ECE 442 Power Electronics1 DC-DC Converter Drives Principle of Power Control Principle of Regenerative Brake Control Principle of Rheostatic Brake Control.

ECE 442 Power Electronics 1

DC-DC Converter Drives

• Principle of Power Control

• Principle of Regenerative Brake Control

• Principle of Rheostatic Brake Control

• Combined Regenerative and Rheostatic Brake Control

• Two and Four Quadrant DC – DC Converter Drives


Converter-fed DC Drive for a Separately-Excited Motor


Waveform Summary Highly Inductive Load

Ripple-free Armature Current


Principle of Power Control

• The average armature voltage is

• The power supplied to the motor is

sa kVV

asaao IkVIVP


Principle of Power Control (continued)

• The average value of the input current is

• The equivalent input resistance seen by the source is

as kII

a

s

s

seq kI

V

I

VR

Control Power Flow by adjusting the duty cycle


Principle of Power Control (continued)

• To find the maximum peak-to-peak ripple current

m

m

m

s

fL

R

R

VI

4tanhmax


Example 15.7 A dc separately excited motor is powered by a dc-dc converter, as shown, from a 600V dc source. The armature resistance is Ra = 0.05Ω. The back emf constant is Kv = 1.527V/A rad/s. The average armature current is Ia = 250A. The field current is If = 2.5A. The armature current is continuous and has negligible ripple. If the duty cycle of the dc-dc converter is 60%, determine:


Example 15.7 Solution

600

250

0.6

0.05

s

a

m a

V V

I A

k

R R

the input power from the source

(0.6)(600 )(250 ) 90o a a s a

o

P V I kV I

P V A kW

the equivalent input resistance of the dc-dc converter drive

1

6004

(250 )(0.6)

s seq

s a

eq

V VR

I I k

VR

A


the motor speed

(0.6)(600 ) 360

360 (0.05 )(250 ) 347.5

347.591.03 /

(1.527 / / )(2.5 )

3091.03 869.3

g v f

g a m m

a s

g

g

v f

E K I

E V R I

V kV V V

E V A V

E Vrad s

K I V Arad s A

rpm

the developed torque

(1.527 / / )(250 )(2.5 ) 954.38

d t f a v f a

d

T K I I K I I

T V Arad s A A N m


Application of a DC – DC Converter in Regenerative Braking


Waveform SummaryArmature Current Continuous

and Ripple-Free


Regenerative Braking

• Begin with the motor turning by kinetic energy of the vehicle

• Armature current flows as shown

• Turn the transistor on• Armature current rises• Turn the transistor off• Diode turns on, current

flows into the supply


Principle of Regenerative Braking

• The average voltage across the transistor is

• The regenerated power can be found from

sch VkV )1(

)1( kVIP sag


Principle of Regenerative Braking (continued)

• The voltage generated by the motor acting as a generator is

• The equivalent load resistance of the motor acting as a generator is

amsamchg

fvg

IRVkIRVE

IKE

)1(

ma

s

a

geq Rk

I

V

I

ER )1(

Control Power by changing k

ECE 442 Power Electronics 15max

max

max

min

min

min

)(0

fv

am

fv

s

samfv

fv

am

amfvg

samg

IK

IR

IK

V

VIRIK

IK

IR

IRIKE

VIRE

Minimum Braking Speed

Maximum Braking Speed


Example 15.8 A dc-dc converter is used in regenerative braking of a dc series motor similar to the arrangement shown below. The dc supply voltage is 600V. The armature resistance is Ra = 0.02Ω and the field resistance is Rf = 0.03Ω. The back emf constant is Kv = 15.27mV/A rad/s. The average armature current is maintained constant at Ia = 250A. The armature current is continuous and has negligible ripple. If the duty cycle of the dc-dc converter is 60%, determine the following:

For this example, the field and armature need to be in series



600

250

0.01527 / /

0.6

s

a

v

m a f

V V

I A

K V Arad s

k

R R R

Determine the average voltage across the converter.

