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Lennart Baruschka, Dennis Karwatzki, Malte Hofen, A. Mertens (2014)
Low-speed drive operation of the modular multilevel converter Hexverter down to zero frequency2014 IEEE Energy Conversion Congress and Exposition (ECCE)
Qin Wang, Hwachang Song, V. Ajjarapu (2006)
Continuation-based quasi-steady-state analysisIEEE Transactions on Power Systems, 21
B. Fan, Kui Wang, Yongdong Li, Zedong Zheng, Lie Xu (2015)
A branch energy control method based on optimized neutral-point voltage injection for a hexagonal modular multilevel direct converter (Hexverter)2015 18th International Conference on Electrical Machines and Systems (ICEMS)
R. Ortega, E. García-Canseco (2004)
Interconnection and Damping Assignment Passivity-Based Control: A SurveyEur. J. Control, 10
Minyuan Guan, Zheng Xu (2012)
Modeling and Control of a Modular Multilevel Converter-Based HVDC System Under Unbalanced Grid ConditionsIEEE Transactions on Power Electronics, 27
Dennis Karwatzki, Lennart Baruschka, Malte Hofen, A. Mertens (2014)
Branch energy control for the modular multilevel direct converter Hexverter2014 IEEE Energy Conversion Congress and Exposition (ECCE)
Lennart Baruschka, A. Mertens (2011)
A new 3-phase direct modular multilevel converterProceedings of the 2011 14th European Conference on Power Electronics and Applications
Ashish Banasawade, Suyog Patil, Dipali Jatte, K. Sunil (2015)
Fractional Frequency Transmission System
Yongqing Meng, Bo Liu, H. Luo, Shuonan Shang, Haitao Zhang, Xifan Wang (2018)
Control scheme of hexagonal modular multilevel direct converter for offshore wind power integration via fractional frequency transmission systemJournal of Modern Power Systems and Clean Energy, 6
Shenquan Liu, Xifan Wang, Yongqing Meng, Pengwei Sun, H. Luo, Biyang Wang (2017)
A Decoupled Control Strategy of Modular Multilevel Matrix Converter for Fractional Frequency Transmission SystemIEEE Transactions on Power Delivery, 32
Wang Xifan, Cao Chengjun, Zhou Zhichao (2006)
Experiment on fractional frequency transmission systemIEEE Transactions on Power Systems, 21
C. Mau, K. Rudion, A. Orths (2012)
Grid connection of offshore wind farm based DFIG with low frequency AC transmission system2012 IEEE Power and Energy Society General Meeting
M. Shayestegan (2018)
Overview of grid-connected two-stage transformer-less inverter designJournal of Modern Power Systems and Clean Energy, 6
S. Angkititrakul, R. Erickson (2006)
Capacitor voltage balancing control for a modular matrix converterTwenty-First Annual IEEE Applied Power Electronics Conference and Exposition, 2006. APEC '06.
Shenquan Liu, Xifan Wang, L. Ning, Biyang Wang, Ming-Shun Lu, Chengcheng Shao (2017)
Integrating Offshore Wind Power Via Fractional Frequency Transmission SystemIEEE Transactions on Power Delivery, 32
Y. Miura, T. Mizutani, Mitsutaka Ito, T. Ise (2013)
A novel space vector control with capacitor voltage balancing for a multilevel modular matrix converter2013 IEEE ECCE Asia Downunder
H. Saad, J. Peralta, S. Dennetière, J. Mahseredjian, J. Jatskevich, J. Martinez, A. Davoudi, M. Saeedifard, V. Sood, X. Wang, J. Cano, A. Mehrizi‐Sani (2013)
Dynamic Averaged and Simplified Models for MMC-Based HVDC Transmission SystemsIEEE Transactions on Power Delivery, 28
Yun Wan, Steven Liu, Jianguo Jiang (2013)
Multivariable Optimal Control of a Direct AC/AC Converter under Rotating dq FramesJournal of Power Electronics, 13
R. Erickson, O. Al-Naseem (2001)
A new family of matrix convertersIECON'01. 27th Annual Conference of the IEEE Industrial Electronics Society (Cat. No.37243), 2
Xifan Wang, Xiuli Wang (1996)
Feasibility study of fractional frequency transmission system, 11
(2014)
Integration techniques and transmission schemes for off-shore wind farms
S. Hamasaki, K. Okamura, Takashi Tsubakidani, M. Tsuji (2014)
Control of hexagonal Modular Multilevel Converter for 3-phase BTB system2014 International Power Electronics Conference (IPEC-Hiroshima 2014 - ECCE ASIA)
R. Ortega, A. Schaft, B. Maschke, G. Escobar (2002)
Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systemsAutom., 38
Q. Song, Wenhua Liu, Xiaoqian Li, H. Rao, Shukai Xu, Licheng Li (2013)
A Steady-State Analysis Method for a Modular Multilevel ConverterIEEE Transactions on Power Electronics, 28
I. Erlich, F. Shewarega, H. Wrede, W. Fischer (2015)
Low frequency AC for offshore wind power transmission - prospects and challenges
Yongqing Meng, Shuonan Shang, Haitao Zhang, Yong Cui, Xifan Wang (2017)
IDA-PB control with integral action of Y-connected modular multilevel converter for fractional frequency transmission applicationIet Generation Transmission & Distribution, 12
Dennis Karwatzki, Lennart Baruschka, A. Mertens (2015)
Survey on the Hexverter topology — A modular multilevel AC/AC converter2015 9th International Conference on Power Electronics and ECCE Asia (ICPE-ECCE Asia)
J. Mod. Power Syst. Clean Energy (2019) 7(6):1495–1506 https://doi.org/10.1007/s40565-019-0549-y A global asymptotical stable control scheme for a Hexverter in fractional frequency transmission systems 1 1 2 1 1 Yongqing MENG , Yichao ZOU , Huixuan LI , Jianyang YU , Xifan WANG Abstract A fractional frequency transmission system to eliminate the steady-state error. In addition, the voltage- (FFTS) is the most competitive choice for long distance balancing control is applied in order to balance the transmission of offshore wind power, while the Hexverter, capacitor DC voltages to obtain a better performance. as a newly proposed direct AC/AC converter, is an Finally, the simulation results and experimental results are attractive choice for its power conversion. This paper presented to verify the effectiveness and superiority of the proposes a novel control scheme characterizing the global IDA-PB controller. stability and strong robustness of the Hexverter in FFTS applications, which are based on the interconnection and Keywords Fractional frequency transmission system damping assignment passivity-based control (IDA-PBC) (FFTS), Hexverter, Port-controlled Hamiltonian (PCH) methodology. Firstly, the frequency decoupled model of system, Interconnection and damping assignment the Hexverter is studied and then a port-controlled passivity-based control (IDA-PBC) Hamiltonian (PCH) model is built. On this basis, the IDA- PB control scheme of the Hexverter is designed. Consid- ering the interference of system parameters and unmodeled 1 Introduction dynamics, integrators are added to the IDA-PB controller Recently, offshore wind power has attracted more and more attention due to its greater superiority including rich resources, high efficiency, no land occupation, etc. As to CrossCheck date: 26 March 2019 the development of offshore wind power, the important Received: 22 October 2018 / Accepted: 26 March 2019 / Published technical issue that remains to be discussed is its grid online: 29 July 2019 integration. Currently, there are three main transmission The Author(s) 2019 technologies for connecting the offshore wind farm to the & Yichao ZOU grid [1]: high voltage AC (HVAC) transmission system, zycstacy@163.com high voltage DC (HVDC) transmission system and frac- Yongqing MENG tional frequency transmission system (FFTS). mengyq@mail.xjtu.edu.cn The HVAC transmission system has the advantages of Huixuan LI low cost and simple structure. But it cannot be applied over 594715409@qq.com long distances due to its large charging current along the Jianyang YU submarine cable [2]. At present, the widely-used wind yujianyang@stu.xjtu.edu.cn power integration strategy is the flexible HVDC system, of Xifan WANG which the two terminals are connected by the high-voltage xfwang@mail.xjtu.edu.cn high-power converter such as the modular multilevel con- School of Electrical Engineering, Xi’an Jiaotong University, verter (MMC) through a DC transmission line [3–5]. Xi’an, China However, the HVDC system needs an offshore converter State Grid Henan Electric Power Company Economic station which will lead to high costs for construction and Research Institute, Zhengzhou, China 123 1496 Yongqing MENG et al. maintenance, and it is difficult to deal with the fault cases is a novel attempt to develop the IDA-PBC scheme of the [6]. In order to overcome the shortcomings of the HVDC Hexverter for FFTS applications. system, the FFTS is proposed, in which the offshore wind This paper focuses on the design of the novel control farm and offshore transmission system works at a relatively scheme of the Hexverter for FFTS based on IDA-PBC low frequency [7–9]. FFTS is demonstrated to be the most methodology. First, a brief introduction of IDA-PBC theory is competitive choice for long distance transmission of off- given in Section 2.In section 3, the detail frequency decou- shore wind power since the charging current can be greatly pled model of the Hexverter is derived, and then the PCH reduced and the technical performance as well as economic model is established. On this basis, Section 4 proposes the performance can be greatly improved compared to HVAC global asymptotical control scheme and the detail design and HVDC systems [10]. process of an IDA-PB controller is presented. Integral action is The key equipment in the FFTS is the high-voltage high- also studied to eliminate any steady-state error. Section 5 and power AC/AC converter. The modular multilevel matrix Section 6 present simulation results and experimental results converter (M3C) is put forward by Erickson and Al- respectively to verify the validity of the proposed control Naseem in 2001 [11], which has nine branches and con- scheme. Concluding remarks are presented in Section 7. nects two AC systems directly without a DC line. Researchers have done a great deal of study on the control strategies of M3C [12–15]. Although the M3C is a feasible 2 Overview of IDA-PBC methodology topology, the nine branches lead to high cost and the numerous circulating current paths also increase the diffi- The PCH system is a class of generalized passive sys- culties of circulating current analysis and suppression [16]. tems which contain most of the practical physical systems. In 2011, Baruschka and Mertens proposed a new direct The lumped parameter PCH systems that have independent AC/AC topology called the Hexverter. Compared to M3C, energy storage elements can be represented as: it reduced the number of branches to six and only has one dx=dt ¼½ JxðÞRxðÞðoHðÞ x =oxÞþgxðÞu ð1Þ circulating current path [17], hence the equipment volume y ¼ g ðÞ x ðoHðÞ x =oxÞ and cost are significantly reduced. In addition, this topol- n m where x 2 R is the state vector; u; y 2 R are the port power ogy is quite suitable for connecting two different frequency vectors that indicate the energy exchange between the sys- systems since the coupling level of the connected system is tem and the external environment; the scalar function weakened. Therefore, the Hexverter is a better choice for HðxÞ 0 is the stored energy of the system; JðxÞ is an n n the FFTS. antisymmetric matrix that indicates the internal intercon- Most researches on the Hexverter focus on the medium- nection structure; RðxÞ is a symmetric matrix that represents voltage or low-voltage applications such as motor-drivers internal dissipation; and gxðÞ is an n m input matrix that [18–20], and the generally adopted control scheme for the Hexverter is the vector control [21–23]. There are few indicates the port interconnection structure. JðxÞ and RðxÞ are interconnection matrix and damping matrix. researches which applied the Hexverter on a transmission The aim of the IDA-PBC method is to find a state system. Reference [24] applies the Hexverter to offshore feedback u ¼ bðxÞ ensuring that the closed-loop system wind power integration via FFTS and the vector control remains to be a PCH system as shown below: scheme of the Hexverter has been discussed in detail. However, while the performance of this scheme relies on dx=dt ¼½ J ðÞ x R ðÞ xðoH ðÞ x =oxÞð2Þ d d d the precise system model, it may deteriorate with consid- where H ðxÞ is the closed-loop energy function, obtains erable interference of system