Switched Reluctance Generators and Their
To obtain generating action with the SRM, the phase ;
current must be timed relative to the rotor position as shown Abstract--This paper reviews the characteristics of the
in Fig. 1 for a 6/4 SRM. In the figure it is assumed that the switched reluctance machine (SRM) operating as a generator. Many of these characteristics are unique compared to those of machine is turning in the positive angular direction so that other machine types because the SRM does not employ generating occurs when the phase torque is negative. Thus permanent magnets or a field winding on its rotor. Not the phase current is timed to flow for those rotor positions employing permanent magnets or a field winding on its rotor where the torque is negative and to be zero for those rotor allows the SRM's rotor to be operated at high temperatures positions where the torque is positive. Because the sign of and speeds. Further it means the SRM, operating as a the SRMs phase torque is independent of the sign of the generator, does not possess the inherent problem of generating SRM's phase current, motoring or generating action is into a shorted winding like a permanent magnet machine. totally controlled by the rotor positions for which the phase Though not having permanent magnets or a field winding on
current is nonzero . the SRM's rotor gives it certain advantages, the lack of a separate excitation source or winding requires special consideration during the design of an SRM generating system Torque(SRG). This paper describes the SRG's excitation and the effect this excitation has on the SRG's operation. The issue of excitation is especially important during load faults. Also this paper describes the duality of SRM generator and motor 2040operation. The implications this duality has for the SRG's ；;control are described. The paper concludes with results for 9060
controlling the SRG.
Index Terms--Switched Reluctance Motor, Switched
Reluctance Machine, Switched Reluctance Generator, Phase CurrentGenerators, Motor Drive, Power Electronics
I. INTRODUCTION Ideal
There has been significant interest in developing SRMs
；for numerous variable speed applications. These range from 090602040low cost consumer applications to high performance aerospace applications [1-6]. This interest in SRMs is due Fig. 1 Static torque and phase current for one phase during generation. to the machine's potential for low cost and/or fault tolerance Zero and 90 degrees are the aligned position and 45 degrees is the [1-7]. Most SRM applications addressed in the literature unaligned position. have utilized the SRM as a motor and have addressed its motoring performance [1-6]. The SRM can also be applied A typical drive system for controlling the SRM's phase as a generator [8-11]. currents relative to its rotor position is shown in Fig. 2. This The SRM requires power electronics to operate as a drive system is basically the same whether or not the SRM generator just as it does to operate as a motor. This means is being used as a motor or as a generator. The drive system that it is best suited for applications that require variable consists of the SRM, a rotor shaft position sensor, a speed. This makes the SRM a candidate for applications controller, and a power electronic converter. Figure 3 shows such as aircraft engine starter/generators, automotive the three states any one of the phases of the power starter/generators, and windmill generators. In addition, electronic converter can be in. In the first state, the two generating issues arise in applications that regenerate. IGBT switches are on and the SRM's phase voltage is Examples include washing machines, flywheels, and hybrid positive, tending to increase the phase current. In the and electric cars. second state, one IGBT switch remains on while the other
one is turned off. The current freewheels through the on
IGBT switch and one diode making the phase voltage zero. The phase current may either increase or decrease. In the ;University of Kentucky third state both IGBT switches are turned off, turning on
Aligned；；；；+2+--112Starting andPositionConverter Control Fault SourceShaftFig. 4 Phase current during generating is the phase current during Positionmotoring mirrored about the aligned position. Microprocessor Control Information busmVFig. 2 Typical SRM drive system for motoring or generating. (2) ：，(？；1)？：，(？；2)！(？；1？(？；2)) m~VbusFor the generating case, integrate (1) over a generating
