Extended Summary pp.1635-1640
` 6
`Improved Power Sharing Scheme for a Microgrid with Multiple Distributed
`Generators
`
`Netra Gyawali Non-member (Kyoto University, netra_002@yahho.com)
`Yasuharu Ohsawa Senior Member (Kyoto University, ohsawa@kuee.kyoto-u.ac.jp)
`
`Keywords : distributed generator, droop regulation, microgrid, R/X ratio
`
`Penetration of large amount of distributed generators (DG),
`liberalized electrical market policy and the reliability concerns of
`electricity supply are main causes for the origination of microgrid
`concept in low voltage distribution system. Such a microgrid can
`be operated in decentralized manner, either in grid connected
`mode, or in the islanded mode, according to the requirements
`and/or network obligation. The decentralize or autonomous
`operation scheme should have the proper power sharing provision
`among the parallel connected DGs, if possible, without using the
`control information among them. The real and reactive power
`controls should be in independent manner, and the DGs should
`share common real and reactive load in proportion to a
`pre-determined ratio, regardless of plant parameters. However,
`MG in distribution network having resistance dominated line
`interconnection, P-Q control can not be decoupled as in
`conventional droop. This paper introduces an improved power
`sharing scheme applicable for the microgrid, without necessiating
`the communication line among the DGs.
`From the well-known network relaionship, the power injected
`by a DG (E
`) to the bus (V 0) connected by the impedance
`(Z ) between them can be simplified as:
`sin cos
`cos sin
`P E V
`EQ eZ
`...................................... (1)
`Where, sin and e = E Ecos -V. Decoupling of P and Q is
`true when X>>R (with P-f and Q-V droop regulation) or R>>X
`(with P-V and Q-f droop regulation). In general the R/X value lies
`around 2 to 6, so the decoupling is no longer possible with either
`of underlined droop regulation schemes. As depicted by Eq. (1),
`the regulation of Q needs the nonlinear control action, though P is
`fairly linear with phase angle.
`In order to get effective power sharing, the proposed scheme
`introduces virtual impedance in voltage regulation loop, which
`varies according to the reactive flow through the DG , aiming to
`reduce the impedance mis-matches among the DGs. Moreover, the
`feedback of P also helps voltage regulation by minimizing the
`effect of P in V. The modified V-Q droop regulation, together with
`the P-f droop as in Eqs. (2) and (3), can provide the proper power
`sharing among the DGs.
`( )
`( )
`( )
`E
`o
`z z k Q
`V V nP z k Q I
`m P P
`0 1
`0 1
`0 0
`............................................ (2)
`( ) ( )
`( ) ( )
`pcc
`pcc
`d m P P
`dt
`de V V nP z k Q Idt
`0 0
`0 0 1
`............................. (3)
`Simulation results (for the two DG-MG system) of P-Q flow
`through the DG1 for different values of line impedance with
`conventional droop scheme is depicted in Fig. 1. The Q flow is
`found to be very sensitive to the variation of line resistance in both
`loading conditions (before and after the step load increase at
`t=0.2s), while P found to be well regulated. In particular, the
`reactive circulating current increases with increasing values of R/X.
`It is justified by Eq.(1) because the change of
`E will cause the
`change of V and/or E, whereas P is relatively linear with . Fig.2
`shows the power flow dynamics of DG1 with proposed scheme
`when step loads are applied to bus#1 and bus#2 at t=0.2s and
`0.35s respectively. The figure shows the good power sharing when
`supplying the loads at different load buses at various R/X values.
`Another notable point of the scheme is that it provides the flexible
`reactive power sharing among the DGs so that the DGs near the
`load can share more Q if required. These simulation results
`validate the applicability of the proposed scheme for low voltage
`MG system.