parameters. Moreover, the minimum value at equilibrium x , the matrixes J ðxÞ¼ tuning of proportional-integral (PI) parameters to assure d T T global stability is also tough work. Since stability is the J ðxÞ and R ðxÞ¼R ðxÞ are the desired interconnec- d d primary problem of a power system, it is of great signifi- tion matrix and damping matrix. cance to do research on control schematics emphasizing The detail content of the IDA-PBC methodology and stability. The interconnection and damping assignment related theorems are presented in [25, 26]. passivity-based control (IDA-PBC) is an effective con- troller design methodology for a non-linear system [25, 26]. By establishing the port-controlled Hamiltonian 3 Mathematical model of Hexverter (PCH) model of the system and properly configuring the interconnection matrix as well as damping matrix, it can 3.1 Configuration of Hexverter keep the system global asymptotically stable and signifi- cantly improve the transient performance of the system. It As shown in Fig. 1, the Hexverter has six branches that directly connect the two AC systems. v ; v ; v ; i ; i ; i u v w u v w 123 A global asymptotical stable control scheme for a Hexverter in fractional… 1497 > i ¼ i i u b1 b6 i > b4 i ¼ i i v b3 b2 L > R > i < i ¼ i i w b5 b4 b5 ð4Þ v b5 v i ¼ i i b4 a b1 b2 o > v v v u i ¼ i i > b b3 b4 b3 i ¼ i i c b5 b6 i i v u where p ¼ d=dt is the differential operator. When both b6 systems are three-wire and symmetrical, the voltages and b3 currents satisfy: i i b c i þi þi ¼ i þi þi ¼ 0 u v w a b c i ð5Þ b6 i þ i þ i ¼ i þ i þ i b1 b3 b5 b2 b4 b6 b v ðv þ v þ v Þðv þ v þ v Þþ 6v ¼ 0 ð6Þ b1 b3 b5 b2 b4 b6 NO b1 i a b2 b2 According to (3) and (4), there are two frequency components in the branch voltages and currents as well as the input and output currents. It causes inconvenience for b1 analysis and control of the converter. Thus, frequency decoupling is necessary. Fig. 1 Configuration of the Hexverter 1) AC dynamic equations Pre-multiply (3) by the transformation matrix C abc/ab0 to obtain the voltage equations in the ab0 reference frame: are the voltages and currents of input system, v ¼ Ri þ Lpi þ v þ v sa ba1 ba1 ba1 la v ; v ; v ; i ; i ; i are the voltages and currents of output a b c a b c > > v ¼ Ri þ Lpi þ v þ v sb bb1 bb1 bb1 lb system. The input frequency is f and the output frequency pffiffiffi v ¼ Ri þ Lpi þ v þ v þ 3v s0 b01 b01 b01 l0 NO pffiffiffi is f . Each branch consists of N H-bridge submodules, a ð7Þ v ¼ Ri þ Lpi þ v v =2 þ 3v 2 > la ba2 ba2 ba2 sa sb resistor R and an inductor L. For each submodule, the > pffiffiffi v ¼ Ri þ Lpi þ v 3v 2 v 2 lb bb2 bb2 bb2 sa sb output voltage can be three levels (±v and 0, v is the c c : pffiffiffi v ¼ Ri þ Lpi þ v þ v 3v l0 b02 b02 b02 s0 NO capacitor voltage). Therefore, the output voltage of N submodules can range from –Nv to Nv and can be con- c c where subscript ‘‘1’’ indicates the variables of branches 1, sidered as a voltage-controlled voltage source whose 3, 5 and subscript ‘‘2’’ indicates the variables of branches 2, voltage is v (k=1,2,…,6). Define expressions with sub- bk 4, 6. Considering the general conditions, divide the script ‘‘s’’ to represent the variables of input system, ‘‘l’’ to variables which contain the two frequency components represent the variables of output system, ‘‘b’’ to represent into the form below: the variables of branches later in this paper. i ¼ i þ i > sa sa;fs sa;fl i ¼ i þ i > sb sb;fs sb;fl 3.2 Decoupled model of Hexverter i ¼ i þ i ba1 ba1;fs ba1;fl i ¼ i þ i > bb1 bb1;fs bb1;fl Assuming that the voltage between the neutral points of v ¼ v þ v > ba1 ba1;fs ba1;fl the two AC systems is v , the following equations can be NO < v ¼ v þ v bb1 bb1;fs bb1;fl determined from Fig. 1: ð8Þ > i ¼ i þ i la la;fs la;fl > v ¼ Ri þ Lpi þ v þ v þ v > i ¼ i þ i u b1 b1 b1 a NO lb lb;fs lb;fl > i ¼ i þ i ba2 ba2;fs ba2;fl > v ¼ Ri þ Lpi þ v þ v þ v v b3 b3 b3 b NO i ¼ i þ i < bb2 bb2;fs bb2;fl v ¼ Ri þ Lpi þ v þ v þ v > w b5 b5 b5 c NO v ¼ v þ v ð3Þ ba2 ba2;fs ba2;fl v ¼ Ri þ Lpi þ v þ v v > a b2 b2 b2 v NO v ¼ v þ v > bb2 bb2;fs bb2;fl v ¼ Ri þ Lpi þ v þ v v > b b4 b4 b4 w NO where subscript ‘‘fs’’ indicates the variables containing v ¼ Ri þ Lpi þ v þ v v c b6 b6 b6 u NO input frequency component; ‘‘fl’’ indicates the variables 123 1498 Yongqing MENG et al. containing output frequency component. Substitute (8) into i i b b (7) and separate the equations in terms of frequency: dc v ¼ Ri þ Lpi þ v sa ba1; fs ba1; fs ba1; fs > v ¼ Ri þ Lpi þ v dc sb bb1; fs bb1; fs bb1; s > C' dc > 0 ¼ Ri þ Lpi þ v þ v ba1; fl ba1; fl ba1; fl la 0 ¼ Ri þ Lpi þ v þ v bb1; fl bb1; fl bb1; fl lb v v v b dc C b v ¼ Ri þ Lpi þ v la ba2; fl ba2; fl ba2; fl v ¼ Ri þ Lpi þ v > lb bb2; fl bb2; fl bb2; fl > pffiffiffi 0 ¼ Ri þ Lpi þ v v =2 þ 3v 2 ba2; fs ba2; fs ba2; fs sa sb pffiffiffi 0 ¼ Ri þ Lpi þ v 3v 2 v 2 bb2; fs bb2; fs bb2; fs sa sb ð9Þ Apply the dq transformation to (9), and write the equations Fig. 2 Equivalent circuit of series submodules in one branch in matrix form: v i i i v sd bd1;fs bd1;fs bq1;fs bd1;fs Cv pv ¼ v m i ¼ v i k ¼ 1; 2; ...; 6 ð14Þ dck dck dck bk bk bk bk > ¼ R þ Lp þ x L þ > v i i i v > sq bq1;fs bq1;fs bd1;fs bq1;fs Let 3v ¼ðÞ v þ v þ v and 3v ¼ðv þ dc1 dc1 dc3 dc5 dc2 dc2 v i i i v ld bd1;fl bd1;fl bq1;fl bd1;fl > ¼ R þ Lp þ x L þ v þ v Þ to keep consistent with the AC dynamic dc4 dc6 v i i i v lq bq1;fl bq1;fl bd1;fl bq1;fl equations, where v , v are the average voltage of dc1 dc2 v i i i v sd bd2;fs bd2;fs bq2;fs bd2;fs A ¼ R þ Lp þ x L þ branches 1, 3, 5 and branches 2, 4, 6, respectively. The v i i i v sq bq2;fs bq2;fs bd2;fs bq2;fs following equations can be determined: > v i i i v > ld bd2;fl bd2;fl bq2;fl bd2;fl : ¼ R þ Lp þ x L þ 3Cv pv ¼ v i þv i þv i v i i i v dc1 dc1 b1 b1 b3 b3 b5 b5 lq bq2;fl bq2;fl bd2;fl bq2;fl ð15Þ 3Cv pv ¼ v i þv i þv i dc2 dc2 b2 b2 b4 b4 b6 b6 ð10Þ "# pffiffiffi 1=2 3 2 Apply the ab0 and dq transformation to (15). Generally, pffiffiffi where A ¼ . 