Handbook of Electrical Engineering

410 HANDBOOK OF ELECTRICAL ENGINEERING

In this case the maximum rms value ofIis,

Imax=

Id

π

√

3

2

2 =

√

6

π

Id ( 15. 11 )

15.2.4.2 Active and reactive power

The rectifying elements of the bridge are assumed to be free of ohmic power losses. Therefore the
power input to the DC motor must be equal to the AC power input to the bridge. Hence the sum of
the active power in each phase of the supply transformer must equal the motor input power.

The input powerPdto the motor is,
Pd=VdId ( 15. 12 )

The output volt-amperes of the transformer is,

Ssec= 3 EI=

3 EId

π

√

3

2

c 1 ( 15. 13 )

The active and reactive powers at the output of the transformer are,

Psec=

3 EId

π

√

3

2

a 1 ( 15. 14 )

and

Qsec=

3 EId

π

√

3

2

b 1 ( 15. 15 )

The power factor of the fundamental currentIis,

cos Ø 1 =

Psec

Ssec

=

a 1

c 1

( 15. 16 )

15.2.4.2.1 Worked example

Certain operations that take place when drilling oil wells require the DC motors to operate at reduced
speed and to produce a moderate or high torque, e.g. reaming holes, running casing, stuck pipe
removal, working over a well. Consider an example where a draw-works is running casing and
several series-wound motors operate in parallel to drive the line drum.

The motor design details are

Rated output power 750 kW

Rated efficiency 93%

Rated voltage 750 volts

Rated current 1075 amps

Rated speed 975 rev/min

Rated torque 7350 nm

Armature and field circuit resistance (hot) 0.0488 ohms

Armature and field circuit inductance 0.006 henry