DC Motors Speed Control_mod

7/28/2019 DC Motors Speed Control_mod

1/9

Solid State Devices Speed Control MTE 320 Spring 2006 E.F. EL-Saadany

1

Solid State Devices Speed Control of DC Motors

1. Basics of DC Motors Speed Control

Since aata RIVE = and maa KE = , Therefore,

a

aatmK

RIV = .

Practically, speed control of DC motors can be fulfilled using on of two methods:

Field Control:by varying the field current. This can be achieved by varying the fieldvoltage.

Voltage Control: by varying the armature terminal voltage.

Up to the rated (base) speed (the speed corresponding to rated operation condition, rated armature

voltage, rated armature current, and rated field current), the armature and the field currents are kept

constant to maintain the torque at its rated value. The speed control within this range is carried out by

varying the armature voltage. Beyond the base speed, the speed control the achieved by varying the

field current. Within this range, the motor power is maintained constant and the torque is reduced with

the increase in the rotational speed as shown in Fig. 1. For series motor, the speed control beyond the

base speed is carried out using the armature current variation (since the armature and the field current

are the same in series motors) as shown in Fig. 2.

Fig. 1 Speed control characteristic of separately excited DC motors [1]


2/9


2

Fig. 2 Speed control characteristic of series DC motors [1]

2. Speed Control using Power Semiconductor Switches

As discussed in previous lectures, there are several power semiconductor switches configuration that

can be used to provide variable output DC voltage. Single and three-phase AC-to-DC converters(rectifiers) can be used to vary the input armature voltage and / or the field voltage of DC machines to

control it speed of rotation as shown in Fig. 3-a. Moreover, DC-to-DC converters can also be used for

speed control as shown in Fig. 3-b. the following subsections will briefly discuss some example of the

used power semiconductor converters in the speed control of DC motors.

Fig. 3 Power seimconductor converters for DC motors speed control[1]


3/9


3

2.1 Single-Phase Rectifiers

In these configurations, the armature and / or the field winding voltage can be varied using single-

phase full bridge AC-to-DC converters as shown in Fig. 4-a. This is a two quadrant converter, as

shown in Fig. 4-b, where the load current is always positive while the load voltage may be positive or

negative. The generated waveforms are shown in Fig. 4-c. Single-phase AC-to-DC semi-converterscan be also used for DC motors speed control as shown in Fig. 5-a. However, this is a first-quadrant

converter, as shown in Fig. 5-b, where the load current and voltage are always positive. The generated

waveforms are shown in Fig. 5-c. Usually the same AC supply is used as an input for the two

converters. The average value of the armature and / or field voltage (and hence the rotational speed)

can be varied and controlled by varying the firing angle of the thyristors used. The equation relating

the armature and the field voltage with the supply voltage and the firing angle can be expressed as

follows,

Fig. 4 DC motor speed control using single-phase full converters [1]

For single-phase full converters connected to the armature terminals:

The average value (DC) of the armature voltage is,

( )am

a

VV

cos

2= for0 a

where Vais the average value of the armature voltage, Vm is the maximum value of the

supply voltage, anda is the armature converters thyristor firing (delay) angle.


4/9


4

For single-phase full converters connected to the field terminals:

The average value (DC) of the field voltage is,

( )fmfV

V

cos2

= for0 f

where Vfis the average value of the field voltage, andfis the field converters thyristorfiring (delay) angle.

Fig. 5 DC motor speed control using single-phase semi-converters [1]

For single-phase semi-converters connected to the armature terminals:

The average value (DC) of the armature voltage is,

( )( )am

a

VV

cos1+= for0 a

For single-phase semi-converters connected to the field terminals:

The average value (DC) of the field voltage is,

( )( )fmfV

V

cos1+= for0 f

2.2 DC Choppers

In these configurations, the armature and / or the field winding voltage can be varied using DC-to-DC

converters as shown in Fig. 6-a. The input DC voltage can be generated using uncontrolled rectifier


5/9


5

circuits. This is a first-quadrant converter as shown in Fig. 6-b. The associated waveforms are given in

Fig. 6-c. The average value of the armature and / or field voltage (and hence the rotational speed) can

be varied and controlled by varying the duty cycle of power semi-conductor device used. The equation

relating the armature and the field voltage with the supply voltage and the firing angle can be

expressed as follows,

Fig. 6 DC motor speed control using first quadrant DC-to-DC converters [1]

The average value for the armature voltage is,

sa VkV =

where Vais the average value of the armature voltage, Vs is the DC supply voltage (the average

value of the output voltage of a AC-to-DC converter), andkis the choppers duty cycle.