321=2 the capacitors of submodules are large enough to suppress the fluctuation of the DC voltage, so the (fs?fl) and (fs–fl) Assuming i =i =i , the equations of the zero b0 b01 b02 components are neglected in the process. The DC dynamic components in (7) can be simplified as: equation can be determined as: 3Cv pv ¼ v i þv i ðÞ v þv =2 ¼Ri Lpi ð11Þ dc1 dc1 bsd1 bd1; fs bsq1 bq1; fs b01 b02 b0 b0 > þ v i þv i þv i bld1 bd1;fl blq1 bq1; fl b01 b0 Apply the ab0 and dq transformation to (4) and simplify, ð16Þ 3Cv pv ¼ v i þv i > dc2 dc2 bsd2 bd2; fs bsq2 bq2; fs then the relationship of the current can be determined as: 8 pffiffiffi þ v i þv i þv i bld2 bd2;fl blq2 bq2; fl b02 b0 > i ¼ i þ i 2 þ 3i 2 sd;fs bd1;fs bd2;fs bq2;fs > pffiffiffi Equations (10), (11) and (16) compose the frequency i ¼ i 3i 2 þ i 2 sq;fs bq1;fs bd2;fs bq2;fs i ¼ i i decoupled mathematical model of the Hexverter. ld;fs bd1;fs bd2;fs i ¼ i i lq;fs bq1;fs bq2;fs pffiffiffi ð12Þ i ¼ i þ i 2 þ 3i 2 > sd;fl bd1;fl bd2;fl bq2;fl > pffiffiffi 3.3 PCH model of Hexverter > i ¼ i 3i 2 þ i 2 sq;fl bq1;fl bd2;fl bq2;fl > i ¼ i i ld;fl bd1;fl bd2;fl : As shown in Fig. 1, the Hexverter is a two-port circuit. i ¼ i i lq;fl bq1;fl bq2;fl The port power variables are (v , i ), (v , i ), (0, sd sd;fs sq sq;fs i ), (0, i ), (0, i ), (0, i ), (v , i ), (v , 2) DC dynamic equations sd;fl sq;fl ld;fs lq;fs ld ld;fl lq i ). Define v ; v ; v ; v as the input port variables, Considering that each submodule capacitor has lq;fl sd sq ld lq basically the same charging and discharging process, N i ; i ; i ; i as the output port variables (the sd;fs sq;fs ld;fl lq;fl submodules of a branch can be equated to one module as current of the output side is negative due to the reference shown in Fig. 2 and: direction) and H as the energy function. H is expressed as: v ¼ Nm v ¼ m v b b b dc dc ð13Þ 0 0 i ¼ C pNv N ¼ Cpv ¼ m i dc dc b b dc where m is the branch modulation signal. For each branch: 123 A global asymptotical stable control scheme for a Hexverter in fractional… 1499 1 the branch currents to obtain the state variables. Then the 2 2 2 2 2 H ¼ ðLi þ Li þ Li þ Li þ Li þ bd1; fs bq1; fs bd1;fl bq1; fl bd2; fs IDA-PBC method is adopted to obtain the modulation 2 2 2 2 2 2 variables in the dq reference frame. Finally, transform the Li þ Li þ Li þ 2Li þ 3Cv þ 3Cv Þ bq2; fs bd2;fl bq2; fl b0 dc1 dc2 modulation variables to the abc reference frame, apply the ð17Þ carrier phase shifted modulation to generate the gate sig- nals of the six branches. In addition, the voltage-balancing Thus, the frequency decoupled mathematical model of the Hexverter can be written in the form of the PCH model control is applied in order to balance the capacitor DC as shown in (1). The variables and matrixes are as follows: voltages of the N submodules in one branch. x ¼½ x x x x x x x x x x x 1 2 3 4 5 6 7 8 9 10 11 4.2 IDA-PBC design i i i i i i ¼ ½ bd1; fs bq1; fs bd1;fl bq1; fl bd2; fs bq2; fs i i i v v bd2;fl bq2; fl b0 dc1 dc2 As shown in Fig. 3, the IDA-PB controller is the core of the control scheme. Being different from the traditional v v v v u ¼½ sd sq ld lq vector control method, it has no need to determine and y ¼½ i i i i sd;fs sq;fs ld;fl lq;fl optimize the PI parameters. Various types of IDA-PB 2 3 x m s bsd1 0 00 0 0 00 0 0 controllers can be designed by solving modulation vari- L 3LC 6 7 x m 6 s bsq1 7 6 00 00 00 0 0 0 7 ables on the basis of the IDA-PBC methodology and 6 L 3LC 7 6 x m 7 l bld1 6 7 00 0 00 0 0 0 0 configuring the interconnection matrix as well as the 6 7 L 3LC 6 7 xl mblq1 6 7 00 00 00 0 0 0 damping matrix, 6 7 L 3LC 6 7 x m s bsd2 6 7 00 0 0 0 00 0 0 6 7 L 3LC 6 7 x m 6 s bsq2 7 J ¼ 6 00 0 0 00 0 0 0 7 4.2.1 IDA-PB controller with constant interconnection 6 L 3LC 7 6 x m 7 l bld2 6 00 0 0 00 0 00 7 structure 6 7 L 3LC 6 7 x m l blq2 6 7 00 0 0 00 00 0 6 7 L 3LC 6 7 m m b01 b02 6 7 00 0 0 00 0 0 0 6 7 Define the expected asymptotically stable equilibrium 6 6LC 6LC 7 m m m m m 6 bsd1 bsq1 bld1 blq1 b01 7 00 0 0 00 6 7 point of the closed-loop as: 4 3LC 3LC 3LC 3LC 6LC 5 m m m m m bsd2 bsq2 bld2 blq2 b02 00 0 0 00 3LC 3LC 3LC 3LC 6LC x ¼½ I I I I I I bd1; fs bq1; fs bd1;fl bq1; fl bd2; fs bq2; fs 2 pffiffiffi 3 I I I V V bd2;fl bq2; fl b0 dcr dcr 1=L 00 0 1=2L 3 2L 00 0 0 0 pffiffiffi 6 7 T 01=L 00 3 2L 1=2L 00 0 0 0 6 7 g ¼ 4 5 The expected interconnection matrix and damping matrix 00 1=L 00 0 1=L 00 0 0 00 0 1=L 00 0 1=L 00 0 of the closed-loop are: R R R R R R R R R J ¼ J ð19Þ R ¼ diag 00 2 2 2 2 2 2 2 2 2 L L L L L L L L L R ¼ R þ R ð20Þ d a Orient the dq reference frame with the grid voltage, the where R is the proposed injected damping matrix: input vector can be determined as: pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi r 00 000000 r 0 T 1 16 u ¼ ð18Þ 3=2V 0 3=2V 0 sdm ldm 6 7 0 r 0 0 00000 r 0 2 17 6 7 6 7 00 r 000000 r 0 3 18 where V and V are the amplitude of input and output 6 7 sdm ldm 6 7 000 r 00000 r 0 4 19 6 7 voltages, respectively. 6 7 000 0 r 00000 r 5 24 6 7 6 7 R ¼ 000 00 r 0000 r a 6 25 6 7 6 7 000 000 r 000 r 7 26 6 7 4 IDA-PBC method of Hexverter 6 7 000 0000 r 00 r 8 27 6 7 6 7 000 00000 r r r 9 29 31 6 7 4.1 Overview of control scheme 4 5 r r r r 0000 r r 0 12 13 14 15 28 10 000 0 r r r r r 0 r 20 21 22 23 30 11 The overview of the control scheme of the Hexverter is presented in Fig. 3. For general solutions, if R is an asymmetric matrix, the The design process is as follows. Firstly, the reference interconnection structure of the closed-loop needs to be values of the input and output currents can be determined changed. Under these circumstances, the original R can be by demand for the active and reactive power. Secondly, the represented as a sum of two matrixes: symmetric matrix current transformation according to (12) is implemented and antisymmetric matrix. Here, in order to obtain an IDA- and the expected values of the branch currents are derived. PB controller with constant interconnection structure, R Thirdly, dq transformation is applied to the actual values of 123 1500 Yongqing MENG et al. b01 b1,3,5 abc bd,q1, fs dq0 bd,q1, fl Voltage-balancing