再生能源是廣泛用來降低石化能源及核能依賴的方案。隨著越來越多的再生能源裝置於電力系統中，電力公司開始要求這些再生能源轉換器於電網故障其間保持併網操作並注入特定的實功或（和）虛功電流。低電壓穿越要求對於離岸風場的轉換器是一個挑戰，這些電力轉換器需於劇烈變動及不平衡的電網電壓中保持控制穩定，並確保故障期間不會觸發系統保護措施而導致系統跳脫電網。
低電壓穿越期間，不平衡的電網電壓與轉換器輸出電流在直流側電容會產生實功率漣波。即使有文獻提出利用負序電流注入降低實功率漣波，但它會導致很大的輸出峰值電流。故，結合限電流控制保障功率元件可靠度與降低實功率漣波的技術在本論文被提出。
當電網電壓故障發生時，瞬間變化的電壓會導致變壓器發生磁通偏移。磁通偏移在高效率變壓器的衰減非常得慢。當電網電壓回歸時，瞬間增加的電壓與變壓器磁通偏移產生非常大的湧浪電流。故，本文提出於低電壓穿越期間結合限電流與磁通補償控制器以加速磁通衰減。
中性點鉗位轉換器的多階層輸出電壓特性非常適用於高功率的風機系統。然而轉換器的動態操作（瞬間改變的電壓或電流）會導致中性點電位產生偏移。此外，低電壓穿越的虛功操作會大幅度降低傳統中性點平衡控制的平衡能力。本文推出一個中性點控制技術加速於虛功系統的控制動態。
在離岸風場中，風機轉換器經由長約50公里的長傳輸線連接至電網。轉換器藉由降低取樣頻率降低功率損失，但這導致系統發生增益性共振的風險。本文提出一個主動阻尼控制器降低系統發生共振的機率並分析了電流控制器的內部及外部穩定度。
離岸風場通常會裝置虛功補償器調節整個系統的電壓，確保系統電壓保持在穩定的區間。由於離岸風場的裝置電壓較高，星接的串接式模組化轉換器常使用於這種電壓層級的應用。藉由負序電流注入及零序電壓注入常被使用於相間電容電壓平衡控制，但他們增加系統發生過電流或過調變的風險。本論文提出一電壓平衡控制維持模組直流電壓平衡，並藉由調節負序電流及零序電壓的比例避免過調變或過電流發生。
本文提出的技術以一個丹麥離岸風場為應用案例。控制概念在本論文會依序各自討論，並藉由模擬及實驗平台驗證本論文提出的控制方法。

The offshore wind farm is popularly installed in the power system to mitigate the nuclear energy and petrochemical energy. With the increasing of the distributed energy resources converter being installed in the power system, the grid operator imposes the low-voltage ride-through requirement on such systems to inject the specific active and/or reactive current during the fault. The unbalanced grid voltage leads to several control challenges in an offshore wind farm system.

In low-voltage ride-through operation, the unbalanced grid voltages and converter output currents lead to active power ripple in the DC capacitor. Although the negative sequence current injection is employed to mitigate the power ripple, it significantly increases the output peak current. Therefore, the peak current limit control integrating with the active power ripple mitigation technique is presented in this thesis to secure the stress on the power transistors and the DC capacitor.

As grid fault occurs, the sudden reduction of grid voltage results in flux deviation of the step-up transformer. The magnetic flux deviation decays very slowly due to high efficiency nature of the transformer, and hence the flux deviation often generates the huge inrush current on the grid-side of the transformer as grid fault restore to normal level. Therefore, the inrush current mitigation integrating with the peak current management is provided in this thesis to accelerate the flux decay.

The neutral-point-clamped converter is well employed to the high power wind power converter for the multilevel output voltage. However, the sudden change of grid voltage and output current result in voltage deviation in the neutral point. Besides, the reactive current injection in low-voltage ride-through reduces the effectiveness of conventional neutral point voltage balancing control. This thesis provides a neutral point voltage balancing control to accelerate the balance dynamic under a reactive power control system.

The offshore wind farm connects to the utility grid through a long transmission cable, where the length of the transmission cable is almost $50$km in general. Moreover, the slow sampling frequency (switching frequency) to reduce the power loss in high power converter increases the risk to amplify the resonance in the system. Therefore, an active damping technique is presented in this study and both of the the current control and external stability are analyzed and discussed.

In offshore wind farm, the reactive power regulator is usually installed in the system to secure the grid voltage is in normal region. The modular multilevel cascaded converter with single-star bridge-cell is very suitable for medium-voltage reactor application. The DC capacitor voltage balancing control is one of the important controls to maintain the system operation. The negative-sequence current and zero-sequence voltage injection are the method to balance the DC capacitor voltage, but they usually result in over-current and over-modulation. This paper provides a DC capacitor voltage balancing control by both of the negative-sequence current and zero-sequence voltage injection with a weighting gain regulator to prevent the over-current and over-modulation during the fault operation.

An offshore wind farm in Denmark (Horns Rev) is an example for these proposed methods application. The control concept of the proposed methods will be introduced, respectively. Finally, the proposed methods will be verified by experiment and simulation results.

