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Power Electronics and Drives
    –Modeling & Simulation
                                A Problem Based and Project Orient...
CONTENTS

                    Pre Requisite of Power Electronics System

                   Power Electronic Systems

    ...
Power Electronics-An Enabling Technology
 Energy System
                                                                  ...
Implementation of problem-oriented and
                  project-organised education


  Literature               Lectures...
Prerequisite for Power Electronics
  • Study of Second Order System, Control
    Concepts and Mathematics
  • Role of Pass...
Modeling & Simulation?
•   Modeling here refers to the process of analysis and syntheses to arrive at a suitable
    mathe...
Simulation Formulation

• Observing the Physical system.
• Formulating the hypotheses or mathematical model to
  explain t...
Mathematical Models

•   Linear or Nonlinear
•   Lumped or Distributed parameters
•   Static & Dynamic
•   Continuous or D...
Simulation Packages
1)General Purpose:
  Equation Oriented in that they require input in the form of
   differential or al...
Power Electronic Systems


         What is Power Electronics ?

             A field of Electrical Engineering that deals...
Power Electronic Systems


         Why Power Electronics ?

     Power semiconductor devices                      Power s...
Power Electronic Systems


            Why Power Electronics ?

       Power semiconductor devices                Power sw...
Power Electronic Systems


         Why Power Electronics ?

     Power semiconductor devices                Power switche...
Power Electronic Systems


         Why Power Electronics ?

    Passive elements                                 High fre...
Passive Elements In Power Electronics

•   Resistors
•   Capacitors
•   Inductors
•   Transformers
•   Filters
•   Integra...
Resistors in
                 Power Electronics
• Resistors   are  mostly   used   in   Power
  Electronics   to  dissipat...
Capacitors in
                 Power Electronics
• Capacitors   are  mostly   used   in   Power
  Electronics   to  by-pas...
Inductors in
                 Power Electronics
• Inductors   are   mostly  used   in   Power
  Electronics to block the f...
Power Electronic Systems


         Why Power Electronics ?


                                                       senso...
Power Electronic Systems


         Why Power Electronics ?

         Other factors:
           • Improvements in power se...
Power Electronic Systems

         Some Applications of Power Electronics :
      Typically used in systems requiring effi...
Modern Electrical Drive Systems


     •   About 50% of electrical energy used for drives


     •   Can be either used fo...
Modern Electrical Drive Systems

    Classic Electrical Drive for Variable Speed Application :




                       ...
Modern Electrical Drive Systems

    Typical Modern Electric Drive Systems

             Power Electronic Converters      ...
Modern Electrical Drive Systems
          Example on VSD application

                Constant speed                      ...
Modern Electrical Drive Systems
          Example on VSD application

                Constant speed                      ...
Modern Electrical Drive Systems
          Example on VSD application

                Constant speed                      ...
Modern Electrical Drive Systems
  Example on VSD application


    Electric motor consumes more than half of electrical en...
Modern Electrical Drive Systems

  Overview of AC and DC drives


     Before semiconductor devices were introduced (<1950...
Modern Electrical Drive Systems

  Overview of AC and DC drives


     After vector control drives were introduced (1980s)...
Modern Electrical Drive Systems

  Overview of AC and DC drives




                                  Courtesy: Electrical...
Power Electronic Converters in ED Systems
                          Converters for Motor Drives
                          ...
Power Electronic Converters in ED Systems
    DC DRIVES

     Available AC source to control DC motor (brushed)

         ...
Power Electronic Converters in ED Systems
     DC DRIVES
          AC-DC
                                                 ...
Power Electronic Converters in ED Systems
     DC DRIVES
          AC-DC
                                                 ...
Power Electronic Converters in ED Systems
    DC DRIVES
      AC-DC



                                          ia

     ...
Power Electronic Converters in ED Systems
    DC DRIVES
      AC-DC



                                +
         3-
     ...
Power Electronic Converters in ED Systems
    DC DRIVES
      AC-DC


                                       F1           ...
Power Electronic Converters in ED Systems
             DC DRIVES
              AC-DC
               Cascade control struct...
Power Electronic Converters in ED Systems
    DC DRIVES
      AC-DC-DC




                            Uncontrolled       ...
Power Electronic Converters in ED Systems
    DC DRIVES
      AC-DC-DC




                                               ...
Power Electronic Converters in ED Systems
    DC DRIVES
      AC-DC-DC        DC-DC: Two-quadrant Converter

             ...
Power Electronic Converters in ED Systems
    DC DRIVES
      AC-DC-DC        DC-DC: Two-quadrant Converter

             ...
Power Electronic Converters in ED Systems
    DC DRIVES
      AC-DC-DC        DC-DC: Two-quadrant Converter

             ...
Power Electronic Converters in ED Systems
    DC DRIVES
      AC-DC-DC        DC-DC: Two-quadrant Converter

             ...
Power Electronic Converters in ED Systems
    DC DRIVES
      AC-DC-DC        DC-DC: Two-quadrant Converter




          ...
Power Electronic Converters in ED Systems
     DC DRIVES
        AC-DC-DC       DC-DC: Four-quadrant Converter
           ...
Power Electronic Converters in ED Systems
     DC DRIVES
          AC-DC-DC       DC-DC: Four-quadrant Converter
         ...
Power Electronic Converters in ED Systems
     DC DRIVES
          AC-DC-DC       DC-DC: Four-quadrant Converter
         ...
Power Electronic Converters in ED Systems
     DC DRIVES
          AC-DC-DC       DC-DC: Four-quadrant Converter
         ...
Power Electronic Converters in ED Systems
           DC DRIVES
                           Bipolar switching scheme – outpu...
Power Electronic Converters in ED Systems
            DC DRIVES
                            Unipolar switching scheme – ou...
Power Electronic Converters in ED Systems
    DC DRIVES
         AC-DC-DC                        DC-DC: Four-quadrant Conv...
Power Electronic Converters in ED Systems
    AC DRIVES
      AC-DC-AC