control dcr bsd,q1 ua bd,q1, fs dq0 m av bld,q1 sd,q bd,q1, fl vb Branch Current IDA-PB bsd,q2 CPS transformation gate controller bd,q2, fs I PWM ld,q signals bw bld,q2 bd,q2, fl wc b01,2 abc b0 ca b02 abc b2,4,6 bd ,q2, fs dq0 bd, q2, fl Fig. 3 Overview of control scheme of the Hexverter should be a symmetric matrix, and the elements of the m ¼ L r I x þ 3CLrðÞ V x V bsd1 1 bd1;fs 1 16 dcr 10 dcr antisymmetric matrix should be zero. Then the energy pffiffiffiffiffiffiffiffi RI x LI 3=2V V bd1; fs s bq1; fs sdm dcr function of the closed-loop H can be designed as the quadric form: ð23Þ 2 2 m ¼ L r I x þ 3CLrðÞ V x V H ¼ Li I þLi I bsq1 2 bq1;fs 2 17 dcr 10 dcr d bd1; fs bd1; fs bq1; fs bq1; fs RI þ x LI V 2 2 bq1; fs s bd1; fs dcr þLi I þLi I bd1;fl bd1;fl bq1; fl bq1; fl ð24Þ 2 2 þLi I þLi I bd2; fs bd2; fs bq2; fs bq2; fs m ¼ L r I x þ 3CLrðÞ V x V 2 2 bld1 3 bd1;fl 3 18 dcr 10 dcr þLi I þLi I bd2;fl bd2;fl bq2; fl bq2; fl . pffiffiffiffiffiffiffiffi RI x LI þ 3=2V V 2 2 2 bd1; fl l bq1; fl ldm dcr þ 2LiðÞ I þ3CðÞ v V þ3CðÞ v V b0 b0 dc1 dcr dc2 dcr ð25Þ ð21Þ m ¼ L r I x þ 3CLrðÞ V x V blq1 4 bq1;fl 4 19 dcr 10 dcr Therefore, the K(x) can be derived by: RI þ x LI V bq1; fl l bd1; fl dcr KðxÞ¼ oH ðÞ x =ox ¼ oðÞ H H ðÞ x =ox ð22Þ a d ð26Þ where K(x) is a column vector and its elements are defined m ¼ L r I x þ 3CLrðÞ V x V bsd2 5 bd2;fs 5 24 dcr 11 dcr as K (i =1,2,…,11). pffiffiffi According to the IDA-PBC methodology, eleven equa- RI x LI 6V =4 V bd2; fs s bq2; fs sdm dcr tions can be derived. Then, the ten modulation variables ð27Þ and the constraint of the damping factors can be solved. Eight of the modulation variables are expressed in (23)– (30): 123 A global asymptotical stable control scheme for a Hexverter in fractional… 1501 m ¼ L r I x þ 3CLrðÞ V x V bsq2 6 bq2; fs 6 25 dcr 11 dcr pffiffiffi RI þ x LI 3 2V =4 V bq2; fs s bd2; fs sdm dcr ð28Þ m ¼ L r I x þ 3CLrðÞ V x V bld2 7 bd2;fl 7 26 dcr 11 dcr pffiffiffiffiffiffiffiffi RI x LI 3=2V V bd2;fl l bq2; fl ldm dcr ð29Þ m ¼ L r I x þ 3CLrðÞ V x V blq2 8 bq2; fl 8 27 dcr 11 dcr RI þ x LI V bq2; fl l bd2;fl dcr ð30Þ Figure 4 depicts the control blocks diagram. The block for the fs components of branches 1, 3, 5 are shown in detail as an example. The other three blocks have similar structures which can be determined based on (25)–(30). The solution to the other two modulation variables (m b01 and m ) depends on the value of K . b02 9 Fig. 4 Control blocks diagram 1) If K =–2LI = 0, m and m can be derived as: 9 b0 b01 b02 T m ¼ 6T CLrðÞ I x =I þ9C V rðÞ V x 3 b01 3 28 b0 9 b0 dcr 10 dcr 10 equation of the damping factors. Notice that R should be a þ T r þ L I r I x 1 12 bd1; fs 1 bd1; fs 1 symmetric matrix, the full constraints of damping factors þ T r þ L I r I x are: 1 13 bq1; fs 2 bq1; fs 2 þ T r þ L I r I x r ¼ r ¼ T I r 1 14 bd1;fl 3 bd1;fl 3 > 16 12 4 bd1; fs 1 > r ¼ r ¼ T I r 17 13 4 bq1; fs 2 þ T r þ L I r I x > 1 15 bq1; fl 4 bq1; fl 4 r ¼ r ¼ T I r 18 14 4 bd1;fl 3 þ T I r þ T I r þ T I r 2 bd1; fs 16 2 bq1; fs 17 2 bd1;fl 18 > r ¼ r ¼ T I r 19 15 4 bq1; fl 4 þ T I r ðÞ V x > 2 bq1; fl 19 dcr 10 > r ¼ r ¼ T I r 24 20 4 bd2; fs 5 2 2 2 2 þ RI þ RI þ RI þ RI r ¼ r ¼ T I r 25 21 4 bq2; fs 6 bd1; fs bd1;fl bq1; fs bq1; fl ð33Þ pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi > r ¼ r ¼ T I r 26 22 4 bd2;fl 7 3=2V I 3=2V I > sdm bd1; fs ldm bd1;fl r ¼ r ¼ T I r > 27 23 4 bq2; fl 8 > r ¼ r ; r ¼ r ð31Þ 28 29 30 31 r þr ¼ 2T I r > 30 28 4 b0 9 T m ¼ 6T CLrðÞ I x =I þ 9C V rðÞ V x 3 b02 3 30 b0 9 b0 dcr 11 dcr 11 > r ¼ T þ2T I r 10 5 4 b0 28 2 > þ T r þ L I r I x 1 20 bd2; fs 5 bd2; fs 5 r ¼ T þ2T I r 11 6 4 b0 30 þ T r þ L I r I x 1 21 bq2; fs 6 bq2; fs 6 2 where þ T r þ L I r I x 1 22 bd2;fl 7 bd2;fl 7 2 8 þ T r þ L I r I x 1 23 bq2; fl 8 bq2; fl 8 T ¼L=ðÞ 3CLV > 4 dcr > . þ T I r þ T I r þ T I r 2 2 2 2 2 2 2 2 2 2 2 bd2; fs 24 2 bq2; fs 25 2 bd2;fl 26 T ¼ L I r þ L I r þ L I r þ L I r 9C V 5 1 2 3 4 bd1; fs bq1; fs bd1;fl bq1; fl dcr þT I r ðÞ V x 2 bq2; fl 27 dcr 11 > 2 2 2 2 2 2 2 2 2 2 T ¼ L I r þ L I r þ L I r þ L I r 9C V 6 5 6 7 8 bd2; fs bq2; fs bd2;fl bq2; fl dcr 2 2 2 2 þ RI þ R þ RI þ RI bd2; fs bd2;fl bq2; fs bq2; fl rffiffiffi rffiffiffi rffiffiffi pffiffiffi 2) If K =–2LI =0, let m =m . Then it can be 1 3 3 3 3 9 b0 b01 b02 V I þ V I þ V I sdm bd2; fs ldm bd2;fl sdm bq2; fs determined that: 2 2 2 2 2 ð32Þ m ¼ m ¼2L rðÞ I x V ð34Þ b01 b02 9 b0 9 dcr where T ¼ 3CLV , T ¼ 3CL, T ¼ I V . 1 dcr 2 3 b0 dcr Substitute all the modulation variables into the redun- On this occasion, the constraints for r -r , r and r will 28 31 10 11 change to: dant equation of the equation set to obtain the constraint 123 1502 Yongqing MENG et al. x_ ¼½ J R oH ðÞ x =ox þ v Start d d d ð36Þ v_ ¼R oH ðÞ x =ox I d K = 2LI 9 b0 where R is a diagonal matrix with factors r (k=1,2,…,11) I Ik r +r =2T I r 30 28 4 b0 9 as diagonal elements. It means that the injected damping r =r , r =r 28 29 30 31 factors r to r in R are changed to the form of (r ?r /s). Is I =0? 1 11 a k Ik b0 r =T +2T I r 10 5 4 b0 28 The state feedback is u ¼ bðÞ x þ v. Define the new closed- r =T +2T I r 11 6 4 b0 30 loop energy function as: r ~r =0 28 31 WðÞ x; v ¼ H ðÞ x ¼ v K v=2 ð37Þ d I r =T , r =T 10 5 11 6 m in (31) b01 where K is a diagonal matrix with factors 1/r I Ik m in (32) b02 (k=1,2,…,11) as its diagonal elements. It can be found m =m in (34) b01 b01 that R r W ¼ R K v ¼ v. Thus, the closed-loop system I v I I can be written in the PCH form: End x_ J R R r W d d I x ¼ ð38Þ v_ R 0 r W Fig. 5 Flow diagram for solution to m and m b01 b02 To ensure that K is a positive definite matrix, it must be satisfied that r [0(k=1,2,…,11). Then, all the conclusions Ik about stability of the equilibrium point x remain preserved. > r ¼ r ¼ 0 28 29 4.3 Voltage-balancing control r ¼ r ¼ 0 30 31 ð35Þ > r ¼ T 10 5 Take branch ua as an example. Figure 6 illustrates the r ¼ T 11 6 control diagram of the voltage-balancing control and the While the constraints for other factors are kept consistent modulation variable can be determined as: with the situation where K 