synchronous frame control for voltage sag swell

IEEJ Journal of Industry ApplicationsVol.6 No.6 pp.353–361 DOI: 10.1541/ieejjia.6.353

Paper

Synchronous Frame Control for Voltage Sag/Swell CompensatorUtilizing Single-Phase Matrix Converter

Kichiro Yamamoto∗a)Senior Member, Sho Ehira∗ Member

Minoru Ikeda∗ Non-member

(Manuscript received Dec. 26, 2016, revised July 7, 2017)

In this paper, a synchronous frame control for a voltage sag/swell compensator utilizing single-phase matrix con-verter is proposed. First, the configuration of the proposed system and its operation are described. Next, the effects ofthe degree of voltage sag and load variation on the system stability are analyzed using the transfer function. Finally,the experimental waveforms of the system with the proposed synchronous frame control are compared with those ofthe system with a stationary frame control. The results demonstrate that the proposed synchronous frame control cansuppress the steady state error and pulsation caused by the LC filter resonance better than the stationary frame control.

Keywords: single-phase matrix converter, voltage sag/swell compensator

1. Introduction

Recently, a lot of kinds of equipments are influenced byinstantaneous voltage sag because of progress of informationsociety. The instantaneous voltage sag may give rise to seri-ous problems in computer systems or electronic equipments.Thus, the authors have already proposed an instantaneousvoltage sag/swell compensator utilizing single-phase matrixconverter (1). The matrix converter is a circuit which convertsan AC voltage into any AC voltage directly. The matrix con-verter has some advantages such as high efficiency, compactand long lifetime compared to conventional rectifier-invertersystem. However, the proposed system needs LC filters to re-duce switching ripple. Therefore, compensating voltage andsource current pulsate due to the filter resonance. In grid-connected inverters, methods to suppress the pulsations us-ing feedback of filter capacitor current or filter inductor cur-rent were proposed (2) (3). The authors investigated suppress-ing characteristics of pulsation of compensating voltage inthe proposed system with stationary frame control (4). It wasshown that the pulsation of compensating voltage was notsuppress enough for 40% voltage swell when only the induc-tor current feedback was applied. The compensating volt-age is regulated by proportional controller. Accordingly, theproposed system has steady state error by limited gain ofthe controller. In the single phase inverter, the proportional-resonant (PR) control and synchronous frame PI control wereproposed to eliminate steady state error (5).

In this paper, a synchronous frame control for the volt-age sag/swell compensator utilizing single-phase matrix con-verter is proposed. First, the configuration of the proposed

a) Correspondence to: Kichiro Yamamoto. E-mail: [email protected]∗ Department of Electrical and Electronics Engineering, Kago-

shima University1-21-40, Korimoto, Kagoshima 890-0065, Japan

system and its operation are described. Next, the effects ofdegree of voltage sag and variation of load on the systemstability with stationary frame control and with synchronousframe control are analyzed using the transfer function. Fi-nally, the experimental waveforms of the system with the pro-posed synchronous frame control are compared with thoseof the system with a stationary frame control. The resultsdemonstrate that the proposed synchronous frame control cansuppress the steady state error and pulsation caused by the LCfilter resonance better than the stationary frame control.

2. Voltage Sag/Swell Compensator UtilizingSingle-Phase Matrix Converter

The configuration of proposed instantaneous voltagesag/swell compensator utilizing single-phase matrix con-verter is shown in Fig. 1. This compensator consists of thesingle-phase matrix converter, two LC filters, and a trans-former. The single-phase matrix converter generates com-pensating voltage vC from source voltage vS . Two LC filtersreduce voltage ripples and current ripples. The transformeradds compensating voltage vC to the source voltage vS . Op-erating principle of the compensator is explained, here. Whenvoltage sag or swell occurs, the compensating voltage vC isproduced with the matrix converter. And produced compen-sating voltage vC is added to the source voltage vS throughthe transformer. As a result, the load voltage vL is kept at theload voltage reference vL

