Model Predictive Control in Medium Voltage Drives

Transcription

1 Model Predictive Control in Medium Voltage Drives Department of Electrical and Computer Engineering The University of Auckland New Zealand In collaboration with

2 Outline Introduction Control problem Performance trade off Control and modulation schemes Model Predictive Control 1 step predictive control Model predictive direct current/torque control Computational efficiency Summary and Outlook

3 Control Problem

4 Control Problem Controller M Electrical Machine Inverter (Active) Rectifier Grid Low current distortions => low thermal losses Low switching losses => high efficiency, low thermal losses Low torque distortions => no excitation of mech. resonances Fast torque response => high dynamic performance

5 Control and Modulation Cascaded control loops: Speed control loop Current control loop Current control problem => split into current controller and modulator Grid (Active) Rectifier Dc-Link * Speed controller T e * i s * Current controller u * Modulator u Inverter i s M Electrical Machine Fundamental trade off between switching losses (frequency) and the current / torque distortion levels

6 Performance Trade Off

7 Trade Off (High Switching Frequency) u * u f sw =700Hz P sw =16.7kW,P con =2.7kW THD I =2.31% THD T =1.93% i s Inverter: 3 level NPC with IGCTs Induction machine: 3.3kV, 2MVA Operation point: w e =1pu, T e =1pu T

8 Trade Off (Low Switching Frequency) u * u f sw =150Hz P sw =3.9kW, P con =2.8kW THD I =6.9% THD T =6.0% i s Inverter: 3 level NPC with IGCTs Induction machine: 3.3kV, 2MVA Operation point: w e =1pu, T e =1pu T

9 Trade Off for PWM / SVM Current THD vs switching losses 7 6 Torque THD vs switching losses THD [%] THD [%]? 2? Switching losses [%] Switching losses [%]

10 Control and Modulation Schemes

11 Control and Modulation Switching losses per distortions large Field Oriented Control with PWM/SVM small fast slow Torque response time (controller bandwidth)

12 Control and Modulation Switching losses per distortions large Model Predictive Field Oriented Control with Control with PWM/SVM PWM/SVM small fast slow Torque response time (controller bandwidth)

13 Control and Modulation Switching losses per distortions large Model Predictive Field Oriented Control with Control with PWM/SVM PWM/SVM small fast V/f Control with Optimized Pulse Patterns slow Torque response time (controller bandwidth)

14 Control and Modulation Switching losses per distortions Controller and modulator large Direct Torque Control Model Predictive Field Oriented Control with Control with PWM/SVM PWM/SVM small fast V/f Control with Optimized Pulse Patterns slow Torque response time (controller bandwidth)

15 Control and Modulation Switching losses per distortions One step Predictive Control Controller and modulator large Direct Torque Control Model Predictive Field Oriented Control with Control with PWM/SVM PWM/SVM small fast V/f Control with Optimized Pulse Patterns slow Torque response time (controller bandwidth)

16 Control and Modulation: Goal Switching losses per distortions One step Predictive Control? large Direct Torque Control Model Predictive Field Oriented Control with Control with PWM/SVM PWM/SVM small? fast V/f Control with Optimized Pulse Patterns slow Torque response time (controller bandwidth)

17 Control and Modulation: New Methods Switching losses per distortions One step Predictive Control Controller and modulator large Direct Torque Control Model Predictive Field Oriented Control with Control with PWM/SVM PWM/SVM small Model Predictive Direct Torque / Current Control fast V/f Control with Optimized Pulse Patterns slow Torque response time (controller bandwidth)

18 Control and Modulation: New Methods Switching losses per distortions One step Predictive Control Controller and modulator large Direct Torque Control Model Predictive Field Oriented Control with Control with PWM/SVM PWM/SVM small Model Predictive Direct Fast Torque Control / of Current Optimized Control Pulse Patterns fast V/f Control with Optimized Pulse Patterns slow Torque response time (controller bandwidth)

19 Control and Modulation: New Methods Goal: Fully utilize capability of drive hardware Minimize switching losses per distortions Achieve very fast torque and current response Approach: Treat control and modulation problem in one stage Work in the time domain Adopt model predictive control Grid (Active) Rectifier Dc-Link * Speed controller T e * i s * Current controller u * Current controller and modulator Modulator u Inverter i s M Electrical Machine

