VARIABLE SPEED OPERATION OF WIND TURBINES
by
D. Goodfellow
Thesis
submitted
for
the
degree
to
the
of
University
Doctor
October
1986
of
of
Leicester
Philosophy
MEMORANDUM
The accompanying
"Variable
the
speed
in
author
during
mainly
All
the
Department
the
period
the
The main
variable
1.
speed
2.
emf
to
the
this
University
is
original
for
another
thesis
Leicester
of
1986.
1983 and September
submitted
phase
with
in
the
unless
otherwise
degree
in
this
any
or
firing
these
below
Results
machine
system
designed
which
enables
machine
smoothly
above
and below
production
emf have
been
to
used
effective
six
both
have
shown the
smoothly
from
the
of
secondary
by computer,
calculated
ensure
current
operation
of
the
phases
a limited
over
generating
of
ability
to
standstill
and
the
just
mains
of
speed
motoring
range
the
has been
above
and
drive
an indu
modes.
to
cycloconverter
below
supply
operating
range
as a generator.
An assessment
converter
in
been
the
technique
operated
speed
includeý
angles.
using
successfully
synchronous
for
secondary
crossing
subject
mode.
requirements
A cycloconverter
and
induction
the
a cycloconverter
using
has
generator
the
induced
turbines
wind
have made to
to
claims
author
an asynchronous
cosine
with
of
signal
angle
a modified
designed
the
control
speed
The firing
equipment
the
of
October
has been
operation
A secondary
synchr'onous
tion
Engineering
by
conducted
on work
by references.
or
contributions
cycloconverter
and
text
work
based
Ph. D. entitled
of
University.
other
in
the
is
between
in
degree
the
turbines"
wind
of
recorded
for
submitted
of
the
work
None of
of
operation
in
acknowledged
thesis
has
been
of
the
achieved
cycloconverter
using
an on-line
as a variable
computer
speed
wind
energy
simulation.
Goodfellow
of Engineering
of Leicester
D.
Department
University
of
LIST
V
Wind
p(V)
Probability
VM
Mean wind
V
Cut-in
0
V
1
OF PRINCIPAL
SYMBOLS
m/s
speed
that
speed
wind
Cut-out
windspeed
V
m/s
speed
wind
exceeds
m/s
speed
m/s
P
Power
Pm
Mechanical
power
W
Pe
Electrical
power
W
Pi
Primary
P2
Secondary
P
Air
Cp
Power
Cpm
Maximum power
coefficient
A
Swept
turbine
X
Tip
W
Rotational
Wmax
Maximum rotational
R
Radius
T
Torque
LS
Low speed
HS
High
s
Slip
Ns
Synchronous
N
Rotational
W
0
Normal
fixed
T
Normal
torque
Normal
power
0
P
0
W
power
W
power
density
Energy
kg
/M3
coefficient
area
speed
Blade
E
W
of
of
blades
M2
ratio
speed
of
blades
speed
blades
rad/s
rad/s
m
Nm
speed
Nm
torque
shaft
shaft
torque
speed
rev/min
speed
inertia
turbine
rating
rating
Nm
reV/min
speed
rad/s
Nm
W
kgM2
Whrs
Fs
Secondary
Fm
Mains
MSB
Most
LSB
Least
Hz
emf frequency
supply
significant
significant
EPROM Electrically
frequency
bit
bit
programmable
Magnetic
flux
B
Magnetic
flux
H
Magnetic
field
Hz
read
only
memory
Wb
density
strength
Wb/M3
A/m
VARIABLE SPEED OPERATION OF WIND TURBINES
D. Goodfellow
ABSTRACT
This work describes
is
a control
system in which a cycloconverter
between the secondary
connected
machine
windings
of a three
phase induction
to give variable
and the a. c. mains supply
speed sub- and super -synchronously
In
secondary
converter
windings
in an asynchronous
to control
the system smoothly
order
has been designed,
emf signal
generator
which enables
in synchronism
to operate
in the
the emf induced
with
of the machine.
mode a
the cyclosecondary
A computer
the required
programme has been written
which calculates
firing
for the cycloconverter
in phase
to produce
angles
secondary
current
An electronic
the secondary
with
emf in the machine.
system has been built
during
that
these firing
which ensures
angles
are used by the cycloconverter
#
actual
operation.
A cycloconverter
has been built,
mains supply,
and has been successfully
synchronous
speed in both generating
Results
show the ability
up from standstill
as a motor
of the
to just
using
an effective
six
operated
over a range
modes.
and motoring
to drive
cycloconverter
below 20% subsynchronous
phases of
of 20% about
the machine
speed.
An on-line
has been developed
computer
simulation
of a wind turbine
to wind
which enables
an assessment
speed generation
applied
of variable
This simulation,
in connection
turbines
to be achieved.
with a d. c. machin
the shaft
and thyristor
controller,
can be used to drive
of the induction
machine and assess operation
of the cycloconverter
control
scheme under
actual
conditions.
wind turbine
operating
CONTENTS
Page
Memorandum
List
of
principal
symbols
Abstract
1.0
2.0
INTRODUCTION
1
1.1
Wind
2
1.2
Alternative
Energy
variable
speed
1.2.1
Alternator
1.2.2
Supersynchronous
1.2.3
Sub-
generation
line
with
techniques
5
inverter
5
induction
5
commutated
recovery
slip
of
operation
and super-synchronous
induction
recovery
generators
1.3
Comparison
1.4
Cycloconverter
1.5
Aims
of
Scherbius
of
slip
6
7
schemes
control
the
generator
8
system
research
9
programme
VARIABLE SPEED WIND ENERGY RECOVERY
11
2.1
Outline
of
12
2.2
Theoret
ical
2-2.1
Steady
2.2.2
Torque
2.3
the
The control
control
strategies
for
basis
state
performance
13
calculations
capture
energy
13
comparison
14
considerations
rating
strategies
15
speed
15
2.3.1
Fixed
2.3.2
Variable
speed
2.3.3
Variable
speed
2.3.4
Fixed
2.3.5
Variable
speed
with
2.3-5.1
Speed
reduction
at
constant
torque
19
2.3-5.2
Speed reduction
at
constant
power
20
2.3-5.3
Control
of
systems
20
2.3-5.4
Torque
rating
speed
pitch
variable
variable
max Cp to
at
fixed
16
pitch
rated
17
power
18
pitch
speed
speed
for
19
reduction
reduction
speed
reduction
systems
22
3.0
2.4
Torque
2.5
Effect
of
2.5.1
Dynamic
2.5.2
Torque
capture
rating/energy
23
25
inertia
25
capture
energy
27
pulsations
2.6
Discussion
27
2.7
Conclusion
29
SLIP
ENERGY RECOVERY USING A CYCLOCONVERTER
30
3.1
Slip
30
3.2
The cycloconverter
3.3
Cycloconverter
3.4
Six
3.5
energy
phase
' Divided
recovery
30
for
Presence
3.7
Stable
energy
of
31
32
33
winding
Generator
3.6
slip
recovery
supply
layer
3.5.1
4.0
results
34
derating
secondary
38
emf
operation
40
CONTROL OF THE CYCLOCONVERTER
42
4.1
The mains
count
45
4.2
The rotor
count
45
4.2.1
Rotor
4.2.2
Synchronising
45
pulses
and rotor
reset
46
47
4.3
The output
4.4
Three
4.5
The EPROM
48
4.6
EPROM page
48
4.7
Output
circuitry
4.8
Firing
circuit
4.9
Gate
4.9.1
4.10
count
47
multiplexing
phase
address
and demultiplexing
drivers
Design
The cycloconverter
49
51
of
the
pulse
transformers
52
53
5.0
6.0
RESULTS
54
5.1
Secondary
emf signal
5.2
Operation
with
page changing
5.2.1
Steady
5.2.2
Dynamic results
5.3
Constant
5.4
Six
5.5
Motoring
5.6
Neutral
5.7
Effect
5.8
Summary
55
generator
56
system
56
results
state
57
59
page operation
62
phase operation
from
63
start-up
63
connection
of
transformer
64
voltage
65
67
CONCLUSIONSAND FURTHERWORK
6.1
Asynchronous
6.2
Output
6.3
Divided
6.4
Six
6.5
Further
6.6
Summary
of slip
operation
waveform
ring
induction
machines
69
69
control
71
winding
71
phase supply
72
work
73
7.0
ACKNOWLEDGEMENTS
75
8.0
REFERENCES
76
9.0
APPENDICES
79
Appendix
A1.1
A1.2
1
Wind
Test
turbine
79
facilities
simulator
A1.1.1
Computer
A1.1.2
Wind
A1.1-3
The rotor
A1.1.4
The electrical
A1.1-5
Computer
Fast
Fourier
79
simulation
turbine
characteristics
dynamics
output
analysis
generator
80
81
81
82
82
83
Appendix
A2.1
2
Thyristor
Programme
control
Flow
A2.1.2
Functions
A2.1-3
Variables
Figures
86
description
A2.1.1
A2.2
84
wave programme
diagram
used in
86
the
88
programme
89
Run time
90
Follow
page
90
1
CHAPTER 1
1.0
Introduction
This
is
thesis
turbines"
as an asynchronous
fixed
proposed
tor
operate
to
be used
energy
wind
removal
of
fluctuations
The
the
power
trolling
torque
system
uses
is
speed
will
is
enable
the
limit
the
This
work
asynchronous
directly
to
speed
has
the
part
each
wind
windings
end of
energy
motoring.
of
its
recovery
the
wind
Variable
system.
energy
capture
from
and
large
the
the
The secondary
the
torque
but
and then
speed
on doubly
the
at
an operis
be
will
and there
which
speed
turbine
fre-
current
characteristic
range,
operating
to
current,
on a variable
cy-
secondary
corresponds
emf and so shaft
operating
by the
The secondary
speed.
operate
by con-
produced
then
which
controls
which
generator
current
a torque-speed
exclusively
can
frequency
changer
sinusoidal
10 Hz,
the
genera-
generation
may result
of
secondary
to
synThe
an induction
greater
an
either
generators.
constant
a frequency
load
a
as
designed
concentrated
to
to
into
systems.
current.
operate
is
at
turbine
secondary
normally
grid
which
machine
generate
speed
speed
problems
synchronous
according
greater
Variable
reasonably
to
enable
of
approximately
to
to
wind
induction
are
an existing
the
of
induction
slip
as
secondary
generator
grid
the
advantages
speed
If
with
phase
controlled
the
to
secondary
+ 207. about
of
mode for
applicable
the
to
characteristic
over
efficiency
fixed
be maintained
be in
torque,
This
with
current.
proportional
bine.
cally
range
to
directly
structural
from
and
to
the
the
be limited
should
controlled
fore
to
to
range.
a cycloconverter
secondary
cloconverter
ating
of
in
the
quency
some
flow
has
conversion
recovery,
recovery
power
fed
energy
as a variable
the
supplying
energy
speed
operation
doubly
a
limited
energy
turbine
a wind
slip
or
slip
speed
of
connected
a variable
operate
converter,
speed
the
to
uses
over
use
generators,
here
variable
using
Generators
speed
system
the
generator,
grid.
chronous
entitled
investigates
arid
established
"The
tur-
wind
its
maximum
automati-
range.
fed
principles
generation
involved
in
an
are
2
1.1
Wind
Energy
Although
day,
it
that
wind
the
reliable
is
cutting
down the
and/or
increasingly
That
the
cost
so the
form
the
is
wind
power
conjunction
energy
in
a future
(ref.
available
of
source
is
varies
wind
It
to
wind
that
c=
scale
parameter
k=
shape
parameter
found
that
in
conditions
with
in
Typical
of
energy
proportional
wind
speed
energy
supplies,
become scarce
will
is
well
to
the
known,
cube
of
its
speed
the
wind
distribution
as a velocity
V
exceeds
distribution
(ref.
W. Europe
mean wind
fuel
agreed
greatly.
"Rayleigh"
the
mean wind
existing
day to
= exp
the
is
a good approximation
2)
= exp
p(V)
=
now generally
which
2
V
Vm
from
energy
Function:
= probability
has been
is
can be expressed
speed
(V)
p
p(V)
It
of
1).
available
a Weibull
of
in
a variable
power
The variation
in
of
basis.
viable
expensive
and as the
speed,
most
as a source
by year
on a year
energy
reliable
not
I
is
varies,
is
wind
4
Vm
speed.
speeds
in
the
U. K.
are
6.5
approximately
7-5m/s
-
(ref
A useful
speed,
hrs/ann,
at
the
multiplied
which
speed
is
which
with
the
the
is
characteristic
probability
by the
turbine
greatest
must
power
operate
potential
the
of
energy
potential
a particular
available
at
at
wind
that
energy
capture.
speed
speed.
maximum efficiency
for
capture
occurring
The wind
should
wind
each
be the
in
speed
wind
3
The type
The power
of
available
A=
swept
V=
wind
tip
area
of
"power
the
radius
blade,
at
torque
is
the
one value
of
the
Cp
against
curves
X
X,
at
optimum
Cp
speed,
can be derived
a fixed
one
over
it
possible
is
for
each
wind
to
speed,
where
A=
But
X=w.
swept
area
of
rotor
the
of
of
for
a
V2
the
should
rotor
wind
produce
as in
blades:
turbine
be possible,
blades
w. R/X
in
the
expression
in
(i)
gives
in
speeds.
torque
curves,
The
Fig-1-3.
(i)
ffR2
pro-
maximum
as follows:
R/V
this
Cp
machine,
It
a range
point
of
blade
the
of
The
speed
speed
efficiency
pitch
windspeed.
the
control
characteristic
the
0.5. p. Cp. A V3
Substituting
to
relation
The theoretical
see Fig. 1.2.
only
to
Fig. 1.1.
Altering
for
so,
aerodynamic
as in
characteristic,
generator,
rotational
the
of
0.59.
is
efficiency
speed
maintain
a measure
against
Cp
for
in
From the
plotted
of
coefficient
maximum
at
to
in
blades
of
limit)
a variable
order
speed
some variation
achieved
for
described
usefully
(rad/s)
blades
and can be plotted
(Betz
maximum
operates
most
X;
ratio
The power
is
by
given
wR/V
R
duces
type.
axis
blades
coefficient",
rotational
the
horizontal
speed
speed
X=
the
density
air
the
is
a turbine
such
using
is
considered
p. CP. V3. A
P=0.5
Cp is
being
turbine
4
p. Cp. A. V. w2.
P=0.5.
T=
and
which
If
torque
gives
the
V
remaining
for
w
vs
by
replaced
w. R/X
0.5. p. Cp. A . W2 R
then
T=0.5.
3/X3
Cp
any given
and its
P. A. R
3.
(CP/X3).
X
associated
W2
this
becomes
equation
K W2
so
is
CP " CPmax
for
in
shown
ating
this
1-3
Fig.
torque
strategy
for
incident
The
loading
In
is
torque
this
2
case
21 m/s.
Note
in
For
turbine
line
wind
that
load
could
be
the
point
the
points
turbine
is
s,
Cp
of
wind
operate
at
a wind
be prevented
from
exceeding
system.
speed
only.
up
reaching
its
optimum
Cp
at
maximum power
(in
at
,
its
e. g.
the
at
fluctu-
problems.
the
torque
a wind
is
However
for
rotational
mode the
speed
variable
at
c
sudden
stability
it
its
down to
produce
upon
7 m/s
(16 m/s)
for
and
,
b
point
example,
achieved.
control
move
exclusively
being
system
simply
in
speed
this
would
dynamic
For
xy).
an oper-
torque
8
!-- m/s
efficiency
the
and
upon
In
rotational
velocity
is
maximum
must
(line
max Cp
corresponding
of
to
of
to
decreases,
torque
may produce
which
of
Fig. 1.4,
decide
generator.
load
be reached
increases
controlled
to
operating
the
the
as an input
speed
would
optimization
absolute
by
be drawn,
can
to
possible
generator
a wind
curve
a function
as
speed
sudden
torque,
blades
as shown in
to
is
required
the
MW) and torque
.5
increasing
ations
not
mode
speed
further
curve.
controlled
corresponding
a,
Cp"
the
of
is
torque-speed
it
form
the
of
1
law
derived
curves
speed
and down a vertical,
point
"Max
loading
wind
a fixed
square
the
as
From the
the
these
becomes
this
can be written
which
For
2/X2
V.
varying
is
term
(ii)
P/w
p. Cp. A. V. w. R
T=0.5.
so
2/X2
R
curve
speed
At
t.
point
large
5m/s
of
wind
speed
both
speeds
limit.
5
The control
schemes
outlined
the
until
torque-speed
fixed
speed
this
over
stability
problems
for
reasons
of
operation
this
the
which
associated
of
use
the
reached,
turbine
to
has been
found
fixed
at
a low
to
speed
curve
the
point
in
a virtually
characteristic
induction
slip
(ref.
operation
gener-
dynamic
the
remove
discussed
are
torque
which
speed
two
the
of
max Cp
operate
torque
with
strategy
a combination
on the
operation
with
this
nearly
The steep
to
corresponds
a mode of
ator,
forces
scheme
is
thesis
operates
is
1.5.
Fig.
see
mode,
period
limit
speed
control
this
The turbine
above.
rotational
in
used
method
4).
more fully
The
Chapter
in
2
thesis.
There
to
energy
a number
are
techniques
of
frequency
a constant
grid
may be used
that
using
system
to
variable
recover
wind
turbine
speed
operation.
1.2
Alternative
1.2.1.
this
give
a line
commutated
inverter.
in
Orkney
Islands,
system
has
to
rectified
the
Orkney
link
The power
i. e.
the
during
transient
devices
output
power
must
of
the
the
alternator
to
the
grid
being
operated
speed
range
is
This
continuous
of
technique
current
be rated
at
and the
an expensive
failure
and commutation
the
250 kW
possible,
in
the
alternator
by
system
at
requires
disturbances
is
mains
in
supply.
ratings,
power
turbine.
Supersynchronous-slip-recovery-induction-generator
1.2.2.
A cage
However,
using
A wide
range.
output
is
Such a system
maintain
electronic
the
transferred
and power
(ref-5).
can occur
total
link,
a 50% speed
to
choke
inverter
Fig. 1.6a
scheme as shown in
a d. c.
the
Techniques
An_alternator_with_line_commutated_inverter
In
d. c.
Speed Generation
I
Variable
the
the
induction
speed
Kramer
machine
range
system
is
of
generates
limited.
slip
energy
when
driven
An extended
recovery
supersynchronously.
speed
shown
in
is
possible
Fig. 1.6b.
This
range
6
requires
a slip
same technique
is
power
square
in
wave currents
a high
they
are
harmonic
back
one
direction,
into
twice
the
increase
1.2-3.
stator
speed
bridge
to
rotor
will
the
in
allow
the
by the
waveforms
machine,
harmonics
only
same
and the
These
of
equal
the
quasi-
the
also
power
flow
power
supersynchronous
voltages
be limited
will
by producing
rating
only
from
slip
failure
generator.
the
the
only
suffers
and produce
system
the
speed
case
commutation
torque
the
of
The diode
the
this
by the
recovered
in
generation.
rated
and
voltage
breakdown
winding
6).
(ref.
voltage,
the
limits
in
the
and so reduce
supply.
which
i. e.
above,
controls
into
in
The system
secondary
content
synchronous
further
the
back
reflected
fed
1.2.1.
system
being
energy
electronics.
The system
a choke.
have
At
as the
slip
However
above.
by the
controlled
for
1.2.1.
as in
disadvantages
need
machine
ring
the
with
Sub--and-super-synchronous-operation-of-slip-recovery-induction
generators
For
both
operation
be able
scheme must
recovery
secondary
(i)
two
secondary
in
in
Fig.
The inverter
quasi-square
the
(ii)
In
is
the
a slip
super-synchronously
control
flow
power
both
to
energy
and from
the
scheme and can be implemented
Scherbius
1.2.2.
system
1.6c,
currents
d. c.
choke
in
to
is
range
is
the
smooth
from
link
flow
to
to
standstill
thyristors
secondary
the
power
1.2.2.
scheme
by a current
replaced
which
6 extra
inverter.
commutated
enables
As in
wave
and line
inverter
requires
capacitors.
commutating
to
The speed
windings.
ous speed.
requires
source
bridge
as shown
and
ways:
Current
The diode
inverter,
This
windings.
in
statically
sub-
of
or
twice
the
the
generator,
from
associated
produces
and
also
7).
Cycloconverter
this
method,
shown in
Fig. 1.6d,
the
two
converters
the
synchron-
inverter
above,
current,
to
and the
(ref.
source
are
replaced
7
by a cycloconverter
ary
the
of
the
is
erator
quality
limited
the
derived
are
from
synchronous
1.3
Comparison
current
may be impossible
circuit,
inverter
a more
The
inverter,
energy
fully
is
inverter
its
link
have
scheme
merely
speed
six
the
of
by the
deterioration
great
by using
supply
+ 20% about
is
a maximum frequency
more
of
phases
range
gen-
1OHz
of
8).
(ref.
,
can
synchronous
the
utilise
this
speed,
than
the
operate
due to
range
lead
may not
207. limited
a+
from
generator
range,
and
dynamic
turbine
wind
to
quasi-square
current,
for
inverter
schemes,
one simple
to
commutate
does
in
the
circuits.
power
the
in
the
secondary
cycloconverter
not
result
is
will
during
occur
those
pro-
relatively
control
system
in
Obviously
high
inverter,
fault
an orderly
but
these
commutated,
currents
restart
are
the
to a large
to
smooth
outage.
indiviThe eon-
as there
whereas
applied
naturally
mains
an inverter.
complex,
each
also
for
commutated
choke
a possible
thyristors
required
a force
a large
and also
one for
is
requiring
system,
more power
than
The cycloconverter
devices.
currents
whereas
capacitors,
demands
rating
requires
complex
and problems'
a lower
control
content,
a more
associated
the
wave
current.
The cycloconverter
different
operating
capture
harmonic
sinusoidal
with
d.
D.
trol
system
inverter
source
produces
a high
with
dually
too
without
will
problems.
The
the
range
can be supplied
that
second-
Systems
twice
to
the
cycloconverter
The speed
this
to
Scherbius
of
greater
instability
In
and the
grid,
the
can be improved
quality
supply.
approximately
a significantly
duce
This
in
currents
across
windings
corresponding
the
to
standstill
secondary
mains
the
speed,
Although
it
the
of
ratio
maximum frequency
quality.
phases
sinusoidal
produced.
waveform
by the
waveform
effective
of
into
cycloconverter
of
The frequency
generator.
determine
near
produces
which
two
cycloconverter
number of
but
and therefore
procedure
a failure
no failure
should
be
8
designed
into
turbines
wind
These
Up to
the
slip
it
1.4
smooth
produced
This
developed
disc
fitted
with
a frequency
only
initially
misreading
waves
ate
at
a fixed
altered,
angles
which
were
all
two
turbines.
the
of
a six-phase
rotor
system
subject
to
current
mal-operation,
retard
current
to
of
which
blanking
and introduced
produced
the
square
attempt
a short
to
a delay
but
in
square
square
prone,
was complex
need
operbe
firing
waves
secondary
occurring
the
or
phase
as the
the
are
due to
losing
to
produce
circuit
This
was
wave could
due to
cycloconverters
techniques.
due to
angles,
frequency
system
cycloconverter
was distorted
output
the
the
firing
only
The problem
supply,
of
on a
this
no longer
only
emf.
device
errors
a signal
which
secondary
However,
allowed
could
generator,
and comparing
of
Previous
needed.
by an optical
generator
the
is
as the
supply.
The amplitude
the
avoided
static
frequency
the
of
emf signal
produced
only
or
by electronic
experience
of
cycloconverter
windings
machine,
mains
which
advance
mains
the
signal
would
of
the
and phase
the
angle.
phases
in
scanned
which
firing
winding.
lack
the
knowledge
secondary
of
the
Also,
equal,
generators.
range.
and an accumulation
frequency,
the
use
cycloconverter
occur,
emf.
in
emf present
wind
pulses
from
The actual
current.
ween
the
could
slip
to
emf induced
synchronised,
the
at
applied
same frequency
derived
induced
the
with
to
pulses
due to
the
by counting
was achieved
only
an electronic
the
of
is
this
machines.
System
of
secondary
a signal
slotted
speed
features
induction
use of
synchronous
11)
Control
control
the
(ref-7)
work
variable
and certain
used
20% speed
a+
Cycloconverter
of
(ref.
operation
with
have
turbines
wind
investigates
system
and phase
use with
9),
demand the
techniques
appear
thesis
For
of
most
machine
This
(ref.
and built
proposed
recovery
would
induction
Scherbius
been
for
10).
present
However,
Cycloconverters
equipment.
have
(ref.
analysed
of
the
for
betwas
and
9
detection
of
converters
zero
are
limited
speed
current.
designed
not
i. e.
range,
standstill
as a motor.
1.5
of
Aims
for
system
control
operation
as
for
strategies
The disadvantages
schemes
are
(i)
into
of
(ii)
By using
a divided
lost
of
or
from
tained
to
required
(iii)
is
used
to
ifmodified
to
cosine
produce
a variable
start
to
The use
up as a motor,
accept
current
in
the
starting
speed
of
in
wind
a divided
from
standstill,
current.
phase
with
such
energy
winding
control
first
secondary,
thyristors
is
supplies
prevented.
which
The
emf.
secondary
by a technique
the
contain
the
with
six
phases
into
the
fire
to
used
in
various
assessed.
