Electrical Drives IWeek 4-5-6: Solid state dc drives

Motor- Load Matching

When an electric motor is connected to a mechanical load, thesystem operates at a speed-torque status that matches the motoras well as the load.

The figure shows 3 characteristics obtained by adjusting thevoltage across a motor where CC1 requires higher voltage than thatcompared to CC2 and CC3.

If the motor is driving a “Hoist” marked in blue, the intersectionbetween CC1 and the hoist curve (point H1) will determine how theload will be driven. If the motor characteristics are changed toCC3, the new operating point will be H3.

At H1 and H3 the system torque is unchanged because of the hoistcharacteristics.

Similarly, the fan load can be examined

Speed torque characteristics of a

motor and mechanical load

Load characteristics are very important as it determines with the motor

characteristics the system’s operating speed and torque.

IT MUST NOT BE NEGLECTED

Speed

Torque

Fan load

Hoist load

Motor

characteristics

H1

H2

H3

F1

F2

F3

CC1

CC2

CC3

Unidirectional and Bidirectional Operation

The load force is divided into 2 components.

1. one perpendicular to the road , F, producing a friction force.

(OPPOSING FORCE)

2. Another is 𝑭𝒍 which is parallel to the road and represents the load

torque exerted on the motor which depends on gravity and the

orientation of the road. (DUE TO MASS AND ACCELERATION)

𝑻𝒍 (load torque) in this case will be = 𝑭𝒍 * (radius of wheel)

If friction is neglected, the motor force, 𝑭𝑴 must match 𝑭𝒍 (𝑭𝑴 is

in opposite direction of 𝑭𝒍)

When the bus is moving downhill, the motor sees that the load

force is reversed. So the motor torque must then change its

direction to balance the load torque.

𝑭𝒎 pulls the system up the hill

Motor speed is unidirectional but in this example the

system torques are bidirectional

Fm

F

Fl

F

Fm

Fl

𝑭𝒍 pulls system down the hill

Example1:

𝐹𝑚 pulls the system up the hill

Fl pulls system down the hill

F producing a friction force

Unidirectional and Bidirectional Operation

Elevator moves passengers in up and down directions

The load force, 𝑭𝒍, is function of the passengers weight, cabin,

cables…etc.

In this case, 𝑭𝒍 is always unidirectional, and the motor force,

𝑭𝑴 is also unidirectional

The speed in this case is bidirectional

Torque is unidirectional but speed is bidirectional

Example2: Fm

Fl

Fm

MotionMotion

Fl

Four Quadrant

Operation in Electric

Drives Motor: machine torque is in the same

direction of the speed. The machine is

delivering mechanical power to load and is

consuming electrical power.

Generator: machine torque is in the

opposite direction of the speed. The

machine is delivering electrical power to

load and is consuming mechanical power.

LoadM

Tl

Tm

Power flow

LoadM

Tm

Power flow

Tl

LoadM

Tm

Power flow

Tl

LoadM

Tl

Tm

Power flow

Speed

Torque

Q2: speed same as Q1, 𝑻𝒍 is

reversed as well as 𝑻𝑴 . Machine

receives mechanical power from

load and acts as a generator

Q1: 𝑻𝒍 is opposite to 𝑻𝑴 ,

machine runs as motor and

power flows from machine

to load.

Q3: speed, 𝑻𝒍 and 𝑻𝑴 are reversed,

with respect to Q1. Machine runs as

motor and power flows from

machine to load.

Q4: speed is reversed, while 𝑻𝒍and 𝑻𝑴 are unchanged with

respect to Q1. Machine acts as

generator

• Q1 and Q3 machine: grinding machine,

horizontal conveyor belt

• Q1 and Q4 machine: elevator going up

and down

Torque-Speed Quadrant of Operation

m

Te

Te

m

Tem

Te

m

T

Direction of positive (forward) speed is arbitrary chosen

Quadrant 1Forward motoring

Quadrant 2Forward braking

Quadrant 3Reverse motoring

Quadrant 4Reverse braking

P = +ve

P = -ve

P = -ve

P = +ve

The beauty of the separately excited d.c. motor is the ease

with which it can be controlled.

