ICICCE0324
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This paper introduces a synchronous frame hysteresis controller for a three-phase uninterruptible power supply (UPS) using a Z-source inverter, enhancing dynamic response and minimizing control time delays. The proposed control method effectively reduces total harmonic distortion to 17.11% under distorted loads and maintains voltage regulation across various load conditions. The controller's design allows for high reliability and efficiency while addressing the complexities of traditional methods.
![Synchronous Frame Hysteresis Controller for Three
Phase UPS Based on Z-Source Inverter
M.Lakshmana Kumar1
PG Scholar,
1
Bannari Amman Institute of Technology
lakshmanakumar2010@gmail.com
K.Chitra2
Assistant Professor
2
Bannari Amman Institute of Technology
E-mail:chitrak@bitsathy.ac.in
Abstract-This paper presents the novel synchronous frame hysteresis controller for three phase Uninterruptible Power Supply
(UPS)based on Z-Source Inverter (ZSI). The proposedsynchronous frame approach minimizes the hysteresis control time delay to
onesixthof the fundamental period such that the dynamic response is significantly improved. The hysteresis band currentcontroller
determines the switching signals, and the algorithm based onanextension of Synchronous Reference Frame(SRF) Theory (d-q-0) is
used to determine thesuitable current reference signals. A filter is applied to further enhance the accuracy of steadystate tracking.Low
total harmonic distortion has been achieved under heavilydistorted nonlinear load and unbalanced load.The ZSI provides agreat
alternative with lower cost, higher reliability and higher efficiency.
Index Terms- CSI, DQ algorithm,Hysteresis Controller,Uninterruptible power supply, VSI, ZSI,
1. INTRODUCTION
Uninterruptable power supply (UPS) is used to supply
very high-quality,continuous, and disturbance-free ac power to
critical loads such as medical equipment,home appliances,
computers, and communication systems[15]. A good UPS system
requires not onlyexcellent steady-state performance in terms of
voltage regulation, switching losses and Total
HarmonicDistortions (THD) but also a fast transientresponse
during load step change.UPS that differ from an emergency
power system or standby generator in that it will provide
instantaneous protection from input power interruptions by
supplying the energy stored in the batteries. UPS is an electrical
apparatus that providesemergency power to a load when the main
power fails.
Some highperformancefeedback control techniques such
asmultiloopstate feedback control,dead-beat control and
predictive control have been proposed and investigated“[7,8]”.
Highqualityoutput voltage and fast dynamic responsehave been
demonstrated with thesemethods. The controllerbandwidth is
limited due todigital implementation.Selective harmonic
compensation employs the idea that eachorder of
harmonicdistortions can be compensated individually.This
technique is targeted at excellentsteady-state outputand it is
implementable either in the stationary frame or insynchronous
rotating frames[14].
____________________________________
M.Lakshmanakumar is currently pursuing Master of Engineering in
Bannari Amman Institute of Technology, India,Ph:9578228161,
E-mail:lakshmanakumar2010@gmail.com
K.Chitra is currently working as Assistant Professor in Bannari Amman
Institute of technology,India,Ph:9976719928,
E-mail: chitrak@bitsathy.ac.in
Dr.A.Jeevanandham is currently working as Professor in Bannari Amman
Institute of technology,India,Ph:9843688895
E-mail: jeeva932@gmail.com
IJTET©2015
Fig.1 Block Diagram of the Controller.
2. HYSTERESIS CONTROLLER
Hysteresis controllers utilize some type of hysteresis in
the comparison of the line currents to the current
references[2].The hysteresis control schemeprovides excellent
dynamic performance, because it acts quickly.Due to the
advances of power electronics and inverter topology, the
currentcontrolledvoltage-sourcepulsewidth
modulated(PWM)inverterisusuallypreferredfor quick response
and accurate control[3].
These power devices may be applicable in ac motors,
active filters, and Uninterruptible Power Supply (UPS). Current
controlled PWM inverter offers substantial advantages
ineliminating stator dynamics in high performance AC
drives[5].One version of hysteresis control, uses three
independent controllers, one foreach phase.The control for one
inverter leg is shown in Fig.2[6].When the line currentbecomes
greater (less) than the current reference by the hysteresis
band,theinverter leg is switched in the negative (positive)
direction, which providesaninstantaneous current limit if the
neutral is connected to the dc bus midpoint.