The waveforms
to
with
phase
are
has been developed
actual
waveforms
technique
voltage
revolution.
cycloconverter,
The
and n-group
has been overcome
current
as a generator
capture
the
with
shaft
current
for
(iv)
phase
sinusoidal
system
Scherbius
generator
motor
p-group
can be programmed
crossing"
the
the
generator
sinusoidal
operate
the
conversion
on the
emf signal
pulses
smoother
provide
from
techniques:
between
rotor
an EPROM which
A 36 element
machine
converter.
induction
circuit
in
per
energy
winding
and firing
misreading
produce
cyclotheir
investigate
energy
following
the
a short
twice
resynchronising
wind
speed
layer
12),
locked
waveforms
the
using
beyond
operation
start
to
wind
variable
of
is
work
speed
previous
windings,
do not
speed
variable
A new secondary
produces
problem
research
by use
separate
any mode of
normally
a variable
(ref.
techniques
recovery
Programme
overcome
by Holmes
proposed
they
this
aim of
energy
have
to
Research
the
The main
Slip
the
the
a way as to
are
ob-
waveforms
emf.
secondary
mains
of
supply
secondary,
thyristors
secondary
of
emf,
optimise
and a
in
order
to
and also
the
energy
converter.
secondary
providing
the
enables
thyristors
the
system
are
to
rated
10
(v)
speed
An assessment
wind
designs,
idea
of
the
and this
of
strategy
problems
control
has been
conversion
A control
programme.
useful
energy
the
which
was implemented
achieved
was devised
may have
in
the
to
a computer
with
which
for
possible
strategies
would
be overcome
cycloconverter
provide
for
control
variable
simulation
the
most
future
scheme.
11
CHAPTER 2
2.0
Variable
The recovery
here,
gated
may be
to
rotational
speed
electronic
techniques
running
to
restricted
relative
system
The existing
rotational
speed.
rotational
speed
This
mode.
system
systems
such
limit
A small
turbine
loss
grid
of
which
approximately
involve
the
scope
parameters
will
have
been
limit
the
also
are
schemes
be
outlined
dually
be
may
optimised
energy
captures
and
methods
of
control
of
of
by
designed
There
could
of
Similarly
the
variable
a fixed
any
of
of
each
be useful
the
rotor
Cp
system
to
utilise
counteract
under
its
speed
rotational
turbine
rotor
which
system,
but
and stress
the
characteristic
may
control
and
indivi-
The-relative
curve.
will
certain
15,16)
wear
Nevertheless
speed.
to
speed
speed
variable
(refs.
considerations
give
or
a
speed
been variable
speed
operating
to
fixed
its
to
increase
and
itself
overspeed
have
to
allowed
assessed.
restrict
allowed
to
stra-
maximum torque
the
been
is
are
which
has been
The
operating
of
general
and
speed.
turbines
set
are
is
here
advantages
for
variation
investigated
in
of
work.
applicable
complexities
which
this
standstill
tuPbine
normal
optimised
advantages
will
rotor
between
the
that
structural
beyond
which
in
overspeed
its
twice
investigations
will
connection).
the
vary
wind
it
a variable
There
different
limits
1.1),
system.
several
have
constant
grid
of
the
have
will
use of
operating
existing
to
the
the
turbine.
a wind
normal
will
comparable
above
of
investi-
(Section
about
investigation
limit
in
proposed
to
speed
the
(e. g.
conditions
This
produce.
but
gusting,
turbines
wind
may necessarily
will
to
applied
due to
being
system
and disadvantages
this
using
the
+ 20%
approximately
advantages
tegies
but
speed,
speed,
concern
to the
connected
.1
the speed to
allow
which
which
speed
here
is
system,
outlined
rotational
investigated
turbine
wind
grid
generator
reasons
the
vary
being
the
a fixed
From the
advantageous
normal
into
energy
implies
frequency.
The systems
twice
wind
of
generally
50 Hz grid
Recovery
Speed Wind Energy
some
investigate
idea
of
the
further.
12
Some benefits
of
speed
variable
are
operation
generally
to
assumed
be:
increased
(ii)
reduced
stressing
(iii)
greater
operational
These
benefits
are
components,
of
flexibility.
for
assessed
sys. tem which
speed
variable
capture,
energy
will
five
operating
+ 207.
allow
for
strategies
variation
about
a
synchronous
speed.
2.1
Outline
the
of
When turbines
inertia
system
behaviour.
as
tion
the
the
of
maximum
account
variable
it
to
when considering
slip
speed
reference
is
the
energy
to
necessary
torque
the
effect
the
dynamic
systems
speed
can be derived
characteristics
for
curves
Cp
control
the
consider
of
torque
opera-
characteristics
from
the
Power
methods
a range
of
Cp
curve
by pitch
are
considered
(b)
Variable
speed
variable
(c)
Variable
speed
at
Note
that
variable
(c)
mode
methods
limitation
are
in
and shown in
groups:
Fig. 2-3.
(FSVP)
pitch
max Cp to
the
two
control.
angle
pitch
exceeds
(VSVP)
power
speed
(MaxCp)
rating
rating
of
the
by stalling.
considered
Fig. 2.2, with
shown in
are
4
limitation
speed
Three
speeds
can be considered
Fixed
Power
wind
strategies
(a)
(ii)
of
indicated.
curve
The control
Three
into
speed
Fig. 2.1).
The torque
the
rotational
variable
Therefore
with
These
turbine.
in
the
speed.
system
with
be taken
Further,
of
strategies
operate
must
a function
(shown
control
and shown
in
Fig. 2.4.
other
systems.
13
(a)
Fixed
(b)
Variable
(c)
Variable
Note
that
fixed
speed
speed
speed
with
speed
(c)
pitch
with
speed
(FSFP)
the
exceeds
reduction
at
reduction
constant
at
constant
limit
torque
continuous
(CTSR)
torque
(CPSR)
power
the
of
other
systems.
2.2
Theoretical
Basis
2.2.1
Steady-state-energy-capture-calculations
The energy
for
point
lating
this
the
number
results
hours
turbine
wind
speed.
the
Watts
range
of
by the
obtained
Comparisons
been
calculated
instantly
wind
wind
operating
are
that
The. wind
Summing
speed.
the
gives
of
number
a Rayleigh
is
model
by calcu-
and multiplying
occurs,
speeds
operating
obtained
wind
state
steady
its
achieves
speed
at
obtained
turbine.
under
The results
a particular
in
power
over
the
hours
of
by the
value
Watt
that
any particular
the
have
figures
capture
assuming
conditions,
Performance
for
distri-
bution:
p( > V)
p( >V)
where
and
speed
the
E= exp
probability
4( Vm
the
that
V)1
wind
speed
V
exceeds
Vm = Vmean.
The
ical
is
Tr
2
power
in
this
given
by
Vmean
used
output
is
the
mode of
been made for
The electrical
equation,
in
given
a
thesis
the
40 m
output
as the
turbine
radius
of
the
torque
being
operation
with
of
the
speed
These
an electrical
calculated
with
MOD-2 system
2.5 Mw):
Pe(V)
(20 mph)
.
x rotational
considered.
is
turbine
efficiency
8.94 m/s
is
0.97.
Pm(V)
10'
55
x
=
-
The mechan-
for
each
wind
have
comparisons
rating
the
(which
of
2.5 MW
following
is
rated
at
-
14
where
The
total
Pe(V)
= electrical
power
at
wind
speed
V
Pm(V)
= mechanical
power
at
wind
speed
V
energy
captured
per
is
annum
by
given
following
the
v
oPe(V).
Ef
'8766 d(V)
p(V).
Whrs/annum
V.
1
cut-in
v0=
wind
cut-out
8766
The
from
energy
Most
mode of
The
this
Curves
were
regime
this
(see
for
and
-1
fixed
are
speed
as the
was used
for
speed
based
were
case
was
datum
for
chosen
to
Cp
above),
curve,
Torque-rating-consideration-for-variable-speed-operation
to
determine
the
consideration
developed
torques
this
R=
rating
also
a figure
for
rapid
ramping
wind
speed
with
modes.
other
for
capture
energy
The calcula-
rating.
of
the
energy
at
the
generator
it
recovery
for
is
important
different
operating
0
The torque
or
and so this
.
modes.
and
(as
angle
machines
the
optimise
and power
1.8 rad/s
be
to
speed
to
pitch
pitch
comparison
2.2.2
addition
derived
curves
degrees
variable
showed
In
on
-4
tions
this
Cp
used.
turbines
operation
wind
calculations
system.
wind
fixed
speed
capture
Fig. 2-5)
shown in
(30 m/s)
hours/year.
of
Nibe
the
speed
wind
number
=
(5 m/s)
systems
analysis
45 m, J=
under
the
28.2
for
inertia
x
maximum
conditions
a figure
an
normal
106
the
of
kgM2).
operating
intermittent
occurring
inertia
22.5
x 106
of
is
conditions
torque
seen
at
rated
power.
the
blade
system
kgM2
is
used
(c. f.
calculated,
due
to
For
is
gusting
the
variable
required,
Boeing
MOD2,
in
15
The gust
as an estimation
"1-cosine"
from
if
equation
this
was. not
angle
2.3
The Control
of
pitch
Compared
energy
control
type
of
the
with
a higher
wind
limited
figure).
or
usually
a hydraulic
through
the
rate
power
tinuous
shaft
at
the
which
there
rating
is
pitch
in
the
analysis;
was used.
turbine
2-3
in
with
limitation
or
and 2.4)
is
part
operating
at
a
for
ratings
2.1
Tables
each
and 2.2.
which
The extra
can
the
operate
energy
the
a higher
at
CPmax
the
at
slip
see Fig. 2.6a.
even
mechanism
control
increases
blade,
power
low
or
by altering
achieved
bring
will
available
pitch
a synchronous
the
of
this
system
strategy
for
wind
speed
incident
weakness
was used
long
speeds
wind
on the
r
for
capture
up to
point
higher
(point
rotational
this
method
over
system.
torque,
at
fixed
technique
The control
ical
as
calculated
can suppress
and torque
given
operates
blade
whole
2.5 MW by the
pitch
figures
are
generator
speed.
This
fixed
are
a system
period
Nibe
modelled
(FSVP)
The power
Figs.
to
If
the
capture
strategies
wind
the
either
(compare
speed,
the
state
generator.
of
amplitudes
duration
for
Fixed_speed_variable_pitch
induction
are
10 seconds
of
data
The gusts
recommended
Strategies
following
This
is
the
(14),
degree.
-1
The steady
2.3.1
and the
reference.
a gust
uses
patterns.
2 seconds
ref.
from
obtained
speed,
the
of
possible
pitch
the
in
a gust
analysis
gust
wind
given
then
gusts
This
of
in
excursions
the
period
discrete
of
been
have
parameters
system
hub.
the
pitch
as its
requiring
Partial
pivoted
pýitch
gusting.
of
The pitch
input.
connections
blade
angle
can
both
along
control
There
deploy.
torque
The Pitch
have
can either
operation
connection.
mechanism
a possibility
due to
the
will
is
mechanism
the
also
blade
implies
itself
and
a mechan-
be a maximum operating
During
operation
and power
exceeding
mechanism
power,
may be fast
at
their
rated
con-
enough
to
16
limit
the
but
limit
limit
to
not
gusting
the
will
The load
time
period
gust
torque
pulsations
in
erator,
developed
the
degree.
upon
generator
by the
These
have
generators
rated
running
2.3.2
Variable_speed_variable_pitch_(VSVP)
is
In
this
of
the
in
shown
a range
also
of
speed
for
torque
fixed
will
produce
region
The
operating
torque
damping
torque
below
control
point
that
and
rated
system
allows
the
wind
can
this
slip
a greater
loads
as
used
system
speed
which
at
are
70
torque
the
which
lesser
or
which
operate
50 MNm/
and
both
speed
with
a
the
increase
the
to
However,
fluctuations
for
this
at
set
the
Cp over
maximum
fixed
speed
scheme will
control
mimic
will
is
characteristic
achieves
which
the
speed
generator.
Power
equal
increase
The torque-speed
wind
gradient
at
must
respectively,
Thereafter
s).
the
speed
maximum rotational
above.
the
The gradient
torque
just
up to
that
of
to
gen-
.
the
system
(point
Cp
max
machine.
some
.5
shaft
simply
generators
MNm
and shows
speeds
vertical
slip
operation
speed
Fig. 2.6b,
wind
2
of
mode of
attains
an almost
and high
a synchronous
and low
blades
longer
the
smooth
slip
amounts
modelled
for
high
The gradients
curves.
for
speed
low
been
rads-1
the
with
seen by the
excursion
torque-speed
steep
limited
allow
speed
second
that
implies
rise,
low
the
at
a2
assumed
with
to
mechanism.
of
to
gusting,
control
control
be able
to
Operation
wind.
is
will
allowed
angle
effect
Operation
measured
will
torque
not
the
It
power.
blades.
is
speed
generators
limit
will
the
which
from
mechanism
pitch
on the
wear
obtained
ramp rate
Blade
gusting.
the
rated
by the
seen
by the
induction
at
variable
developed
torque
is
rating
occurring
the
gusts
increase
greatly
by low
produced
rapid
of
effects
torque
period
fluctuations
torque
excess
action
occur
produce
a fixed
of
and so provides
inevitably,
steep
system
gusting
torque
operating
speed.
maintain
and so some of
the
the
torque
steep
torque
produced
curve
by gusting
above
wind
the
rated
conditions
17
be absorbed
can
increases.
speed
be
can
During
of
increase
inertia
of
rated
in
the
be used
to
The
give
so large
is
a2
second
in
characteristic
the
torque
gust
the
speed
2.2.
If
period
here,
increase
variable
pitch
this
be of
the
be held
does not
then
to
with
presented
can simply
the
gusts
have
would
excessive
case
line
torque
increase
torque
the
speed
has a limited
this
of
that
Table
long
of
gradient
In
as the
energy
which
a large
either
vice-versa.
suppression
prevent
at
not
were
electronically
some definite
gradient
increase.
speed
Variable-speed-at-max-Cp-to-rated-power-(MaxCp)
2.6b
ý previously,
maximum
This
the
generator
torque
maximum
not
speed
be achieved
where
its
reaches
the
calculations
power
is
is
stalls
completely,
speeds
again
speed.
As
this
the
turbine
to
the
case
control
to
have
to
its
For
produce
maintain
rated
to
to
restrict
system
(see
1.8
continues
and the
rad/s
limitation
the
at
and
maximum
a further
to
provide
at
power
Cp
the
until
30 m/s
set
capture
energy
power
V>
the
could
limit.
new speed
Cp
speed
Fig. 2.6c).
maximum speed
power
corresponding
action
the
simpler
increasing
Gust
maximum
at
diagram.
to
assumed
A much
at
simplified.
due to
changes,
continue
beyond
characteristic
speed
limit.
range
1.8 rad/s
to
thesis
maximum power
speed
operating
on
aerodynamic
generator
speed
need
and then
reached,
require
the
is,
system
maximum
curve
scheme outlined
has abrupt
operate
greatly
this
torque
the
this
are
P
point
to
pitch
of
the
seen,
reached
therefore
blades
in
be
purposes
pseudo-fixed
extending
would
limit,
can
it
until
characteristic
the
the
allow
the
require
system
speed
line
by merely
This
rated
be to
Cp
for
exceeding
variable
speed
have
would
not
of
scheme would
would
As
speed.
requirement
on the
variable
was limited,
rotational
control
the
shows
which
upon which
the
or
and for
for
Figure
the
speed
torque
order
2.3.3
to
stored
mechanism
pitch
operating.
as can be seen
controlled
in
also
turbine
value
excessively,
to
is
rotational
the
time
electronically
small
the
this
response
set
in
as an increase
-
until
blade
High
wind
increase
in
operation
18
CPmax
the
along
and control
limited,
the
the
maintains
than
the
and
method
as the
the
fixed
If
for
a
of
2.3.4
the
and
mode of
the
so
at
system
is
these
tip
be used
to
spoiling
prevent
over-
may now be available
as an input
measurement
for
criterion
of
to
variable
wind
power
or
speed
a2s
for
is
low
a
shown
point
and the
means
that
for
low
a
wind
speed.
system
is
is
a particular
used
the
gusting
is
gusting
torque
be
calculated
must
rating
may be able
system
for
shown
is
r. egion
to
comparison.
an extension
simply
induction
(the
rated
on small
either
connected
generator.
These
CPmax
at
at
naturally
only
the
range
of
distance
wind
the
speed,
energy
turbines
characteristic
speeds
between
on the
the
capture
due to
its
of
this
simplicity,
is
power
this
used
CPmax
the
This
figure).
CPmax
The
speed.
for
Cp
s-r
a syn-
essentially
characteristic
broad
wind
one wind
to
and so rated
stalls
The torque-speed
a large
limits
is
turbine
Due to
point
This
figure
blade
speed.
Fig. 2-7a.
stalling
widely
slip
as the
there
systems
the
operating
reached
in
gust
the
(FSFP)
one wind
only
torque
governing
speed
operation
or
load
the
limiting
of
curve.
constant,
speed
rating
control
of
are
possibilities
can be used
no method
then
CPmax
generator,
occurs
in
is
there
characteristic
law
this
produced
form
techniques
simpler
conventional
Fixed_speed_fixed_pitch
chronous
power
that
gusts
square
In
hold
more
However
The torque-speed
the
the
gust.
these
suppress
is
speed
torque
be a much more effective
would
aerodynamically
10 s
initiate
to
systems.
we assume
fluctuations
the
may already
turbine
the
of
This
system.
than
These
cases).
speed
speed
as the
be a simpler
and
(which
flaps
operated
limiting
that
could
techniques,
mentioned
rotational
power
As long
ensure
limitation
power
emergency
control
can be used
speed
method.
will
control
of
centrifugally
in
braking
in
2.5 MW
at
previously
speeding
in
electronic
increase
the
aerodynamic
power
This
then
curve
achieved
system.
at
This
requiring
19
no control
scheme.
In
stall
this
regulation
torque
at
gusting
The
at
rated
at
the
study
rated
evaluation
rated
due to
this
phenomenon
of
Extra
r).
power,
was set
The load
power.
(point
power
speed
rotational
the
is,
limit
torque
is
to
then
for
taken
however,
blade
the
beyond
the
provide
the
may be produced
torque
time
1.45 rad/s
at
during
to
rapid
stall.
scope
this
of
thesis.
2.3.5
Variable_speed_with_speed_reduction
It
is
variable
speed
consequent
the
variable
of
an operating
still
torque
must
reached
at
with
wind
speeds.
pitch
the
rotor
speed.
constant
torque,
with
be achieved
this
method
system
described
control
control,
must
for
limit
power
scheme a
angle
system
and the
torque,
reduced
This
control
is
blade
blades.
high
the
speed
variable
Speed
of
to
must
try
must
and speed
is
the
same
2.3.2.
detected,
is
scheme
by
Section
in
Two systems
either
to
obtain
investigated
are
reduction
with
(point
point
provide
at
operating
produced
its
on the
a torque
For
x) .
point
operating
In
y.
a greater
wind
the
that
an increase
to
is
torque
maximum rotational
shaft
by the
exceeding
this
wind
value
in
speed,
is
than
wind
the
i. e.
order
blade
turbine
1.8 rad/s
reduce
a
to
torque,
slow down,
t9*
to
at
speed
rated
at
and the
shown at
in
reached
turbine
14 mls
at
is
be obtained
make the
(loading)
speed
limit
power
could
order
(CTSR)
torque
constant
can be seen
When the
torque.
provide
it
speed
a reduced
at
reduction
12.5 m/s
corresponding
ating)
for
for
need
operating
power.
speed
generator
speed
or
From Fig. 2-7b
14 m/s,
of
speed
reduction
2.3-5.1
wind
the
cost
electrical
the
avoid
power
point
speed
constant.
wind
maximum speed
measurement
here;
the
rotational
rated
When the
could
in
Below
as for
by
system
saving
the
reducing
by a suitable
that
possible
the
(acceleris
the
,
The generator
the
turbine
20
speed.
The amount
of
extra
at
the
is
required
which
system
torque
required
to
depend
would
down and reach
slow
the
upon
its
rate
new operating
point.
The turbine
decreasing
15 m/s,
would
would
increasing
with
and then
after
to
require
its
speed
limit
in
wind
speed
the
generator,
all
during
rated
power.
than
to
ponds
scheme would
reduce
same
it
energy
would
power.
as
dynamic
under
for
(i)
In
point
x
the
control
problems
gusting
outlined
with
rapid
and
two
case,
2.8,
Fig.
on
of
wind
12.5m/s
to
(point
further
it
z),
reach-
increase
induction
slip
down
to
For
v.
iý
generator
producing
(CPSR)
way to
the
system
Fig. 2-7c,
as shown in
terms,
capture
energy
speed
eventually
a low
the
pitch
rating
at
except
which
corres-
produce
the
However
system.
z'
above,
.
systems
systems
knowledge
attempting
with
ramping
"worst
Positive
this
associated
For
phase
(requiring
scheme
x) .
x
reduction
speed
speed,
from
torque
of speed reduction
the
wind
its
with
15 mls
at
variable
speed
continuous
from
power
line
state
steady
a variable
a higher
A disadvantage
the
in
speeds
mimic
a similar
rated
Control
of
in
at
require
complexity
constant
a torque
capture
2.3.5.3
at
along
scheme would,
line
reduction
speed
operation
This
s-peed
operate
in
(point
a vertical
Speed reduction
This
would
the
line
point
be made to
could
to
wind
an increase
at
generator
speeds
2.3-5.2
it
again
for
stall
26 m/s
torque
constant
speed
the
up for
corresponding
wind
less
wind
reaching
speed
ing
on the
operate
speed
to
would
of
be both
wind
speed)
the
control
and
turbine
These
conditions.
the
can
be
cases":
gusting
at
rated
to
corresponding
the
gust
will
power,
a gust
produce
average
occurring
an increase
wind
during
in
speed
12
m/s
.5
-
operation
the
torque
at
21
by the
produced
to
point
wind
This
tor.
If,
after
can be achieved
time
a certain
can
begin
to
greater
than
the
shaft
This
problem
complex,
(ii)
torque
control
(point
20 m/s
duces
to
torque,
load
shed
blades.
in
this
the
shaft
reduction
torque
torque
is
This
is
used
difficult
the
drop
in
the
torque
by
the
steeper
low,
due to
is
blades
line
past
that
to
genera-
then
the
a torque
applying
using
a suitable,
speed
wind
than
to
the
fall
the
the
torque
used
have
to
the
wind,
away.
torque-speed
pro-
some
speed
small
as this
system
must
generator
by the
by the
to
generator
blades
drive
torque-speed
could
above
be
gust
control
produced
point.
allow
speed
produced
torque
stalling
(i)
example
the
this
steep
in
for
and so a decelerating
extremely
by the
produced
achieve
mode,
reduction
wind
and may require
their
,
condition,
as the
the
would
16 m/s
blades,
speeds
phase).
speed
power
this
wind
reduction
a positive
than
initially
would
in
less
achieve,
be very
procedure
the
is
to
This
but
produced
which
and to
the
torque-speed
gusting,
In
that
A similar
the
subsided,
average
than
the
instance.
such
could
constant
from
up,
of
allow
rise
wind.
speed
point,
excursion
for
the
greater
this
at
speed
around.
by
at
power,
the
is
speed
wind
to
characteristic
steep
in
operation
g2
condition
the
characteristic.
has not
as outlined
(during
turbine
the
requires
by the
rated
at
16 m/s
torque
point
that
induction
slip
torque-speed
speed
the
system.
y on Fig. 2.8)
a negative
the
reduce
e. g.
reduce
could
a low
speed
be controlled
gusting
the
where
wind
produced
then
can
we consider
a point
to
system
of
a steep
the
to
attempt
scheme may assume
operation
period,
exceeding
at
the
must
and the
gust
torque,
accelerating
control
by using
attempt
Positive
If
to
similar
control
thýugh
the
a temporary
only
increase,
to
speed
is
speed
however,
Initially,
speed.
a net
and so provide
The generator,
g1
rotational
in
blades
to
be used,
drop
to
prevent
would
cause
A torque-speed
line
characteristic
of
i. e.
react
to
even
more
the
must
the
a
be
turbine
22
in
to
order
effectively
the
torques
this
overcome
problem.
is
generator
during
This
applying
suddenly
fluctuations,
wind
be so steep
would
which
could
speed
of
and
removing
cause
control
as to
imply
very
large
that
and stability
problems.
The problem
increasing
wind
for
strategy
requiring
speed
the
operating
in
to
order
in
and
apply
large
the
torques,
fluctuations
It
in
to
it
by shutting
either
ation
to
In
the
these
cases
2.3-5.4
For
gusts
the
in
increase
must
increase,
in
which
largest
loading
speed,
when the
the
been
blades
chosen
MOD2 test
for
the
too
case
torques
the
will
generator
provide
as a2
analysis,
in
m/s
ref
as
turbine
will
during
occur
to
slow
the
turbine
(13),
in
though
wind
it
to
a rapid
blades
increase
torque
have
the
produced
the
into
a ramp
down again.
ramp
increase
be noted
in
The worst
as used
that
The
wind
torque
a greater
2s,
an
speed
slow
down.
in
by wind
by allowing
systems
with
speed
must
this
2-7).
on Fig.
may resolve
load
by oper-
or
drastically.
reduction
must
order
drop
area,
than
greater
z
problems
systems
the
"gust"
the
also
these
16 m/s
point
would
speed
remove
and
problem
can be suppressed
the
as
at
reduction
generator
great
speeds
systems
in
the
over
wind
held
opera-
rapidly
overcome
exceeds
for
speed
to
problem
speed
figures
capture
However,
be
wind
removed
or
grid.
completely
operate
machine
reduction
at
power
not
to
speed
rating
to
way
only
turbine
energy
speed.
increase
the
the
the
During
point.
a dynamic
to
supplied
a rotational
non-speed
rated
at
power
complex,
determine
may be necessary
produce
will
The control
be applied
must
a new operating
which
speed
Torque
torques
it
down when the
as a pseudo-fixed
(corresponding
to
to
order
during
a turbine
be necessarily
in
speed
loading
move
the
allow
wind
of
obvious.
will
conditions
the
that
seem
would
be not
would
turbine
wind
these
of
rotation
intuitively
systems
Large
point.
make
is
reduction
knowledge
fluctuating
tion
conditions
speed
accurate
required
the
reducing
of
in
the
than
case
in
has
a
event
of
23
increases
braking
operating
the
constant
the
wind
duty
though
2.4
power
750 kNm
be
will
it
incur
Rating/Energy
The energy
derived
from
to
refers
the
the
effects
of
Fig. 2-5).
NIBE4
the
state
This
occurs).
Nibe
blades
was done
this
NIBE1
change
percentage
case.