∗ (= 100 Vrms).Next, the control method is described in detail. A syn-

chronous frame controller in Fig. 1 was proposed in this pa-per. A virtual orthogonal signal is needed to implement thesynchronous frame controller in the single-phase system (6) (7).In this paper, as the orthogonal signal, a quarter cycle de-layed signal is generated from the original signal. Funda-mental components of source voltage, compensating voltageand inductor current are transformed into DC componentsby applying d, q frame transformation. The compensating

c© 2017 The Institute of Electrical Engineers of Japan. 353

Synchronous Frame Control for Voltage Sag/Swell Compensator（Kichiro Yamamoto et al.）

Fig. 1. System configuration of instantaneous voltage sag/swell compensator utilizing single-phase matrix con-verter

voltage reference vCd∗ is calculated from the difference be-

tween the load voltage reference vLd∗ and the source voltage

vSd, and the compensating voltage vCd is controlled by the PIcontroller. A PLL algorithm is used in the voltage phase de-tection block in Fig. 1 to detect the phase of source voltage,θS .

And the algorithm is demonstrated in the flow chart onFig. 2. The value of proportional gain was set to 0.3, inte-gral gain was set to 150, and inductor current feedback gainKi2d was set to 1.6. And, q axis component of the compensat-ing voltage is not controlled. Output signal from controlleris compared with the triangular carrier waveform modulatedby amplitude of vS . And gate signals for each switches ofthe matrix converter are produced. For performance com-parison, the stationary frame controller used in our previoussystem (3) is implemented as shown in Fig. 1. In the controller,the compensating voltage vC is controlled by the proportionalcontroller. Gain K′ is used to compensate for the steady stateerror of vC , and the value of the gain was set to 2. Further-more, the value of proportional gain K was set to 1, the in-ductor current feedback gain Ki2 was set to 5.4. Output signalof synchronous frame controller is selected as input signal ofgate signal generator when Sa is on. Output signal of station-ary frame controller is selected as input signal of gate signalgenerator when Sb is on.

3. System Analysis by Transfer Function

In this section, the transfer function of the system withstationary frame control is derived by state space averagingmethod to analyze the effects of the degree of voltage sag

Fig. 2. Flow chart of voltage phase detection

and load variation on the system stability. From the circuitshown in Fig. 3, in the case that S1 and S4 are on, differential

354 IEEJ Journal IA, Vol.6, No.6, 2017


Fig. 3. Model of instantaneous voltage sag/swell com-pensator utilizing single-phase matrix converter

equations are obtained as

vS − L1diL1

dt− RL1iL1 = v1 · · · · · · · · · · · · · · · · · · · · · · (1)

−v1 + L2diL2

dt+ RL2iL2 + v2 = 0 · · · · · · · · · · · · · · · · · (2)

C1dv1

dt= iL1 +

vs − v1

R1− iL2 · · · · · · · · · · · · · · · · · · · · · (3)

iL2 −C2dv2

dt− iL = 0 · · · · · · · · · · · · · · · · · · · · · · · · · · · (4)

RLoadiL = vS + v2 − 2LTdiL

dt− 2RT iL · · · · · · · · · · · · · (5)

where RL1 is the equivalent series resistance (ESR) of L1, RL2

is the ESR of L2, LT is the leakage inductance of the trans-former, and RT is the winding resistance of the transformer.Similarly, in the case that S2 and S4 are on, differential equa-tions are obtained as

vS − L1diL1

dt− RL1iL1 = v1 · · · · · · · · · · · · · · · · · · · · · · (6)

L2diL2

dt+ RL2iL2 + v2 = 0 · · · · · · · · · · · · · · · · · · · · · · · (7)

C1dv1

dt= iL1 +

vS − v1

R1· · · · · · · · · · · · · · · · · · · · · · · · · · (8)

iL2 −C2dv2

dt− iL = 0 · · · · · · · · · · · · · · · · · · · · · · · · · · · (9)

RLoadiL = vS + v2 − 2LTdiL

dt− 2RT iL. · · · · · · · · · · · (10)