• Firstly, the steady-state speed is determined by the applied

voltage, so we can make the motor run at any desired speed

in either direction simply by applying the appropriate

magnitude and polarity of the armature voltage.

• Secondly, the torque is directly proportional to the armature

current, which in turn depends on the difference between

the applied voltage 𝑉𝑡 and 𝐸𝑎. We can therefore make the

machine develop positive (motoring) or negative

(generating) torque simply by controlling the extent to

which the applied voltage is greater or less than 𝐸𝑎.

An armature voltage controlled d.c. machine is

therefore inherently capable of what is known as

‘four-quadrant’ operation,

Controlled Rectifier Fed DC Drives

To obtain variable DC voltage from fixed AC source

DC current flows in only 1 direction

For small motors (few kilowatts), single phase supply is used but with large motors three

phase supply is always used

The main power circuit consists of a six-thyristor bridge circuit which rectifies the incoming

a.c. supply to produce a d.c. supply to the motor armature. By altering the Wring angle of the

thyristors the mean value of the rectifies voltage can be varied, thereby allowing the motor

speed to be controlled.

T

Q1Q2

Q3 Q4

Controlled Rectifier Fed DC Drives Controlled rectifier produces a crude form of d.c. with a pronounced ripple in the output voltage.

This ripple component gives rise to pulsating currents and fluxes in the motor, and in order to avoid excessive

eddy-current losses and commutation problems, the poles and frame should be of laminated construction.

It is accepted practice for motors supplied for use with thyristor drives to have laminated construction, but older

motors often have solid poles and/or frames, and these will not always work satisfactorily with a rectified supply.

It is also the norm for drive motors to be supplied with an attached ‘blower’ motor as standard. This provides

continuous through ventilation and allows the motor to operate continuously at full torque even down to the

lowest speeds without overheating.

Controlled Rectifier Fed DC Drives

Single-phasesupply

+

Va

ia

M

S1 S2

S3S4

i1

ia

Ra

La

Vs

i2

Ea

There are two pulses per mains cycle, hence the description ‘two-pulse’ or full-wave. At every instant

the load is either connected to the mains by the pair of switches T1 and T4, or it is connected the

other way up by the pair of switches T2 and T3, or it is disconnected. The load voltage therefore

consists of rectified chunks of the mains voltage. It is much smoother than in the single-pulse circuit,

though again it is far from pure d.c.

Controlled Rectifier Fed DC Drives

T1 and T4 are fired together when terminal A of the supply is positive, while on the other half cycle, when

B is positive, T2 and T3 are fired simultaneously.

The larger the delay angle, the lower the output voltage. The maximum output voltage, 𝑽𝒐 is obtained

with a α=0: this is the same as would be obtained if the thyristors were replaced by diodes

Single-phasesupply

T1

ia

T4

T2

T3

Resistive load

Vo

π0 2π

-va

α

α

ωt

Vdc=Vo

ωt

va

T1 and T4T2 and T3

Controlled Rectifier Fed DC DrivesResistive load

rmsdo VV 22

When the thyristors are replaced by diodes, the 𝑉𝑜 is

by:

Using thyristors the 𝑉𝑜 is by:

2

cos12

2

2

cos1

rmsdodc VVV

For a resistive load the d.c. voltage can be varied from a

maximum of 𝑉𝑑𝑜 down to zero by varying a from 0 to 180◦.

Vo

π0 2π

-va

α

α

ωt

Vdc=Vo

ωt

va

Vo

α

Vdc=Vo

ωt

the mean output voltage is NEVER

negative for any values of firing

angle.

Controlled Rectifier Fed DC Drives: Inductive (Motor) load motor loads are inductive, where current cannot change instantaneously.

The expected behavior of the converter with an inductive load is different than that of a resistive load, in which

the current can change instantaneously.