The
system
only.
figure
energy
torque
rating
the
the
operation
The results
.
is
been
before
change
upon
to
refers
degrees
-4
at
to
based
figures
control
drive
or
train.
fixed
pitch
shape
at
a pitch
are
are
shown
Table
2.1
in
Table
curve
curves
angle
fixed
on the
(this
angles
Cp
Cp
shown in
curves
limitation
the
(the
results
pitch
control
of
Cp
for
calculated
and assess
were
Table
2.1
speed
variable
for
below
E(7. )
the
E(7. )
1.51
7735
86
91
F. Speed
V. Pitch
1.8
8932
100
1.8
8303
93
2.15
8672
97
2.0
8017
89
1.8
9226
103
1.8
8868
99
2.15
9231
104
2.0
8880
99
1.8
8095
91
1.8
8102
91
2.15
7258
81
2.0
7537
84
V. Speed
Const P.
Speed Red.
1.8
9226
103
1.8
8868
99
2.15
9231
104
2.0
8880
99
V. Speed
2.15
9231
104
2.0
8880
99
(. n
,
where
NIBE1
E
w max
shown in
pitch
NIBE4
E
power
degree
-1
of
2.2
of
8119
Mt: jv
by
equipment
1.45
V. Speed
Const-T
Speed Red.
For
1200 kNm
F. Speed
F. Pitch
V. Speed
V. Pitch
its
produced
is
system
NIBE1
w max
to
speed
that
above
speed
-
application.
generator
different
two
the
the
its
of
torque
the
the
The
Results
have
at
of
accordingly
reduce
torque
for
penalties
system
of
cost
to
time
constant
the
figures
the
braking
Capture
capture
the
the
in
any
from
extra
for
reflected
may not
Torque
this
and
,
be able
so as to
10 seconds
system
be increased
must
rating
chosen
in
point
is
torque
has been
torque
new
This
the
>2m/s
24
Table
Operation
2.2
Maximum
Continuous
Intermittent
Torque
Wors t
Case
Values
Torque
LS
Speed
LS
peak
HS
(kNm)
F. S. F. P.
1811
(rad/s)
peak
HS
(rpm)
1811
16.7
1.45
1500
F. S. V. P.
W
S. M.
1463
2 s gust
2632
30.16
1.8
1500
(ii)
2% I. M.
1463
2 s gust
2520
28.8
1.815
1512
(iii)
5% I. M.
1463
2 s gust
2276
26.1
1.827
1522
1463
2 s gust
1463
13.9
1.865
1865
Constant
Torque
1463
2 s ramp
3243
30-97
1.81
1810
Constant
Power
1811
2 s ramp
2793
26.67
1.81
1810
Max Cp
1330
1717
19-57
2.387
1998
V. S. V. P.
Speed
Reduction
A power
on NIBE1
vs.
how the
against
data
is
speed
wind
wind
the
VSCT system
but
the
higher
in
20% increase
VS MaxCp
operating
speed
complete
Fig.
in
due to
Fig. 2.10
for
system.
less
the
very
the
speed
calculated
rating,
higher
may result
WrG installation.
line
achieves
operation
1m/s
for
the
in
effective
graphs
keep
the
in
show
differ
at
loss
energy
increments
as the
same energy
is
additional
energy
annum
torque
wind
of
con-
speed,
clarity.
and this
with
to
per
These
considerable
needed
reduction
operating
systems
capture
each
particular
for
various
energy
in
achieves
which
Also
more or
VSCP system
torque
2.9.
the
are
are
speed
for
profile
strategies
control
Note
speed
as a continuous
plotted
incurring
in
plotted
speeds.
Only
the
is
The figures
are
wind
given
different
ent
stant.
10 s gust
but
only
achieved
control
at
a significant
the
VSVP without
with
a possible
difficulties.
expense
increase
of
in
17% higher
the
cost
of
25
2.5
Effect
2.5.1
Dynamic-energy-capture
of Inertia
The theoretical
have
turbines
gible
inertia
point
for
this
energy
been
based
capture
In
windspeed.
and so the
dynamic
the
will
differ
been
obtained
results
the
speed
steady
state
system
inertia
will
from
the
wind
has negli-
turbine
its
achieves
practice
variable
that
assumption
instantly
and therefore
each
the
upon
for
results
operating
prevent
derived
theoretically
figures.
The dynamic
simulation
of
D. Donegani
wind
data
ultaneous
was input
to
(see
the
calculated.
were
comparison
of
by running*a
in
was written
BBC
B microcomputer,
a
generated
energy
This
turbine.
a wind
for
Two-second
have
results
performance
cooperation
1 for
Appendix
The
computer
for
the
with
further
programme
following
computer
details).
Watt-hours
and the
simulator
time
real
of
the
allowed
three
sim-
operating
situations.
(i)
Fixed
This
is
held
is
that
it
(ii)
speed
steep
torque
case
which
(i)
the
for
which
then
the
Cp
be a vertical
steady
is
It
state
should
by the
pitch
this
a speed
line,
i. e.
be noted
theoretical
generated
recorded
was
The rotational
comparison.
the
variable
preventing
curve
above.
.
it
the
If
speeds
CPmax
giving
to
speed
wind
all
for
so limited
been
Variable
For
assumed
2.5 MW then
have
would
datum
1.8 rad/s
at
than
pitch.
variable
as the
used
constant
be greater
speed
set
giving
that
energy
could
instantly
this
figures
assumption
inertia.
- zero
the
to
calculated
mechanism.
pitch
increase
is
2.5 MW on the
as
system
power
speed
run
1.8
rad/s
same generated
corresponds
were
a rotational
CPmax-
at
above
at
to
The
was
power
the
calculated.
as in
way in
26
(iii)
Variable
This
towards
time
its
the
operate
until
below
the
data
linear
are
speed
is
The pitch
control
was not
During
reached.
the
obtained
data
of
for
three
at
2-second
Results
for
corres-
different
sets
intervals
each
(kg m2
Ine rtia
and
x
101)
10
50
155-01
VSVP
MaxCp
179.21
179.21
177.47
177.46
177-72
177.47
2
343-11
VSVP
MaxCp
352-35
353.89
349-36
352.88
348.49
350.08
3
573.4
VSVP
MaxCp
573.92
580.5
572.81
590-13
582.4
610.81
be noted
to
10 m/s - operation
to
15 m/s
the
is
that
ensure
run
state
was
the
wind
mainly
partly
along
in
point.
to
the
samples
CPmax
CPmax
the
and
power
power
limiting
of
energy
into
begin
and
end
at
are:
velocities
curve.
the
transfer
net
kW hrs
(VSVP)
curve
mostly
arranged
operating
the
on the
limit
torque
in
are
for
is
- operation
steep
figures
that
15 m/s - operation
computer
s.teady
wind
1
should
To
with
different
three
of
2.3
Control
Strategy
Fixed
Speed
It
to
acceleration
2.3.
Table
All
along
to
assumed
torques
0
1-
limit
controls
speed.
Table
Wind
Sample
decelerate
or
may exceed
rated
0.4s
every
in
pitch
16 minutes
containing
shown
the
been
inertia.
accelerate
point.
torque
at
have
results
interpolation
regimes
i. e.
blade
the
to
operating
2.5 MW generation
each
time
rotational
limit,
Comparative
wind
state
speed,
maximum
to
ponding
the
speed
takes
including
-
pitch
variable
turbine
new steady
by limiting
power
speed
operation
with
limiting
region.
region.
the
the
curve
inertia
same wind
is
zero
speed
27
Comparison
for
windspeeds
theoretical
at
rated
Cp
.
and not
wind
the
2.11
a 10 minute
wind
speed
operation,
blade
torque,
From the
an inertia
is
which
to. hold
inertia
does
not
significantly
fluctuations
seen
slow
the
taken
for
the
it
not
operating
is
turbine
the
about
system
down during
its
than
fluctuating
are
that
shows
less
obtains
time
speeds
to
torque
figure
shaft
it
the
its
at
rated
drops
term
short
by
that
the
fluctuations
torques
region,
and
is
characteristic.
back
so
not
have
the
at
in
allowing
quite
into
the
in
the
the
Note
to
in
that
VS MaxCp
the
so
the
also
VSVP
on the
operation
This
in
grid.
reduces
and
fluctuation.
a greater
present
into
change
0 75 MNm correspond
.
a fixed
to
considerably
grid.
for
torques
fluctuations
back
a speed
captures,
marked.
restricted
complete
fluctuations
is
generator
were
the
accept
energy
generator
speed
used
generator
than
greater
to
power
can be seen
seen
generators
the
affect
and variable
have
would
corresponding
it
power
torque
If
sample.
then
blade
the
shows
with
the
reduces
steep
case.
Discussion
Various
of
wind
turbine
fluctuations
torque
2.6
the
the
the
upon
Figure
torque
of
the
during
point,
when
a system
due to
is
available
Torque_pulsations
effect
steep
effect
allow
AltHough
case
operating
energy
speed.
2.5.2
its
new
rating,
This
However,
the
speed,
point,
below
capture.
its
reach
maximum
and theoretical
actual
predominantly
energy
to
speed
the
of
variable
(ii)
studies,
speed
wind
refs.
energy
Increased
energy
Reduction
in
(15,16,18)
recovery
have
that
considered
the
advantages
are:
capture.
intermittent
torque
levels
on
the
generator,
28
and hence
reduction
(iii)
Reduction
in
(iv)
Flexibility
(V)
Motoring
from
(vi)
Operation
at
power
This
work
different
The
calculated
for
(see
annum
Table
157- (Table
(ii)
to
its
are
blade
extra
shown
torque
(iv)
and
schemes
advantage
for
the
the
constant
of
input
This
intermittent
into
will
depend
have
wind
assessing
turbine.
been obtained.
variable
facility
speed
3
is
4%
to
per
CPmax
speeds
at
which
can
be
approximately
captured
levels
on the
depends
proposed
in
operating
peak
intermittent
turbine
structure
and
on the
as an increase
inertia
the
Continuous
limit.
ability
speed,
strategy
and
torque
levels
2.2.
of
effects
fixed
a range
over
of
the
the
machines
for
a range
site
system
beyond
speed
optimised
CPmax
on the
stressing
is
thus
for
wind
regime
torque
torque
these
Whereas
the
of
(ii)
1).
speeds
over
down.
shut
with
an existing
wind
energy
and rotational
obtain
during
and
points
by
a range
extra
sample
wind
other
captured
Over
Reduction
are
grid.
conditions.
operation
(i)
to
distribution
2.1).
Table
of
assessment
speed,
in
site
braking
e.
g.
,
applied
energy
speed
associated
differing
on points
strategies
Fig. 2.11).
(iii)
the
concentrated
Reduction
absorb
(see
has
possible,
2.3,
the
structure.
up/assisted
Cp
into
output.
a Rayleigh
is
operation
for
demanded
some implications
(i)
the
of
operation
start
fluctuations
power
stressing
of
operating
However,
of
one
will
scope
obtain
have
of
conditions.
wind
this
CPmax
particular
of
to
site,
speeds
will
accept.
depend
The
thesis.
at
only
variable
one wind
speed
and so can be used
to
on
29
(v)
The slip
from
motoring
will
(vi)
an
Operation
duce
constant
stant
power
2.7
Conclusion
power
scheme
Despite
the
importance
Designs
energy
by the
capture
are
to
systems
power
of
generation
allow
of
control
unsophisticated
characteristic
operation
characteristic
of
the
and
and
work
VSVP type
the
the
in
can
of
or
costs
which
best
to
pro-
con-
with
implement.
to
to
merit
study
has
considershown the
assessment.
increase
to
may not
be justified
fluctuations
Of
operation.
at
operation
The
currents.
by means
speed
torque
speed
the
slip
capture
power
severe
wind
speeds
high
a realistic
torque
giving
give
the
and
reduction
This
in
low
may be achieved
energy
the
wind
may be difficult
potential.
will
high
advantages
or
than
resulting
speed
in
as
max Cp
be
turbine
must
energy
capture,
be
implemented
by
in
this
a torque
to
the
the
capable
greatest
a relatively
system.
for
Specifically
of
this
fluctuations
torque
the
variable
technique
overall
but
20% overspeed
smoothing
the
best
to
added
of
torque,
during
Control
The reduction
the
the
Cp)
features
speed
advantage
considered
the
allow
supplement
be greater
torques
turbines.
wind
incur
to
main
(or
sufficient
in
gained.
the
has
rating
about
be
accept
which
operating
increases
energy
to
improvement
of
all
liable
large
equivalent
may have
including
very
X
2.3-5.2,
to
way during
this
will
generator
to
characteristic.
low
operation
which
extra
be rated
relatively
next
of
may prove
five
the
speed
for
ation
to
thesis
may be possible
down in
provide
Section
of
This
to
is
output
the
equipment
any desired
at
this
may be used
require
blades.
torque-speed
appropriate
variable
have
will
would
shut
generator
devices
braking
recovery
the
However,
the
require
energy
from
conditions.
recovery
This
slip
torque
accelerating
speed
the
in
scheme outlined
Electrical
up.
techniques.
by
controlled
of
start
braking
other
recovery
power
also
over
involved
was used.
electronic
a steep
system
torque
This
both
thesis
was to
over
characteristic.
be able
"max
a
speed
to
Cp"
assess
type
30
CHAPTER
3.0
Slip
Energy
Recovery
3.1
Slip
Energy
Recovery
Slip
energy
recovery
induction
machine,
by
range
(ref-7).
3.2
the
of
A block
in
that
this
both
23).
the
so
Several
different
In
such
a system
flow
must
this
of
case
is
that
the
as the
for
Fig-3-1.
Note
at
speed.
If
this
induced
voltage
a cycloconverter
flow
the
is
to
recovery
(ref.
directions
windings
secondary
been
and
to
system
both
the
converter.
in
outlined
be used
will
sub-
energy
a frequency
have
this
in
in
by
achieved
slip
flow
Figure
primary.
power
power
achieving
windings,
operation
the
speed
secondary
of
then
ring
a variable
direction
control
be
the
shown in
was used
directions
over
of
out
a slip
to
the
this
achieve
conversion.
The Cycloconverter
3.2
low
can produce
This
supply.
This
link.
frequency,
Pulses
(ref.
of
a normally
a fixed
8).
to
current
passive
to
achieved
control
frequency
are
a single
produced
resistive
a. c.
the
by
frequency
waveforms
directly
a. c.
A conventional
produce
to
a. c.
and current
voltage
is
can be used
supply
mains
frequency
conversion
between
flowing
a direct
is
A cycloconverter
of
of
the
methods
introduction.
frequency
to
operate
and
synchronous
able
to
grid,
super-synchronously
be
enabling
into
flow
at
of
flow
Note
frequency
power
the
winding
power
and
then
As the
varies
rotor
changes
sub-
must
equipment
the
of
speed.
windings
operate
power
required
super-synchronous
secondary
a technique
to
diagram
scheme
the
shows
is
connected
control
Cycloconverter
Usinga
voltage
firing
and inductive
output
portions
load,
the
and
circuit,
of
of
mains
see Fig-3.4.
current
varying
using
shown in
the
a d. c.
of
a voltage
is
mains
utilising
and amplitude
cycloconverter
phase
from
and without
direction
which
converter
3 phases
Fig. 3-3.
supply
A low
into
31
frequency
current
the
using
thyristors
the
load
the
required
at
achieved
frequency
the
the
current,
and vice
its
with
firing
the
the
of
tude
3.3
three-phase
waveforms
the
the
of
current
slip
the
over
Table
the
to
neutral
device
the
line
20%
for
slip
control
flow
of
this
the
of
associated
the
of
amplitude
with
amplitude
of
units
for
system,
neutral
output
are
used,
simplicity,
Variation
supplies.
produces
in
variation
the
ampli-
in
recovery
flow
power
current
power
torque
required
energy
of
the
Speed
rpm
Slip
1200
1300
1400
1500
1600
1700
1800
+0.2
+0-13
+0.06
0.0
-0.06
-0-13
-0.2
1.0
P-u-
torque
supersynchronous
delivered
ronic
the
usually
in
the
by the
produced
the
speed
machine
for
generator
is
windings
The
cycloconverter.
between
operation
(see Section
characteristic
2.7)
+20%
are
in
3.1.
The
is
in
to
waveform
Table
at
waveform"
cycloconverter
In
wave.
control
by controlling
for
increase
is
which
An increase
an
are
at
produced.
The required
figures
control
are
Cycloconverter
achieved
be fired.
modulated
points
waveform",
and a "firing
produces
associated
amplitude
of
The firing
into
voltage
being
angles
by
supply
versa.
these
of
to
frequency
frequency
phase
"control
the
output,
waveform
high
see Fig-3.5.
device
the
the
high
the
the
of
with
of
required
across
Three
each
the
control
angles,
intersection
the
of
segments
frequency,
output
supply
of
phase
from
produced
fire
to
varying
at
is
waveform
equipment
by the
only
stator,
controls
3.1
Torque
P. u
PM
Pi
P-u
P-u
0.0
0.15
0.175
0.205
0.23
o. 4
1.0
0.0
0.11
0.13
0.17
0.20
0.37
1.0
0.0
0.13
0.14
0.17
0.19
0.33
0.83
and
1.0
speed.
At
and
17%
the
rotor
p. u.
this
power
are
Power,
0.0
-0.02
-0.01
0.0
+0.01
+0.04
+0-17
defined
83%
point
by the
P2
P. u
rotor.
the
of
as ocurring
the
As the
cYcloconverter
total
power
power
electlosses
32
dependent
are
on this
The change
be obtained
produced
secondary
a negative
times
is
for
smooth
converter.
This
phases
of
recovery:
energy
is
due to
mains
frequency
the
reduced
frequency
output
a possibility
if
supply
limit
ap
of
group
to
number
current
flow
power
its
speed
with
the
of
of
mains
at
all
range.
associated
output
direction
be kept
must
throughout
system
can
into
current
positive
relationship
slip
This
positive
this
and problems
an upper
is
the
speed
cycloconverter-
firing
and
limitations
is
a high
By firing
phase
synchronous
the
of
emf.
required
There
There
relationship
at
supersynchronously,
of
for
required
subsynchronously,
emf
certain
during
(ii)
phase
secondary
operation
are
(i)
the
secondary
a cycloconverter
available
direction
emf
obtained.
There
of
flow
power
and the
current
change
only.
by changing
a positive
into
in
proportion
supply
the
use
a cyclo-
waveforms
cycle.
a short
circuit
and
group
n
between
occurring
fires
thyristor
simul-
taneously.
(iii)
The load
This
amplitude.
In
these
3.4
thesis
this
in
problems
recovery
is
the
the
but
passive,
not
techniques
novel
operation
contains
emf induced
secondary
several
of
an emf source
in
are
the
varying
windings.
applied
a cycloconverter
of
as
to
a slip
counteract
energy
system.
Six
Phase
SuPPlY
The frequency
is
windings
given
and amplitude
of
Fs = s. Fm
and
the
emf induced
in
the
by
S
and
where
is
s
is
the
slip
Fs
is
the
frequency
Vs = s. k. Vm
N-Ns
Ns
induced
in
the
secondary
windings
secondary
two
33
Fm
is
the
mains
Vs
is
the
peak
value
of
the
secondary
Vm
is
the
peak
value
of
the
mains
k
is
the
turns
ratio
Ns
is
the
generator
N
is
the
actual
From this
induced
emf
it
greater
than
speed
restriction
large
there
so
This
of
leads
The
before
A feature-of
this
mains
This
output
cycle.
in
secondary
the
the
enable
using
two
3.5
Divided
there
supply
blanking,
three
been
has
is
a problem
which
control,
or
system,
the
of
a
the
quality
that
the
is
system
smoother
of
The six
in
connected
six
supply
see Fig-3.6,
generator,
upon
degree.
current
sinusoidal
output
waveform
uses
mains
the
dependent
a large
cycloconverter
number
the
of
to
becomes
during
available
recovery
a greater
in
group
a conventional
a possible
is
increases
separate
p
cycles
be extended.
to
or
implies
frequency
output
deteriorates
waveform
generate
mentioned,
This
phases.
required
in
slip
is
This
emf.
to
phases
waves
waveforms
and should
phases
are
opposing
per
obtained
also
by
senses.
Winding
Layer
As
the
of
transformers
phase
the
of
be equal
must
secondary
supply
induction
the
and amplitude
scheme as a whole.
the
mains
provides
range
speed
the
of
slip
system
will
of
frequency
cycloconverter
a deterioration
the
which
supply,
the
recovery
high
range
allowed
slip
speed
the
of
slip
fewer
to
speed
that
frequency
at
are
volts
speed
limit
on the
and
supply
volts
speed.
maximum
operation
produced.
the
with
During
period.
operating
induced
machine
synchronous
frequency
the
the
of
can be seen
varies
The upper
frequency
supply
short
normally
considerably
intergroup
devices
circuit
overcome
the
only
between
occurring
by
either
complexity
In
reactors.
are
system
cycloconverter
allowed
the
use
of
of
the
electronic
an electronic
to
fire
two
during
mains
electronic
blanking
a positive
34
half
'of
cycle
output
Similarly
cycle.
the
A zero
current
necessary
devices
off,
to
the
that
ensure
In
this
end
connections
one
being
This
(ref.
Holmes
12),
it
speed
the
allows
a motor
machine
runs
derating
the
of
is
winding
only
Under
the
the
just
up
as
drive
to
its
a motor
to
1000
the
separated,
range
rpm,
see Section
n
by
winding
high
of
supply.
of
this
scheme
from
machine
as
the
and
the
possibility
mains
of
to
machine
induction
the
complete
were
advantage
operating
1200 rpm,
of
phases
an additional
below
is
rated
of
the
current
the
of
being
used
This
for
a generator,
lowest
generating
5.5.
is
system
is
cycloconverter
cycloconverter
intuitively
half
time.
of
each
system,
and
the
is
generator
connected
10 A rms,
is
windings
can be seen
the
conditions
windings
the
separating
machine.
normal
secondary
In
put
to
two
and the
proposed
the
simply
Fig-3.8.
other
the
uses
reactors
shown in
Fig. 3-10.
Generator_derating
A disadvantage
of
that
cycloconverter
diagram
detailed
between
the
was first
very
circuit
winding
layers
and
effectively
eliminates
layer
The
arrangement
This
detection
as shown in
had a double
the
operation
Intergroup
achieved.
thyristors,
half
blank
when to
zero
accessible.
group
work
current
half
negative
positive
current
current
used
occurring
this
the
the
during
decide
to
has been
winding
and
(20% subsynchronous)
A more
3.5.1
in
in
were
p
reactor,
as
the
layer
layer
currents
standstill
i. e.
generator
the
blanked
intergroup
see Fig-3-9.
was found
that
the
divided
circuit
It
the
each
are
during
Discontinuous
zero
limit
to
intergroup
an
short
is
for
connected
group.
as
scheme
off
necessary
delay
a time
current
to
is
3-7Fig.
see
a true
may be introduced
detect
for
need
blanked
devices
group
n
cycles.
introduces
and are
current,
Positive
in
each
is
cycles
the
the
a net
that
two
generator
each
layers
used
5A
carrying
half
with
For
layer
is
by noting
operated
parallel.
layer
there
that
taken
to
a separate
of
current
are
sent
out-
35
one layer,
along
the
as the
generator
With
the
5A
exceed
Where
layers
negative
along
in
copper
1
refers
91
to
the
layer
I
refers
to
the
line
Subscripts
1
in
parallel
and
N
is
With
and
of
in
leads
being
not
in
current
is
to
a derating
used
efficiently.
layer
each
of
must
not
shown as follows:
current
current
to
refer
the
case
of
operation
the
with
respectively.
pairs
layers.
of
and the
parallel,
1
Total
the
derating
separated
number
layers
the
2
is
windings
The effective
.
the
the
This
other.
fitted,
cycloconverter
rms
the
as shown in
currents
Fig-3.11a:
11 /2
9,1
N. I
A. T.
1
With
the
divided,
layers
and the
94212
2
the
limit,
at
1
rating,
9-2":
1
Fig-3.11b:
//2
/2.1
In
as in
currents
9,2
9'1
Y12 1 9,1
v/2.1 1
/2
ii /v/2
Total
N-I
A. T.
=
i. e.
This
in
the
the
shows
and so the
that
the
maximum torque
However,
advantage
upon
A. T.
the
in
due
torque
restrictions
torque
layer
split
for
available
to
operation
rating.
implied
at
This
in
2
N. Il/2
rating
is
a higher
a
30%
reduction
machine.
speed,
rotational
be
can
shown
wind
down.
implies
arrangement
a given
the
1/v/2
turbine
in
three
operation.
cases,
there
is
an
depending
36
(i)
Torque
If
we use
(synchronous
running
and speed
a slip
the
speed,
is
generator
at
where
speed),
gear
ratio
is
w0
when the
speed
T0,
provide
the
be changed.
must
synchronous
to
generator
recovery
rotational
(Fig-3-12a)
limit
w0
fixed
normal
This
111.2
at
Ns
speed
mean that
will
is
turbine
1.2
at
the
i. e.
0.8333 P-u- speed.
The maximum torque
for
torque
by the
generated
The
at
rated
is
can be reduced
limits
copper
the
in
same reduction
have
would
to
operation
be specified
to
fixed
this
at
rated
torque
1//2
size
of
requirement.
use
the
the
with
normal,
generator
i. e.
P v/2/1.2
0
be
to
the
of
inefficient
operation
slip
capability
the
the
used
of
torque.
generator
speed
mode of
its
its
Thus
is
winding
a current
So for
torque.
by
been
has
less
with
the
of
power
speed
speed).
the
of
layer
divided
turbine
specified
synchronous
111.2
be
only
a higher
at
83%
to
will
maximum
normally
near
very
the
Týe
running
rating
however,
generator
case.
generator
(i. e.
slip
If,
size
speed
generator
generator
of
fixed
the
the
at
1.18 P
0
If
be
P
the
Y/2/1.41
0'
could
be used
(ii)
Suppose
limit
a
the
at
the
were
windings
factor
1.41
of
If
achieved
85%).
used
the
frame
generator
operating
capable
from
changed
not
was
is
generator
a
with
If,
is
generator
However,
.
1.2
however,
a+
would
size
generator
technique
winding
size.
the
of
41%
would
have
power
is
output
then
41%
slip
in
a
20%
generator
range
is
of
fixed
speed
to
increase
rating,
cyclooperation.
divided
the
layer
by a
be increased
increased
possible
the
range
and if
unchanged
rating
(20% slip)
an increase
the
layer
divided
6
the
then
(Fig-3.12b)
ratio
gear
The maximum torque
the
only
within
was
the
i. e.