`
`
`Fig. 1. Power flow dynamices of DG1 (conventional
`droop scheme)
`
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`Fig. 2. Power flow dynamices of DG1 (proposed
`scheme)
`GENERAC 1013
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`© 2008 The Institute of Electrical Engineers of Japan. 1635
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`Improved Power Sharing Scheme for a Microgrid with Multiple Distributed
`Generators
`
`Netra Gyawali Non-member
`Yasuharu Ohsawa Senior Member
`
`This paper explores the active and reactive power sharing scheme for the parallel operation of inverter interfaced distributed
`generators (DGs) in a microgrid system. Applicability of conventional wireless control technique, based on P-f and Q-V droop
`regulations, is also investigated for the load sharing among the DGs with the help of small signal analysis. The conventional
`droop technique is found to be ineffective in a distribution system with resistive dominated line. In particular, the reactive power
`becomes highly uncontrolled with large circulating VAR in the presence of high R/X. The virtual impedance concept proposed in
`the paper intends to address this problem. The so-called virtual impedance is self-regulated variable aiming to reduce the
`impedance mismatch thereby eliminating the circulating VAR. Consequently, the scheme provides effective active and reactive
`power sharing among the DGs by adjusting the magnitude and frequency of the voltage at steady-state. Simulation results
`presented for the two-DGs microgrid system, confirms the validity of the proposed scheme.
`
`Keywords : distributed generator, droop regulation, microgrid, R/X ratio
`
`1. Introduction
`Penetration of large amount of distributed generators (DG),
`liberalized electrical market policy and the reliability concerns of
`electricity supply are motivating to form autonomously operable
`DGs (eg. Photo-V oltaic, micro-turbine, Fuel cell, micro-hydro etc),
`electrical loads and local storage system, which is often called
`microgrid (MG). Such MG can be operated in grid connected
`mode if required, and can automatically transfers into the islanded
`mode when there is fault in the upstream side. From the grid side,
`MG is regarded as a controlled entity within the power system
`which can be operated as a single aggregate load or, given suitable
`remuneration, a power source. From the user side, MG is similar
`to traditional low voltage (LV) distribution network which
`provides the thermal and the electrical needs, but additionally,
`reduce emission, enhance the reliability at potentially lower cost
`of energy supply(1).
`In order to provide the electricity at reasonable quality and
`reliability, the MG operational scheme has many challenges to
`address. Requirement of power electronic interfaces (dc/ac or
`ac/dc/ac), presence of diverse nature of DGs, presence of
`non-dispatchable DGs, requirement to cope islanded and grid
`connected modes, are few prominent concerns among them.
`Besides, the MG operational scheme should have the proper
`power sharing provision among the parallel connected DGs in the
`absence of the utility supply, if possible, without using the control
`information among them. The real and reactive power controls
`should be independent to each other, and the DGs should share
`common real and reactive load in proportion to a pre-determined
`ratio, regardless of plant parameters. The important classes of
`autonomous load-sharing techniques that have been proposed to
`date are: (i) the frequency and voltage droop technique(2)(3), termed
`as conventional droop scheme, (ii) P-Q sharing using
`communication between DGs(4), (iii) signal injection technique (5),
`and (iv) the adaptive impedance method (6). Although the active
`power sharing is satisfactory with these schemes, neither of them
`could satisfactorily address the reactive power sharing in a
`distribution network with high R/X value. Utilizing the insights
`gained from a detailed study of conventional droop techniques,
`this paper first investigates the applicability of conventional droop
`scheme in P-Q sharing with respect to varying R/X, and proposes a
`new reactive power sharing scheme by including virtual
`impedance. The new scheme ensures that DGs on a distributed
`power network share a common load regardless of the line
`impedance.
`2. Study Scheme
`Fig. 1 shows a single line diagram of the study scheme used to
`investigate possible MG operation and control. The scheme
`includes the inverter interfaced DGs with different capacity
`connected to the main grid. Each DG represents a dispatchable
`source with adequate capacity to meet active and reactive power
`within limit. Such a dispatchable source includes battery as energy
`storage interfaced at the converter dc bus to assist the transient
`power balance. The distribution line is modeled as the lump series
`R-L elements.