                                           cont...
Modeling and Control of Electrical Drives

          •   Control the torque, speed or position

          •   Cascade cont...
Modeling and Control of Electrical Drives
      Current controlled converters in DC Drives - Hysteresis-based


          ...
Modeling and Control of Electrical Drives
    Current controlled converters in AC Drives - Hysteresis-based

          i*a...
Modeling and Control of Electrical Drives
    Current controlled converters in AC Drives - Hysteresis-based




      iq

...
Modeling and Control of Electrical Drives
  Current controlled converters in AC Drives - Hysteresis-based
                ...
Modeling and Control of Electrical Drives
      Current controlled converters in AC Drives - Hysteresis-based

           ...
Modeling and Control of Electrical Drives
  Current controlled converters in AC Drives - Hysteresis-based



             ...
Modeling and Control of Electrical Drives
  Current controlled converters in DC Drives - PI-based




                    ...
Modeling and Control of Electrical Drives
      Current controlled converters in DC Drives - PI-based

i*a      +
        ...
Modeling and Control of Electrical Drives
   Current controlled converters in DC Drives - PI-based




                  •...
Modeling and Control of Electrical Drives
      Current controlled converters in AC Drives - PI-based

i*a      +
        ...
Modeling and Control of Electrical Drives
      Current controlled converters in AC Drives - PI-based

i*a

              ...
Modeling and Control of Electrical Drives
  Current controlled converters in AC Drives - PI-based

                       ...
Modeling and Control of Electrical Drives
     Current controlled converters in AC Drives - PI-based

         Stationary ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with Controlled rectifier



     ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with Controlled rectifier
  Cosine...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with Controlled rectifier
  Cosine...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with Controlled rectifier

     Va...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with Controlled rectifier

     Va...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with Controlled rectifier

       ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with Controlled rectifier


      ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with Controlled rectifier

       ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with Controlled rectifier

       ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters




           ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters



            ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters
               ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters
               ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters
               ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters
               ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters
     Thus relat...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters

Taking Laplace...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters
 Bipolar switch...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters
 Bipolar switch...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters
               ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters
 Unipolar switc...
Modeling and Control of Electrical Drives
     Modeling of the Power Converters: DC drives with SM Converters

 DC motor –...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters

 DC motor – se...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters

 DC motor – se...
Modeling and Control of Electrical Drives
      Modeling of the Power Converters: DC drives with SM Converters
           ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters

  Closed-loop ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: DC drives with SM Converters

  Closed-loop ...
Modeling and Control of Electrical Drives
    Modeling of the Power Converters: IM drives


                         INDUC...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: IM drives


   Control of induction machine ...
Modeling and Control of Electrical Drives
  Modeling of the Power Converters: IM drives
    Te

Pull out
Torque           ...
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Power Electronics

