Constant speed drive with compensation using differential gears

The electrical supply system on aircraft may employ a constant speed drive (CSD) to convert variable engine speed to constant speed for operation of synchronous 400 Hz electrical generators. The heart of these devices is a differential which mechanically sums the input of two shafts and outputs this sum to a third shaft. Connected to this third shaft is a constant speed synchronous generator. Connected to one of the input shafts is the turbine generator (most likely through gearing). The second input shaft is connected to a speed compensating drive which accounts for engine speed changes. The speed compensating device disclosed herein is an electrically compensating motor/generator arrangement. Bidirectional power flow in the electric compensation link uses two high-speed, permanent-magnet, three-phase machines interconnected by a power conditioning network. One machine is operated as a brushless dc machine, while the other functions as a variable speed synchronous machine. Steady-state performance of two types of power conditioning are presented--a dc link inverter and a cycloconverter link.

BACKGROUND OF THE INVENTION 
This invention relates to a constant speed drive device to convert variable 
engine speed to constant speed for operation of synchronous electrical 
generators, using differential gears, particularly for use on aircraft. 
The need for a highly efficient link, capable of bilateral power flow, 
connecting a variable speed shaft to a constant speed shaft is manyfold. A 
particular need is to drive an onboard aircraft alternator at constant 
speed while the turbine engine speed varies. Presently, two methods are 
employed to provide a constant frequency on aircraft: 
1. Constant Speed Drive (CSD) 
2. Variable-Speed, Constant Frequency (VSCF) 
The VSCF system allows the alternator shaft to vary directly with turbine 
speed. The variable frequency alternator output is then conditioned by a 
cycloconverter to obtain a constant frequency. The VSCF system is not 
sensitive to attitude changes, and thus, functions well on highly 
maneuverable aircraft. However, total output power of the alternator must 
pass through the cycloconverter, leading to bulky and expensive power 
conditioning and filter circuitry. 
The CSD scheme utilizes a mechanical differential which mechanically sums 
the input of two shafts and outputs this sum to a third shaft. Connected 
on this third shaft is a constant speed synchronous generator. Connected 
to one of the input shafts is the turbine (nost likely through gearing). 
The second input shaft is connected to a speed compensating device which 
accounts for engine speed changes. The speed conpensating device has been 
a hydraulic motor supplied by a hydraulic pumping mechanism driven from 
the engine. A constant alternator shaft speed is maintained by proper 
clockwise or counterclockwise rotation of the differential carrier housing 
through use of a reversible hydraulic pump-motor drive. For a 1.7:1 
turbine speed range and a lossless system, a maximum of 21.5% of the 
alternator shaft power must pass through the compensating hydraulic drive, 
while 78.5% to 100% of the power is transmitted directly through the 
differential gearing. The hydraulic CSD's are extremely sensitive to 
attitude and require special oil systems and filling procedures to ensure 
proper operation during all flight modes. Without the special oil systems, 
there is a problem during maneuvers that produce negative gravity. In such 
cases, fluid level shifts can cause the hydraulic system to momentarily 
malfunction, creating an out-of-frequency range condition and leading to 
loss of electrical power. 
Regardless of the above described potential failure mode, the concept of 
the CSD system has a quite desirable feature in that a large percentage of 
its output power is transmitted only through a low-order-mesh gear train, 
which by nature is highly efficient. 
The following items relating to electrical machinery are referenced in the 
detailed description: 
1. E. Ohno, T. Kishimoto, and M. Akamatsu, "The Thyristor Commutatorless 
Motor," IEEE Trans. Mag., Vol. MAG-3, September 1967, pp. 236-240. 
2. T. Tsachiya, "Basic Characteristics of Cycloconverter-Type 
Commutatorless Motors," IEEE Trans. IGA, Vol. IGA-7, No. 4, July-August 
1970, pp. 349-356. 
3. N. Sato and V. V. Semenos, "Adjustable Speed Drive with a Brushless DC 
Motor," IEEE Trans. IGA, Vol. IGA-7, No. 4, July-August 1971, pp. 539-543. 