interval where the angles are greater than zero to obtain C+busgVV， (3) (2)？(1)！(2？1)：，；：，；；；-m~
Now require that ：(-；) be equal to ：(；) and eliminate ，2，2these variables from (2) and (3) by adding the two VbusVbusVbusequations together
+busmbusg(；)VVCCC++ (4) ：，(；？1)？：，；(1)！(；2？；1)VVV，，-，m~--For the flux linkage at -； to equal the flux linkage at +；, 11V must be equal to the negative of V. Because the busmbusgState 2. OneState 3. BothState 1. BothSRMs flux linkage curves are symmetrical around the Switch On, OneSwitches OffSwitches Onaligned position, the phase currents will also be equal at -； 1Switch Off and +；. The equality of the phase flux and current at +/- ； 11Fig. 3 States of one phase of the power electronic converter. and +/- ； means that the SRM's phase current is mirrored 2 around the aligned position from motoring to generating. both diodes. This reverses the phase voltage decreasing the This mirroring of the phase current around the aligned phase current [12,13]. rotor position is shown in Fig. 5. Here the simulated phase
currents for low speed motoring and generating are shown II. DUALITY BETWEEN MOTORING AND GENERATING with the converter states labeled. The SRG simulated has a The SRM as generator is the dual of the machine as a rated speed of 25,000rpm, rated voltage of 270Vdc, and motor [12,13]. In fact the machine phase current waveforms rated power of 33kW . In the figure the simulated during generating are simply the mirror images, around the motoring and generating phase currents are shown at a aligned rotor position, of the phase currents during machine speed of 5,000rpm and a bus voltage of motoring as illustrated in Fig. 4. This statement can be 270Vdc.During these simulations all of the system losses, proven precisely if the machine's winding resistance is zero phase resistance etc., were set to zero. At the speed and it is essentially true for actual machines with reasonable simulated, the converter chopped using a strategy called efficiencies. The flux linked by an energized phase winding is 500 State 2State 2dtd：：；，()，()V400 (1) bus~m！！dtd； 300where the bus voltage V is approximately a constant. In busState 3State 1iphwhat follows the rotor position angles, defined in Fig 4, are 200less than zero if they occur before the aligned rotor position State 3State 1and greater than zero for angles greater than the aligned 100rotor position. It will be assumed that the machine is always
turning in the same direction so that the rotor angle is
always increasing for both motoring and generating. Thus 0-50-40-10-30-2001020304050the generating angles are greater in value than the motoring (t)； angles. For the motoring case, integrate (1) over a motoring Fig. 5 Simulated phase current for low speed motoring and generating with converter states labeled. interval where the angles are less than zero to obtain
freewheel chopping. In motoring, both IGBT switches are Motoring Generating
Both switches on - Current Both switches off - Current first turned on (state 1) until the current command is increases decreases reached. At this point one IGBT switch is turned off so the One switch on, one switch off One switch on, one switch off - current freewheels through the remaining IGBT and one - Current decreases Current increases diode (state 2). This shorts the phase and the back EMF of Both switches off - Current Both switches on - Current the SRM drives the phase current down. When the current decreases increases decreases to the commanded value minus a fixed hysteresis Current starts before pole Current ends after pole overlap, value, the off IGBT is turned back on causing the phase overlap, before alignment after alignment current to increase. When the current command is reached Current ends after alignment Current begins before again, one IGBT switch is again turned off, causing the alignment phase to be shorted. Typically the opposite IGBT switch to Table 1 Summary of SRM duality between motoring and generating.
the one turned off previously is turned off, halving the
switching frequency of the switches. This process repeats until the end of the phase conduction period is reached and both IGBT switches are turned off (state 3). Now the two diodes turn on reversing the voltage on the phase and forcing the phase current to zero as rapidly as possible.