By defining a duty ratio of switch S1 as D, matrix equa-tion is obtained by using the state space averaging method asfollows:

x(t) = Ax(t) + bvS (t) · · · · · · · · · · · · · · · · · · · · · · · · · · (11)

y(t) = cx(t) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (12)

where

A =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

−RL1

L10 − 1

L10 0

0 −RL2

L1

DL2

− 1L2

0

1C1

− DC1− 1

C1R10 0

01

C20 0 − 1

C2

0 0 01

2LT−RLoad + 2RT

2LT

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

b =[

1L1

01

C1R10

12LT

]T

x(t) =[diL1

dtdiL2

dtdv1

dtdv2

dtdiL

dt

]T

and D is a control variable in A, thus, the equation (11) isnonlinear. Accordingly, the equation is linearized by break-ing variables into a steady state component and a small per-turbation (8).

Δx(t) = A0Δx(t) +∂A∂DΔD(t)x0 + bΔvS (t) · · · · · · · (13)

Δy(t) = cΔx(t) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14)

where

A0 =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

−RL1

L10 − 1

L10 0

0 −RL2

L1

D0

L2− 1

L20

1C1

−D0

C1− 1

C1R10 0

01

C20 0 − 1

C2

0 0 01

2LT−RLoad + 2RT

2LT

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦D0 =

K(K′V∗C0 − VC0) − Ki2I20

VS 0

x0 =[IL10 IL20 V10 V20 IL0

]T

∂A∂D=

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

0 0 0 0 0

0 01L2

0 0

0 − 1C1

0 0 0

0 0 0 0 00 0 0 0 0

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦.

D0 is a steady state component of duty ratio D. It is ob-tained from block diagram of stationary frame control part inFig. 1.

Each value of x0 can be found by solving the equation (11)with setting all of time derivatives to zero. The transfer func-tion between ΔD and Δy(t) is expressed by equation (15).

Δy(s)ΔD(s)

∣∣∣∣∣ΔvS (s)=0

= c(sI − A0)−1 ∂A∂D

x0. · · · · · · · · · · · · (15)

Accordingly, the block diagram of the instantaneous volt-age sag/swell compensator can be obtained as shown inFig. 4. The transfer function between ΔD and ΔiL2 can beobtained by substituting the equation (16) into c in the equa-tion (15). Similarly, the transfer function between ΔD andΔv2 can be obtained by substituting the equation (17) into cin the equation (15).

c1 = [0 1 0 0 0] · · · · · · · · · · · · · · · · · · · · · · · · (16)

c2 = [0 0 0 1 0]. · · · · · · · · · · · · · · · · · · · · · · · · (17)

From Fig. 4, the closed loop transfer function of the innercurrent loop is expressed as



Fig. 4. Block diagram of instantaneous voltage sag/swell compensator

Gi2d(s) =ΔDΔi2∗

=HD(s)

VS 0 + Ki2 · HZ(s) · Δi2ΔD· HD(s)

· · · · · · · · · · · · · · · · · · · (18)

where HZ(s) is a zero order hold, and HD(s) is a computationdelay of DSP. Each transfer function is expressed as

HZ(s) =1 − e−sT

sT· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (19)

HD(s) = e−sT · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (20)

where T is the sampling period and the value was 100 μs.From Fig. 4, the closed loop transfer function between ΔvC

∗and ΔvC is expressed as

Gvc(s) =K′ · HZ(s) ·G(s) ·Gi2d(s) · ΔvC

ΔD·GL(s)

1 + HZ(s) ·G(s) ·Gi2d(s) · ΔvC

ΔD·GL(s)

· · · · · · · · · · · · · · · · · · · (21)

where

GL(s) =RLoad

RLoad + 2(sLT + RT ). · · · · · · · · · · · · · · · · · · (22)

For the stationary frame control, G(s), the transfer functionof the A part in Fig. 4, becomes a proportional gain as

G(s) = KP · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (23)

Substitution of the equation (23) to the equation (21) yieldsthe transfer function for the stationary frame control,

Gvc(s) =K′ · HZ(s) · KP ·Gi2d(s) · ΔvC

ΔD·GL(s)

1 + HZ(s) · KP ·Gi2d(s) · ΔvC

ΔD·GL(s)

.

