the order of designing the proposed controller is

P SS G1 "*P SS G2 "*P SS G3.

D. Design of Robust Decentralized Controller

The weight for sequential design is fixed while comparing

the influence on the operation of the controller in the design

procedure. Weights for sequential design do not adjust during

controller design; weight was adjusted for improving control

performance using normal robust PSS design.

As seen previously, optimal sequential design robust PSS

is designed in the order PSSG1!$PSSG2!$PSSG3. Thus in

Table 3. Eigenvalue-analysis(I).Mode No. with-conventional controller with-proposed controller

ζ f (rad/s) ζ f (rad/s)

1 0.511 0.69 0.511 1.162 0.118 2.47 0.729 1.983 0.202 3.51 0.217 3.01

Table 4. Eigenvalue-analysis(II).Mode No. with-normal robust PSS with-proposed controller

ζ f (rad/s) ζ f (rad/s)

1 0.408 0.79 0.511 1.162 0.699 2.01 0.729 1.983 0.215 3.01 0.217 3.01

designing each controller, this procedure is optimal sequential

design robust PSS123. The other options of order design result

in inferior controllers.

The singular value plot is shown in Figs. 5 and 6 as well

as Fig. 4. Resonance points may be determined from each

singular value plot. The resonance points can be confirmed

from the figures in the low frequency area. Therefore, the

design of PSS that can control the inter-area oscillation is

needed. The order of controller model is found to be of order16th. The method of sequential design becomes high-order

of controller for the new-model incorporating the existing

PSS. Therefore, the plant is a reduced model of order for

designing the realizable controller. The perturbation generated

by transforming to the reduced plant model is assumed; it

is the modeling error margin at µ-synthesis. Moreover, all

sequential design robust PSS are reduced 5th order for premise

implementation.

Table 3∼4 shows the eigenvalue analysis of each controller

and the optimal sequential design robust PSS. It is understood

that the proposed controller has a good overall damping ratio.

The optimal sequential design robust PSS is designed while

considering sequential existing controllers and by improving

damping performance in the entire electric power system.Therefore, it can be said that the proposed method is more

effective than the method of the normal robust controller

design.

V. SIMULATION RESULTS

The effectiveness of the proposed controller is demonstrated

through computer simulations by considering a multi-machine

power system as shown in Fig. 1. Generated power is trans-

mitted to the load distribution center by means of parallel

transmission lines. System constants and operating conditions

used in the simulations are shown in Tables 1 and 2. A

three-phase to ground fault was applied at the middle of one

transmission line between Bus 7 and Bus 8 at tf = 0.10sec,

cleared at ts = 0.12sec by removing the faulted line. The

optimal sequential design robust PSS123 was compared with

normal robust PSS and sequential design robust PSS321. Figure

7 shows the simulation results.

The inter-area oscillation is not restrained in conventional

PSS. The optimal sequential design robust PSS123 and se-

quential design robust PSS321 designed in consideration of the

entire electric power system have good control performance.

This can be confirmed from the results of simulations. Further,

it is seen that the optimal sequential design robust PSS123 has

868

8/13/2019 04075867


0 2 4 6

0

0.05

0.1

0 2 4 60

0.1

0.2

0 2 4 6

0

0.05

0.1

time [s]

δ 1 4

[ r a d ]

δ 2 4 [ r a d ]

δ 3 4

[ r a d ]

(a) Phase angle δ

-0.05

0 2 4 6

0

0.2

0.4

0 2 4 6

0

0.1

0.2

0 2 4 6

0

0.05

0.1

0.15

0 2 4 6

0

0.05

0.1

time [s]

∆ ω 3 [ p . u . ]

∆ ω 4 [ p . u . ]

∆ ω 1

[ p . u . ]

∆ ω 2

[ p . u . ]

(b) Speed deviation ∆ω

the best performance when compared with all the other meth-

ods. The effectiveness of our proposed method is confirmed

from the results, notably, the eigen-value analysis and the time-

domain simulations.

VI. CONCLUSIONS

In this paper, a robust decentralized controller based on

optimal sequential design is proposed. In the design phase, the

inter-area oscillations are considered directly for the controller

to stabilize the entire electric power system. In addition, a new

distributed controller can be realized by applying the method

of sequential controller design in consideration of an existing

controller. Moreover, the appropriate design order of the

controller is decided by using the evaluated condition number.

The damping performance and the robustness performance

in the entire electric power system by sequential design are

improved. The eigenvalue analysis was performed. The inter-

area oscillation is not restrained in the conventional PSS.

