DIGITAL CONTROL OF RECTIFIER FIRING ANGLES FOR THE ZERO GRADIENT ...

226 Pages·2006·8.53 MB·English

DIGITAL CONTROL OF RECTIFIER FIRING ANGLES FOR THE ZERO
GRADIENT SYNCHROTRON (ZGS) RING MAGNET POWER SUPPLY5
Martin J. Knott, Lloyd G. Lewis, and Herbert H. Rabe
Argonne National Laboratory
Argonne, Illinois
Abstract equivalent of a 12-phase supply in each quadrant of the
ring' magnet.
The heart of the new control system for the ZGS
ring magnet power supply is a counter that counts The rectifiers in each of these eight supplies are
from 0 to 3600 each voltage cycle of the main genera- mercury vapor tubes. The excitation arc operates
tor. This provides an electrical degree scale that is continuously so that firing control is provided by two
synchronized with the generator voltage wave by a grids placed between the cathode arc and the anode.
phase-lock feedback loop. Digital gates compare the
Each of the eight supplies is provided with a low
number in the counter with the desired angle forfiring
pass LC filter. The filter has a rolloff of 40 dB/dec-
each of the 12 rectifier phases. At eauality, a pulse
ade and a corner frequency of about 40 Hz. The fil-
is generated and applied to the control grids of the
ter is underdamped with a damping ratio of about 0.3.
appropriate mercury vapor rectifiers. Fast digital
arithmetic adder circuits upclate the desired firing
Ripple Amplitudes
angles for each of the 12 phases in response to com-
mands from the ZGS programmer and in response to. Ripple amplitudes produced by the ZGS ring mag-
feedback slgnals from beam spill monitors and fromB net power supply were measured in two ways. The
pickup coils on the ring magnet. Separate digital first was to use the fast gauss clock in the ZGS pro-
arithmetic adders and selectors provide individual ad- grammer. The clock output was sent to a digital-to-
justment of each phase in order to reduce low fre- analog (D-A) converter and to an oscilloscope. The
quency ripple. This system has greatly reduced 50-, gauss pictures from the oscilloscope showed that most
loo-, and 150-cycle ripple on the ring magnet field on of the ripple produced by the original analog con-t rol
flattop and on porches, has provided fast action to system was at low frequencies. Amplitudes at 50
permit spill control when the RF accelerating cavity cycles (generator frequency) were of the order of 1 or
is off, and has provided stable operation in full rectify 2 G. The 12th harmonic was not readily observed on
for the accelerating part of the ZGS cycle. this display.
The second method was to look at the dc voltage
Introduction
across one pair of ring magnets. This was a more
The new slow resonance extraction system for the convenient signal for ripple studies since the relative
ZGS provides two simultaneous beams that have no RF amplitudes of the several harmonics were more fa-
structure. The system accomplishes this by turning vorable for measurement.
off the RF accelerating cavity early in flattop and then,
The relatively large low frequency ripple (at less
after the beam has debunched, by moving the beam to
than the 12th harmonic) results from a variety of
the vr = 2/3 extraction point with the ring magnet con-
causes. One cause is the incorrect spacing of rectifi-
trol system. The rate of extraction is then controlled
er firing pulses. A second cause is the characteris-
through manipulation of the ring nlagnet field.
tics of the low pass filter which attenuates poorly at
This magnetic spill mode places specific demands the low frequencies. Additional causes include possi-
on the control system for the ring magnet power sup- ble errors in the number of turns on the polyphase
ply. One of these demands is that the system must be transformer windings, variations in the leakage in-
able to rapidly change the voltage applied to the ring ductance from one phase winding to another, lack of
magnet. The required speed and accuracy are deter- symmetry in circuit resistances, and imbalances be-
mined by the amount of beam steering needed to start tween phases of the generator voltage.
and maintain the extraction at a selected rate.
The effects of some of these causes of low fre-
A second demand is that the control system for quency ripple can be cancelled on flattop by properly
the ring magnet minimizes the generation of low fre- retarding or advancing the firing time of one or sev-
quency ripple. This is important because the ripple eral of the 12-phase rectifiers with respect to the
produces modulation of the extracted beam intensity. others. From this, it is apparent that exactly uni-
form spacing of the firing pulses to the rectifiers will
An additional requirement is that the ring magnet
not produce minimum ripple.
control system be capable of operating in full rectify;
that is with natural commutation from phase to phase.
Firing Accuracy
This provides the minimum accelerating time and the
desired conditions for beam injection into the ZGS. The bias voltages to the unijunctions in the origi-
nal firing control system were readjusted to produce a
ZGS Ring Magnet significant change in the ripple at the generator fre-
quency. These changes in firing angles were mea-
The ZGS ring magnet circuit contains eight mag-
sured with the digital phase-angle meter used for
nets and eight power supplies connected in a series
routine monitoring of the ZGS ring magnet supply.
circuit with four-fold symmetry. The result is the
The data showed that substantial reductions in the
*Work performed under the auspices of the U. S.
low frequency ripple could be obtained if the firing
Atomic Energy Commission.