Thus
P0.
increasing
without
Torque
converter
1.0
i. e.
were
possible
range
speed
41%
+
to
in
power
(net
then
a. P
0.
can be
derating
a
41%
to
increase
37
in
can be achieved
power
(iii)
Operation
Suppose
case,
ý
that
and
that
in
the
be uprated
must
rating
ator
Cp
will
T0 /ý
1.41
for
divided
1.41/ý
is
ý
happened
is
if
an increase
for
curve
If
of.
Again,
without
obtained
k
change
P0.
power
by
the
dependent
in
the
upon
3.12c)
not
changed
from
a fixed
the
operating
winding
turbine
ý
P0
output
be
could
a function
is
of
the
be of
the
kw 2,
T=
form
where
then
W3
1/3
p
0)
k
ß. w
0=(
so
normal
a gener-
as follows:
characteristic,
P=k.
i. e.
the
then
size.
to
curve
can so be derated,
operation,
1.41
be
to
speed
range.
deliver
to
required
generator
Max Cp
the
(Fig.
The generator
.
rating.
P0
and can be calculated
turbine,
we assume
within
be
The maximumýtorque
but
is
figure
the
is
generator
to
curve
ratio
gear
in
rise
Cp
maximum
along
again
an identical
with
p
wT0
also
0
ý-w
To
0
-=ý-2
wk
so
1/3
Y3
p
0
4
For
turbine
a given
These
results
Table
2.2
rating
of
in
the
can be used
Chapter
thyristor
may outweigh
2 to
wind
complete
The advantage
for
design
blanking
the
of
in
cases
conjunction
provide
(i)
or
with
disadvantage
turbine
the
torque
of
the
the
most
likely.
figures
rating
required
of
torque
system.
and the
of
are
some indication
control
a much simplified
etc.,
(ii)
this
ability
derating.
to
circuit,
start
avoiding
up from
the
standstill
need
38
3.6
Presence
It
is
has
obtained
been
Under
is
used,
output
frequency.
poidal
output
inductance
the
this
the
it
is
would
This
due to
the
problem
in
Another
required
the
generation
induced
of
this
of
the
firing
and so all
the
to
sinusoidal
produce
fied
to
counteract
For
this
cycle
the
an
of
output
opposing
emf,
build
that
flow
the
crossing"
the
required
produce
a sinu-
due to
waveform,
sinusoidal
As the
use
the
the
load
is
no longer
with
speed.
current
wave is
output
a square
may aid
or
on
oppose
this
as a generator
it
and aids
wave of
a fixed
same,
as in
current
in
the
load,
the
firing
torques
are
and a firing
Depending
can be shown clearly
the
the
but
passive,
current
are
in
wave,
cycle.
subsynchronously,
angles
two
every
operation
now
Fig-3-13.
shown in
zero
emf
are
phase
control
up from
During
on the
windings
a sinusoidal
secondary
in
current
as has been
varies
of
production
important
be
an
emf may
current
form
current.
control
these
application
control
operating
of
to
"control"
the
"cosine
the
tends
produce
amplitude
The effect
that
the
simply
the
to
is
power
sinusoidal
supersynchronously.
frequency,
a sinusoid
windings.
to
having
scheme
the
the
of
emf whose
emf opposes
we assume
in
a current
direction
the
to
possible
current
an induced
contains
is
"firing"
the
cycloconverter
a system
lags
which
was attempted
longer
produce
such
produced
device,
wound machine,
waveform
with
emf induced
no
the
thyristors
see Fig-3-13.
it
work,
as this
is
control
waveform
load,
secondary
separate,
a normally
the
where
the
output
with
the
electronically
across
required
circumstances,
and with
current
supply
for
point
two
of
the
with
Operation
in
In
the
with
normal
load,
a passive
technique
if
intersection
of
and one associated
waveform.
with
point
a firing
that
stated
one associated
waveform,
emf
previously
the
at
waveforms,
into
of Secondary
Figs-3-14a
amplitude,
and b.
angles
must
In
order
be modi-
problems.
which
large
problem
firing
angle
as,
angles
limit
for
instance,
have
to
required
in
subsynchronously
be decreased
may be reached.
half
a Positive
to
counteract
However,
for
the
39
turbine
wind
and the
an output
waveform
problems
outlined
A computer
a new control
supply
As the
This
range.
effectively
over
the
waveform
fore
istic
modification
forms
for
sub-
with
its
operate
waveto
calculated
correct
in
Fig. 1-5).
amplitude.
to
overcome
torque
amplitude
In
the
to
also
and super-synchronous
this
speed
produce
actual
then
would
to
provide
produce
by the
demanded
obviates
the
operation
can be scaled
waveforms.
are
emf signal
system,
each
(and
there-
current
for
shown
64
The correct
torque-speed
need
current
into
the
simplify
0
speed
sinusoidal
secondary
correct
with
programme
waveform.
the
control
the
over
was divided
range
the
amplitude
by the
produced
further
to
change
control
characteristic
the
the
of
changes
this
order
speed
scheme over
of
to
used
representation
waveforms
Also,
speed
firing
required
then
were
windings
for
required
This
the
waveform,
appropriate
order
the
the
speed.
4.6).
in
to
in
range,
at
Section
the
a
control
required
calculate
use'a
compensate
had its
which
was calculated
of
the
the
firing
of
a waveform
and of
cosine
system.
control
operating
The given
system.
the
shape
was addressed
(see
six-phase
must
angles
of
but
These
firing
as the
emf induced
each
(shown
to
secondary
means that
torque)
was decided
the
complete
generator,
details.
device
the
changed
intervals,
waveform
It
to
further
timing'of
firing
the
speed,
2 for
across
the
simplify
but
modifications
was developed
programme
wave.
volts
the
the
above.
see Appendix
angles,
to
technique
was retained,
sinusoidal
incorporate
then
basic
sinusoid,
is
subsynchronously,
a difficulty.
the
waveforms
which
required
a modification
this,
be a simple
current
would
In
are
great
problems,
was devised.
of
torques
too
present
these
now no longer
would
produce
not
intersection
the
at
low
relatively
overcome
technique
device
the
to
order
crossing
This
only
emf does
opposing
In
form
system
character-
a servo
as a whole
Some typical
in
control
Fig. 3.15.
by
wave-
40
3.7
Stable
Operation
Conventionally
on the
into
secondary
the
effectively
is
injected
could
under
likely
the
the
speed
but
and
phase
4
the
is
generator
can be used
with
for
pletely
the
control
the
removes
to
is
This
the
of
for
a
operating
of
be known,
to
the
operation
and the
Such
system.
input
(wind
speed)
not
forced
the
the
any
emf.
control
The
the
cycloconverter
control
the
of
This
emf.
secondary
wave required
correct
instability.
phase
as
the
The
8
bit
an
secondary
with
to
to
in
is
word
The
emf
above
of
all
to
previously.
with
phase
gener-
electronically,
the
signal
speeds
and
be output
is
of
corresponding
derived
output
at
phase
emf signal
word
is
same
Changes
and
secondary
digital
the
current.
frequency
relationship
described
be of
current
proportional
use
secondary
are
speed
With
torque...
of
the
machine
directly
by the
phase
emf.
secondary
operation
in
enable
of
machine
type
frequencies
emf.
provides
observing
locked
is
torque
This
here,
by the
secondary
obtained
of
angle
to
the
this
as this
fluctuating
proposed
controlled
by
4).
Chapter
actually
the
the
emf is
phase
without
as
obtained
are
(see
scheme
are
emf,
secondary
ator
to
operating
secondary
desired
However,
demanded
and then
the
frequency
the
torque,
have
would
injected
speed.
reached.
Also,
inherently
on an
required
shaft
speed
demanded,
source
complex.
rotor,
frequency
is
speed
is
to
changing
be unstable.
calculated
depends
the
incrementally
wind
is
speed
a fluctuating
the
A voltage
mode.
reaches
demanded
to
speed
be rather
to
In
the
demand,
which
by
with
prove
operating
a control
in
still
speed
optimum
the
operating
it
frequency
a variable
corresponding
in
change
until
the
until
with
a frequency
a large
overcome
machine
a synchronous
at
control
usually
turbine
into
of
voltage
scheme
is
If
out
problem
winding
21).
fed
in
operates
secondary
(ref.
speed,
wind
a doubly
thus
in
so
phase
obtained
This
com-
41
For
provide
other
control
cycloconverter
the
applications,
of
doubly
motoring
fed
or
machines
other
generator
signal
static
in
other
Scherbius
output
modes of
systems.
can be used
operation,
to
e. g.
42
CHAPTER
4.0
Control
Cycloconverter
the
of
I
For
correct
synchronous
phase
the
this
tributor
the
speed,
with
achieve
operation
control
a signal
oped
a digital
digital
to
the
with
of
any
for
The
thyristors
windings
tion
flow
of
of
the
firing
These
in
power
control
flow
control
nous
speed.
The
Information
be found
(j)
be derived
the
Near
considerable
the
the
study
devel-
associated
to
aimed
for
system
providing
pro-
The
problems
This
For
a reliable
the
voltage
in
and the
secondary
frequency
and
amplitude
of
the
frequency
and
about
by direct
emf must
for
measurement,
synchronous
super-imposed
speed,
slot
the
noise.
change
the
several
secondary
thyristor
3.6).
windings
for
by 180*
the
of
through
emf
the
the
synchro-
varies
secondary
with
emf
reasons;
emf
amount
remain
relationship
of
direc-
and must
secondary
phase
The
supply
the
and
(Section
secondary
The phase
correctly.
the
emf
emf.
waveforms
the
mains
current
electronically
induced
the
secondary
secondary
control
be produced
must
between
a given
the
of
of
from
flow
current
sign
magnitude
be controlled
to
waveform
speed.
cannot
with
to
(ref-7)
Smith
were
a dis-
used
order
a self-checking
generator.
upon
the
waveforms
synchronism
power
with
are
angles
there
therefore
and
to
information.
electronics.
incorporating
the
of
upon
to
the
control
depends
flow
power
in
23)
in
machine
similar
but
been used
(ref.
emf.
be in
must
environment.
must
and secondary
provide
problems,
a commercial
have
methods
secondary
reasonable,
technique,
electronic
the
to
system
pulses
cycloconverter
induction
the
of
with
seemed most
digital
overcoming
phase
of
and below
above
Ohno and Akamatsu
shaft
electronic
the
system
in
misreading
improve
the
locked
approach
A number
emf.
generator
by the
provided
requirement.
connected
vide
current
secondary
induction
the
of
approaches
zero,
43
(ii)
zero
The voltage
only
to
equal
the
secondary
emf at
current.
(iii)
mains
If
supply
be
found,
frequency
derive
the
amplitude
The
be
secondary
be
will
shaft
those
the
of
the
of
derived.
It
secondary
is
emf
supply
rotor,
possible
in
the
of
supply
phase
volts.
by an
scanned
speed
mains
a particular
and
generator
is
known
to
electronically
the
way,
locked
phase
angle
this
slip
in
emf.
actual
the
of
the
and rotational
angle
the
of
frequency
the
position
can
the
with
seen
to
phase
a representation
synchronism
disc
the
between
voltage
angular
if
and
and
the
a slotted
device,
optical
then
wave,
firing
is
a thyristor
By fitting
can
is
measured
is
emf
secondary
by
given
Fs = s. Fm
(Ns-Nr)lNs
s=
where
Fs
emf
= secondary
Ns = synchronous
If
two
Fm
frequency
mains
slip
s=
Nr
frequency,
one
produced,
are
counts
speed.
rotor
= actual
speed
rotor
to
proportional
the
of
f
the
mains
rotation,
supply,
the
and the
"rotor
the
produced;
The
1500
with
mains
there
and
rpm,
the
at
angle
phase
and
must
and rotor
the
rotor
2N
be
counts
count
remains
phase
angle.
this
to
proportional
"secondary
synchronous
subtracted
count"
a count
electronically,
the
rotor
from
the
the
"mains
frequency
slip
of
phase
shaft
count"
is
angle
phase
count".
induction
the
speed
of
speed
the
If
at
counts
progress
per
at
of
there
speed
synchronous
revolution
the
to
the
are
is
turning
of
the
same rate.
corresponding
in
generator
frequency
unchanging.
unchanged,
to
proportional
other
In
this
is
work
secondary
emf
is
N
per
cycle
counts
at
25 revs/sec
shaft
such
that
this
case
the
a constant
zero,
secondary
the
of
then
mains
difference
emf
44
At
Fig.
other
4.1.
speeds
The figure
secondary
on the
the
counts
rotor
shaft,
as will
F2, N2 are
secondary
N is
the
T
time
total
in
the
mains,
as in
rotor,
by positioning
4.2.2.
Section
in
frequency,
speed,
period,
and
disc
the
of
below.
count
count
frequency,
synchronous
slip
zero
can be achieved
supply
rotor
s is
time
at
be explained
nr, Nr are
ns is
that
which
zero
Fm, Tm, Nm are
At
counts
assumes
are
diagrammatically
be
shown
can
count
speed
in
count
Fig. 4.1
the
one cycle
counts
of
the
mains.
can be described
mathematically
as
f ollows
Nm = N. T/Tm
N. T. Fm
=
Nr = 2. N. T. nr
N2 = Nm - Nr
(Fm
2nr)
T.
N.
=
(Fm
2ns(l-s))
N.
T.
=
Fm
=
2ns
Now
N2 = N. T. (Fm - Fm(l-s))
Fm
N.
T.
s.
T.
F2
N.
=
N2
Therefore
shows
mains
that
counts
when the
are
with
synchronism
is
in
8
bit
an
mode of
digital
arithmetic
for
then
N
has
counting
being
cycle
of
secondary
if
rotor
synchronised,
any
speed
the
This
emf.
the
secondary
and
is
count
in
emf.
secondary
The maximum count
per
initially
are
accurate
the
of
a count
counts
N
used
been
system,
(see
256
chosen
at
and to
overcome
Section
4-3).
to
ensure
no redundancy
any problems
with
the
45
4.1
The Mains
Count
The mains
and then
multiplying
continually
taining
synchronism
the
reset
phase
electronics
angle
The Rotor
4.2.1
Rotor_pulses
to
signal
generator,
must
be progressing
method
to
the
of
fitted
of
by use
pulses,
These- pulses
pulse
the
of
also
the
must
on
correct
supply,
thus
main-
being
pulses
digital
word
diagram
lost
representhe
of
mains
slot
on the
positive
be made short
counts
slots
per
revolution
was tried
lock-in
was
positive
enough
to
ensure
revolution.
and so some
is
possible
in
counter
required,
i. e.
multiplied
by
finally
edges
conse-
to. be
range
edges
of
the
no collision
is
case
and found
and negative
negative
counts
be two
It
required.
emf
this
per
and a divide-by-4
frequency
and
must
512
This
large
in
speed
count
is
secondary
and rotor
i. e.
loop
count.
the
mains
rotor
by four
locked
due to
the
128
has
the
disc
a slotted
the
of
Synchronous
and so the
frequency
The
both
revolution,
rotor
scanning
operation
same rate.
a phase
triggered
frequencies.
clocked
8
bit
an
A schematic
supply.
IC
into
frequency
8
bit
an
is
speed
rpm),
this
range.
monostables
the
per
unstable,
and
any high
by optically
synchronous
256
to
slip
mains
of
loop
Fig. 4.2.
in
shown
(1500
way as for
207.
mains
For
multiplying
occasionally
the
edges
are
supply
locked
a phase
pulses
counter
shaft.
at
counts
similar
the
produced
at
second
do this
a+
rotor
per
of
of
is
count
fitted
The disc
event
of
is
using
mains
Count
The rotor
cutive
the
of
required
4.2
25 revs
in
on positive
50 Hz
up the
256
by
The resultant
The output
misread.
ting
frequency
counters.
counter,
by squaring
produced
this
and divide-by-N
or
is
count
of
the
over
means
slot
resulting
at
a
pulses.
high
slot
46
4.2.2
Synchronising-and_rotor_reset
The secondary
through
passes
count
in
zero
Mains
so that
must
when the
be zero.
phase
the
with
180
slots
degrees
256 as mentioned
mains
and
count
should
pulse
is
this
alignment
and is
left
in
It
is
be used
been
to
only
be done
that
position
must
if
phase
reset
pulses,
angle
of
With
of
the
count
of
emf,
the
pulses
the
mains
is
and
locked
counts
in
the
will
give
synchronism
an
with
disc.
the
the
These
two counts
so that
the
point
of
the
rotor
so that
a reset
zero.
Note
disc
to
the
that
shaft,
operation.
8
bit
an
revolution
the
the
of
reset
shaft.
pulses
256 pulses
can
have
should
rotor
reset
Under
these
twice
0
on each
per
positive
of
edge
revolution,
the
conditions
representation
the
representing
word
shaft.
reset
by the
reset
counter,
digital
count
accurate
it.
be in
to
the
which
continually
rotor
will
achieved.
the
accurately.
maintained
two
being
count
at
count
turned
However,
point
count
this
count
half
per
8
bit
an
of
is
aligned
then
subsequent
into
produces
a half-rotation
supply,
been
clocked
are
which
mains
the
to
on fitting
once
rotor
of
is
may be misread.
has not
track
rotor
rotor
the
as follows:
At
the
set
all
at
secondary
phaso.
256 pulses
receive
counter
this
to
for
pulses
the
disc
shown above;
count
achieved
the
in
The slotted
need
secondary
emf
Count
corresponding
exactly
used
The rotor
rotor
standstill
'and
reset
even
read
At
are
Secondary
=
on a second
apart,
emfs
that
possible
available
read,
The system
is
secondary
As has been
met the
This
mechanical
be zero.
being
is
emf.
are
the
equals
condition
above.
secondary
Count
when the
zero
sense.
Rotor
-
count
this
from
start
positive
Count
secondary
Two extra
are
the
mains
If
must
the
subtraction
secondary
each
47
4.3
The Output
Count
The output
count
digital
8 bit
count.
This
secondary
the
words
count
as shown below:
MSB
from
8
bit
an
If
the
is
negative)
(i.
e.
rotor
is
then
the
mains
in
count
the
subtracting
i. e.
above,
digital
count
minus
synchronism
greater
than
output
two
rotor
the
with
the
mains
count
number
is
given
in
Output
Count
(i. e.
form
the
complement)
Rotor
LSB
the
count
two's
Count
Mains
by electronically
obtained
produced
produces
emf.
output
is
MSB
Count
LSB
MSB
LSB
00
00
00
01
00 00 00 00
(0)
00 00 00 01
(1)
00
00
00
01
00 00 00 01
(1)
00 00 00 00
(0)
00
00
00
01
00 00 00 10
(2)
11 11 11 11
(255)
00
00
00
01
00 00 00 11
(3)
11 11 11 10
(254)
etc.
The output
count
The information
will
is
page
However,
for
used
correct
a count
up to
if
the
designed
to
the
EPROM was
another
255),
counts
and supersynchronously
up,
This
the
4.4
Three
has
Phase
of
to
85
through
phase
is
to
required
order
a count
address.
count
outPut
waveforms
In
of
change
necessary
to
the
effect
produce
Note
that
it
counts
not
down,
thus
255(-1)
around".
instance
count
have
of
the
for
addressed
any data
the
subsynchronously
synchronous
the
"wrap
and the
EPROM would
the
of
an error,
250
to
merely
pages
and if
number
pages
in
coded
waveform,
an address
would
continually
operate
a control
EPROM.
the
of
EPROM is
the
then
number
were
programmed
at
in
as in
output,
in
8 LSB addresses
required
waveform,
each
(i. e.
this
the
corresponds
maximum count
-1
into
is
which
the
produce
fed
Each page
256 x 256 bits.
whole
is
output
count
the
providing
speed.
addressed
to
an EPROM which
contains
cycloconverter.
Multiplexing
produce
and
three
171
phases
subtracted
of
output
from
signal,
it,
the
corresponding
output
to
count
120
48
and 240 degrees
two
counts
three
the
4.5
original
then
correspond
the
of
thyristors
the
induction
control
waveforms
This
contained
to
voltage
forms
three
phase
into
and these
the
secondary
EPROM.
These
induced
emfs
20%
27128,
continually
the
required
directly
in
the
D-A
output
of
in
the
speed
likely
to
in
(Section
in
this
operate
amplitude
set
control
the
of
mode of
reference
control
of
waveforms
of
wave-
change
EPROM is
the
speed
The EPROM is
It
much faster
is
than
delay
no time
a
emf count.
secondary
phase
operation,
shape
programmed
of memory.
EPROM is
the
of
the
intervals
three
from
characteristic
supersynchronous.
multiplexed
capability
and also
by changing
(= 64 pages of 8x8 bytes)
the
to
torque-speed
64
to
20%
of
3.6),
fire
required
characteristic
complete
As the
range,
and
with
occur
the
corresponding
128 k
speed
changes
However,
amplitude.
subsynchronous
addressed
EPROM.
angles
torque-speed
on this
operate
converter,
waveforms
operational
changes
means that
to
containing
As the
desired
waveforms
firing
calculated
the
order
over
64 pages
the
control
over
be scaled
could
between
to
the
with
in
the
and amplitude
any
problems
observed.
EPROM Page Address
EPROM is
The
data
from
pages
so
bit
the
respectively,
together
multiplexed
to
programmed
generator
2.
4.6
waveform
generator.
according
Chapter
were
are
output
The EPROM
the
with
the
of
induction
The EPROM is
are
angle
and the
counts
rotor
phase
the
that
digital
pulses
frequency
as
addressed
secondary
the
word
correct
emf count
representing
A d. c.
to
converter
secondary
emf
is
produced
is
speed
voltage
which
is
at
derived
obtained
produces
frequency
above.
as explained
waveform
follows.
voltage
the
with
the
from
from
a voltage
and
To address
appropriate
the
the
the EPROM
speed
rotor
rotor
phase
a
count
pulses
proportional
by
to
a
49
This
speed.
voltage
EPROM, the
range
two
+ 207..
of
output
from
filter
was used,
speed.
its
with
tant
This
was not
large
inertia,
obtain
in
a wind
in
the
a smooth
page
speed
voltage
capacitative
to
response
to
used
rapid
energy
converter,
this
may be an
speed
in
changes
impor-
1200
10
00
00
00
1500
10
10
00
00
1800
10
11
11
11
AboveRange
11
xx
xx
xx
as below
speed
LSB
the
enable
output
delay
second
from
MSB's using
the
secondary
emf signal
and disabling
on enabling
instability
excessive
and prevent
the
of
Care
Dont
can be detected
range
within
X'=
is
the
at
simple
generator.
introduced
to
limits
operating
testing.
Circuitry
control
present
a digital
waveforms
This
amplitude
of
and Demultiplexing
EPROM produces
This
converter.
the
the
xx
required.
amount
to
corresponds
xx
phase
output
are
5.2.2).
xx
a2
the
representing
within
a large
changes
01
system
The
mode
step
BelowRange
Output
three
for
to
order
a problem
MSB
to
in
in
Speed
add hysteresis
4.7
but
count
and used
during
considered
bits
operation
converter,
a lag
word
significant
that
voltage
implied
(see Section
Operation
this
to
digital
indicate
to
used
be noted
must
which
The 8 bit
In
are
frequency
the
effect
logic
The 6 least
others
It
8
bit
an
to
converted
by an A-D converter.
speed
the
is
current
system
of
is
these
this
This
by
the
manually;
in
will
determine
determine
Section
however,
3.2).
it
the
a D-A
using
to
voltage
(see
multiplexed
cycloconverter
form
amplitude
cycloconverter
was coptrolled
the
analogue
a reference
waveforms.
produced
operate
to
converted
requires
the
representing
to
required
output
converter
output
would
the
the
In
provide
50
a suitable
method
control
of
amplitude
of
output
in
current
a servo
system.
The demultiplexing
achieved
the
after
Sample-and-Hold
down (i.
e.
a more
and tested
synchronous,
rotor
is
system
4.8
limit
count
shown
in
upon
the
the
signal
keep
to
by means of
the
chip
count
D-A converters).
However,
be to
probably
demultiplex
the
up to
as required
determined
by
the
has been
which
a speed
30%
of
super-
for
requirement
diagram
A simplified
four.
by
generator,
emf signal
multiplying
the
of
whole
Fig. 4.4.
the
over
points
torque
required
being
at
produced
of
a representation
the
calculated
which
program
system
firing
and
order
three
of
form,
analogue
is
waveforms
Circuit
Firing
of
in
would
secondary
being
frequency
The computer
tion
was done
control
EPROM.
and worked
the
to
converted
one instead
the
completes
phase-displaced
demultiplexing
of
the
of
outputs
built
This
only
form
three
has been
signal
requiring
This
the
of
devices.
suitable
digital
the
the
controlling
the
speed
opera-
was based
characteristic
the
of
control
device
the
across
voltage
for
angles
intersection
the
supply
firing
be
to
f ired.
The control
scaled
of
representations
The
formers.
point
the
six
phase
intersection
of
of
signal
an analogue
provides
which
erator,
will
signal
by the
be produced
of
10 V
supplies
these
two
Similarly
amplitude.
are
from
derived
waveforms
gen-
emf signal
secondary
is
transby
obtained
a comparator.
4.5
Figure
phase
(making
comparator
control
positive
is
shows
reference
shown
waveforms.
half
to
cycle.
to
only
change
In
Figure
If
the
one
state
4-5a
'p'
into
can be controlled
how current
of
the
six
at
the
intersection
the
group
rotor
thyristors
supply
emf
one secondary
waveforms).
of
is
The
the
considered
were
triggered
supply
to
be
from
and
on a
monostables
they
turn
would
'n'
on as they
thyristors
group
the
edge
of
Thus
only
half
cycle
'p'
emf is
rotor
can be seen
by similar
Therefore,
as a natural
that
not
The pulses
4.9
for
the
on
Gate
are
to
to
fire
will
the
p
and
half
negative
that
the
of
the
falling
on the
are
reverse
biased.
the
correct
polarity
is
there
n
generated
no need
for
fire.
any blanking
that
of
devices
the
biased.
edges
of
are
the
by firing
obtained
comparator
2.5
length
a fixed
devices
group
thyristors
group
negative
'n'
scheme is
control
Fig. 4-5b,
as shown in
cycle,
the
only
be reverse
and
thyristors,
the
to
connection
output
millisecond
pulse.
power
level
and electri-
Pulse
thyristors.
transformers
this.
provide
for
is
This
in
be amplified
must
pulses
before
The circuit
Fig. 4.6.
give
If
area).