We can specify the output voltage waveform once we have fixed the delay angle α.

Based on the desired mean output voltage, α is being selected. Since the voltage relation is somehow complex

with inductive load, therefore we cannot give a simple general formula for the mean output voltage in terms of α.

This very undesirable: if for example we had set the speed of our unloaded d.c. motor to the target value by

adjusting the firing angle of the converter to produce the correct mean voltage, the last thing we would want is for

the voltage to fall when the load current drawn by the motor increases, as this would cause the speed to fall below

the target.

Fortunately however, it turns out that the output voltage waveform for a given α does become independent

of the load inductance once there is sufficient inductance to prevent the load current from falling to

zero. This condition is known as ‘continuous current’; and happily, many motor circuits do have sufficient

self-inductance to ensure that we achieve continuous current. Under continuous current conditions, the

output voltage waveform only depends on the Wring angle, and not on the actual inductance present.

Controlled Rectifier Fed DC Drives: Inductive (Motor) load We see that, as with the resistive load, the larger the delay

angle the lower the mean output voltage.

However, with the resistive load the output voltage was

never negative, however for short periods the output

voltage can now be negative.

This is because the inductance smoothes the current so that

at no time does it fall to zero. As a result, one pair of

thyristors is always conducting, so at every instant the load

is connected directly to the mains supply, and the load

voltage always consists of chunks of the supply voltage.

Vo

π0 2π

-va

α

α

ωt

Vdc=Vo

ωt

va

Vo

α

Vdc=Vo

ωt

15°

60°

cos22

cos rmsdodc VVV

If α is greater than

90˚ the mean

output voltage is

negative, could be

used in

regenerative mode

V relation in single phase full wave continuous mode at different firing

angles

Controlled Rectifier Fed DC Drives: Notes It is sometimes suggested (particularly by those with a light-current background) that a capacitor could be used to smooth the

output voltage, this being common practice in cheap low-power d.c. supplies. Although this works well at low power, there are

two reasons why capacitors are not used with controlled rectifiers supplying motors.

Firstly, as will be seen later, it is not necessary for the voltage to be smooth as it is the current which directly determines

the torque, and as already pointed out the current is always much smoother than the voltage because of inductance.

Secondly, the power levels in most drives are such that in order to store enough energy to smooth out the rectified

voltage, very bulky and expensive capacitors would be required.

It is noticed that the voltage waveform consists of a mean d.c. level 𝑉𝑑𝑐 and a superimposed pulsating or ripple component

which we can denote loosely as 𝑉𝑎𝑐. The mean voltage 𝑉𝑑𝑐 can be altered by varying the firing angle, which also incidentally

alters the ripple (i.e. 𝑉𝑎𝑐).

The current smoothing effect occurs due to the presence of the armature inductance, thus current ripple is relatively small in

comparison with the corresponding voltage ripple. The armature acts as a low-pass filter, blocking most of the ripple, and

leading to a more or less constant armature current. The average value of the ripple current is zero, so it has no effect on the

average torque of the motor.

There is a variation in torque every half-cycle of the mains, but because it is of small amplitude and high frequency the

variation in speed (and hence 𝐸𝑎) will not usually be noticeable.

Controlled Rectifier Fed DC Drives: Notes

Since the no-load speed of motor is determined by the applied voltage (which depends

on the firing angle of the converter) there is a small drop in speed with load and the

average current is determined by the load.

In Figure, for example, the voltage waveform in (a) applies equally for the two load

conditions represented in (b), where the upper current waveform corresponds to a high

value of load torque while the lower is for a much lighter load; the speed being almost

the same in both cases.

The current waveforms are referred to as ‘continuous’, because there is never any time

during which the current is not flowing. This ‘continuous current’ condition is the norm

in most drives, and it is highly desirable because it is only under continuous current

conditions that the average voltage from the converter is determined solely by the firing

angle, and is independent of the load current.

In heavily loaded motors with high armature inductance, the conduction period may equal or exceed 180˚.

