Operating Modes its maximum torque per ampere characteristic. From the pha-

34.4.6 Operating Modes its maximum torque per ampere characteristic. From the pha-

sor diagram of Fig. 34.40b, it is clear that the input current I

A synchronous motor may be driven with a view to achieving phasor now lags the voltage V phasor at the motor terminals. various operating characteristics, such as power factor com- (see the phasor diagram in the figure). Note that the level of pensation, maximum torque per ampere characteristic, and E f ,which is determined by the level of excitation, also deter- field weakening. The power factor at which a synchronous mines the angle θ to some extent. Clearly, when maximum motor operates is an important issue, especially for a large torque per ampere characteristic is required, a power factor drive. A large angle θ between the input voltage and current less than unity has to be accepted.

34 Motor Drives 941

FIGURE 34.39 (a) Phase back-emf and current waveforms and (b) the phasor diagram with I lagging E f .

l f d-axis

FIGURE 34.40 (a) Phase back-emf and current waveforms and (b) phasor diagram for I in phase with E f .

34.4.6.3 Case 3: Operation with I Leading E f 34.4.7 Vector Controls

If I is chosen to lead E f , the overall power factor can be The foregoing controls were based on the steady-state equiva- higher, including unity, as is indicated in Fig. 34.41. Note that lent circuit of the motor. Even though the torque Eq. (34.65) the motor now operates with less than maximum torque per for a current-source drive evokes vector-control-like relation- ampere characteristic. Note also that the d-axis component of ships, they do not address the dynamics of the current controls

I now tends to demagnetize the rotor and that the operation as is possible in an orthogonal reference frame. Using an with field weakening is implied.

orthogonal set of reference attached to the rotor, a simple With a CSI-driven motor, the amplitude and the angle of set of decoupled, dc-motor-like torque control relationships

the phase current relative to the back-emf can be selected is readily obtained. Following the transformation technique according to one of the desirable operating characteristics used in Section 34.3.4, the stator voltage equations of a mentioned above. Additionally, other operational limits such synchronous motor with fixed rotor excitation in the rotor as the inverter/motor current limit, the maximum stator volt- reference frame are age limit, and the maximum power limit can also be addressed. The amplitude of the stator current I clearly determines the

R + pL q ω L d q

developed torque of the motor. Consequently, the error of

d 0 the speed controller is used to determine the amplitude of

d −ωL q R + pL d i

T = P f i q + (L d −L q )i d i q (34.69) described by Fig. 34.42.

I . The overall control system with an inner torque loop can be

942 M. F. Rahman et al.

I leading

FIGURE 34.41 Back-emf and current waveforms and phasor diagram for I leading E f .

i aref +

FIGURE 34.42 Structure of a speed-control system with a CSI-driven synchronous motor.

where all the quantities in lower case represent instantaneous case, the inner torque loop consist of two separate current quantities in the rotor dq-frame. The λ f is the flux linkage per loops; one for i d and the other for i q , as indicated in Fig. 34.43. phase due to the rotor excitation, ω is the electrical angular The i q current loop generally derives its reference signal from velocity in rad/sec, and P is the number of pole pairs. Here, the output of the speed controller and constitutes the inner

p is the time derivative operator d/dt. Assuming the magnetic torque loop. The reference for the i d current loop is normally linearity, the stator flux linkages are

specified by the extent of field weakening for which a neg- ative i d reference is used. Otherwise, the d −axis current is λ d =L d i d +λ f maintained at zero. Note that for large synchronous motors (34.70) with variable external excitation, field weakening is normally

λ q =L q i q applied through adjustment of the rotor excitation, using a spillover signal from the output of the speed controller.

Note that the Eq. (34.68) can be written down directly from From Eq. (34.68), it is clear that the couplings of q- and Eq. (34.31), taking into account the fixed rotor excitation so d-axes voltages exist through the d- and q-axes currents, that the third and fourth rows and columns of Eq. (34.31) may respectively, and the back-emf. During dynamic operation,

be dropped. Since the reference frame now rotates at the speed such coupling effects become undesirable. The coupling effects of the rotor, ω e = ω. The induced back-emf due to the fixed of d- and q-axes currents and the back-emf into q- and d-axes rotor excitation occurs in the rotor q-axis and is included in voltages, respectively, can be removed by the feedforward terms Eq. (34.68), as a separate term. Similarly, the torque expression shown in the shaded part of the block the diagram of Fig. 34.44 of Eq. (34.69) may also be written down from Eq. (34.41), which also shows the two current-control loops. The two out- using the flux linkages of Eq. (34.70).

puts v ∗ d and v q ∗ from the decoupled current controllers are Equations (34.67)–(34.69) are for a salient-pole motor for transformed to the stator reference frame before being sub- which L d q . For a nonsalient-pole motor, L d is equal to L q jected to pulse-width modulators or hysteresis comparators. and the developed torque is proportional to i q only. In either Note that the current references i ∗ d and i q ∗ are obtained with

34 Motor Drives 943

q-axis current

d -axis

FIGURE 34.43 Inner torque loop of a vector-controlled synchronous motor drive.

d-axis current controller the rotor. In fact, they are dc quantities when the motor runs

v d at a constant speed. Consequently, the following error (or lag) −

g d (t)

associated with tracking a sinusoidally time varying current

reference, which is the case when current control is exercised i d

wl f + wL i

in the stator a–b–c reference frame, can be reduced easily by

w using an integral-type current controllers.

−wL q i q

g q (t)

34.5 Permanent-magnet AC

q-axis current controller

Synchronous Motor Drives

FIGURE 34.44 The d- and q-axis decoupling compensation.