0195136047.pdf

556 ROTATING MACHINES

Synchronous speed=

120 f

P

r/min (13.1.2)

wherefis the frequency of the system of which the machine is a part andPis the number of poles

of the machine.

The electromagnetic torque, produced by the nonsalient-pole (or cylindrical-rotor) machine,

can be expressed in terms of the resultant fluxφper pole produced by the combined effect of the

stator and rotor mmfs (see Problem 12.4.15),

Te=Kφ Frsinδr (13.1.3)

whereKis a constant,Fris the rotor mmf, andδris the angle between the rotor mmf and the

resultant flux or mmf axis. When the armature terminals are connected to a balanced polyphase

infinite bus(which is a high-capacity, constant-voltage, constant-frequency system), the resultant

air-gap fluxφis approximately constant, independent of the shaft load. Under normal operating

conditions the resultant air-gap fluxφ, which is given by Equation (12.2.13) as

φ=

terminal phase voltage

4. 44 kWfNph

(13.1.4)

is essentially constant. The rotor mmfFrdetermined by the direct field current is also a constant

under normal operating conditions. So, as seen from Equation (13.1.3), any variation in the torque

requirements of the load has to be accounted for entirely by variation of the angleδr, which is

whyδris known as thetorque angle(orload angle) of a synchronous machine. The effect of

salient poles on the torque-angle characteristic is discussed in Section 13.3.

The torque-angle characteristic curve of a cylindrical-rotor synchronous machine is shown

in Figure 13.1.3 as a function of the angleδr. Forδr<0,Te>0, the developed torque is positive

and acts in the direction of the rotation; the machine operates as a motor. If, on the other hand,

the machine is driven by a prime mover so thatδrbecomes positive, the torque is then negative,

and the machine operates as a generator. Note that at standstill, i.e., whenωm=0, no average

unidirectional torque is developed by the synchronous machine. Such a synchronous motor is not

capable of self-starting because it has no starting torque. The designer must provide a method for

bringing the machine up to synchronous speed.

Torque

angle, δr

Te (or power)

Pull-out torque as a motor

Pull-out torque as a generator

Motor operation Generator operation

Te > 0 Te < 0

π

−π −π/ 2 π/ 2

Figure 13.1.3Torque-angle char-

acteristic curve of a cylindrical-

rotor synchronous machine (for a

given field current and a fixed ter-

minal voltage, i.e., for a constant

resultant air-gap flux).