20 Model Predictive Control for MV Electrical Drives

21 Classification of MPC Schemes for Electrical Drives Model Predictive Control: Direct methods (without a modulator) Reference tracking Hysteresis bounds Trajectory control Current control Torque / flux ctrl. Current control Torque / flux ctrl. Current trajectory Flux trajectory Very short prediction horizons (typically one step) Medium to long prediction horizons (20 to 150 steps) Closed loop control of precomputed pulse patterns

22 Classification of MPC Schemes for Electrical Drives Model Predictive Control: Direct methods (without a modulator) Reference tracking Hysteresis bounds Trajectory control Current control Torque / flux ctrl. Current control Torque / flux ctrl. Current trajectory Flux trajectory Very short prediction horizons (typically one step) Medium to long prediction horizons (20 to 150 steps) Closed loop control of precomputed pulse patterns

23 One Step Predictive Current Control i sα i sα (k) i sα (k+1) k k+1 i sα,ref time Algorithm Enumerate all 27 switch transitions Predict currents at k+1 Choose switch transition with minimal current error at k+1 i sβ i sβ (k) i sβ,ref i sβ (k+1) k k+1 time

24 One Step Predictive Current Control Performance Index: Deviation from current reference Penalty on switching effort Constraints Model of machine Discrete valued switch positions Restrictions on switch transitions Main features: prediction horizon is one machine model minimization of switching effort (e.g. frequency) λ n => trade off between tracking accuracy and switching conceptually and computationally very simple

25 One step Predictive Current Control Current TDD vs switching losses Torque TDD vs switching losses OPP PWM 1-step pred. current ctrl PWM 1-step pred. current ctrl. TDD [%] TDD [%] 4 3 OPP Switching losses [%] Switching losses [%] Current THD similar to PWM Torque THD significantly worse than PWM

26 Classification of MPC Schemes for Electrical Drives Model Predictive Control: Direct methods (without a modulator) Reference tracking Hysteresis bounds Trajectory control Current control Torque / flux ctrl. Current control Torque / flux ctrl. Current trajectory Flux trajectory Very short prediction horizons (typically one step) Medium to long prediction horizons (20 to 150 steps) Closed loop control of precomputed pulse patterns

27 One step Predictive Torque Control Current TDD vs switching losses Torque TDD vs switching losses OPP PWM 7 6 PWM 12 1-step pred. torque ctrl. 5 1-step pred. torque ctrl. TDD [%] TDD [%] 4 3 OPP Switching losses [%] Switching losses [%] Torque THD similar to PWM Current THD significantly worse than PWM

28 Classification of MPC Schemes for Electrical Drives Model Predictive Control: Direct methods (without a modulator) Reference tracking Hysteresis bounds Trajectory control Current control Torque / flux ctrl. Current control Torque / flux ctrl. Current trajectory Flux trajectory Very short prediction horizons (typically one step) Medium to long prediction horizons (20 to 150 steps) Closed loop control of precomputed pulse patterns

29 Model Predictive Direct Current Control: Step 1 Predict current trajectories for (all) possible switching sequences i ripα NP potential not shown here Key ingredients: Drive model Extrapolation i ripβ t Switching horizon, e.g. esese S: consider all switch transitions E: extrapolate/extend currents and NPP u t e: optional E a b Prediction horizon N p Typically time steps c k e S E S E N p t

30 Model Predictive Direct Current Control: Step 1 Predict current trajectories for (all) possible switching sequences i ripα NP potential not shown here Key ingredients: Drive model Extrapolation i ripβ t Switching horizon, e.g. esese S: consider all switch transitions E: extrapolate/extend currents and NPP e: optional E Prediction horizon N p Typically time steps u a b c t t k e S E S E N p

31 Model Predictive Direct Current Control: Step 2 Evaluate and minimize sw. losses i ripα NP potential not shown here => Optimal switching sequence U i ripβ t u a b c t t k e S E S E N p

32 Model Predictive Direct Current Control: Steps 2 & 3 Evaluate and minimize sw. losses i ripα NP potential not shown here => Optimal switching sequence U t i ripβ Apply only the first element of U Do k Plan t u t Do k+1 Plan t a b Do k+2 Plan t c t k e S E S E N p