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 LVRT operation on wind power converter . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Fundamental current injection technique . . . . . . . . . . . . . . . . . 2
1.1.2 Inrush current reduction technique . . . . . . . . . . . . . . . . . . . . 2
1.2 A novel neutral point voltage balancing control on three-level neutral-pointclamped
converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 An impedance-based stability analysis in a multiple-paralleled converter system 5
1.4 A DC capacitor voltage balancing control on star-connected modular-multilevel
converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Dissertation organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1 Current injection strategies during LVRT operation . . . . . . . . . . . . . . . 8
2.1.1 Additional current injection and active power ripple . . . . . . . . . . . 8
2.1.2 Peak current limit control and active ripple mitigation . . . . . . . . . . 9
2.1.3 The proposed current injection technique for LVRT operation . . . . . 9
2.2 Inrush current mitigation technique during LVRT operation . . . . . . . . . . . 10
2.2.1 Flux compensation technique in previous works . . . . . . . . . . . . . 10
2.2.2 The proposed inrush current mitigation technique for LVRT operation . 10
2.3 The neutral point voltage balancing control for three-level NPC converter . . . 11
2.3.1 The switching state and neutral point voltage balancing control . . . . . 11
2.3.2 The proposed neutral point voltage balancing control . . . . . . . . . . 12
2.4 Impedance-based stability analysis on the active damping technique . . . . . . 12
2.4.1 Impedance-based stability analysis . . . . . . . . . . . . . . . . . . . . 12
2.4.2 Active damping technique for LCL-filter system . . . . . . . . . . . . 13
2.5 The DC capacitor voltage balancing control on star-connected MMC converter 13
2.5.1 The zero sequence voltage injection and negative sequence current injection
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5.2 The proposed DC capacitor voltage balancing control . . . . . . . . . . 14
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 The Low-Voltage Ride-Through Technique for Grid-Connected ConvertersWith
Reduced Power Transistor Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 System configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 The active current and the reactive current requirements . . . . . . . . . . . . . 19
3.4 Operation principles of the proposed method . . . . . . . . . . . . . . . . . . . 21
3.4.1 Peak current limit control . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4.2 Active power ripple cancellation . . . . . . . . . . . . . . . . . . . . . 23
3.4.3 Implementation of proposed current injection strategy . . . . . . . . . 24
3.5 Laboratory test result and verification . . . . . . . . . . . . . . . . . . . . . . 31
3.5.1 Reactive current injection only . . . . . . . . . . . . . . . . . . . . . 31
3.5.2 Both active and reactive positive sequence current injections . . . . . . 32
3.5.3 The required current capacity of zero active ripple operation . . . . . . 33
3.6 Discussion of DC capacitance and transistor loss . . . . . . . . . . . . . . . . 33
3.6.1 The capacitance and the power loss of DC electrolytic capacitors . . . . 35
3.6.2 The loss of semiconductor power electronic devices . . . . . . . . . . . 39
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4 The Transformer Inrush Reduction Technique for Low-Voltage Ride-Through
Operation of Renewable Converters . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Fundamental active and reactive current strategy . . . . . . . . . . . . . . . . . 41
4.2.1 Converter voltages and currents . . . . . . . . . . . . . . . . . . . . . 43
4.2.2 LVRT with peak current limit . . . . . . . . . . . . . . . . . . . . . . 44
4.3 Proposed transformer flux mitigation method . . . . . . . . . . . . . . . . . . 44
4.3.1 Transformer circuit model . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3.2 The proposed method to mitigate the magnetic DC flux deviation . . . 50
4.3.3 Peak current control . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4 Laboratory test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4.1 Type-B 50% voltage reduction . . . . . . . . . . . . . . . . . . . . . . 53
4.4.2 Successive voltage reduction : 80% type-E →80% type-B . . . . . . 53
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5 A Modulation Technique for Neutral Point Voltage Control of the Three-Level
Neutral-Point-Clamped Converter . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2 System configuration and PWM strategy . . . . . . . . . . . . . . . . . . . . . 63
5.3 The NP potential charging analysis . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3.1 The NP potential charging by v∗
m and v0 . . . . . . . . . . . . . . . . . 67
5.3.2 The NP potential charging by γm . . . . . . . . . . . . . . . . . . . . . 68
5.4 The Proposed NPVB control . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.4.1 The γm selection strategy . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.5 NP voltage ripple mitigation analysis . . . . . . . . . . . . . . . . . . . . . . . 72
5.5.1 Application of three-phase three-wire system . . . . . . . . . . . . . . 72
5.5.2 Application of three-phase four-wire system . . . . . . . . . . . . . . . 73
5.6 Laboratory test results and analysis . . . . . . . . . . . . . . . . . . . . . . . . 74
5.6.1 Tested under three-phase three-wire system . . . . . . . . . . . . . . . 74
5.6.2 Tested under three-phase four-wire system . . . . . . . . . . . . . . . 78
5.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.7.1 Maximum NP charging analysis . . . . . . . . . . . . . . . . . . . . . 80
5.7.2 Power loss of power electronic semiconductor devices . . . . . . . . . 80
5.7.3 The output current performance . . . . . . . . . . . . . . . . . . . . . 82
5.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6 A Impedance-based Stability Analysis of the Active Damping Technique in the
Offshore Wind Farm Application . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2 Control block diagram and the System configuration . . . . . . . . . . . . . . 86
6.2.1 Offshore wind farm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.2.2 Long transmission cable modeling . . . . . . . . . . . . . . . . . . . . 89
6.2.3 Control block diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.3 The proposed virtual resistor technique . . . . . . . . . . . . . . . . . . . . . . 90
6.4 Stability analysis of the proposed active damping control . . . . . . . . . . . . 92
6.4.1 Passivity-based stability analysis . . . . . . . . . . . . . . . . . . . . . 92
6.4.2 The stability analysis of single-converter system . . . . . . . . . . . . 95
6.4.3 The stability analysis of multiple parallel-converter system . . . . . . . 97
6.5 Laboratory and simulation results . . . . . . . . . . . . . . . . . . . . . . . . 102
6.5.1 Laboratory experiment results . . . . . . . . . . . . . . . . . . . . . . 102
6.5.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.6 Dynamic performance and Rv regulation in the system . . . . . . . . . . . . . 103
6.6.1 Dynamic performance analysis . . . . . . . . . . . . . . . . . . . . . . 103
6.6.2 The stability of Rv regulation . . . . . . . . . . . . . . . . . . . . . . 105
6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7 A DC bus Voltage Balancing Technique for the Cascaded H-Bridge STATCOM
with Improved Reliability under Grid Faults . . . . . . . . . . . . . . . . . . . . 108
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7.2 System configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.3 System operation of MMCC-SSBC . . . . . . . . . . . . . . . . . . . . . . . . 112
7.3.1 Overall DC voltage control and reactive power control . . . . . . . . . 114
7.3.2 DC capacitor voltage balancing control . . . . . . . . . . . . . . . . . 114
7.4 Average power flow management . . . . . . . . . . . . . . . . . . . . . . . . . 115
7.5 The proposed phase cluster voltage balancing control strategies . . . . . . . . . 118
7.5.1 The converter output peak current management . . . . . . . . . . . . . 118
7.5.2 The application of modulation index management . . . . . . . . . . . . 119
7.6 Laboratory test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.6.1 Verification of peak current management . . . . . . . . . . . . . . . . 123
7.6.2 Verification of modulation index management . . . . . . . . . . . . . . 123
7.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
8 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
8.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
8.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
APPENDICES
Appendix A: Negative sequence current injection for the minimum active power
ripple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Appendix B: The definitions of voltage sags types . . . . . . . . . . . . . . . . . 131
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

[1] C.-T. Lee, C.-W. Hsu, and P.-T. Cheng, “A low-voltage ride-through technique for gridconnected
converters of distributed energy resources,” IEEE Transactions on Industry
Applications, vol. 47, no. 4, pp. 1821–1832, 2011.
