Modeling and simulation of pmsm
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The document discusses Permanent Magnet Synchronous Motors (PMSM) utilizing Direct Torque Control (DTC) for efficient torque management in servo applications, highlighting its faster response compared to traditional methods. It details the mathematical modeling of PMSM, various control strategies, and the performance advantages of DTC, especially under varying load conditions and parameters. Additionally, it presents simulation results demonstrating the effectiveness of DTC in achieving smooth and rapid torque and speed responses.
![Different switching states & corresponding space
vectors.
Switching state
[a b c]
Space Vector Vs
Rectangular form Polar form
V0 = [0 0 0] Vdc (0 + j0) 0 0
V1 = [1 0 0] Vdc (1 + j0) Vs 0
V2 = [1 1 0] Vdc (0.5 + j ) Vs 60
V3 = [0 1 0] Vdc (-0.5 + j ) Vs 120
V4 = [0 1 1] Vdc (-1 + j0) Vs 180
V5 = [0 0 1] Vdc (-0.5 – j ) Vs 240](https://image.slidesharecdn.com/modelingandsimulationofpmsn-130630024439-phpapp01/85/Modeling-and-simulation-of-pmsm-27-320.jpg)
Modeling and simulation of pmsm
- 1. Guide : Mr. M. SRINIVASA RAO ASSO. PROFFESOR
- 2. Abstract » The use of Permanent Magnet Synchronous Motors (PMSM) combined with Direct Torque Control (DTC) scheme offers many opportunities to achieve rapid and accurate torque control in servo applications. » The DTC is implemented by selecting the proper voltage vector according to the switching status of inverter which was determined by the error signals of reference flux linkage and torque with their measured real values. » Here, model of Interior type of PMSM is studied. Its performance for various motor parameters is tested on MATLAB-SIMULINK.
- 3. » DTC was proposed by TAKAHASHI and NOGUCHI in 1986 for application in Induction Motors. Their idea was to control the stator flux linkage and the torque directly, not via controlling the stator current. » This was accomplished by “ OPTIMUM SWITCHING TABLE”. » M. F. RAH MAN investigation of direct torque control (DTC) for PMSM drives. » It was mathematically proven that the increase of electromagnetic torque in a PMSM is proportional to load angle. Literature Review
- 4. » Control of the amplitude and rotating speed of the stator flux linkage are analyzed. » Torque response with DTC was found to be 7 times faster than with PWM current control. » JAWAD FAIZ introduced a new analytical technique for generating the reference flux from the torque. It is shown how the maximum torque per ampere (MTPA) can be followed in the control process. » Salient-pole PMSM motor is simulated using the maximum torque per flux (MTPF) and the reference flux determined.
- 5. » In Permanent magnet synchronous motors the rotor winding are replaced by permanent magnets. » A permanent magnet synchronous machine is basically ordinary AC machine with winding distributed in the stator slots so that the flux created by stator current is approximately sinusoidal. » Permanent magnet drives are replacing classic DC and induction machine drives in a variety of industrial applications such as industrial robots and machine tools. Introduction to PMSM
- 6. » Two types of permanent magnet ac motor drives are available : 1) PMSM drive with a sinusoidal flux distribution. 2) Brushless dc motor drive with a trapezoidal flux distribution. Xq>Xd There are two major topologies of rotors of PMSMs
- 7. » The modeling of PM motor drive system is required for proper simulation of the system. » The d-q model has been developed on rotor reference frame as shown in figure: δ Modelling of PMSM
- 8. Stator and Rotor flux linkages in different frames » The model of PMSM without damper winding has been developed on rotor reference frame using the following assumptions: » Saturation is neglected. » The induced EMF is sinusoidal » Eddy currents and hysteresis losses are negligible. » There are no field current dynamics.
