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ELECTRIC DRIVES

INTRODUCTION TO ELECTRIC DRIVES
           MODULE 1

         Dr. Nik Rumzi Nik Idris
    Dept. of Energy Conversion, UTM
                  2006
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1




                               Electrical Drives

 Drives are systems employed for motion control



                                Require prime movers



                        Drives that employ electric motors as
                        prime movers are known as Electrical Drives
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1




                               Electrical Drives


           •   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)


           •   MEP 1522 will be covering variable speed drives
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1




         Example on VSD application

               Constant speed                  Variable Speed Drives


                            valve

Supply
             motor         pump




   Power                          Power out
     In




                            Power loss
                            Mainly in valve
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1




         Example on VSD application

               Constant speed                                 Variable Speed Drives


                            valve

Supply                                         Supply
             motor         pump                                     motor
                                                        PEC                       pump




   Power                          Power out
     In                                             Power                      Power out
                                                      In




                                                                            Power loss
                            Power loss
                            Mainly in valve
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1




         Example on VSD application

               Constant speed                                 Variable Speed Drives


                            valve

Supply                                         Supply
             motor         pump                                     motor
                                                        PEC                       pump




   Power                          Power out
     In                                             Power                      Power out
                                                      In




                                                                            Power loss
                            Power loss
                            Mainly in valve
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1




  Conventional electric drives (variable speed)




                    •    Bulky
                    •    Inefficient
                    •    inflexible
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


 Modern electric drives (With power electronic converters)




                    •    Small
                    •    Efficient
                    •    Flexible
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Modern electric drives




                                                                    Machine design
    Utility interface
                                                                    Speed sensorless
    Renewable energy
                                                                    Machine Theory


                                      Non-linear control
                                      Real-time control
                                      DSP application
                                      PFC
                                      Speed sensorless
                                      Power electronic converters

               •        Inter-disciplinary
               •        Several research area
               •        Expanding
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Components in electric drives

         e.g. Single drive - sensorless vector control from Hitachi
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Components in electric drives

         e.g. Multidrives system from ABB
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Components in electric drives

       Motors
       • DC motors - permanent magnet – wound field
       • AC motors – induction, synchronous (IPMSM, SMPSM),
         brushless DC
       • Applications, cost, environment


        Power sources
        • DC – batteries, fuel cell, photovoltaic - unregulated
        • AC – Single- three- phase utility, wind generator - unregulated

       Power processor
       • To provide a regulated power supply
       • Combination of power electronic converters
                  •More efficient
                  •Flexible
                  •Compact
                  •AC-DC DC-DC DC-AC AC-AC
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Components in electric drives



      Control unit
      • Complexity depends on performance requirement
      • analog- noisy, inflexible, ideally has infinite bandwidth.
      • digital – immune to noise, configurable, bandwidth is smaller than
        the analog controller’s
      • DSP/microprocessor – flexible, lower bandwidth - DSPs perform
        faster operation than microprocessors (multiplication in single
        cycle), can perform complex estimations
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Overview of AC and DC drives




                                             Extracted from Boldea & Nasar
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Overview of AC and DC drives



     DC motors: Regular maintenance, heavy, expensive, speed limit
                    Easy control, decouple control of torque and flux




    AC motors: Less maintenance, light, less expensive, high speed
                     Coupling between torque and flux – variable
                     spatial angle between rotor and stator flux
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  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 (1950s)
      • 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
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  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
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1

  Classification of IM drives (Buja, Kamierkowski, “Direct torque control of PWM inverter-fed AC motors - a survey”,
  IEEE Transactions on Industrial Electronics, 2004.
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Elementary principles of mechanics
                           v

                              x                           Newton’s law

             Fm                                                      d( Mv )
                              M                          Fm − Ff =
                                             Ff                         dt




      Linear motion, constant M

                               d( v )    d2 x
                   Fm − Ff = M        = M 2 = Ma
                                dt       dt

