Research on model predictive control for multilevel converters

BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC BÁCH KHOA HÀ NỘI - - -  - HOÀNG THÀNH NAM NGHIÊN CỨU PHƯƠNG PHÁP ĐIỀU KHIỂN DỰ BÁO CHO CÁC BỘ NGHỊCH LƯU ĐA MỨC RESEARCH ON MODEL PREDICTIVE CONTROL FOR MULTILEVEL CONVERTERS LUẬN VĂN THẠC SĨ KHOA HỌC ĐIỂU KHIỂN VÀ TỰ ĐỘNG HÓA LỜI CAM ĐOAN Tơi xin cam đoan cơng trình tơi Tất ấn phẩm công bố chung với cán hướng dẫn khoa học đồng nghiệp đồng ý tác giả trước đưa vào luận án Cáckết luận án trung thực, chưa công bố sử dụng để bảo vệ luận án khác Tác giả luận án Trần Duy Trinh HÀ NỘI-2018 BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC BÁCH KHOA HÀ NỘI - - -  - HOÀNG THÀNH NAM NGHIÊN CỨU PHƯƠNG PHÁP ĐIỀU KHIỂN DỰ BÁO CHO CÁC BỘ NGHỊCH LƯU ĐA MỨC RESEARCH ON MODEL PREDICTIVE CONTROL FOR MULTILEVEL CONVERTERS LUẬN VĂN THẠC SĨ KHOA HỌC ĐIỂU KHIỂN VÀ TỰ ĐỘNG HÓA LỜI CAM ĐOAN Tơi xin cam đoan cơng trình Tất ấn phẩm NGƯỜI HƯỚNG DẪNnghiệp KHOA công bố chung với cán hướng dẫn khoa học đồng HỌC đồng ý tác giả trước đưa vào luận án Cáckết luận án trung thực, chưa công bố sử dụng để bảo vệ luận án khác Tác giả luận án Trần Duy Trinh PGS TS TRẦN TRỌNG MINH HÀ NỘI-2018 LỜI CAM ĐOAN Tôi xin cam đoan luận cơng trình riêng tơi, tự thiết kế hướng dẫn thầy giáo PGS TS Trần Trọng Minh Các số liệu kết hoàn toàn trung thực Để hoàn thành luận văn sử dụng tài liệu ghi danh mục tài liệu tham khảo không chép hay sử dụng tài liệu khác Nếu phát có chép tơi xin chịu hoàn toàn trách nhiệm Hà Nội, ngày 10 tháng 10 năm 2018 Tác giả luận văn TỔNG QUAN VỀ ĐỀ TÀI Lý chọn đề tài Điều khiển biến đổi đa mức cầu H nối tầng đặt nhiều vấn đề số lượng module tăng nên nhiều theo số mức Bằng cấu trúc điều khiển thơng thường mạch vịng điều khiển phức tạp Phương pháp điều khiển dự báo FCS-MPC dựa tính tốn tối ưu hàm mục tiêu (cost funcion) không gian hữu hạn trạng thái làm việc cho phép xây dựng nên hệ thống điều khiển có cấu trúc đơn giản hơn, lược bỏ khâu điều chế PWM, đưa đến ứng dụng thực tế Đối tượng nghiên cứu Nghiên cứu phương pháp điều khiển dự báo dựa không gian hữu hạn trạng thái làm việc sơ đồ nghịch lưu đa mức cấu trúc cầu H nối tầng Sau áp dụng thuật tốn điều khiển cho ứng dụng nghịch lưu nối lưới điều khiển động không đồng Trong khuân khổ luận văn này, tính đắn thuật toán điều khiển dự báo FCS-MPC kiểm chứng thơng qua mơ hình mơ phần mềm Matlab-Simulink Đóng góp khoa học luận văn Đưa thuật toán điều khiển dự báo FCS-MPC cho biến đổi mức cấu trúc cầu H nối tầng với số bước tính hai bước, giúp bù thời gian trễ q trình tính tốn, đo lường, deadtime, v.v… triển khai thực nghiệm Thuật toán lựa chọn tập hợp vector liền kề giúp giảm đáng kể khối lượng tính tốn tối ưu hóa hàm mục tiêu THESIS OVERVIEW Problem statement Control multilevel converters such as cascaded H-Bridge multilevel converters pose many problems as the number of module increases By the conventional control strategies, the control loops will be very complex The finite control set model predictive control (FCS-MPC) control strategies is based on cost function optimization in the finite number of switch states This could allow the control system to be simpler structure, the system does not need a modulator, can be led to practical applications Object of the study The FCS-MPC control strategy for three-phase CHB multilevel converter is studied in this thesis It is applied in grid-connected CHB as DC-AC converter for isolated DC sources such as PV panels generating power