4 Chopper-Controlled DC Motor Drive

Transcription

1 4 Chopper-Controlled DC Motor Drive Chopper: The vrible dc voltge is controlled by vrying the on- nd off-times of converter. Fig. 4.1 is schemtic digrm of the chopper.

2 Its frequency of opertion is f 1 + t c = = (ton off ) 1 T nd its duty cycle is defined s d = t T on Assuming tht the switch is idel, the verge output is t V on dc = Vs = T dv s vrying the duty cycle chnges the output voltge.

3 The duty cycle d cn be chnged in two wys: (i) vrying the on-time (constnt switching frequency). (ii) vrying the chopping frequency. Constnt switching frequency hs mny dvntges in prctice.

4 4.3 Four-Qudrnt Chopper Circuit Fig. 4.2 is the chopper circuit with trnsistor switches.

5 Fig. 4.3 is first-qudrnt opertion.

6 Fig. 4.4 is first-qudrnt opertion with zero voltge cross the lod.

7 Fig. 4.5 voltge nd current wveforms in first-qudrnt opertion.

8 Fig. 4.6 second-qudrnt opertion

9 Fig. 4.7 voltge nd current wveforms in second-qudrnt opertion.

10 Fig. 4.8 Modes of opertion in the third qudrnt.

11 Fig. 4.9 wveform in third-qudrnt opertion

12 Fig Wveforms in fourth-qudrnt opertion.

13 4.4 Chopper for inversion Converter: DC DC (different voltge) The chopper is the building block for tht: AC DC DC(different voltge)

14 4.5 Chopper with other power devices MOSFETs, IGBTs, GTOs, or SCRs re used for different power level. The MOSFET nd trnsistor choppers re used t power levels up to 50kW.

15 4.6 Model of The Chopper The trnsfer function of the chopper is G r K (s) = r st 1+ 2 where K r = V s /V cm, V s is the source voltge, nd V cm is the mximum control voltge. Incresing the chopping frequency decreses the dely time, nd its becomes simple gin.

16 4.7 Input to the chopper The chopper input: bttery or rectified c supply. Fig is the chopper with rectified circuit.

17 Its disdvntge: it cnnot trnsfer power from dc link into c mins. Fig Chopper with regenertion cpbility

18 The generting converter hs to be operted t triggering ngles greter tht 90.

19 4.8 Other Chopper Circuits Fig one- nd two-qudrnt opertion.

20 4.9 Stedy-stte nlysis Anlysis by verging The verge rmture current is I v Vdc E = R where V dc = dv s The electromgnetic torque is T v = K b I v = K b (dv s -K b w m )/R (N m)

21 The normlized torque is T en = T T v b / V / V b b = K b (dv K s b K I R b b ωm ) / / V b V b = dvn ω R n mn, p.u. I R where R b n =, p.u. V s V n =, p.u. ω m mn =, p.u. b Vb ωb Instntneous stedy-stte computtion (including hrmonics) The equtions of the motor for on nd off times (continuous current conduction) di V E R i L s = + + dt di 0 = E + R i L +, dt, 0 dt t t V dt T ω

22 Fig The wveform of pplied voltge nd rmture current.

23 The solutions of the bove equtions: t V E i (t) s T (1 e T ) I e = + 0, 0 < t < R i (t) = E R (1 e 1 t T ) + I 1 e where T = L /R (Armture time constnt) t 1 = t - dt By using boundry condition I 1 = V (1 e s R (1 e dt / T T / T ) ) E R 1 t T t, I dt 0 = t V (e s R dt dt (e dt / T T / T 1) 1) E R

24 The criticl duty cycle: the limiting or minimum vlue of duty cycle for continuous current; I 0 equtes to zero. The relevnt equtions for discontinuous current-conduction mode V s = E + R i + L di dt di 0 = E + R i L +, dt t tx dt with i (t x + dt) = 0; i (0) = 0, 0 t + dt dt

25 Hence, i I 1 (t x = Vs R + dt) = E (1 e E R dt / (1 e T t T x ) ) + tx is evluted from (4.25) nd the bove eqs. s tx = T loge[1 + I 1 R E ] I 1 e t T x

26 The solution for the rmture current in three time segments is V E i (t) s (1 e = ), 0 < t < R i (t) = I 1 e (t dt) T t T E R (1 e dt (t dt) T i (t) = 0, (tx + dt) < t < ), T dt t t x - dt

27 4.10 Rting of the device The rms vlue of the power switch current I t = 2 mx I 2T (T + dt) = 1+ d 2 mx The verge diode current I 1 d = ( ) 2 d I mx I

28 Trnsistor nd diode currents for motoring opertion in the continuous-conduction mode.

29 4.11 Pulsting Torque The verge of the hrmonic torque is zero. High-performnce pplictions require the pulsting torque to be minimum. The pplied voltge is resolved into Fourier components s V where = V + n=1 A sin(nω (t) n c t n ) dt V = Vs = dv T A n 2V = s nπ s nω dt sin c 2 ω θ c n 2π = 2πf c = T π nωcdt = θ

30 The rmture current is expressed s i (t) = Iv + n = where I v φ n 1 A Z n n sin(nω c t + θ n φ = V E Zn = R + jnωcl R = cos 1 { R 2 R + n 2 ω 2 c L 2 } n ) The input power is P i = V V I = + V (t)i v + I (t) v n = 1 sin(nω t + θ An = ω + θ φ + n 1 sin(n ct n n) n = Z n A n c n ) 1 A ( Z 2 n n sin(nω c t + θ n )sin(nω c t + θ n φ n ))

31 4.12 Closed-loop opertion Fig is the closed-loop speed-controller dc motor drive.

32 The current controller cn be (i) Pulse-Width-Modultion (PWM) controller (ii) Hysteresis controller Fig shows on- nd off-time for PWM

33 Fig is the implementtion of PWM current controller.

34 Fig shows hysteresis-controlled opertion * i i i, set v = * V i i + i, reset v = s 0

35 Fig. 4.23

36 Fig is reliztion of hysteresis controller.