Electric Power Generation, Transmission, and Distribution

where Tdev¼EM torque, produced by the motor, Nm
Tm¼torque absorbed by the mechanical load, including the load losses and that used for useful
mechanical work, Nm
TRL¼rotational loss torque, internal to the motor, Nm
T^0 m¼TmþTRL¼equivalent load torque, Nm
J¼mass polar moment of inertia of all rotating parts, kg-m^2
vrm¼angular velocity of rotating parts, rad=s
Observe that whenever Tdev>T^0 m, the system accelerates; if Tdev<T^0 m, the system decelerates. The
system will inherently seek out the equilibrium condition of Tdev¼T^0 m, which will determine
the running speed. In general, the steady state running speed for any motor-load system occurs at the
intersection of the motor and load torque-speed characteristics, i.e., where Tdev¼T^0 m.IfTdev>T^0 m,
the system is accelerating; for Tdev<T^0 m, the system decelerates. Thus, torque-speed characteristics for
motors and loads are necessary for the design of a speed (or position) control system.

Electrical

Source MechanicalLoad

Mechanical

Load

Translator

Translator

Stator

Stator

Mechanical

Load

Mechanical

Prime

Mover

Energy Flow

Energy Flow

X, VX

Energy Flow

Energy Flow

a. the EM rotational machine; motor convention

b. the EM rotational machine; generator convention

c. the EM translational machine; motor convention

d. the EM translational machine; generator convention

Tdev

TRL Tm

Wrm

Tdev

Fdev

Fdev

TRL

FTL

Fm

Tm

Wrm

EM Machine

(“motor”)

EM Machine

(“motor”)

EM Machine

(“motor”)

EM Machine

(“generator”)

Electrical

Source

Electrical

Source

Electrical

Sink

FTL

Fm

X, VX

FIGURE 27.1 Motor and generator sign conventions for EM machines.