to gird and an IM driver application Within the framework of the thesis, the correctness of the MPC algorithm will be verified through Matlab-Simulink software My contributions Proposal FCS-MPC control strategy for three-phase CHB seven level, predictive horizon at two-steps compensate delay time The subset of adjacent vector state (SAVS) method is proposed to reduce computational when optimizing cost function Acknowledgments Acknowledgments First of all, I would like to express sincere thanks to my supervisor: Assos Prof Tran Trong Minh for his constant encouragement and guidance He has walked me through all the stages of the work of my Master of Science project The work in this thesis is based on research carried out at the Institute for Control Engineering and Automation (ICEA), Hanoi University of Science and Technology (HUST) I would like gratitude ICEA as well as the financial support provided by the National project number: KC.05.03/16-20, “Nghiên cứu, thiết kế chế tạo hệ thống khắc phục nhanh cố tăng/giảm điện áp ngắn hạn cho phụ tải” and: ĐTĐLCN.44/16, “Nghiên cứu thiết kế chế tạo hệ truyền động servo xoay chiều ba pha” Contents Contents Acknowledgments Contents List of figures List of tables List of abbreviations Overview FCS-MPC for CHB multilevel converter 1.1 Three-phase CHB multilevel converter 1.1.1 Structure of a three-phase CHB multilevel converter 1.1.2 Modulation techniques 1.2 Modeling of three-phase CHB multilevel converter 11 1.3 FCS-MPC control strategy 14 FCS-MPC for gird-connected three-phase CHB 17 2.1 FCS-MPC for grid-connected formulation 17 2.1.1 Discrete-time model predictive current control 18 2.1.2 Cost funcion optimization and vector state selection .19 2.1.3 Subset of adjacent vector state 20 2.2 Current reference generation 21 2.3 Simulation results 22 2.4 Conclusion 24 FCS-MPC based current control of an IM 25 3.1 Mathematical model of an IM 25 3.2 FCS-MPC for IM formulation .25 3.2.1 The required signal estimation 27 3.2.2 Discrete-time model predictive current .27 3.2.3 Cost funcion optimization and vector state selection .28 3.3 Simulation results 28 3.4 Conclusion 31 Contents Summary and future works 32 References 33 Appendix A Simulation FCS-MPC for a gird-connected details 35 A.1 Simulation model .35 A.2 MPC algorithm function 36 Appendix B Simulation FCS-MPC for an IM details 37 B.1 Simulation model 37 B.2 MPC algorithm function .38 Appendix C List of publications 40 List of figures List of figures Figure 1.1 H-Bridge switch state Figure 1.2 Three-phase CHB seven level converter Figure 1.3 SPWM multicarrier strategy Figure 1.4 Space vector for three-phase CHB three level 10 Figure 1.5 H-Bridge converter .11 Figure 1.6 Vector state in CHB seven level converter 13 Figure 1.7 Classification of MPC strategies applied to power converter .14 Figure 1.8 FCS-MPC block diagram 15 Figure 2.1 Block diagram of FCS-MPC gird-connected 17 Figure 2.2 Vector state for CHB seven level three-phase 20 Figure 2.3 Simulation results of the proposed FCS-MPC 23 Figure 2.4 FFT analysis output current (phase A) .24 Figure 3.1 Block diagram of FCS-MPC for IM .26 Figure 3.2 Simulation results of output current and voltage 29 Figure 3.3 Simulation results of the proposed FCS-MPC 30 Figure 3.4 FFT analysis output current (phase A) .31 Figure A.1 Simulation overview of FCS-MPC for a grid-connected 35 Figure A.2 FCS-MPC controller in subsystem 36 Figure B.1 Simulation overview of FCS-MPC for an IM 