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  1. 1. Power Electronics and Drives –Modeling & Simulation A Problem Based and Project Oriented Learning B.Chitti Babu Member IEEE (USA), Student Member IET (UK) Department of Electrical Engineering, National Institute of Technology,Rourkela bcbabunitrkl@ieee.org B Chitti Babu, 14 August 2009 1 EE NIT Rourkela
  2. 2. CONTENTS Pre Requisite of Power Electronics System Power Electronic Systems Power Electronic Converters in Electrical Drives :: DC and AC Drives Modeling and Control of Electrical Drives :: Current controlled Converters :: Modeling of Power Converters :: Scalar control of IM B Chitti Babu, 14 August 2009 2 EE NIT Rourkela
  3. 3. Power Electronics-An Enabling Technology Energy System REFRIGERATOR SOLAR CELLS TELEVISION DC AC SOLAR LIGHT ENERGY TRANSFORMER 3 3 3 1-3 MOTOR POWER STATION TRANSFORMER PUMP FACTS ROBOTICS COMPEN- SATOR INDUSTRY TRANSFORMER FUEL DC CELLS AC ☯ 3 POWER SUPPLY a d WIND TURBINE ~ FUEL = COMMUNICATION TRANSPORT COMBUSTION ENGINE B Chitti Babu, 14 August 2009 Courtesy: EE NIT Rourkela Aalborg University,Denmark 3
  4. 4. Implementation of problem-oriented and project-organised education Literature Lectures Group studies Problem Problem Report analysis solving Field work/ Experiments/ Tutorials Simulation Prototyping B Chitti Babu, 14 August 2009 4 EE NIT Rourkela
  5. 5. Prerequisite for Power Electronics • Study of Second Order System, Control Concepts and Mathematics • Role of Passive Elements • Physics concepts of Devices • Device Selection ……………………………… • Modeling and Simulation • Build and Evaluate • Design & Development • Research and Innovate B Chitti Babu, 14 August 2009 5 EE NIT Rourkela
  6. 6. Modeling & Simulation? • Modeling here refers to the process of analysis and syntheses to arrive at a suitable mathematical description that encompasses the relevant dynamic characteristics of the component, preferably in terms of parameters that can be easily determined in practice • Model supposely imitates or reproduces certain essential characteristics or conditions of the actual-This is called SIMULATION. • Modeling & Simulation-Simulation is a technique that involves setting up a model of a real situation and performing experiments on the model. • Simulation to be an experiment with logical and mathematical models, especially mathematical representations of the dynamic kind that are characterized by a mix of differential and algebraic equations. B Chitti Babu, 14 August 2009 6 EE NIT Rourkela
  7. 7. Simulation Formulation • Observing the Physical system. • Formulating the hypotheses or mathematical model to explain the observation. • Predicting the behavior of the system from solutions or properties of the mathematical model. • Testing the validity of the Hypotheses or Mathematical Model. B Chitti Babu, 14 August 2009 7 EE NIT Rourkela
  8. 8. Mathematical Models • Linear or Nonlinear • Lumped or Distributed parameters • Static & Dynamic • Continuous or Discrete • Deterministic or Stochastic Courtesy: Dynamic Simulation of Electric Machinery- By Chee Mun Ong B Chitti Babu, 14 August 2009 8 EE NIT Rourkela
  9. 9. Simulation Packages 1)General Purpose: Equation Oriented in that they require input in the form of differential or algebraic equations. Eg:IESL, SABER, IMSL, ODEPAK & DASSL etc. 2)Application-Specific Packages: Ready to use models of commonly used components for a specific applications. Eg:SPICE2, EMTP, PSCAD etc. MATLAB & SIMULINK:They are Registered Trade mark of the THE MATHWORKS. Inc., USA B Chitti Babu, 14 August 2009 9 EE NIT Rourkela
  10. 10. Power Electronic Systems What is Power Electronics ? A field of Electrical Engineering that deals with the application of power semiconductor devices for the control and conversion of electric power sensors Input Power Source Electronics Load - AC - DC Converters Output - unregulated - AC - DC POWER ELECTRONIC CONVERTERS – the Reference Controlle heart of power a power r electronics system B Chitti Babu, 14 August 2009 10 EE NIT Rourkela
  11. 11. Power Electronic Systems Why Power Electronics ? Power semiconductor devices Power switches isw ON or OFF + vsw − =0 isw = 0 Ploss = vsw× isw = 0 + vsw − Losses ideally ZERO ! B Chitti Babu, 14 August 2009 11 EE NIT Rourkela
  12. 12. Power Electronic Systems Why Power Electronics ? Power semiconductor devices Power switches K K K − − − G G Vak Vak Vak + + + ia ia ia A A A B Chitti Babu, 14 August 2009 12 EE NIT Rourkela
  13. 13. Power Electronic Systems Why Power Electronics ? Power semiconductor devices Power switches D C iD + ic + VDS G G VCE − − S E B Chitti Babu, 14 August 2009 13 EE NIT Rourkela
  14. 14. Power Electronic Systems Why Power Electronics ? Passive elements High frequency + VL transformer − i L + + Inductor V V2 1 + VC − − − i C B Chitti Babu, 14 August 2009 14 EE NIT Rourkela
  15. 15. Passive Elements In Power Electronics • Resistors • Capacitors • Inductors • Transformers • Filters • Integrated Magnetics B Chitti Babu, 14 August 2009 15 EE NIT Rourkela
