Thme de Thse Contribution la Commande Robuste des

Thème de Thèse : Contribution à la Commande Robuste des Systèmes Éoliens Autonomes Ph. D Topic: Contribution to Robust Control for Autonomous Wind Systems Supervisor: Kassa IDJDARENE S. Meddouri Presented By: Soufiane MEDDOURI Ph. D Thesis Defense 03/10/2020 10: 13: 42

Outline Introduzione Hardware di base Architettura OS & Funz. IEC 61131 Conclusioni Ø Introduction Brief State of The Art / Motivation and Objectives Ø Studied System and Modeling Ø Implemented Control Techniques for The Production System Ø Energy Storage System Ø Concluding Remarks Ø Research Activities Scientific Publication / Attended Courses / Attended Seminars and Summer Schools S. Meddouri Ph. D Thesis Defense 2

Outline Introduzione Hardware di base Architettura OS & Funz. IEC 61131 Conclusioni Ø Introduction Brief State of The Art / Motivation and Objectives Ø Studied System and Modeling Ø Implemented Control Techniques for The Production System Ø Energy Storage System Ø Concluding Remarks Ø Research Activities Scientific Publication / Attended Courses / Attended Seminars and Summer Schools S. Meddouri Ph. D Thesis Defense 3

Introduction – Context Description Introduction Studied system and modeling Implemented Control techniques Energy storage system Concluding Remarks ► General motivations n Increase interest of using renewable energies to overcome environmental issues ( 392 GW June 2015 / 04%) [WWEA]. n Problem of transmission of electricity over long distances (a great investment for cables, pylons, and loss during transport is relatively important, 7% to 10%). n Absence of an efficient storage system in particular for long term storage systems. n In this context, popular increasing of small autonomous operating units to ensure supply of isolated sites using wind energy. n Different electrical generator can be used to fulfil the electromechanical task. n Squirrel Cage Induction Generator (SCIG) is useful for this kind of applications. n Advantages of SCIG: • Absence of DC supply, Small size, robustness, low maintenance cost… n Drawbacks of the SCIG : • Absorption of the reactive power for its magnetization. • Inherently poor voltage regulation. S. Meddouri Ph. D Thesis Defense 4

Introduction – Detailed Description of the work goals Introduction Studied system and modeling Implemented Control techniques Energy storage system Concluding Remarks ► General goals n Design of an innovative control scheme to overcome the inherently poor voltage regulation. n Study and improve the performance of a chain of autonomous wind conversions based on a squirrel cage induction machine. n Study the performance of the system with a good accuracy using a saturated induction generator model. n Using a PWM inverter/rectifier structure connected to a single capacitor to provide the isolated IG a reactive power to be excited. n Include a suitable storage system which can contribute in the ancillary service. S. Meddouri Ph. D Thesis Defense 5

Introduction – Detailed Description of the work goals Introduction Studied system and modeling Implemented Control techniques Energy storage system Concluding Remarks ► Detailed objectives n To design a control scheme for autonomous induction generator system based on robust controller. n To have a constant voltage regardless of rotor speed variation, load and the parameter uncertainties of the generator model. n To improve the weak performances of the control schemes based on traditional controllers previously developed (PI). n To test the effectiveness of linear MPC controller applied to a non-linear plant, under different conditions. n Improve the electric power using a suitable storage system. S. Meddouri Ph. D Thesis Defense 6

Outline Introduzione Hardware di base Architettura OS & Funz. IEC 61131 Conclusioni Ø Introduction Brief State of The Art / Motivation and Objectives Ø Studied System and Modeling Ø Implemented Control Techniques for The Production System Ø Energy Storage System Ø Concluding Remarks Ø Research Activities Scientific Publication / Attended Courses / Attended Seminars and Summer Schools S. Meddouri Ph. D Thesis Defense 7