Drivers
isolated
used
to
then
output
operating
on as they
operate
a system,
positive
The monostable
cally
such
The monostable
waveform.
would
on the
effect
required
a monostable
(shaded
biased
turn
not
reasoning
using
devices,
are
devices
group
comparator
a monostable
via
would
the
of
positively
fired
they
edge
current.
of
When the
it
are
were
comparator
the
leading
on the
operating
the
to
used
amplification
the
provide
isolate
to
and also
power
the
is
and isolation
gate
necessary
electronics
current
from
the
were
transformed
gate
shown in
to
fire
of
the
the
thyristors.
If
into
the
the
2.5
gate
drive
In
required.
trains
pulse
pulse
this
which
system
require
The monostable
from
drive
a
100 kHz
the
clock
pulses
pulse
monostable
millisecond
then
a large
these
much
are
as shown
MOSFETs on alternative
pulses
smaller
gated
in
the
half
transformer
are
transformers
with
f igure
cycles
into
converted
the
and
high
fewer
and
Q
turns
many
with
directly
Q(bar)
frequency
turns.
outputs
-
The output
of
of
the
switching
clock,
would
these
gates
a
be
32
square
wave of
pulses
are
the
gate
4.9.1
the
at
pulse
circuit
are
the
onto
rectified
continuous
in
voltage
also
ms
side
pulse
the
of
diagram
.A
in
shown
the
of
secondary
2.5
of
primary
transformer
the
of
The
transformer.
to
pulse
give
a
configurations
figure.
the
Design_of_the_pulse_transformers
The pulse
has
point
as shown
been
gate
be designed
can only
A load
established.
on the
circuit
open
transformer
line
6V
of
voltage
the
gate
and a peak
of
operating
was chosen
This
current
gate
gate
circuit
Fig. 4.7.
in
characteristics
for
when the
indicates
0.46 A
an
be
will
required.
With
the
2.5 ms
a
112 mW
well
,
approximately
a supply
amplitude
The average
below
the
12V
of
Secondary
12 V centre
tapped.
Primary
24 V centre
tapped,
However,
this
be a function
does
of
Law
500 mW
-
of
for
specification
wire
rating
0 056 A
.
the
total
primary
ti
is
the
high
frequency
N,
12
=
(secondary
current
the
of
magnetising
=0-
current
113 A
which
turns.
BA
ý=
dý/dt
e=
is
The magnetising
A
turns
clock
high
period
turns).
is
calculated
H. dl
giving
be
will
rating
rating
and number
core
N,
N2=6
so
power
wire
N112 = V. ti/B.
giving
,
the
dissipation
0.161V2
for
account
not
the
From Faradays
where
gate
average
available
voltage
power
20 ms
every
occurring
becomes
transformer
will
of
0.16 A.
be
will
rms current
With
pulse
0.46 A
B. dl/p
opr
i=0.4A
from
Ni
=
i/2
N1,
=
of
5 microsecs,
the
5
Assuming
primary
a waveform
rms current
The diodes
to
ensure
accurate
BYV 96.
are
0.8A
of
the
of
was thus
size
output
current
this
scheme has
chosen
a
34 SWG
as
type
recovery
The devices
pulses.
0 03 A,
.
is
gives
be fast
must
2.5 ms
forward
this
compared
used
with
rated
The Cycloconverter
The cycloconverter
feeding
supply,
windings,
used
These
To calculate
and conduction
each
thyristor
value
equal
angle
the
its
over
this
at
current
is
by the
is
dissipated
linear
with
on the
devices
and
sinks
were
derive
data
circuit
of
for
7A
of
sinusoidal
to
carry
is
60*
(over
sheet
for
the
device
it
1 Watt
(at
these
low
devices
Fig. 4.9.
current
.
one period
that
a
output
this
and using
per
1 Watt/Amp)
simpli-
having
current
of
the
rms,
current
One may assume
device
the
than
Certain
that
angle
is
approximately
larger
cycle
conduction
current
diagram,
waveform
One assumes
of
available
mean forward
the
this.
can be assumed
cycloconverter
profile
The R-C suppression
26.
ref.
group
a gradient
schematic
to
were
required.
one half
angle.
From the
The temperature
shown
the
of
and so the
point,
1 06 A.
.
is
power
in
is
supply
order
value
a mean forward
assumptions
device
current"
current.
device,
per
a rectangular
average
which
mains
of
6 groups
in
required,
CS21,
type
phases
"negative
3
and
36 thyristors
dissipation
carries
effective
16 A mean forward
at
each
conduction
produced
supply)
rated
may be made in
Each device
current
are
six
windings
Westinghouse
power
of
group
to
current.
graph
are
current"
there
were
the
assumptions
inuous
3 tvpositive
and as a result
beforehand.
fying
in
into
The devices
froin
the
of
reconstitution
The average
shown
The wire
rectification
Fig. 4.8,
in
.
4.10
the
type
0.11 A.
of
for
the
level
is
of
cont-
The maximum
the
of
above
mains
can be seen
that
the
currents
.
and sinks
Evidently
in
are
calculated
and
this
case
the
sizes
were
derived
necessary.
(Fig.
4.10)
component
6.
54
CHAPTER
5.0
Results
The results
the
assess
These
were
novel
on the
working
system
in
primarily
introduced
and techniques
concepts
in
this
to
order
thesis.
are
Use of
the
taken
operation
machine
the
the
of
secondary
emf signal
to
cycloconverter
to
generator
the
synchronise
emf induced
secondary
in
the
windings.
(ii)
Control
current
in
control
its
phase
of
the
with
in
amplitude
thyristor
firing
secondary
emf in
the
develop
to
order
to
angles
the
provide
machine
and to
secondary,
torque
a required
sinusoidal
speed
charact-
order
to
eristic.
(iii)
improve
the
Use
(iv)
Motoring
The results
mains
and
in
supply,
extend
so possibly
the
start-up.
the
use
torque
this
of
was considered
obtained
by loading
on the
thyristor
induction
DC machine
measured
generator
being
under
either
operating
transducer
in
characteristic
wind
2.
the
the
same shaft,
controller
A torque
speed
Chapter
in
were
control.
current
ing
for
connected
a regenerative
waveform
output
from
applications
DC machine
the
of
range.
The reasons
energy
phases
effective
of
quality
speed
operating
six
of
the
a
by
controlled
or
speed
torque
with
on
the
connect-
shaft.
In order
converter
computer,
oscilloscope,
to assess
a commercial
and
the
of
Fourier
waveforms
which
of the waveforms
the quality
more
analysis
taken
details
from
are
program
was
a current
in
Appendix
produced
used
probe
1.
by the
cyclo-
BBC
B
microa
on
and
digital
storage
55
No assessment
to
the
low
had
which
selection
power
be used.
of
optimally
Financial
rated
be meaningless
in
terms
of
efficiency
lossy
restraints
for
a practical
the
which
design
the
machine
version
and
was a relatively
figures
efficiency
commercial
due
system,
and components
prevented
Also
machine,
the
of
transformers
components.
teaching
universal
total
large
and the
rating
to
inefficient
the
was made of
of
would
the
system
the
output
as
a whole.
Operation
6 phase
Using
pages
be obtained
could
(ii)
With
with
speed,
(iii)
With
the
or
3 phase
secondary
holding
or
in
emf
the
several
modes:
supplies.
signal
generator
same output
changing
page
the
over
complete
EPROM
speed
range.
5.1
Secondary
With
was
the
secondary
below
and above
the
has
the
is
of
components
remains
phase
in
with
in
current
shown
two waveforms
output
respect
the
with
to
flow
the
phase
in
has
It
lag
be
the
the
the
that
the
signal
generator
output
but
the
the
actual
secondary
emf.
The
power
high
the
just
the
two waveto
generator
the
out
seen
between
cycloconverter
signal
gen-
speeds
corresponding
speed,
smoothed
signal
of
emf
throughout
for
relationship
with
can
the
Fig-5-1
emf
secondary
synchronism
(with
With
compared
the
an inherent
direction.
plotter
waveform.
in
wave shape)
is
secondary
from
shown
synchronous
secondary
The
current
that
actual
signal
are
There
through
power
Fig-5.2.
the
phase
of
the
remained
signal
speed.
1800
by
thyristors.
cycloconverter
circuited
produced
Note
plotter.
change
in
open
electronically
synchronous
changed
required
ating,
put
on the
pens
windings
an unchanging
producing
the
Generator
and the
range,
to
voltages
The electronic
generator.
erator
forms
the
with
operating
supply
emf Signal
the
compared
signal
two
varying
operout-
frequency
current
latter
flow,
has changed
therefore,
56
has
direction
changed
During
signal
Large
occur.
tors
to
When other
capacity
were
being
gated
the
problem
isolate
in
However,
area.
Further
the
.1
a disastrous
prevented
to
distortion
it
this
combat
would
from
waveforms
firing
the
of
5.2.1
Steady-state-results
emf
pared
This
four
torque
the
torque
computer
part
tude
of
torque
the
reference
the
on this
such
to
order
firing
these
conditions.
i. e.
mode,
current
secondary
scheme from
the
considerations
i. e.
the
had been
characteristic
of
the
in
amplitude
5.3,
com-
of
shown in
are
changes
Figure
and secondary
shape
any adjustment
measured
were
are
waveform
second-
changing
shown in
characteristic
without
speed
in
In
derive
to
due
probably
supply.
and these
control
waveform,
current
Fig-5.4.
the
of
amplitude
to
required
into
programmed
the
EPROM
program.
that
system,
control
required
of
operating
emf output
Considering
in
operating
was produced
the
the
required
future
designed
and
speeds,
operating
Examples
speeds
secondary
from
of
torque
the
in
source
its
in
operating
speed,
with
the
2.
develop
system
range
with
Chapter
for
the
pages
the
over
With
is
winding
System
Page Changing
Operating
ary
independent
a completely
5.2
With
be advisable
probably
the
thyris-
be required
layer
sblit
from
occasionally
that
would
mal-operation
derived
waveforms
operated
would
work
separated
This
circuit.
short
were
indicating
time,
the
the
with
mal-operation
time.
wrong
phase
harmonics
this
at
from
waveform
in
generating
observed
the
output.
correctly
laboratory
the
were
at
the
thyristors
equipment
supply
currents
manner.
operation,
the
operated
emf.
low
the
a controlled
cycloconverter
generator
secondary
on
the
in
speed
there
the
are
closed
The
characteristic.
is
to
the
not
signal
loop
torque
fully
main
output,
current
closely
deviation
achieved.
generator
or
quite
corresponds
operation
characteristic
signal
no
is
servos
to
that
By adjusting
this
torque
the
the
the
steep
ampli-
charact-
57
eristic
be scaled
could
incorporated
to
but
accurate
Typical
Fig. 5.5
this
modify
with
the
on the
results
torque-speed
the
evident
to
"peaky"
has
machine
at
inductive
shown in
are
analyses
of
speeds
is
shapes it
From the waveform
a relatively
were
complexity.
characteristic
low
servo
be made much more
control
Fourier
their
with
torque
or
could
in
1275 and 1725 rpm (+ and - 15% slip).
that
a current
increase
waveforms
operation
and if
signal,
a corresponding
current
for
down,
up or
leading
component,
a
very
be compared
Fig
-
30OHz
six
frequency
harmonics
so current
the
this
at
It
is
current
these
at
speeds,
low
harmonic)
correspond
evident
at
output
harmon-
frequency
any major
that
these
1275 rpm,
can
results
to
the
be notice-
will
as the
torque
and
low.
is
speed
of
( =40th
discontinuous
more
the
free
quite
These
cycloconverter.
of
frequency.
supply
in
greater
ably
are
phase
the
predictions
waveforms
higher
the
pulses
computer
with
Both
5.6.
ics;
current
from
6
5.2.2
Dynamic-results
The speed
demand speed
of
the
signal
of
The torque
It
torque
steps
in
caused
was
not
the
inability
speed
such
accurately.
in
fluctuation
for
two
shown in
operation
over
the
steep
greater
than
1650 rpm,
speed
increase
of
d. c.
drive
in
system,
not
howeýrer,
and
is
in
the
controller
containing
Fig-5-7.
part
of
the
the
This
but
maintain
a large
large
problem
electronics
to
the
machine
due to
emf output.
changing
energy
should
This
secondary
page
a wind
may occur,
a small
are
the
drive.
thyristor
slightly.
pages
loading
In
range
speeds
incorrect
any
the
of
A problem
torque
by
speed
fluctuate
to
between
torque
d. c.
the
over
by means of
manually
steed
variable
i. e.
tend
was changed
during
that
characteristic,
and torque
the
and speed
can be seen
speed
generator
by
constant
inertia,
occur.
due
rotational
to
this
speed,
large
i. e.
step
increase
a small
increase
in
in
58
speed
in
a large
produces
speed,
which
speed
again,
reduce
the
compared
rate
load
torque,
which
which
produces
load
torque,
Even in
such
a situation,
fluctuation,
of
the
in
the
removes
etc ..
with
increase
effect
and this
of
would
wind
speeds
a reduction
an increase
in
inertia
turbine
effect
input
gusting
the
causes
would
be slight
probably
on a fixed
speed
turbine.
The dynamic
by demanding
the
The resulting
to
change
speed
Fig-5.8a
shape
edge
due to
the
effect
the
of
secondary
emf.
At
in
the
Fig-5.8b
speed
the
shows
The strange
rpm.
bination
an
of
the
the
two
speeds
there
is
a large
and therefore
but
the
shallow
part
similar
to
Fig-5.8a,
waveform
is
small,
of
the
the
d. c.
by the
natural
emf opposing
reduced
torque.
system.
torque-speed
i. e.
the
change
has
and therefore
effect
time
lag
in
torque-speed
accelerating
torque
esponding
operation
of
a speed
change
the
leading
edge
at
occurring
characteristic
to
effect
between
peak
still
paging
at
as
on
approx,
above,
the
and
mentioned-above,
falling
shallow
1675
part
to
of
the
a com-
abrupt
change
a torque
the
and
1750
due to
Initially
rpm.
back
1550
is
-
rising
show the
changing
the
of
on the
emf is
opposing
page
4.6.
waveform
generator
the
with
control
peak
current,
quite
control
the
a
effect.
Fig-5.8c
in
are
results
and shape
cfamplitude
change
between
see Section
torýue
This
due
that,
lag
a time
the
modes.
page
be noted
with
obtained
The results
address,
accelerating
between
in
is
change
windings.
over
occurs
page
1250 rpm
an increase
same speed
change
characteristic,
little
to
the
shows
As this
current
leading
in
are
constant
must
The initial
levels
torque
of
a speed
produced
in
production
1450 rpm,
change
of
and
there
in
speed
controller.
It
electronics,
constant.
torque
The change
drive.
the
held
drive
Fig-5.8.
in
result
rotational
changing
page
resulting
the
shows
d. c.
the
the
the
in
changes
to
shown
of
and the
and amplitude
is
are
requirements
in
step
in
operation
torques
certain
of
increase
step
for
obtained
were
effects
there
level
torque-speed
is
corrcurve,
at
59
where
page
changing
has
to
operation
on
ponding
addressed
taken
and this
more
this
It
is
effect
on the
wholly
steep
waveform
phase,
which
responded
output
waveform
the
phase
will
never
present.
large
inertia,
i. e.
work
correctly.
Constant
Results
constant,
with
to
the
set
the
to
data
the
is
If
results
are
characteristic,
is
when operation
e).
in
present
for
to
the
the
in
paging
but
and
i. e.
speed,
the
frequency
the
the
of
frequency
slip
changes
incorrect
momentarily
rpm
the
for
given
during
a step
turbine
wind
system
turbine,
a wind
in
change
shape
and
was designed
these
Such
speed.
due to
operation,
and under
show operation
page
of
the
used
for
large
the
use with
circumstances
1350
at
a
would
as shown
same
was changed.
torque
In
this
,
1750
case
the
page
address
the
to
have
any useful
Such
in
the
1650
and
a square
(Fig-5-9).
the
changing
over
1500,
held
at
with
page
used
present
to
amplitude
complete
system.
waveforms
was equivalent
waveform
the
shape
control
simple
a very
the
operation
be found
could
operation
with
for
taken
also
one waveform
characteristic
produce
all
are
normally
pages
speed
in
5.8d,
was only
The control
three
using
With
speed
only
provide
1500
the
lag
not
was
were
mode of
assessed
the
eliminated
(Figs.
instantaneously
results
system.
would
curve
is
curve
torque.
operating
corres-
Page Operation
The above
it
but
occur
inertia
this
of
effects
blade
If
and it
in
the
of
a page
torque-speed
increase
part
the
the
of
a large
steep
that
shape,
The above
5.3
the
part
later
correct.
were
a change
in
part
output
of
steep
reduced,
be noted
must
the
on
Some time
effect.
results
completely
unusual
little
constant
each
and
change
then
in
range.
speed
characteristics,
operation
was
ROM, corresponding
Note
rpm.
wave output
The amplitude
rpm,
whole
held
page
of
held
amplitude
that
waveform.
produced
each
at
waveform
this
of
a torque
the
value
current
was
as
60
is
determined
the
opposes
production
current
should
the
current
waveform
plotted
but
ously,
the
more
improvement
in
The
both
the
torque
is
cases
super-
the
emf and also
theory
of
quality
speed
versus
linear
subsynchron-
This
due
be
to
may
due
supersynchronously,
quality
in
speed,
However,
supersynchronously.
waveform
secondary
sinusoidal
aiding
rapidly
in
it
with
speed.
The emf
speed.
and aids
speed.
with
The gradient
increases
general
with
change
also
emf with
linearly
emf changes
linearly
will
Fig-5-9.
in
secondary
subsynchronously
secondary
increase
the
in
change
current
of
As the
synchronously.
is
by the
simply
more continuous
nature
to
the
of
the
current.
As
the
over
expected
of
operation
out.
bility
Each phase
of
the
in
transition
The
characteristic
ging
system
has
except
over
the
nearest
at
speed
sub-
shown in
the
for
the
rival
for
advantage
low
is
of
using
subsynchronous
14%).
This
waveform
was
speed.
At
output
the
count
the
operation
It
of
which
the
calculated
speed
is
to
(1250
the
it
at
must
operation
page.
current,
but
shows
a smooth
the
speed.
the
but
fire
sinusoidal
torque-speed
required
can be seen
speeds,
all
speed
Steady
super-synchronous
on
give
synchronous
amounts
figure,
to
adjusted
stops
a constant
carried
changing
page
(as
using
differing
the
signal
constant.
mode
amp capa-
per
to
remains
Fig-5-10.
figures
best
and
with
wave
in
as shown
amp figures
The
considerably.
small,
between
per
are
angle
torque
compared
each
wherever
may receive
a torque
torque
torque
firing
winding
produces
effect
that
synchronous
at
achieved
also
at
its
of
control
a square
uses
ensures
speed),
range,
and
torque
so
system
the
terms
the
of
and
This
synchronous
speed
amplitude
changing
in
was
system)
than
this
of
assessment
changing
page
actual
assessed
was
current
the
better
was
operation
such
a more detailed
range,
to
complete
The
page
net
respect
over
thyristors.
is
(with
the
required
the
operating
waveform
technique.
the
the
Each
produced
current
of
quality
by
that
the
the
page
values
actual
is
waveforms
rpm
where
be expected,
as
chan-
the
the
vary
rather
advantage
secondary
61
this
emf at
is
this
the
will
case
where
technique
crossing
results
However,
level
torque
in
the
is
the
over
torque
be a large
speed
is
more
the
over
Figs-5.11a
here
in
of
torque
per
i. e.
only
2 or
analyses
has
system
the
the
of
torque
advantages
in
amp figures,
are
not
As this
bears
evaluated
in
The general
system,
and are
EPROM, are
it top II
The
.
and
current
effect
large
counteracts
been
of
aiding
shown
reducing
the
in
true
at
the
Figs-5.4d
secondary
part
firing
emf
the
page
the
with
where
the
page
least
harmonics.
best
of
The advantage
next
best
the
Fourier
changing
As with
but
results,
2,
is
the
desired
to
the
operate
and so be extremely
two waveforms
the
most
of
for
waveforms
and
5.6b.
angle
present.
of
effect
large
The
and
the
so
with
with
in
a sinusoidal
the
of
From
middle
the
the
production
quick
the
page
in
contained
effect
experimental
the
slips
supersynchronous
dip
charact-
fixed
inductance.
counteracts
However,
use this
the
edge,
the
shown
torque-speed
turbine
in
waveforms
helps
edge
been
simple.
used
leading
sharp
leading
lagging
the
sub-
has
as
the
amplitude
linear
essentially
to
then
fixed
at
may be possible
it
would
of
the
waveforms
supersynchronously,
a relatively
control
the
these
which
atall,
of
have
levels
two
in
the
gives
a constant
reflected
also
with
output,
cosine
worst
results,
compared
are
using
This
generally
rise
that
Chapter
system
they
amp figures.
some relationship
qualities
rapid
program
computer
have
that
per
small
changing
steep
turbine.
no control
virtually
is
a more
with
above
Figs-5.12a-h,
characteristic
speed
done for
and
great.
point
on a wind
eristic
page
the
for
the
results
waveform
particularly
a torque
is
paging
shown in
current
to
torque
These
waveforms,
per
relationship
best
the
a conventional
waveforms
has been
which
production,
wave produces
the
assess
Similarly
3%.
best
Fig. 5.9.
range,
amp for
the
synchronously,
to
gives
An interesting
produces
useful
and b.
system
figure,
range.
current
of
The square
speed
speed
opposing
modification
required.
changing
terms
greatest
complete
it
voltage
has
the
of
results
the
do
62
indicate
not
that
as a good
dip.
sinusoidal
This
secondary
the
Three
of
the
of
tions
as
the
three
as the
trol
associated
three
phase
rpm speed
three
the
are
waveform
case
to
the
the
in
current
the
the
program
angle.
prominent.
which
average
contributes
explains
in
current
1750 rpm
harmonics
The analyses
a lower
the
case
torque
per
that
the
in
of
per
con-
and so are
and their
for
worst
with
the
case
1750
for
discontinuous
the
the
of
amp due
the
speeds
shown
the
a torque
supply,
by the
show that
in
at
three
maxi-
at
before
waveforms
shows
produced
in
torque
phase
percentage
decrease
taken
waveform
three
operation
however
for
Fig-5.14
only
results
in
The current
phase
the
a six
cost
same condi-
be achieved
Note
as the
using
the
previous
decrease
20%.
assuming
shown
The results
under
were
shown
given
per
However,
not
results
as
pulses
three-phase
could
These
the
senses,
waveform.
the
for
levels
This
where
current
three-phase
was assessed
with
performance.
are
of
amp results
be obtained
and a six
system,
most
per
two
using
operation.
phase
shown
calculated
analyses
fundamental
winding,
the
firing
opposing
the
of
approximately
comparison.
phase
this
possessing
i. e.
in
performance
current
phase
operation,
for
six
are
not
is
been
three
Fourier
in
torques
operation
optimising
low,
by
number
quality
was reached.
these
have
the
results
required
At
waveforms
not
a greater
could
angle
phase
necessary,
not
for
a given
obtained
The torque
phase
maximum.
for
connected
be great,
supply.
maximum firing
to
secondaries
could
Results
mum torque
was too
were
obtained
were
six
Fig. 5.11b..
component
supply
absolutely
waveforms
calculation
supplied
and so improves
mains
with
program
being
provides
transformers
phases
half
their
This
above
presented
resistive
mains
of
with
cycle
output
obtained
the
is
waveform
Operation
phases
Fig-5-13.
is
in
current
Phase
transformers
in
the
control
of
current
winding
Six
type
may mean that
overestimated
5.4
this
three
total
phase
rms supplied
amp obtained.
63
5.5
Motoring
from Start-Up
Although
a
frequency
limits,
energy
slip
implying
recovery
start
ately
1000 rpm.
In
this
between
is
is
two
firing
so
mains
the
affecting
the
same
the
and
in
the
with
during
if
be obtained
The
operation.
current
Start-up
devices,
the
there
scheme,
in
given
larger
emf were
secondary
in
start-up
there
this
way
is
fewer
are
be different,
will
is
a neutral
without
and
ap
voltage
supply
start-up
as
pro-
secondary
both
are
produced
waveform
the
winding
However,
shown.
also
This
with
bias
to
receiving
emf is
divided
the
ability
then
emf is
the
emf
secondary
system
although
However,
here
positive.
phase
a
approxim-
secondary
phase
reverse
to
are
is
emf
progressively
torque.
starting
a
and current
the
making
when the
secondary
point,
supply.
available,
points
fire
six
phase
it
secondary
In
would
three
with
possible
also
the
to
respect
torque
A typical
for
presented
and drive
devices
the
its
speed
system
standstill
torque.
The torque
Extra
the
is
circuit.
short
that
which
as to
such
avoided.
Fig. 5.17.
with
is
found
Fig-5.16,
the
at
rotational
devices
when
in
minimum
voltage;
group
group
fire
a momentary
this
Fig. 5-15-
a motoring
device
the
in
p
n
produces
group
n
a zero
as shown
a current
and
emf
the
and
negative,
duces
the
operate
by effectively
to
between
can only
and
from
was achieved
equal
situation
was
machine
as shown
pulses
it
system,
This
waveform
firing
a maximum
induction
the
would
control
cycloconverter
normal
also
possible.
5.6
In
the
are
tb
order
shown
at
in
Fig-5.18,
nearly
be seen
paging
provide
is
that
a square
synchronous
wave,
the
The
required.
which
removing
voltage
zero
a stable
a neutral
thyristors
angle,
can
Connection
Neutral
the
shows
speed
(i. e.
neutral
output
current
point
of
effects
thyristors
the
is
the
firing
fired
at
no secondary
a constant
a qua'si
square
of
the
removing
being
virtually
and using
for
neutral
a constant
emf).
firing
angle,
wave.