6¼ 0. m ¼ v =N þ K i ðv v Þ V i ¼ 1; 2; .. .; N ua;i ua C ua cua cua;i dcr The solution to modulation variables m and m can b01 b02 ð39Þ be illustrated as the flow diagram shown in Fig. 5. The expression of modulation variables can be simpli- where v is the modulating voltage of branch ua; v is ua cua fied. And the damping matrix of the closed-loop R can be the reference DC voltage of each submodule capacitor; determined by (20). To keep the system global asymptot- v is the DC voltage of the capacitor i; and K is the cua,i c ical stable, R should be a positive definite matrix. Since proportional gain. the expressions of the tenth order principal minor and the Assuming that the branch current is positive, if determinant of R are excessively complicated, the range of v [v , the modulation variable will decrease. Thus cua,i cua damping factors cannot be directly analytically solved. the charging time of the capacitor i in one carrier cycle Here a numerical calculation is adopted to solve the will be shortened to lower v . The regulating process cua,i damping factors while ensuring that R is a positive acts in a similar way when v \v . It can be found cua,i cua definite. that the modulation variables of the submodules in one branch are not identical and the DC voltage of each 4.2.2 IDA-PB controller with integrators submodule is controlled to the reference voltage by this control method. The IDA-PB controller with a constant interconnection structure can ensure that the whole system is asymptoti- cally stable at the equilibrium point x . However, if the system parameters are inaccurate or there exist unmodeled dynamics, a steady-state error will arise. Thus, the IDA-PB v cu a,i ua controller with integrators is proposed to eliminate the cu a + K steady-state error. The closed-loop system model with v m + ua,i ua,i integrators can be expressed as: ua 1/N 1/V + dc r Fig. 6 Voltage-balancing control diagram 123 A global asymptotical stable control scheme for a Hexverter in fractional… 1503 5 Simulation results i i i 1.0 v u w 0.5 Figure 7 shows the configuration of the simulation -0.5 -1.0 model which has been built in a MATLAB/Simulink to 3.00 3.02 3.04 3.06 3.08 3.10 verify the effectiveness of the IDA-PBC scheme. The Time (s) offshore fractional frequency (FF) system is connected to (a) Input current i , i , i (THD=1.04%) u v w the onshore Hexverter through a 50 km submarine cable 1.0 i i i b c a and low frequency transformer. The main parameters of the 0.5 system are listed in Table 1. The Hexverter operates as a -0.5 unity power factor, both the q components of the input and -1.0 3.00 3.02 3.04 3.06 3.08 3.10 output currents are controlled to zero. Time (s) 1) Simulation results of steady state (b) Output current i , i , i (THD=1.05%) a b c The input and output currents, as shown in Fig. 8a 1.5 and b, have good symmetry and the total harmonic 0.5 distortions are 1.04% and 1.05%, respectively. It -0.5 confirms that the designed IDA-PB controller has -1.5 superior performance of steady state. Figure 8c and d 3.20 3.25 3.30 3.35 3.40 Time (s) present the current and voltage of branch ua as a Branch current i (c) ua representation of all branches. It can be seen that there are two different frequency components. As the output voltage of each submodule can be three levels (±v and 0) and each branch contains six submodules, it can -10 -30 be observed that the voltage shown in Fig. 8d has 3.20 3.25 3.30 3.35 3.40 Time (s) (d) Branch voltage u ua 3.39 220 kV 1 Offshore Land system 50 Hz 3.36 Hexverter Submarine cable 3.33 220/10 kV 10/110 kV 50 km 110 kV 3.30 Sea 50/3 Hz 3.90 3.95 4.00 4.05 4.10 4.15 Time (s) Fig. 7 Configuration of FFTS based on the Hexverter (e) DC voltage of submodules in branch ua Fig. 8 Performance of steady-state control Table 1 Main parameters of simulation model thirteen levels. Figure 8e verifies the effectiveness of the voltage-balancing control. With the voltage-bal- Device Parameter Value ancing control added at t , the capacitor voltages Hexverter No. of submodules per branch 6 coincide with each other in the fast regulation. Branch resistance 0.02 X 2) Transient state simulation results Branch resistance 10 mH In order to verify the transient performance of the Submodule capacitance 40 mF IDA-PB controller, a step change of active power is set Initial voltage of submodule 3kV during the simulation process. Ensure the output active capacitance power drops from 10 MW to 5 MW at t =4 s and rises Reference value of equivalent DC 20 kV back to 10 MW at t =6 s. Some simulation results of voltage the IDA-PB controlled system are presented in Fig. 9 Reference value of active power 10 MVA in comparison with the results of the vector controlled Submarine Resistance per unit length 0.0139 X system. cable Inductance per unit length 0.159 mH Figure 9a shows the equivalent DC voltage of the Capacitance per unit length 0.231 lF branch capacitors. It can be observed that the DC Controller r - r 100000 1 9 voltage under the IDA-PBC almost remains unchanged, whereas the voltage under vector control shows drastic Voltage (kV) Voltage (kV) Current (kA) Current (kA) Current (kA) 1504 Yongqing MENG et al. 2.1 t t 2 1 2 t IDA-PB control 2.0 0 -1 Vector control 1.9 -2 3 4 5 6 7 8 1.8 2.0 2.2 2.4 Time (s) Time (s) (a) Equivalent DC voltage of branch capacitors i ; i ; i u v w (a) Input current i , i , i u v w t t 1 2 P ; P t 1 Vector control PBC VECTOR Q ; Q PBC VECTOR IDA-PB control -5 34 5 6 7 8 1 2 3 4 Time (s) Time (s) (b) Input active and reactive power (b) Equivalent DC voltage of branch capacitors t t 6 1 2 s-vector s-IDA-PBC P ; P PBC VECTOR 2 Q ; Q PBC VECTOR s-IDA-PBC s-vector -2 -5 -4 34 5 6 7 8 1 2 3 4 Time (s) Time (s) (c) Output active and reactive power (c) Input active and reactive power 1.5 Fig. 10 Control performance comparison of IDA-PB controller and t t 1 2 vector controller when voltage drops 1.0 i ; i d,ref q,ref i ; q,IDA d,IDA 0.5 i ; d,vecto r q,vecto r 3) Fault simulation results Ensure the input voltage drops from 10 kV to 6 kV -0.