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Three-phase CHB multilevel converter

Structure of a three-phase CHB multilevel converter

The Figure 1.1 shows three switch state of H-Bridge (as named is cell), each cell make three level voltage: -1; 0 and 1

STATE = -1 v ac v dc v dc v ac v dc v ac

Chapter 1 Overview FCS-MPC for CHB multilevel converter

In CHB multilevel converter, number of cells are connected in series Each cell has separate DC source which is obtained from fuel cells, batteries, capacitors, transformers,…

The activity of M cells in each phase generates a total of 2m+1 voltage levels For instance, Figure 1.2 illustrates a three-phase CHB (Cascade H-Bridge) multilevel converter with seven levels Essentially, a three-phase CHB multilevel converter operates similarly to three single-phase converters arranged in a wye configuration.

Figure 1.2 Three-phase CHB seven level converter

• It doesn’t need capacitors or diodes for clamping

• Entire IGBT switching in basic fundamental frequency (or near this frequency), so that reduce power lose switch

• The harmonics reduce because IGBT switching small frequency

• The wave is quite sinusoidal in nature

• CHB needs separate DC sources for each leg

• Controller will be complex if number of cells increase

Additional detail can be found in Appendix C [2], [3] and [4].

Modulation techniques

a Sin-PWM (SPWM) multicarrier strategy

In Sinusoidal Pulse Width Modulation (SPWM), each phase employs a single sinusoidal reference signal To achieve this, cells require m triangular carriers, each with a frequency and peak-to-peak amplitude that are consistent The sinusoidal reference is then compared against each triangular carrier to establish the switching output voltages for the power converter.

U c2 d POD carrier Figure 1.3 SPWM multicarrier strate gy

Multicarrier PWM encompasses four distinct strategies, as illustrated in Figure 1.3, which depicts the multicarrier PWM approach for a single-phase CHB five-level inverter This method requires four triangular carrier signals and a single sinusoidal reference waveform.

• Phase-shift (PS) carrier PWM strategy Each carrier is phase-shift by 360° ° from it/4 ’s adjacent carrier

• Phase disposition (PD), all carriers are in phase 0°

• Alternative phase opposite disposition (APOD), all carriers are alternatively in phase opposition

• Phase opposite disposition (POD) all the carriers above the zero reference , are in phase among them

For single-phase converters, Sinusoidal Pulse Width Modulation (SPWM) remains a viable option; however, three-phase converters have benefited from advanced techniques designed to minimize harmonics Among these, Space Vector Modulation (SVM) stands out as the most widely used method, effectively leveraging the advantages of three-phase systems.

The SVM technique effectively minimizes the impact of common-mode voltages, eliminating the need for triangular carriers This method offers enhanced flexibility, including redundant switching sequences and adjustable duty cycles, making it particularly advantageous for digital implementations.

Figure 1.4 Space vector for three-phase CHB three level

These advantages of SVM can lead to a significantly improved performance of multilevel converters, especially when the level number of the converter is large

The space vector representation of a three-phase CHB three-level converter is illustrated in Figure 1.4 Implementing Space Vector Modulation (SVM) for higher-level converters presents challenges due to the presence of 6(n-1) triangles in the space vector diagram The reference vector can be positioned within any of these triangles, prompting SVM to select appropriate switch states corresponding to the triangle in which the reference vector resides, and apply them for the necessary duty cycles in the switching sequence.

Modeling of three-phase CHB multilevel converter

Each cell of converter described in is Figure 1.5 v dc

The IGBT switch state is indicated by "0" for the off position and "1" for the on position As detailed in Table 1.1, the switch states for each cell determine the output voltage, which can be either 0, V dc, or -V dc, depending on the switch states of 0; 1 and -1.