`The primovers of the DGs may be the types (fuel cell,
`micro-turbine etc), which supply the controllable dc power to the
`inverter. Considering the quite larger time constant of primemover
`load transient time, the prime-mover and battery are lumped as
`constant dc voltage source for the time period of interest. Thus,
`the DGs are represented by a three-phase equivalent of voltage
`source inverter (VSI) lumped with dc power source. Each phase of
`the inverter is connected to the system through L-C filter and a
`lump reactor. The control action of VSI is performed in
`0
`frames and utilizes the instantaneous power (P-Q) control concept
` * Department of Electrical Engineering, Kyoto University, Kyoto
`(e-mail: netra_002@yahoo.com)
` ** Department of Electrical Engineering, Kyoto University, Kyoto
`(e-mail: ohsawa@kuee.kyoto-u.ac.jp)
`Paper
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` 1636 IEEJ Trans. EIS, Vol.128, No.11, 2008
`to specify the magnitude and the phase angle of the voltage(3). The
`microgrid is connected with the utility grid which is represented
`by ac voltage source with finite impedence.
`In this study, the DGs are operating in islanded mode to share
`the load at the different buses, i.e, the utility grid not connected to
`the microgrid. If utility grid is to be connected, the power
`exchange between the microgrid and utility grid can be
`determined by the appropriate management schemes, tie-line
`regulation (regulate tie-line power) or unit regulation (regulation
`of power from each unit) schemes (which is beyond the scope of
`this study and not included in it). The utility grid is included here
`to represent the general microgrid-grid interconnection structure
`owing to open the comprehensive model.
`3. Applicability of Droop Regulation
`The idea behind the conventional droop control is that the
`generator themselves can set their instantaneous P-Q flow based
`upon the decoupled relationship between the P/Q with f/V , so that
`the power demand within a system can be shared among the
`generators as pre-specified manner. However in low-volt (LV) and
`medium-volt (MV) microgrid, the line connection being highly
`resistive, the decoupling is not possible and hence wireless droop
`scheme is quite difficult. To get the clear picture of coupling
`nature of network variables, consider a system as in Fig. 2. For
`this system, the P-Q supplied by the voltage source to the bus can
`be represented by Eq. (1).
`cos cos sin sin
`cos sin cos sin
`EV V EVP Z Z Z
`EV V EVQ Z Z Z
`2
`2
`................ (1)
`Defining control variable as e= E Ecos - V and sin we
`have,
`sin cos
`cos sin
`P E V
`EQ eZ
`...................................... (2)
`Clearly, Eq.(2) depicts the fact that P-Q flow through the power
`source is decoupled with -e only in ideal case; namely pure
`resistive ( =0) or pure inductive ( = /2) case. For the high X/R
`value, traditional droop sharing scheme can be implemented
`where P-f and Q-V are decoupled. Conversely for highly resistive
`line coupling, the droop sharing is needed to be reversed. In
`practice the L V line has R/X ratio lies between 2 to 6. In such case,
`neither of the above techniques seems to fit.
`In order to find proper control scheme, applicability of
`conventional droop scheme against different values of R/X is
`checked first, and based upon the limitations, the proper scheme
`will be investigated. The frequency and the voltage droop derived
`from the conventional scheme is written as(2):
`min
`max
`min
`max
`( )
`,
`o
`no load
`m P P
`V V nQ
`with m P
`V Vn Q
`0 0
`0
`........................................... (3)
`Here P 0, V 0, 0 are the nominal values of active power, voltage
`and frequency respectively. Similarly, Pmax ,Qmax, no-load, min,,
`and Vmin represent maximum active power, maximum reatcive
`power, frequency at no-load, frequency at Pmax, and minimum
`allowable load voltage of the system respectively. The coefficient
`m and n are the droop coeffiecient as defined in the equation. For a
`microgrid m and n are normally chosen as 2% and 5%
`respectively in per unit system(8).
`The control law for the control variables ( ,e) can be written as:
`( ) ( )
`( )
`pcc
`pcc
`d m P P
`dt
`de V V nQ
`dt
`0 0
`0
`..................................... (4)
`Here, pcc and Vpcc represent the frequency and the voltage at the
`point of common coupling .. It has been reported that by
`controlling, e, rather than E or V, the impedance mismatch of
`coupling reactance is minimized (7). The block diagram of the
`droop regulation is also shown in Fig. 3.
