Brushless DC Operation of the CSI-driven trolling the amplitude of the rotor field (field control), or

34.4.5 Brushless DC Operation of the CSI-driven trolling the amplitude of the rotor field (field control), or

more conveniently, by controlling the amplitude of the stator The torque characteristic of the CSI drive scheme of the fore- phase current. The highest torque per ampere characteristic is

Motor

going section can be easily analyzed using the phasor diagrams achieved when γ =0 ◦ . Note that the operation with a fixed γ shown earlier, if the harmonics in the motor current waveform angle is key to this dc-motor-like torque characteristic. are neglected or if the motor current waveforms are indeed sinusoidal as in the second scheme described earlier. In the

34.4.5.1 Operation with Field Weakening

following analysis, it is assumed that the supply current wave- If the stator impedance drop is neglected, the maximum E f forms are sinusoidal. It is also assumed that the phase angle is largely determined by the dc-link voltage and E f =Kλ f ω of these current sources with respect to the induced voltage in implies that speed ω can be increased by decreasing λ f . Con- each phase can be arbitrarily chosen.

sequently, the operation above base speed is normally achieved The phase back-emf and the current waveforms and the with field weakening. In this speed range, because of the

phasor diagram of the nonsalient-pole motor are shown in limited dc-link voltage, the rotor field must be weakened; oth- Fig. 34.37. The phase angle γ between the E f and I phasors and erwise, the amplitude of the phase-induced emf will exceed the the RMS value (or amplitude) of I are determined according dc-link voltage and current control will not be effective. Field to the desired torque and power factor considerations. The weakening is a means of keeping this voltage at the rated level developed torque is found from the phasor diagram to be

for speeds higher than the base speed. The flux linkage due to the rotor excitation, λ f , can be

3E f I cos γ T =

(34.65) adjusted when a variable rotor supply is available. This may ω r

= K φI cos γ Nm

also be achieved by demagnetizing the rotor mmf by using

940 M. F. Rahman et al.

l f d-axis

(a)

(b)

FIGURE 34.37 Phasor relationships of CSI-driven motor: (a) back-emf and current waveforms and (b) the phasor diagram.

q-axis

phasors of the motor results in a poor overall power factor. Operation of the synchronous motor with a CSI which deliv- ers the stator current waveforms with phase angle with respect

E f to the respective phase back-emf waveforms that allows inter-

I esting power factor compensation possibilities. Consider the

following three cases.

l f 34.4.6.1 Case 1: Operation with I Lagging E f

d-axis

In this case, the motor is under-excited and I lags E f , by an

I d angle γ, as indicated in Fig. 34.39. The overall power factor in FIGURE 34.38 Field weakening using stator mmf.

this case is lagging, since I lags V by an angle θ. The power- factor angle θ is larger than γ. Note that I d now magnetizes

the rotor field.

the mmf produced by the stator currents. For motors with permanent-magnet excitation, the latter is the only means

of weakening the λ f . Referring to the phasor diagram of

34.4.6.2 Case 2: I is in phase with E f ; Maximum Fig. 34.38, if I is made to lead E ◦ f , the d-axis component of Torque per Ampere Operation (γ = 0 )

I , i.e. I d , will lead E f by 90 ◦ . The mmf due to I d then opposes If γ =0 ◦ is used, the motor input current i a is in phase with the rotor d-axis mmf. The net rotor flux linkage along the the back-emf e a , as indicated in the waveforms of Fig. 34.40a. q-axis is then given by

From Eq. (34.65), the developed torque is given by

λ ′ f =λ f +L d I d (34.66)

T = K φI

where I d is negative when I leads E f . If the airgap is small,

the d-axis component of the armature current may reduce the Thus, for a fixed rotor excitation, the developed torque is rotor flux to the required extent.

the highest that can be achieved per ampere of stator current

I . In other words, if γ =0 ◦ is chosen, the drive operates with