- 9. » The angle between the stator and rotor flux linkage δ is the load angle when the stator resistance is neglected. » In the steady state, δ is constant corresponding to a load torque and both stator and rotor flux rotate at synchronous speed » In transient operation δ varies and the stator and rotor flux rotate at different speeds. » Since the electrical time constant is normally much smaller than the mechanical time constant, the rotating speed of the stator flux with respect to the rotor flux can be easily changed
- 10. » Voltage equations in rotor reference frame are given by » The flux Linkages are given by » Substituting the flux linkages in the above voltage equations » Arranging above equations in matrix form qdrqqq iRV Motor Equations dqrddd iRV qqq iL fmddd LiL qqfddrqsq iLiLiRV )( )( fddqqrdsd iLiLiRV f fr d q dsqr drqs d q i i LRL LLR V V
- 11. » The developed motor torque is being given by » Substitution of the flux linkages in terms of the inductances and current yields » The mechanical torque equation is » The rotor mechanical speed is given by » id and iq in terms of Im » The electromagnetic torque equation is given by dqqde ii p T 22 3 dqqdqfe iiLLiPT )( 2 3 dt d JBTT m mLe dt J BTT mLe m cos sin m d q I i i sinI2sinILL 2 1 2 p 2 3 T mf 2 mqde
- 12. » V/F control is among the simplest control. The control is an open-loop and does not use any feedback loops. » The idea is to keep stator flux constant at rated value so that the motor develops rated torque/ampere ratio over its entire speed range. CONTROL SCHEMES FOR PMSM Variable Frequency Control Vector Control FOC DTC Scalar Control V/F Control
- 13. Field Oriented Control Vector Control Direct Torque Control DTC vs FOC
- 14. There are 3 signals which affect the control action in a DTC system; » Torque – » The amplitude of the Stator Flux linkage – » The angle of the resultant flux linkage vector – (angle between stator flux vector and rotor flux vector)
- 16. » The stator flux linkage of PMSM is » Neglecting the stator resistance, the stator flux linkage can be directly defined as dtRiV sss )( 0 stsss dtiRtV 0 stss tV Amplitude Control of Stator Flux Linkage (Ψs)
- 17. 0 stss tV 0 stss tV HB- hysteresis-band width
- 18. HB- hysteresis-band width 0 stss tV
- 19. Flux and torque variations Due to Applied Voltage vector
- 20. » For counter-clockwise operation, » if the actual torque is smaller than the reference, the voltage vector that keeps Ψs rotation in the same direction is selected. » Once the actual torque is greater than the reference, the voltage vectors that keep Ψs rotation in the reverse direction are selected » By selecting the voltage vectors in this way, the stator flux linkage is rotated all the time and its rotational direction is determined by the output of the hysteresis controller for the torque. The control of the rotation of stator flux linkage
- 21. If the actual flux linkage is smaller than the reference flux value then Ø = 1. The same is true for the torque. Working principle of Direct Torque Control for PMSM
- 22. » When an upper transistor is switched on, i.e., when a, b or c is “1”, the corresponding lower transistor is switched off, i.e., the corresponding a’, b’ and c’ will be “0”. VOLTAGE SOURCE INVERTER
- 23. switching voltage vectors STATE Sa Sb Sc V0 OFF OFF OFF V1 ON OFF OFF V2 ON ON OFF V3 OFF ON OFF V4 OFF ON ON V5 OFF OFF ON V6 ON OFF ON V7 ON ON ON
- 24. » There are eight possible combinations of on and off patterns for the upper power switches and lower power devices. » STATE 1: ( 000 ) STATE 2: ( 100 ) » STATE 3: ( 110 ) STATE 4: ( 010 ) 0,0,0 00 coba VVV 0V,VV,VV codc0bdc0a 0V,0V,VV co0bdc0a 0,,0 00 codcba VVVV