  16. 16. Resistors in Power Electronics • Resistors are mostly used in Power Electronics to dissipate the trapped energy from other components as well to provide damping. • Thus, resistors can carry significant amount of high frequency currents. • Resistors can carry fundamental ac component currents in ac circuits and also carry dc component currents under steady state. • No resistor is ideal, so their behavior depends upon the applied frequency The peak temperature rise depends on the energy dissipated in the resistors. B Chitti Babu, 14 August 2009 16 EE NIT Rourkela
  17. 17. Capacitors in Power Electronics • Capacitors are mostly used in Power Electronics to by-pass high frequency components of voltages and currents. • Thus, capacitors can carry significant amount of high frequency currents Capacitors can carry fundamental ac component. • currents in ac circuits but cannot carry dc component currents under steady state. • No capacitor is ideal, so their behavior depends upon the applied frequency • The breakdown voltage depends on the peak voltage charge B Chitti Babu, 14 August 2009 17 EE NIT Rourkela
  18. 18. Inductors in Power Electronics • Inductors are mostly used in Power Electronics to block the flow of high frequency components of currents. • Thus, inductors can drop significant amount of high frequency voltages. • Inductors can have fundamental ac component voltage drop in ac circuits but cannot drop dc component voltages under steady state. • No inductor is ideal, so their behavior depends upon the applied frequency • The peak flux density depends on the peak instantaneous current. Courtesy: Dr.Sujit K. Biswas, Lecture Notes, Jadavpur University B Chitti Babu, 14 August 2009 18 EE NIT Rourkela
  19. 19. Power Electronic Systems Why Power Electronics ? sensors Input Power Source Electronics Load IDEALLY - AC Converters LOSSLESS ! Output - DC - unregulated - AC - DC Reference Controlle r B Chitti Babu, 14 August 2009 19 EE NIT Rourkela
  20. 20. Power Electronic Systems Why Power Electronics ? Other factors: • Improvements in power semiconductors • fabrication • Power Integrated Module (PIM), Intelligent Power Modules (IPM) • Decline cost in power semiconductor • Advancement in semiconductor fabrication • ASICs • FPGA • DSPs • Faster and cheaper to implement complex algorithm B Chitti Babu, 14 August 2009 20 EE NIT Rourkela
  21. 21. Power Electronic Systems Some Applications of Power Electronics : Typically used in systems requiring efficient control and conversion of electric energy: Domestic and Commercial Applications Industrial Applications Telecommunications Transportation Generation, Transmission and Distribution of electrical energy Power rating of < 1 W (portable equipment) Tens or hundreds Watts (Power supplies for computers /office equipment) kW to MW : drives Hundreds of MW in DC transmission system (HVDC) B Chitti Babu, 14 August 2009 21 EE NIT Rourkela
  22. 22. Modern Electrical Drive Systems • About 50% of electrical energy used for drives • Can be either used for fixed speed or variable speed • 75% - constant speed, 25% variable speed (expanding) • Variable speed drives typically used PEC to supply the motors DC motors (brushed) AC motors SRM - IM BLDC - PMSM B Chitti Babu, 14 August 2009 22 EE NIT Rourkela
  23. 23. Modern Electrical Drive Systems Classic Electrical Drive for Variable Speed Application : • Bulky • Inefficient • inflexible B Chitti Babu, 14 August 2009 23 EE NIT Rourkela
  24. 24. Modern Electrical Drive Systems Typical Modern Electric Drive Systems Power Electronic Converters Electric Motor Electric Energy Electric Energy Electric Mechanical - Unregulated - - Regulated - Energy Energy POWER IN Power Moto Loa Electronic d r Converters feedback Reference Controller B Chitti Babu, 14 August 2009 24 EE NIT Rourkela
  25. 25. Modern Electrical Drive Systems Example on VSD application Constant speed Variable Speed Drives valve Supply motor pump Power out Power In Power loss Mainly in valve B Chitti Babu, 14 August 2009 25 EE NIT Rourkela
  26. 26. Modern Electrical Drive Systems Example on VSD application Constant speed Variable Speed Drives valve Supply Supply motor pump motor PEC pump Power out Power out Power Power In In Power loss Power loss Mainly in valve B Chitti Babu, 14 August 2009 26 EE NIT Rourkela
  27. 27. Modern Electrical Drive Systems Example on VSD application Constant speed Variable Speed Drives valve Supply Supply motor pump motor PEC pump Power out Power out Power Power In In Power loss Power loss Mainly in valve B Chitti Babu, 14 August 2009 27 EE NIT Rourkela
  28. 28. Modern Electrical Drive Systems Example on VSD application Electric motor consumes more than half of electrical energy in the US Fixed speed Variable speed Improvements in energy utilization in electric motors give large impact to the overall energy consumption HOW ? Replacing fixed speed drives with variable speed drives Using the high efficiency motors Improves the existing power converter–based drive systems B Chitti Babu, 14 August 2009 28 EE NIT Rourkela
  29. 29. Modern Electrical Drive Systems Overview of AC and DC drives Before semiconductor devices were introduced (<1950) • AC motors for fixed speed applications • DC motors for variable speed applications After semiconductor devices were introduced (1960s) • Variable frequency sources available – AC motors in variable speed applications • Coupling between flux and torque control • Application limited to medium performance applications – fans, blowers, compressors – scalar control • High performance applications dominated by DC motors – tractions, elevators, servos, etc B Chitti Babu, 14 August 2009 29 EE NIT Rourkela