37 Figure B.2 FCS-MPC in subsystem .38 List of tables List of tables Table 1.1 Switch state H-Bridge converter 11 Table 1.2 Level state CHB seven level converter 12 Table 2.1 Simulation FCS-MPC for grid connected parameters .22 Table 3.1 Simulation FCS-MPC for IM parameters 28 Chapter FCS-MPC based current control of an IM the way in which the control of torque and speed are directly based on the electromagnetic state of the motor, similar to a DC motor So that, internal PI current loop can be replaced by FCS-MPC predictive current The block diagram of FCS-MPC for IM is showed in Figure 3.1 This chapter will focus to design internal current loop using FCS-MPC control strategy A, B, C N IM HB HB HB i abc (k ) CHB abc Sopt  * (k ) PI  (k ) iq* (k ) dq * i (k ) Cost function optimization IE i (k ) i (k + 2) External loop  (k ) Prediction (k+2)th * d i (k )  (k ) FCS-MPC Ψ r , (k ) Rotor flux estimation Figure 3.1 i (k ) Block diagram of FCS-MPC for IM Based on FOC control strategy, external PI speed loop generates current reference of FCS-MPC in the sampling time instant k The FCS-MPC will predict output current at two-steps sampling time k+2 and cost function calculations is reduced by SAVS method In αβ coordinate, the procedure designs FCS-MPC included mainly three steps [5]: • Estimation rotor flux; known speed, current reference in the sampling time instant k • The prediction horizon at two-steps sampling time k+2 to predictive current * i (k + 2) , the variables are compared with the current reference i (k ) 26 Chapter FCS-MPC based current control of an IM • The optimum vector state is selected corresponding to the minimum cost function and applied it to power converter 3.2.1 The required signal estimation Based on a induction motor model is presented in sector 3.1, the rotor flux can be expressed [5][6]: Ψr + Tr dΨr = Lmis dt (3.7) where Tr = Lr / Rr By applying the backward Euler’s approximations, rotor flux as following: Ψr ( k ) = L Lr Ψr (k − 1) + m is (k ) r Lr + Ts Rr +1 Ts (3.8) where Ts is a sampling time 3.2.2 Discrete-time model predictive current From the induction motor model, the current stator can be expressed as: i = − R  di  1  − kr  − j  r − v   L dt r    (3.9) Using the forward Euler’s approximations, the discrete equation (3.9) can be obtained as follows:  T i (k + 1) = 1 − s      Ts   kr  − j(k )  Ψr (k ) + v (k )  (3.10)  i (k ) +  R    r    where  =  Ls / R Predictive stator current horizon at two-steps sampling time k+2 as follows [5][6]:   T   T  1 i (k + 2) = 1 − s  i (k + 1) + s kr  − j.(k )  Ψr (k + 1) + v (k )  (3.11)  R    r      27 Chapter FCS-MPC based current control of an IM 3.2.3 Cost function optimization and vector state selection As can be seen in the previous chapter, the cost function can be expressed: J = i (k ) − i (k + 2) + i (k ) − i (k + 1) * * 2 (3.12) Apply SAVS method, the cost function optimization calculate seven time to choose Sopt and apply to the converters 3.3 Simulation results The simulation uses IM 2.2kW and CHB seven level because of the FCS-MPC control strategy will be experimented in laboratory (C9-203 HUST) Simulated parameters are showed in Table 3.1 Table 3.1 Simulation FCS-MPC for IM parameters Parameters Description Value P V In f p Rs Ls Rr Lr Lm wn φ Cdc Vdc Nominal power IM voltage (line-to-line RMS) Rated phase current (RMS) IM frequency Number of pole pairs Stator resistance Stator inductance Rotor resistance Rotor inductance Mutual inductance