In the generating case, state 1 is again entered first (both IGBTs on), but now the phase current trajectory is the reverse of the state 3 motoring trajectory (both IGBTs off). When the current reaches its commanded value both IGBTs are turned off (state 3) to force the current to decrease. When the current decreases to the commanded value minus a fixed hysteresis value, one off IGBT is turned back on shorting the phase and causing the converter to enter state 2. In the generating case, the current in the phase increases when it is shorted rather than decreasing as in the motoring case. This is because the sign of the back EMF for motoring is opposite the sign for generating. This process repeats until the end of the phase conduction period is reached and both IGBT switches are turned off (state 3) to force the phase current to zero. Now the generating phase current trajectory follows the trajectory of the motoring phase current at the beginning of the cycle in the reverse direction. The mirroring of the phase currents between motoring and Fig. 6 Measured phase current for high speed motoring and generating generating is not as good as shown in Fig. 5 when losses are using only converter states 1 and 3. included in the simulation. The mirroring of the SRM's phase current waveforms about the aligned position between motoring and generating III. EXCITATION OF THE SWITCHED RELUCTANCE operation is summarized in Table 1. These results allow the GENERATOR
converter switch state control strategy for generating to be The basic SRG is normally operated in its constant obtained from a known control strategy for motoring power region [9-13]. In the constant power region of [12,13]. operation the inverter operates in the square wave mode A comparison between measured motoring and where each IGBT switch in Fig. 2 turns on and off generating phase currents, obtained from an experimental simultaneously once per SRM phase cycle. Thus only SRM system [6, 12], is shown in Fig. 6 [12,13]. This SRG converter states 1 and 3 are used. This mode of operation is is the same system that was simulated to obtain the results limited to higher machine speeds where the back EMF of in Fig. 5. In the figure the measured motoring and the machine is comparable to or higher than the dc output generating phase currents are shown at a machine speed of voltage as in Fig. 6. The SRG can generate at lower speeds approximately 17,000rpm and a bus voltage of 270Vdc. than this, but it will be limited to a constant torque The speed of the machine is high enough that the converter capability rather than the constant power capability required does not have to chop to regulate the phase current. Thus of a generator. At these lower speeds the back EMF of the the converter is only using states 1 and 3 in Fig. 6. The machine is too low to limit the phase current so that the motoring and generating conditions for the data shown in inverter must chop to regulate the current. The generating Fig. 6 were not exactly the same since the data for the two phase current waveform in Fig. 5 is typical of the constant conditions were not taken at the same time and the data was torque region of operation. In the constant torque region of not specifically taken for comparison. However, the data is operation the maximum power the SRM can generate will consistent with the theoretical results. decrease linearly as the speed decreases.
A typical SRM phase current waveform when where
generating in the square wave mode of operation is shown
in Fig. 7 [12,13]. The SRM draws energy from the DC bus 1 Rk！while the switches are on during the interval labeled t and exck(；on,；off,~m,Vbus)it returns energy to the bus through the diodes when the switches are off during the interval labeled t. During genThen the bus capacitor voltage must satisfy generating, the energy that is returned to the bus through the diodes while the switches are off exceeds the energy 11dVcdrawn from the bus while the switches are on. The energy (6) ；？！()0cVdrawn from the bus through the switches while they are on loadkdtRCRCis called the SRM's excitation energy. Note that the excitation time is equal to the generating time and that the Here the proportionality constant k(；,；,~,V), or onoffmbusSRM phase current can last for no more than one phase equivalently 1 / R, depends on the inverter turn on and turn kcycle. Note too, since the magnitude of the phase voltage is off angles, the machine speed, and potentially the bus approximately constant and equal in both the excitation and capacitor voltage. It is clear from (6) that the system will be generating time periods, the excitation and generated unstable if R is less than the load resistance R (a lighter kloadenergies are proportional to the area under the current load). In this case the bus voltage will rise exponentially. A waveform in Fig. 7 during their respective periods. simulation of this condition for the SRM in [6, 12] is shown in Fig. 8 where the instability is clearly visible. If R is kI(t)greater than the load resistance (a heavier load) the bus phase
voltage will decay to zero. During a load fault the feedback
loop controlling the SRG's output voltage will saturate to its
maximum possible difference in turn on and turn off angles.
Thus these angles will become fixed as assumed above.