4. E. P. Cornell and D. W. Novotny, "Commutation by Armature Induced 
Voltage in Self-Controlled Synchronous Machines," IEEE Trans. PAS, Vol. 
PAS-93, 1974, pp. 760-766. 
5. N. Sato, "A Brushless DC Motor with Armature Induced Voltage 
Commutation," IEEE Trans. PAS, Vol. PAS-91, July-August 1972, pp. 
1485-1492. 
6. J. M. D. Murphy, Thyristor Control of AC Motors, (Pergamon Press, 
Oxford, 1973), pp. 140-149. 
7. F. J. Bourbeau, "Synchronous Motor Railcar Propulsion," IEEE Trans. IAS, 
Vol. IA-13 No. 1, January-February 1977, pp. 8-17. 
8. T. Maeno and M. Kobata, "AC Commutatorless and Brushless Motor," IEEE 
Trans. PAS, Vol. PAS-91, July-August 1972, pp. 1476-1484. 
9. Y. Shrinryo, I. Hosono, and K. Syoji, "Commutatorless DC Drive for Steel 
Rolling Mill," IEEE-IGA Conference Record, 1977Annual Meeting, pp. 
263-271. 
10. A. C. Williamson, N. A. H. Issa, and A. R. A. M. Makky, "Variable-Speed 
Inverter-Fed Synchronous Motor Employing Natural Commutation," Proc. IEEE, 
Vol. 125, No. 2, Feb. 1978, pp. 118-120. 
11. N. A. Demardash, T. W. Nehl, and E. Maslowski, "Dynamic Modeling of 
Brushless DC Motors in Electric Propulsion and Electromechanical Actuation 
by Digital Techniques," IEEE IAS Conference Record, 1980 Annual Meeting, 
September 28-October 3 1980, pp. 570-579. 
SUMMARY OF THE INVENTION 
An object of the invention is to provide a link connecting a variable speed 
shaft to a constant speed shaft, having improved efficiency, that is 
insensitive to aircraft attitude changes, while retaining the desirable 
features of a Constant Speed Drive (CSD). Another object is to 
substantially reduce the cost of such a link. 
According to the invention, the hydraulic compensation drive is replaced 
with an electric compensation drive in a Constant Speed Drive (CSD) 
device. 
An advantage is that a properly designed electric drive offers an increase 
in overall efficiency, due to reduction in losses through the speed 
compensation path. Also, the potential exists for a greater interval 
between maintenance than for the compensating hydraulic drive system.

DETAILED DESCRIPTION 
I. Introduction 
The diagram of FIG. 1A applies to both the prior art hydraulic constant 
speed drives, and to the electrically compensated constant speed drives 
according to the invention. The heart of these devices is a differential 
10 which mechanically sums the input of two shafts 20 and 22 and outputs 
this sum to a third shaft 24. Connected to this shaft 24 is a constant 
speed synchronous 400 Hz generator 40. Coupled to one of the input shafts 
20 is the turbine engine 42 (most likely through gearing, represented in 
the drawing as spur gears 30 and 36). The second input shaft 22 is 
connected to a speed compensating drive device M2 which accounts for 
engine speed changes. To date, the speed compensating device M2 has been a 
hydraulic motor supplied by a pumping mechanism driven from the engine. In 
the hydraulic system, the source M1 is an hydraulic pump, shown coupled 
via a spur gear 38 and gear 26 to the engine. The control unit 50 and line 
52 are part of the hydraulic pumping mechanism. Additional components are 
also required to ensure satisfactory operation during all aircraft flight 
regimes. These include: charge pump, scanvenge pumps, all attitude 
reservoir, relief valves, and filters. The invention described herein 
removes the attitude-sensitive hydraulic motor/pump and replaces them with 
an electrically compensating motor/generator arrangement. 
The input shaft 20 is geared to produce the primary input speed to the 
differential, n.sub.1. The speed of the second input shaft 22 is n.sub.2. 