· · · · · · · · · · · · · · · · · · · (24)

On the other hand, for the synchronous frame control, G(s),the transfer function of the A part in Fig. 4, becomes as

G(s) = GPI(s) =

⎛⎜⎜⎜⎜⎜⎝KP +Kis

s2 + ω2f

⎞⎟⎟⎟⎟⎟⎠ − Kiω f

s2 + ω2f

OGM(s)

· · · · · · · · · · · · · · · · · · · (25)

where OGM(s) stands for orthogonal (imaginary) term gen-eration method and we used a quarter cycle delay (9) as thefollowing:

Fig. 5. Root loci of the stationary frame control and syn-chronous frame control in the case that the load resistanceRLoad was increased

Fig. 6. Root loci of the stationary frame control and syn-chronous frame control in the case that the voltage sagwas changed

OGM(s) = exp

(− π

2ω fs

). · · · · · · · · · · · · · · · · · · · · · · (26)

From the equations (21), (25) and (26), the transfer func-tion for the synchronous frame control is obtained as

Gvc(s) =K′ · HZ(s) ·GPI ·Gi2d(s) · ΔvC

ΔD·GL(s)

1 + HZ(s) ·GPI ·Gi2d(s) · ΔvC

ΔD·GL(s)

.

· · · · · · · · · · · · · · · · · · · (27)

The loot loci of the transfer functions for the stationaryframe control (the equation (24)) and for the synchronousframe control (the equation (27)) are shown in Figs. 5 and6. In Fig. 5, the load resistance RLoad was changed from 20Ωto 100Ω. In the figure, the poles move to the right direc-tion as the value of RLoad increases. In Fig. 6, the voltage sagwas changed from severe (40%) to mild (10%). For chang-ing from severe to mild of the voltage sag, the poles moveto the right direction. From both figures, one can find thatlighter load and more mild sag make the system more unsta-ble. And, in comparison between the stationary frame control



(a) 40% voltage sag, 250 W resistive load (b) 40% voltage sag, 100 W resistive load

(c) 20% voltage sag, 250 W resistive load (d) 20% voltage sag, 100 W resistive load

(e) 40% voltage sag, 100 W resistive – inductive load (f) 20% voltage sag, 100 W resistive – inductive load

Fig. 7. Experimental waveforms of compensator with conventional stationary frame control. (Steady state)

and proposed synchronous frame control in Figs. 5 and 6, it isclear that proposed synchronous frame control is more stablethan the stationary frame control.

4. Experimental Results

In this section, experimental waveforms for the systemwith proposed synchronous frame control were comparedwith those for the system with stationary frame control. Inthe experimental system, reverse block IGBT, IXRH 40N120manufactured by IXIS, was used as bi-directional switch andDSP TMS320F2808 was used as a controller. The switchingfrequency of the matrix converter was 10 kHz and its com-mutation time was 4 μs. The total harmonic distortion (THD)was calculated by the equation

THD =

√V2

rms − V21

V1· · · · · · · · · · · · · · · · · · · · · · · · · · · (28)

where Vrms is the rms value of a target waveform and V1 isthe rms value of fundamental component of the target wave-form. And sampling time was 5 ns and measuring frequencyof oscilloscope was 1 MHz.

Experimental waveforms for the system with stationaryframe control are shown in Fig. 7. In the case of 40% voltagesag for 250 W resistive load shown in Fig. 7(a), the pulsationof load voltage is suppressed enough. However, the steadystate error is not eliminated enough (vL

∗ = 100 Vrms, vL =

87.6 Vrms), and the pulsation of source current cannot be sup-pressed (THD = 27.9%). Figure 7(b) shows the waveformsfor lighter load condition than the case of Fig. 7(a). FromFig. 7(b), it is clear that the THD of load voltage increasesfor the light load. Fig. 7(c) shows the waveforms for the casethat the variation of source voltage is 20% (mild compared tothe case of Fig. 7(a)). From Fig. 7(c), it is clear that the THDof load voltage increases when the source voltage variation issmall. These experimental results match the results examinedin the section 3.