Table 1.1 Switch state H-Bridge converter

Gate state v ac Switch state

Three-phase CHB seven level converter is showed in Figure 1.2, level state shows in Table 1.2 Output voltage v AN , v BN ,v CN ; load voltage: v AZ , v BZ , v CZ and

Chapter 1 Overview FCS-MPC for CHB multilevel converter common-mode voltagev ZN

Table 1.2 Level state CHB seven level converter

Switch state v ac Level state

Assume, V dc each cell is balance, V dc,k = V dc (k = 1, ) Output voltage n v AN , v BN , v CN obtains { 3- V dc , - V2 dc, -1V dc, 0, V+1 dc , +2V dc , +3V dc }, corresponding {3, 2,

1, 0, -1, -2, -3}*V dc , this is called level state {3, 2, 1, 0, -1, -2, -3}

Level state phase A, B and C are grand total 127 reasonable different vector state v

And, output voltage CHB multilevel converters express:

Assuming, load is balance, output voltage each phase can be showed:

Figure 1.6 Vector state in CHB seven level converter Because of v AZ +v BZ +v CZ =0, so common-mode v ZN as express:

The level state can be expressed by the vector as following:

= The vector state can be expressed in terms of complex coordinate v by using the Clarke transformation: v = v  + jv  (1.6)

Chapter 1 Overview FCS-MPC for CHB multilevel converter where: 1 ( )

FCS-MPC control strategy

Model Predictive Control (MPC) is a versatile control strategy that utilizes a system model to predict the future behavior of controlled variables over a defined predictive horizon By optimizing a user-defined cost function, MPC generates a sequence of control actions It's important to note that the algorithm is recalculated at each sampling period, applying only the first value of the optimal sequence to the system at each time step.

Figure 1.7 Classification of MPC strategies applied to power converter

The classification of Model Predictive Control (MPC) strategies for power converters, illustrated in Figure 1.7, reveals two main types: continuous control set MPC (CCS-MPC) and finite control set MPC (FCS-MPC).

The CCS-MPC generates a continuous control signal to produce output voltage in power converters, offering the significant benefit of maintaining a fixed switching frequency However, its complexity in formulating the MPC problem poses a notable drawback.

The Finite Control Set Model Predictive Control (FCS-MPC) utilizes a finite number of switching states to develop its algorithm, eliminating the need for a modulator FCS-MPC can be categorized into two main types: Optimal Switching Vector MPC (OSV-MPC) and Optimal Switching Sequence MPC (OSS-MPC) OSV-MPC is widely recognized as the leading control strategy for power converters, leveraging the output vector state of the power converter as its control set A key advantage of OSV-MPC is its ability to simplify the optimization problem to an enumerated search algorithm, making the formulation of the MPC strategy more intuitive However, a significant drawback of OSV-MPC is that it applies only one optimal output vector state throughout the entire sampling period, resulting in uncontrolled switching frequency.

In FCS-MPC, the system's prediction model must be discretized, leading to the implementation of MPC algorithms on digital hardware such as DSP or FPGA Typically, FCS-MPC employs Euler approximation for the discretization of one-step or multiple-step processes.

Figure 1.8 FCS-MPC block diagram shows FCS-MPC block diagram Assume, control variable

Figure 1.8 x follow the reference variable x * , procedure design FCS-MPC following basic steps:

• Measurement, estimation the control variable in the sampling time instant

• For every switch states of the converters, predictive (using the mathematical model) the behavior of variable in the x n-steps time

• Evaluate the cost function for each prediction

• Select the switch states that minimize the cost function, S opt applied to the converters

In the experiment, delays from the driver, measurements, and IGBT adversely affect the predictive control algorithm's performance The computational time required for predicting variables, along with processor delays, hampers the system's efficiency To address this issue, the predictive horizon can be adjusted to the (ve k+n) th sampling time for variable prediction, allowing for comparisons with reference values and the determination of cost functions The optimal selection of S opt is made based on the minimum cost function, which is then applied to the power converter.