- 25. dccodc0b0a VV,VV,0V dcco0b0a VV,0V,0V dcco0bdc0a VV,0V,VV dccodc0bdc0a VV,VV,VV » STATE 5: ( 011 ) STATE 6: ( 001 ) » STATE 7: ( 101 ) STATE 8: ( 111 )
- 26. Vao = Vdc ; Vbo = Vdc ; Vco = 0 The space vector is Vs = Vao + Vbo ej2/3 + Vco e-j2/3 Substituting the values of Vao, Vbo and Vco: Vs = Vdc(1/2 + j 3/2) (in rectangular form) = Vdc 600 (in polar form) Similarly the switching vectors can be computed for the rest of the inverter switching states. Computation of Switching vectors For state-2 (+ + -):
- 27. Different switching states & corresponding space vectors. Switching state [a b c] Space Vector Vs Rectangular form Polar form V0 = [0 0 0] Vdc (0 + j0) 0 0 V1 = [1 0 0] Vdc (1 + j0) Vs 0 V2 = [1 1 0] Vdc (0.5 + j ) Vs 60 V3 = [0 1 0] Vdc (-0.5 + j ) Vs 120 V4 = [0 1 1] Vdc (-1 + j0) Vs 180 V5 = [0 0 1] Vdc (-0.5 – j ) Vs 240
- 28. cn bn an q d v v v V V 2 3 2 3 0 2 1 2 1 1 3 2 22 qdref vvV ftt v v d q 2tan 1 » To implement the Space Vector PWM, the voltage equations in the abc reference frame can be transformed into the stationary d-q reference frame that consists of the horizontal (d) and vertical (q) axis.
- 29. » The three-phase variables are transformed into d-q axes variables with the following transformation dtirv dsdd )( dtirv qsqq )( )( 22 qds )( 2 3 dqqde iipT Flux and Torque Estimator
- 30. Trajectory of stator flux vector in DTC control Inverter voltage vectors and corresponding stator flux variation in time Δt It receives the input signals Ф, τ θ and generates the appropriate control voltage vector (switching states Sa, Sb, Sc) for the inverter Switching Table
- 31. Switching table of inverter voltage vectors
- 32. Basic block diagram of DTC for PMSM
- 33. Digital outputs of the flux and torque controller have following logic: FEATURES, ADVANTAGES AND DISADVANTAGES OF DTC :
- 34. Simulink Block of the DTC for PMSM
- 35. Simulink Block of the DTC for PMSM
- 36. 1. Simulink model of the controller 2. Sub block of the direct torque control switching.
- 37. 1. 2. Study of effect of magnet strength and change in M.I on PMSM under no load and full load Electromagnetic torque (1) and speed (2) for Ipm = 1.4 A under noload:
- 38. 1. 2. Electromagnetic torque (1) and speed (2) for Ipm = 1.4 A under full load:
- 39. 1. 2. Electromagnetic torque (1) and speed (2) for Ipm = 1.8 A under noload:
- 40. 1. 2. Electromagnetic torque (1) and speed (2) for Ipm = 1.8 A under fullload:
- 41. 1. 2. Electromagnetic torque (1) and speed (2) for M.I = 0.03 under noload:
- 42. 1. 2. Electromagnetic torque (1) and speed (2) for M.I = 0.03 under fullload:
- 43. 1. 2. Electromagnetic torque (1) and speed (2) for M.I = 0.09 under noload:
- 44. 1. 2. Electromagnetic torque (1) and speed (2) for M.I = 0.09 under fullload:
- 45. Torques produced in the PMSM Excitation torque with varying the Ipm values
- 46. Induction torque with varying the Ipm values Reluctance torque with varying the Ipm values
- 47. Study of effect of Ipm, change in M.I on PMSM with DTC for torques
- 48. » DTC strategy realizes almost ripple-free operation for the electromagnetic torque and speed under no-load as well as full-load for different values of Ipm and M.I. » When magnetic strength value (Ipm) increases from 1.4 to 2.2, excitation torque and reluctance torque are increased and induction torque remains unchanged. » With the increase in moment of Inertia the response time of drive without DTC is more, and with DTC, the drive has smooth synchronization process. » The simulation results verify the proposed control and also shown that the transient response of torque and speed of drive with DTC is much faster than the drive without DTC Results and Conclusions