511
angles of the 12-phase rectifiers were reproducible to voltage wave that are as large as 25% of the peak volt-
1/10 of an electrical degree. This is far beyond the age. For this reason, a zero crossing type of refer-
accuracy and stability of conventional analog ramp ence is not suitable even when the input wave is
type control systems. For this reason, a digital con- heavily filtered. This is true because the filters that
trol system was designed and installed at the ZGS. were tried produced variable phase shifts andlor large
transients when entering flattop and invert. The
Rectifier Grid Drive phase-lock loop shown in the upper right portion of
Fig. 1 was found to operate satisfactorily.
The control of firing angles to 0. 1' electrical
corresponds to controlling the turn-on of a rectifier In this loop, a dc tachometer voltage from the
to about 5 ps. Any variation in the turn-on time of a main generator and the output voltage from the filter
single rectifier must be smaller than this if the con- are added in an operational amplifier. The resultant
trol accuracy is to be achieved. In a similar way, voltage drives a voltage-to-frequency (v-f) converter
variation in the average time delay from one rectifier that produces a sawtooth wave. This sawtooth drives
to another must be shorter than 5 ps. a binary that divides the frequency by two and pro-
duces a square wave with *lO V output levels.
High voltage switch-transistors were used to pro-
vide the drive to the grids of the rectifier tubes. The It is well known that the mathematical product of
firing pulse from the control circuit was coupled two sine waves of the same frequency but different
through a well insulated pulse transformer to a drive phases produces a dc component plus a second har-
module that operated at rectifier cathode potential. monic component. The dc component depends on the
The l/2 ps pulse was lengthened to 4 ms by a single phase difference between the two sine waves.
shot amplifier located at cathode potential. This
In a similar way, the product of a square wave
lengthened pulse was applied to switch-transistors
and a distorted sine wave of the same period produces
that supplied the grid drive signal.
a dc component that is a function of the phase differ-
The grids were switched to t300 V with respect ence between the two waves. This fact is utilized in
to the cathode with a rise time of 600 ns. Under these the loop in Fig. 1 by feeding the distorted sine wave
conditions, the tube turn-on was about 1 ~s at low from the generator bus and the square wave from the
currents and also at high currents when the tube was frequency divider to a transconductance type analog
first used. At high currents, the time delay and the multiplier. The output which contains dc and ac com-
jitter increased during the first two minutes. At ponents is fed to the low-pass filter to complete the
equilibrium, the delay varied from a minimum of feedback loop.
about 2 ps to a maximum of about 5 ps. We believe
This loop would operate without the dc tachometer
that this increase in turn-on delay is caused by out-
input; but since the maximum loop gain is finite, the
gassing of the electrodes under high current loads.
phase difference between the ac reference and the
Turn-off of the rectifier by removal of the posi- square wave in locked operation would vary with gen-
tive anode voltage left a plasma in the space between erator speed. The dc tachometer input amplitude is
the grids and the cathode arc. This caused grid cur- adjusted so that the dc output of the filter is nearly
rents that lasted long enough to influence the next zero in the locked condition. In this way, the phase
turn-on. For this reason, a switch-transistor was difference between the ac reference and the square
used to clamp grid #1 to a negative bias when the tube wave is made very nearly 90° and independent of gen-
was off. This bias swept out the ions left in the inter- erator speed.
electrode space in about 1/2 ms.
Main Counter Loop
Number System and Logic
The MAIN COUNTER and its associated feedback
The digital parts of the control system shown in loop are shown in the upper left part of Fig. 1. The
the block diagram of Fig. 1 use the binary number function of this counter is to provide a digital degree
system. This was chosen since the input from the scale that has 360. 0' per generator cycle and that is
ZGS programmer is in one's complement form and phase synchronized with the square wave from the
because of convenience in construction. phase-lock loop. Its operation is described below.
The DISPLAY system uses LED numeric display The dc tachometer voltage, shown in the upper
elements driven by a binary coded decimal counter. left of Fig. 1, is multiplied by a constant in the
This is convenient for checkout by the maintenance SERVO CONTROL. The product is then applied to the
personnel. input of the v-f converter. The gain constant is ad-
justed to give very nearly 160 counts per electrical
The digital logic utilizes 7400 series TTL-MSI
degree of the generator wave. In this way, the main
integrated circuits. About 250 integrated circuit
counter receives very nearly 16 x 3600 counts each
chips are mounted in dual in-line packages and are
generator cycle, without the feedback loop's correc-
interconnected by wire-wrap wiring. The propagation
tion. This makes the action of the feedback loop al-
delays for this logic series vary from package to
most independent of generator speed.
package but are of the order of a few tens of ns.