Chapter 2 FCS-MPC for gird-connected three-phase CHB

FCS-MPC for gird-connected three-phase CHB

FCS-MPC for grid-connected formulation

Discrete-time model predictive current control

Grid-connected three-phase CHB converter, the following continuous time dynamic equation for each phase current can be expressed:

( ) i ( ) ( ) ( ) ( ) v abc abc i abc v g abc NO d t t L r t t v t dt

= + + + (2.1) where and r L the resistance and inductance of the output filteris ; v abc is phase output voltage; v g abc , is grid voltage Therefore, from (2.1) can be inferred:

( ) ( ) 1 ( ) ( ) ( ) i abc i abc v abc NO v g abc d t r t t v t t dt L L

For a three-phase cell CHB converter, the phase output voltage in become: n

, v abc = V dc v l abc (2.3) where level state v l abc , = − − + n n, 1, ,0, , 1,n− n 

Additionally, common-mode voltage is given by:

The ﬁrst order forward Euler’s approximations:

By applying (2.5) to (2.2) with sampling time T s , the discrete-time of current as bellow:

( 1) 1 ( ) ( ) ( ) , ( ) i abc k rT s i abc k T s v abc k v NO k v g abc k

The discrete-time dynamic model can be expressed [10]:

( 1) ( ) ( ) ( ) x k + = Ax k + Bv l abc k + Ev g abc k (2.7) where:

As applying the Forward Euler’s approximations, similarly (2.7), the predictive horizon at two-steps sampling time k+2 as following [5][6]:

( 2) ( 1) ( ) ( ) x k + = Ax k + + Bv l abc k + Ev g abc k (2.8)

2.1.2 Cost function optimization and vector state selection

The final step in the optimization process involves creating a flexible cost function tailored to specific control objectives In the context of predictive control for grid-connected systems with delay compensation, the cost function can be defined to effectively represent these goals.

  is the reference current For sufficiently small sampling time, it can be assumed that

( 2) ( 1) ( ) x k+ x k+ x k Therefore, cost function (2.9) can be rewritten as:

The cost function is assessed for each possible three-phase level state, identifying the one that minimizes the cost Subsequently, the optimal level state is chosen and applied to the load This process involves calculating the relevant equations multiple times to ensure accuracy and efficiency.

Chapter 2 FCS-MPC for gird-connected three-phase CHB a seven level in order to obtain the optimal solution However, level state can be defined from vector state By that way, the calculation can be still reduced 12 7 times The selection criterion is to select the voltage level states that minimize the common voltage vector

2.1.3 Subset of adjacent vector state

In the previous section, each sampling time cost function needs to be calculated

The vector state rapidly increases with the formula 12m² + 6 + 1 as the number of cells (m) grows significantly To address this computational challenge, the Subset of Adjacent Vector State (SAVS) method has been proposed This approach effectively narrows down the vector states to be evaluated, focusing only on those closest to the most recently applied vector, as illustrated in Figure 2.2.

Number of redundancies for each vector

Figure 2.2 Vector state for CHB seven level three-phase r the calculation of the adjacent vectors to the last applied vector, the

Fo distance between vectors can be calculated with the following function:

If v x near v y , the distance should be equal or less than 2V dc /3 The calculation of distance is made offline, and it is stored in database In this way, the

Subset of adjacent vector state

In the previous section, each sampling time cost function needs to be calculated

The vector state can rapidly increase to 127 times, following the equation 12m^2 + 6 + 1, as the number of cells (m) grows significantly To address this computational challenge, the Subset of Adjacent Vector State (SAVS) has been proposed This approach effectively narrows down the set of vector states to be evaluated, focusing only on those closest to the last applied vector, as illustrated in Figure 2.2.

Number of redundancies for each vector

Figure 2.2 Vector state for CHB seven level three-phase r the calculation of the adjacent vectors to the last applied vector, the

Fo distance between vectors can be calculated with the following function:

If v x near v y , the distance should be equal or less than 2V dc /3 The calculation of distance is made offline, and it is stored in database In this way, the

Chapter 2 FCS-MPC for gird-connected three-phase CHB number of calculation is reduced to only seven predictions, irrespective of the number of cells

The predictive control algorithm present below:

Algorithm 1 The FCS-MPC predicts horizon at two-steps algorithm

1 Initialize the system and build a table: Subset of Adjacent vector state

2 Measurements of i abc ( )k and v g abc , ( ) k

3 Determines of i * abc ( ) k and vector state v ( k − 1)

4 Predictions of i abc ( 1)k+ and i abc (k+2)

The minimum value of and the corresponding vector state J v ( ) k are kept end for

6 v ( ) k is injected into the converters.