The speed of the output shaft 24 is n.sub.0 For the type of differential 
depicted, the relation between the differential shaft speeds is given by 
n.sub.2 =r (n.sub.1 -n.sub.0), where r is a constant depending on 
differential design. 
The views of FIGS. 1B and 1C are provided to give a clearer picture of the 
gearing for those readers not intimately acquainted with this type of 
machinery. Note in FIGS. 1A-1C, that all support and bearing structure for 
the gears is omitted. The view in FIG. 1A can be considered as being 
through the centers of all of the gears and shafts, but cross hatching is 
omitted for clarity. The spur gears 38, 36 and 30 are shown in FIG. 1B, 
with a view along lines 1B--1B of FIG. 1A. For clarity, the apparatus 
behind these three gears is omitted in FIG. 1B. 
The differential 10 is shown in FIG. 1C, with a view along lines 1C--1C of 
FIG. 1A. Note that the differential is the same in principle as that used 
in automobiles between the drive shaft and the rear wheels (shaft 22 
coupled to the drive shaft, and shafts 20 and 24 enclosed in the rear 
axle). The entire differential assembly 10 is contained in an oil-filled 
enclosure (not shown). There are four bevel gears 11-14 in a ring 
formation, enclosed in a differential carrier or cage 18 which is also an 
outer gear. Note that the bevel gear 13 connected to the input shaft 20 
does not appear in the view of FIG. 1C. However as seen in FIG. 1A, it 
drives the bevel gears 11 and 12, which in turn together drive the bevel 
gear 14 which is coupled to the output shaft 24. The bevel gears 11 and 12 
have shafts 15 and 16 respectively which are mounted on bearings of the 
cage 18; and these shafts rotate freely with no torque except for that 
produced by frictional losses. Note that cage 18 as shown in FIG. 1C is 
rotated to a different position from that shown in FIG. 1A. If the cage 18 
is not turning, then shafts 20 and 24 rotate in opposite directions at the 
same speed (n.sub.0 =n.sub.1, n.sub.2 =0). When the cage 18 rotates, it 
carries with it the shafts 15 and 16, and therefore the entire bevel gear 
ring 11-14. It is possible for shafts 20 and 24 to rotate in the same 
direction at the same speed as the cage 18 rotates (n.sub.1 =n.sub.2 
=-n.sub.0) (the normal situation of an automobile traveling in a straight 
line). The coupling between the shaft 22 and the cage 18 is represented 
here as a spur gear 32 meshing with spurs around one edge of cage 18. 
In the electric constant drive, the major components are the same as in the 
hydraulic system with the exception of the compensating network where the 
hydraulic pump M1, motor M2, and control 50 are replaced by electrical 
components. Both the alternator M1 and the motor M2 are preferably 
brushless permanent magnet machines. This type of machine will yield an 
electrically compensated CSD with the least weight while at the same time 
yielding the greatest reliability and effeciency. The compensating 
alternator M1, motor M2 and control 50 can be either oil or air cooled. 
The gear surfaces as well as the bearings should be oil cooled/lubricated 
to ensure long life. Additional components such as scavenge pumps and 
filters will be required to ensure oil system integrity. The following 
advantages of the electrical compensation are noted over hydraulic 
compensation. 
1. Attitude insensitivity. The hydraulic CSDs are extremely sensitive to 
attitude and require special oil systems and filling procedures to ensure 
proper operation during all flight modes. The electrical CSDs are 
essentially impervious to attitude and can operate at extended periods of 
time (1 to 2 minutes) with no oil. The limitation is cooling. 
2. Efficiency--15% increase minimum, 30% maximum. 
3. Cost--20 to 30% savings over hydraulic CSDs. 
4. Reliability--Hydraulic CSDs are presently yielding around 2000 hours 
between failures. The electrical CSDs are expected to yield 10,000 hours 
between failure. 