Simulation results confirm that the proposed controller for the

0 2 4 6

-0.02

0

0.02

0.04

0.06

0 2 4 6

-0.02

0

0.02

0.04

0 2 4 6

-0.02

0

0.02

0 2 4 6

-0.05

0

0.05

time [s]

∆ P e 1

[ p . u . ]

∆

P e 2

[ p . u . ]

∆ P e 3

[ p . u . ]

∆ P e 4

[ p . u . ]

(c) Electric power output deviation ∆P e

time [s]

0 2 4 6-0.02

0

0.02

0 2 4 6-0.02

0

0.02

0 2 4 6-0.01

0

0.01

0.02

0 2 4 6-0.01

0

0.01

∆ V t 1 [ p

. u . ]

∆ V t 2

[ p . u . ]

∆ V t 3

[ p . u . ]

∆ V t 4

[ p . u . ]

(d) Terminal voltage deviation ∆V t

time[s]

0 2 4 6

0

2

4

0 2 4 6

0

2

4

0 2 4 6

1

2

3

4

0 2 4 6

2

4

e f d 1 [ p . u . ]

e f d 2 [ p . u . ]

e f d 3 [ p . u . ]

e f d 4 [ p . u . ]

(e) Excitation voltage efd

Fig. 7. Simulation results(Nominal conditions).

solid line : proposed controller,

broken line : sequential design robust PSS,

doted line : conventional PSS.

869

8/13/2019 04075867


entire electric power system has good control performance.

The proposed controller improved the stability in the entire

system compared with the conventional PSS, and confirmed

the control performance and the robustness performance im-

proved further by additionally using the condition number

evaluation compared with the sequential design controller.

The proposed controller is made to reduced 5th order for

application to the real system. The practicality of the proposedcontroller is shown by the improvement in the damping

performance for the entire multi-machine system, based on

output feedback control.

REFERENCES

[1] H. Okamoto and A. Kurita, “A Method for SVC Damping ControllerDesign Using Robust Pol Assignment Method,” Trans. of IEE. Japan,vol. 117-B, no. 4, pp. 578-584, 1997.

[2] Kwang M. Son and Jong K. Park, “On the Robust LQG Control of TCSCfor Damping Power System Oscillations,” IEEE Trans. Power Systems,vol. 15, no. 4, pp. 1306-1312, 2000.

[3] L. Sun and T. Oyama, “Power System Stabilization with TCSC Basedon H ∞ Theory,” Trans. of IEE. Japan, vol. 119-B, no. 2, pp. 276-283,1999.

[4] G. N. Taranto, J. K. Shiau, J. H. Chow, and H. A. Othman, “Robustdecentralized design for multiple FACTS damping Controllers,” IEEE Trans. Distrib., vol. 144, no. 1, pp. 61-67, 1997.

[5] H.Quinot, H.Bourles and T. Margotin, “Robust Coordinated AVR+PSSfor Damping Large Scale Power Systems,” IEEE Trans. Power Systems,vol. 14, no. 4, pp. 1446-1451, 1999.

[6] K. A. Folly, N. Yorino, and H. Sasaki, “Improving the robustness of H ∞-PSSs using the polynomial approach,” IEEE Trans. Power Systems,vol. 13, no. 4, pp. 1359-1364, 1998.

[7] Hardiansyah, Seizo Furuya, and Juichi Irisawa, “LMI-Based Robust H 2Controller Design for Damping Oscillations in Power System,” Trans. of

IEE Japan, vol. 124-B, no. 1, pp. 113-120, 2004.[8] George E. Boukarim, Shaopeng Wang, Joe H. Chow, Glauco N Taranto,

and Nelson Martins, “A Comparison of Classical, Robust, and Decen-tralized Control Designs for Multiple Power System Stabilizers,” IEEE Trans. on Power Systems, vol. 15, no. 4, pp. 1287-1292, 2000.

[9] T. Senjyu, Y. Morishima, T. Yamashita, K. Uezato, and H. Fujita, “Sta-bilization Control for Multi-Machine System using Decentralized H ∞Excitation Controller Realizing Terminal Voltage Control and Damping

Control,” Trans. of IEE Japan, vol. 122-B, no. 12, pp. 1280-1288, 2002.[10] T. Senjyu, T. Yamashita, K. Uezato, and H. Fujita, “Stabilization Control

for Multi-Machine Power Systems by Using Decentralized Excitation

H ∞ Controller Based on LMI Approach,” Power Engineering and Power Systems Engineering, IEE Japan, PE-02-44/PSE-02-54, pp. 7-14, 2002.