Studied System and Modeling Introduction Studied system and modeling Implemented Control techniques Energy storage system Concluding Remarks Variable wind turbine n Saturated induction generator (IG) n Variable load n Suitable storage system (flywheel) n Wind Turbine Induction Generator Variable Load Gearbox Storage System (Flywheel) S. Meddouri Ph. D Thesis Defense 8

Studied System and Modelling Introduction Studied system and modeling Implemented Control techniques Energy storage system Concluding Remarks n Detailed system description: The induction generator (IG) driven by variable wind turbine speed n A PWM converter connected to a single capacitor to excite the IG, and a battery in order to start up the system n A diode for decoupling rectifier from the battery as soon as the voltage generated at the output of the rectifier is higher than the battery side n Control algorithm for DC voltage and flux control n S. Meddouri Ph. D Thesis Defense 9

Studied System and Modelling Introduction Studied system and modeling Concluding Remarks Implemented Control techniques Energy storage system Concluding Remarks ► The widely used Induction generator model: n The proposed model here takes into account the saturation effect of magnetic circuit by the expression of the magnetizing inductance Lm with respect to the magnetizing current im n To express Lm in function of im, a polynomial approximation of degree 12 is adopted S. Meddouri Ph. D Thesis Defense 10

Studied System and Modelling Introduction n Studied system and modeling Concluding Remarks Implemented Control techniques Energy storage system Concluding Remarks The evolution of the magnetizing inductance in function of magnetizing current im ► Saturated induction generator model: S. Meddouri Ph. D Thesis Defense 11

Outline Introduzione Hardware di base Architettura OS & Funz. IEC 61131 Conclusioni Ø Introduction Brief State of The Art / Motivation and Objectives Ø Studied System and Modeling Ø Implemented Control Techniquesfor The Production System ( Fuzzy Logic Control) Ø Energy Storage System Ø Concluding Remarks Ø Research Activities Scientific Publication / Attended Courses / Attended Seminars and Summer Schools S. Meddouri Ph. D Thesis Defense 12

Implemented Control Techniques –Vector Control Principal Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks Rotor flux oriented control principle has been used in the proposed control scheme ( rd = r and rq=0). n The operating of the machine can be then considered practically linear (Lm=M=constant) S. Meddouri Ph. D Thesis Defense 13

Implemented Control Techniques – Fuzzy Vector Control Introduction Studied system and modeling Implemented control techniques Energy storage system n The detailed control scheme applied n The estimated rotor flux and stator pulsation are given as follow: S. Meddouri Ph. D Thesis Defense Concluding Remarks 14

Implemented Control Techniques – Fuzzy Vector Control Studied system and modeling Introduction e Ke e e’ Implemented control techniques Energy storage system E Kd K’ FZ- PI RULE BASE U’ Concluding Remarks U_PI 1/s K 1 U_PID FZ- PD RULE BASE U_PD U K 2 n. General fuzzy-PI/PD rule base de/ e NB NM NS ZE PS PM PB n. Input output membership function de/e NB NM NS ZE PS PM PB S. Meddouri Ph. D Thesis Defense NB NB NB NM NS ZE NB NB NB NM NS NS NM NB NB NB NM NS ZE PS NM NB NB NB NM NS NS NB NB NM NS ZE PS PM NS NB NB NM NS NS ZE NB NM NS ZE PS PM PB PS NM NS ZE PS PM PB PB PM NS ZE PS PM PS PB PB ZE NS NS NS ZE PS PS PM PM PB PM PS PS PS PM PB PB ZE PS PM PB PB PB PS PS PM PB PB 15

Results Analysis Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks The following simulations have been performed: n Impact of rotor speed changes (rotor speed varied by 20% WRT the synchronous speed) with variable reference rotor flux value n Impact of rotor speed changes with fixed reference rotor flux value n Impact of load changes (load varied by ≈ 43%) S. Meddouri Ph. D Thesis Defense 16