[2] S.-F. Chou, C.-T. Lee, H.-C. Ko, and P.-T. Cheng, “A low-voltage ride-through method
with transformer flux compensation capability of renewable power grid-side converters,”
IEEE Transactions on Power Electronics, vol. 29, no. 4, pp. 1710–1719, 2014.
[3] E. Netz, “Grid code; high and extra high voltage,” E-One Netz GmbH, Bayreuth, vol. 4,
2006.
[4] A. of O.P. 12.2, “Restricted to the technical requirements of wind power and
photovoltage facilities(draft),” Red Electrica, October 2008. [Online]. Available:
http://www.ree.es.
[5] “Tranmission code 2007 ordinance on system services by wind energy
plants sdlwindv,” E.ON, EnBW, Aug 2007. [Online]. Available:
http://www.esb.ie/esbnetworks/en/downloads/Distribution-Code.pdf
[6] W. Bartels, F. Ehlers, K. Heidenreich, R. Huttner, H. Kuhn, T. Meyer, T. Kumm, J. Salzmann,
H. Schafer, and K. Weck, “Generating plants connected to the medium-voltage
network,” Technical Guideline of BDEW, 2008.
[7] “Supplement to the guideline on generating plants connected to the medium-voltage
network,” BDEW, January 2009. [Online]. Available: http://www.bdew.de
[8] Energinet, “Wind turbines connected to grids with voltages below 100 kv,” Regulation
TF 3.2.6, Denmark, 19 May 2010.
[9] M. Altın, O. Goksu, R. Teodorescu, P. Rodriguez, B.-B. Jensen, and L. Helle, “Overview
of recent grid codes for wind power integration,” in 12th International Conference on
Optimization of Electrical and Electronic Equipment. IEEE, 2010, pp. 1152–1160.
[10] P. Christiansen, K. K. Jørgensen, and A. G. Sørensen, “Grid connection and remote
control for the horns rev 150 mw offshore wind farm in denmark,” in Proceedings of the
2nd International Workshop on Transmission Networks for Offshore Wind Farms, 2000,
pp. 29–30.
[11] R. Wu, F. Blaabjerg, H. Wang, M. Liserre, and F. Iannuzzo, “Catastrophic failure and
fault-tolerant design of igbt power electronic converters-an overview,” in IECON 2013 -
39th Annual Conference of the IEEE Industrial Electronics Society. IEEE, 2013, pp.
507–513.
[12] M. L. Gasperi, “Life prediction modeling of bus capacitors in ac variable-frequency
drives,” IEEE Transactions on Industry Applications, vol. 41, no. 6, pp. 1430–1435,
2005.
[13] K. Lee, T. M. Jahns, T. A. Lipo, G. Venkataramanan, and W. E. Berkopec, “Impact of
input voltage sag and unbalance on dc-link inductor and capacitor stress in adjustablespeed
drives,” IEEE Transactions on Industry Applications, vol. 44, no. 6, pp. 1825–
1833, 2008.
[14] K. Lee, T. M. Jahns, G. Venkataramanan, and W. E. Berkopec, “Dc-bus electrolytic
capacitor stress in adjustable-speed drives under input voltage unbalance and sag conditions,”
IEEE Transactions on Industry Applications, vol. 43, no. 2, pp. 495–504, 2007.
[15] M. Bollen, “Voltage recovery after unbalanced and balanced voltage dips in three-phase
systems,” IEEE Transactions on Power Delivery, vol. 18, no. 4, pp. 1376–1381, Oct
2003.
[16] J. Pedra, L. Sainz, F. Corcoles, and L. Guasch, “Symmetrical and unsymmetrical voltage
sag effects on three-phase transformers,” IEEE Transactions on Power Delivery, vol. 20,
no. 2, pp. 1683–1691, April 2005.
[17] M. Hagiwara, P. V. Pham, and H. Akagi, “Calculation of dc magnetic flux deviation in
the converter-transformer of a self-commutated btb system during single-line-to-ground
faults,” IEEE Transactions on Power Electronics, vol. 23, no. 2, pp. 698–706, Mar. 2008.
[18] M. Steurer and K. Frohlich, “The impact of inrush currents on the mechanical stress of
high voltage power transformer coils,” IEEE Transactions on Power Eelivery, vol. 17,
no. 1, pp. 155–160, 2002.
[19] J. Faiz, B. M. Ebrahimi, and T. Noori, “Three-and two-dimensional finite-element computation
of inrush current and short-circuit electromagnetic forces on windings of a
three-phase core-type power transformer,” IEEE Transactions on Magnetics, vol. 44,
no. 5, pp. 590–597, 2008.
[20] D. Energy, “Anholt offshore wind farm,” 2014.
[21] A. Nabae, I. Takahashi, and H. Akagi, “A new neutral-point-clamped pwm inverter,”
IEEE Transactions on Industry Applications, no. 5, pp. 518–523, 1981.
[22] YasKawa Electric Corp. [Online]. Available: http://www.yaskawa.co.jp
[23] H. Akagi, “Classification, terminology, and application of the modular multilevel cascade
converter (mmcc),” IEEE Transactions on Power Electronics, vol. 26, no. 11, pp.