Rate speed Power factor DC capacitor per HB DC capacitor voltage per HB 2.2 kW 400 V 4.7 A 50 Hz 1.99 Ω 0.043 H 1.99 Ω 0.043 H 0.3452 H 2880 rpm 0.86 2500 F 150 V Simulink model, cost function is presented in Appendix B The simulation follows scenario: • At t = 0s, the magnetization process • At t = 0.2s, acceleration to the nominal value 300 rad/s • At t = 0.2s, connection of nominal load 10Nm • At t = 0.6 s, reversing process down to -300 rad/s 28 Chapter FCS-MPC based current control of an IM In the speed loop, proportional and integral is 0.8 and 60, rotor flux current reference value 2.5 A Sampling time internal loop Ts = 50us and external loop value 10.Ts The simulation results are presented in Figure 3.2 and Figure 3.3 iabc (A) 20 -20 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.7 0.8 0.9 a Output current i abc vAN (V) 500 -500 0.2 0.3 0.4 0.5 0.6 b Output voltage vAN Figure 3.2 Simulation results of output current and voltage Simulation results in Figure 3.3.a and Figure 3.3.b show that both the flux forming and torque forming currents accurately follow the set point trajectories (coming from the magnetic flux controller and the speed controller in the outer loop) in all working mode When the reference changed to negative direction, the speed real is started to following the speed reference at exact time of 0.2s and 0.6s at high and low speed, respectively, with the reverse high torque between 10 and 10 Nm at 300 rad/s and -300 rad/s (see Figure 3.3.c and Figure 3.3.d) The threephase current is showed in Figure 3.2.a, waveforms sine It proves that at the rated condition, the controller IM with FCS-MPC method operates smooth The output voltage phase A is showed in Figure 3.2.b, when speed acceleration, state level increase from three to five and seven level, value per level is 150V 29 Chapter FCS-MPC based current control of an IM 15 3.5 Ref Real 10 2.5 isq (A) isd (A) Ref Real 1.5 -5 -10 0.5 -15 0.2 0.4 0.6 0.8 1.2 1.4 0.4 0.6 0.8 1.2 1.4 1.2 1.4 b Output current isq a Output current isd 15 400 Ref Real 10 Torque (kg.m2) 200 w (rad/s) 0.2 -200 -5 -10 -15 -400 0.2 0.4 0.6 0.8 1.2 1.4 0.2 0.4 0.6 0.8 d Torque response c Speed response Figure 3.3 Simulation results of the proposed FCS-MPC The result of FFT analysis output current phase A is presented in Figure 3.4, starting analyze time from 0.5s to 0.58s (four cycles) with fundamental frequency 50Hz and max frequency 1000Hz The obtained result proves that the distortion in the system is less The current THD of the MPC is only 2.55% 30 Chapter FCS-MPC based current control of an IM Fundamental (50Hz) = 8.465 , THD= 2.55% Mag (% of Fundamental) 1.5 0.5 0 10 12 14 16 18 20 Harmonic order Figure 3.4 3.4 FFT analysis output current (phase A) Conclusion The simulation results show that the FCS-MPC control strategy is a promising control tool that is powerful to control the power converters and electrical drives Compensation delay time with the predictive horizon at two-steps sampling time k+2 The delay time compensation has been taken in consideration in the predictive control algorithm Results in well tracking of the reference variables at high speed, even at low speed regions of the IM It is performance of IM will be improved However, the ripple of electromagnetic torque is significantly high Further implement needs to reduce the ripple 31 Chapter Summary and future works Chapter Summary and future works The FCS-MPC control strategy is a very