II. Objectives 
Electrically-compensated, constant-speed drives (ECCSD) that have potential 
for application as drive links between a turbine engine and an aircraft 
alternator have been researched. Objectives were established to study the 
nature of ECCSD systems in the steady-state. The specific objectives that 
were pursued are enumerated below: 
1. Define candidate electrical machinery and power conditioning circuitry 
arrangements suitable for use with an ECCSD system. 
2. Determine nature of torques, currents, and voltages for each candidate 
system operating as an ECCSD. 
3. Identify special requirements on machines, controls, and power 
electronic devices that result from the ECCSD application. 
III. Basic Requirements and Characteristics of ECCSD 
An understanding of the power flow and torque requirements of the ECCSD 
concept underlies any study as these characteristics must serve as a basis 
for selection of candidate electric machine and power conditioning 
systems. 
A. Nature of Power Flow. 
A physical arrangement of the ECCSD power level components is shown in FIG. 
1A, where variable input speed n.sub.1, constant output speed n.sub.0, and 
differential carrier speed n.sub.2 are related by: 
EQU n.sub.2 =1/2(n.sub.1 -n.sub.0) (1) 
Speed compensation to maintain n.sub.0 constant can be accomplished by two 
basically different control approaches: 
1. Reversing differential operation. Ratios are selected so that n.sub.0 
lies between the extremes of n.sub.1. Thus, from equation (1) it is 
apparent that n.sub.2 can range from negative to positive values or that 
the differential carrier 18 must be reversed to maintain a constant 
n.sub.0 over the range of n.sub.1 excursion. 
2. Unidirectional differential operation. Ratios can be selected so that 
n.sub.1 is always greater than (or always less than) n.sub.0, leading to 
the conclusion from equation (1) that n.sub.2 does not change sign as 
n.sub.1 varies; or, the differential carrier 18 is always rotated in the 
same direction for speed compensation. 
For study of basic characteristics, a typical turbine speed range of 1.7:1 
(10,588 to 1800 rpm) was used. The 400 Hz alternator 40 was modelled as a 
44.444 KW load at a constant 12,000 rpm (40 kVA output at unity power 
factor operating at 90% efficiency). Constant efficiencies were assumed as 
follows: 
1. Electric machines--90% 
2. Power conditioning units--95% 
3. Gear mesh--99% 
Energy balance equations were written for the arrangement of FIG. 1A and 
turbine speed was incremented across its speed range to examine both the 
case of reversing differential carrier 18 and the case of unidirectional 
differential carrier operations. A power flow diagram of the ECCSD system 
is shown by FIG. 1D where the flow direction of compensating loop power 
(P.sub.c) depends upon the polarity of (n.sub.1 -n.sub.0) as indicated on 
the diagram. 
The reversing differential carrier 18 results in minimum torque 
requirements for motor M2 if the midrange speed of n.sub.1 is set to equal 
n.sub.0, which also gives a symmetric range on n.sub.2 about the zero 
speed point. FIG. 2 displays the performance results of this system. It is 
observed that the torque requirements of motor M2 are nearly constant 
across the range of operation. However, the torque requirements of 
alternator M1 range from zero at the mid-range speed point to a maximum 
value at the point of minimum turbine speed. It is further noted that the 
maximum torque requirement of alternator M1 is greater than that of motor 
M2. The two maximum torque requirements could be made equal by an 
unsymmetric shift of the differential carrier 18 zero speed point with a 
net result of increasing the torque requirement of motor M2 while 
decreasing the requirement of alternator M1. The ratio of power flowing 
into the speed compensation loop to power delivered to the 400 Hz 
alternator 40 (P.sub.c /P.sub.o) is plotted to use as an indication of 
power apportionment between that transmitted by the compensation loop and 
that transmitted in mechanical form through the ECCSD. 
Calculated torque requirements and performance results for unidirectional 
differential operation, if n.sub.1 is less than n.sub.0, are depicted by 
FIG. 3. System gear ratios were selected so that n.sub.2 ranges from 2% to 
100% of the motor M2 base speed circumventing the necessity of dealing 
with low frequency torque pulsations at near zero speed. 