85](https://image.slidesharecdn.com/icicce0324-150502053729-conversion-gate02/85/ICICCE0324-1-320.jpg)
![Therefore, the hysteresis band specifies the maximum current
ripple as summing neither controller nor inverter delays[1].The
inverter switching frequency will vary over a fundamental
inverter periodsince the current ripple is specified by the
hysteresis band. In a system without a neutral connection, the
actual current error can reachdouble the hysteresis band assuming
the three-phase current reference sums tozero[10].
Fig.2 Circuit for Hysteresis Current Controller
3. SYNCHRONOUS FRAME CONTROL ALGORITHM
In the SRF control, the load current signals are
transformed into the conventional rotating frame d-q. If theta is
the transformation angle, the transformation is defined by:
xd
xq
x0
=
cos(⍬) cos(⍬ −
2π
3
) cos(⍬ −
4π
3
)
−sin(⍬) −sin(⍬ −
2π
3
) −sin(⍬ −
4π
3
)
1
2
1
2
1
2
xa
xb
x0
(1)
Fig.3 shows the basic configuration of synchronous
reference frame [13]. In the SRF is atime varying anglethat
represents the angular position of the referenceframe which
isrotating at constant speed insynchronism with the three phase ac
voltages. In the SRF is a time varying angle that represents the
angular position of the reference framewhich is rotating at
constant speed in synchronism with the three phase ac voltages
[16]. In this case thespeedof the reference frame is practically
constant, that is, the method behaves as if the reference frame
moment of inertia is infinite.
Fig.3 Principle of Synchronous Frame Theory
This is accomplished using high pass filters (HPF).
Inspite of a high pass filter, allow low pass filter is used to obtain
the reference source current in d-q coordinates[4].
IJTET©2015
Fig.4 Block Diagram of Synchronous Frame DQ Extraction
Unbalanced and sinusoidal mains voltage conditions
withangle θ is a uniformlyincreasing function of time.This
transformation angle is sensitive to voltageharmonicsand
unbalance; therefore dθ/dt may not beconstant over a mains
period[9]. With thistransformation the direct current component is
iα
iβ
= C
Ia
Ib
Ic
(2)
id
iq
=
cos ⍬ sin ⍬
− sin ⍬ cos ⍬
iα
iβ
(3)
where ⍬ = tan−1 vβ
vα
id
iq
=
1
vα
2+vβ
2
vα vβ
−vβ vα
iα
iβ
(4)
Icomp ,a
Icomp ,b
Icomp ,c
= [c]T
iα
iβ
(5)
The fundamentalcurrents of the d-q components are now dc
values. Theharmonics appear like ripple. Harmonic isolationof the
d-q transformed signal isachieved byremoving the dc offset [11].
4. SIMULATION AND RESULTS
The Fig.5 shows the simulation of Synchronous frame
hysteresis controlled Z-Source inverter for UPS applications. The
input DC voltage of 100V is given to the three phase inverter
through the impedance network. The current from the inverter is
given to the DQ extraction frame in order to increase the dynamic
response of the system and to reduce the switching frequency of
the hysteresis current controller.
86](https://image.slidesharecdn.com/icicce0324-150502053729-conversion-gate02/85/ICICCE0324-2-320.jpg)
![REFERENCES
[1] Abdel-Rahim N.M and Quaicoe .J.E, “Analysis and design of a
multiple feedback loop control strategy for single-phase
voltage-source UPSinverters,” IEEE Trans. Power Electron.,
vol. 11, no. 4, pp. 532–541, Jul.1996.
[2] Andrea Tilli and Alberto Tonielli,”Sequential Design of
Hysteresis Current Controller for Three-Phase Inverter”,IEEE
Transactions On Industrial Electronics, Vol. 45, No. 5, October
1998
[3] Casaravilla .G, Salvia .A, Briozzo .C and Watanabe .E,”Control
strategies of selective harmonic current shunt active
filter”,IEEE Proc.-Gener. Trunsm.Distrib., Vol. 149, No. 2,
December 2002
[4] Escobar .G, Valdez .A.A, Leyva-Ramos .J, and Mattavelli .P,
“Repetitive based controller for a UPS inverter to compensate
unbalance and harmonic distortion,” IEEE Trans. Ind.
Electron., vol. 54, no. 1, pp. 504–510, Feb.2007.