Current reference generation

The cost function in equation (2) requires references for the current i* By utilizing the references for three-phase active power (P*), reactive power (Q*), and grid voltages (v_sd,g, v_sq,g), the current i* can be calculated This approach allows for the determination of three-phase active and reactive power references in a coherent manner.

2 sd g sd sq g sq sq g sd sd g sq

(2.12) where v sd g , , v sq g , and i i * sd sq , * are gird voltage and current references in dq coordinate

Therefore, i i * sd sq , * can be express:

2 3 sd g sq g sd sd g sq g sq g sd g sq sd g sq g

Simulation results

The simulation of FCS-MPC horizons at the (k+2)th sampling time for a three-phase CHB seven-level converter was validated using Matlab-Simulink software, with the parameters utilized in the simulation detailed in Table 2.1.

Table 2.1 Simulation FCS-MPC for grid connected parameters

P * Three-phase active power 1 MVA

Q * Three-phase reactive power 1 MVar

C dc DC capacitor per H-Bridge 2500 F

V dc DC capacitor voltage per H-Bridge 2300 V

L Filter inductor 10 mH r Filter resistor 6 Ω

T s Sampling time 100 às f Grid frequency 50 Hz

V g Grid voltage (line- -line RMS) to 6.6 kV

The simulink model and cost function are showed in Appendix A, main results are presented in Figure 2.3

The analysis in Figure 2.3.b demonstrates that the real current closely tracks the reference current with a rapid response Additionally, the common-mode voltage is maintained at a minimal level centered around zero, as illustrated in Figure 2.3.d A symmetric output voltage is achieved with seven levels, as depicted in Figure 2.3.c Figures 2.3.e and 2.3.f show that the real active power and reactive power remain consistent with the reference values Furthermore, the output currents for phases A, B, and C are presented in Figure 2.3.a.

200 i ab c (A) a Output current phase A, B and C i a (A)

Real b Gird, reference current phase A

Ref Real e Three-phase active power

Ref Real f Three-phase reactive power Figure 2.3 Simulation results of the proposed FCS-MPC

M ag (% of F un da m en ta l)

Figure 2.4 FFT analysis output current (phase A)

The Fast Fourier Transform (FFT) analysis of output current phase A was conducted from 0.01s to 0.09s, covering four cycles at a fundamental frequency of 50Hz and a maximum frequency of 1000Hz, as illustrated in Figure 2.4 The total harmonic distortion (THD) observed was minimal, recorded at 1.91%.

Conclusion

The FCS-MPC horizons at a two-step sampling time of k+2 for the CHB seven-level converter demonstrate excellent reference tracking and a significant reduction in common-mode voltage The cost function calculation is optimized using the SAVS method, while the selection among adjacent vectors effectively reduces dv/dt at the load side of the FCS-MPC This control strategy is easily applicable to CHB multilevel converters as the number of cells increases and can also be extended to other multilevel converter topologies.

Chapter 3 FCS-MPC based current control of an IM

FCS-MPC based current control of an IM

Mathematical model of an IM

An induction motor can be described by complex equations [4]: s s s v i Ψ s

The voltage equation of the phase winding, as presented in Equation (3.1), illustrates the relationship among stator voltage, stator current, and stator flux linkage In Equation (3.2), the rotor voltage vector is zero, indicating that a squirrel-cage motor is being analyzed, which results in a short-circuited rotor winding The calculations for winding and rotor flux can be derived from the stator and rotor currents, as shown in Equations (3.3) and (3.4) Finally, the electromagnetic torque is expressed in Equation (3.5).

 m is a mechanical rotor speed and it is related to the electric rotor speed

 by the number of pole : p

FCS-MPC for IM formulation

The required signal estimation

Based on a induction motor model is presented in sector 3.1, the rotor flux can be expressed ][6]: [5 r r s Ψ Ψ i r m

By applying the backward Euler’s approximations, rotor flux as following:

Discrete-time model predictive current

From the induction motor model, the current stator can be expressed as:

Using the forward Euler’s approximations, the discrete equation (3.9) can be obtained as follows:

Predictive stator current horizon at two-steps sampling time k+2 as follows [5][6]:

Cost funcion optimization and vector state selection

3.2.3 Cost function optimization and vector state selection

As can be seen in the previous chapter, the cost function can be expressed:

Apply SAVS method, the cost function optimization calculate seven time to choose S opt and apply to the converters.