For
It
by
64
three
phase
method
of
supplies
effect
the
of
converter
Section
5.7
Effect
firing
any
secondary
: thyristor
over
and its
both
to
the
cyclo-
in
natural
where
output
waveform.
the
current
wave
that
(and
the
subsynchronous
the-generating
mode.
This
voltage
opposing
over
these
speeds
problem
order
is
less
to
assess
with
the
wind
is
energy
current,
will
there
the
over
with
shown in
Section
plotted
against
speed
is
at
occurs
most
due to
net
difficult
the
net
system
firing
requires
5.3
for
angle).
low
speeds
to
produce
reduction
subsynchronous
of
For-
speeds.
less
firing
torque
severe.
a varying
the
effect
amount
of
of
this
thyristor
ratio
with
supply
speed,
volts.
a
be
must
emf varies
a fixed
as
produce
has been
problem
it
the
of
required
secondary
therefore
emf*at
secondary
current
were
major
ratio
of
generation,
output
However,
the
of
ratio
a decrease
the
of
necessary
where
the
operated
an increase
the
upon
a particular
the
general,
subsynchronous
require
cases
slips),
due to
In
for
and current
control
current
tunately
cycle
torque
can be seen
it
half
on the
effect
of
will
(provided
In
depends
In
the
optimise
thyristors
voltage.
volts.
ratio
to
the
emf
this
provide
in
was
the
neutral
as described
be possible
current
The amplitude
range.
amplitude
high
of
In
chapter,
Essentially
so the
the
standstill,
secondary
supply
a positive
voltage
speed
this
e.
due to
when generating,
supplying
a particular
and smoother
supply
a fixed
(i.
deteriorate
will
Without
should
voltage
peak
volts
continuous
operating
peak
the
and
Fig-5.20.
in
enough
the
an increase
angle
it
system
for
emf
firing
speed
and this
Voltage
required
instance,
more
up from
starting
commercial
between
angle
shown
speeds
see Fig-5-19.
emf,
allows
a transformer),
for
The waveform
subsynchronous
of Transformer
relationship
of
secondary
be available,
to
5.5 above.
For
by
low
at
still
likely
not
may be suitable.
operation
however,
rapidly,
is
a neutral
the
system
These
and
65
results
Note
are
that
the
test,
but
the
the
to
firing
waveforms
figure
can
least
were
the
maximum
firing
idea
the
some
of
remained
throughout
its
and at
the
supply
maximum,
the
of
simplification
restricted
voltage
preferable
90*
for
the
supply
the
of
to
The
-
machine
voltage
torque-speed
required
rating.
by variation
to
is
the
amplitude
constant
due
optimum
as the
in
modified
most
up to
changed
angle
the
as long
possible,
not
Also,
thyristors.
torque
of
was being
As has been mentioned
used.
values
angle
available
the
give
firing
the
voltage
volts
for
waveforms
and that
net
Fig-5.21
control
supply
the
in
shown
be
will
characteristic
can be achieved.
using
at
To give
some
reduced
volts,
a given
speed
shown
for
a reduction
the
waveform
that
of
the
the
the
5.8
Summary
These
i. e.
done
effects
methods
varying
of
300 Hz
have
been
was
of
a neutral
six
taken
advantage
control
as
and
connection
The
effect
is
are
without
are
in
in
to
available.
a six
phase
considered.
50%
to
shown
in
Note
Fig-5.23-
these
of
in
of
this
previous
waveform
40
are
but
volts,
harmonics.
components.
supply
contained
operation
results
also
frequency
high
for
and so some distortion
volts,
an assessment
may be found
which
amp of
modification
phase
described
the
per
full
waveform
These
volts.
torque
the
of
system
control
with
in
output
obtained
analyses
the
reduction
operation
operation
for
be inherent
the
shape
in
Fourier
designed
were
supply
volts.
associated
which
its
supply
the
novel
but
of
is
to
the
changing
for
will
the
successful,
other
shape
operation
of
method
been
results
for
quality
and
point
correspond
in
of
amp figures
per
for
torque,
has
system
These
torque
50%
quality
essential
relative7improvement
and show an increase
of
current
the
of
the
and
Fig-5.22
in
idea
the
output
current
The
system.
sections
of
this
speed,
was
the
with
be small
This
supply
A very
in
comparison
assessment
facility,
useful
thesis,
most
with
has been
and
the
capability
66
of
motoring
in
wind
have
in
up from
turbine
been
this
of
The
applications.
considered,
These
area.
designer
standstill
provisionally
discovered,
was
a slip
results
energy
recovery
effects
of
though
more
be
should
in
variation
analytical
for
use
in
useful
supply
is
work
importance
considerable
of
system
may be very
which
wind
turbine
volts
required
to
the
appli-
cations.
It
due to
such
must
the
use
a technique
be noted
of
the
is
that
all
secondary
very
strongly
these
results
emf signal
were
generator,
recommended.
made easily
and that
available
the
use of
67
CHAPTER
6.0
Conclusions
Variable
speed
significantly
For
blades
to
reduction
so
power
be
the
to
in
terms
have
order
system,
to
prevent
interest
in
energy
turbines,
area
this
for
study
Considerable
(ref.
wind
the
in
turbine
application
of
variable
Therefore
investigation.
be a useful
interest
has
been
speed
in
Outline
in
must
These
speed
wind
increasing
techniques
as
will
in
be avoided
regarded
to
in
this
based
wind
a worthwhile
in
investigated
system
papers
about
especially
has been
knowledge
a
be obtained
to
generating
particular
to
available
operation,
there
is
operation
the
is
a variable
speeds
contribution
shown
of
Recently
variable
speed
range
certain
problems.
structural
should
if
indicate
as a result
frequencies.
resonant
speed
operating
speed
Section
in
operating
needs
to
capture,
energy
data
turbines
wind
and
may prove
and given
little
leads
generator
fluctuations
variable
structure
on the
and
of
effects
wind
simulator
information
more
This
This
speed
very
of
the
reduced.
torque
At present
Obviously
and will
are
turbine
reduction
by
state
by allowing
produced.
seen
variable
characteristics
bearing
great
of
is
on the
a steady
however,
system
supply
by
207.
i. e-a+
mainly
obtained
produce
turbine.
thesis,
Dynamically,
-
seem to
wind
operation
energy
a wind
operation.
mode.
the
grid
from
taken
and structural
of
turbine
the
this
fluctuations
torque
advantage
operational
dynamic
5%
with
a much softer
significant
speed
speed
variable
speed,
into
extra
speed
in
outlined
speed,
of
gusting
Results
the
order
a fixed
than
type
the
significant
variable
the
the
show the
about
in
vary
variations
27).
the
of
does not
turbines
wind
synchronous
the
of
of
most
2.5.2,
capture
characteristic,
is
calculation
(ref.
energy
about
Cp
maximum
the
of
scheme
variation
Work
operation
greater
an operating
speed
of
and Further
on
area.
this
study
28).
The
cycloconverter
slip
energy
recovery
system
investigated
has
both
68
and disadvantages
advantages
been
described
configuration
during
transient
be
has
overcome
There
douýly
with
fed
an economic
and reliable
system.
The stability
problem
failure
does not
range
appear
is
capability
are
known
well
machines
stability
and cycloconverters.
these
of
(i. e.
semiconductors
a motoring
turbine.
elimination
by
to
problems
The problems
by
overcome
the
angles
of
values
derived
of
provide
have
that
been
a computer
in
output
a suitable
conjunction
phase
the
values
secondary
waveform
firing
the
calculated
previously
These
with
current
controls
which
with
accordance
program.
in
has been
machine
asynchronously
technique
in
fed
generator.
an electronic
current
sinusoidal
operate
producing
cycloconverter
from
to
machine
problem
a doubly
of
emf signal
secondary
The
been
the
allowing
a novel
produce
associated
commutation
are:
resolved
has
the
up
speed
as
power
power
The restricted
have
which
has a simple
to
active
particularly
concentrated
schemes,
subject
on the
for
a basis
is
and only
).
run
problems
study
with
initially
to
(which
outages)
etc.
alternative
The cycloconverter
link
disadvantage,
a major
and control
This
mains
capacitors
available
1.2.
no d. c.
with
no chokes,
to
Section
in
to
compared
designed
are
emf in
the
to
rotor
windings.
The possibility
of
phases
the
mains
by the
removed
use
of
supply
of
circuit
a short
due
to
a divided
in
overlap
the
cycloconverter
frequencies
(v)
speed
wind
program.
The
deterioration
has
been
The
control
turbine
of
reduced
have
by
strategy
been
the
current
using
six
and
obtained
two
has
been
arrangement.
winding
0
(iv)
between
occurring
waveform
phases
prediction
by the
of
of
use
of
for
mains
high
output
supply.
performance
a computer
for
a variable
simulation
69
6.1
Asynchronous
Other
slip
synchronous
energy
manner
into
voltages
Operation
the
this
its
new
the
machine
required,
produce
greatly,
the
by
ously,
this
means
emf induced
shaft
in
the
of
synchronism
the
with
and the
correct
are
being
emf,
and
the
to
in
remove
applied
phase
angle
over
minor
These
models.
generator
secondary
disc
to
emf signal
though
the
of
fitted
the
have
in
machine
complete
generator
changes
to
in
operate
the
runs
provided
secondary
signal
a slotted
effectively
is
was effective,
further
This
asynchron-
was
in
4
design
been noted
in
Chapter
6.2
Waveform
Output
means of
"control
the
wave
"Cosine
wave"
a sinusoidal
for
inductive
and
resistive
an
is
Control
load,
in
the
which
crossing"
technique.
used to control
the
output
current
inductive
load.
into
operates
cycloconverter
conventional
a
fluctuating
operate
cycloconverter
which
control
the
of
to
allowed
by means of
allows
and smooth
operation
is
generator.
frequency
This
and improve
simplify
signal
windings,
The principle
range.
speed
torques
is
machine
emf
secondary
mode,
an asynchronous
the
the
machine
rotor.
wind
is
change
tends
to
if
as
speed
difficult
slip
generator.
about
the
incident
acts
and this
control,
be very
This
machine
a large
a
by forcing
achieved
the
in
operate
frequency.
if
and decelerating
the
is
and
of
would
as the
a secondary
of
This
However,
out
to
controlled
speed,
This
problem,
information
produces
could
of
are
Machines
a particular
speed.
especially
shaft
To remove
at
is. temporarily
system,
to
speed
synchronous
Induction
range.
a rotational
and so accelerating
rapidly
the
speed
windings
to
Ring
systems
instability.
control
turbine
wind
their
machine
corresponds
were
recovery
over
frequency
Slip
of
waveform,
In
a slip
firing
a completely
angles
In this
firing
which
of the
is
energy
are
passive
produced
by
technique
a sinusoidal
thyristors,
producing
usually
recovery
lagging
system,
the control
however,
70
a variable
tional
amplitude
cosine
This
study
to
and to
modify
produce
converter
these
the
associated
waveform,
EPROM.
an
This
firing
angles,
speeds
worked
simple
piece
intermediate
control
firing
for
for
or
exact
In
firing
for
is
a three-page
analysis
if
for
which
a more
a commercial
as
for
however,
proposed
general
system
different
at
an essentially
system,
for
approach
for
high
(it
be
would
the
CPU time
desired.
to
torque
or
the
achieved.
required
on a Cyber
difficulty
an analysis.
obtaining
speed
so that
calculate
of the
one
may be
a current
waveform
may have
An
synchronous
this,
such
control
supersynchronous
synchronous
30 mins.
to
over
using
Some knowledge
above
is
calculated
advantages
nearer
an idea
gives
from
produce
page
the
in
contained
whole
to
calculation.
angle
necessary,
system
ran
a page
had
speed
range.
speed
program
computer
output
a sinusoidal
any
of
speed
near
of
sinusoid.
of
with
amplitude
at
and using
pages
programmed
required
the
speeds
conjunction
the
control
that
for
angles
fewer
one
cyclo-
was achieved
shapes
a three
speeds,
the
emf,
This
sufficient
the
over
that
waveform
using
with
waveforms
each waveshape,
parameters
wave,
the
torque
therefore
solution
machine
to
i. e.
subsynchronous
shape).
may be noted
mainframe
control
be used
angles
on-line
in
system,
wave
of
techniques
possess
secondary
increment
waveform
may not
helpful,
square
that
square
and
It
an
Fig-5.4
could
current
low
of
these
waveform
may be
a virtually
and
nearly
servo
one control
for
pages
firing
conventional
and each
a control
though
it
the
consisting
producing
simpler
solution
from
noted
page
even
waveform
speeds,
are
an even
64 parts
separate
firing
of
the
ensure
angles.
calculated
waveform
of
equipment,
firing
waveform.
required
with
to
conven-
output
the
phase
method
wave instead
However,
well.
or
waveforms,
the
each
and using
be
could
from
into
principle
of
these
control
was divided
in
control
and the
a distorted
a computer.,
current
with
load,
the
produce
using
crossing
shapes
as the
range
would
output
operated
waveforms
what
cosine
in
contained
calculate,
sinusoidal
waveform
The speed
its
to
actually
by deriving
technique
crossing
proposed
angles
is
emf source
of any
the
of
A one-
sacrifice
a suitable
such
71
As indicated,
is
control
method
not
the
yet
completely
in
6.3
Divided
a similar
divided
machine.
The
net
derating
operation
at
full
rated
removal
of
slip
energy
the
of
if
at
the
in
eous
not
the
Phase
phase
However,
system
the
use of
a
up
angles
for
which
standstill
will
not
would
be
speed
cycloconverter
would
begin
secondary
machines
axis
is
will
low
toward
A suitable
the
to
machine
1200 rpm (i. e.
to
the
advantag-
machines
beyond
the
took
also
1000 rpm.
particularly
allow
terms
and
the
to
self-start.
to
in
180*,
into
as vertical
axis
the
arrangement
at
firing
is
standstill
also
this
as a motor
horizontal
system
wind
by
current
possible
advantages
held
are
is
as
derating,
this
that
seeins
improved
speed
great
especially
run
This
generate.
of
a six
phase
terms
of
the
maximum
torque
torques
torque
per
of
the
obtained
the
shown
three
by
to
phase
a three
shown in
clearly
current
OutPut
amp is
which
has been
supply
would
be
20% over
supply
phase
can
system
the
three
attain.
is
the
Its
waveform.
up
20% sub-
0
and smoothness
at
It
from
may be
the
of
Supply
continuity
advantage
above
implement.
to
easy
in
for
rated
provides
firing
up from
this
the
The advantage
added
1),
and if
be extremely
Six
the
of
a derating
Despite
generate
trend
for
slip),
synchronous
6.4
(ref.
than
greater
applications,
strategy
1000 rpm,
to
motor
and the
blades
operating
to
to
incurs
technique.
the
run
will
energy
self-start
at
equipment.
alloýved
ability
wind
solidity
current
principle
possibilities
however,
system,
problem
standstill
machine
This
torque
control
is
cycloconverter
emf,
are
general
arrangement
the
of
circuit
the
that
The
output
below).
winding
recovery
short
simplifying
means
for
method
Winding
the
the
a suitable
and there
(see
system
Use of
using
of
resolved.
however,
seems useful,
micro
problem
only
72
I
50% of
approximately
the
particular
weighed
six
Six
For
designer
thyristor
have
system,
and it
regime.
This
probably
reduction
decrease
ary
in
in
emf
the
tion
has not
will
tortion
be
to
phase
path,
phase.
as
device
A more
specification
three
in
complex
one
ring
some
phase
starting
firing
for
but
of
one attempted
to
into
taking
the
emf
volts
advantage
of
a 50%
the
second-
of
running
torque
up
the
assist
will
ap
system
the
produc-
there
group
would
firing
do the
to
is
dis-
produces
neutral
the
angle
effect
calculations
terms
tend
provided
voltage
of
are
in
a neutral
without
in
predic-
accurate
zero
the
operation
that
when
is
per amp for
account
winding,
difficulty
system
phase
the
and
emf will
of
approach
amplitude
the
mean
will
control
of
a steady
Also,
difficult.
a given
torque
The
Removal
of
phases
recovery
secondary
given
in
possible
scheme,
may provide
been
volts
slip
circuit
open
production
If
emf
up.
necessary.
Thi*s
firing
the
of
secondary
is
waveform.
more
the
operation
An analytical
the
start
current
is
current.
continuous
during
on other
system
the
for
work.
has
for
the
of
them for
torque.
a given
a non-neutral
even
be
to
provide
secondary
a 50% increase
a neutral
output
firing
ratio
as a greater
for
system,
circuit
optimise
this
consequences
angles
for
thyristors
group
volts
neutral
calculations
current
for
without
the
of
0
three
volts,
and torque
by a constant
in
the
i. e.
current
of
likely
volts.
have
to
done
recovery
performance
Some idea
mode,
firing
to
benefits
for
phases,
have
will
needed
have
open
on the
optimise
self-start
of
the
and
been
to
also
energy
be possible
should
Operation
tion
bearing
supply
transformers
may also
a slip
great
supply
of
of
volts
supply
the
of
advantage
six
below).
supply
necessary
thyristor
cost
by using
obtained
This
used.
operation
(see
Work
machine
voltage
added
Further
the
maximum torque
phase
a neutral
the
the
to
the
phases.
6.5
of
supply
against
without
the
of
produce
a more
not
necessarily
device
fires
be required
a
providing
an
in
to
dis-
another
ensure
n
a
73
that
two
that
a neutral
of
devices
these
the
advent
then
produced,
firing
angle
cheap
this
is
time
modify
firing
in
angle
is
complete
system
powers).
This
from
supplied
6.6
seems
necessary,
used
in
the
need
for
in
would
of
the
the
using
thesis,
although
this
then,
continuous
micro
an initial
with
outputting
this
wave-
though
calculation
be an on-line
effect
waveform
resource,
begin
could
as
current
merely
use
as a control
act
Calculating
and
micro
their
of
adaptive
into
be required
will
the
was not
grid
supply
(i.
in
this
possible
harmonics
the
of
the
e.
the
sum of
as the
work
by the
produced
rotor
and
stator
and rotor
stator
were
transformers.
separate
Summary
In
previous
total
the
work
done
and
range,
this
the
on
operate
at
then
a cycloconverter.
achieved
its
speed
operating
wind
system
With
a slip
using
was
built
the
A more
has been
which
for
speed
excessive
implemented
demands.
system
characteristic
limit
This
29).
A scheme
efficiency
was
(ref.
and
advantage
upon
advance
a considerable
turbine
compared.
automatically
study.
is
University,
Leicester
maximum
This
here
presented
strategies
operating
various
work
a variable
of
assessment
with
output
solution.
the
required,
This
the
of
could
seems a waste
it
as
may have
these
impossible,
circuit
avoided.
Some assessment
for
unlikely
method.
control
to
it
crossing
memory
is
is
and so some resolution
a processor
quality
If
shape,
an increase
the
technique
waveform
a cosine
If
crossing
accuracy.
into
It
time.
microprocessors,
virtually
increasing
and
one
many sites,
be an effective
could
cosine
any
scheme.
possibly
form
for
and assess
every
as a digital
of
control
generator,
at
be required.
will
a cycloconverter
waveform
firing
always
be provided
will
problems
With
in
were
of
the
allows
much
energy
and
obtained,
increase,
tested
detailed
of
the
was
recovery
and
a new
turbine
speed
chosen
scheme
successfully
secondary
74
emf
signal
generator,
and running
of
phase
This
etc.
and will
each,
Work
does
is
experience
inverter)
give
with
based
a good
be useful
wind
to
idea,
turbines
on the
control
however,
of
computer
of
University
with
a system
wind
turbine
design,
many novel
modified
a designer
Leicester
at
proceeding
winding,
to
studies
actual
i. e.
this
of
systems.
operating
by
of
system
generation,
speed
variable
(implemented
the
design
advantages
relative
obtain
the
components,
waveform
the
further
in
encountered
generation
too
with
over-complex,
divided
supply,
were
As a second
equipment.
a little
was probably
six
the
difficulties
no major
a d. c.
thesis.
link
75
CHAPTER
7.0
Acknowledgements
The author
the
Department
Particular
thanks
are
the
grateful
to
Mr.
R. G.
assisted
in
the
laboratory.
Finally,
prepared
the
thanks
text
and
for
expressed
work
Professor
thank
Engineering,
of
who supervised
to
wishes
to
to
relating
Stephens,
to
the
Mrs.
Mr.
the
use
of
Dr.
G. A.
this
D.
Department's
Smith
thesis.
Donegani
H. Townsend
drawings.
G. D. S. MacLellan,
and
and Mrs.
Head of
facilities.
and Mr.
G. E. Gardner,
The author
is
Mr.
Skeete
J.
C. W. M.
Gardiner
also
who
who
76
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rotor
Transactions
Nov.
25.
on Power
M. S.
motor;
and Systems,
Apparatus
Erlicki,
I. E. E. E.
Vol. PAS-84,
No. 11,
1965.
Super-synchronous
fur
an induction
of
static
converter
Stromrichtertechnik
P. Zimmermann,
cascade,
und Antriebsregulung,
Institut
Technische
Hochschule,
Darmstadt.
26.
Voltage
J.
27.
and dv/dt
transient
Merrett,
Mullard
Multi-speed
T. S. Anderson
Pittsburgh,
28.
Control
29.
Static
Preliminary
for
Wind
system
of
turbines,
Westinghouse
speed
wind
1986,
Proc.
induction
turbine
wind
energy
Electric
1968.
Corporation,
speed
D. Goodfellow,
recovery,
energy
B. W. E. A.
motor
wind
Conference.
control,
Aldborough
Manor,
of
D. Goodfellow,
Engineering
control,
Boroughbridge,
D.
Conference
for
generator
Sir
a doubly
Goodfellow,
D.
Engineering
turbine,
Power
layer
operation
recovery.
Power
Universities
boundary
the
frequency
constant
simulated
Smith,
Co. Ltd.
for
Universities
speed
computer
32.
wind
to
application
variable
considerations
Smith,
Variable
G. A.
March
G. A.
Smith,
I. E. E. Vol. 124, No. 6, June 1977.
generator
31.
for
& G. E. Gardner,
scherbius
G. A.
No. 92,
Pennsylvania.
Smith
Proc.
30.
generator
bridges,
thyristor
Communications
& H. S. Kirschbaum,
strategies
G. A.
Technical
electrical
in
suppression
&
1985.
using
D. Donegani
a
&
1986.
Lawson-Tancred
N. Yorkshire.
induction
Donegani
evaluation
Conference
Henry
fed
Sons &
79
APPENDIX 1
TEST FACILITIES
A1.1
Wind Turbine
Simulator
The consideration
turbine
to
in
changes
differ
upon
from
this
wind
the
(steady
During
any
can be neglected,
However,
Max Cp
to
ponding
energy
steep
as the
may affect
a variable
of
by
the
wind
characteristic
is
in
shallow
torque
the
energy
capture
turbine
wind
will
this
an almost
speed
to
turbine
depending
torque-speed
operating
wind
turbine
an amount
the
speed
speed
by the
gained
value
system
on
a variable
of
response
state)
operation
region
Mathematically,
inertial
The actual
speed.
theoretical
manner.
capture
energy
the
account
response.
difference
speed
into
take
must
the
of
curve
a greater
fixed
corresextent.
can be described
system
as follows:
If
it
should
curve
is
we assume
be
a good
an
simply
to
approximation
inverted
square
Cp=C
pm
C=
pm
where
near
predominantly
operation
Kc=
and
peak
peak
over
(X
M-x
C
p
speed
shape
ratio
at
max Cp
parameter.
Now
P=KCV
where
WpW2
=KWV3
[C
pm
3 cc;
w
pm
3
KwV (C
AV
3+
-Kc
K
PA
)2 1
(X
M-X
WR )2
(X
K
cmV
X2)
KcmV
V3
KWKC
+
2WXMR
KWK
cV3w2R2
v2
pm
BV
2w-
this
i. e.
wave,
maximum
Xm = tip
that
assume
-Kc
the
cvw
2
of
the
Cp
curve,
range
the
Cp
80
Dynamically
the
speaking,
rate
of
change
TL
is
load
the
torque
One may
obtain
assume
a response
13V 2_
+
jw
in
change
P
with
generated
available
It
cally
CVW 2-K2,
V
the
of
a wind
wind
spectral
response
eristic,
in
terms
of
derived
from
the
above
for
power
to
with
working
the
slip
the
the
time
the
by
and
linearising
this
equation,
jyt
w1)
generated
of
simulation
This
thyristor
controller
recovery
to
density
However,
useful.
energy
turbine
a given
this
could
simulation
also
and a DC machine
under
system
conditions
the
with
it
thesis
turbine
a wind
wind
mathemati-
speed
charact-
function
one may produce
compared
in
to
above,
and a transfer
From this
power
wind.
taken
assumptions
equations.
actual
in
a real
be more
would
tion
the
available
produce
W
2
91
given
expression
2)
3
may be possible,
analyse
by
KWC V3
pm
P
and
CVW 2-Kw
_
oK
given
form,
the
of
BV2W
+
(LV'3
a step
is
speed
=KzW2
dw
(AV3
=1
dt
Jwz
=1
rotational
1 (p
Jw
dw
dt
where
of
an analytical
theoretical
was decided
that
on a microcomputer
then
to
be used
in
drive
actually
to
similar
conjunca
actual
operation.
A1.1.1
Computer_simulation
The computer
system
performance
an actual
variable
A diagram
the
of
model
but
also
speed
system
was developed
to
control
constant
is
shown
not
only
a d. c.
frequency
in
Fig. Al. l.
as a means for
motor
generator
driving
coupled
assessing
the
to
shaft
of
the
grid.