Implemented Control Techniques – Fuzzy Vector Control Introduction n n Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks 20% upper and lower variation of the synchronous speed ( = 750 tr / mn = 78. 5398 rad / s) The rotor flux reference is changing inversely proportional to the variable speed Undershoot 47 V ≈ 10% S. Meddouri t (s) 0 -2 2 -4 4 -6 (rpm) 750 900 600 Ph. D Thesis Defense 17

Implemented Control Techniques – Fuzzy Vector Control Introduction S. Meddouri Studied system and modeling Implemented control techniques Energy storage system Ph. D Thesis Defense Concluding Remarks 18

Implemented Control Techniques – Fuzzy Vector Control Introduction n n Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks Rotor speed changes: 20% upper and lower variation of the synchronous speed (( = 750 tr / mn = 78. 5398 rad/s) The rotor flux reference ref=0. 7 (Wb) t (s) 0 -2 2 -4 4 -6 (rpm) 750 900 600 47 V ≈ 10% S. Meddouri Ph. D Thesis Defense 19

Implemented Control Techniques – Fuzzy Vector Control Introduction n Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks Load changes (≈ 43%) t (s) R( ) 0 -2 70 2 -4 100 4 -6 70 66 V ≈ 15% S. Meddouri Ph. D Thesis Defense 20

Implemented Control Techniques – Fuzzy Vector Control Introduction n Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks Load changes S. Meddouri Ph. D Thesis Defense 21

Outline Introduzione Hardware di base Architettura OS & Funz. IEC 61131 Conclusioni Ø Introduction Brief State of The Art / Motivation and Objectives Ø Studied System and Modeling Ø Implemented Control Techniques for The Production System (Model Predictive Control MPC) Ø Energy Storage System Ø Concluding Remarks Ø Research Activities Scientific Publication / Attended Courses / Attended Seminars and Summer Schools S. Meddouri Ph. D Thesis Defense 22

Implemented Control Techniques – MPC control Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks MPC controller: control action is obtained by solving finite horizon optimal control problem at each time instant. S. Meddouri Ph. D Thesis Defense 23

Implemented Control Techniques – MPC control Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks MPC controller: control action is obtained by solving finite horizon optimal control problem at each time instant. S. Meddouri Ph. D Thesis Defense 24

Implemented Control Techniques – MPC – Model Identification Introduction n Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks The estimated model is numerically constructed by a step response identification method around specified equilibrium point. change of rotor speed S. Meddouri Ph. D Thesis Defense 25

Implemented Control Techniques – MPC Formulation Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks The obtained transfer functions of the MIMO system are as follows: n The transfer functions are subsequently transformed into a discrete state space model : S. Meddouri Ph. D Thesis Defense 26

Implemented Control Techniques – MPC Formulation Introduction n Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks According to Dynamic Matrix Control, the outputs’ prediction is formulated taking into account also last outputs’ measurement error: the vector of future outputs prediction (ΔΦ and ΔVdc) estimated value of state variables S. Meddouri vector of future control actions increments the latest actual control actions i. e. , Δisd, Δisq vector of predicted mechanical pulsation Ph. D Thesis Defense measurement error 27

Implemented Control Techniques – MPC Formulation Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Cost function Smoothing isd Smoothing isq DC voltage tracking Flux tracking S. Meddouri Ph. D Thesis Defense 28

Implemented Control Techniques – MPC – Reference trajectory Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks A reference trajectory is proposed and implemented as a gradual transition to the desired set-point inside the MPC formulation. S. Meddouri Ph. D Thesis Defense 29

Implemented Control Techniques – Switched and adaptive MPC Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Introducing switched and adaptive MPC • • • A single linear system model is rarely a good enough. Innovative control schemes (a switched an adaptive MPC) are proposed. Employment of a set of models estimated around different operational points of the system. ► Introducing switched and adaptive MPC Models switching M 1 M 2 Predicted output Mn S. Meddouri Ph. D Thesis Defense 30