[5] FengGuo, Lixing Fu, Chien-HuiLin,Cong Li, Student,
Woongchul Choi, and Jin Wang, “Development of an 85-kW
Bidirectional Quasi-Z-Source Inverter With DC-Link Feed-
Forward Compensation for Electric Vehicle Applications”
IEEE Transactions On Power Electronics, Vol. 28, No. 12,
December 2013
[6] Gerardo Escobar, Perla G. Hernandez-Briones, Panfilo R.
Martinez,Michael Hernandez-Gomez, and Raymundo E.
Torres-Olguin,” A Repetitive-Based Controller for the
Compensation of 6n±1 Harmonic Components”, IEEE
Transactions On Industrial Electronics, Vol. 55, No. 8, August
2008.
[7] Kamran .F and Habetler .T.G, “A novel on-line UPS with
universal filtering capabilities,” IEEE Trans. Power Electron.,
vol. 13, no. 3, pp. 410–418, May 1998.
[8] Kim .E, Kwon .J, Park .J, and Kwon.B, “Practical control
implementation of a three-to single-phase online UPS,”IEEE
Trans. Ind. Electron., vol. 55,no. 8, pp. 2933–2942, Aug. 2008.
[9] Long Huang, Ming Zhang, Lijun Hang, Wenxi Yao, and
ZhengyuLu,”A Family of Three-Switch Three-State Single-
Phase Z-Source Inverters”, IEEE Transactions On Power
Electronics, Vol. 28, No. 5, May 2013
[10] Miao Zhu,KunYu, and Fang Lin Luo,” Switched Inductor Z-
Source Inverter” IEEE Transactions On Power Electronics,
Vol. 25, No. 8, August 2010
[11] Naser M. Abdel-Rahim and John E. Quaicoe,” Analysis and
Design of a Multiple Feedback Loop Control Strategy for
Single-phase Voltage- Source UPS Inverters”, IEEE
Transactions On Power Electronics, Vol. 11, No. 4, July 1996.
[12] Poh Chiang Loh, Michael John Newman, Daniel Nahum
Zmood and Donald Grahame Holmes,” A Comparative
Analysis of Multiloop Voltage Regulation Strategies for Single
and Three-Phase UPS Systems”, IEEE Transactions On Power
Electronics, Vol. 18, No. 5, September 2003.
[13] ParagKanjiya, Bhim Singh, Ambrish Chandra, and Kamal Al-
Haddad,”SRF Theory Revisited to Control Self-Supported
Dynamic Voltage Restorer (DVR) for Unbalanced and
Nonlinear Loads”,IEEE Transactions On Industry Applications,
Vol. 49, No. 5, September/October2013.
[14] Ryan .M.J, Brumsickle .W.E, and Lorenz .R.D, “Control
topologyoptions for single-phase UPS inverters,”IEEE Trans.
Ind. Appl., vol. 33,no. 2, pp. 493–501, Mar./Apr. 1997.
IJTET©2015
[15] Shuai Jiang, Dong Cao, YuanLi, Jianfeng Liu, and Fang
ZhengPeng, “Low-THD, Fast-Transient, and Cost-Effective
Synchronous-Frame Repetitive Controller for Three-Phase UPS
Inverters”, IEEE Transactions On Power Electronics, Vol. 27,
No. 6, June 2012
[16] Tomas Hornik and Q. C. Zhong, “A current-control strategy for
voltage-source inverters in microgrids based on
H∞andrepetitive control,”IEEETrans.Power Electron., vol. 26,
no. 3, pp. 943–952, Mar. 2011.
[17] Yang.S, Ding .X, Liu .J, and Qian .Z, “Analysis and design of a
costeffective voltage feedback control strategy for EPS
inverters,” in Proc. IEEE Power Electron. Spec. Conf., 2007,
pp. 477–482.