`Fig. 1. Single line diagram of study MG system
`
`
`
`Fig. 2. Volltage source connected to the local Bus
`
`
`Fig. 3. Block diagram of droop regulation scheme; (a)
`V-Q droop, (b) f-P droop
`
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`Improved Power Sharing Scheme for a Microgrid
`
`C 128 11 2008 1637
`From Eqs. (2) to (4) and performing the small signal analysis
`around the operating point, we have:
`~ ~
`~ ~
`sin cos
`cos sin
`mE md V
`nE ndt Ze e
`......................... (5)
`whereas the quantity with capital letters are the values at the
`operating point. The characteristic equation of the system
`represented by Eq. (5) can be written as:
`0,
`sin ( )
`s B s C with
`V EVB Em n and C mnZ Z
`2
`1 1
`2
`1 1 2
`..................... (6)
`Since B 1,C1> 0, the poles always situate at the stable plane
`indicating that the small signal model of the system is stable for
`any value of R/X. The choice of m and n is trade-off between the
`stability and the voltage regulation.
`Simulation Results The above scheme is tested to the MG
`(Fig. 1) under the Matlab ® simulink platform. The rating of DG1
`and DG2 are kept 20 kV A and 30 kV A respectively. The graphs in
`Fig. 4 shows the dynamics of the power flow through the DGs,
`with different R/X values of line impedance. Initially a load of
`(15+j8) kV A was connected to the bus#1 and (5+j3)kV A at bus#2.
`At t=0.2s another step load of (8+j3)kV A is introduced at the
`bus#1. It can be seen that P is apparently regulated against
`different R/X values, whereas the Q is heavily affected by the
`value. With the increasing value of R/X, the circulating Q
`increases, though the voltage regulation satisfactory (Fig. 5). The
`circulating Q is not allowed in the system as it creates the extra
`burden to the system. Hence the conventional droop scheme is not
`applicable in the system with resistive dominated line.
`4. Introduction of Virtual Impedance
`While observing the power follow dynamics in Fig. 4, it can be
`noticed that the origin of the circulating var is due to the mismatch
`of impedance between respective DGs and the load bus. Larger
`the impedance, the smaller is the var flow and vice-versa. Thus the
`var flow from the DG with smaller interconnecting impedance
`supplies the circulating var to the DG with larger interconnecting
`impedance.
`To solve this, a large interface inductors can be included
`between the inverter and the load bus, but they are heavy and
`bulky. In Ref. (8), resistive compensation is made by adding its
`effect in setting the reference voltage. However, the amount of
`resistive part to be compensated is related to the location of load
`change, which, being the random event, can not be predicted in
`multi load-buses system. In Ref. (6), authors have proposed the
`concept of adaptive impedance which varies with the reactive
`power flow. However, the model is not appealing for the
`predominately resistive line as it compensates mainly the
`reactance part. Moreover, the effective impedance sought by the
`DGs is susceptible with current transient. This paper tries to
`addressing these limitations by introducing the virtual impedance
`which varies with Q as in Eq. (7).
`( )E
`z z k Q0 1 ............................................................... (7)
`where z0 is the reference impedance and the k1 is the constant
`which determines the sensitivity of Q over zE. Both parameters are
`carefully selected depending upon the network and operational
`circumstances. This impedance compensates for the reactive
`power difference due to line impedance unbalance by providing
`the proper reference voltage given by (8).
`, ( )oV V n P z k Q I
`0 1 .............................................. (8)
`Here is the constant coefficient to decouple the effect of active
`power on V . It is worthwhile to note that the voltage regulation in
`the Eq. (8) has sought two important considerations; (i) regulation
`of virtual impedance, (ii) decoupling of the effect of P over V .
`Thus the set of differential equation to represent the P-Q
`regulation evolves from Eq. (4) to (9). Notice that though the
`active power is also affected by the output impedance, it is
`effectively controlled by self-adjusting of the phase angle alone.
`
`Fig. 4. Power flow dyanamics of DGs
`
`
`Fig. 5. Voltage dyanamics of load bus
`
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` 1638 IEEJ Trans. EIS, Vol.128, No.11, 2008
`,
`( ) ( )
`( ) ( )
`pcc
`pcc
`d m P P
`dt
`de V V n P z k Q Idt
`0 0
`0 0 1
`............................ (9)
`The block diagram of the proposed scheme is also shown in Fig.6.