Implemented Control Techniques – Switched and adaptive MPC Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Introducing switched and adaptive MPC (RPM) R ( ) P 1 750 70 P 2 900 70 P 3 600 70 P 4 750 140 ► Introducing adaptive MPC Linear interpolation for the load changes Quadratic interpolation for the rotor speed changes S. Meddouri Ph. D Thesis Defense 31

Implemented Control Techniques – Switched and adaptive MPC Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Nonlinearity of the system Cx C 1 G∆isd-∆ µ=0. 1047 =0 1=0. 0847 2=0 G∆isd-∆vdc µ=84. 708 =0. 002 1=0. 069 2=0. 087 G∆isq-∆vdc µ=-18. 358 =0 1=0. 0695 2=0 G∆w-∆vdc µ=1. 8867 =0 1=0. 0695 2=0 C 2 µ=0. 1048 =0 1=0. 851 2=0 µ=106. 44 =0. 00094 1=0. 06878 2=0. 0866 µ=-18. 503 =0 1=0. 0699 2=0 µ=1. 564 =0 1=0. 0694 2=0 C 3 µ=0. 1045 =0 1=0. 0844 2=0 µ=57. 64 =0. 0034 1=0. 05718 2=0. 09907 µ=-18. 448 =0 1=0. 0692 2=0 µ=2. 4002 =0 1=0. 06997 2=0 C 4 µ=0. 1058 =0 1=0. 08718 2=0 µ=92. 936 =0. 0036 1=0. 0761 2=0. 1407 µ=-49. 155 =0 1=0. 1351 2=0 µ=1. 3916 =0 1=0. 140 2=0 S. Meddouri Ph. D Thesis Defense 32

Results Analysis Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks The following simulations have been performed: n Impact of rotor speed changes (rotor speed varied by 20% WRT the synchronous speed) n Impact of load changes (load varied by 100 %) n Impact of introducing the switched for large changes n Impact of introducing the adaptive MPC for small changes S. Meddouri Ph. D Thesis Defense 33

Results Analysis – load change Studied system and modeling Introduction Implemented control techniques Energy storage system Concluding Remarks ► Impact of load variation using Single MPC: n Small load variations, while V*dc and * r are constants t(s) R( ) 0 -1. 5 -2. 5 -3. 5 -4. 5 -5. 5 -6. 5 -7 70 100 120 140 120 100 70 66 V reduction ≈ 100 % of improvement comparing to FLC S. Meddouri Ph. D Thesis Defense 34

Results Analysis – load change Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Impact of load variation using Single MPC and Switched MPC: n S. Meddouri Large load variations of about 100% while V*dc and * r are constants using Single MPC and Switched t (s) 0 -1. 5 -3 3 -4 R( ) 70 140 70 Ph. D Thesis Defense 20 V reduction ≈ 76 % of improvement 35

Results Analysis – load change Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Impact of load variation: n S. Meddouri Large load variations of about 100% while V*dc and * r are constants using Single MPC and Switched Ph. D Thesis Defense 36

Results Analysis – load change Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Impact of load variation using Adaptive MPC: n Small load variations, while V*dc and * r are constants t(s) R( ) 0 -1. 5 -2. 5 -3. 5 -4. 5 -5. 5 -6. 5 -7 70 100 120 140 120 100 70 2 V reduction ≈ 33 % of improvement comparing to Single MPC S. Meddouri Ph. D Thesis Defense 37

Results Analysis - rotor speed changes Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Impact of rotor speed changes caused by wind speed variation: n Rotor speed varies 20% below and above the synchronous speed ( = 750 rpm = 78. 5398 rad/s), as a step t (s) (rpm) n n S. Meddouri 0 -2 2 -4 4 -6 750 900 600 Desired DC voltage reference and load are kept constant (V*dc =465 V, R=70 ) Rotor flux reference is inversely proportional to the speed to make IG work at lower saturation level in case of high speeds Ph. D Thesis Defense 38