Figure 7(d) shows the waveforms for the case that the loadis lighter and the variation of source voltage is smaller thanthose of Fig. 7(a). In this case, the THD of load voltage hasthe worst value in Fig. 7. Besides, the results in the case of40% and 20% voltage sags for 100 W resistive-inductive loadare shown in Figs. 7(e) and (f). One can find that tendenciesof THD and steady state error of load voltage are almost same



(a) 40% voltage sag, 250 W resistive load (b) 40% voltage sag, 100 W resistive load

(c) 20% voltage sag, 250 W resistive load (d) 20% voltage sag, 100 W resistive load

(e) 40% voltage sag, 100 W resistive – inductive load (f) 20% voltage sag, 100 W resistive – inductive load

Fig. 8. Experimental waveforms of compensator with proposed synchronous frame control. (Steady state)

as the results of resistive load.Experimental waveforms for the system with proposed

synchronous frame control are shown in Fig. 8. From Fig. 8,experimental waveforms demonstrate that proposed syn-chronous frame control can compensate for the voltage sagwith lower steady state error and lower THD of load voltagethan those for the system with stationary frame control.

Furthermore, when the 40% instantaneous voltage sag/swell occurred, operations of the system were investigatedfor 250 W resistive load. Experimental waveforms for thesystem with stationary frame control are shown in Fig. 9. Asfar as the voltage sags, the pulsation of load voltage is sup-pressed in Fig. 9(a). However, for the voltage swells, the pul-sation is not suppressed enough in Fig. 9(b). Experimentalwaveforms for the system with synchronous frame controlmethod are shown in Fig. 10. For the voltage sags and swells,the synchronous frame control can suppress the pulsation ofload voltage and source current better than the stationaryframe control. In Fig. 10(a), the peak value of load voltageis 137.5 V at the time after one cycle from the start of thevoltage sag. In Fig. 10(b), the peak value of load voltage

is 141.0 V at the time after one cycle from the start of thevoltage swell. The proposed synchronous frame control canreduce the steady state error immediately.

Next, effects of sudden frequency change of source voltagewere investigated and the results are shown in Figs. 11 and12. The frequency was changed from 60 Hz to 63 Hz or from60 Hz to 57 Hz for 250 W resistive load, suddenly. The effectof sudden frequency change of the source voltage is not so se-vere. And the results demonstrate that for sudden frequencychange, proposed synchronous frame control can reduce theTHD better than the stationary frame control. And then, theeffect of line impedance on the control was also investigatedby simulation because the effect of inductance have alreadybeen included in the all experimental results. The results areshown in Figs. 13 and 14. From the figures, it is clear that theeffect of line inductance are very small.

5. Conclusions

In this paper, a synchronous frame control for a volt-age sag/swell compensator utilizing single-phase matrix con-verter was proposed. First, the configuration of the proposed



(a) 40% instantaneous voltage sag, 250 W resistive load (b) 40% instantaneous voltage swell, 250 W resistive load

Fig. 9. Experimental waveforms of compensator with conventional stationary frame control. (Instantaneousvoltage change)

(a) 40% instantaneous voltage sag, 250 W resistive load (b) 40% instantaneous voltage swell, 250 W resistive load

Fig. 10. Experimental waveforms of compensator with proposed synchronous frame control. (Instantaneousvoltage change)

(a) Frequency of source voltage change to 63 Hz, 250 W resistive load (b) Frequency of source voltage change to 57 Hz, 250 W resistive load

Fig. 11. Experimental waveforms of compensator with conventional stationary frame control. (Sudden fre-quency of source voltage)

(a) Frequency of source voltage change to 63 Hz, 250 W resistive load (b) Frequency of source voltage change to 57 Hz, 250 W resistive load

Fig. 12. Experimental waveforms of compensator with proposed synchronous frame control. (Sudden frequencychange of source voltage change)



(a) Without Ls, 250 W resistive load (b) With Ls ( = 27.3μH), 250 W resistive load

Fig. 13. Simulation waveforms of compensator with conventional stationary frame control. (Effect of the lineinductance)

(a) Without Ls, 250 W resistive load (b) With Ls ( = 27.3μH), 250 W resistive load

Fig. 14. Simulation waveforms of compensator with proposed synchronous frame control. (Effect of the lineinductance)

system and its operation were described. Next, the effectsof the degree of voltage sag and load variation on the sys-tem stability was analyzed using the transfer function. Fromthe loot loci, it was summarized that the larger the load re-sistance was, the poorer the system stability was, and thesmaller the variation of the source voltage was, the poorerthe system stability was. And also better stability of proposedsynchronously frame control was demonstrated.