(1 )

(1 0.6)(600 ) 240ch s

ch

V k V

V V V

Determine the power regenerated to the dc supply

(1 )

(250 )(600 )(1 0.6) 60

g a s

g

P I V k

P A V kW

Determine the equivalent resistance of the motor acting as a generator

(1 )

0.02 0.03 0.05

600(1 0.6) 0.05 1.01

250

g seq m

a a

m a f

eq

E VR k R

I I

R R R

VR

A


Determine the minimum permissible braking speed ωmin

min

min

0.05 2503.274 /

0.01527 / / 250

1 603.274 / 31.26

2 1min

m a

v f

R I Arad s

K I V Arad s A

rev srad s rpm

rad

Determine the maximum permissible braking speed ωmax

max

max

max

max

600 0.05

(0.01527 / / )(250 ) 0.01527 / /

160.445 /

30160.445 1532.14

s m a

v f v f

V R I

K I K I

V

V Arad s A V Arad s

rad s

rpm

Determine the motor speed

(1 ) 240 (0.05 )(250 ) 252.5

252.566.14 /

(0.01527 / / )(250 )

3066.14 631.6

gg v f

v f

g s m a

EE K I

K I

E k V R I V A V

Vrad s

V Arad s A

rpm


Rheostatic Brake ControlDynamic Braking


Waveform Summary


Principle of Rheostatic Brake Control

• The average current in the braking resistor is

• The average voltage across the braking resistor is

)1( kII ab

)1( kIRV abb


Principle of Rheostatic Brake Control (continued)

• The equivalent load resistance of the generator

• The power dissipated in the resistor Rb is

mba

beq RkR

I

VR )1(

)1(2 kRIP bab


Example 15.9 A dc-dc converter is used in rheostatic braking of a dc separately excited motor as shown below. The armature resistance is Ra = 0.05Ω. The braking resistor is Rb = 5Ω. The back emf constant is Kv = 1.527V/A rad/s. The average armature current is maintained constant at Ia = 150A. The armature current is continuous and has negligible ripple. The field current is If = 1.5A. If the duty cycle of the dc-dc converter is 40%, determine:



150

1.527 / /

0.4

0.05

a

v

m a

I A

K V Arad s

k

R R

the average voltage across the dc-dc converter.

(1 )

(5 )(150 )(1 0.4) 450ch b b a

ch

V V R I k

V A V

the power dissipated in the braking resistor

2

2

(1 )

(150 ) (5 )(1 0.4) 67.5

b a b

b

P I R k

P A kW

the equivalent resistance of the motor acting as a generator

(1 )

(5 )(1 0.4) 0.05 3.05

beq b m

a

eq

VR R k R

I

R


the motor speed ω

457.5199.74 /

(1.527 / / )(1.5 )

30199.74 1907.4

g v f

g

v f

E K I

E Vrad s

K I V Arad s A

rpm

the peak dc converter voltage

(150 )(5 ) 750

p a b

p

V I R

V A V


Combined Regenerative and Rheostatic Brake Control


Combined Regenerative and Rheostatic Brake Control (continued)

• Used when the supply is partly “receptive”

• Remove regenerative braking if line voltage is too high– Turn thyristor TR on

– Divert current to RB

– Apply rheostatic braking

– TR is “self-commutated”


Two-Quadrant DC–DC Converter Drive


Quadrant Operation Summary

Regenerative Braking Control Power Control


Power Control

• Q1 and D2 operate

• Q1 ON, Vs applied to the motor

• Q1 turned OFF, D2 “free-wheels”

• Armature current decays


Regenerative Control

• Q2 and D1 operate

• Q2 turned ON, motor acts as a generator, and the armature current rises

• Q2 turned OFF, motor returns energy to the supply via D1 “free-wheeling”


Four Quadrant DC-DC Converter Drive


Quadrant Operation Summary

Forward Regeneration Forward Power Control

Reverse Power Control Reverse Regeneration


Forward Power Control

• Q1 and Q2 turned ON

• Supply voltage appears across the motor

• Armature current rises

• Q1 and Q2 turned OFF

• Armature current decays via D3 and D4


Forward Regeneration

• Q1, Q2, and Q3 turned OFF

• Turn Q4 ON

• Armature current rises and flows through Q4, D2

• Q4 turned OFF, motor acts as a generator, returns energy back to the supply via D1, D2

ia reverses


Reverse Power Control

• Q3 and Q4 turned ON• Supply voltage appears

in the reverse direction across the motor

• Armature current rises and flows in the reverse direction

• Q3 and Q4 turned OFF• Armature current

decays via D1 and D2

ia


Reverse Regeneration

• Q1, Q3, Q4 turned OFF

• Q2 turned ON

• Armature current rises through Q2 and D4

• Q2 turned OFF

• Armature current falls and returns energy via D3 and D4

i a

ECE 442 Power Electronics1 DC-DC Converter Drives Principle of Power Control Principle of Regenerative Brake Control Principle of Rheostatic Brake Control.

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