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

V IM voltage (line- -line RMS) to 400 V

I n Rated phase current (RMS) 4.7 A f IM frequency 50 Hz p Number of pole pairs 1

L m Mutual inductance 0.3452 H w n Rate speed 2880 rpm φ Power factor 0.86

C dc DC capacitor per HB 2500 F

V dc DC capacitor voltage per HB 150 V

Simulink model, cost function presented in is Appendix B The simulation follows scenario:

• At t = 0.2s, acceleration to the nominal value 300 rad/s

• At t = 0.2s, connection of nominal load 10Nm

In the speed loop, proportional and integral is 0.8 and 60, rotor flux current reference value 2.5 A Sampling time internal loop T s = 50us and external loop value 10.T s

The simulation results are presented in Figure 3.2 and Figure 3.3

Figure 3.2 Simulation results of output current and voltage

Simulation results demonstrate that the flux and torque forming currents effectively track the set point trajectories provided by the magnetic flux and speed controllers across all operating modes When the reference shifts to the negative direction, the actual speed begins to align with the speed reference at precisely 0.2 seconds for high speed and 0.6 seconds for low speed, while exhibiting reverse high torque between 10 and -10.

The three-phase current waveforms, depicted in Figure 3.2.a, demonstrate a smooth operation of the FCS-MPC method at rated conditions, with a torque of 10 Nm at speeds of 300 rad/s and -300 rad/s (refer to Figures 3.3.c and 3.3.d) Additionally, Figure 3.2.b illustrates the output voltage of phase A in the induction motor (IM) during speed acceleration, showing an increase in state levels from three to five and seven, with each level corresponding to a voltage of 150V.

Chapter 3 FCS-MPC based current control of an IM i sd (A)

Ref Real b Output current i sq w (rad/s)

Torque (kg.m 2 ) d Torque response Figure 3.3 Simulation results of the proposed FCS-MPC

The result of FFT analysis output current phase A is presented in Figure

The analysis was conducted over a duration of 0.5s to 0.58s, covering four cycles at a fundamental frequency of 50Hz and a maximum frequency of 1000Hz The results indicate minimal distortion within the system, with the current Total Harmonic Distortion (THD) of the Model Predictive Controller (MPC) measured at just 2.55%.

M ag (% o f Fu nd am en ta l)

Figure 3.4 FFT analysis output current (phase A)

Co nclusion

The simulation results indicate that the FCS-MPC control strategy is an effective tool for managing power converters and electrical drives By incorporating compensation delay time with a predictive horizon at two-step sampling (k+2), the predictive control algorithm successfully tracks reference variables at high speeds, even in low-speed regions of the induction motor (IM) While this approach enhances IM performance, it also reveals a significant ripple in electromagnetic torque, necessitating further implementation efforts to mitigate this issue.

Chapter 4 Summary and future works

The FCS-MPC control strategy offers an effective solution for managing power electronic applications, particularly in grid-connected and induction motor (IM) systems utilizing a three-phase CHB seven-level converter This control approach features a straightforward algorithm structure, making it easy to implement even with an increased number of cells, and is versatile enough to be applied to various multilevel converter topologies.

The FCS-MPC control strategy eliminates the need for a modulator stage, but it often results in spread harmonics in the output waveforms This approach faces critical challenges, including model accuracy, high sampling rates, and significant computational costs However, advancements in microprocessor technology and ongoing research efforts are paving the way to overcome these disadvantages.

Future work will focus on the experimental evaluation of the FCS-MPC control strategy, specifically assessing algorithm performance and delay time compensation at sampling time k+2 Additionally, longer prediction time steps, such as 4 and 6, may be explored The approach will incorporate a multi-variable cost function with a weighting factor, exemplified by the application of FCS-MPC in controlling torque and flux in an induction motor (IM).