This may result in an over lap between 𝑖1and 𝑖2 resulting in continuous conduction

V-I relation in single phase full wave

continuous mode

Controlled Rectifier Fed DC Drives: Discontinuous mode

When the load torque is reduced, there will come a point

where the minima of the current ripple touches the zero

current line, and the current reaches the boundary

between continuous and discontinuous current. The load

at which this occurs will also depend on the armature

inductance, because the higher the inductance the

smoother the current (i.e. the less the ripple).

Discontinuous current mode is therefore most likely to be

encountered in small machines with low inductance

(particularly when fed from two-pulse converters) and

under light-load or no-load conditions.

Vo

π0 2π

-va

θ

ωt

Vdc=Ea

ωt

va

Io

Idc

ωt

60°

at EVLdt

di

1V-I relation in single phase full wave discontinuous mode

Controlled Rectifier Fed DC Drives: Discontinuous mode

The following current relation shows that the rate of

change of current (i.e. the gradient of the lower graph) is

determined by the instantaneous difference between the

applied voltage 𝑉𝑡 and the 𝐸𝑎.

at EVLdt

di

1

Vo

π0 2π

-va

θ

ωt

Vdc=Ea

ωt

va

Io

Idc

ωt

60°Vt

Values of 𝑉𝑡 − 𝐸𝑎 are shown by the vertical hatchings in

the figure, from which it can be seen that if 𝑉𝑡 > 𝐸𝑎, the

current is increasing, while if 𝑉𝑡 < 𝐸𝑎 , the current is

falling. The peak current is thus determined by the area of

the upper or lower shaded areas of the upper graph.𝑉𝑡 > 𝐸𝑎 𝑉𝑡 < 𝐸𝑎

V-I relation in single phase full wave discontinuous mode

Controlled Rectifier Fed DC Drives: Discontinuous mode

In the discontinuous mode, the current falls to zero

before the next firing pulse arrives and during the

period shown as θ the motor floats free, its terminal

voltage during this time being 𝑬𝒂Vo

π0 2π

-va

θ

ωt

Vdc=Ea

ωt

va

Io

Idc

ωt

60°Vt

𝑉𝑡 > 𝐸𝑎 𝑉𝑡 < 𝐸𝑎

The average voltage in discontinuous mode is

higher than that of the continuous mode and

hence the speed is higher in the discontinuous

mode despite both having the same firing angle.

In continuous mode a load increase can be met by

an increased armature current without affecting

the voltage (and hence speed), the situation is

different when the current is discontinuous. In the

discontinuous mode, the only way that the

average current can increase is when speed (and

hence 𝑬𝒂) falls so that the shaded areas in the

figure become larger. V-I relation in single phase full wave discontinuous mode

Controlled Rectifier Fed DC Drives: Discontinuous mode

Discontinuous mode is much worse

than the continuous current mode,

because as the load torque is

increased, there is a serious drop in

speed The resulting torque–speed

curve therefore has a very

unwelcome ‘droopy’ characteristic

in the discontinuous current region

firing angle is set to zero and the

motor is fully loaded, the average

armature voltage and current having

their full (rated) values

load is reduced, current remains

continuous, there is the expected

slight rise in speed--- about the verge

of discontinuous mode

reduction in the load torque produces a

frightening increase in speed, especially if

the load is reduced to zero

THEN WHAT

SHALL WE DO???1. Add extra inductance in

series with the armature to

further smooth the current

waveform and lessen the

likelihood of discontinuous

current.

2. Switch from a single-phase

converter to a 3-phase

converter which produces

smoother voltage and current

waveforms

What about

closed loop

control?Speed torque relation of dc motor driven by a

solid state converter

Discontinous

CurrentContinous Current

α1

α2

α3

α4

α1> α2> α3

Torque

Speed

Speed torque relation of dc motor driven

by a solid state converter

Controlled Rectifier Fed DC Drives:

T

Forward

motoring

Forward

regeneration