               •     First order differential equation for speed
               •     Second order differential equation for displacement
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Elementary principles of mechanics

                          θ              Rotational motion

                                             - Normally is the case for electrical drives
            Tl
                                                                 d( Jωm )
                                                     Te − Tl =
    Te , ω m                                                        dt
                              J

                      With constant J,

                                              d( ωm )   d2θ
                                  Te − Tl = J         =J 2
                                                dt      dt

        •        First order differential equation for angular frequency (or velocity)
        •        Second order differential equation for angle (or position)
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Elementary principles of mechanics
       For constant J,                                                   dωm
                                                           Te = Tl + J
                                                                          dt
           d( ωm )
       J             Torque dynamic – present during speed transient
              dt

        d( ωm )      Angular acceleration (speed)
           dt

           The larger the net torque, the faster the acceleration is.
                                                 200

                                                 100
                        speed (rad/s)




                                                   0

                                                 -100

                                                 -200
                                                    0.19   0.2   0.21    0.22   0.23   0.24   0.25


                                                  20

                                                  15
                                   torque (Nm)




                                                  10

                                                   5

                                                   0
                                                   0.19    0.2   0.21    0.22   0.23   0.24   0.25
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Elementary principles of mechanics


           Combination of rotational and translational motions


                         Fl                              Fe
                                                                          Te, ω
       ω
                r                          M                          r
                       Tl
                                               v

                                  d( v )
                    Fe − Fl = M                    Te = r(Fe),   Tl = r(Fl),   v =rω
                                   dt

                                     dω
                    Te − Tl = r 2M
                                     dt

                    r2M - Equivalent moment inertia of the
                    linearly moving mass
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Elementary principles of mechanics – effect of gearing


         Motors designed for high speed are smaller in size and volume

         Low speed applications use gear to utilize high speed motors

                             ωm              ωm1
              Motor               Load 1,               n1
              Te                  Tl1
                                                                J2

                                                        ωm2
                                                   n2         Load 2,
                             J1                               Tl2
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Elementary principles of mechanics – effect of gearing



                                  ωm             ωm1
                 Motor                 Load 1,               n1
                 Te                    Tl1
                                                                        J2
                                                             ωm2
                                                       n2            Load 2,
                                  J1
                                                                     Tl2




                                                             J equ = J1 + a 2 J 2
                                                                            2
                     ωm
         Motor                  Equivalent
         Te                     Load , Tlequ
                                                            Tlequ = Tl1 + a2Tl2

                         Jequ
                                                                  a2 = n1/n2
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Motor steady state torque-speed characteristic

 SPEED



                                Synchronous mch


                                                  Induction mch

                                                      Separately / shunt DC mch


                        Series DC




                                                                  TORQUE




   By using power electronic converters, the motor characteristic
   can be change at will
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Load steady state torque-speed characteristic
  Frictional torque (passive load)              • Exist in all motor-load drive
                      SPEED
                                 T~ C             system simultaneously
                         T~ ω2
                                                • In most cases, only one or two
                                     T~ ω         are dominating

                                                • Exists when there is motion

                                              TORQUE



                                             Coulomb friction
                                             Viscous friction

                                             Friction due to turbulent flow
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Load steady state torque-speed characteristic
  Constant torque, e.g. gravitational torque (active load)


              SPEED               Gravitational torque
                                                         Vehicle drive




                                                                               Te
                                        TORQUE

                                                             TL


                                                                     gM
                                                             α


                                                                          FL


                                                                  TL = rFL = r g M sin α
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Load steady state torque-speed characteristic
  Hoist drive

                            Speed




                                                         Torque

                                             Gravitational torque
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Load and motor steady state torque

  At constant speed, Te= Tl
  Steady state speed is at point of intersection between Te and Tl of the
  steady state torque characteristics

       Torque                                Te           Tl




                                                               Steady state
                                                               speed




                                  ωr3         ωr
                                              ωr1   ωr2          Speed
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Torque and speed profile

                 speed                                          Speed profile
                 (rad/s)
                 100




                             10      25          45        60             t (ms)




          The system is described by:           Te – Tload = J(dω/dt) + Bω

           J = 0.01 kg-m2,        B = 0.01 Nm/rads-1 and        Tload = 5 Nm.