81
Al-1.2
Wind_turbine_characteristics
The torque
developed
by a wind
turbine
1
is
P)
V2
p
2
by
given
3
(i)
TrR
where
V=
wind
R=
radius
speed
The swept
of
blades
area
and
and can be input
available,
can be used
and a curve
manually
taken
or
(i)
is
used
(ii)
From
an
being
to
to
Cp
The wind
them.
intervals
from
transducer
of
X
and
figures
can be input
speed
a disc
model
on the
a d. c.
control
internally
The
program
aims
the
inertia
of
derived
the
infinite
actual
that
the
the
overall
shaft
data.
wind
the
of
drive
coupled
value
of
to
torque
generator
the
when
generatoP,
the
when
or
computer
system.
test
a turbine
generator
is
of
is
shaft
will
low
of
This
size.
across
The shafts
then
follow
it
the
demand is
speed
are
has been
present
inertia
in stantly
computer.
any
transferred
inertia.
rotor
generator
generator
the
model
and any damping
stiffness
from
derived
to
turbine
the
with
the
is
To simplify
the
the
and
gearbox
considered
to
ignored.
As
to
reasonable
demand for
produced
assume
speed
from
follow-
the
equation
J.
where
J
generator
the
Also
program.
be
will
The_rotor_dynamics
combined
be of
to
used
the
fitted
From a torque
is
model
to
any turbine
derived:
computer
A1.1-3
ing
is
for
characteristic
2 second
at
The torque
the
Cp
generator
dw/dt
= Tr
represents
the
sum of
the
inertia,
Tr
is
torque
torque
referred
the
across
turbine
rotor
developed
the
(ii)
Tg
-
gearbox.
inertia
by the
and referred
blades
and
Tg
is
82
The two
second
blade
torque
give
the
the
torque
is
The rotor
demand speed
When the
to
is
This
intervals
is
torque
the
update
rotor
speed
from
0.4 s
at
become
to
drive.
speed
is
generator
with
determined
a D/A converter
through
to
compared
and an acceleration
output
variable
0.4s
at
(i).
to
used
test
actual
interpolated
generator
speed
the
is
equation
by the
this
and
,
intervals.
the
from
developed
(ii)
equation
data
wind
being
its
used
is
torque
measured
0
by
transducer
a shaft
to
scaled
A1.1.4
much
to
the
higher
level
to
control
computer
torque
of
it
where
is
suitably
by
produced
the
gener-
The_electrical-generator
by
controlled
torque-speed
the
the
slip
the
the
speed
and therefore
generated,
energy
recovery
to
equipment
a limited
This
models.
be used
can
to
of
the
variable
the
load
lie
on the
These
,tics
characteris
enables
the
model
induction
slip
generator.
torque-speed
given
providing
coýputer
induction
ring
slip
these
power
generator,
a synchronous
circuit
used
speed
is
torque,
required
characteristic.
However,
speed
is
computer
on test
generator
whole
generator
are
including
system
or
a variable
modelled
simply
than
detailed
equiv'alent
the
performance
rather
comparative
investigation
performance
including
of
as
generators.
Computer-output
Al-1-5
The
kWhrs
the
Alternatively
in
Fig. A1.2
+
Cp curve
which
represents
The
operating
continuous
and
power,
and
input
simulated.
When the
of
the
represent
being
ator
is
and
required
and the
can be displayed
dynamic
x
the
in
behaviour
torque
inertia.
load
developed
shown
by the
At
present
on the
screen.
graphically
due to
torque
the
characteristics-for
blade
be
can
the
represents
form
tabular
Cp
torque,
speeds,
as
power
shown
in
generation
turbine.
memory
the
of
the
program
computer
are
the
has data
for
the
,
83
Nibe
and MOD-2 systems,
to
curve
input
to
possible
to
the
from
mode of
A printout
A1.2
Fast
Fourier
curve
and the
the
has been
It
equations.
program
fit
will
be
will
a suitable
being
of
the
program
Typical
which
and perform
analysis
is
is
shown
results
The analytical
Mr. D. Donegani
conditions
in
shown
currents
to
speed
in
or modified
can
the
program
Fig. Al-3.
grid
of
the
a fast
achieved
in
supply
cycloconverter
have
will
cycloconverter
download
will
by the
produced
the
from
t
bearing
a digital
been
given
parts ofthe
program
most of the
writing
to
in
Chapter
5 of
were written
graphics.
random
vibrations
A system
storage
A printout
program.
this
by the
thesis.
author,
and spectral
the
on the
waveform.
Fig. Al. 4.
have
in
system.
on the
analysis
a published
great
control
a waveform
Fourier
using
An introduction
D. E.
1984.
Longman
analysis,
Newland,
and operating
investigated.
is
program
ratio
Analysis
developed.
oscilloscope
as gearbox
operating
and desirability
efficiency
the
actual
and back
windings
Fourier
such
control
of
The quality
rotor
CP
of
figures
curve
information
be input
suit
Cp
form
the
them.
Other
either
in
The
of
84
APPENDIX 2
THYRISTOR CONTROL WAVE PROGRAM
A normal
in
to
order
the
which
usually
lags
the
applied
as envisaged
here
the
load
were
be of
aiding
could
be used
to
modified
for
Advancing
in
method
the
or
retarding
distortion
To
the
secondary
In
current
to
for
the
secondary
the
these
it
the
cosine
the
the
firing
net
fed
may be
technique
control
angle
as the
modulated
but
crossing
of
inductive
emf voltage
current
amplitude
was also
considered
secondary
which
wave
with
respect
the
system
was
and
negative
secondary
did
wave
the
of
control
wave
lag
the
the
are
emf generator
emf
totally
would
but
type,
current
separate,
waveform
try
emf present.
secondary
a circulating
groups
to
advantageous
not
to
a computer
effects
firing
that
generator
4
the
current
simply
and
produces
winding
is
to
program
obtain
was
current
in
be of
the
should
developed
phase
correct
to
with
the
amplitude
characteristic.
current
machine
assumed
to
angles
the
predict
is
required
is
a doubly
a secondary
The
voltage;
torque-speed
induction
winding
as the
if
For
wave..
contains
load
the
wave
output.
and also
order
of
used
the
a required
knowledge
if
required
emf,
produce
the
positive
counteract
calculate
to
the
If
control
phase.
factor
power
in
this
control
the
also
current.
system
in
improve
advancing
in
this
the
control
system
a sinusoidal
output.
be sinusoidally
emf are
a current
produce
this
'still
However,
this
in
counteract
would
and secondary
this
opposing
uses
current
same frequency
the
or
still
thyristors
to
technique
a sinusoidal
will
either
Crossing
produce
current
system
Cosine
by
produced
parameters
shown in
be a simple
is
circuit,
In
angle
The model
necessary.
Fig. A2.1.
R-L
firing
a particular
the
with
program
the
an associated
emf source.
The computer
program
was run
for
20 speeds
between
+ 207. and - 207.
85
For
slip.
calculated
istic
each
the
and
that
required
conduction
same
average
period,
fied
converter
output
and required
advanced
the
accuracy,
to
order
time
manually
and
from
the
program
run
most
effective
firing
angle
as
soon
the
affected
once
modified
calculated
The
angle
at
firing
angle
passed
the
pass,
equation
giving
the
the
so had
to
required
in
modified
could
alone
actual
be
to
was then
modification
cyclo-
the
to
calculations
number
current
the
firing
required
along
was
angle
to
be
not
nearly
be
over-
input
to
over,
and less
current
the
time
through
This
on its
was the
one
and an answer
the
and
wave-
modifying
so
obtained,
for
averages
This
be recalculated.
that,
available
these
once.
calculated,
effect
angles
remain
current,
and had to
previous
firing
of
and ran
was attempted
changed
and then
next
the
each
it
angle
were
the
of
satisfied
and
This
needed
sinusoid
the
be modi-
could
between
angle
computer,
output
obtain
firing
next
comparison
current
for
again.
If
to
order
firing
previous
turn
in
This
its
This
rms current
were
produced
output.
to
of
over
A2.2.
which
peak
This
the
current
cycloconverter
comparison
modifying
solution.
the
as
last,
Fig.
firing
current
thyristor
of
value
character-
of
of
each
output,
the
on the
required
of
to
the
cycle
quantity
comparisons
calculated
scheme
first
/2.
iterative
programs
cycle
of
rms output.
for
a half
forms
correct
limit
The iterative
during
ratio
of
as the
program
average
whether
amplitude
by
was
by an iterative
sinusoidality
fired
rms of
When these
the
produce
by the
the
ran
peak
correct
necessarily
retarded.
the
required
operating
a half
had a peak
waveform
waveform
calculated,
produce
waveform
indicated
averages
or
the
current
torque-speed
current
with
as the
not
the
then
assess
of
the
required
is
to
a sinusoidal
obtain
is
modification
the
to
order
current
to
order
(from
required
quantity
assuming
of
The program
compared
sinusoidal
in
done
is
angle
required
In
period
rms
angles
rms.
the
waveform,
required
firing
the
time
was input.
required)
process,
the
speed
the
in
When each
on.
neighbours
could
was
be
wasted.
produced
by
an applied
voltage
across
86
a resistor-inductor
is
combination
(V-iR)/L
=
di/dt
where
i=
t
current
= time
V = voltage
R = resistance
L = inductance
The calculation
The current
method.
being
to
set
was either
fired
as an initial
used
half
Given
being
half
of
tive
half
the
of
for
this
case
the
control
for
angles
the
to
thyristor
zero,
if
or,
current
was
angle.
the
output
off,
that
present
currents
negative
switching
firing
next
a Runge-Kutta
using
firing
for
angles
a
only.
the
be easily
is
wave
devices,
simply
devices),
the
inversion
the
of
waves
positive
see Fig. A2.3.
derived,
an
firing
the
and also
the
across
supplies
wave could
control
the
decay
was still
and then
current
firing
these
used
of
the
current
calculated
cycle
(in
while
condition
The computer
positive
to
computer
to
allowed
corresponding
zero,
thyristor
another
on the
was achieved
The negahalf
positive
cycle.
The control
waves
To produce
and - 20% these
control
A2.1
Programme
were
waves
were
derived
the
linearly
for
control
the
20 increments
waves
interpolated
in
speed
for
the
64 pages
for
the
other
of
speeds
between
the
required.
Description
Flow_diagram
A2.1.1
The numbers
Fig. A2.5-
refer
to
Fig. A2.4.
A printout
of
the
program
is
EPROM,
in
87
(1)
A preliminary
analysis,
Mmax
the
(2)
tive
M
edge
phase
total
of
number
is
the
supplies
is
thyristor
that
(4)
the
This
loop
SUMSQ and
reached
(FA(m+l))
in
current
The actual
average
Tperiod/2
is
actual
agree
calculated
the
all
and the
determined
reach
by the
a satisfactory
and output
the
input
the
and
angle
six
angle,
find
to
the
and
firing
next
FA(m+l)
and
using
the
for
cycle
of
a half
angle
period
If
(i. e.
the
output
loop
the
with
the
0-05A)
of
and
FAW
SUM variable.
this
completed,
agree
is
N.
and
(within
current,
angle
between
calculated
rms figure
the
current
accordingly.
angles
the
two
current.
compares
required
current
IOGOOD count
the
IOGOOD
complete
is
reaches
Mmax)
waveform
is
ends.
J
firing
angles
program
re-run.
before
is
is
above
This
.
answer
reached.
firing
average
M
firing
accuracy
outlined
The maximum
first
actual
has been
each
firing
program
J-loop
period
period
over
output,
The analysis
the
is
loop
firing
the
are
results
time
a determined
If
incremented.
the
to
the
If
resets
current
Runge-Kutta
and modifies
figures
and then
produced
current
the
over
( 5)
the
the
of
posi-
listing).
calculation
updated.
calculates
program
held
current
then
sums are
arrays,
which
the
zero.
are
After
the
the
average
required
which
SUM
tim. e.
wasted
from
variable
the
with
perf. Orms the Runge-Kutta
and the
the
is
current
starts
the
cycle.
angles
defines
(see
on
operating
process
firing
N
current.
which
half
the
the
numbers
output
angles,
for
initialise
to
was used
retarded
angles
which
The Runge-Kutta
assumes
firing
of
required
angles
fully
with
an integer
the
firing
of
begin
than
rather
is
set
set
is
required
the
to
determined
for
done
time
end the
the
number
the
as often
limit
for
program
so far.
the
could
times
program
Cyber
before
These
of
the
did
had been
time
then
limit
be re-
not
88
A2.1.2
Functions_used_in_the_program
(i)
Function
As part
current
the
of
t,
at
Runge
the
calculation
program
the
of
must
at
t+6t
value
of
current
the
calculate
given
,
the
V-iR/L
over
increment.
the
Where
V=
net
i=
current
applied
voltage
resistance
inductance
Now
V=
Where
Vsupply
Vp. sin(100.7.
function
{[Vp.
Runge
This
fslip
to
FAM in'the
fslip.
t)
value
ff. t)-N-7/31-ET
rat.
,
XIND
s. 98. sin(2.
ff. fslip.
RES
t)]I-Y.
RQC
Function
function
calculates
FA(m+l)
and peak
N-7r/3
-
the
-
(ii)
FA(m)
calculates
sin(100.
t)
s. 98. sin(2.7T.
Trat.
Vslip
and so the
Vslip
-
Vsupply
required
a demanded
given
Apeak-
the
(FA(m+l)
average
current
sinusoidal
FA(m)
and
current
are
of
the
over
the
frequency
to
abbreviated
range
FAM1 and
program).
FA(m+l)
I
Average
A
FA(m+l)-FA(m)
peak.
sin(2.7T.
fslip.
t)dt
FAW
FA(m+l)
FA(m+l)-FA(m)
A
peak'[2.7T.
fslip
cos(2.7.
f
slip-t
FAW
eak-Exl-X21
FA(m+l)-FA(m)
where
and
X1
X2
-1
=-
2.7T. f
=
-1
2. Tr. f
slip
cos(2.7T.
fslip.
FA(m+l))
slip
cos(2.
ff. fslip-FA(m))
89
(iii)
This
Function
Volts
the
calculates
voltage
Volts
Where
Vp = Peak
N=0
A2.1.3
the
of
six
Vp.
sin(100.7T.
=
supply
phase
t
-
supplies.
Nff/3)
volts
5
to
Variables
TRAT
Turns
SLIP
slip
FSLIP
slip
RES
secondary
resistance
XIND
secondary
inductance
VPEAK
peak
six
APEAK
peak
required
FA(
firing
angle
SUM(
area
AAC(
actual
RAC(
required
DT
time
M7N
L
see
Ratio
Machine
of
frequency
of
phase
supply
sinusoidal
current
pulse
average
current
for
increment
number
of
current
of
current
average
Section
volts
current
pulse
current
of
Runge-Kutta
pulse
calculations
A2.1.1
increments
time
to
corresponding
FA(l)
RCURO-4/
A1-5
variables
XAMPS
current
SUM$Q
SUM
Of
in
[i2]
Runge-Kutta
dt
(for
( = area 2 for
sum of
i. dt
IOGOOD
number
of
FINC
firing
angle
increment
RMS
R. M. S.
value
of
SUM
firing
calculation
average
angles
complete
R. M. S.
i
calculation)
calculation)
producing
waveform
required
current
90
A2.2
Run Time
The program
For
an initial
to
complete
set
of-firing
the
accuracy
give
of
of
in
set
of
the
an on-line
The program
firing
run
program
complexity
micro
2000
this
the
to
required
the
for
angles
calculations
angles
an idea
using
was set
set
the
to
for
was written
one
such
for
was not
required
or
two
may be
of
seconds
the
necessarily
accuracy.
to
runs
felt
to
calculation,
be
( =30
CPU time
achieve
too
mins.
enough
On average
time
each
Although
this.
severe,
these
and show the
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speed w
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torque s-, eed reduction
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power speed reduczý, on
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15
16
fms-')
17
18
19
20
21
22
23
24
15-1
Wind
speed
(mS-')
10
5
Blooe, torque
Generator
to,rque
Shc ft
torque
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a
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0.5
1000-
Rotaticncl
speed
(rpm)
800,
E31cde torque
1.0
Shaft
torque
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Yox
0-5
1000-
Rotational
speed
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Fig 2-11
Blades
Slotted
disc
Slip Rings
/I \
GearBox
Mains
Supply
ion
I nduct
chine
Rotor
TTStator
Secondary
emf Signat
Generator
Cyc(oco erter
F
Transformers
Fig 3.1
Pi
Pm
Pi
Pm
P2
P2
PL
PL
Subsynchronous
Generation
Pm
p1
P2
PL
Supersynchronous
Generation
Mechanical Input Power
Primary Electrical Output Power
Secondary Electricat Power
Iron / Copper Losses
Fig 3.2
3 phase
supply
p, group
devices
11-1
Fig 3-3
-
Fig 3-4
I
nknelm
rnnfrni
clinniv
%anup
III
III
C
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C-
U
Fig 3-5
IjjII
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IiII
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C
I
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6 phase supply
phase supply
Fig 3-6
p group off
n group on
p group on
n group off
zero current
detect
Fig 3-7
supply
supply
I
InfergrouP
reactor
If
Machi ne
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Fig 3.8
Fig 3-9
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01
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current
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current
totai
current
Fig 3-11
Fig 3.11 b
To
To
V
Gj
cr
0
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speed
wo
Rotational
speed
W.
W.
C>C
Fig 3-12 b
Fig 3 -12
P= Po
To
To, Wo, Po Torque, rotationat
speed power rating ( derived
f rom f ixed speed case )
N
N
C7
N
Max Cp characteristic
Torque -speed operating
characteristic
Rotationat
speed
Fig 3-12
Wo Pwo
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F---i
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8
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wl
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from
-C
transtormer)
71
Phase Locked
Loop
8 bit
+Tr
T1
ICounter
Clock
Reset
Monostabie
Fig 4-2 Mains Count
Rotor
count
holes
Rotor
pulses
8 bit
O-P-
Rotor
reset
holes
Rotor
reset
Fig 4-3 Rotor Count
4-
C3.
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0
It
LL
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forward biassed
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y
if
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firing pulses
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ig4. - 5 ci
p' group
torward biassed
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Fig 4- 5b
0.P. to
p group
device
F-O.
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P.
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MonostabIe
output
pulse
ov.
2
Monostable
gated with
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clock
ov
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4
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ov
Fig 4.6
Voltage
across
Rectified
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2.0
Current
1.5
1.0
0.5
0"
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1
Volts
Fig 4.7
Gate characteristic
Primary
current
Magnetising current
Total current
Fig 4.8
junction
vnk
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5 oc
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0
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Fig 4.9
dv
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suppression
50 R
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Fig 4.10
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16.50 page
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148
ORIGINALWHVEFORII
FORANALYSIS
FUNDAIMIENTRL
FREQUENCY
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190
Page
100
110
120
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ries
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30
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en
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40
50
68
1650 rpm
70
80
90
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3 phase
IA
supply
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Fig 5,14c
40
50
60
1750 rpm
70
80
90
100
3 phase
110
1 01
12
supply
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'13
140
II
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20
39
d
10
Fig 5.14d
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50
6a
1750 rpm
78
90
01aIia
100 1.18 12
6 phase
supply
2
25
i- IJ
Mains
sunnitoc
Firing
pulses
Dup
DUP
oup
roup
Fig 5.15
Fig 5.16
Firing pulses at
standstill
Secondary current ct standsoil
0
c3L4-0
CL
4n
0
0
0
U
c26
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c
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Gener-a-torL"I-o
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Current
Without
NeutroJ
Generator
k-"twlý
u.Lok ýr*li
WAP tj
urrent
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Fig
Neutrat
5,18 D2-Pect
Neutraý
o-P
If
I
Lo
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90
68
40
10
0
211L'1314 15 1& 17 18 19 23 2-30 9 1-011 14
456
2' 24 255
10
60
10
'10
A
30
Fig 5,19a
tn
40
50
60
1250 rpm
70
90
Without
190
110
129
neutral
3
11to
14a
-1
1A
188
439
no
0
70
60
9A
40
It
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11
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16
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14
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0
LJL.
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60
a
10
20
30
lp
Fig 5.19b
40
ab
1750 rpm
'70
80
90
Without
100
110
1,719 IA
neutral
140
25
L--ý
Fig 5.20
Effect of
TX volts
04%-0
D«w
D4)
-6
C
4A
0
cr-
X
1ý-
CPO
c
0
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>
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Is
W
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F4
ui
cp
t
0
Ln
LO
9
CIL
%. W
J8
0--
3.0
Torque
per
amp
2.0
1.0
0
50
60
Fig 5.2 2
70
80
90
*/. TX volts
100
6
Torque per Gmp
T= 0.5 P.u.
TX supply volts
at 2 speeds
vs
to
Ll I
14,
l@M-1
98
38
78
68
4@
19
a
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2416
li.1 12
23s
24
221
Z-
14 15 IN Ilf 10
13 19 0
122
70
60 -H
50
40
19
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39
.
Fig 5,23a
40
50
68
16150 rpm
70
So
90
100
119
100% TX volts
IA
'19
1Sa
140
-j
it
I AIR
70
60
58
40
3451"2B"I,
S-
324Lj 25
15 10 17 12, L"-I -,-, "Z-,,
--, -L ý4
739
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40
0
10
,)0
Fig 5.23b
Ili 4.4.1111i`
58
60
40
1650 rpm
70
80
90
190
110
TX
50%
volts
11
23
1300
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ri
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1
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1
1 21,211 2"'
A.
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24 25
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0
70
60
5A
49
aA
20
30
10
Fig 5,23c
em
46
5
110
60
1.350 rpm
0u
C,a
99
1007
100
119
TX volts
129
133
I
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lilt.
;
ei
188
99
70
6a
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14
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32 -t "25
15 1'0' 17 180 19 '2ll 2-1
I IRA
68
40
N
10
0
Ficy 5.23d
ýn
-419
68
ilp
14
1350 rpm
-9
1V
d
18
go
10
LA
50% TX volts
4 L,
Lq
0
in
cl
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lw (»
0-%
4A
0
Z;
ob
(NK)4-b
0
CJ
Lci
mm
r-
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1ý
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92
.
dm x
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cl
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0
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Fig Al.2
WTS screen output
10
12-
printer$="off":
first=C)
graph=l:
old=4:
demand=500
MODE
7: *DRIVE2
20
50
REM WIND
TURBINE
DATA
5'2- i ner ti a=6.9E6
54
radius=45.7
56
synchLtb=1.5
AT SYNCH.
ROT.
SPEED
: REM HUB SPEED
,
58
-)(:)/synchLtb
BOX RATIO
gbratio=l()(.
: REM GEAR
60
B
gbeff=.
: REM GEAR BOX EFFICIENCY
62
CPma>, =. 42
: REM Cp MAXIMUM
lamCF*mx=9
64
AT CP MAX
: REM LAMBDA
66
(gbr at io-*"';
sc aI e=1.
-;
ad ius-*-5/
-*'---*,
-ý*lamCF'm>,
-'9.4)
67
SPEED
VALUES
: REM FROM TORQUE
70
REM LINE
1050
NEEDS
TO BE REWRITTEN
THE CORRECT
WITH
EQUATION
80 REM DISC
DATA
82
title$="WIND2"
84
"30"
pages$=
Be cutout=185)
CLS
100
llo
VDU 23; 8202;
0; (--); 0;
? &FE6. -;2=255:
120
?. 9:,FE6(-)=(-)
130
CLOSE#(--)
GOSUB
200
10000:
REM MANUAL/AUTO
210
IF
GOSUB
PAGE
ll(--)(--)(-): REM START
mode$="auto"
GOSUB
220
15(--)00
REM RUN UP TO 50(--) RPM
230
240
rator=500
250
? &FE60=500*224/20(-.
)0+32
260
IF
ADVAL(1)*.
0305-;: *45(--) GOTO -.260
REM MAIN
PROG
300
305
IF
rotor=demand
mcde$=l'manUal":
IF wind,;... 'cý'ýi. 4: wind=wind+.:
';.
INi: *,EY(-33):
306
IF
IF
mode$="manual":
IF wind. '. 4: wind=wind-.
INý'fEY(-120):
307
": IF
IF
I'manual
mode$=
GOTO 380
308
IF
made$=I'manual"
ýata=lT0490
310
FOR
SOUND
320
19-10924-C)Q91
THENSOUND1ý-151230,225
330
IF
data=485
INPUT#Zgwind'.
340
'-'
350
FOR interp=OT09
36(--) rator=demand
':
)
370
wind=windl-f-interp*(wind.
L-windl)/l(.
3(-)(. )C)(-)
GOSUB
THEN
ADVAL(1)*.
380
IF
(-: j. 05'--c: utout
PROCcalcs
400
?' RxFE6(-- =de(nand*"'4/ .c. ZL
460
GOSUB
14(--)()()
470
5(-)(--)
"
GOTO
4E3(--) IF
manUal
made$="
interp
490
NEXT
540
GOTO
500
IF
printer$="Off"
1: @%=&20208
510
VDU2,2
Cp, torqUe/
1(-)(-)()C)C)(
ADVAL (1) *. o3o5,
wind,
PRINT;
520
rotor
"demand
00, power/
5Z-.(--) VDU 6,3
INý-:.'EY(-9(--))THEN
IF
printer$="off"
540
INK. EY(-106)THEN
printer$="on"
55(--) IF
300
"
GOTO
IF
manUal
555
mode$=',
Fig
A1,3 Wind Turbine
Simu(ator
Programme
FOR
CP
IN
560
windl=wind2
565
rotor=demand
57(--) NEXT data
600
CLOSE#(--)
6(-.)5 update$="yes"
610
page$=STR$(VAL(page$)+l)
62C-) IF page$=pagess
THEN GOTO
0004.
)
..,
630
file$="WIP"+page$
640
GOTO 30c)
l0oC_) REM CALCULATIONS
10 10 DEF PROCcalcs
1015
hubsp=rotor/gbratio
1C120 gamma= (wind*.
2.,,: 374) /hUbsp
1 04C-) 1 amb d a=2.2374*r
ad i us /g aMMa
1050
Cp=(--). 5*(gamma-5.6)*EXP(-.
17*gafnma)
1060
REM Torque
CALC.
T=. 5*rho*Cp*wind-*".