B. Electric Machines. 
The wide speed range, constant torque requirements suggested for motor M2 
by the above work is the characteristic of a shunt dc machine; but, due to 
the brush-commutator maintenance requirement and poor adaptability to 
liquid cooling, the commutator dc machine is not suitable for aircraft 
application. However, the brushless dc motor offers the same desired 
speed-torque characteristics as the dc machine without the disadvantages 
of the commutator dc machine (references 1-10). Further, use of a machine 
with a permanent magnet rotor offers two additional advantages: 
1. Field excitation is eliminated which removes the complexity of supplying 
power to a rotating member. Also, machine efficiency is increased due to 
absence of field excitation losses. 
2. Higher speed design is possible for permanent magnet rotors than is 
feasible with wound rotors permitting increased gear ratios and 
substantial reduction in electric machine size. 
Some of the brushless dc motor performance reported in the literature is 
experimental data (references 1, 3, 5). Others have presented calculations 
based on formulas derived using approximations of sinusoidal waveforms or 
neglecting commutation intervals giving results with some degree of 
correlation to test data but with appreciable error (references 2, 3, 9). 
However, the non-linearities introduced by the circuit switching leads to 
equations that are best solved by numerical techniques, and the reported 
performance data calculated by numerical solution of network differential 
equations show the least error between theoretical prediction and test 
results (references 4, 10, 11). When analyzing PM machines with rare earth 
magnets and stainless steel retaining rings for rotor constuction, 
Demerdash has reported (reference 11) that rotor eddy current effects, 
armature raction, and position dependence of inductances can be neglected 
leading to a simple third-order system of equations to describe a 
balanced, three phase, wye-connected PM machine: 
EQU v=[R]i+[L]pi+e (2) 
where 
v is a vector of terminal phase voltages (v.sub.1, v.sub.2, v.sub.3), 
i is a vector of phase current (i.sub.1, i.sub.2, i.sub.3), 
e is a vector of phase generated voltages (e.sub.1, e.sub.2, e.sub.3), 
[R] is a diagonal matrix with each entry being phase resistance, 
[L] is a diagonal matrix with each entry being half of line-to-line 
inductance, and 
p () is understood to mean d/dt (). 
Since the equations given by (2) are decoupled, each can be used in 
networks formed by addition of the power conditioning circuitry with 
minimum difficulty. 
C. Power Electronics. 
Obviously, the power conditioning circuitry of this application must be 
capable of bidirectional power flow when utilized in conjunction with the 
electric machinery. No reporting in the literature is available of an ac 
PM machine-to-brushless dc PM machine drive system. However, two basically 
different power conditioning links are candidates for use with this ECCSD 
under study: 
1. A dc link inverter using a phase-controlled converter for rectification 
and synchronous inversion. 
2. A cycloconverter link to perform ac-to-ac conversion. 
Either of these power conditioning links can use thyristor or transistors 
as switching elements, but the practicality of transistors depends on 
values of voltage and current ratings dictated by the final system design. 
Much of the logic and signal manipulation of either power conditioning 
link will lend itself to digital processing and microprocessor control 
giving a finished product in which a large percentage of the signal level 
electronics is integrated circuits. 
IV. DC Link Inverter with Reversing Differential 
A. System Description. 
Power level components of a dc link drive system for use with the reversing 
differential are shown in FIG. 4 where motor M2 is operated as a brushless 
dc machine while alternator M1 functions as a variable speed synchronous 
machine. 