           What is the torque profile (torque needed to be produced) ?
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Torque and speed profile


   speed
   (rad/s)

                                                                   dω
   100

                                                             Te = J + Bω + Tl
                                                                   dt

                 10         25       45       60           t (ms)



             0 < t <10 ms        Te = 0.01(0) + 0.01(0) + 5 Nm = 5 Nm

             10ms < t <25 ms     Te = 0.01(100/0.015) +0.01(-66.67 + 6666.67t) + 5
                                    = (71 + 66.67t) Nm

             25ms < t< 45ms      Te = 0.01(0) + 0.01(100) + 5 = 6 Nm

             45ms < t < 60ms     Te = 0.01(-100/0.015) + 0.01(400 -6666.67t) + 5
                                    = -57.67 – 66.67t
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Torque and speed profile
                speed
                (rad/s)
                 100
                                                        Speed profile




                           10    25           45   60         t (ms)
                Torque
                (Nm)

                 72.67
                                                         torque profile
                 71.67




                       6
                       5
                           10    25          45     60       t (ms)


                -60.67
                -61.67
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Torque and speed profile
          Torque
          (Nm)


           70                                     J = 0.001 kg-m2, B = 0.1 Nm/rads-1
                                                   and Tload = 5 Nm.


                6

                    10     25           45   60      t (ms)


            -65




         For the same system and with the motor torque profile
         given above, what would be the speed profile?
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Thermal considerations


   Unavoidable power losses causes temperature increase
           Insulation used in the windings are classified based on the
           temperature it can withstand.

   Motors must be operated within the allowable maximum temperature



   Sources of power losses (hence temperature increase):
   - Conductor heat losses (i2R)
   - Core losses – hysteresis and eddy current
   - Friction losses – bearings, brush windage
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Thermal considerations

       Electrical machines can be overloaded as long their temperature
       does not exceed the temperature limit

        Accurate prediction of temperature distribution in machines is
        complex – hetrogeneous materials, complex geometrical shapes

        Simplified assuming machine as homogeneous body

                                                         Ambient temperature, To



            p1                                             p2
                           Thermal capacity, C (Ws/oC)

     Input heat power
                           Surface A, (m2)               Emitted heat power
                           Surface temperature, T (oC)
         (losses)                                          (convection)
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Thermal considerations
    Power balance:
                                 dT
                             C      = p1 − p 2
                                 dt

     Heat transfer by convection:

                             p 2 = αA (T − To )             , where α is the coefficient of heat transfer

     Which gives:
                              d∆T Aα      p
                                  +   ∆T = 1
                               dt   C     C


     With ∆T(0) = 0 and p1 = ph = constant ,


                              ∆T =
                                      ph
                                      αA
                                          (
                                         1 − e −t / τ   )            , where τ =
                                                                                     C
                                                                                     αA
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Thermal considerations
                              ph
       ∆T                     αA                  ∆T =
                                                         ph
                                                         αA
                                                            (1 − e −t / τ )
                                                 Heating transient




                                             t
                  τ
          ∆T
                                                   ∆T = ∆T(0) ⋅ e − t / τ
  ∆T(0)
                                                 Cooling transient




                  τ                          t
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Thermal considerations

     The duration of overloading depends on the modes of operation:

      Continuous duty
       Load torque is constant over extended period multiple
                          Continuous duty
                          Short time intermittent duty
       Steady state temperature reached
                          Periodic intermittent duty
       Nominal output power chosen equals or exceeds continuous load
                                     p1n
                                             Losses due to continuous load
               ∆T                    αA

               p1n




                                                          t
                          τ
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Thermal considerations