89](https://image.slidesharecdn.com/icicce0324-150502053729-conversion-gate02/85/ICICCE0324-5-320.jpg)
ICICCE0324
- 1. Synchronous Frame Hysteresis Controller for Three Phase UPS Based on Z-Source Inverter M.Lakshmana Kumar1 PG Scholar, 1 Bannari Amman Institute of Technology lakshmanakumar2010@gmail.com K.Chitra2 Assistant Professor 2 Bannari Amman Institute of Technology E-mail:chitrak@bitsathy.ac.in Abstract-This paper presents the novel synchronous frame hysteresis controller for three phase Uninterruptible Power Supply (UPS)based on Z-Source Inverter (ZSI). The proposedsynchronous frame approach minimizes the hysteresis control time delay to onesixthof the fundamental period such that the dynamic response is significantly improved. The hysteresis band currentcontroller determines the switching signals, and the algorithm based onanextension of Synchronous Reference Frame(SRF) Theory (d-q-0) is used to determine thesuitable current reference signals. A filter is applied to further enhance the accuracy of steadystate tracking.Low total harmonic distortion has been achieved under heavilydistorted nonlinear load and unbalanced load.The ZSI provides agreat alternative with lower cost, higher reliability and higher efficiency. Index Terms- CSI, DQ algorithm,Hysteresis Controller,Uninterruptible power supply, VSI, ZSI, 1. INTRODUCTION Uninterruptable power supply (UPS) is used to supply very high-quality,continuous, and disturbance-free ac power to critical loads such as medical equipment,home appliances, computers, and communication systems[15]. A good UPS system requires not onlyexcellent steady-state performance in terms of voltage regulation, switching losses and Total HarmonicDistortions (THD) but also a fast transientresponse during load step change.UPS that differ from an emergency power system or standby generator in that it will provide instantaneous protection from input power interruptions by supplying the energy stored in the batteries. UPS is an electrical apparatus that providesemergency power to a load when the main power fails. Some highperformancefeedback control techniques such asmultiloopstate feedback control,dead-beat control and predictive control have been proposed and investigated“[7,8]”. Highqualityoutput voltage and fast dynamic responsehave been demonstrated with thesemethods. The controllerbandwidth is limited due todigital implementation.Selective harmonic compensation employs the idea that eachorder of harmonicdistortions can be compensated individually.This technique is targeted at excellentsteady-state outputand it is implementable either in the stationary frame or insynchronous rotating frames[14]. ____________________________________ M.Lakshmanakumar is currently pursuing Master of Engineering in Bannari Amman Institute of Technology, India,Ph:9578228161, E-mail:lakshmanakumar2010@gmail.com K.Chitra is currently working as Assistant Professor in Bannari Amman Institute of technology,India,Ph:9976719928, E-mail: chitrak@bitsathy.ac.in Dr.A.Jeevanandham is currently working as Professor in Bannari Amman Institute of technology,India,Ph:9843688895 E-mail: jeeva932@gmail.com IJTET©2015 Fig.1 Block Diagram of the Controller. 2. HYSTERESIS CONTROLLER Hysteresis controllers utilize some type of hysteresis in the comparison of the line currents to the current references[2].The hysteresis control schemeprovides excellent dynamic performance, because it acts quickly.Due to the advances of power electronics and inverter topology, the currentcontrolledvoltage-sourcepulsewidth modulated(PWM)inverterisusuallypreferredfor quick response and accurate control[3]. These power devices may be applicable in ac motors, active filters, and Uninterruptible Power Supply (UPS). Current controlled PWM inverter offers substantial advantages ineliminating stator dynamics in high performance AC drives[5].One version of hysteresis control, uses three independent controllers, one foreach phase.The control for one inverter leg is shown in Fig.2[6].When the line currentbecomes greater (less) than the current reference by the hysteresis band,theinverter leg is switched in the negative (positive) direction, which providesaninstantaneous current limit if the neutral is connected to the dc bus midpoint. 85