  30. 30. Modern Electrical Drive Systems Overview of AC and DC drives After vector control drives were introduced (1980s) • AC motors used in high performance applications – elevators, tractions, servos • AC motors favorable than DC motors – however control is complex hence expensive • Cost of microprocessor/semiconductors decreasing –predicted 30 years ago AC motors would take over DC motors B Chitti Babu, 14 August 2009 30 EE NIT Rourkela
  31. 31. Modern Electrical Drive Systems Overview of AC and DC drives Courtesy: Electrical Drives by Ion Boldea ,CRC Press B Chitti Babu, 14 August 2009 31 EE NIT Rourkela
  32. 32. Power Electronic Converters in ED Systems Converters for Motor Drives (some possible configurations) DC Drives AC Drives AC Source DC Source AC Source DC Source DC-AC- DC-DC DC AC-DC- AC-DC- DC-DC- AC-DC AC-AC DC-AC DC AC AC Const. Variable NCC FCC DC DCChitti Babu, B 14 August 2009 32 EE NIT Rourkela
  33. 33. Power Electronic Converters in ED Systems DC DRIVES Available AC source to control DC motor (brushed) AC-DC- AC-DC DC Uncontrolled Rectifier Single-phase Control Control Three-phase Controlled Rectifier DC-DC Switched mode Single-phase 1-quadrant, 2-quadrant Three-phase 4-quadrant B Chitti Babu, 14 August 2009 33 EE NIT Rourkela
  34. 34. Power Electronic Converters in ED Systems DC DRIVES AC-DC 400 200 0 + 2 Vm Vo = cos α -200 π -400 0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44 50Hz Vo 10 1-phase Average voltage 5 over 10ms − 0 0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44 500 0 50Hz + -500 3-phase 0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44 3VL − L , m Vo Vo = cos α π 30 20 − Average voltage 10 over 3.33 ms 0 B Chitti Babu, 0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44 14 August 2009 34 EE NIT Rourkela
  35. 35. Power Electronic Converters in ED Systems DC DRIVES AC-DC 2 Vm π + 2 Vm Vo = cos α π 50Hz Vo 90o 180o 1-phase Average voltage over 10ms − 2 Vm − π 3VL − L , m π 50Hz + 3-phase 3VL − L , m Vo Vo = cos α π 90o 180o − Average voltage over 3.33 ms 3VL − L , m − π B Chitti Babu, 14 August 2009 35 EE NIT Rourkela
  36. 36. Power Electronic Converters in ED Systems DC DRIVES AC-DC ia + Vt 3-phase Vt Q2 Q1 supply − Q3 Q4 Ia - Operation in quadrant 1 and 4 only B Chitti Babu, 14 August 2009 36 EE NIT Rourkela
  37. 37. Power Electronic Converters in ED Systems DC DRIVES AC-DC + 3- phase 3-phase Vt supply supply − ω Q2 Q1 Q3 Q4 T B Chitti Babu, 14 August 2009 37 EE NIT Rourkela
  38. 38. Power Electronic Converters in ED Systems DC DRIVES AC-DC F1 R1 3-phase supply + Va - R2 F2 ω Q2 Q1 Q3 Q4 T B Chitti Babu, 14 August 2009 38 EE NIT Rourkela
  39. 39. Power Electronic Converters in ED Systems DC DRIVES AC-DC Cascade control structure with armature reversal (4-quadrant): iD ω ωref + Speed iD,ref + Current Firing control Control Circuit ler _ ler _ iD,ref Armature iD, reversal Babu, B Chitti 14 August 2009 39 EE NIT Rourkela
  40. 40. Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC Uncontrolled control rectifier Switch Mode DC-DC 1-Quadrant 2-Quadrant 4-Quadrant B Chitti Babu, 14 August 2009 40 EE NIT Rourkela
  41. 41. Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC control B Chitti Babu, 14 August 2009 41 EE NIT Rourkela
  42. 42. Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter Va T1 D1 + ia Vdc Q2 Q1 + Ia − D2 T2 Va - T1 conducts → va = Vdc B Chitti Babu, 14 August 2009 42 EE NIT Rourkela
  43. 43. Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter Va T1 D1 + ia Vdc Q2 Q1 + Ia − D2 T2 Va - D2 conducts → va = 0 T1 conducts → va = Vdc Va Eb Quadrant 1 The average voltage is made larger than the back emf B Chitti Babu, 14 August 2009 43 EE NIT Rourkela
  44. 44. Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter Va T1 D1 + ia Vdc Q2 Q1 + Ia − D2 T2 Va - D1 conducts → va = Vdc B Chitti Babu, 14 August 2009 44 EE NIT Rourkela
  45. 45. Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter Va T1 D1 + ia Vdc Q2 Q1 + Ia − D2 T2 Va - T2 conducts → va = 0 D1 conducts → va = Vdc Va Eb Quadrant 2 The average voltage is made smallerr than the back emf, thus forcing the current to flow in the reverse direction B Chitti Babu, 14 August 2009 45 EE NIT Rourkela
  46. 46. Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter vc 2vtri + vA Vdc - 0 + vc B Chitti Babu, 14 August 2009 46 EE NIT Rourkela
  47. 47. Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + D1 D3 Q1 Q3 + Va − Vdc − D4 D2 Q4 Q2 Positive current va = Vdc when Q1 and Q2 are ON B Chitti Babu, 14 August 2009 47 EE NIT Rourkela
  48. 48. Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + D1 D3 Q1 Q3 + Va − Vdc − D4 D2 Q4 Q2 Positive current va = Vdc when Q1 and Q2 are ON va = -Vdc when D3 and D4 are ON va = 0 when current freewheels through Q and D B Chitti Babu, 14 August 2009 48 EE NIT Rourkela
  49. 49. Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + D1 D3 Q1 Q3 + Va − Vdc − D4 D2 Q4 Q2 Positive current Negative current va = Vdc when Q1 and Q2 are ON va = Vdc when D1 and D2 are ON va = -Vdc when D3 and D4 are ON va = 0 when current freewheels through Q and D B Chitti Babu, 14 August 2009 49 EE NIT Rourkela