The main counter is provided with gates that
Phase Lock Loop clear the counter to zero each time the total count
reaches 16 x 3600. The gates generate a ROLLOVER
The generator voltage wave varies in frequency
pulse at the same time that the counter is cleared.
during the ZGS cycle and is very distorted. Rectifier
No other input clears the counter, thus assuring
commutation produces notches in the generator
360. Oo per main counter cycle.
5 12
The main counter is synchronized with the phase- Lag Register
lock loop in the following way. The positive-going
edge of the square wave from the phase-lock loop + 2 In normal operation, the ZGS programmer makes
the major part of the changes in rectifier firing an-
loads a register with the number from the main count-
gles. This is done through the programmer input to
er. This number is then subtracted from a reference
the SELECTOR at the bottom of Fig. 1. The number
number, obtained by adding a BIAS to the number con-
of degrees of firing delay is put in the 0005 register at
tained in the RECTIFY D.S. digital switch. This dif-
any time. The number is then transferred to the
ference is the digital servo-loop error signal and
0005' register under internal timing control.
represents the amount that the main counter is ahead
or behind the reference square wave from the phase- The number in the LAG REGISTER is subtracted
lock loop. The difference is loaded into a second reg- from the number in the 0005' register. The difference
ister that feeds a d-a converter, thus furnishing a is divided by 256 and the quotient added to the initial
voltage error signal. value of the number in the lag register. The lag reg-
ister then approaches the number in the 0005' register
This voltage error signal feeds a proportional and
an integral network in the servo control. The effect along a digitally generated "exponential. 'I The time
constant is controlled by the RATE logic and is select-
is to speed up or slow down the v-f converter so that
ed from the ZGS programmer. The output "L" is thus
the number transferred from the main counter is
made to change slowly enough to prevent arc faults in
equal to the reference number.
the rectifiers and to prevent distortions in the ring
magnet field that would reduce the beam intensity.
Full Rectify Adjustment
Under fault conditions, the safety interlocks
The main counter control loop contains a refer-
switch the selector from programmer input to a steady
ence number that may be changed to adjust the firing
invert angle.
pulse times for full rectify. At full rectify (000. Oo
from the programmer), the RECTIFY D, S. is changed
Maximum Invert Angle
in 0. 1' increments until the firing pulses are correct-
ly timed. The digital phase angle meter is used to The rectifier arc fault rate is dependent on the
check this. At correct adjustment, the RECTIFY D.S. amount of firing delay used. Less delay is permissi-
plus the BIAS has a nominal value of 180. 0'. Small ble at high magnet currents than at low currents. The
variations are caused by the effects of noise on the control system is therefore provided with logic that
phase-lock loop. limits the firing delay.
The MAXIMUM INVERT adjustment digital switch
Preset Counter
is shown at the lower left of Fig. 1. The hold button
Under ideal conditions at full rectify, rectifier #I on the register permits changes during operation of
turns on when the number in the main counter is 30°, the ring magnet. The digital switch angle is added to
rectifier #Z when the number is 60°, etc., and recti- a fixed 108.8' to get the total maximum angle.
fier #12 when the number is 360'. At invert, each
The CURRENT COMPENSATION input at the low-
rectifier turn-on is delayed up to 155O so that several
er left of Fig. 1 is a voltage obtained from a magnet
of the rectifier turn-on angles will occur in the follow-
current transductor. This voltage is fed to a sample
ing cycle of the main counter. The logic problems
and hold (S/H) and then to an a-d converter. The num-
associated with this situation are avoided by using the
ber in the associated register is proportional to mag-
PRESET COUNTER shown below the main counter in
net current. The amplifier gain may be changed to
Fig. 1.
adjust the amount of compensation.
The preset counter counts by 0. lo steps and has a
The current compensation angle is subtracted
range of 819. lo. It is not cleared to zero but is pre-
from the maximum invert angle to give a limit "MI'
set to the number in the main counter at a specific
thzt varies with magnet current. This value "MI' and
time each cycle. The PRESET CONTROL logic oper-
the lag register number "L" go to a COMPARATOR
ates so that in effect, the time for the presetting is af-
and SELECTOR that make the number at "GI' equal to
ter rectifier #12 has turned on and also is after the
the smaller of these two inputs to the comparator.
rollover of the main counter. If rollover has not OC-
curred before turn-on of rectifier #12, the preset con-
Phase Counter
trol in effect locks out the unwanted comparator output
pulses generated between the time of rectifier #12 The phase counter (+CNT), located in the lower
turn-on and the time of rollover. right of Fig. 1, controls the distribution of firing
pulses to the several rectifiers and determines the an-
The range of the preset counter and the method of
gular increments between the rectifier firings. The
presetting it require that the "B" inp ut to the compar-
operation is as follows.
ator has the following- ranges:
Consider the +CNT to be in the first of its 12
Rectifier #1 varies from 15O to 200'
states. The counter output and DECODE gates condi-
Rectifier #2 varies from 45' to 230°
tion DRIVER #I to transmit the next comparator pulse
Rectifier #3 varies from 75' to 260°
to rectifier #l. The counter output causes the 30°1NC
. . . . . . . . . . . . . e . . . . . . generator output 'IC" to be zero and connects D. S. 1
Rectifier #12 varies from 345O to 530°
digital switch to the E input to the adder. The output
of this adder can be adjusted between Oo and 30' by
adjusting D. S. 1.