      Short time intermittent duty
       Operation considerably less than time constant, τ
       Motor allowed to cool before next cycle
       Motor can be overloaded until maximum temperature reached
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Thermal considerations
      Short time intermittent duty                 p1s
        p1

                                             p1n




             ∆T                      p1s
                                     αA



                                     p1n
                                     αA
     ∆Tmax




                           τ                             t
                    t1
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Thermal considerations
                                                                     p1s p p1                         τ
         Short time intermittent duty                                    ≤ 1n ≥=p 1(s1 −1eτ e −t )/ τ )
                                                                         p             ( ≈t
                                                                                     − t 1 /−
                                                                                              − t1 / τ
                                                                                                         1


         ∆T                                                          p1n αA − αA
                                                                            1 e 1n   1s
                                                                                                        1




                                        ∆T =
                                               p1s
                                               αA
                                                   (1 − e −t / τ )
                                 p1n
                                 αA
 ∆Tmax




                       τ                                                    t
                 t1
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Thermal considerations




      Periodic intermittent duty

      Load cycles are repeated periodically

      Motors are not allowed to completely cooled

      Fluctuations in temperature until steady state temperature is reached
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Thermal considerations

      Periodic intermittent duty



          p1
                                                     heating   coolling
                                  heating coolling
               heating coolling




                                                                          t
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Thermal considerations

     Periodic intermittent duty

           Example of a simple case – p1 rectangular periodic pattern

                 pn = 100kW, nominal power
                 M = 800kg
                 η= 0.92, nominal efficiency
                 ∆T∞= 50oC, steady state temperature rise due to pn

                1                                   p1   9000
       p1 = p n  − 1 = 9kW
                η                   Also,   αA =       =      = 180 W / o C
                                                   ∆T∞    50

           If we assume motor is solid iron of specific heat cFE=0.48 kWs/kgoC,
           thermal capacity C is given by

           C = cFE M = 0.48 (800) = 384 kWs/oC

           Finally τ, thermal time constant = 384000/180 = 35 minutes
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Thermal considerations

     Periodic intermittent duty

           Example of a simple case – p1 rectangular periodic pattern

         For a duty cycle of 30% (period of 20 mins), heat losses of twice the nominal,

                   35


                   30


                   25


                   20


                   15


                   10


                   5


                   0
                        0     0.5    1       1.5   2     2.5
                                                                 4
                                                               x10
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Torque-speed quadrant of operation


                                             ω




                            2                      1
                            T -ve                T +ve
                            ω +ve                ω +ve
                            Pm -ve               Pm +ve


                                                          T




                            3                    4
                           T -ve                 T +ve
                           ω -ve                 ω -ve
                           Pm +ve                Pm -ve
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  4-quadrant operation


                                  ω                  Te
                                                               • Direction of positive (forward)
                                                                 speed is arbitrary chosen
             ωm                                 ωm
                      Te                                       • Direction of positive torque will
                                                                 produce positive (forward) speed




               Quadrant 2         Quadrant 1
               Forward braking    Forward motoring
                                                                   T
               Quadrant 3         Quadrant 4
               Reverse motoring   Reverse braking    Te
                       Te
                    ωm                                    ωm
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Ratings of converters and motors

                                              Torque

                               Transient               Power limit for
                               torque limit            transient torque

                               Continuous
                               torque limit                     Power limit for
                                                                continuous torque