In order to simplify the analysis, the phase-controlled converter and 
alternator M1 of FIG. 4 are modelled as a dc source which, when coupled to 
the inverter and motor M2, forms a nonplanar network. In this resulting 
network, the various SCRs (or transistors) and diodes are represented by 
nonlinear resistors the resistance of which are assigned small values when 
forward conducting and large values when reverse biased. For a 
wye-connected motor M2, the constraint that the phase currents must add to 
zero exists; thus, a system of two first-order differential equations is 
sufficient to describe the network. These equations have nonlinear 
coefficients due to the values of SCR (or transistor) and diode resistance 
being functions of the dependent variable (phase currents). Further, each 
60.degree. (electrical), a switching operation transpires in the inverter 
circuitry requiring a revised set of differential equations to describe 
the system; therefore, the differential equation coefficients are also 
functions of the position (.theta..sub.2) and speed (.omega..sub.2) of 
motor M2 rotor. In matrix notation, the network equations can be written 
as 
EQU pi=[A(i,.theta..sub.2)]i+[B(.omega..sub.2)]u (3) 
where i is a vector of two independent phase currents (i.sub.1, i.sub.2), 
and u is a vector the entries of which are phase generated voltages and 
the dc source which models the phase-controlled converter and alternator 
M1 combination. 
B. Control Approach. 
A block diagram of a control approach for unit 50 that can be applied to 
this dc link drive system is displayed in FIG. 5. A primary control loop 
is established with a speed reference signal via line 54 to assure that 
the 400 Hz alternator 40 maintains rated speed. A secondary control loop 
is present to guarantee that equation (2) is satisfied. The SCRs (or 
transistors) of the inverter are fired in a manner to maintain a constant 
commutation angle .gamma., related to the angle between the mmf wave of 
the rotor and the no-load mmf wave of the stator. The delay angle of the 
phase-controlled converter is varied to regulate the value of dc link 
voltage applied to the inverter terminals. Steady-state characteristics of 
this drive are quite similar to those of a dc machine system (references 
1, 10) except for the extra degree of freedom that exists in selecting 
.gamma.. 
The block diagram of FIG. 5 (unit 50), is shown with a microprocessor based 
control on current limit and SCR firing. It is likely that summing 
functions of the primary and secondary speed loops can also be handled as 
microprocessor operations if timing and sample rates do not become 
limiting factors. 
E. Performance Results. 
Values were selected for motor and choke coil parameters as R.sub.a 
=0.006.OMEGA., L.sub.a =25.times.10.sup.-6 H, R.sub.o =0.003.OMEGA., and 
L.sub.o =43.times.10.sup.-6 H. A numerical solution of the equations 
represented by (3) was implemented using a fixed increment, fourth-order 
Runge-Kutta procedure to find performance of the dc link drive for various 
values of constant speed. A trial-and-error search was made for the 
average values of motor M2 shaft torque (T.sub.sav) to satisfy the 
requirements established by FIG. 2. Results of points calculated across 
the speed range for forward flow of compensating loop power and partial 
range values for reverse flow of compensating loop power are shown in 
Table I. 
TABLE I 
______________________________________ 
PERFORMANCE OF DC LINK WITH 
REVERSING DIFFERENTIAL 
Speed T.sub.sav 
.alpha. .gamma. 
I.sub.ave 
I.sub.rms 
(rpm) (N-m) (degrees) 
(degrees) 
(A) (A) 
______________________________________ 
45,000 2.46 18.2 45 56.4 69.5 
22,000 2.48 61.6 45 56.2 69.2 
5,000 2.51 82.8 45 56.4 69.8 
500 2.24 88.2 45 55.2 66.3 
50 2.53 88.5 45 
-500 -2.45 89.3 165 47.0 56.8 
-5,000 -2.36 91.3 150 81.9 92.9 
-10,000 -2.46 90.3 140 115.2 130.6 
______________________________________ 
It can be observed that the values of average and RMS current required to 
produce the needed torque when motor M2 is in the regeneration mode 
(reverse flow of compensating power) increase as speed becomes more 
negative. This increase in current values is attributable to a marked 
increase in the magnitude and time that current flows through the inverter 
shunting diodes. At some point for speed more negative than -22,000 rpm, 
the shunting diode current reaches a conduction angle equal to 60.degree. 
at which point commutation failure occurs. A full range regenerative range 
operation with motor M2 acting as a brushless dc machine is not possible. 