513
If the programmer input is Oo (full rectify) and if indicated that the delta and wye connected transform-
the FEEDBACK is not in use (F= 15'), the B input to ers did not produce voltage waves that are 30° apart.
the comparator may be from 15' to 45O depending on It appears that the angles are about 28O.
the D.S. 1 setting.
The feedback connection is used with the B coil on
As soon as the number in the preset counter the ring magnet to control the slope of the magnet flat-
equals or exceeds the number B, a comparison pulse top for energy loss extraction. In this mode, in-
is generated. This pulse is transmitted to rectifier creased ripple amplitudes appear on the ring magnet
#1 and causes the hCNT to advance to the second voltage. These are at low frequencies and are not re-
state. producible from cycle to cycle. It ?ppears that low
frequency noise is picked up in the B system. Even
In this second state, D.S. 2 digital switch is con-
so, the ripple is less than with the old control system.
nected by the selector to output E and driver #2 is
conditioned. In this case, the 30°1NC generator out- The feedback input is used during resonant ex-
put has a value of 30.0'. traction to control the extraction rate.3 The signal is
supplied from beam monitoring devices to magnetical-
This process continues to fire each of the 12 rec-
ly program the beam position during extraction.
tifiers in the proper sequence. The ACNT is self-
synchronizing at startup of the system because of the
Acknowledgments
equal to or greater than action of the comparator.
Many people have enthusiastically contributed to
Feedback the digital firing control system project. Their ef-
forts have made the system operational in a remark-
The digital control system is provided with a fast
ably short time.
channel that may be used in cpnjunction with other
control systems such as the B feedback control and We wish to thank Mr. Ray Kickert for his efforts,
the external beam intensity control. especially during the measurements of the dynamic
characteristics of the mercury vapor rectifiers and
The feedback system, located at the bottom of
during debugging and testing of the system.
Fig. 1, consists of an input amplifier, a S/H, an a-d
converter, and a register (REG). The input voltage The ring magnet power group, under Mr. George
range is -20 to t20 V. The a-d converter has an out- West, did an outstanding job of constructing many of
put range of 0' to 30. Oo. When the feedback input is the circuit modules and making the many changes in
not in use. the REG is held at 15. 0'. the control and interlock circuits. We wish to thank
P. Bertucci, L. Johns, P. Roth, E. Kulovitz,
Model W. Welch, and the whole ring magnet power group.
Dynamic checks of the digital control of the recti-
References
fier firing angles are done through use of the MODEL.
This model contains two small 6-phase transformers 1. J. F. Sellers, E. F. Frisby, W. F. Praeg, and
supplied from the generator bus. One transformer A, T. Visser, Ring Magnet Power System for the
has a delta primary and the other a wye connected Zero Gradient Synchrotron, 1965 Particle Accel-
primary. The secondaries connect to 12 small photo- erator Conference, Washington, D. C., March 10
coupled SCR's that are operated by the 12 drivers of to 12, 1965, IEEE Transactions on Nuclear Sci-
Fig. 1. The rectified voltage is fed to an operational ence, Volume NS-12, No. 3, p. 338 (1965)
amplifier analog model of the ZGS passive filter and
ring magnet system. Magnet voltage, magnet cur- 2. Lloyd G. Lewis and Anthony D. Valente, Argonne
rent, and current through the filter inductor are National Laboratory, PHASOR: A Control Com-
available. Model current and magnet voltage are puter Method for Displaying Amplitude and Phase
transmitted to the power house display system for the of Ripple Components in the Ring Magnet Voltage,
operators' inspection. IXth International Conference on High Energy
Accelerators, Stanford, California, May 2 to 7,
Discussion 1974.
The control system has been in routine use since
3. Y. Cho, E. A. Crosbie, L. G. Lewis, C. W.
November 1973. Initial startup was with all the digi-
tal switches, D.S. 1 - D.S. 12, set for equal inter- Potts, and L. G. Ratner, Argonne National Labo-
ratory, Slow Resonance Extraction of Two Simul-
vals between rectifier firings. No particular prob-
taneous Beams without RF Structure, IXth Inter-
lems with arcbacks were encountered.
national Conference on High Energy Accelerators,
Readjustments of the individual rectifier angles Stanford, California, May 2 to 7, 1974.
were made to minimize ripple. This was done with
2
the aid of the control computer using the PHASOR
program. The amplitudes of the first, second, and
third harmonics were reduced to values that were
about a factor of 20 smaller than with the old analog
ramp control system. This was done without the feed-
back input.