attractive solution for controlling power electronic applications In the thesis presented the FCS-MPC for gird-connected and IM application with a three-phase CHB seven level converter The control strategy has a simple algorithm structure, it is easy to implement with increased number of cell, also it can be applied to other multilevel converter topologies FCS-MPC control strategy does not need a modulator stage However, this usually leads to spread harmonic of the output waveforms Such critical challenges as the accuracy of the model, high sampling rates, and high computational cost function, etc… are disadvantages of FCS-MPC control strategy But nowadays, the continuous evolution of the microprocessor technology and the efforts of the researchers, those problems will be overcome A future work is experimental the FCS-MPC control strategy It can be effectively evaluated of algorithm and delay time compensation at two-steps sampling time k+2 And probably longer prediction time steps as 4, 6, etc… Applying a multi-variable into cost function with the weighting factor The example is FCS-MPC for controlling the torque and flux in an IM [2][6] 32 References References [1] Sergio Vazquez, Jose I Leon, Leopoldo G Franquelo, Jose Rodriguez, Hector A Young, Abraham Marquez, and Pericle Zanchetta, "Model Predictive Control: A Review of Its Applications in Power Electronics", IEEE Industrial Electronics Magazine, March 2014 [2] Sergio Vazquez, Jose Rodriguez, Marco Rivera, Leopoldo G Franquelo, Margarita Norambuena, “Model Predictive Control for Power Converters and Drives: Advances and Trends”, IEEE Transactions on Industrial Electronics, November 2016 [3] Samir Kouro, Patricio Cortés, René Vargas, Ulrich Ammann and José Rodríguez, “Model Predictive Control-A Simple and Powerful Method to Control Power Converters”, IEEE Transactions on Industrial Electronics, November 2008 [4] J Holtz, “The dynamic representation of AC drive systems by complex signal flow graphs”, Industrial Electronics, 1994 Symposium Proceedings [5] Fengxiang Wang, “Model predictive torque control for electrical drive systems with and without an encoder”, PhD Thesis, Technischen Universitat Munchen, July 2014 [6] Muslem Uddin, Saad Mekhilef, Mutsuo Nakaoka, Marco Rivera, “Model predictive control of induction motor with delay time compensation: An experimental assessment”, 2015 IEEE Applied Power Electronics Conference and Exposition (APEC), May 2015 [7] Patricio Cortes, Alan Wilson, Samir Kouro, Jose Rodriguez, Haitham AbuRub, “Model Predictive Control of Multilevel Cascaded H-Bridge Inverters”, IEEE Transactions on Industrial Electronics, February 2010 [8] Ricardo P Aguilera, Yifan Yu, Pablo Acuna, Georgios Konstantinou, Christopher D Townsend, Bin Wu, Vassilios G Agelidis, “Predictive Control algorithm to achieve power balance of Cascaded H-Bridge converters”, 2015 33 References IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics, February 2016 [9] Ricardo P Aguilera, Daniel E Quevedo, “Predictive Control of Power Converters: Designs With Guaranteed Performance”, IEEE Transactions on Industrial Informatics, October 2014 [10] Ricardo P Aguilera, Yifan Yu, Pablo Acuna, Georgios Konstantinou, Christopher D Townsend, Bin Wu, Vassilios G Agelidis, “Predictive Control Algorithm to Achieve Power Balance of Cascaded H-Bridge Converters”, 2015 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics [11] Ricardo P Aguilera, Pablo Acuna, Yifan Yu, Bin