                                                            Maximum
                                                            speed limit

                                                                          Speed
INTRODUCTION TO ELECTRIC DRIVES - MODULE 1


  Steady-state stability

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Electric drives

  • 1. ELECTRIC DRIVES INTRODUCTION TO ELECTRIC DRIVES MODULE 1 Dr. Nik Rumzi Nik Idris Dept. of Energy Conversion, UTM 2006
  • 2. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Electrical Drives Drives are systems employed for motion control Require prime movers Drives that employ electric motors as prime movers are known as Electrical Drives
  • 3. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Electrical Drives • 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) • MEP 1522 will be covering variable speed drives
  • 4. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Example on VSD application Constant speed Variable Speed Drives valve Supply motor pump Power Power out In Power loss Mainly in valve
  • 5. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Example on VSD application Constant speed Variable Speed Drives valve Supply Supply motor pump motor PEC pump Power Power out In Power Power out In Power loss Power loss Mainly in valve
  • 6. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Example on VSD application Constant speed Variable Speed Drives valve Supply Supply motor pump motor PEC pump Power Power out In Power Power out In Power loss Power loss Mainly in valve
  • 7. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Conventional electric drives (variable speed) • Bulky • Inefficient • inflexible
  • 8. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Modern electric drives (With power electronic converters) • Small • Efficient • Flexible
  • 9. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Modern electric drives Machine design Utility interface Speed sensorless Renewable energy Machine Theory Non-linear control Real-time control DSP application PFC Speed sensorless Power electronic converters • Inter-disciplinary • Several research area • Expanding
  • 10. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Components in electric drives e.g. Single drive - sensorless vector control from Hitachi
  • 11. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Components in electric drives e.g. Multidrives system from ABB
  • 12. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Components in electric drives Motors • DC motors - permanent magnet – wound field • AC motors – induction, synchronous (IPMSM, SMPSM), brushless DC • Applications, cost, environment Power sources • DC – batteries, fuel cell, photovoltaic - unregulated • AC – Single- three- phase utility, wind generator - unregulated Power processor • To provide a regulated power supply • Combination of power electronic converters •More efficient •Flexible •Compact •AC-DC DC-DC DC-AC AC-AC
  • 13. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Components in electric drives Control unit • Complexity depends on performance requirement • analog- noisy, inflexible, ideally has infinite bandwidth. • digital – immune to noise, configurable, bandwidth is smaller than the analog controller’s • DSP/microprocessor – flexible, lower bandwidth - DSPs perform faster operation than microprocessors (multiplication in single cycle), can perform complex estimations
  • 14. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Overview of AC and DC drives Extracted from Boldea & Nasar
  • 15. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Overview of AC and DC drives DC motors: Regular maintenance, heavy, expensive, speed limit Easy control, decouple control of torque and flux AC motors: Less maintenance, light, less expensive, high speed Coupling between torque and flux – variable spatial angle between rotor and stator flux
  • 16. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 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 (1950s) • 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
  • 17. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 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
  • 18. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Classification of IM drives (Buja, Kamierkowski, “Direct torque control of PWM inverter-fed AC motors - a survey”, IEEE Transactions on Industrial Electronics, 2004.