The amplitude of the sixth harmonic could be
minimized but remained large. The minimum was
fairly broad, and the values of D.S. 1 - D.S. 12
5 14
v D. C.
D.C. TACH.
D + A REG. LOAD TACH.
0
J
v v
SUB. v-* f SUM
SERVO CONTROL
RECTIFY D.S.
160 COUNTS / DEG.
COUNTS / DEGREE
START
DISPLAY
CONTROL
I
G
ADD
I
I1 I
I
'1
SEL- f2 56 0
0
M 0
COMP ADD CONTROL
1 0
+ + w 0
0
SUB. RATE LAG REG. TIMING
1 I 0
9 F
I 0
1I I
REG. ADD SUB, REG. k 1 5 O 0
0
0005' 30' INC.
0005 SELECTOR
MAX.
D.S. D.S. t
-----_-
INVERT SEL. I 12 DECOD
ADJUST
1
FEED INDIVIDUAL DRIVERS
CURRENT INVERT MAN,
COMP. PROGRAMMER BACK ANGLE ADJUST
FIG. 1 - DIGITAL FIRING ANGLE CONTROL SYSTEM BLOCK DIAGRAM
515
PHASOR: A CONTROL COMPUTER METHOD FOR DISPLAYING AMPLITUDE
AND PHASE OF RIPPLE COMPONENTS IN THE RING MAGNET VOLTAGE*:
Lloyd G. Lewis and Anthony D. Valente
Argonne National Laboratory
Argonne, Illinois
Abstract in an attempt to analyze the ripple during a 700 ms
flattop of the ZGS ring magnet. At the low ripple fre-
Deviations of 12-phase generator -transformer- quencies, 50-600 Hz, the sweep rate for the required
rectifier systems from ideal performance result in resolution was so low that an analysis could not be per-
the generation of ring magnet ripple at the fundamen- formed in the length of the flattop, In addition, no
tal and at low harmonics of the generator frequency. phase angle information is given by such an instrument.
Analysis and display of the amplitude and phase of
The ZGS control computer system was used in
each of these harmonic components makes it possible
conjunction with the program PHASOR to analyze the
for the systems engineer to minimize the ripple by re-
ripple and display the results. The program is of the
adjusting the control system. The Zero Gradient Syn-
interactive type where the computer operator directs
chrotron (ZGS) control computer samples both the fil-
the logic flow after observing the results of each sec-
tered voltage on the ring magnet and a reference volt-
tion of the program.
age produced by a phase-lock loop connected to the
generator bus. Data are taken during a selected inter-
Data Input
val of the ZGS cycle and are then analyzed. Computer
driven graphic displays plot the raw ripple data, am-
The reference for all phase angles was a square
plitude and phase bar graphs for each harmonic corn-
wave produced by a phase-lock loop that had one phase
ponent, reconstructed ripple data for checking, and
of the generator voltage as its input. This loop acted
graphs for comparing ripple components under differ-
as a filter for the distortions in the generator voltage
ent operating conditions. Numerical information is
wave and gave sharp indications of corresponding
also displayed. The PHASOR program corrects the
points in each generator voltage cycle. The loop was
phase angles for the phase shifts produced by the ZGS
adjusted so that the positive -going square wave transi-
passive filter. These corrected angles indicate whlch
tions were at 90° on the generator voltage sine wave
of the 12-phase firing angles should be retarded or acl-
and were independent of generator voltage and fre-
vanced to reduce the ripple.
quency.
Introduction This square wave, shown in Fig. lA, was the in-
put to an analog integrator that was voltage limited at
*
Power supplies for synchrotron ring magnets 10 V. The waveform from this is shown in Fig. 1B.
usually consist of phase -controlled rectifiers operated The rise and fall times were adjusted to be slightly
from an ac power line or from ac generators. The longer than the control computer data sampling intpr-
number of ac phases is often high to minimize the rip- Val. In this way, the computer was assured of one
ple. The ripple on the magnet is reduced even more data point on the rlse even through the computer was
in some systems by inserting a low-pass filter be- not synchronized to the generator.
tween the rectifiers and the ring ;nagnet.
The second input to the ZGS control computer
In a 12-phase system with a low-pass filter, the data station was a voltage cGntaiiiing the magnet ripplr
amplitude of the ripple component at the fundamental rnformation. It was obtained by capacitively coupling
frequency of the power line may exceed the amplitude the voltage which was across one quadrant of the ring
of the 12th harmonic. This is caused in part by the magnet to an amplifier with a high common mode re-
filter's attenuation being larger at the higher frequen- jection. Zener dlode networks eliminated most of the
cy. Additional causes include errors in the number. OE C~L component.