  50. 50. Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + D1 D3 Q1 Q3 + Va − Vdc − D4 D2 Q4 Q2 Positive current Negative current va = Vdc when Q1 and Q2 are ON va = Vdc when D1 and D2 are ON va = -Vdc when D3 and D4 are ON va = -Vdc when Q3 and Q4 are ON va = 0 when current freewheels through Q and D va = 0 when current freewheels through Q and D B Chitti Babu, 14 August 2009 50 EE NIT Rourkela
  51. 51. Power Electronic Converters in ED Systems DC DRIVES Bipolar switching scheme – output AC-DC-DC swings between VDC and -VDC vc 2vtri Vdc Vdc + + vA vA vB 0 - - Vdc vB 0 vc Vdc + vAB _ -Vdc B Chitti Babu, 14 August 2009 51 EE NIT Rourkela
  52. 52. Power Electronic Converters in ED Systems DC DRIVES Unipolar switching scheme – output AC-DC-DC swings between Vdc and -Vdc vc Vtri -vc Vdc + + Vdc vA vB vA - 0 - Vdc vc vB 0 + Vdc _ vAB 0 -vc B Chitti Babu, 14 August 2009 52 EE NIT Rourkela
  53. 53. Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter Armature 200 current 200 150 150 Armature Vdc 100 Vdc 100 current 50 50 0 0 -50 -50 Vdc -100 -100 -150 -150 -200 -200 0.04 0.0405 0.041 0.0415 0.042 0.0425 0.043 0.0435 0.044 0.0445 0.045 0.04 0.0405 0.041 0.0415 0.042 0.0425 0.043 0.0435 0.044 0.0445 0.045 Bipolar switching scheme Unipolar switching scheme • Current ripple in unipolar is smaller • Output frequency in unipolar is effectively doubled B Chitti Babu, 14 August 2009 53 EE NIT Rourkela
  54. 54. Power Electronic Converters in ED Systems AC DRIVES AC-DC-AC control The common PWM technique: CB-SPWM with ZSS 14 August 2009 SVPWM B Chitti Babu, 54 EE NIT Rourkela
  55. 55. Modeling and Control of Electrical Drives • Control the torque, speed or position • Cascade control structure Example of current control in cascade control structure θ* ω* T* + + + − − − position speed current controller controller controller converter Motor kT ω θ 1/s B Chitti Babu, 14 August 2009 55 EE NIT Rourkela
  56. 56. Modeling and Control of Electrical Drives Current controlled converters in DC Drives - Hysteresis-based + ia Vdc + iref − Va − va iref + ierr q _ q • High bandwidth, simple implementation, insensitive to parameter variations ierr • Variable switching frequency – depending on operating conditions B Chitti Babu, 14 August 2009 56 EE NIT Rourkela
  57. 57. Modeling and Control of Electrical Drives Current controlled converters in AC Drives - Hysteresis-based i*a + Converter i*b + i*c + • For isolated neutral load, ia + ib + ic = 0 ∴control is not totally independent 3-phase • Instantaneous error for isolated neutral load can AC Motor reach double the band B Chitti Babu, 14 August 2009 57 EE NIT Rourkela
  58. 58. Modeling and Control of Electrical Drives Current controlled converters in AC Drives - Hysteresis-based iq is Δh Δh Δh Δh id • For isolated neutral load, ia + ib + ic = 0 ∴control is not totally independent • Instantaneous error for isolated neutral load can reach double the band B Chitti Babu, 14 August 2009 58 EE NIT Rourkela
  59. 59. Modeling and Control of Electrical Drives Current controlled converters in AC Drives - Hysteresis-based • Δh = 0.3 A • Vdc = 600V Con u s tin ou • Sinusoidal reference current, 30Hz load • 10Ω, 50mH powergui Scope iaref TW o orkspace1 g + i A + - D Voltage Source C B Series R BranchC LC 3urrent Measurem 3 ent c1 p1 - C i c2 p2 + - U ersal Bridge 1 niv c3 p3 Series R Branch urrent M LC C1 easurem 1 ent ina p4 i + - Sine W e av inb p5 Series R Branch urrent M LC C2 easurem 2 ent inc p6 Subsystem Sine W e 1 av Sine W e 2 av B Chitti Babu, 14 August 2009 59 EE NIT Rourkela
  60. 60. Modeling and Control of Electrical Drives Current controlled converters in AC Drives - Hysteresis-based Actual and reference currents Current error 0.5 10 0.4 0.3 5 0.2 10 0.1 0 0 9 -0.1 -0.2 -5 8 -0.3 7 -0.4 -10 -0.5 0.005 0.01 6 0.015 0.02 0.025 0.03 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 5 4 4 6 8 10 12 14 16 -3 x 10 B Chitti Babu, 14 August 2009 60 EE NIT Rourkela
  61. 61. Modeling and Control of Electrical Drives Current controlled converters in AC Drives - Hysteresis-based Actual current locus Current error 10 0.5 5 0 0.6A -0.5 0 0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06 -5 0.5 -10 -10 -5 0 5 10 0 0.6A -0.5 0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06 0.5 0 0.6A -0.5 0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06 B Chitti Babu, 14 August 2009 61 EE NIT Rourkela
  62. 62. Modeling and Control of Electrical Drives Current controlled converters in DC Drives - PI-based Vdc iref + vc vPulse width tri PI vc modulator q q q − B Chitti Babu, 14 August 2009 62 EE NIT Rourkela
  63. 63. Modeling and Control of Electrical Drives Current controlled converters in DC Drives - PI-based i*a + PI PWM Converter i*b + PI PWM i*c + PWM PI • Sinusoidal PWM Motor • Interactions between phases → only require 2 controllers • Tracking error B Chitti Babu, 14 August 2009 63 EE NIT Rourkela
  64. 64. Modeling and Control of Electrical Drives Current controlled converters in DC Drives - PI-based • Perform the 3-phase to 2-phase transformation - only two controllers (instead of 3) are used • Perform the control in synchronous frame - the current will appear as DC • Interactions between phases → only require 2 controllers • Tracking error B Chitti Babu, 14 August 2009 64 EE NIT Rourkela