Results Analysis - rotor speed changes Introduction ► Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks Comparison between MPC and FLC n Controlled DC voltage at the output of the rectifier using FLC and MPC controllers 10 V reduction ≈ 22 % of improvement comparing to FLC S. Meddouri Ph. D Thesis Defense 39

Results Analysis - rotor speed changes Introduction n Studied system and modeling Implemented control techniques Energy storage system Controlled rotor flux using FLC and MPC controllers FLC S. Meddouri Concluding Remarks Single MPC Ph. D Thesis Defense 40

Results Analysis - rotor speed changes Introduction n S. Meddouri Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks Stator currents Isd and Isq using Single MPC strategy Ph. D Thesis Defense 41

Results Analysis - rotor speed changes Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Switched MPC strategy n S. Meddouri Controlled DC voltage at the output of the rectifier using Switched MPC ≈ 3 V reduction Comparing to Single MPC Ph. D Thesis Defense 42

Results Analysis - rotor speed changes Introduction ► Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks Adaptive and Single MPC strategy n Controlled DC voltage at the output of the rectifier using Adaptive and Single MPC for small changes in rotor speed Single MPC S. Meddouri Adaptive MPC Ph. D Thesis Defense 43

Results Analysis – robustness analysis Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Robustness analysis on magnetizing inductance and stator resistance n n Adding white Gaussian noise N(0, 0. 0001) that accounts for approximately adding 10% error of inductance values. + 100% and – 100% of stator resistance varaiton in a ramp manner S. Meddouri Ph. D Thesis Defense 44

Outline Introduzione Hardware di base Architettura OS & Funz. IEC 61131 Conclusioni Ø Introduction Brief State of The Art / Motivation and Objectives Ø Studied System and Modeling Ø Implemented Control Techniques for The Production System Ø Energy Storage System Ø Concluding Remarks Ø Research Activities Scientific Publication / Attended Courses / Attended Seminars and Summer Schools S. Meddouri Ph. D Thesis Defense 45

Energy Storage System Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Energy Storage Technologies Classification n Increase in renewable energies => increase the storage problem. Energy storage is one of the components od sustainable energy. The electricity cannot be stored easily, it requires a transformation process to another energy S. Meddouri Ph. D Thesis Defense 46

Energy Storage System Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Energy storage solution based on Flywheel. S. Meddouri Ph. D Thesis Defense 47

Energy Storage System Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Studied system including the mechanical part and storage system using flywheel: S. Meddouri Ph. D Thesis Defense 48

Energy Storage System Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Studied system including the mechanical part and storage system using flywheel: The aerodynamic torque of the turbine The reference of electromagnetic torque The active power exchanged between FESS and DC-link circuit and the reference energy for FESS The reference speed The reference flux S. Meddouri Ph. D Thesis Defense 49

Energy Storage System Introduction S. Meddouri Studied system and modeling Implemented control techniques Ph. D Thesis Defense Energy storage system Concluding Remarks 50

Energy Storage System Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Results Analysis: Fig. 1 – Wind speed profile (m/s) Fig. 2 – Tip speed ratio Fig. 3. Power coefficient Fig. 4 – Generator speed Fig. 5– Electromagnetic torque of the generator Fig. 6. Rotor flux of the generator Fig. 7 –isd and isq of the generator Fig. 8– Wind and load power Fig. 9. Power FESS S. Meddouri Ph. D Thesis Defense 51

Energy Storage System Introduction Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks ► Results Analysis: Fig. 10 – Flywheel speed and its reference Fig. 11, Rotor flux of the machine Fig. 12 – Stator current isq of the machine Fig. 13. Power coefficient S. Meddouri Ph. D Thesis Defense 52

Outline Introduzione Hardware di base Architettura OS & Funz. IEC 61131 Conclusioni Ø Introduction Brief State of The Art / Motivation and Objectives Ø Studied System and Modeling Ø Implemented Control Techniques for the system production Ø Energy Storage System Ø Concluding Remarks Ø Research Activities Scientific Publication / Attended Courses / Attended Seminars and Summer Schools S. Meddouri Ph. D Thesis Defense 53