3119–3130, Nov. 2011.
[24] J. S. Lai and F. Z. Peng, “Multilevel converters-a new breed of power converters,” IEEE
Transactions on Industry Applications, vol. 32, no. 3, pp. 509–517, May./Jun. 1996.
[25] J. Rodriguez, J. S. Lai, and F. Z. Peng, “Multilevel inverters: a survey of topologies,
controls, and applications,” IEEE Transactions on Industrial Electronics, vol. 49, no. 4,
pp. 724–738, Aug. 2002.
[26] A. Marzoughi and H. Imaneini, “A new control strategy for cascaded h-bridge multilevel
converter to operate as a d-statcom,” in 2012 11th International Conference on
Environment and Electrical Engineering (EEEIC). IEEE, 2012, pp. 122–127.
[27] K. Sano and M. Takasaki, “A transformerless d-statcom based on a multivoltage cascade
converter requiring no dc sources,” IEEE Transactions on Power Electronics, vol. 27,
no. 6, pp. 2783–2795, 2012.
[28] B. Gultekin and M. Ermis, “Cascaded multilevel converter-based transmission statcom:
System design methodology and development of a 12 kv±12 mvar power stage,” IEEE
Transactions on Power Electron, vol. 28, no. 11, pp. 4930–4950, 2013.
[29] S. Alepuz, S. Busquets-Monge, J. Bordonau, J. A. Mart´ınez-Velasco, C. A. Silva,
J. Pontt, and J. Rodr´ıguez, “Control strategies based on symmetrical components for
grid-connected converters under voltage dips,” IEEE Transactions on Industrial Electronics,
vol. 56, no. 6, pp. 2162–2173, 2009.
[30] F. A. Magueed, A. Sannino, and J. Svensson, “Transient performance of voltage source
converter under unbalanced voltage dips,” in 2004 IEEE 35th Annual Power Electronics
Specialists Conference, vol. 2. IEEE, 2004, pp. 1163–1168.
[31] H.-s. Song and K. Nam, “Dual current control scheme for pwm converter under unbalanced
input voltage conditions,” IEEE Transactions on Industrial Electronics, vol. 46,
no. 5, pp. 953–959, 1999.
[32] A. Junyent-Ferre, O. Gomis-Bellmunt, T. C. Green, and D. E. Soto-Sanchez, “Current
control reference calculation issues for the operation of renewable source grid interface
vscs under unbalanced voltage sags,” IEEE Transactions on Power Electronics, vol. 26,
no. 12, pp. 3744–3753, 2011.
[33] P. Rodriguez, G. Medeiros, A. Luna, M. C. Cavalcanti, and R. Teodorescu, “Safe current
injection strategies for a statcom under asymmetrical grid faults,” in 2010 IEEE Energy
Conversion Congress and Exposition (ECCE). IEEE, 2010, pp. 3929–3935.
[34] M. Castilla, J. Miret, J. L. Sosa, J. Matas, and L. G. de Vicu˜na, “Grid-fault control
scheme for three-phase photovoltaic inverters with adjustable power quality characteristics,”
IEEE Transactions on Power Electronics, vol. 25, no. 12, pp. 2930–2940, 2010.
[35] C. H. Ng, L. Ran, and J. Bumby, “Unbalanced-grid-fault ride-through control for a wind
turbine inverter,” IEEE Transactions on Industry Applications, vol. 44, no. 3, pp. 845–
856, May 2008.
[36] Z. Ivanovic, M. Vekic, S. Grabic, and V. Katic, “Control of multilevel converter driving
variable speed wind turbine in case of grid disturbances,” in 2006 12th International
Power Electronics and Motion Control Conference. IEEE, 2006, pp. 1569–1573.
[37] Z. R. Ivanovic, E. M. Adzic, M. S. Vekic, S. U. Grabic, N. L. Celanovic, and V. A. Katic,
“Hil evaluation of power flow control strategies for energy storage connected to smart
grid under unbalanced conditions,” IEEE Transactions on Power Electronics, vol. 27,
no. 11, pp. 4699–4710, 2012.
[38] P. Rodriguez, A. V. Timbus, R. Teodorescu, M. Liserre, and F. Blaabjerg, “Flexible
active power control of distributed power generation systems during grid faults,” IEEE
Transactions on Industrial Electronics, vol. 54, no. 5, pp. 2583–2592, 2007.
[39] Z. Chen, J. M. Guerrero, and F. Blaabjerg, “A review of the state of the art of power
electronics for wind turbines,” IEEE Transactions on Power Electronics, vol. 24, no. 8,
pp. 1859–1875, 2009.
[40] F. Blaabjerg, M. Liserre, and K. Ma, “Power electronics converters for wind turbine
systems,” IEEE transactions on Industry Applications, vol. 48, no. 2, pp. 708–719, 2012.
[41] K. Ma, M. Liserre, and F. Blaabjerg, “Operating and loading conditions of a three-level
neutral-point-clamped wind power converter under various grid faults,” IEEE Transactions
on Industry Applications, vol. 50, no. 1, pp. 520–530, 2014.
[42] M. H. Bollen, “Voltage recovery after unbalanced and balanced voltage dips in threephase
systems,” IEEE Transactions on Power Delivery, vol. 18, no. 4, pp. 1376–1381,
2003.
[43] J. Pedra, L. S´ainz, F. C´orcoles, and L. Guasch, “Symmetrical and unsymmetrical voltage
sag effects on three-phase transformers,” IEEE Transactions on Power Delivery, vol. 20,
no. 2, pp. 1683–1691, 2005.
[44] G. M. Hajivar, S. Mortazavi, and M. Saniei, “The neutral grounding resistor sizing using
an analytical method based on nonlinear transformer model for inrush current mitigation,”
in 2010 45th International Universities Power Engineering Conference (UPEC).
IEEE, 2010, pp. 1–5.
[45] K. Basu and A. Asghar, “Reduction of magnetizing inrush current in a delta connected
transformer,” in 2008 IEEE 2nd International Power and Energy Conference. IEEE,
2008, pp. 35–38.