  65. 65. Modeling and Control of Electrical Drives Current controlled converters in AC Drives - PI-based i*a + PI PWM Converter i*b + PI PWM i*c + PWM PI Motor B Chitti Babu, 14 August 2009 65 EE NIT Rourkela
  66. 66. Modeling and Control of Electrical Drives Current controlled converters in AC Drives - PI-based i*a PI SVM Converter i*b 3-2 2-3 PI i*c 3-2 Motor B Chitti Babu, 14 August 2009 66 EE NIT Rourkela
  67. 67. Modeling and Control of Electrical Drives Current controlled converters in AC Drives - PI-based va* id* + PI controller − vb* id dq→abc SVM or SPWM IM iq* + VSI PI vc* − iq controller ωs Synch speed ωs estimator abc→dq B Chitti Babu, 14 August 2009 67 EE NIT Rourkela
  68. 68. Modeling and Control of Electrical Drives Current controlled converters in AC Drives - PI-based Stationary - ia Stationary - id 4 4 2 3 0 2 -2 1 -4 0 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 4 Rotating - ia 4 Rotating - id 2 3 0 2 -2 1 -4 0 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 B Chitti Babu, 14 August 2009 68 EE NIT Rourkela
  69. 69. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier + vc firing α controlled circuit rectifier Va – vc(s) va(s) ? DC motor The relation between vc and va is determined by the firing circuit B Chitti Babu, 14 August 2009 69 It is desirable to have a linear NIT Rourkela EE relation between vc and va
  70. 70. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier Cosine-wave crossing control Vm Input voltage 0 π 2π 3π 4π vc vs Cosine wave compared with vc Results of comparison trigger SCRs Output voltage B Chitti Babu, 14 August 2009 70 EE NIT Rourkela
  71. 71. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier Cosine-wave crossing control cos(ωt) Vscos(α) = vc Vm ⎛v ⎞ 0 π 2π 3π 4π α = cos −1 ⎜ c ⎟ ⎜v ⎟ ⎝ s⎠ vc vs α 2Vm v c ⎛ −1 ⎛ v c ⎞ ⎞ Va = cos⎜α ) ⎜ ⎟ ⎟ ( π vs ⎝ ⎜ cos ⎜ v ⎟ ⎟ ⎝ s ⎠⎠ α A linear relation between vc and Va B Chitti Babu, 14 August 2009 71 EE NIT Rourkela
  72. 72. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier Va is the average voltage over one period of the waveform - sampled data system Delays depending on when the control signal changes – normally taken as half of sampling period B Chitti Babu, 14 August 2009 72 EE NIT Rourkela
  73. 73. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier Va is the average voltage over one period of the waveform - sampled data system Delays depending on when the control signal changes – normally taken as half of sampling period B Chitti Babu, 14 August 2009 73 EE NIT Rourkela
  74. 74. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier T − s G H (s) = Ke 2 Single phase, 50Hz vc(s) Va(s) 2Vm K= T=10ms πVs Three phase, 50Hz 3VL − L ,m K= T=3.33ms πVs Simplified if control bandwidth is reduced to much lower than the sampling frequency B Chitti Babu, 14 August 2009 74 EE NIT Rourkela
  75. 75. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier + iref current vc firing α controlled controller Va circuit rectifier – • To control the current – current-controlled converter • Torque can be controlled • Only operates in Q1 and Q4 (single converter topology) B Chitti Babu, 14 August 2009 75 EE NIT Rourkela
  76. 76. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier • Input 3-phase, 240V, 50Hz • Closed loop current control with PI controller Scope3 + - v Continuous Voltage Measurement4 + i powergui - Scope2 AC Voltage Source Current Measurement 1 Step s AC Voltage Source1 + g - + v A Controlled Voltage Source Series RLC Branch AC Voltage Source2 B To Workspace + - i - v C - + ia Voltage Measurement2 Universal Bridge Current Measurement To Workspace1 + + - v - v alpha_deg Voltage Measurement Voltage Measurement3 AB ux Scope BC pulses + - v CA Block Voltage Measurement1 Synchronized Mu 6-Pulse Generator Scope1 ir To Workspace2 PID acos -K- Signal PID Controller Saturation 1 Generator 7 Constant 1 B Chitti Babu, 14 August 2009 76 EE NIT Rourkela
  77. 77. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with Controlled rectifier • Input 3-phase, 240V, 50Hz • Closed loop current control with PI controller 1000 1000 500 500 0 Voltage 0 -500 -500 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.22 0.23 0.24 0.25 0.26 0.27 0.28 15 15 10 10 5 Current 5 0 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 B Chitti Babu, 14 August 2009 77 EE NIT Rourkela
  78. 78. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters B Chitti Babu, 14 August 2009 78 EE NIT Rourkela
  79. 79. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Vdc Switching signals obtained by comparing control signal with triangular wave + Va − vtri q vc We want to establish a relation between vc and Va AVERAGE voltage vc(s) Va(s) ? DC motor B Chitti Babu, 14 August 2009 79 EE NIT Rourkela
  80. 80. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Ttri ⎧1 Vc > Vtri q=⎨ vc ⎩0 Vc < Vtri 1 t + Ttri d= Ttri ∫ t q dt 1 t on = 0 Ttri ton Vdc 1 dTtri Va = ∫ Vdcdt = dVdc Ttri 0 B Chitti Babu, 14 August 2009 0 EE NIT Rourkela 80
  81. 81. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters d 0.5 vc -Vtri Vtri -Vtri vc For vc = -Vtri → d = 0 B Chitti Babu, 14 August 2009 81 EE NIT Rourkela