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 at t =2 s to simulate a short-circuit fault. Figure 10 Time (s) shows the simulation results. Also, the results of the (d) d and q components of input current vector-controlled system are presented as a compari- 1.5 t t son. 1 2 1.0 The waveforms of the input current in Fig. 10a d,ref i ; d,PBC d,vecto r 0.5 illustrates that the system under IDA-PBC can be 1 t i ; i i 2 q,PBC q,ref q,vecto r restored to steady state after a large disturbance. -0.5 Figure 10b and c present the DC voltage and input 34 5 6 7 8 power respectively. It can be observed that when the Time (s) (e) d and q components of output current input voltage suddenly drops, the DC voltage under the IDA-PBC will restore in a short time after a small Fig. 9 Transient performance comparison of IDA-PBC and vector fluctuation and the input power can also restore to the control reference value, whereas the system under vector fluctuations when the power suddenly changes, which control will have severe oscillation and lose stability. implies that the IDA-PB controller has a fast responding Therefore, the simulation results verify the effective- speed and good tracking performance. Figure 9b and c ness of the IDA-PB controller with integrators for present the actual input and output power of the system enhancing system robustness. and Fig. 9d and e present the d and q components of the input and output currents. The d current has the same changing tendency with its corresponding active power 6 Experiment results and the same conclusion is applicable to q current and reactive power. It can be seen that the input power or Experimental results performed on the control-hard- current under the IDA-PBC and vector control are ware-in-loop simulation platform (AppSIM) are presented approximately coincident, but the output power or here to reflect system performance. Figure 11 shows the current waveforms indicate that the IDA-PB controller structure of the experimental system, where the main has much better regulating ability. Current (kA) Current (kA) Voltage (kV) Power (MW) Power (MW) Power (MW) Voltage (kV) Current (kA) A global asymptotical stable control scheme for a Hexverter in fractional… 1505 Measuring signals Figure 12a, b, c show the input current, output current, (voltage¤t) and output power in steady-state respectively, from which Main circuit in Controller AppSIM platform we can see that they satisfy waveform quality. Figure 12d, Gating signals e, f show the dynamic performance. The input and output Input system: 50 Hz, 10 kV current decrease smoothly as the active power drops from Output system: 50/3 Hz, 6 kV 10 MW to 5 MW, meanwhile the reactive power suffers Fig. 11 Experiment system little fluctuation. In conclusion, the IDA-PB controller of the Hexverter system has a satisfying performance. i i i u w v 7 Conclusion -1 This paper proposes a novel control scheme for a Hex- -2 Time (10 ms/div) verter with global asymptotical stability and strong (a) Input current in steady-state robustness. A frequency decoupled model is built for the a i b i convenience of analysis and control. And then the PCH model of the Hexverter is built. On this basis, the IDA-PB -1 controller is designed by solving modulation variables and -2 configuring the interconnection matrix as well as the Time (20 ms/div) damping matrix. Considering that the interference of sys- (b) Output current in steady-state tem parameters may lead to steady-state error, integrators 1.5 are added to the IDA-PB controller to improve the per- 1.0 0.5 Q formance without losing its global asymptotical stability. The voltage-balancing control is applied in order to balance -0.5 Time (20 ms/div) the capacitor DC voltages. The simulation results and (c) Output power in steady-state experimental results verify that the IDA-PB controller has 1.5 good regulating ability and strong robustness. i i u w i Acknowledgements This work was supported by National Natural Science Foundation of China (No. 51677142) and Science and -1.5 Technology Foundation of SGCC (Research on efficient integration Time (10 ms/div) of large scale long distance offshore wind farm and its key tech- (d) Dynamic performance of input current nologies in operation and control). 1.5 a i i b c 1.0 0.5 Open Access This article is distributed under the terms of the -0.5 Creative Commons Attribution 4.0 International License (http:// -1.0 creativecommons.org/licenses/by/4.0/), which permits unrestricted -1.5 Time (20 ms/div) use, distribution, and reproduction in any medium, provided you give (e) Dynamic performance of output current appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were 1.0 made. 0.5 -0.5 Time (20 ms/div) References (f) Dynamic performance of output power [1] Mau CN, Rudion K, Orths A et al (2012) Grid connection of Fig. 12 Experiment performance of the Hexverter system offshore wind farm based DFIG with low frequency AC trans- mission system. In: Proceedings of IEEE PES general meeting, San Diego, USA, 22–26 July 2012, 7 pp circuit is built into the simulation computer, and the con- [2] Erlich I, Shewarega F, Wrede H et al (2015) Low frequency AC troller provides the gating signals. The currents and volt- for offshore wind power transmission - prospects and chal- ages are measured by the oscilloscope. The system lenges. In: Proceedings of IET international conference on AC and DC power transmission, Birmingham, UK, 10–12 February parameters are consistent with the simulation model built 2015, 7 pp in MATLAB/Simulink in Section 5, as shown in [3] Guan M, Xu Z (2012) Modeling and control of a modular Table 1. multilevel converter-based HVDC system under unbalanced Power (p.u.) Power (p.u.) Current (p.u.) Current (p.u.) Current (p.u.) Current (p.u.) 1506 Yongqing MENG et al. grid conditions. IEEE Trans Power Electronics hexagonal modular multilevel direct converter (Hexverter). In: 27(12):4858–4867 Proceedings of international conference on electrical machines [4] Saad H (2013) Dynamic averaged and simplified models for and systems, Pattaya, Thailand, 