  • 19. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Elementary principles of mechanics v x Newton’s law Fm d( Mv ) M Fm − Ff = Ff dt Linear motion, constant M d( v ) d2 x Fm − Ff = M = M 2 = Ma dt dt • First order differential equation for speed • Second order differential equation for displacement
  • 20. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Elementary principles of mechanics θ Rotational motion - Normally is the case for electrical drives Tl d( Jωm ) Te − Tl = Te , ω m dt J With constant J, d( ωm ) d2θ Te − Tl = J =J 2 dt dt • First order differential equation for angular frequency (or velocity) • Second order differential equation for angle (or position)
  • 21. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Elementary principles of mechanics For constant J, dωm Te = Tl + J dt d( ωm ) J Torque dynamic – present during speed transient dt d( ωm ) Angular acceleration (speed) dt The larger the net torque, the faster the acceleration is. 200 100 speed (rad/s) 0 -100 -200 0.19 0.2 0.21 0.22 0.23 0.24 0.25 20 15 torque (Nm) 10 5 0 0.19 0.2 0.21 0.22 0.23 0.24 0.25
  • 22. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Elementary principles of mechanics Combination of rotational and translational motions Fl Fe Te, ω ω r M r Tl v d( v ) Fe − Fl = M Te = r(Fe), Tl = r(Fl), v =rω dt dω Te − Tl = r 2M dt r2M - Equivalent moment inertia of the linearly moving mass
  • 23. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Elementary principles of mechanics – effect of gearing Motors designed for high speed are smaller in size and volume Low speed applications use gear to utilize high speed motors ωm ωm1 Motor Load 1, n1 Te Tl1 J2 ωm2 n2 Load 2, J1 Tl2
  • 24. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Elementary principles of mechanics – effect of gearing ωm ωm1 Motor Load 1, n1 Te Tl1 J2 ωm2 n2 Load 2, J1 Tl2 J equ = J1 + a 2 J 2 2 ωm Motor Equivalent Te Load , Tlequ Tlequ = Tl1 + a2Tl2 Jequ a2 = n1/n2
  • 25. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Motor steady state torque-speed characteristic SPEED Synchronous mch Induction mch Separately / shunt DC mch Series DC TORQUE By using power electronic converters, the motor characteristic can be change at will
  • 26. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Load steady state torque-speed characteristic Frictional torque (passive load) • Exist in all motor-load drive SPEED T~ C system simultaneously T~ ω2 • In most cases, only one or two T~ ω are dominating • Exists when there is motion TORQUE Coulomb friction Viscous friction Friction due to turbulent flow
  • 27. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Load steady state torque-speed characteristic Constant torque, e.g. gravitational torque (active load) SPEED Gravitational torque Vehicle drive Te TORQUE TL gM α FL TL = rFL = r g M sin α
  • 28. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Load steady state torque-speed characteristic Hoist drive Speed Torque Gravitational torque
  • 29. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Load and motor steady state torque At constant speed, Te= Tl Steady state speed is at point of intersection between Te and Tl of the steady state torque characteristics Torque Te Tl Steady state speed ωr3 ωr ωr1 ωr2 Speed
  • 30. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Torque and speed profile speed Speed profile (rad/s) 100 10 25 45 60 t (ms) The system is described by: Te – Tload = J(dω/dt) + Bω J = 0.01 kg-m2, B = 0.01 Nm/rads-1 and Tload = 5 Nm. What is the torque profile (torque needed to be produced) ?
  • 31. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Torque and speed profile speed (rad/s) dω 100 Te = J + Bω + Tl dt 10 25 45 60 t (ms) 0 < t <10 ms Te = 0.01(0) + 0.01(0) + 5 Nm = 5 Nm 10ms < t <25 ms Te = 0.01(100/0.015) +0.01(-66.67 + 6666.67t) + 5 = (71 + 66.67t) Nm 25ms < t< 45ms Te = 0.01(0) + 0.01(100) + 5 = 6 Nm 45ms < t < 60ms Te = 0.01(-100/0.015) + 0.01(400 -6666.67t) + 5 = -57.67 – 66.67t
  • 32. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Torque and speed profile speed (rad/s) 100 Speed profile 10 25 45 60 t (ms) Torque (Nm) 72.67 torque profile 71.67 6 5 10 25 45 60 t (ms) -60.67 -61.67
  • 33. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Torque and speed profile Torque (Nm) 70 J = 0.001 kg-m2, B = 0.1 Nm/rads-1 and Tload = 5 Nm. 6 10 25 45 60 t (ms) -65 For the same system and with the motor torque profile given above, what would be the speed profile?