[46] M. Wani, K. Kurundkar, and M. Bhawalkar, “Use of power electronic converters to
suppress transformer inrush current,” in PEDES 2012 IEEE International Conference
on Power Electronics, Drives and Energy Systems. IEEE, 2012, pp. 1–5.
[47] Y.-H. Chen, C.-Y. Lin, J.-M. Chen, and P.-T. Cheng, “An inrush mitigation technique of
load transformers for the series voltage sag compensator,” IEEE Transactions on Power
Electronics, vol. 25, no. 8, pp. 2211–2221, 2010.
[48] Y.-H. Chen, M.-Y. Yeh, P.-T. Cheng, J.-C. Liao, and W.-Y. Tsai, “An inrush current
reduction technique for multiple inverter-fed transformers,” IEEE Transactions on Industry
Applications, vol. 50, no. 1, pp. 474–483, 2014.
[49] YasKawa Electric Corp. [Online]. Available: http://www.yaskawa.co.jp
[50] K. Yamanaka, A. M. Hava, H. Kirino, Y. Tanaka, N. Koga, and T. Kume, “A novel neutral
point potential stabilization technique using the information of output current polarities
and voltage vector,” IEEE Transactions on Industry Applications, vol. 38, no. 6, pp.
1572–1580, 2002.
[51] H. du Toit Mouton, “Natural balancing of three-level neutral-point-clamped pwm inverters,”
IEEE Transactions on Industrial Electronics, vol. 49, no. 5, pp. 1017–1025,
2002.
[52] K. H. Bhalodi and P. Agrawal, “Space vector modulation with dc-link voltage balancing
control for three-level inverters,” in 2006 International Conference on Power Electronics,
Drives and Energy Systems (PEDES). IEEE, 2006, pp. 1–6.
[53] B. U¨ stu¨ntepe and A. M. Hava, “A novel two-parameter modulation and neutral point
potential control method for the three-level neutral point clamped inverter,” in 2007
IEEE International Electric Machines and Drives Conference (IEMDC), vol. 1. IEEE,
2007, pp. 742–747.
[54] A. K. Gupta and A. M. Khambadkone, “A simple space vector pwm scheme to operate a
three-level npc inverter at high modulation index including overmodulation region, with
neutral point balancing,” IEEE Transactions on Industry Applications, vol. 43, no. 3, pp.
751–760, 2007.
[55] H. R. Pinkymol, A. I. Maswood, O. H. Gabriel, and L. Ziyou, “Analysis of 3-level inverter
scheme with dc-link voltage balancing using ls-pwm & svm techniques,” in 2013
International Conference on Renewable Energy Research and Applications (ICRERA).
IEEE, 2013, pp. 1036–1041.
[56] W. Song, X. Feng, and K. M. Smedley, “A carrier-based pwm strategy with the offset
voltage injection for single-phase three-level neutral-point-clamped converters,” IEEE
Transactions on Power Electronics, vol. 28, no. 3, pp. 1083–1095, 2013.
[57] L. Masisi, P. Pillay, and S. S. Williamson, “A modulation strategy for a three-level inverter
synchronous reluctance motor (synrm) drive,” IEEE Transactions on Industry Applications,
vol. 52, no. 2, pp. 1874–1881, 2016.
[58] N. F. Alias, A. Jidin, H. Ismail, R. Firdaus, M. K. Rahim, A. Razi, andW. Abd Halim, “A
simple potential balancing strategy for neutral-point-clamped inverter fed direct torque
control induction machines,” in 2015 IEEE 11th International Conference on Power
Electronics and Drive Systems (PEDS). IEEE, 2015, pp. 1002–1006.
[59] A. Choudhury, P. Pillay, and S. S. Williamson, “Dc-bus voltage balancing algorithm
for three-level neutral-point-clamped (npc) traction inverter drive with modified virtual
space vector,” IEEE Transactions on Industry Applications, vol. 52, no. 5, pp. 3958–
3967, 2016.
[60] C. Newton and M. Sumner, “Neutral point control for multi-level inverters: theory, design
and operational limitations,” in Industry Applications Conference, 1997. Thirty-
Second IAS Annual Meeting, IAS ’97., Conference Record of the 1997 IEEE, vol. 2.
IEEE, 1997, pp. 1336–1343.
[61] Q. Song, W. Liu, Q. Yu, X. Xie, and Z. Wang, “A neutral-point potential balancing algorithm
for three-level npc inverters using analytically injected zero-sequence voltage,”
in 2003 Applied Power Electronics Conference and Exposition (APEC), vol. 1. IEEE,
2003, pp. 228–233.
[62] R. M. Tallam, R. Naik, T. Nondahl et al., “A carrier-based pwm scheme for neutral-point
voltage balancing in three-level inverters,” IEEE Transactions on Industry Applications,
vol. 41, no. 6, pp. 1734–1743, 2005.
[63] J. Pou, R. Pindado, D. Boroyevich, and P. Rodriguez, “Evaluation of the low-frequency
neutral-point voltage oscillations in the three-level inverter,” IEEE Transactions on Industrial
Electronics, vol. 52, no. 6, pp. 1582–1588, 2005.
[64] J.-S. Lee and K.-B. Lee, “Time-offset injection method for neutral-point ac ripple voltage
reduction in a three-level inverter,” IEEE Transactions on Power Electronics, vol. 31,
no. 3, pp. 1931–1941, 2016.
[65] J. Pou, J. Zaragoza, P. Rodriguez, S. Ceballos, V. M. Sala, R. P. Burgos, and D. Boroyevich,
“Fast-processing modulation strategy for the neutral-point-clamped converter with
total elimination of low-frequency voltage oscillations in the neutral point,” IEEE Transactions
on Industrial Electronics, vol. 54, no. 4, pp. 2288–2294, 2007.
[66] J. Zaragoza, J. Pou, S. Ceballos, E. Robles, and C. Jaen, “Optimal voltage-balancing
compensator in the modulation of a neutral-point-clamped converter,” in 2007 IEEE
International Symposium on Industrial Electronics. IEEE, 2007, pp. 719–724.
