Principles of Electric Machines and Power Electronicsli/slides/ch04-3 Sli.pdf · Principles of...

Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.

Chapter 4DC Machines

Third Edition

P. C. Sen

Principles of Electric Machines

and

Power Electronics

Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.Fig_1-1

Chapter 4 DC machine

•Main contentsDC motor

o Self-excited shunt type

o Separately excited dc motor: torque-speed characteristics

o Speed control

o Self-excited series type

Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.

Review of classifications of DC machines(a) Separately excited

(b) Self-excited (series-type)

(c) Self-excited (shunt-type)

(d) Self-excited (compound-type—short shunt and long shunt)

DC steady-state analysis : neglect winding inductance


Shunt dc motor equivalent circuit

t a a a

t a f

a a m t a a

V I R E

I I I

E K V I R

Armature current and speed depend on the mechanical load

Ea is back emf voltage

Apply DC source of fixed voltage Vt

Rheostat is used to control field

Field circuit is independent of armature circuit

Armature current and speed depend on mechanical load


Power losses in a shunt dc machine

output

input

EffP

P

Rotational loss

Windage

Friction

Rotor core loss


Example (practice)


Speed control

• Separately/shunt excited dc motor

𝑇𝑒 − 𝑇𝑙 = 𝐽𝑑𝜔𝑚

𝑑𝑡

• Three ways to control the speed Armature voltage

Field flux

Armature resistance

𝐸𝑎= 𝐾𝑎∅𝜔𝑚 = 𝑉𝑡 − 𝐼𝑎𝑅𝑎

𝜔𝑚 =𝑉𝑡 − 𝐼𝑎𝑅𝑎𝐾𝑎∅

=𝑉𝑡𝐾𝑎∅

−𝑅𝑎𝐾𝑎∅

2𝑇

Torque-speed characteristics when terminal

voltage and flux is constant

In steady state, load torque Tl equals Te

𝑇𝑒 = 𝐾𝑎∅𝐼𝑎


Speed control: armature voltage control

Constant load torque Constant terminal voltage

Constant armature current and torque:

Input power is linear with speed

𝜔𝑚 = 𝑘1𝑉𝑡 − 𝑘2𝑇

𝑃𝑜𝑢𝑡 = 𝑇𝜔𝑚

𝑃𝑖𝑛 = 𝑃𝑜𝑢𝑡 + 𝐼𝑎2𝑅𝑎

• Ra remains unchanged

• If is kept constant

• Smooth speed variation

• Expensive




2𝑇


Speed control: field (current) control

𝐾𝑎∅ = 𝐾𝑓𝐼𝑓

No load condition T=0

𝜔𝑚 =𝑉𝑡𝐾𝑓𝐼𝑓

−𝑅𝑎

𝐾𝑓𝐼𝑓2 𝑇




2𝑇

• Ra remains unchanged

• Vt is constant

• Flux is proportional to If

• Simple to implement

• Less expensive

• Sluggish response

𝐼𝑓 =𝑉𝑡

𝑅𝑓𝑐 + 𝑅𝑓𝑤

𝜔m =k1If−k2

If2 T


Speed control: armature resistance control

1. If remains unchanged

2. Vt is constant

3. Less efficient

4. Simple to implement

5. Expensive

𝜔𝑚 =𝑉𝑡𝐾𝑎∅

−𝑅𝑎 + 𝑅𝑎𝑒𝐾𝑎∅

2𝑇


Series DC motor

Control speed

𝐾𝑎∅ = 𝐾𝑠𝑟𝐼𝑎

𝐸𝑎 = 𝐾𝑠𝑟𝐼𝑎𝜔𝑚

𝑇 = 𝐾𝑠𝑟𝐼𝑎2

𝐸𝑎 = 𝑉𝑡 − 𝐼𝑎(𝑅𝑎 + 𝑅𝑎𝑒 + 𝑅𝑠𝑟)

𝜔𝑚 =𝑉𝑡

𝐾𝑠𝑟𝐼𝑎−𝑅𝑎 + 𝑅𝑠𝑟 + 𝑅𝑎𝑒

𝐾𝑠𝑟

𝜔𝑚 =𝑉𝑡

𝐾𝑠𝑟 𝑇−𝑅𝑎 + 𝑅𝑠𝑟 + 𝑅𝑎𝑒

𝐾𝑠𝑟


Starter

DC motor directly connects to DC supply? Back EMF is 0 at start

Starting current is dangerously high

Solutions Limit by an external resistance

Variable DC voltage supply

DC motor starter At start, handle moves to position 1

As motor speeds up, handle changes

Finally, position 5

Development of a dc motor starter

start| ta

a

VI

R

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