25–28 October 2015, 5 pp MMC-based HVDC transmission systems. IEEE Trans Power [21] Karwatzki D, Baruschka L, Hofen M et al (2014) Branch energy Delivery 28(3):1723–1730 control for the modular multilevel direct converter Hexverter. [5] Song Q, Liu W, Li X et al (2013) A steady-state analysis method In: Proceedings of IEEE energy conversion congress and for a modular multilevel converter. IEEE Trans Power Elec- exposition, Pittsburgh, USA, 14–18 September 2014, tronics 28(8):3702–3713 pp 1613–1622 [6] Liu S, Wang X, Ning L et al (2017) Integrating offshore wind [22] Hamasaki SI, Okamura K, Tsubakidani T et al (2014) Control of power via fractional frequency transmission system. IEEE Trans Hexagonal modular multilevel converter for 3-phase BTB sys- Power Delivery 32(3):1253–1261 tem. In: Proceedings of international power electronics confer- [7] Wang XF (1994) The fractional frequency transmission system. ence, Hiroshima, Japan, 18–21 May 2014, pp 3674–3679 In: Proceedings of Paper presented in International Sessions in [23] Karwatzki D, Baruschka L, Mertens A (2015) Survey on the IEE Japan, Power and Energy Society Annual Conference Hexverter topology — a modular multilevel AC/AC converter. Tokyo, August 1994 In: Proceedings of international conference on power electronics [8] Wang XF, Wang XL (1996) Feasibility study of fractional fre- and ECCE Asia, Seoul, Korea, 1–5 June 2015, pp 1075–1082 quency transmission system. IEEE Trans Power Systems [24] Meng Y, Liu B, Shang S et al (2018) Control scheme of 11(2):962–967 Hexagonal modular multilevel direct converter for offshore [9] Wang X, Cao C, Zhou Z (2006) Experiment on fractional fre- wind power integration via fractional frequency transmission quency transmission system. IEEE Trans Power Systems system. J Modern Power Syst Clean Energy 6(1):168–180 21(1):372–377 [25] Ortega R (2002) Interconnection and damping assignment pas- [10] Wang X, Wei X, Ning L (2014) Integration techniques and sivity- based control of port-controlled Hamiltonian systems. transmission schemes for off-shore wind farms. Proceedings of Automatica 38(4):585–596 the CSEE 34(31):5459–5466 [26] Ortega R, Canseco EG (2004) Interconnection and damping [11] Erickson RW, Al-Naseem OA (2001) A new family of matrix assignment passivity-based control: a survey. European journal converters. In: Proceedings of 27th annual conference of the of control 10:432–450 IEEE industrial electronics society, Denver, USA, 29 Novem- ber-2 December 2001, 6 pp Yongqing MENG is an Assistant Professor with the School of [12] Angkititrakul S, Erickson RW (2006) Capacitor voltage bal- Electrical Engineering, Xi’an Jiaotong University. His research ancing control for a modular matrix converter. In: Proceedings of IEEE applied power electronics conference and exposition, interests include renewable energy systems, high-voltage direct Dallas, USA, 19–23 March 2006, 7 pp current transmission systems and fractional frequency transmission [13] Miura Y, Mizutani T, Ito M et al (2013) A novel space vector systems, flexible alternative current transmission systems and power control with capacitor voltage balancing for a multilevel mod- quality of the grid. ular matrix converter. In: Proceedings of IEEE ECCE Asia Downunder, Melbourne, Australia, 3–6 June 2013, pp 442–448 Yichao ZOU is currently working toward her M.S. degree at Xi’an [14] Shayestegan M (2018) Overview of grid-connected two-stage Jiaotong University, Xi’an, China. Her research interests include the transformer-less inverter design. J Modern Power Syst Clean control strategy of modular multilevel converters in FFTS and the Energy 6(1):642–665 control strategy of offshore wind power systems. [15] Liu L, Wang X, Meng Y et al (2017) A decoupled control strategy of modular multilevel matrix converter for fractional Huixuan LI is now working at the State Grid Henan Electric Power frequency transmission system. IEEE Trans Power Delivery Company Economic Research Institute. Her research interests include 32(4):2111–2121 modeling and control strategy of modular multilevel converters and [16] Meng Y, Shang S, Zhang H et al (2018) IDA-PB control with Hexverters, and control methods of unified power flow controllers integral action of Y-connected modular multilevel converter for based on the Hexverter. fractional frequency transmission application. IET Generation, Transmission & Distribution 12(14):3385–3397 Jianyang YU is currently pursuing his M.S. degree at Xi’an Jiaotong [17] Baruschka L, Mertens A (2011) A new 3-phase direct modular University. His research interests include wind energy generation and multilevel converter. In: Proceedings of European conference on conversion, renewable energy systems and technologies for a novel power electronics and applications, Birmingham, UK, 30 modular multilevel AC/AC converter applied to the low frequency August-1 September 2011, pp 1–10 power transmission and distribution system [18] Wan Y, Liu S, Jiang J (2013) Multivariable optimal control of a direct AC/AC converter under rotating dq frames. Journal of Xifan WANG is a Professor in the School of Electrical Engineering, Power Electronics 13(3):419–428 Xi’an Jiaotong University. He has authored and coauthored ten books, [19] Baruschka L, Karwatzki D, Hofen M et al (2014) Low-speed and more than 200 journal and conference papers. He is an drive operation of the modular multilevel converter Hexverter Academician of the Academy of Chinese Sciences, Beijing, China. down to zero frequency. In: Proceedings of IEEE energy con- His research interests include power system analysis, generation version congress and exposition, Pittsburgh, USA, 14–18 planning and transmission system planning, reliability evaluation, September 2014, pp 5407–5414 power markets, and wind power. [20] Fan B, Wang K, Li Y et al (2015) A branch energy control method based on optimized neutral-point voltage injection for a
Journal of Modern Power Systems and Clean Energy – Springer Journals
Published: Jul 29, 2019
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