[67] J. Zaragoza, J. Pou, S. Ceballos, E. Robles, P. Ibanez, and J. L. Villate, “A comprehensive
study of a hybrid modulation technique for the neutral-point-clamped converter,”
IEEE Transactions on Industrial Electronics, vol. 56, no. 2, pp. 294–304, 2009.
[68] W. Srirattanawichaikul, Y. Kumsuwan, S. Premrudeepreechacharn, and B. Wu, “A
carrier-based pwm strategy for three-level neutral-point-clamped voltage source inverters,”
in 2011 IEEE Ninth International Conference on Power Electronics and Drive
Systems (PEDS). IEEE, 2011, pp. 948–951.
[69] S.Wang,W. Song, J. Zhao, and X. Feng, “Hybrid single-carrier-based pulse width modulation
scheme for single-phase three-level neutral-point-clamped grid-side converters
in electric railway traction,” IET Power Electronics, vol. 9, no. 13, pp. 2500–2509, 2016.
[70] S. Wang, W. Song, X. Feng, and R. Ding, “A hybrid cbpwm scheme for single-phase
three-level converters,” Journal of Power Electronics, vol. 16, no. 2, pp. 480–489, 2016.
[71] S. K. Giri, S. Chakrabarti, S. Banerjee, and C. Chakraborty, “A carrier-based pwm
scheme for neutral point voltage balancing in three-level inverter extending to full power
factor range,” IEEE Transactions on Industrial Electronics, vol. 64, no. 3, pp. 1873–
1883, 2017.
[72] B. P. McGrath, D. G. Holmes, and T. Lipo, “Optimized space vector switching sequences
for multilevel inverters,” IEEE Transactions on Power Electronics, vol. 18, no. 6, pp.
1293–1301, 2003.
[73] P. Brogan, “The stability of multiple, high power, active front end voltage sourced converters
when connected to wind farm collector systems,” in Proc. EPE Wind Energy
Chapter Seminar, 2010, pp. 1–6.
[74] J. L. Agorreta, M. Borrega, J. L´opez, and L. Marroyo, “Modeling and control of nparalleled
grid-connected inverters with lcl filter coupled due to grid impedance in pv
plants,” IEEE Transactions on Power Electronics, vol. 26, no. 3, pp. 770–785, 2011.
[75] X. Wang, F. Blaabjerg, and W. Wu, “Modeling and analysis of harmonic stability in an
ac power-electronics-based power system,” IEEE Transactions on Power Electronics,
vol. 29, no. 12, pp. 6421–6432, 2014.
[76] L. Harnefors, L. Zhang, and M. Bongiorno, “Frequency-domain passivity-based current
controller design,” IET Power Electronics, vol. 1, no. 4, pp. 455–465, 2008.
[77] L. Harnefors, A. G. Yepes, A. Vidal, and J. Doval-Gandoy, “Passivity-based controller
design of grid-connected vscs for prevention of electrical resonance instability,” IEEE
Transactions on Industrial Electronics, vol. 62, no. 2, pp. 702–710, 2015.
[78] X. Wang, F. Blaabjerg, and P. C. Loh, “Passivity-based stability analysis and damping
injection for multi-paralleled voltage-source converters with lcl filters,” IEEE Transactions
on Power Electronics, 2017.
[79] Y. W. Li, “Control and resonance damping of voltage-source and current-source converters
with filters,” IEEE Transactions on Industrial Electronics, vol. 56, no. 5, pp.
1511–1521, 2009.
[80] J. Dannehl, F. W. Fuchs, S. Hansen, and P. B. Thogersen, “Investigation of active damping
approaches for pi-based current control of grid-connected pulse width modulation
converters with lcl filters,” IEEE Transactions on Industry Applications, vol. 46, no. 4,
pp. 1509–1517, 2010.
[81] J. He and Y. W. Li, “Generalized closed-loop control schemes with embedded virtual
impedances for voltage source converters with lc or lcl filters,” IEEE Transactions on
Power Electronics, vol. 27, no. 4, pp. 1850–1861, 2012.
[82] Y. Tang, P. C. Loh, P. Wang, F. H. Choo, F. Gao, and F. Blaabjerg, “Generalized design
of high performance shunt active power filter with output lcl filter,” IEEE Transactions
on Industrial Electronics, vol. 59, no. 3, pp. 1443–1452, 2012.
[83] W. Li, X. Ruan, D. Pan, and X. Wang, “Full-feedforward schemes of grid voltages for a
three-phase-type grid-connected inverter,” IEEE Transactions on Industrial Electronics,
vol. 60, no. 6, pp. 2237–2250, 2013.
[84] D. Pan, X. Ruan, C. Bao,W. Li, and X.Wang, “Capacitor-current-feedback active damping
with reduced computation delay for improving robustness of lcl-type grid-connected
inverter,” IEEE Transactions on Power Electronics, vol. 29, no. 7, pp. 3414–3427, 2014.
[85] Z. Xin, P. C. Loh, X. Wang, F. Blaabjerg, and Y. Tang, “Highly accurate derivatives for
lcl-filtered grid converter with capacitor voltage active damping,” IEEE Transactions on
Power Electronics, vol. 31, no. 5, pp. 3612–3625, 2016.
[86] D. Pan, X. Ruan, X. Wang, C. Bao, and W. Li, “Robust capacitor-current-feedback active
damping for the lcl-type grid-connected inverter,” in 2013 IEEE Energy Conversion
Congress and Exposition. IEEE, 2013, pp. 728–735.
[87] C. Han, A. Q. Huang, Y. Liu, and B. Chen, “A generalized control strategy of per-phase
dc voltage balancing for cascaded multilevel converter-based statcom,” in PESC 2007
IEEE Power Electronics Specialists Conference. IEEE, 2007, pp. 1746–1752.
[88] S. Kouro, M. Malinowski, K. Gopakumar, J. Pou, L. G. Franquelo, B.Wu, J. Rodriguez,
M. A. P´erez, and J. I. Leon, “Recent advances and industrial applications of multilevel
converters,” IEEE Transactions on Industrial Electronics, vol. 57, no. 8, pp. 2553–2580,
2010.