`4.1 Small Signal Modeling and Control Design Rules
`In order to investigate the stability and the transient response of
`the system, small-signal analysis is performed. The closed-loop
`system dynamics has been derived, taking into acccount of well
`known stiff load-bus approximation (9). The small-signal dynamics
`of the phase angle difference and the voltage difference ( ,e) are
`obtained by linearizing Eqs. (2) and (9), at =450. This is fairly
`reasonable for small signal anlysis and controller gain estimation
`of the considered microgrid with R/X>1 with inductive coupling
`(X/R>1) between DG and point of common coupling. Although
`the complete modeling requires the several low pass filters with
`signals P, Q, and I, for the sake of simplicity, the low pass filters
`are excluded from the small signal analysis. It is apparently true,
`as it will not cause any considerable effect on the closed loop
`dynamics if the corner frequency of low pass filter is selected
`quite higher than the dominant poles.
`~
`~
`~
`~ ~ ~ ~, ( )
`d m pdt
`d e n p z i k q I k Q idt 0 1 1
`.............................. (10)
`Noting that,
`~ ~ ~
`( ) /
`,
`SI P Q V
`V
`or I P p Q q
`SV
`2 2
`2
`and substituting the values from Eq. (2) to (10) we get,
`~
`~
`~
`~ ~
`d m p
`dt
`d e p qdt
`
`Simplifying,
`~ ~
`~ ~( )
`mE md V
`Edt Ze e2
`......................(11)
`,, ( )
`( )
`Pwhere n z k Q
`SV
`Qz k Q k S
`V S
`0 1
`0 1 1
`2
`1 2
`
`Thus the characteristic equation of the system becomes,
`0s B s C2
`2 2 .......................................................... (12)
`with,
`,
`( )
`V k S P QB mE n z k Q
`V SZ
`V mE QC z k Q k SSZ
`1
`2 0 1
`2 0 1 12
`2
`2
`2
`
`The small signal stability of the system is ensured if B2, C2>0. For
`a DG the value of is comparable to mcos , implying that
`. Thus, when the DG is supplying the lagging var, the
`stability can be achieved for any value of the parameter. But, when
`the DG is supplying the leading var, the stability is, granted if,
`max
`max,
`z k Q
`or z k Q
`0 1
`0 1
`0 ......................................................... (13)
`where, Q max is the maximum leading var supplied by the DG .
`Thus it can be concluded that the small signal stability is
`confirmed when Eq. (13) is satisfied.
`4.2 Simulation Results The proposed scheme is tested
`on the matlab simulink model of the MG (Fig. 1). The loads are
`assumed to be three phase balanced. The main aim of the scheme
`is to regulate the reactive power, against the different values of
`R/X, as the conventional scheme is only able to regulate the active
`power. The values of necessary parameters used in simulation are
`shown in Table 1. It should be noted that the rating of DGs are
`chosen to be same (20 kV A each), which is not necessary in
`general (the rating of DGs only need to alter the values of m,n).
`Fig. 7 shows the power flow dynamics through the DGs when the
`line impedance is changed. Initially the load of (20+j8)kV A at the
`bus#1 and (5+j3)kV A bus#2 is shared by the DGs. At t=0.2 sec
`another load of (5+j3)kVA is connected to bus#1, which is
`followed by injection of another load of (5+j3)kV A at bus#2, at
`t=0.35 sec. It can be seen that the active power and reactive power
`are shared between the DGs, proportional to their ratings, in all
`conditions, irrespective of the different R/X of line impedance.
`Similarly, the voltage dynamics curve shown in Fig. 8. indicates
`that load voltage is well regulated within the limit, eliminating the
`circulating var. Another notable merit of the scheme is that the
`reactive load sharing by the DGs can be made flexible. For
`example, it is not likely that the DGs which are separated far apart,
`equally share the common reactive load irrespective of the load
`location. It is expected that the DGs near the load should share
`more reactive load than that of DG situated in farther distance, so
`that the line loss can be reduced (this concept is, however, not
`effective for the active power sharing as there are many constraint
`in doing so). The proposed scheme can provide this option by the
`choice of the of z0 and k 1. Fig. 9 shows how the individual DG
`responds with the load change in the nearest load bus. For the ease
`in analysis purpose, the equal ratings of DGs are selected again.