At some negative value of speed, it would be necessary to change modes of 
operation; motor M2 would be allowed to operate as a variable frequency 
synchronous generator with the inverter shunting diodes acting as a 
three-phase, full-wave bridge rectifier and the phase-controlled converter 
could be controlled for synchronous inversion. However, use of a bridge 
switch as shown in FIG. 4 would be necessary to establish proper polarity 
of dc voltage to the phase-controlled converter for synchronous inversion. 
Calculations show that the average values of current can be reduced to 
acceptable levels with the synchronous inversion operation; however, the 
mode change creates control complexities. Further, with addition of the 
bridge switch, the number (16) of power level switching devices has 
closely approached the quantity (18) necessary for the cycloconverter link 
which is capable of full speed range regenerative operation without a 
control mode change. 
Cycloconverter Link with Reversing Differential 
A. System Description. 
Power level components of a cycloconverter drive system for use with the 
reversing differential are shown in FIG. 6. As in the dc link case 
previously discussed, motor M2 operates as a brushless dc machine while 
alternator M1 functions as a variable speed synchronous machine. 
It is permissible to model alternator M1 as seen from the terminals of 
motor M2 as a dc source that is magnitude dependent on both the speed of 
alternator M1 and an SCR firing delay angle .alpha.. However, since the 
response of motor M2 due to the frequency of alterntor M1 is desired it is 
necessary to describe V.sub.d, the instantaneous waveform of alternator M1 
generated voltage as seen from the terminals of motor M2, in 60.degree. 
increments of the alternator M1 voltage waveform giving the expression 
EQU V.sub.d =V.sub.m sin(.omega..sub.1 t-.phi.+.pi./3+.alpha.) (4) 
where V.sub.m depends on the speed of alternator M1, .omega..sub.1, is the 
electrical angular frequency of alternator M1 and .phi. is a phase shift 
angle that depends upon the particular 60.degree. increment of the motor 
M1 waveform that is applicable at the instant of solution. The nonplanar 
network that results when V.sub.d is coupled to motor M2 through the 
cycloconverter is described by a set of two differential equations with 
nonlinear coefficients as discussed in section IV except that now the 
forcing function coefficient matrix has entries that depend on the 
electrical angular frequency of motor M1: 
EQU pi=[A(i,.theta..sub.2)]i+[B(.omega..sub.1, .omega..sub.2)]u (5) 
B. Control Approach. 
A control approach is suggested by the block diagram of FIG. 7. The 
philosophy is basically that of the dc link system given by FIG. 5 
(discussed in Section IV) except that gating of the SCRs must be handled 
in such a manner to assure that both the commutation angle .gamma. and 
delay angle .alpha. are both simultaneously satisfied. 
C. Performance Results. 
The PM machine constants were unchanged from the dc link study. Values for 
the choke coil parameters were selected as R.sub.0 =0.003.OMEGA. and 
L.sub.0 =150.times.10.sup.-6 H. A numerical solution of the equations 
represented by (5) was implemented and a trial-and-error search made for 
average values of motor M2 shaft torque (T.sub.sav) to satisfy the 
requirements established in FIG. 2. 
Performance points across the speed range for forward and reverse flow of 
compensating power are tabulated in Table II. It is observed that control 
across the region of reverse compensating power flow is nicely 
accomplished by shift of delay angle .alpha. greater than 90.degree. and 
an additional forward shift of .gamma. by 120.degree.. No increase in 
motor M2 phase current occurs as in the case of dc link when 
TABLE II 
______________________________________ 
PERFORMANCE OF CYCLOCONVERTER LINK 
WITH REVERSING DIFFERENTIAL 
Speed T.sub.sav 
.alpha. .gamma. 