[89] M. Malinowski, K. Gopakumar, J. Rodriguez, and M. A. Perez, “A survey on cascaded
multilevel inverters,” IEEE Transactions on Industrial Electronics, vol. 57, no. 7, pp.
2197–2206, 2010.
[90] K. H. Law, M. S. Dahidah, G. S. Konstantinou, and V. G. Agelidis, “She-pwm cascaded
multilevel converter with adjustable dc sources control for statcom applications,”
in IPEMC 2012 IEEE 7th International Power Electronics and Motion Control Conference,
vol. 1. IEEE, 2012, pp. 330–334.
[91] R. Betz, T. Summers, and T. Furney, “Symmetry compensation using a h-bridge multilevel
statcom with zero sequence injection,” in Conference Record of the 2006 IEEE
Industry Applications Conference Forty-First IAS Annual Meeting, vol. 4. IEEE, 2006,
pp. 1724–1731.
[92] N. Hatano and T. Ise, “A configuration and control method of cascade h-bridge statcom,”
in 2008 IEEE Power and Energy Society General Meeting-Conversion and Delivery of
Electrical Energy in the 21st Century. IEEE, 2008, pp. 1–8.
[93] L. Zhao, S. Yan-jun, D. Shan-xu, K. Yong, and C. Tian-jin, “The research of dc capacitance
voltages balancing strategy based on cascade statcom using individual phase
instantaneous current tracking,” in IPEMC 2009 IEEE 6th International Power Electronics
and Motion Control Conference. IEEE, 2009, pp. 1136–1140.
[94] C.-t. Lee, B.-s. Wang, S.-w. Chen, S.-f. Chou, J.-l. Huang, P.-t. Cheng, H. Akagi, and
P. Barbosa, “Average power balancing control of a statcom based on the cascaded hbridge
pwm converter with star configuration,” IEEE Transactions on Industry Applications,
vol. 50, no. 6, pp. 3893–3901, 2014.
[95] H.-C. Chen, P.-H. Wu, C.-T. Lee, C.-W. Wang, C.-H. Yang, and P.-T. Cheng, “Zerosequence
voltage injection for dc capacitor voltage balancing control of the starconnected
cascaded h-bridge pwm converter under unbalanced grid,” IEEE Transactions
on Industry Applications, vol. 51, no. 6, pp. 4584–4594, 2015.
[96] H.-C. Chen and P.-T. Cheng, “Improved dc voltage utilization for the star-connected
cascaded h-bridges converter under unbalanced voltage sags,” in 2015 9th International
Conference on Power Electronics and ECCE Asia (ICPE-ECCE Asia). IEEE, 2015,
pp. 1339–1346.
[97] N. Hatano and T. Ise, “Control scheme of cascaded h-bridge statcom using zerosequence
voltage and negative-sequence current,” IEEE Transactions on Power Delivery,
vol. 25, no. 2, pp. 543–550, 2010.
[98] H.-C. Chen, P.-H.Wu, C.-T. Lee, C.-W. Wang, C.-H. Yang, and P.-T. Cheng, “A flexible
dc voltage balancing control based on the power flow management for star-connected
cascaded h-bridge converter,” IEEE Transactions on Industry Applications, vol. 52,
no. 6, pp. 4946–4954, 2016.
[99] R. E. de Espa˜na, “Procedimiento de operaci´on 12.3. requisitos de respuesta frente a
huecos de tensi´on de las instalaciones e´olicas,” Resoluci ´on de, vol. 4, pp. 37 017–37 019,
2006.
[100] T. Gehlhaar, “Grid code compliance beyond simple lvrt,” Germanischer Lloyd, Germany,
2012.
[101] IEEE IAS P1668 Voltage Sag Ride-through Working Group, Recommended Practice for
Voltage Sag and Interruption Ride-Through Testing for End-Use Electrical Equipment
Less Than 1,000 Volts. Wiley-IEEE Press.
[102] “Draft of annex of p.o.12.2, restricted to the technical requirements od wind power and
photovoltaic facilities,” Red Electrica, Oct 2008.
[103] “Electrolytic capacitor catalog 2003, north america,” Evox Rifa, Espoo, Finland, 2003.
[104] K. Ma and F. Blaabjerg, “Modulation methods for neutral-point-clamped wind power
converter achieving loss and thermal redistribution under low-voltage ride-through,”
IEEE Transactions on Industrial Electronics, vol. 61, no. 2, pp. 835–845, 2014.
[105] “Fast recovery diode 5sdf 10h4503,” ABB semiconductors, September 2001.
[106] “Asymmetric integrated gate-commutated thyristor 5shy 40l4511,” ABB semiconductors,
March 2011.
[107] P. C. Sen, Principles of electric machines and power electronics. John Wiley & Sons,
2007.
[108] G. Baoming, A. T. De Almeida, Z. Qionglin, and W. Xiangheng, “An equivalent instantaneous
inductance-based technique for discrimination between inrush current and
internal faults in power transformers,” IEEE Transactions on Power Delivery, vol. 20,
no. 4, pp. 2473–2482, 2005.
[109] IEEE IAS P1668 Voltage Sag Ride-through Working Group, Recommended Practice for
Voltage Sag and Interruption Ride-Through Testing for End-Use Electrical Equipment
Less Than 1,000 Volts. Wiley-IEEE Press.
[110] H. c. Chen, M. j. Tsai, Y. b. Wang, and P. t. Cheng, “A novel neutral point potential
control for the three-level neutral-point-clamped converter,” in 2016 IEEE Energy Conversion
Congress and Exposition (ECCE), Sept 2016, pp. 1–7.
[111] A. M. Hava, R. J. Kerkman, and T. A. Lipo, “Simple analytical and graphical methods
for carrier-based pwm-vsi drives,” IEEE Transactions on Power Electronics, vol. 14,
no. 1, pp. 49–61, 1999.
[112] R. Teodorescu, F. Blaabjerg, M. Liserre, and A. Dell’Aquila, “A stable three-phase lclfilter
based active rectifier without damping,” in 2003 38th IAS Annual Meeting. Conference
Record of the Industry Applications Conference, vol. 3. IEEE, 2003, pp. 1552–
1557.