  • 34. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Thermal considerations Unavoidable power losses causes temperature increase Insulation used in the windings are classified based on the temperature it can withstand. Motors must be operated within the allowable maximum temperature Sources of power losses (hence temperature increase): - Conductor heat losses (i2R) - Core losses – hysteresis and eddy current - Friction losses – bearings, brush windage
  • 35. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Thermal considerations Electrical machines can be overloaded as long their temperature does not exceed the temperature limit Accurate prediction of temperature distribution in machines is complex – hetrogeneous materials, complex geometrical shapes Simplified assuming machine as homogeneous body Ambient temperature, To p1 p2 Thermal capacity, C (Ws/oC) Input heat power Surface A, (m2) Emitted heat power Surface temperature, T (oC) (losses) (convection)
  • 36. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Thermal considerations Power balance: dT C = p1 − p 2 dt Heat transfer by convection: p 2 = αA (T − To ) , where α is the coefficient of heat transfer Which gives: d∆T Aα p + ∆T = 1 dt C C With ∆T(0) = 0 and p1 = ph = constant , ∆T = ph αA ( 1 − e −t / τ ) , where τ = C αA
  • 37. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Thermal considerations ph ∆T αA ∆T = ph αA (1 − e −t / τ ) Heating transient t τ ∆T ∆T = ∆T(0) ⋅ e − t / τ ∆T(0) Cooling transient τ t
  • 38. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Thermal considerations The duration of overloading depends on the modes of operation: Continuous duty Load torque is constant over extended period multiple Continuous duty Short time intermittent duty Steady state temperature reached Periodic intermittent duty Nominal output power chosen equals or exceeds continuous load p1n Losses due to continuous load ∆T αA p1n t τ
  • 39. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Thermal considerations Short time intermittent duty Operation considerably less than time constant, τ Motor allowed to cool before next cycle Motor can be overloaded until maximum temperature reached
  • 40. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Thermal considerations Short time intermittent duty p1s p1 p1n ∆T p1s αA p1n αA ∆Tmax τ t t1
  • 41. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Thermal considerations p1s p p1 τ Short time intermittent duty ≤ 1n ≥=p 1(s1 −1eτ e −t )/ τ ) p ( ≈t − t 1 /− − t1 / τ 1 ∆T p1n αA − αA 1 e 1n 1s 1 ∆T = p1s αA (1 − e −t / τ ) p1n αA ∆Tmax τ t t1
  • 42. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Thermal considerations Periodic intermittent duty Load cycles are repeated periodically Motors are not allowed to completely cooled Fluctuations in temperature until steady state temperature is reached
  • 43. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Thermal considerations Periodic intermittent duty p1 heating coolling heating coolling heating coolling t
  • 44. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Thermal considerations Periodic intermittent duty Example of a simple case – p1 rectangular periodic pattern pn = 100kW, nominal power M = 800kg η= 0.92, nominal efficiency ∆T∞= 50oC, steady state temperature rise due to pn 1  p1 9000 p1 = p n  − 1 = 9kW η  Also, αA = = = 180 W / o C   ∆T∞ 50 If we assume motor is solid iron of specific heat cFE=0.48 kWs/kgoC, thermal capacity C is given by C = cFE M = 0.48 (800) = 384 kWs/oC Finally τ, thermal time constant = 384000/180 = 35 minutes
  • 45. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Thermal considerations Periodic intermittent duty Example of a simple case – p1 rectangular periodic pattern For a duty cycle of 30% (period of 20 mins), heat losses of twice the nominal, 35 30 25 20 15 10 5 0 0 0.5 1 1.5 2 2.5 4 x10
  • 46. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Torque-speed quadrant of operation ω 2 1 T -ve T +ve ω +ve ω +ve Pm -ve Pm +ve T 3 4 T -ve T +ve ω -ve ω -ve Pm +ve Pm -ve
  • 47. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 4-quadrant operation ω Te • Direction of positive (forward) speed is arbitrary chosen ωm ωm Te • Direction of positive torque will produce positive (forward) speed Quadrant 2 Quadrant 1 Forward braking Forward motoring T Quadrant 3 Quadrant 4 Reverse motoring Reverse braking Te Te ωm ωm
  • 48. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Ratings of converters and motors Torque Transient Power limit for torque limit transient torque Continuous torque limit Power limit for continuous torque Maximum speed limit Speed
  • 49. INTRODUCTION TO ELECTRIC DRIVES - MODULE 1 Steady-state stability