[11] E. J. Davison, and et al., “Decentralized stabilization and pole as-signment for general proper systems,” IEE Proc. Gener. Trans. Distrib.,vol. 142, no. 1, pp. 179-184, 1995.

[12] K. Ohtsuka, Y. Morioka, M. Nishida, and K. Yachida, “A decentralizedcontrol system for stabilizing multimachine power systems,” Trans. of

IEE Japan, vol. 115-B, no. 6, pp. 600-609, 1995.[13] M. Makino, H. Ukai, S. Cui, M. Kobayashi, and H. Kandoh, “Stabi-

lization of Multi-Machine Power System by Using Decentralized H ∞Controller,” Trans. of IEE Japan, vol. 118-B, no. 1, pp. 23-30, 1995.

[14] S. Niioka, R. Yokoyama, G. Fujita, and G. Shirai, “Decentralized ExciterStabilizing Control for Multi-Machine Power Systems,” Trans. of IEE

Japan, vol. 120-B, no. 6, pp. 808-814, 2000.[15] Y. Morioka, S. Kitagawa, and T. Kojima, “A Study on Power System

Stabilization by A Generator Control System Considering Multi-MachinePower Systems,” Trans. of IEE Japan, vol. 120-B, no. 8/9, pp. 1136-1145,2000.

[16] Balarko. Chaudhuri, Bikash C. Pal, Aygyrios C. Zolotas, Imad M.Jaimoukha, and Tim C. Green, “Mixed-Sensitivity Approach to H ∞ Con-trol of Power System Oscillations Employing Multiple FACTS Devices,”

IEEE Trans. Power Systems, vol. 18, no. 3, pp. 1149-1156, 2003.

Yoshitaka Miyazato (S’06) was born in Okinawa, Japan, in 1984. He receivedthe B.S. degree in electrical engineering from the University of the Ryukyus,Okinawa, Japan, in 2006. He is currently pursing and M.S. degree at the

University of the Ryukyus.His research interests include the power system control.Mr. Miyazato is a student member of the Institute of Electrical Engineers

of Japan.

Tomonobu Senjyu (A’89–M’02–SM’06) was born in Saga, Japan, in 1963.He received the B.S. and M.S. degrees from the University of the Ryukyus,

Okinawa, Japan, and the Ph.D. degree from the Nagoya University, Nagoya,Japan, in 1986, 1988, and 1994, respectively, all in electrical engineering.

In 1988, he joined the University of the Ryukyus, where he is now aProfessor. His research interests include stability of ac machine, advanced

control of electrical machines, and power electronics.Dr. Senjyu is a member of the Institute of Electrical Engineers of Japan.

Ryo Kuninaka (M’06) was born in Okinawa, Japan, in 1980. He received theB.S. and M.S. degrees from the University of the Ryukyus, Okinawa, Japan,in 2004 and 2006, respectively, all in electrical engineering.

His research interests include the power system control.Mr. Kuninaka is a member of the Institute of Electrical Engineers of Japan.

Naomitsu Urasaki (M’98) received the B.S., M.S., and Ph.D. degrees fromthe University of the Ryukyus, Okinawa, Japan, in 1996, 1998, and 2004,

respectively, all in electrical engineering.Since 1998, he has been with the Department of Electrical and Engineering,

Faculty of Engineering, University of the Ryukyus, where he is currently aResearch Associate. His research interests include the areas of motor drives.

Dr. Urasaki is a member of the Institute of Electrical Engineers of Japan.

Toshihisa Funabashi (M’90–SM’96) was born in Aichi, Japan, in 1951. Hereceived the B.S. degree from the Nagoya University, Aichi, Japan, in 1975,

and the Ph.D. degree from the Doshisha University, Kyoto, Japan, in 2000,both in electrical engineering.

He has been with the Power System Engineering Division, MeidenshaCorporation, Tokyo, Japan, since 1975, and is now a Senior Engineer, engaged

in research on power system analysis.Dr. Funabashi is a member of the Institute of Electrical Engineers and the

Institute of Electrical engineers of Japan. He is also a Chartered Engineer inthe U.K.

Hideomi Sekine was born in Japan, in 1943. He received the M.S. degree inelectrical engineering from the Gunma University Graduate School, Gunma,Japan, in 1969, and Ph.D. degree from the Tokyo Institute of Technology,Tokyo, Japan, in 1977.

In 1969, he was an Assistant at the Gunma University Graduate School,and in 1983 was an Associate Professor. Since 1996, he has been a Professorin the Department of Technology Education, Faculty of Education, Universityof the Ryukyus, Okinawa, Japan.

870

04075867

Documents