- 2. Therefore, the hysteresis band specifies the maximum current ripple as summing neither controller nor inverter delays[1].The inverter switching frequency will vary over a fundamental inverter periodsince the current ripple is specified by the hysteresis band. In a system without a neutral connection, the actual current error can reachdouble the hysteresis band assuming the three-phase current reference sums tozero[10]. Fig.2 Circuit for Hysteresis Current Controller 3. SYNCHRONOUS FRAME CONTROL ALGORITHM In the SRF control, the load current signals are transformed into the conventional rotating frame d-q. If theta is the transformation angle, the transformation is defined by: xd xq x0 = cos(⍬) cos(⍬ − 2π 3 ) cos(⍬ − 4π 3 ) −sin(⍬) −sin(⍬ − 2π 3 ) −sin(⍬ − 4π 3 ) 1 2 1 2 1 2 xa xb x0 (1) Fig.3 shows the basic configuration of synchronous reference frame [13]. In the SRF is atime varying anglethat represents the angular position of the referenceframe which isrotating at constant speed insynchronism with the three phase ac voltages. In the SRF is a time varying angle that represents the angular position of the reference framewhich is rotating at constant speed in synchronism with the three phase ac voltages [16]. In this case thespeedof the reference frame is practically constant, that is, the method behaves as if the reference frame moment of inertia is infinite. Fig.3 Principle of Synchronous Frame Theory This is accomplished using high pass filters (HPF). Inspite of a high pass filter, allow low pass filter is used to obtain the reference source current in d-q coordinates[4]. IJTET©2015 Fig.4 Block Diagram of Synchronous Frame DQ Extraction Unbalanced and sinusoidal mains voltage conditions withangle θ is a uniformlyincreasing function of time.This transformation angle is sensitive to voltageharmonicsand unbalance; therefore dθ/dt may not beconstant over a mains period[9]. With thistransformation the direct current component is iα iβ = C Ia Ib Ic (2) id iq = cos ⍬ sin ⍬ − sin ⍬ cos ⍬ iα iβ (3) where ⍬ = tan−1 vβ vα id iq = 1 vα 2+vβ 2 vα vβ −vβ vα iα iβ (4) Icomp ,a Icomp ,b Icomp ,c = [c]T iα iβ (5) The fundamentalcurrents of the d-q components are now dc values. Theharmonics appear like ripple. Harmonic isolationof the d-q transformed signal isachieved byremoving the dc offset [11]. 4. SIMULATION AND RESULTS The Fig.5 shows the simulation of Synchronous frame hysteresis controlled Z-Source inverter for UPS applications. The input DC voltage of 100V is given to the three phase inverter through the impedance network. The current from the inverter is given to the DQ extraction frame in order to increase the dynamic response of the system and to reduce the switching frequency of the hysteresis current controller. 86
- 3. Fig.5 Simulation Diagram of Proposed Method Thepulses generated from the hysteresis current controller are given to the three phaseinverter. Fig.6 Simulation Diagram of DQ Extraction The simulation diagram of DQ extraction frame is shown in the Fig 6. Theload voltage is compared with the reference voltage and the error signal is amplifiedwith the PI controller. The output of the PI controller is given to the Low pass filter inthe DQ transformation block. The output current waveform shows the dynamicresponse of the system. IJTET©2015 Fig.7 Simulation of Hysteresis Controller The simulation diagram of the Hysteresis Current Controller is shown in Fig 7.The output current of DQ extraction and the actual current is given as input to thecontroller. The error signal is passed through the hysteresis band and pulses aregenerated. 4.1 OUTPUT WAVEFORMS Fig.8 Current waveform after DQ Extraction Fig.9 Reference Current Given To the Hysteresis Controller 87
- 4. Fig.10 Actual Current Waveform for Hysteresis Controller Fig.11 Pulse Generated From the Hysteresis Controller Fig.12 Output Voltage Waveform IJTET©2015 Fig.13 Output Current Waveform 4.2 THD ANALYSIS OF THE SYSTEM Fig.13 THD analysis of the system The output waveforms of the Synchronous frame hysteresis controlled Z-sourceinverter at various stages are shown. The output current from the DQ extraction showsthe dynamic response of the system. The pulses generated from the hysteresiscontroller are shown in Fig 11. THD analysis of the system is carried out whichresults in 17.11%. 