Conclusions – Main results Introduction Studied system and modeling Implemented control techniques Results Analysis Concluding Remarks ► Main achieved results : n An innovative control schemes using MPC controller for an autonomous induction generator based on saturated model n Good improvement of results compared to fuzzy logic control : • Better transient performance • DC voltage limited change n Testing performed with a linear MPC (linearized model based on step response identification method) and a nonlinear plant n Further improvements obtained through • A special smoothing technique n successful implementation of performant switched and adaptive MPC n Successful design and control of the extended system which includes storage system n Modeling and control of mechanical and electrical parts including the storage system with successful association of different control schemes S. Meddouri Ph. D Thesis Defense 54

Outline Introduzione Hardware di base Architettura OS & Funz. IEC 61131 Conclusioni Ø Introduction Brief State of The Art / Motivation and Objectives Ø Studied System and Modeling Ø Implemented Control Techniques for the system production Ø Energy Storage System Ø Concluding Remarks Ø Research Activities Scientific Publication / Attended Courses / Attended Seminars and Summer Schools S. Meddouri Ph. D Thesis Defense 55

Research Activities – Publications Introduction ► Studied system and modeling Predictive Control Formulation Results Analysis Research Activities publications: Conference Papers n A presented conference paper in CISTEM 2014 conference, Tunis – Tunisia 3 -6 November 2014. Title: “Fuzzy Vector Control of Isolated Induction Generator Taking the Saturation Effect Into Account”. n A presented conference paper in IEEE ICCEP 2015 conference, Taormina, Sicily – Italy, 16 -18 June 2015. Title: “A Predictive Control Scheme for an Autonomous Induction Generator with Saturation Effect’’ n A presented conference paper in IEEE CASE 2015 conference, Gothenburg – Sweden August 24 -28, 2015. Title: “Performance Analysis of an Autonomous Induction Generator Under Different Operating Conditions Using Predictive Control”. n An accepted conference paper in IEEE ICCEP 2017 conference. Santa Margherita Ligure , Liguria– Italy 27 -29 June 2017. Title: “A Nonlinear Lyapunov-Based Control for an Autonomous Variable-Speed Wind Turbine’’ S. Meddouri Ph. D Thesis Defense 56

Research Activities – Publications Introduction Studied system and modeling Predictive Control Formulation Results Analysis Research Activities Journal Papers n An accepted journal paper in Journal of La Revue Roumaine des Sciences Techniques, Série Électrotechnique et Énergétique. TITLE: “Control of Autonomous Saturated Induction Generator Associated to a Flywheel Energy Storage System” n An accepted journal paper in Journal of Electrical Engineering (JEE) TITLE : “ Predictive Control Strategies for Variable Speed Wind Turbine With Saturated Induction Generator” Forthcoming Journal Papers n Preparation of an article review TITLE : “ A Comparative Study of Control Strategies in SCIG Wind Turbine System ” S. Meddouri Ph. D Thesis Defense 57

Research Activities – Attended courses and Summer schools Introduction ► Studied system and modeling Predictive Control Formulation Results Analysis Research Activities Attended and Validated Courses : S. Meddouri Ph. D Thesis Defense 58

Thanmirth Chukran Merci Thank you Grazie S. Meddouri Ph. D Thesis Defense 59

Implemented Control Techniques – Switched and adaptive MPC ► Introducing adaptive MPC The switched MPC has shown very good performances with respect to the large changes of load. However, if the load takes different values with respect to the operation points around which the models are constructed, the MPC controller will be set-up with anyway a wrong model. For this reason, an adaptive MPC strategy has been designed, with following practical advantages in comparison with the switched MPC: • The control model related to a bunch of operating points is first computed offline; clearly, the number of operating points will depend on the estimated load range. • The MPC architecture is parametrized with respect to the plant model. • The plant model will be interpolated continuously so that the online MPC control is constantly updated with respect to plant. Using the transfer function presented in the previous table, a linear interpolation of gain and time constants is computed as a function of the load. Hence, for any value of load, which is supposed to be estimated by a load sensor, corresponding values of gain and time constants are derived S. Meddouri Ph. D Thesis Defense 60