[113] M. Liserre, F. Blaabjerg, and S. Hansen, “Design and control of an lcl-filter-based threephase
active rectifier,” IEEE Transactions on Industry Applications, vol. 41, no. 5, pp.
1281–1291, 2005.
[114] W. Gullvik, L. Norum, and R. Nilsen, “Active damping of resonance oscillations in lclfilters
based on virtual flux and virtual resistor,” in Power Electronics and Applications,
2007 European Conference on. IEEE, 2007, pp. 1–10.
[115] J. Dannehl, M. Liserre, and F. W. Fuchs, “Filter-based active damping of voltage source
converters with lcl filter,” IEEE Transactions on Industrial Electronics, vol. 58, no. 8,
pp. 3623–3633, 2011.
[116] W. Yao, Y. Yang, X. Zhang, and F. Blaabjerg, “Digital notch filter based active damping
for lcl filters,” in Applied Power Electronics Conference and Exposition (APEC), 2015
IEEE. IEEE, 2015, pp. 2399–2406.
[117] X. Wang, C. Bao, X. Ruan, W. Li, and D. Pan, “Design considerations of digitally
controlled lcl-filtered inverter with capacitor-current-feedback active damping,” IEEE
Journal of Emerging and Selected Topics in Power Electronics, vol. 2, no. 4, pp. 972–
984, 2014.
[118] R. Pe˜na-Alzola, M. Liserre, F. Blaabjerg, M. Ordonez, and Y. Yang, “Lcl-filter design for
robust active damping in grid-connected converters,” IEEE Transactions on Industrial
Informatics, vol. 10, no. 4, pp. 2192–2203, 2014.
[119] D. Pan, X. Ruan, C. Bao, W. Li, and X.Wang, “Optimized controller design for lcl-type
grid-connected inverter to achieve high robustness against grid-impedance variation,”
IEEE Transactions on Industrial Electronics, vol. 62, no. 3, pp. 1537–1547, 2015.
[120] X. Li, X. Wu, Y. Geng, X. Yuan, C. Xia, and X. Zhang, “Wide damping region for
lcl-type grid-connected inverter with an improved capacitor-current-feedback method,”
IEEE Transactions on Power Electronics, vol. 30, no. 9, pp. 5247–5259, 2015.
[121] X. Wang, F. Blaabjerg, and P. C. Loh, “Virtual rc damping of lcl-filtered voltage source
converters with extended selective harmonic compensation,” IEEE Transactions on
Power Electronics, vol. 30, no. 9, pp. 4726–4737, 2015.
[122] D. Pan, X. Ruan, and X. Wang, “Direct realization of digital differentiators in discrete
domain for active damping of lcl-type grid-connected inverter,” IEEE Transactions on
Power Electronics, 2017.
[123] A. Aapro, T. Messo, T. Roinila, and T. Suntio, “Effect of active damping on output
impedance of three-phase grid-connected converter,” IEEE Transactions on Industrial
Electronics, vol. 64, no. 9, pp. 7532–7541, 2017.
[124] M. Khatir, S. Zidi, S. Hadjeri, and M. K. Fellah, “Comparison of hvdc line models in
psb/simulink based on steady-state and transients considerations,” Acta Electrotechnica
et Informatica, vol. 8, no. 2, pp. 50–55, 2008.
[125] M. Zubiaga, G. Abad, J. Barrena, S. Aurtenetxea, and A. C´arcar, “Spectral analysis of a
transmission system based on ac submarine cables for an offshore wind farm,” in 2009
35th Annual Conference of IEEE Industrial Electronics (IECON). IEEE, 2009, pp.
871–876.
[126] M. Lu, X. Wang, P. C. Loh, F. Blaabjerg, and T. Dragicevic, “Graphical evaluation of
time-delay compensation techniques for digitally controlled converters,” IEEE Transactions
on Power Electronics, vol. 33, no. 3, pp. 2601–2614, 2018.
[127] U. R¨adel, “Beitrag zur entwicklung leistungselektronischer komponenten f¨ur windkraftanlagen,”
Ph.D. dissertation, Dissertation, Ilmenau, 2008.
[128] J. M. Bloemink and T. C. Green, “Reducing passive filter sizes with tuned traps for distribution
level power electronics,” in Proceedings of the 2011-14th European Conference
on Power Electronics and Applications (EPE). IEEE, 2011, pp. 1–9.
[129] K. R. Meyer, “Fault-ride-through-regelung von windenergieanlagen mit vollumrichter
und lcl-netzfilter,” Ph.D. dissertation, 2014.
[130] S. Buso and P. Mattavelli, “Digital control in power electronics,” Lectures on power
electronics, vol. 1, no. 1, pp. 1–158, 2006.
[131] D. M. VandeSype, K. DeGusseme, F. M. DeBelie, A. P. VandenBossche, and J. A.
Melkebeek, “Small-signal z-domain analysis of digitally controlled converters,” IEEE
Transactions on Power Electronics, vol. 21, no. 2, pp. 470–478, 2006.
[132] L. Harnefors and H.-P. Nee, “Model-based current control of ac machines using the
internal model control method,” IEEE transactions on Industry Applications, vol. 34,
no. 1, pp. 133–141, 1998.
[133] L. Maharjan, S. Inoue, and H. Akagi, “A transformerless energy storage system based
on a cascade multilevel pwm converter with star configuration,” IEEE Transactions on
Industry Applications, vol. 44, no. 5, pp. 1621–1630, 2008.
[134] H. Kim and H. Akagi, “The instantaneous power theory on the rotating pqr reference
frames,” in Proceedings of the IEEE 1999 International Conference on Power Electronics
and Drive Systems (PEDS), vol. 1. IEEE, 1999, pp. 422–427.
[135] L. Maharjan, S. Inoue, H. Akagi, and J. Asakura, “State-of-charge (soc)-balancing control
of a battery energy storage system based on a cascade pwm converter,” IEEE Transactions
on Power Electronics, vol. 24, no. 6, pp. 1628–1636, 2009.