5. CONCLUSION A new synchronous frame hysteresis control Strategy has been developed forthree phase UPS inverters. By designing the Hysteresis control to compensate theharmonics in three different synchronous rotating frames, all the stationary frameharmonic distortions are reduced considerably. Therefore, the voltage regulationrequirement can be satisfied under general load conditions (linear and non-linear loads). But this controlstructure also hassome drawbacks, such as the destructionof the inverter if its highest switchingfrequency is not limitedand the interdependence of the load phases. In order to limitthis frequency in a single-phase case and extend this result to the three-phase case througha transformation (were dq transformation is employed)avoiding thecomplexity.Hysteresis current controller results high dynamic response,easy toimplementand eliminates the complex calculations of the existing methods. The Totalharmonic distortion of the proposed method achieved is 17.11%. 88
- 5. REFERENCES [1] Abdel-Rahim N.M and Quaicoe .J.E, “Analysis and design of a multiple feedback loop control strategy for single-phase voltage-source UPSinverters,” IEEE Trans. Power Electron., vol. 11, no. 4, pp. 532–541, Jul.1996. [2] Andrea Tilli and Alberto Tonielli,”Sequential Design of Hysteresis Current Controller for Three-Phase Inverter”,IEEE Transactions On Industrial Electronics, Vol. 45, No. 5, October 1998 [3] Casaravilla .G, Salvia .A, Briozzo .C and Watanabe .E,”Control strategies of selective harmonic current shunt active filter”,IEEE Proc.-Gener. Trunsm.Distrib., Vol. 149, No. 2, December 2002 [4] Escobar .G, Valdez .A.A, Leyva-Ramos .J, and Mattavelli .P, “Repetitive based controller for a UPS inverter to compensate unbalance and harmonic distortion,” IEEE Trans. Ind. Electron., vol. 54, no. 1, pp. 504–510, Feb.2007. [5] FengGuo, Lixing Fu, Chien-HuiLin,Cong Li, Student, Woongchul Choi, and Jin Wang, “Development of an 85-kW Bidirectional Quasi-Z-Source Inverter With DC-Link Feed- Forward Compensation for Electric Vehicle Applications” IEEE Transactions On Power Electronics, Vol. 28, No. 12, December 2013 [6] Gerardo Escobar, Perla G. Hernandez-Briones, Panfilo R. Martinez,Michael Hernandez-Gomez, and Raymundo E. Torres-Olguin,” A Repetitive-Based Controller for the Compensation of 6n±1 Harmonic Components”, IEEE Transactions On Industrial Electronics, Vol. 55, No. 8, August 2008. [7] Kamran .F and Habetler .T.G, “A novel on-line UPS with universal filtering capabilities,” IEEE Trans. Power Electron., vol. 13, no. 3, pp. 410–418, May 1998. [8] Kim .E, Kwon .J, Park .J, and Kwon.B, “Practical control implementation of a three-to single-phase online UPS,”IEEE Trans. Ind. Electron., vol. 55,no. 8, pp. 2933–2942, Aug. 2008. [9] Long Huang, Ming Zhang, Lijun Hang, Wenxi Yao, and ZhengyuLu,”A Family of Three-Switch Three-State Single- Phase Z-Source Inverters”, IEEE Transactions On Power Electronics, Vol. 28, No. 5, May 2013 [10] Miao Zhu,KunYu, and Fang Lin Luo,” Switched Inductor Z- Source Inverter” IEEE Transactions On Power Electronics, Vol. 25, No. 8, August 2010 [11] Naser M. Abdel-Rahim and John E. Quaicoe,” Analysis and Design of a Multiple Feedback Loop Control Strategy for Single-phase Voltage- Source UPS Inverters”, IEEE Transactions On Power Electronics, Vol. 11, No. 4, July 1996. [12] Poh Chiang Loh, Michael John Newman, Daniel Nahum Zmood and Donald Grahame Holmes,” A Comparative Analysis of Multiloop Voltage Regulation Strategies for Single and Three-Phase UPS Systems”, IEEE Transactions On Power Electronics, Vol. 18, No. 5, September 2003. [13] ParagKanjiya, Bhim Singh, Ambrish Chandra, and Kamal Al- Haddad,”SRF Theory Revisited to Control Self-Supported Dynamic Voltage Restorer (DVR) for Unbalanced and Nonlinear Loads”,IEEE Transactions On Industry Applications, Vol. 49, No. 5, September/October2013. [14] Ryan .M.J, Brumsickle .W.E, and Lorenz .R.D, “Control topologyoptions for single-phase UPS inverters,”IEEE Trans. Ind. Appl., vol. 33,no. 2, pp. 493–501, Mar./Apr. 1997. IJTET©2015 [15] Shuai Jiang, Dong Cao, YuanLi, Jianfeng Liu, and Fang ZhengPeng, “Low-THD, Fast-Transient, and Cost-Effective Synchronous-Frame Repetitive Controller for Three-Phase UPS Inverters”, IEEE Transactions On Power Electronics, Vol. 27, No. 6, June 2012 [16] Tomas Hornik and Q. C. Zhong, “A current-control strategy for voltage-source inverters in microgrids based on H∞andrepetitive control,”IEEETrans.Power Electron., vol. 26, no. 3, pp. 943–952, Mar. 2011. [17] Yang.S, Ding .X, Liu .J, and Qian .Z, “Analysis and design of a costeffective voltage feedback control strategy for EPS inverters,” in Proc. IEEE Power Electron. Spec. Conf., 2007, pp. 477–482. 89