Results Analysis - rotor speed change with low-pass filter Introduction Studied system and modeling Implemented control techniques Results analysis Concluding Remarks ► Variation of rotor speed with low-pass filter (τ = 0. 016 s ): n Controlled DC voltage at the output of the rectifier using MPC controller with filter S. Meddouri without filter Ph. D Thesis Defense 61

Results Analysis – perfect prediction Introduction Studied system and modeling Implemented control techniques Results analysis Concluding Remarks ► Impact of perfect prediction of rotor speed on controlling DC voltage: same conditions as in the first experiment n Controlled DC voltage at the output of the rectifier using MPC controller approx 50% reduction S. Meddouri Ph. D Thesis Defense 62

Results Analysis – perfect prediction Introduction Studied system and modeling Implemented control techniques Results analysis Concluding Remarks ► Annexe 1 Paramètres de la machine asynchrone modélisée Les caractéristiques électriques : Rotor de type de cage d’écureuil 4 paires de pôles 230/400 V – 23, 8/13, 7 – 5, 5 k. W – 50 Hz – 690 tr/mn ► Rs = 1, 07131 Rr = 1, 29511 ls = 8, 9382 m. H ► lr = 4, 8613 m. H ► Les paramètres mécaniques de l’ensemble machine asynchrone couplée à la machine à courant continu. J = 0, 230 kg. m 2 f = 0, 0025 N. m/rad. s-1 Paramètres de simulation avec convertisseur en boucle ouverte Batterie d’une valeur de 12 V ; Résistance de batterie de 0. 1 ; Capacité de filtrage en sortie redresseur de 1000 F ; Porteuse triangulaire d’amplitude 350 V et de fréquence 1000 Hz ; Amplitude des tensions de référence de la MLI est de 220 V ; S. Meddouri Ph. D Thesis Defense 63

Results Analysis – perfect prediction Introduction Studied system and modeling Wind turbine [ 20] Induction generator [4] Parameter Value Pn 5, 5 k. W Parameter Pn Value 7, 5 k. W tn 296 tr/mn Rs Rt 3, 24 m G opt Cp-max 3, 45 9 0, 46 S. Meddouri Implemented control techniques Results analysis Concluding Remarks Induction machine [13] Parameter Pn Value 1, 5 k. W 1, 07131Ω Rs 4, 85Ω Rr 1, 29511Ω Rr 3, 805Ω ls 8, 9382 m. H Ls 0, 274 H lr M p J f 4, 8613 m. H 0, 10474 H 4 0. 23 kgm 2 0. 001 N. m. s-1 Lr M p J f 0, 274 H 0, 258 H 2 0. 1 kgm 2 0. 0001 N. m. s-1 Ph. D Thesis Defense 64

Implemented Control Techniques – Fuzzy Vector Control Introduction n n Studied system and modeling Implemented control techniques Energy storage system Concluding Remarks Rotor speed changes: 10% upper and lower variation of the synchronous speed (( = 750 tr / mn = 78. 5398 rad / s) The rotor flux reference is changing inversely proportional to the variable speed Undershoot 17 V ≈ 3, 6 % t (s) 0 -2 2 -4 4 -6 (rpm) 750 825 675 0, 6 S 0, 4 S S. Meddouri Ph. D Thesis Defense 65

Implemented Control Techniques – Fuzzy Vector Control Introduction S. Meddouri Studied system and modeling Implemented control techniques Energy storage system Ph. D Thesis Defense Concluding Remarks 66

Ph. D thesis defense make it green, so make it clean Welcome S. Meddouri Ph. D Thesis Defense