33 Model Predictive Direct Current Control Performance Index: Short term avg. switching losses (power) Model of machine and inverter Constraints Outputs (currents and NP) Bounds on currents and NP Discrete valued switch positions Restrictions on switch transitions Main features: short switching horizon but long prediction horizon models of machine, inverter and losses minimization of switching losses receding horizon policy tailored online solution approach

34 Performance during Transients 3 level NPC inverter with 2MVA induction machine Speed: w e =0.6 pu Torque: reference steps between T=1 and 0 pu Torque Stator currents Switch positions Torque (current) response time of 2 ms

35 Performance at Steady State 3 level NPC inverter with 2MVA ind. machine w e =0.6 pu, T e =1 pu Current Current spectrum Switch positions FOC with PWM and f c =270 Hz I THD = 7.69% P sw = 4.15kW MPDCC e(se) 3 N p =70 I THD = 4.56% P sw = 4.02kW Current THD reduced by 40% (for the same switching losses) Similar to optimal pulse patterns

36 MPDCC outperforming OPP 3 level NPC inverter with 2MVA ind. machine w e =0.6 pu, T e =1 pu Optimized Pulse Pattern Model Pred. Direct Current Ctrl. P sw = 1.92 kw 40% less P sw = 1.15 kw I THD = 8.18 % 5% more I THD = 8.60 % Time [ms] Time [ms] OPPs: for a given switching frequency, minimize the current THD MPDCC: for a given current THD, minimize the switching losses

37 Model Predictive Direct Current Control Current TDD vs switching losses Torque TDD vs switching losses OPP PWM 7 6 PWM 12 5 TDD [%] % TDD [%] OPP MPDCC ese MPDCC e(se)3 2 MPDCC ese MPDCC e(se) Switching losses [%] Switching losses [%] Long switching horizon esesese ( steps): Current THD: better than with optimized pulse patterns Torque THD: similar to PWM

38 Tuning 3 level NPC inverter with 2MVA IM w e =0.6 pu, T e =1 pu, MPDCC with ese In percent, normalized to maximum Switching losses Switching frequency Current THD Torque THD Current bound width [*100] Current and torque distortions: linear function of bound width Switching frequency (and losses): hyperbolic function of bound width

39 Classification of MPC Schemes for Electrical Drives Model Predictive Control: Direct methods (without a modulator) Reference tracking Hysteresis bounds Trajectory control Current control Torque / flux ctrl. Current control Torque / flux ctrl. Current trajectory Flux trajectory Very short prediction horizons (typically one step) Medium to long prediction horizons (20 to 150 steps) Closed loop control of precomputed pulse patterns

40 Direct Torque Control Torque T e * s * DTC look-up table u Dc-link T e [pu] Stator flux magnitude 1.05 T e s Observer i s Psi s [pu] M 0.05 Neutral point potential Control objectives: Keep torque, stator flux and neutral point potential within given bounds Minimize the switching losses Control variable: Discrete inverter switch positions NP [pu] u abc Switch positions Time [ms]

41 Model Predictive Direct Torque Control Torque T e * s * DTC look-up table replace by Model Predictive DTC u Dc-link T e [pu] Stator flux magnitude 1.05 T e s Observer i s Psi s [pu] M 0.05 Neutral point potential Challenging control problem: Nonlinear Hybrid MIMO Sampling interval T s = 25us NP [pu] u abc Switch positions Time [ms]

42 Model Predictive Direct Torque Control Current TDD vs switching losses Torque TDD vs switching losses OPP PWM 7 6 PWM 12 5 TDD [%] MPDTC ese MPDTC e(se)3 TDD [%] 4 3 OPP MPDTC ese MPDTC e(se) Switching losses [%] Switching losses [%] Long switching horizon esesese ( steps): Current THD: similar to optimized pulse patterns (OPP) Torque THD: significantly better than OPP, but at the expense of current THD points on curves do not correspond to each other!