Furthermore, the experimental waveforms of the systemwith the proposed synchronous frame control were comparedwith those of the system with the stationary frame control.These experimental results matched the results obtained fromthe loot loci. It is clear that the pulsation of load voltageincreases when the load is light and the variation of sourcevoltage is small, and also proposed synchronous frame con-trol can compensate for the voltage sag with lower steadystate error and lower THD of load voltage than those for thesystem with stationary frame control.

Finally, when the 40% instantaneous voltage sag/swell oc-curred, operations of the system were investigated for 250 Wresistive load. The experimental waveforms demonstratedthat the proposed synchronous frame control can suppress thesteady state error and the pulsation caused by the LC filterresonance better than the stationary frame control.

References

( 1 ) K. Yamamoto, K. Ikeda, Y. Tsurusaki, and M. Ikeda: “Characteristics of Volt-age Sag/Swell Compensator Utilizing Single-Phase Matrix Converter”, Jour-nal of International Conference on Electrical Machines and Systems, Vol.2,No.4, pp.447–453 (2013)

( 2 ) D. Pan, X. Ruan, C. Bao, W. Li, and X. Wang: “Capacitor-Current-FeedbackActive Damping With Reduced Computation Delay for Improving Robust-ness of LCL-Type Grid-Connected Inverter”, IEEE Trans. Power Electron.,Vol.29, No.7, pp.3414–3427 (2014)

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( 4 ) K. Yamamoto, Y. Tsurusaki, S. Ehira, and M. Ikeda: “Suppression of Com-pensation Voltage Pulsations for Voltage Sag/Swell Compensator UtilizingSingle-Phase Matrix Converter”, International Conference on Electrical Ma-chines and Systems 26P11-10 (2015)

( 5 ) D. Dong, T. Thacker, R. Burgos, F. Wang, and D. Boroyevich: “On ZeroSteady-State Error Voltage Control of Single-Phase PWM Inverters With Dif-ferent Load Types”, IEEE Trans. Power Electron., Vol.26, No.11, pp.3285–3297 (2011)

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( 7 ) Y. Hirase, O. Noro, E. Yoshimura H. Nakagawa, K. Sakamoto, and Y.Shindo: “Virtual Synchronous Generator Control with Double DecoupledSynchronous Reference Frame for Single-Phase Inverter”, IEEJ Journal IA,Vol.4, No.3, pp.143–151 (2015)

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Kichiro Yamamoto (Senior Member) received the B.Eng.and M.Eng. degrees from Kagoshima University,Kagoshima, Japan, and the Ph.D. degree fromKyushu University, Fukuoka, Japan, in 1987, 1989,and 1996, respectively. He was a Research Associateat Kagoshima National College of Technology, Kago-shima, from 1989 to 1993. Since 1993, he has beenwith the Department of Electrical and Electronics En-gineering, Kagoshima University, where he is a Pro-fessor. His research interests are ac motor drives and

power converter circuits. He is a member of Institute of Electrical EngineersJapan and Institute of Electrical and Electronics Engineers.

Sho Ehira (Member) received the B.Eng. degree from KagoshimaUniversity, Kagoshima, Japan in 2015. Since 2015,he has been a master student of Department of Elec-trical and Electronics Engineering, Kagoshima Uni-versity. His student research dealt with single phasematrix converter and voltage sag compensation. He isa member of Institute of Electrical Engineers Japan.

Minoru Ikeda (Non-member) graduated from Kanoya technical se-nior high school in 1975. Since 1975, he has beenwith the Department of Electrical and Electronics En-gineering, Kagoshima University, where he is a se-nior technical specialist. His research interest is in-verter drive of electric motors.


synchronous frame control for voltage sag swell

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