I.sub.ave 
I.sub.rms 
(rpm) (N-m) (degrees) 
(degrees) 
(A) (A) 
______________________________________ 
45,000 2.59 33.0 45 55.6 66.9 
22,000 2.48 68.6 45 54.3 65.6 
5,000 2.53 84.7 45 58.2 62.6 
500 2.48 88.8 45 53.7 58.8 
50 2.49 89.1 45 
0 2.49 89.1 45 
5,000 -2.45 92.6 165 47.4 58.0 
-22,000 -2.45 103.2 165 50.7 58.8 
-45,000 -2.53 116.1 166 48.0 58.2 
45,000 3.76 0 47 73.7 87.1 
______________________________________ 
The last entry of Table II presents a set of control conditions and results 
for meeting a 150% load case (short time overload). Operation at such a 
point is automatically permitted by the control system unless prohibited 
by limits. Since current is monitored, the microprocessor can allow a 
timed interval of operation at any point above rated value before 
initiation of a limit action creating quite a flexible approach to 
overload management. 
FIGS. 8A and 8B display the steady-state instantaneous motor M2 torque at a 
forward and a reverse compensating power flow point. There is inherently a 
pulsating torque component present in the brushless dc motor operation of 
a frequency that is six times the electrical angular frequency of motor 
M2. At low speeds, this pulsation frequency can decrease to within a range 
at which the mechanical components respond. The control system will have a 
feature to assure that at low mechanical speeds, the gate drives are 
cyclically enabled and disabled at a frequency above that at which 
mechanical response is possible. 
VI. DC Link Inverter with Unidirectional Differential 
A. System Description and Control. 
Power level component arrangement of a dc link drive system for use with a 
unidirectional differential is the same as shown in FIG. 4 except that the 
bridge switch is not needed. The system equations are formulated as 
discussed in section IV and are given by (3). The block diagram of FIG. 5 
is applicable in describing a control system 50 for this unidirectional 
differential drive. 
B. Performance Result. 
The drive system must meet the performance criteria of FIG. 3. Since the 
torques required are approximately 50% greater than for the reversing 
differential case, the PM machines will necessarily be about 50% larger in 
size. The parameters for motor M2 and the choke coil values are adjusted 
accordingly to give R.sub.a =0.004.OMEGA., L.sub.a =15.times.10.sup.-6 H, 
R.sub.0 =0.003.OMEGA., and L.sub.0 =25.times.10.sup.-6 H. A numerical 
solution for values of average torque to satisfy the requirements of FIG. 
3 and the results are presented in Table III. 
TABLE III 
______________________________________ 
PERFORMANCE OF DC LINK WITH 
UNIDIRECTIONAL DIFFERENTIAL 
Speed T.sub.sav 
.alpha. .gamma. I.sub.ave 
I.sub.rms 
(rpm) (N-m) (degrees) 
(degrees) 
(A) (A) 
______________________________________ 
45,000 
4.09 22.7 45 92.7 114.2 
22,000 
3.98 62.5 45 89.6 110.7 
5,000 
3.98 82.6 45 91.0 111.5 
900 4.12 86.9 45 100.6 120.9 
______________________________________ 
Inspection of Table III shows that average current values are approximately 
60% greater than for the reversing differential case (See Table I). 
Although this unidirectionally operated differential offers control 
simplification in that only one direction of compensating power flow is 
required and the necessity of dealing with torque pulsations at near zero 
speed is eliminated, the increased size requirements on the PM machines 
(to deliver approximately 50% more torque) and the increased current 
ratings on the SCRs or transistors (to conduct approximately 60% more 
current) are considered to be significant weight and cost penalties. 
The invention is described in a paper "Electrically Compensated Aircraft 
Alternator Drive" by J. J. Cathey, published in the Proceedings of the 
IEEE 1983 National Aerospace and Electronics Conference--NAECON 1983--Held 
May 17-19, 1983. The paper reports on a study directed by applicant, and 
is hereby incorporated by reference. 
It is understood that certain modifications to the invention as described 
may be made, as might occur to one with skill in the field of this 
invention, within the scope of the appended claims. Therefore, all 
embodiments contemplated hereunder which achieve the objects of the 
present invention have not been shown in complete detail. Other 
embodiments may be developed without departing from the spirit of the 
invention or from the scope of the appended claims.