The power supplied to the motor is,

asaai IVkIVP ==

where Piis the supplied (input) power to the DC motor,Ia is the average value of the armature

current.

Assuming losseless power converter, the input power to the DC motor is the source output power,

is PP =

where Psis the source output power.


6/9


6

The average value for the input current is,

as IkI =

whereIs is the average value of the input current.

The equivalent input resistance of the DC chopper as seen by the supply is given by,

a

s

s

seq

Ik

V

I

VR ==

whereIs is the average value of the input current.

3. Numerical Examples

Example 1: A separately excited DC motor is controlled using single-phase AC-to-DC semi-

converters connected to its armature and field terminals as shown in Fig 7. The AC

supply connected to the armature and field semi-converters is a single-phase, 208 V,

60 Hz, AC source. The armature and field resistances are 0.25 and 147 ,

respectively. The motor voltage constant is 0.7032 V/A rad/s. The field current is set

to its maximum possible value. The armature and the field currents are assumed

continuous and ripple free. If the load torque is 45 N.m. at 1000 rpm, calculate

1. The field current,2. The armature current, and3. The delay angle for the thyristors in the armature converter.

Given: Vs = 208 V, f = 60 Hz, If = max, Ra = 0.25 , Rf = 147 , kv = 0.7032 V/A rad/s,

TL = 45 N.m., and n = 1000 rpm.

Solution: For separately excited DC motor is controlled using single-phase AC-to-DC semi-

converters shown in Fig. 7.

1. The average value for the field voltage is,

( )( )fmfV

V

cos1+=

The average value for the field current is


7/9


7

f

ff

f

f

fR

V

R

VI

cos1+==

Fig. 7 DC motor speed control using single-phase semi-converters [1]

Therefore, the field current will maintain its maximum possible value iff= 0.

( )( ) VVf 27.1870cos12208

max, =+=

, and

The maximum possible value for the field current is,

AR

VI

f

f

f 274.1147

27.187max,

max,

===

2. The developed (load) torque is given by,

afvaad IIKIKT ==

Therefore, the armature current is,

AxIK

TI

fv

d

a23.50

274.17032.0

45===

3. The armature back emf is

VxxxIKKE mfvmaa 82.93100060

2274.17032.0 ====

aaaa RIVE =Q


8/9


8

VxRIEV aaaa 38.10625.023.5082.93 =+=+=

However, the average value of the armature voltage is related to the delay angle of

the armatures converter by,

( )( )am

aVV

cos1+=

( ) 136.012208

38.1061cos ===

x

V

V

m

aa

= 18.82a

Example 2: A separately excited DC motor is controlled using a DC-to-DC converter as shown

in Fig 8. The DC supply used is a 600 V source. The armature resistance is 0.05

.The constant for the back emf is 1.527 V/A rad/s. The armature current is set to

250 A and is continuous and ripple free. The field current is set to 2.5 A. If the

operating duty cycle of the DC-to-Dc converter is 60 %. Calculate

1. The input power from the DC supply,2. The motor speed,3. The developed torque, and4. The input equivalent resistance as seen by the DC supply.

Given: Vs = 600 V, Ia = 250 A, Ra = 0.05 , If= 2.5 A, kv = 1.527 V/A rad/s and k = 60 %.

Solution: For separately excited DC motor is controlled using a DC-to-DC converter shown in

Fig. 8.

1. The input power from the DC supply is,

kWWxxIVkIVP asaai 90000,902506006.0 =====

2. The average value for the armature voltage is,

VxVkV sa 3606006.0 ===

The armature back emf is

VxRIVE aaag 5.34705.0250360 ===


9/9


9

Fig. 8 DC motor speed control using first quadrant DC-to-DC converters [1]

The motor rotational speed can be determined using the following relation,

mfvmag IKKE ==

sradxIK

E

fv

g

m /028.915.2527.1

5.347===

3. The developed torque is given by,

..375.9542505.2527.1 mNxxIIKIKT afvaad ====

4. The input equivalent resistance as seen by the DC supply is given by,

==== 42506.0

600

xIk

V

I

VR

a

s

s

seq

References

[1] Muhammad H. Rashid, Power Electronics, Third Edition, Pearson Prentice Hall, NJ, USA, 2004.

[2] Theodore Wildi, "Electrical Machines Drives, and Power Systems," Prentice Hall, Ohio, 2006.

DC Motors Speed Control_mod

Documents

Transcript of DC Motors Speed Control_mod