43 Classification of MPC Schemes for Electrical Drives Model Predictive Control: Direct methods (without a modulator) Reference tracking Hysteresis bounds Trajectory control Current control Torque / flux ctrl. Current control Torque / flux ctrl. Current trajectory Flux trajectory Very short prediction horizons (typically one step) + Computational efficiency Medium to long prediction horizons (20 to 150 steps) Closed loop control of precomputed pulse patterns

44 Search Tree E S S Search tree induced by optimization problem Computational burden number of nodes So far: full enumeration S Not candidates E time Candidate switching sequence Optimal switching sequence

45 Search Tree E S S Search tree induced by optimization problem Computational burden number of nodes So far: full enumeration time S Not candidates E Candidate switching sequence Optimal switching sequence Approaches to reduce computation time? More efficient implementation of algorithm More efficient extension / extrapolation step Reduce number of nodes explored in search tree by using Branch & Bound

46 Evolution of the Optimal Cost during Optimization Without Branch & Bound Cost (kw) c c* u* found Iteration step (number of nodes visited) Certificate of optimality found Search tree fully explored

47 Evolution of the Optimal Cost during Optimization With Branch & Bound Cost (kw) c c* c c u* found u* found Certificate of optimality found Upper and lower bound converged Certificate of optimality found Search tree fully explored Iteration step (number of nodes visited)

48 Computational Effort Full enumeration Example: MPDTC with the switching horizon essesese 50% percentile 95% percentile 99% percentile Probability distributions: Number of nodes required to be explored to obtain the optimal cost c* B&B B&B with upper bound on number of computations

49 Performance vs Computational Burden Short switching horizon (esse): B&B => computational burden reduced by factor 5.5 Switching losses and THDs merely affected Benefit: simplify implementation for short switching horizons

50 Performance vs Computational Burden Short switching horizon (esse): B&B => computational burden reduced by factor 5.5 Switching losses and THDs merely affected Benefit: simplify implementation for short switching horizons Long switching horizon (essesese): B&B => computational burden reduced by factor 13 Switching losses and THDs merely affected Benefit: enable implementation for long switching horizons

51 Performance Results ACS 6000, w e =0.6 pu, T e =1 pu; Same torque bounds, flux bounds relaxed by +/ 0.01pu ABB s simulation environment Torque Stator flux Switch positions Standard DTC T THD = 100% I THD = 100% P sw = 100% MPDTC esse T THD = 103% I THD = 104% P sw = 58% N p =22 MPDTC esse(se) 2 N p =88 T THD = 94% I THD = 97% P sw = 39%

52 Summary and Conclusions

53 Commercial Benefits Higher rating of inverter possible 40% higher power capability (e.g. from 5 MVA to 7 MVA) Hardware remains the same Standard machines can be used No derating of machine required For complicated topologies MPC is enabling technology Fully utilize the drive hardware

54 Summary and Conclusions Goal: Fully utilize capability of drive hardware Minimize switching losses per distortions Achieve very fast torque and current response Approach: Treat control and modulation problem in one stage Work in the time domain Adopt model predictive control Results: MPDxC family MP 3 C

55 For More Information

56 Selected Literature T. Geyer: ʺLow complexity model predictive control in power electronics and power systemsʺ, PhD thesis, Automatic Control Laboratory, ETH Zurich, Switzerland, Mar P. Cortés, M. P. Kazmierkowski, R. M. Kennel, D. E. Quevedo, and J. Rodríguez: ʺPredictive Control in Power Electronics and Drivesʺ, IEEE Trans. on Industrial Electronics, vol. 55, no. 12, pp , Dec T. Geyer, G. Papafotiou, and M. Morari: ʺModel predictive direct torque control part I: concept, algorithm and analysisʺ, IEEE Trans. on Industrial Electronics, vol. 56, no. 6, pp , June G. Papafotiou, J. Kley, K. Papadopoulos, P. Bohren, M. Morari: ʺModel predictive direct torque control part II: implementation and experimental evaluationʺ, IEEE Trans. on Industrial Electronics, vol. 56, no. 6, pp , June T. Geyer: ʺGeneralized model predictive direct torque control: long prediction horizons and minimization of switching lossesʺ, Proc. of the 48rd IEEE Conference on Decision and Control, Shanghai, China, Dec T. Geyer: ʺA comparison of control and modulation schemes for medium voltage drives: emerging predictive control concepts versus field oriented controlʺ, Proc. of the Energy Conversion Congress and Exposition, Atlanta, GA, Sep T. Geyer: ʺModel predictive direct current control for multi level convertersʺ, Proc. of the Energy Conversion Congress and Exposition, Atlanta, GA, Sep