[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

[2] Sergio Vazquez, Jose Rodriguez, Marco Rivera, Leopoldo G Franquelo, Margarita №rambuena, “Model Predictive Control for Power Converters and Drives: Advances and Trends”, IEEE Transactions on Industrial Electronics,

[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,

[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 ,

In their 2015 paper presented at the IEEE Applied Power Electronics Conference, Muslem Uddin, Saad Mekhilef, Mutsuo Nakaoka, and Marco Rivera explore the experimental assessment of model predictive control for induction motors, focusing on the compensation of delay time Their research highlights the effectiveness of this control strategy in improving motor performance and reliability.

[7] Patricio Cortes, Alan Wilson, Samir Kouro, Jose Rodriguez, Haitham Abu- Rub, “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

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)

The article titled "Multistep Model Predictive Control for Cascaded H-Bridge Inverters: Formulation and Analysis," authored by Roky Baidya, Ricardo P Aguilera, Pablo Acuña, Sergio Vazquez, and Hendrik du Toit Mouton, was published in the IEEE Transactions on Power Electronics in January 2018 (Volume 33, Issue 1) This study presents a comprehensive analysis of multistep model predictive control strategies specifically designed for cascaded H-bridge inverters, emphasizing their formulation and effectiveness in power electronics applications.

Luca Tarisciotti, Pericle Zanchetta, Alan Watson, Stefano Bifaretti, and Jon C Clare present a study on "Modulated Model Predictive Control for a Seven-Level Cascaded H-Bridge Back-Back Converter," published in the IEEE Transactions on Industrial Electronics, Volume 61, Issue 10, in October 2014 This research focuses on advanced control strategies for enhancing the performance of multi-level converters, contributing to the field of industrial electronics.

In the article "A Digital Predictive Current Mode Controller for Single Phase High Frequency Transformer Isolated Dual Active Bridge DC to DC Converter," published in the IEEE Transactions on Industrial Electronics (Volume 63, Issue 9, September 2016), authors Sumit Dutta, Samir Hazra, and Subhashish Bhattacharya present an innovative digital control strategy This strategy enhances the performance of a dual active bridge DC to DC converter, specifically designed for single-phase applications involving high-frequency transformers The proposed predictive current mode controller aims to improve efficiency and stability, addressing critical challenges in power electronics.

The article "State of the Art of Finite Control Set Model Predictive Control in Power Electronics," authored by Jose Rodriguez, Marian P Kazmierkowski, Jose R Espinoza, Pericle Zanchetta, and Haitham Abu-Rub, was published in the IEEE Transactions on Industrial Informatics in May 2013 It provides a comprehensive overview of the advancements in finite control set model predictive control (MPC) techniques within the field of power electronics, highlighting their significance and application in modern industrial systems.

Appendix A Simulation FCS-MPC for gird-connected details a

Simulation FCS-MPC for gird-connected details a

Simulation model

Q* v_grid i_abc i_ref i_ref Calculator

Three-Phase Cascaded H-Bridges i_abc i_ref v_grid

Figure A.1 Simulation overview of FCS-MPC for a grid-connected

Appendix A Simulation FCS-MPC for gird-connected details a

Figure A.2 FCS-MPC controller in subsystem

MPC algorithm function

% Author: Eng Hoang Thanh Nam

% Advisor: Assoc Prof Tran Trong Minh

% PELAB HUST - function k = fcn(i_k, i_ref_k, v_g_k, Vdc, Ts, k_last)

L = 10e 3; - % Inductance load (H) r = 6; % Resistance load (Ohm) u_k = zeros(3,1);

% 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

Appendix B Simulation FCS-MPC for an IM details

Simulation FCS-MPC for an IM details

Figure B.1 Simulation overview of FCS-MPC for an IM

Figure B.2 FCS-MPC in subsystem

% 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);

Ls_sigma = 0.043; %Dien cam ro stato (H)

Lr_sigma = 0.043; %Dien cam ro rotor (H)

Lm = 0.3642; %Dien cam tu hoa (H) p = 1; %So doi cuc

Ls = Ls_sigma + Lm; %Dien cam stato

Lr = Lr_sigma + Lm; %Dien cam rotor

R_sigma = Rs + kr*kr*Rr;

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 +

% -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)); -

% 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