  82. 82. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters d 0.5 vc -Vtri -Vtri Vtri vc Vtri For vc = -Vtri → d = 0 For vc = 0 → d = 0.5 14 August 2009 EE NIT → Rourkela For vc = VtriChitti d = 1 B Babu, 82
  83. 83. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters d 0.5 vc -Vtri -Vtri Vtri vc 1 d = 0.5 + vc 2Vtri Vtri For vc = -Vtri → d = 0 For vc = 0 → d = 0.5 14 August 2009 EE NIT → Rourkela For vc = VtriChitti d = 1 B Babu, 83
  84. 84. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Thus relation between vc and Va is obtained as: V dc V a = 0 . 5 V dc + vc 2 V tri Introducing perturbation in vc and Va and separating DC and AC components: V dc DC: V a = 0 . 5 V dc + vc 2 V tri AC: ~ = V dc ~ va vc 2 V tri B Chitti Babu, 14 August 2009 84 EE NIT Rourkela
  85. 85. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Taking Laplace Transform on the AC, the transfer function is obtained as: v a (s) V dc = v c ( s ) 2 V tri vc(s) V dc va(s) DC motor 2 V tri B Chitti Babu, 14 August 2009 85 EE NIT Rourkela
  86. 86. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Bipolar switching scheme Vdc vc 2vtri -Vdc q vtri + Vdc Vdc vA + VAB − 0 − vc Vdc vB 0 q Vdc vAB v v d A = 0.5 + c dB = 1 − d A = 0.5 − c -Vdc 2Vtri 2Vtri Vdc Vdc Vdc VA = 0.5Vdc + vc VB = 0.5Vdc − vc VA − VB = VAB = vc 2Vtri 2Vtri Vtri B Chitti Babu, 14 August 2009 86 EE NIT Rourkela
  87. 87. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Bipolar switching scheme v a ( s ) V dc = v c (s) V tri vc(s) V dc va(s) DC motor V tri B Chitti Babu, 14 August 2009 87 EE NIT Rourkela
  88. 88. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Vdc Unipolar switching scheme vc Leg b Vtri + -vc vtri Vdc qa vc − vA Leg a vtri -vc qb vB vc − vc vAB d A = 0.5 + dB = 0.5 + 2Vtri 2Vtri Vdc Vdc Vdc VA = 0.5Vdc + vc VB = 0.5Vdc − vc VA − VB = VAB = vc 2Vtri 2Vtri Vtri The same average value we’ve seen for bipolar ! B Chitti Babu, 14 August 2009 88 EE NIT Rourkela
  89. 89. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Unipolar switching scheme v a ( s ) V dc = v c (s) V tri vc(s) V dc va(s) DC motor V tri B Chitti Babu, 14 August 2009 89 EE NIT Rourkela
  90. 90. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters DC motor – separately excited or permanent magnet dia dωm v t = ia R a + L a + ea Te = Tl + J dt dt Te = kt ia ee = kt ω Extract the dc and ac components by introducing small perturbations in Vt, ia, ea, Te, TL and ωm ac components dc components ~ ~ = ~ R + L d ia + ~ v t ia a ea Vt = Ia R a + E a a dt ~ ~ Te = k E ( ia ) Te = k E Ia ~ = k (ω ) ee ~ Ee = k Eω E ~ ~ ~ ~ + J d(ω ) Te = TL + B ω Te = TL + B(ω) 14 August 2009 dt B Chitti Babu, 90 EE NIT Rourkela
  91. 91. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters DC motor – separately excited or permanent magnet Perform Laplace Transformation on ac components ~ ~ ~ = i R +L d ia ~ Vt(s) = Ia(s)Ra + LasIa + Ea(s) vt a a a + ea dt ~ ~ Te(s) = kEIa(s) Te = k E ( ia ) ~ = k (ω ) ee ~ Ea(s) = kEω(s) E ~ ~ ~ ~ + J d(ω ) Te = TL + B ω Te(s) = TL(s) + Bω(s) + sJω(s) dt B Chitti Babu, 14 August 2009 91 EE NIT Rourkela
  92. 92. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters DC motor – separately excited or permanent magnet Tl (s ) - Va (s ) I a (s ) Te (s ) ω (s ) 1 1 kT + Ra + sL a + B + sJ - kE B Chitti Babu, 14 August 2009 92 EE NIT Rourkela
  93. 93. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters q vtri Torque + controller Tc + Vdc – − q kt DC motor Tl (s ) Converter T e (s ) Torque V dc Va (s ) 1 I a (s ) Te (s ) - 1 ω (s ) kT controller Ra + sL a B + sJ + V tri ,peak + + - - kE B Chitti Babu, 14 August 2009 93 EE NIT Rourkela
  94. 94. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Closed-loop speed control – an example Design procedure in cascade control structure • Inner loop (current or torque loop) the fastest – largest bandwidth • The outer most loop (position loop) the slowest – smallest bandwidth • Design starts from torque loop proceed towards outer loops B Chitti Babu, 14 August 2009 94 EE NIT Rourkela
  95. 95. Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Closed-loop speed control – an example OBJECTIVES: • Fast response – large bandwidth • Minimum overshoot good phase margin (>65o) BODE PLOTS • Zero steady state error – very large DC gain METHOD • Obtain linear small signal model • Design controllers based on linear small signal model • Perform large signal simulation for controllers verification B Chitti Babu, 14 August 2009 95 EE NIT Rourkela
  96. 96. Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives INDUCTION MOTOR DRIVES Scalar Control Vector Control Const. V/Hz is=f(ωr) FOC DTC Rotor Flux Stator Flux Circular Hexagon DTC Flux Flux SVM B Chitti Babu, 14 August 2009 96 EE NIT Rourkela
  97. 97. Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Control of induction machine based on steady-state model (per phase SS equivalent circuit): Is Lls Llr’ Rs Ir’ + + Lm Vs Rr’/s Eag – Im – B Chitti Babu, 14 August 2009 97 EE NIT Rourkela
  98. 98. Modeling and Control of Electrical Drives Modeling of the Power Converters: IM drives Te Pull out Torque Intersection point (Tmax) (Te=TL) determines the Te steady –state speed Trated TL sm ωratedrotorωs ω ωr s B Chitti Babu, 14 August 2009 98 EE NIT Rourkela
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