`Initially, when both buses were equally loaded, the power sharing
`between the DGs was equal. When a load of (5+j3)kV A is applied
`to bus#1, DG1 shares more reactive power than DG2. Again when
`Fig. 6. Block diagram of proposed voltage and
`reactive power regulation scheme
`
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`Improved Power Sharing Scheme for a Microgrid
`
`C 128 11 2008 1639
`another load of (5+j3)kV A is connected to bus#2, DG2 shares
`more Q than DG1. Thus, the DG situated nearer to the load can be
`commanded to share more reactive load unless they are
`overloaded. Active power sharing remain, however, unaffected by
`the choice of k1 and zo, as required.
`5. Conclusion
`This paper proposed a new power-sharing scheme applicable
`for parallel operating DGs in a distribution microgrid. The scheme
`is based on the droop regulation, which does not necessitate the
`communication channel among the DGs. In contrast to
`conventional droop schemes which are only applicable to line with
`X>>R, it can provide proper power sharing in distribution
`microgrid (where R/X>2 in general). Based upon the fact that line
`parameter ( R/X) negligibly affects the active power sharing and
`highly affects the reactive power sharing, the scheme introduces
`virtual impedance in V-Q droop keeping the P-f droop unchanged.
`This allows sharing of active and reactive power without
`sacrificing frequency/amplitude regulation in the steady-state.
`Another notable merit of the scheme is that it provides the flexible
`reactive power sharing among the DGs so that the DGs near the
`load can share more Q if required (for the purpose of loss
`reduction).
`The simulation results have been reported to validate the
`proposed control techniques, showing good power sharing when
`supplying the loads at different load buses at various R/X values.
`The results justifiy their applicability to distribution microgrid
`having inverter interfaced distributed generation units.
`(Manuscript received Feb. 15, 2008, revised May. 2, 2008)
`R
`eferences
`Technical Report 22, Tyndall Centre for Climate Change Research (2005)
`Specialists Conference,. PESC 04. V ol.6, pp.4285- 4290 (2004)
`IEEE Trans. Power System, V ol.21, No.2 (2006-5)
`IEEE Trans. Power Electronics, Vol.19 (2004)
`IEEE trans.
`Industrial Applications, V ol.36, No.1 (2000)
`IEEE Trans. Industrial Electronics,
`V ol.53, No.5, pp.1461-1470 (2006)
`IEEE Trans. Power Delivery, V ol.20, No.2 (2005)
`Distributed Energy Resources, V ol.1, No.1 (2005)
`IEEE Trans. Industry Applications,
`V ol.38, pp.533-542 (2002)
`Table 1. Parameters used for simulation
`zo( ) k 1 m1,m2 n 1,n2 DG1 DG2 Pf
`0.02 10 -5 /20*10-3 0.3*10 -3 20kV A 30kVA 0.9
`
`
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`Fig. 7. Power flow dynamics of proposed scheme
`
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`Fig. 8. Voltage dynamics of proposed scheme
`
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`Fig. 9. Active and reactive power sharing
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` 1640 IEEJ Trans. EIS, Vol.128, No.11, 2008
` Netra Gyawali (Non-member) received BE degree in electrical
`engineering from IOE, Tribhuvan University Nepal
`in 1999. Since 2000, he is involved in the academic
`career in the department of electrical engineering
`Pulchowk Campus, Nepal. Currently he is pursuing
`graduate study in Kyoto University, Kyoto, Japan.
`His research area includes power system dynamics,
`control of distributed resources, and operation and
`management aspects of microgrid.
` Y asaharu Ohsawa (Senior Member) received BS, MS and Dr. Eng.
`degrees in electrical engineering all from Kyoto
`University in 1969, 1971 and 1982, respectively. He
`joined the Dept. of Electical Engineering, Kyoto
`University as a research associate in 1972. After
`serving as an assistant professor and associate
`professor in the Univ. of Tsukuba, and as associate
`professor and professor in Kobe Univ., he is
`currently a professor in Kyoto University. His main research areas include
`stability analysis and stabilizing control of electric power systems and
`application of SMES in power systems.
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