turns on the polyphase transformer windings, variation
in the leakage inductance from one phase winding to Data Taking
another, lack of symmetry in circuit resistances, and
imbalances between phases of the power line or gen- The manual keyboard at the computer driven
erator. scope was used to specify the point in the ZGS cycle
lor the start of data taking (e. g. 250 ms after the start
The magnitude of the low frequency ripple com-
of flattop). The keyboard was then used to enter the
ponents may be reduced on flattop by properly retard-
niimber of data samples of the ripple voltage that are
ing or advancing the firing time of each of the 12-
to be taken. The computer then generates requisitions
phase rectifiers with respect to the others.
fcr all of the data points. Measurements are made at
Proper adjustment of the firing delays of cach of ZOO us intervals and alternate between the reference
the 12 phases is extremely difficult by trial and error wave: and the ripple wave.
methods and an optimum is difficult to determine by
When the operator pushes &e DISPLAY NEW
eye. For these reasons, analytical methods are re-
SET key, a new set of data is taken on the next ZGS
quired.
cycle. These data are then displayed on the scope
A swept frequency spectrum analyzer was used screen. Figure 3 top plots the samples taken on the
relerence wave. The points that are circled are on the
::::Work performed under the auspices of the U. S. rising and falling slopes of the reference. Fig1n-e 3
Atomic Energy Commission. bottom plots the samples taken on the ripple wave.
516
searches the reference wave data points, Fig. 3 top,
to locate all the positive-going edges. It counts the
number of data points in each cycle and calculates the
fractional intervals at the beginning and end of each
cycle. These fractional intervals are calculated from
the position of the circled points, Fig. 3 top. The to-
tal number of intervals is then divided into 360 to get
the number of degrees per interval. Od for the first
data point in each cycle and the frequency of each cy-
cle are displayed on the scope screen. A value of Od
for each data point is then assigned.
Fig. 1 Phase Lock Loop Waveforms
The computer uses the equations (4),( 5), and
(8) to compute the amplitude and phase of the first 12
The computer operator, by inspection of the
harmonic components. The sums, equations (4)a nd
scope display, determines that the amplitude range of
(5), may be extended over more than one cycle if the
the data is acceptable and that enough points are taken.
operator so specifies.
He may then proceed to analyze the data by pushing
the ANALYZE button on the scope. The phase angles, xr of equation (7), are then
corrected for the phase shifts produced by the ZGS
Analysis passive filter, shown in Fig. 2. The results give the
phase angle of each frequency component at the output
A finite, periodic function V(t) may be written as of the rectifier.
Display Derived Ripple
n
The operator may push the DISPLAY DERIVED
where
. . . -2lT RIPPLE button to check the computation. In this
n=O. 1, 2, 3. and w =
mode, the computer uses the phases and amplitudes of
the ripple components derived from the data to calcu-
and the coefficients are given by
late V(t) at each value of Bd. The graph is shown in
.7 Fig. 3 center. The amplitudes and phase angles of
(2) the components are given in the table at the bottom of
. . Fig. 3.
+L z n = O , l , 2 . .
A measure of the error is given by a number
2 JL labelled FIT. This number is found by taking the dif-
B = - Vtsb ntut dt
Ti ference between each measured ripple voltage and the
-2 voltage calculated from the phases and amplitudes of
the ripple. This difference is divided by the measured
where Bo = 0 and A. = twice the dc value of the signal.
voltage at each point and the ratio is squared. The
number FIT is one minus the mean of this ratio.
If we make k measurements during one period
of the function V(t), we may approximate the integrals
Graph Phasor Set
(2) and (3) by the following:
-.k_
The operator may see the results of the harmon-
a = v cd~(r e,) r = 0, 1, 2, 3 . . . (4) ic analysis by pushing a button labelled GRAPH
d
d=l PHASOR SET. This activates a subroutine that con-
structs the graphic display that is shown in Fig. 4.
$k1
b = Vc sln (re,) (5) The top lines on the right of Fig. 4 give the date
and time of day for starting to take the set of data.
d=l The remaining lines on the right give the point in the
. ZGS cycle at which the data taking began. In this case
ThenV(t)=la t a c a r c u t t a m 2 w t t . . it was 400.0 ms after the start of block 16 (flattop).
2 0 1 2
. . (6)
t b sin w t t b 2sh 2ot+.
1
or V(t) = -1 a t c1 sln (cuttxl) + cz sin (ottx,) t . . (7) 15. mH $ 7250
2 0 7 u F
(e) 1 I
IN OUT
where d-
b
cr = and x = arctan (8) 2 200 I OHM
T
PF
with the restriction -180° < xr S + 180'.