Wu, "Predictive Control of Cascaded H-Bridge Converters Under Unbalanced Power Generation", IEEE Transactions on Industrial Electronics (Volume: 64, Issue: 1, Jan 2017) [12] Roky Baidya, Ricardo P Aguilera, Pablo Acuña, Sergio Vazquez, Hendrik du Toit Mouton, "Multistep Model Predictive Control for Cascaded H-Bridge Inverters Formulation and Analysis", IEEE Transactions on Power Electronics (Volume: 33, Issue: 1, Jan 2018) [13] Luca Tarisciotti, Pericle Zanchetta, Alan Watson, Stefano Bifaretti, Jon C Clare, "Modulated Model Predictive Control for a Seven-Level Cascaded HBridge Back-to-Back Converter", IEEE Transactions on Industrial Electronics (Volume: 61, Issue: 10, Oct 2014) [14] Sumit Dutta, Samir Hazra, Subhashish Bhattacharya, "A Digital Predictive Current Mode Controller for Single Phase High Frequency Transformer Isolated Dual Active Bridge DC to DC Converter", IEEE Transactions on Industrial Electronics (Volume: 63, Issue: 9, Sept 2016) [15] Jose Rodriguez, Marian P Kazmierkowski, Jose R Espinoza, Pericle Zanchetta, Haitham Abu-Rub, "State of the Art of Finite Control Set Model Predictive Control in Power Electronics", IEEE Transactions on Industrial Informatics (Volume: 9, Issue: 2, May 2013) 34 Appendix A Simulation FCS-MPC for a gird-connected details Appendix A Simulation FCS-MPC for a gird-connected details A.1 Simulation model Continuous P* P* powergui Q* i_ref v_grid Q* Vdc i_abc i_ref i_ref Calculator Vector i_ref v_grid iabc i_abc MPC Controller Iabc Vector A A v_grid Vabc A N 6,6kV - 50Hz Figure A.1 A a a B B b b C C c c a B b C c Three-Phase Grid A Grid Measure RL Filter 6ohm, 10mH Vdc B B C C Load Measure Three-Phase Cascaded H-Bridges Simulation overview of FCS-MPC for a grid-connected 35 Appendix A Simulation FCS-MPC for a gird-connected details Figure A.2 A.2 FCS-MPC controller in subsystem MPC algorithm function % Simulation file % Master of Science Thesis % Author: Eng Hoang Thanh Nam % Advisor: Assoc Prof Tran Trong Minh % Version: V2.0 % Date: Aug/2018 % PELAB-HUST function k = fcn(i_k, i_ref_k, v_g_k, Vdc, Ts, k_last) % Parameters L = 10e-3; r = 6; u_k = zeros(3,1); A = [(1-r*Ts/L), 0; 0, (1-r*Ts/L)]; B = ((Vdc*Ts)/(3*L))*[2 -1 -1; -1 -1]; E = (-Ts/L)*[1 0; 1]; temp = inf; k = inf; % Inductance load (H) % Resistance load (Ohm) % MPC function for i = 1:7 ss_temp = top(k_last+1,i) + 1; u_k(1) = va(ss_temp); u_k(2) = vb(ss_temp); u_k(3) = vc(ss_temp); x_load_k1 = A*i_k + B*u_k + E*v_g_k; x_load_k2 = A*x_load_k1 + B*u_k + E*v_g_k; J = (x_load_k1(1) - i_ref_k(1))^2 + (x_load_k1(2) - i_ref_k(2))^2 + (x_load_k2(1) - i_ref_k(1))^2 + (x_load_k2(2) - i_ref_k(2))^2; temp = min(temp, J); if temp == J k = ss_temp - 1; end end 36 Appendix B Simulation FCS-MPC for an IM details Appendix B Simulation FCS-MPC for an IM details B.1 Simulation model id Torque isd iq Speed isq Scope1 Scope2 Vdc Continuous w Vector w* w* Ramp powergui is MPC Controller Tm A p Load torque A m Vdc B B C C Asynchronous Machine SI Units Figure B.1 Vector Three-Phase Cascaded H-Bridges Simulation overview of FCS-MPC for an IM 37 Appendix B Simulation FCS-MPC for an IM details Figure B.2 B.2 % % % % % % % FCS-MPC in subsystem MPC algorithm function Simulation file Master of Science Thesis Author: Eng Hoang Thanh Nam Advisor: Assoc Prof Tran Trong Minh Version: V2.0 Date: Aug/2018 PELAB-HUST function k = fcn(i_s_k_ref, flux_r_k, i_s_k, Vdc_k, Ts, w_k, k_last) % Input flux_r_a_k = flux_r_k(1); flux_r_b_k = flux_r_k(2); i_s_a_k = i_s_k(1); i_s_b_k = i_s_k(2); i_s_a_k_ref = i_s_k_ref(1); i_s_b_k_ref = i_s_k_ref(2); % IM parameters J = 0.0018; Rs = 1.99; Rr = 1.99; Ls_sigma = 0.043; Lr_sigma = 0.043; Lm = 0.3642; p = 1; Ls = Ls_sigma + Lm; Lr = Lr_sigma + Lm; %Momen quan tinh (kg.m2) %Dien tro stato %Dien tro rotor %Dien cam ro stato (H) %Dien cam ro rotor (H) %Dien cam tu hoa (H) %So doi cuc %Dien cam stato %Dien cam rotor % Const kr = Lm/Lr; R_sigma = Rs + kr*kr*Rr; sigma = - (Lm*Lm)/(Ls*Lr); 38 Appendix B Simulation FCS-MPC for an IM details L_sigma = sigma*Ls; to_sigma = sigma*Ls/R_sigma; to_r = Lr/Rr; gab_temp = inf; k = inf; va_k = (2/3)*Vdc_k*(2*vg+vh)/2; vb_k = (2/3)*Vdc_k*(sqrt(3)/2)*vh; for i = 1:7 j = top(k_last+1,i) + 1; % Predictive current stator alapha, beta(k+1) -i_s_a_k1 = (1-Ts/to_sigma)*i_s_a_k + (Ts/(to_sigma*R_sigma))*(kr*(1/to_r-0*w_k)*flux_r_a_k+va_k(j)); i_s_b_k1 = (1-Ts/to_sigma)*i_s_b_k + (Ts/(to_sigma*R_sigma))*(kr*(1/to_r-w_k)*flux_r_b_k+vb_k(j)); % Predictive flux rotor alapha, beta(k+1) -flux_r_a_k1 = (Lr/(Lr+Ts*Rr))*flux_r_a_k + (Lm/(to_r/Ts+1))*i_s_a_k1; flux_r_b_k1 = (Lr/(Lr+Ts*Rr))*flux_r_b_k + (Lm/(to_r/Ts+1))*i_s_b_k1; % Predictive current stator alapha, beta(k+2) -i_s_a_k2 = (1-Ts/to_sigma)*i_s_a_k1 + (Ts/(to_sigma*R_sigma))*(kr*(1/to_r-0*w_k)*flux_r_a_k1+va_k(j)); i_s_b_k2 = (1-Ts/to_sigma)*i_s_b_k1 + (Ts/(to_sigma*R_sigma))*(kr*(1/to_r-w_k)*flux_r_b_k1+vb_k(j)); % MPC -% Cost function % Quadratic cost function % gab = (i_s_a_k_ref-i_s_a_k1)^2 + (i_s_b_k_ref-i_s_b_k1)^2; gab = (i_s_a_k_ref-i_s_a_k1)^2 + (i_s_b_k_ref-i_s_b_k1)^2 + (i_s_a_k_ref-i_s_a_k2)^2 + (i_s_b_k_ref-i_s_b_k2)^2; gab_temp = min(gab,gab_temp); if gab_temp == gab k = j-1; end end 39 Appendix C List of publications Appendix C List of publications [1] Hoàng Thành Nam, Trần Hùng Cường, Trần Trọng Minh, Phạm Việt Phương, “Điều khiển dự báo cho nghịch lưu bảy mức cấu trúc cầu H nối tầng”, CASD 2017 [2] Hoàng Thành Nam, Trần Hùng Cường, Phạm Việt Phương, Trần Trọng Minh, Vũ Hồng Phương, “Giảm số lượt tính tốn hàm mục tiêu phương pháp điều khiển dự báo cho biến đổi đa mức cầu H nối tầng để giảm tần số đóng cắt van”, VCCA-2017 [3] Trần Hùng Cường, Hoàng Thành Nam, Trần Trọng Minh, Phạm Việt Phương, Vũ Hoàng Phương, “Điều khiển dự báo hữu hạn trạng thái đóng cắt van cho biến đổi đa mức có cấu trúc MMC”, VCCA-2017 [4] Hồng Thành Nam, Nguyễn Đình Ngọc, Nguyễn Văn Tiệp, Vũ Hồng Phương, Trần Trọng Minh, “Mô khôi phục điện áp động hệ thống điều áp liên tục AVC”, VCCA-2017 [5] Vũ Hoàng Phương, Hoàng Thành Nam, Trần Trọng Minh, Nguyễn Huy Phương, “Điều khiển chỉnh lưu tích cực sử dụng mạch lọc LCL điều kiện lưới điện không cân bằng”, Chuyên san Đo lường, Điều khiển Tự động hóa, số 20, 12/2017 [6] Ha Thanh Vo, Nam Thanh Hoang, Phuong Hoang Vu, Minh Trong Tran, “FCS-Model Predictive Control of Induction Motors feed by MultilLevel Casaded H-Bridge Inverter”, RCEEE 2018 40 ... CCS-MPC Continuous control set model predictive control OSV-MPC Optimal switching vector model predictive control OSS-MPC Optimal switching sequence model predictive control IM Induction motor... disposition APOD Alternative phase opposite disposition POD Phase opposite disposition SVM Space vector modulation MPC Model predictive control FCS-MPC Finite control set model predictive control. .. statement Control multilevel converters such as cascaded H-Bridge multilevel converters pose many problems as the number of module increases By the conventional control strategies, the control loops