-::*pi*R-*"-3/lamda
225: pi
14
rho=l.,
-,
1070
torque=Cp*wind*wind*1.9,
':L42*radiL(s*radiLts*radius/lai-nbda
1080
REM GET LOAD: scale
factor:
torval
is
torqUe
as scaling
actual
measured
1085
torval=ADVAL(2)/692
IF torval>30
1090
THEN torval=torval+((torval-7*,
"o) /9)
1095
load=torval*scale
REM Power
1100
CALC.
power=torque*
1110
power=load*hubsp
1120
accel=torqUe-load
1130
REM demand
speed
1140
demand=((accel*..:
'-ý)/inertia)*gbratio+rotor
ENDPROC
1150
10000
REM WINDDATA
OR MANUAL
CLS
10010
l0r), 4.0 PRINT: PRINT
SIMULATOR"
WIND TURBINE
100: 30 PRINTCHR$(141)"
SIMULATOR"
PRINTCHR$(141)"
WIND TURBINE
10040
1 005(-_) PRINT: PRINT
RUNNING
ENTER REQUIRED
MODE: "
PRINTCHR$(141)"PLEASE
10060
RUNNING
MODE: "
ENTER REQUIRED
-)7() PRINýCHR$(141)"PLEASE
1(--)(.
1008C-) PRINT: PRINT: PRINT
A. ORý-:'NEY WIND DATA"
1(--)(-.
)90 PRINTCHR$(141)"
A. ORý-:.
*NEY WIND DATA"
PRINTCHR$(141)"
10100
PRINT: PRINT
loll0
B. MANUAL CONTROL OF WIND"
PRINTCHR$(141)"
10120
B. MANUAL CONTROL OF WIND"
10131C-) PRINTCHR$(141)"
PRINT: PRINT: PRINT
10140
CONTINUE"
TYPE'A'OR'B'TO
101510 PRINTCHR$(141)"PLEASE
CONTINUE"
TYPE'A'OR'B'TO
1016(--) PRINTCHR$(141)"PLEASE
THEN mode$="
IF INKEY(-66)
auto ": GOTO 10,2.00
10 170
GOTO
"NO":
10200
":
"manual
THEN
nd=4:
wi
Update$=
IF INk'EY(-101)
10180
mode$=
GOTO 10170
10190
102100 CLS
PRINT: PRINT: PRINT
1021()
SIZE"
GRAPH
PRINTCHR$(141)"'SELECT
10,220
GRAPH SIZE"
10,2130 PRINTCHR$(141)"SELECT
10 24 C-) PRINT: PRINT
Fig
A1,3
continuecl
I
1 0-25CD, PR I NTCHR$ (14 1)"1.
NORMAL SIZE"
104252 F'RINTCHR$(141)"
1.
NORMAL SIZE"
10'. 260 PRINT
10227 C-) F'RINTCHR$(141)"
2.
TWICE SIZE"
1 02`72
PRINTCHR$(141)"
TWICE SIZE"
.4
1 Od.
2,a C-) IF INK'EY(-49)
THEN graph=1:
RETURN
10290
IF INKEY(-50)
THEN graph=2:
RETURN
10: 30c) GOTO 102.280
REM GET STARTING
11000
PAGE
114) 10 CLS
PRINT: PRINT: PRINT: PRINT
1102o
ll(--)7. o F'RINTCHR$(141)"
START PAGE FROM "; title$;
"
F'RINTCHR$(141)"
11040
START PAGE FROM "; title$;
"
ll(-. )45 *FX15,0
1105(--) pagel$=GET$
GOTO 11070
110 5 15 IF page1$="0"
OR VAL(pagel$)=()
IF VAL (pagel$)
11060
*1(-- "VAL (pages$)
VDU1(: )98
PRINT
11070
pagel$;:
VDU11
1IOE30 PRINT
pagels;:
11090
page'd-'1'$=GET$
11100
page$=pagels+page2$
GOTO 11090
IF VAL(page$)>VAL(pages$)
11110
1112C-) PRINT
page2$. -,: VDU1(. -)IIE3
111.3 C-) PRINT
page2$,,
file$="WIP"+page$
11140
Z=OPENIN(file$)
11150
INPUT#Z,
11160
windl
11170
update$="NO"
RETURN
11180
REM UPDATE GRAPH
14000
REM REMOVE POINT
14020
GOSUB 145C-)0
IF first=1
140-0
@%=&20104
14040
GCOL 090
14050
1406C-) MOVE 7-.2(--)j30. -PRINTold
141(--)0 REM PLOT POINT
'
Xa,,,.is=15(--)+rotor/.;.
14110
00
C-)Q
0*gr
h1
16
Q
Q
0+t
15
0Yaxis=
127
14
ap
or qu e*
)(-)(--)(--)
1412'. 2' Ya, -.,is2=15()+load*16(--)*graph/lC)(--)(.
14 13.0 GOSUB 14500
GCOL 013
14140
'.O: PRINTwind
MOVE 72(), -:.
@%=&20104:
14145
14150
old=wind
first=1
14160
RETURN
14170
REM PLOT
14500
3(--)9yaxi5
MOVE Xaxis-:
14510
1452C-) PLOT 10 1 60,0
1453(--) MOVE Xax is, Yax i s-:! -(--)
109 01 64)
PLOT
14540
Ya,
is'2-21
21,
Xaxis-.
MOVE
14550
-,
4--110,43.,
PLOT
14560
Ya>,, is...
1457(--) MOVE Xa,,.fis+21,
3,4
4:
7'.
10.,
PLOT
-)
1458(.
RETURN
14600
PICTURE
GET
REM
15000
ya,
i
Xax
s=
150o5
1
MODE
1501(--)
*DRIVE
15015
CLS
15020
Fig
A1,3
continued
(01-".
pages$")"
(01-11 -, pages$")",:
GOTO
11C 50
VDU
150: 7-C-) IF graph=l:
PIC1
*LOAD
15(--)4(-) IF graph=',:.:
PIC21
*LOAD
15)05 (--) VDU55
1506C-) MOVE 3,70,70
15070
PRINT"ROTOR
SPEED
(RPM)"
15075
MOVE 4(: )(-),. (--):PRINT"windspeed="
-:,
1508C-) *DRIVE
2
1509C. ) IF mode$="auto"
RETURN
GCOL 0,2
15100
15110
MOVE 1(:), 30: F'RINT"Fo=INCREASE"
15120
MOVE 9(--)(.
-), 3(: ): PRINT"F9=DECREASE"
15130
RETURN
30000
CLS
30002
MODE7
30005
PRINT. -PRINT:
PRINT:
30010
PRINT
CHR$(141)"OVER
SPEED AUTO
PRINT
CHR$(141)"OVER
SPEED AUTO
7-0012
30020
? &FE6()=O
FOR K=1 TO 3.
30024
FOR I=100
TO 150 STEP2
:1.0025
SOUND 1, -15,
I, l
30026
300227 NEXT I
30028
NEXT K,
END
30030
-9
Fig
A1.3
continued
CUTOUT
CUTOUT
I,
I,
L.
90
95
3,0 5
31C.)
1.20
3
330
340
345
350
4(.-)(-)
500
6(--)(.
-)
700
900
IM)
(n
1200
MODE7
*FX 15,0
DIM A(10'. 24)
CLOSE#O
MODE7
VDU 2-2',, 1,0; 0; 0;
CLS: PRINT: PRINT: PRINT
PRINT
"DATA
INPUT
FROM SCOPE OR DISC""'
PRINT: PRINT
"TYPE
S OR D ": G$=GET$
IF G$="S"
THEN 4()(.-)
IF G$="D"
THEN
G0T0 :7," (-_)
REM COLLECTION
OF DATA
CLS: VDU 23.1 1,0
022(-)5
C-); C-) @%
PRINT
PRINTCHR$(141);
COLLECTION
FROM SCOPE"
"DATA
PRINTCHR$(141);
"DATA
COLLECTION
FROM SCOPE"
PRINT: PRINT: PRINT:
PRINT"
The wave
digital
form
on the
scope
(ie.
amplitude
clipping
possible
PRINT
PRINT"
When thewaveform
is
stored
suitably
G=GET
FORI=1TO7:
VDU11: NEXT
": NEXT
FORI=1TO7:
PRINTTAB(38)"
VDU11: NEXT
FORI=lTO9:
PRINT: PRINT: PRINT: PRINT
Samples
(2---N)",
"NUMBER OF SAMPLES
INPUT
": VDU 11
VDU 11: PRINTTAB(3-5)"
FOR CYCLE OF FUNDAMENTAL"
PRINT11TIME
", Cycle
(MICROSECONDS)
INFUT"WAVEFORM
": VDU 11,11
VDU 11: PRINTTAB(35)"
WHEN STORING
/ DIVISION
PRINT"TIME
Store
(MILLISECONDS)
2ZT,1(--) INPUT11WAVEFORM
11: VDU 11,11
20 VDU 11: PRINTTAB(35)"
23 'x.
235C. ) MPT=Samples*Store*4(--)/Cycle
FOR PLAY BACK, *,-"MPT
/ DIVISION
24(--)(--) PRINT11TIME
.
", Playback
(SECONDS)
THE WAVEFORM
INPUT"OF
2410
": VDU 11
242C-) VDU 11: PRINTTAB(315)"
)0)
250(. -) T=Cycle*Playback/(Store*10(-'
11:NEXTI
PRINTTAB(30)1i
FOR I=1TO4:
"600
11,
11,11j11.,
VDU
27CIC-)
r11. j11
PRINT
SECONDS
'#; T"
PERIOD
TIME
3 100 PR I NT
PRINT
HZ
"; Safnples/T"
RATE
SAMPLING
330C-) PRINT"
-74(-)(.-) PRINT: PRINT: PRINT
data
the
To inpUt
press"
PR I NT "
3500
:36(--)(-.
) PR I NT
'PEN-START'"
370C) PRINT"
at the
stored
"
OCCUring.
quite
be
Must
is
not
press'SPACE-BAR'to
1300
1400
150(--)
1600
1700
2LL10(--)
2110
220C-)
22
ZL.LL10
2220
Fig
ALA Fourier
Analysis
Programme
II
maxi
continLIE
38()(-)
3900
3950E-3960
397(--)
PRINT
FIR I NT
on the
oscilloscope"
IF ADVAL(4)/16,
'. l(: )(-)() GOTO 397()
GOTO 395)()
FOR I=lTO7:
VDU11: NEXT
FOR I=1T07:
PRINTTABCý8)"
": NEXT
FOR I=IT019:
VDU11: NEXT
VDU31117,1:
PRINTCHR$(141)"
COLLECTING
DATA"
VDU'_',1q17,2:
PRINTCHR$(141)"
COLLECTING
DATA"
FIR I NTTAB
3ý, 12. ) "CLOCK
SECONDS"
REM MAIN PROG
X=T-1
TIME=O
FOR I=1TO
Samples
IF TIME*-(T*I*10(:
)/Samples):
A(I)=ADVAL(:
ý): NEXT
IF T-TIME/lC)(),::
X: X=X-1
=X: F'RINTTAB(20,12);
IF I<Samples
GOTO 4100
FOR I=lTO4:
VDU11: NEXTI
FOR I=1TO4:
PRINTTAB(_-, I8)"
": NEXT
FOR I=lTO4:
VDU11: NEXTI
REM DRAW WAVEFORM
MODE4
-3-971
3972
3980
3981
399(--)
4000
4()l(--)
4020
4C.)50
4100
4150
4200
4300
4310
432:. ()
50(--)0
5(-.)()5
5006
C01OUr=6
5007
VDU 19,1,
5010
GCOL 0,3
coloLtr,
5014
PRINTTAB(6,3)"THIS
5 02.20 MOVE
140, '20C.)
(:), O, (--)
IS
THE
WAVEFORM
STORED"
5o3O
DRAW 1401 800
504()
DRAW 1164,8(-)()
5050
DRAW 1164
20()
9
5060
DRAW 140, '.200
5400
MOVE 141
(A(
1
128)
25
+-JO
9
550C-) FOR I=1
TO Samples-1
5600
DRAW I*(1024/Samples)+140,
(A(I)/l'-78)+25()
57(--)0 NEXT
,
5710
PRINTTAB(7128)"PRESS
SPACE-BAR
TO CONTINUE"
59ge
G=GET
5999
MODE7
6(--)C)(:
) CLS: VDU ':23,1,0;
6001
PRINT: PRINT: PRINT
6002
PRINT"THE
WAVEFORM IS NOW STORED. "
6003
PRINT"DO
YOU WISH TO :"
6(--)(:)4 PRINT: PRINT"(A)
IT NOW"
ANALYSE
PRINT"(B)
SAVE I-T ONTO THE CURRENT DISC"
6005
6(: )(.-)6 PRINT"(C)
GETANOTHER
WAVEFORM FROM SCOPE"
6007
PRINT"(D)
GET ANOTHER WAVEFORM FROM DISC"
6(--)()8 PRINT"(E)
EXIT":
G$=GET$
THEN 6015
6009
IF G$="A"
THEN
6010
IF G$="B"
THEN 400
IF G$="C"
6011
60 12" IF G$=11D11 THEN 17D)OO
THEN CLS: END
IF G$="E"
601GOTO 6(--)(-)9
6014
60 15 CLS: FIR I NT: FIR I
"ANALYSIS
IN PROGýESS"
6(--)16 F'RINTCHR$(141).;
"ANALYSIS
IN PROGRESS"
602 () F'RINTCHR$(141),
C(1(__)214)
B(10'24),
DIM
1 (:)(:)0(: )
Fig A1.4
continued
10 05 C-) PROCsignalin
DEF PROCdft
10 11 C-) FOR J%=lTOF'%:
B (J%) =B
1016(--) PROCdfteval("dft")
10 17(--) ENDPROC
I C-)18 C-) DEF PROCinvdft
10 190 PR I NT "I nverse
DFT to
1 o20C_) PROCdfteval("invdft")
ENDPROC
10210
1(--)22(--) DEF PROCdfteval(A$)
REM Reorder
D)230
seqUence
1 024C-) R%=P%/2: Q%=P%-1
1026C-) J %= 1: FOR L%= 1 TO 0%:
1(--)29(--) T=D(J%):
V=C(J%):
D(J7.
1035C-) P.
',%=R%
1036C-) IF i.-..%>=J% THEN GOTO
(J7-) /p7.:
yi el d
according
c (j%)
Nb "
to
=C (J%) /F'%: NEXT
si gnal
Fig.
J%
samp I es.
12.8
1F L% >J % OR L%=J % THEN GOTO
C(J%)=C(L%):
)=D(L%):
B(L%)=T:
C(L%)=V
1040()
1039(3
G0T0
1036 0
J%=J%+K. %
10410
NEXT L%
FFT accordind
1044C-) REM Calculate
to Fiq.
1.1-5
2
I () 45 C-) FOR M%= I TON%: W= 1: X=(--): S%=2-"-M%: K%=S%/2: Y=COS (P I /K%)
IF A$="dft"THENZ=-SIN(PI/i:
105 10
*."/`) ELSE Z=SIN(F'I/[:
'..`/")
10 52 C-) FOR J%=1TOk1%
FOR L%=J% TO P% STEP S%
105-30
V=C(H%)*W+B(H%)*X:
B(H%)=B(L%)-T:
10540
H%=L%+i:: '.%: T=B(H%)*W-C(H%)*X:
C(L%)=C(L%)+V
(L%)=B(L%)+T:
1061C-) NEXT L%
Sr=W: W=W*Y-X*Z:
X=X*Y+Sr*Z
10620
1065C-) NEXT J%
1(--)66(--) NEXT M%
1067C-) ENDPROC
1(--)68(--) DEF PROCsignalin
TO Samples
1069C-) FOR I%=1
10 6 9',5 B(I %)V=A (I %) / 16
1070C-) NEXT I%
1(.-)7(.-)5 @%=I(-)
PRINT
10709
',
", -Samples"
has
"Signal
107 10 PRINTCHR$(141)
sample
ValUes.
": PRINT
"; Samples"
has
"Signal
ValUes.
1 C-)
sample
71-,:2 PRINTCHR$(141)
10720
N%= 1: F'%=..::
P%.':;.=Samples
REPEAT: N%=N%+I: P%=P%*2: UNTIL
10730
1(--)74(--) PROCdft
CLOSE#C)
E=OPENOUT " w--Rvf rm
D=OPENOUT " amp 1
10745
"
1(--)770 D=OPENOUT"ampl.
Samples
F,RINT#D,
10772
1(--)773 PR I NT4*D, Cyc Ie
E=OPENOUT"wavfrm"
775
1 C-)
P%= I NT (F*%/2+(--). 5)
10780
REM FOUrier
10790
coefficients
FOR J%=1 TO Samples/2
10810
C) 8
&21
10811
Cd %=
10 8.2 0
1085C-)
10860
10870
D)87,2
A=SQR (9 W 7. ) *B (J 7. ) +C (J 7. ) *C (J 7. )
F'RINT#DA
NEXT Yl.
GOTO 10880
: step=I:
IF Samples,:. '257
56
step=Samples/22c,
10880 -
FOR
Fig AlA
J%=1
TO
_24
102
continued
STEP
step
C(H%)=C(L%)-V:
1 C-)
B90 PRINT#E,
A(J7. )
109(--)(--) NEXT
10910
CLOSE#C)
110 C-)
C-) CHAIN
"A. DISP4"
12000
CLS:
MODE7
12C-)10 PRINT: PRINT: PRINT
120,, 2(_-) INPUT
"FILE
NAME FOR DATA STORAGE".. *flname$
12030
D=OF'ENOUT(flname$)
122040 PRINT#D,
Samples
12050
PR I NT#D, Cyc 1e
FOR I=1
12060
TO Samples
122070 PRINT#D,
A(I)
T NEXT I
12(-_)E3C.
090
CLS: PRINT: PRINT: PRINT
1 -21
1 'a"10 0 PRINT"DO
YOU WANT TO TAý::'E ANOTHER WAVEFORM"
PRINT"FROM
THIS
12110
THE SCOPE OR ANALYSE
ONE NOW'."'
12120
PRINT11TYPE
S OR A"; G$=GET$
IF G$="S"
THEN 150
12130
THEN 6015
IF G$="A"
1'2140
1215C. ) GOTO 1 '.2 1 -.20
13C_)(.
-)() CLS: @%=&.202:205
MODE7
13010
1302LO PRINT: PRINT: PRINT
"; flname$
FILENAME
INPUT
"DATA
13030
13(-.)31 PRINT: PRINT: PRINT
DATA"
"READING
13oZ.. 2 PRINTCHR$(141);
DATA"
"READING
130: 33 PRINTCHR$(141);
D=OPENIN(flname$)
13040
Samples
1305C-) INPUT#D,
Cycle
INPUT#D,
13060
TO Samples
FOR I=1
1'3070
INF, UT#D, A(I)
13080
1:1.(--)90 NEXT I
CLS. -GOTO, ')(-)O(--)
13100
v
Fig A1,4
continued
1-95R 0.009H k=1-94
2.06 R
0-018H
120V
Cycloconverter
Prmary(Rotor)
Secondary(Stator)
Fig A2.1
Actual current
Required
sinusoid
II
Required
averages
FAI
FA3
FA2
FA4
Fig A2.2
Control wave
V
FAI
FA2
FA3
FA4
Fi9A2.3
FA5
FA6
FA7
DATA SET UP
T
INPUT FM1-Mmax)
NOTE 1
M=L N=4
N13TE2
D-13RUNGEKUTTA
I
NOTES 3,4
T=T+DT I
N.
ýý'
ý
T=FACM+D?
N13TE4
CALCULATE ACTUAL,
REQUIRED AVERAGES
I
M=M+l
L<T>Tperiod/2?
0"-
NOTE 5
%%
N13TE6
M=O
NOTE 7
FA(M)=FA(M)+DFA
17r
DREWODU
ACT
X'N 61J
r wa Ir
!
ACT I(REQD 17
--t-FA(M)=FA(M)-DFA
N
I[IG013D=IIIG[113D+l
I[3GE313D=MmcLx?
y
N
m=m+i
NOTE 8
y-
-,.%
M=Mmax?
Fig A2.4
Flow Diagram
PRINT13UT
PEN
IF
ll9
PROGIýAl
ANS I
4
GUESS
I
2
ýILZ
5
6
7
8
)
12
13
14
15
16
17
18
19
20
21
22
23
24
25'
26
27
28
29
30
31
3
33
34
35
4176
38
39
40
41
42
43
4u
45
46
47
48
49
5C
51
52
53
54
55
56
57
58
59
6Q
61
62
63
64
65
66
67
68
69
7C
71
72
73
C
7ý/73
CP'
ri
=ý
+D
PROGPAM GUESS (D, OUT t OUTPUT, Tý-O'---5=l'ýPUT,
T;. P-----JU7PU-7)
0-- "L-1 ;--fA71ON L: ST NO N4tIS7
FA (3 1C ), -Ut4 ( 31 ),
1:: N (
3!
7),
'7
:ý
C(
)
--.
L"I,133
-ýC
-^
-Orl
K=j
cl I= 3.1 1-159263
TR4T=1.94
SLIP=+
!5
.
F -LIP=A35
( SL ! P*51' . r)
64ASLIO*3*2§ý)
HS=2*
0T=1E-5
x IND=,
118
VP=AK =*. 1ý6. c
AP=AK=
7
.,
(-0 2 rp=!, Is
FA(IP).
793)
3R
MA T (F, 5 59 2F 6*2
3
2 C ONT
FA 19
625 3
FA2Z
lj'66,.;
00 loý
R.:
00 lLi _J=ý4kq5-,
zoET-1 9 jr 11
j.
SUM( 19 s;L=T
-:
su-4SQ='. ý. c
CONTINUE
P,=1
H=4
L=(Fa(l)/DT)
XA,MC)S=
6M3
;2 151
1)01L9
T =1*0 T
CALCUL. ATION
RUNGE-KUTTA
S
CUR-=XAtl?
RCURI=RCUR. ý+(AI/7)
N,
5, XINC , FSV.-- -7-K , 7: ý 1- , -L
(T+ ( 07/ 3
2=0T*:; UrlG-7( RCURI( Al/E:
ý;
+( A2 /5)
-L
VP -'ýK 979
N9P. ' R-- S9X. &'.'IL ,F 3L
3=DT*P. UNG; -'+( ýýCUR2 (T + (OT /!
A-CUR2=RCUP
-:
(A 1/8
R CUR3=RCURr+
+( 3* 43/ o)
IP
S,
F--L
V-:
PI
ý:.
(7 +( 07 /2'
:
XIND
44=0T*ýi. UNGEA RCUR3
v
9
9
9N 9
--<
--)+(2*--)
:--CUPL=RCU: ý'+(A'ý/2)-(3*k'3/,
45=OT* FUNGzý-ý
( -1+0'r) , Ng ý51 'ýE-S, X! N-D9 FSLIP,
VPL, ý< , T-; 4 T, ýL : P)
(ý CUR.
XA'ýPS=FcuRr+(( Al+ (-t*A ") +-, =-) /ý
LE.,. ., ')Tri;
IF(XAMPS.
--N
XAMPS='
=-,Q IF
ýUt-IS"Q=SU! lSrl+((XA?
IPS**2)*"T)
ýumim)
=sum c. I) + (XAMPS-c
THEN
GE. FA(M+'l
IF(T,
FAMl=FAVl+l)
FAM=FA(M)
M"-gFA,
19FSL
4C(,
)=RCC(FA.
'-',
-.
PIA9<
+1
IF( ti. ZT
HE
LS
NN+
IF
-NDIF
ND
ONT1 NL;=*
IOGOOD=.
00 5,.- ! CHECK=1,18
AC(IL; HECK)). GT. I. f.')THI--, ýý
! F(ABS(AAC(ICHECK)-;.
FINC=J960005
l:'L Sr
C. 2)T
11CHC K)
AC(ICH :-0KST.
IF(ABSAAC(
FIt; C0o00002
:'L (z: IF (A. BS (A sýC('CH EG KC(ICH
FINCý0-006616
LL :ý)c.
FINC=C.
I
IOGOOD=IOGOO9+
EN 0 IF
Fig A2.5
:-CKGT@07HEtI
Control wave programme
OrjRAl
74
75
76
77
78
79
80
81
33
ý4
35
36
87
88
89
90
94
A.
*92
93
94
95
96
97
9a
99
I
ANSI
FUNCT-&. ON
GUZZSS
cp-,
RUNGE
73/73
RQC
73/73
FTti
OPT=O
PEALFUNCTIOWýUNGýl
N((I'j.
qUNGE=(((VPEAK*S!
/tTY7, AT*SLIP*98,
ý*SIN(2.
K ET UR N
END
FUNCTION
F
IF
ýNc
NO IF
1F( AAC (ICH--CK)
G'
"C"E
RAC
CK)
7,
(
HE N
.
"
;74( ! CH--CK) =FA ( ! CH7-CK) + r-INC
LS: '
FZk( ICH-CK)
=FA ( ICH= CK ) -FINC
F NO IF
-F(lOSOOD.:
7r)
ýP)THEN
Z-1
OL).* 51 OP
W;; Ir " ("7 9 +2) FA ( IOP
AAC (100)
C (100
r?,
-e
FORý! i'l(3F8.5)
42
CONT 'NU! 7
45
IRT
:; MS-': c(SUMSQ4
2. [ "FSL : P)
"
NT *9R MS
STOP
7
NO IF
5^ ýONTIIU7
IC
ON 71 NUZ
00 55
ý
2) FA (I C 7') p At C(1 Cr-) C AC I r7WR1 TE (7
52 F ORM,ý T (F 3a 59 2FEa2i
55 CON rI NUE
MS=SQR T (S UMS C*2. ý'*F SL IP)
RI NlT
MS
STOP
NO
-z
ERROR IN
GUESS
I
2
3
4
5
O. --*PI*T)-(N*OI/7
J*PI*FSý-IP*T)))-(;
/X114c,
FT ri
OP7 =0
-1+552
552
P194Pý: "K)
F". M, FSLIP,
qCC(FAMI,
PEAL FUNCTION
ý
F4 ý11)
*PSLIý*
) *COS (2,2*P!
*PI*FSLIP)
X7, =(-I/(2.
C-*PI*FS-1r,
*F; ý1)
X2=(-I/(2.
-'*PI*FSLIP))*C)S(2.
FGC=(AP--AK*(XI-X2))/(FAMI-FAti)
ETUR, N
NO
2
3
4
6
FUNCTION
2
3
4
73/73
VOLTS
73/73
;; EaL FUNCTION
VQLT S=VP : AK*S!
PET UR IN
1 -N0
OPT
VOLTS( 7tN
N( (100
Pr,
\/P---AK)
0
i
Fig A 2.5 continued