The first step in the analysis is to assign an
angle Bd to each of the data points. The computer Fig. 2 ZGS Passive Filter
5 17
-
PHASOR
0 0
0 a 15 NOV. 1973
21:04:36
0
0
a START AT 16 400.0
300 SAMPLES TAKEN
2 PERIOD ANALYSIS
HZ 1 ST THETA
I 50.15 4.82
2 50.10 2.28
RETAINED SET
ALPHA SET AMP. PHASE AMP. PHASE ALPHA SET
0 0 0 - .2 0 dc 0 0 0 0
I .I 29.3 I 0 0
0 0 0 I .I -I 11.7 2 0 0 0 0
.2 -I 12.0 3 0 0
0 0 0 .3 -130. I 4 0 0 0 0
.I -145.9 5 0 0
0 0 0 I .4 - 76.6 6 0 0 0 0
.I - 82.1 7 0 0
.o
0 138.0 8 0 0 0
.o
11.1 9 0 0
.o
47.8 IO 0 0
.o
- 5.9 I I 0 0
.6 15.6 12 0 0
Fig 3. Display New Set and Derived Ripple
Three hundred data samples were taken and two peri- The lower part of Fig. 4 lists several sets of
ods were analyzed. The first period had a frequency numeric data. The column in the center lists dc and
of 50.15 Hz, while the second had 50.10 Hz. This dif- phases 1-12. The two columns to the left of center
ference is caused by the slowing down of the generator give the amplitudes in volts and the phase angles in
during the ZGS cycle. The angle 8d for the first data degrees for the 12 phases and the amplitude of the dc
point in each cycle was 4.82O and 2.27O. component. These are the values used to calculate
the derived ripple plotted at the top of Fig. 4.
The top graph gives the reconstructed ripple
data that was calculated from the amplitudes and The table of numbers at the lower left records
phases of the derived ripple components. The FIT the alpha angle settings for the 12 phases and in addi-
number is also given. This graph is included in Fig. tion, the full rectify setting. These are the settings
4, as well as in Fig. 3, for identification purposes and of the ZCS control system that produced the ripple re-
because many people get a better "feel" for the data constructed at the top of Fig. 4. The numbers are in
from an analog type display. octal code and represent deviations from the ideal uni-
form spacing of rectifier firing angles. These num-
The upper bar graph of Fig. 4 plots the dc com-
bers are recorded in the exact format in which they
ponent and the amplitudes of the first 12 harmonics of
appear on the control panel of the digital firing angle
the generator frequency. The vertical scale for this
control system.
plot is shown above and to the left of the bar graph.
The scale factor in volts per inch is changeable at will These numbers are entered through the use of
through the scope keyboard. These amplitudes are for the ENTER/MODIFY ALPHA SET subroutine, and
the filtered voltage applied to the ring magnet. can be used by the operator when desired.
The lower bar graph of Fig. 4 plots the phase
Retained Set
angles x for the first 12 harmonics. The range of
angles isrfixed at t 180° to -180° in accordance with
The operator may save a set of results, such as
the restriction on xr in equation (8). These angles
that presented in Fig. 4, by pushing the button labelled
have been corrected for the phase shifts produced by
RETAIN THIS PHASOR SET. This activates a sub-
the passive filter of Fig. 2. They are, therefore, the
routine that stores the information in computer memo-
phase angles of the harmonic components at the output
ry for comparison with future data.
of the rectifiers. This is done to make it possible to
determine which rectifier firing angles should be re- The operator may then analyze a new set of data
tarded or advanced to reduce the amplitudes of the rip- and call for GRAPH PHASOR SET. The result is the
ple components. generation of a display such as shown in Fig. 5.
518
PHASOR
15 NOV. 1973
21 : 04 : 36
1.00 START AT 16 400.0
I
300 SAMPLES TAKEN
AMP. MAG. I I I I
2 PERIOD ANALYSIS
HZ 1 ST THETA
I 50.15 4.82
P. s. 2 50.10 2.28
-180
RETAINED SET
ALPHA SET AMP. PHASE AMP. PHASE ALPHA SET
77 36 77 - .2 0 dc 0 0 0 0 0
I ,I 29.3 I nV
37 76 36 I .I -I 11.7 2 0 0 0
-2 -I 12.0 3 0
76 36 77 .3 -I 30. I 4 0 0 0
.I -145.9 5 0
36 74 36 1.4 - 76.6 6 0 0 0
.I - 82.1 7 0
.o
472 138.0 8 0
.o 11.1 9 0
.o 47.8 IO 0
.o - 5.9 I1 0
.6 15.6 12 0
Fig. 4 Graph PHASOR Set
The numeric information at the top right of Fig. COPY NEW SET -- similar to Fig. 3,
5 is similar to that of Fig. 4 except it is for the new COPY LEFT SHIFTED -- that portion of Fig. 3
set of data. The derived ripple curve and the FIT that was analyzed,
number are aIso for the new set of data. COPY DERIVED - - derived ripple,
COPY PHASOR ?Ai LPHA SET -- similar to
The bar graph for the amplitude now has two
Fig. 4, 5.
lines at each harmonic locstion. The left line in each
The 'hard-copy" unit can produce a print in about ten
pair gives the amplitude of that harmonic component
seconds. No line printer output is provided.
in the new set of data, while the right line in each pair
gives the amplitude of that harmonic component in the
Calibration
retained set. In this way, the amplitudes may be com-
pared visually to determine the effect of the changes
The effects produced by changes in rectifier fir-
in the firing angles.
ing angle were experimentally investigated. For ex-
The bar graph for the phases also has a pair of ample, the firing angle of phase number 1 was ad-
lines at each harmonic location. The left line in each vanced several electrical degrees to produce a large
pair gives the phase angle for that harmonic compo- ripple on flattop. PHASOR was then used to measure
nent in the new set of data, while the right line gives the amplitude and phase of the harmonic components
the phase angle of that harmonic component in the re- of the ripple thus produced. This procedure was re-
tained set. peated for several combinations of change s in firing
angles of selected rectifiers.
The numeric information, at the bottom of Fig. 5
on the right, gives the amplitude and phase angles for The calibration data were useful in predicting
the retained set and in addition the alpha set that pro- which of the 12 rectifier groups should have their fir-
duced them, The numeric information, at the bottom ing angles altered to reduce a given observed ripple.
on the left, gives the amplitude and phase angles for
the new set of data and the corresponding alpha set. Discus sion
output Analyses of ripple data were made for a variety
of firing angle combinations during the calibration runs
The program PHASOR is an interactive one so and for many actual operating conditions while ripple
that most of the output is through visual observation of reduction adjustments were made. In all cases, the
the computer driven scope display. Several options in bar graphs similar to Figs. 4 and 5 showed very small
the interaction can produce copies of the scope display or no amplitudes for the 5th, 7th, 8th, 9th, IOth, and
on 8%" x 11" photographic paper. These include: 1 lth harmonics. The phase angles computed for these
519
...
PHASOR
15 NOV. 1973
23:2 5 : 16
START AT 16 600,O
500 SAMPLES TAKEN
AM
2 PERIOD ANALYSIS
HZ 1 ST THETA
I 48.82 4#58
s.
P. 2 48.76 3.27
'
-180 RETAINED SET
ALPHA SET AMP. PHASE AMP. PHASE ALPHA SET
77 32 77 - -6 0 dc -. \.o 0 77 50 77
.3 26.4 I .3 - 106.3
32 76 32 .3 170.8 2 .I 43.I 46 76 47
.2 - 96.2 3 .I - 153.2
101 32 77 .2 - 117.8 4 .I - 158.2 76 47 77
.o - 146.0 5 .I - 73.6
32 76 32 .I - 78.3 6 2.0 - 77.1 46 74 46
.o - 63.7 7 *I -90.2
47 3 .o - 166.4 8 .I I 38.3 470
.o - 30.I 9 .o - 153.7
.o - 68.0 10 .o -131.3
.o 78.I I1 .o - 136.6
,2 , 42.0 12 .7 136.0
Fig. 5 Graph PHASOR Set With Retained Set for Comparison
harmonic components varied widely from one data set A perfect rectifier system will produce only the
to the next which leads us to the conslusion that these 12th harmonic, therefore this cannot be eliminated or
effectively reduced by adjusting firing angles. On the
harmonic components are largely the result of "noise"
or inaccuracies in the input data. other hand, the 6th harmonic can be increased or de-
creased in only one way. That is, all even numbered
We were not able to find a combination of recti- phases should be advanced an equal amount and all qdd
fier firing angles that produced large or significant numbered phases retarded by the same amount. This
amounts of 5th, 7th, 8th, 9th, loth, and Ilth, harmon- method reduced the 6th harmonic amplitude to a mini-
ics. We therefore have amplitude and phase mea- mum but would not make it vanish. The data indicate
aurements at harmonic numbers l, 2, 3, 4, 6, and 12
that the phase shift between our delta and wye connect-
for a total of 12 measurements. ed transformers is only 28' rather than the theoretical
The control system has adjustments for each of 30°.
the 12 phases but only 11 of these are independent var- The first harmonic amplitude may be reduced by
iables as far as ripple is concerned. The 12th phase
changing all of the 12 angles. In this case, the
control and the "full rectify" control adjust the slope
changes are distributed sinusoidally with the peak of
of the flattop. This slope is adjusted to zero before
the distribution determined by the phase angle of the
the ripple measurements are made. 1st harmonic of the ripple. The 2nd harmonic may be
Some thought was given to writing a program reduced by a similar procedure except that the sinus-
that would compute new firing angle settings from the oid for the distribution is the 2nd harmonic.
ripple component amplitudes and phase angles. There
This program was used successfully to reduce
appear to be enough measurements to permit the solv-
the flattop ripple at the ZGS with the distributions for
ing of a set of 12 equations. No adequate algorithm alpha angle changes determined manually. It is hoped
for this was developed in the very limited effort ex- that additional subroutines can soon be added to per-
pended. mit the computer to calculate the alpha settings that
Inspection of the problem indicates that the rip- will minimize the ripple.
ple may be reduced one component at a time. This is
the procedure used.
5 20