During faults the load is always too heavy (the load tttexcgenresistance too small) so the SRG output voltage will t = texcgen= tcollapse. Also, the above result indicates that there is a = toffon
maximum permissible load for any particular machine, Fig. 7 Phase current during generating with the excitation and generating intervals identified. independent of thermal considerations. For loads greater than the maximum, the bus voltage will collapse to zero As can be seen from Fig. 2, the SRM obtains its unless the additional current required by the load is drawn excitation from the same bus that it generates into [12,13]. from a battery or other source as shown in Fig. 2. This leads to unexpected generating behavior in the square To complete the above analysis R must be calculated kwave mode when the turn on angle (rotor position) and turn or measured. To measure R the average generated current koff angle (rotor position) of the IGBT switches in each must be measured as a function of the DC bus voltage for phase of the inverter are fixed. It would be expected that the fixed turn on and turn off angles [12,13]. The circuit in Fig. output voltage of the open loop SRG, operating with fixed 2 can be used to measure R without experiencing the kturn on and turn off angles, would go to a steady stable instability described in (6). This is accomplished by putting value. In reality this open loop SRG is unstable. To a load on the SRG that is too heavy for the gating angles understand why, consider that with a given bus voltage a chosen so that the output of the SRG is predicted to go to certain amount of power and thus average generated current zero by (6). Then an external supply is diode "ORed" with will be produced. If a perturbation increases the bus voltage, the SRG's output, as indicated in Fig. 2, to maintain the bus the amount of current that builds up in the machine while at the desired value. Under these experimental conditions the IGBT switches are closed will increase compared to the load current is measured and the current from the dc when the bus voltage was less. Thus the SRM's excitation supply is measured. These two currents are subtracted to will increase, increasing the amount of current that is obtain the average current generated by the SRG. Typical generated when the switches are turned off. This increase in measured and computed results for the experimental SRM generated current will tend to increase the output bus in [6, 12] are shown in Fig 9 for a excitation interval of 30.5 voltage still further. A similar argument holds if the voltage degrees, a load resistance of 2.42，, and a 270V bus voltage decreases. This behavior is due to the fact that the SRG gets [12,13]. Note that the current I in this figure is equal to genits excitation from the same voltage bus it generates into the average current out of the SRG. The value of R kand thus there is inherent and positive feedback in its obtained from this data is about 2.5 ，. This says that the operation with fixed turn on and turn off angles. Thus there SRG output should increase exponentially for load resistors is the potential for instability [12,13]. with values greater than this value for an excitation interval To address this problem analytically, assume that the equal to 30.5 degrees. average current generated for a given set of turn on and turn
off angles is proportional to the bus capacitor voltage.
Vciav！k(on,off,m,Vbus)?Vc！；；~ (5) Rk
Power BusExcitation Bus
Fig. 10 SRG system with separate excitation and power busses.
in Fig. 10. Then when the IGBT switches turn off, all of Fig. 8 Simulation of constant angle instability showing the phase current this excitation energy is delivered to the load along with the and output voltage at 18,000rpm. generated power and thus lost from the excitation circuit. 120 To reduce the power rating of the excitation source it is desirable to recover the excitation energy delivered to the 100 load each electrical cycle so it does not have to come from calculated the excitation source. The excitation power required from 80 Mean the excitation source can be made zero during normal
generated operation by diode OR'ing the excitation source with the 60 current generated power bus as shown in Fig. 11. The excitation measured A source voltage is set to a lower value than the SRG's output 40 voltage so that it only supplies power at start up and during
a load fault [13,14]. 20 It would be desirable for the SRG to generate its own
excitation during load faults as well as when there are no 0 50 100 150 200 250 300 load faults so that the excitation source does not have to be Vout - V sized to handle the load fault. A circuit for accomplishing Fig. 9 Measured and calculated average current generated by an SRM as a function of dc bus voltage. this objective is shown in Fig 12 . In the figure there are still two busses, an excitation bus and a load bus, like the
SRG in Fig. 10. Diodes are connected to the excitation bus
IV. LOAD FAULTS AND THE SWITCHED RELUCTANCE in a manner analogous to the diodes in a conventional SRM
GENERATOR converter. The SRM is connected to the load bus through
controllable power switches. The basic requirements of The classic SRG shown in Fig. 2 suffers from the these switches are satisfied by thyristors as indicated in Fig. disadvantage that it is self-excited and thus there exists a 12. If the thyristor switches are off, the power bus is maximum load that it can support [12,13]. A load fault on disconnected from the generator system and all generating the output of the SRG will always exceed its maximum load action is into the excitation bus. The only load on this bus is capability and bring the voltage at the output of the SRG to the machine excitation itself. There is no load resistance so zero. Then, even if a fuse is blown disconnecting the load the generator will be unstable with fixed turn on and turn fault, the SRG will not recover generating operation. Thus a off angles, charging the excitation capacitor. When the separate fault clearing power supply is required as shown in excitation bus has risen to its desired value the appropriate Fig. 2. thyristor switch is gated on sending the rest of the generated Providing a separate bus to excite the SRM as shown in power to the power bus. This will occur as long as the Fig. 10 can circumvent this problem . In this case the power bus voltage is less than the excitation bus voltage. In excitation for the SRM is separate and independent from fact, the operation of the circuit is such that the excitation the voltage generated and from the load. This is bus voltage will always be greater than or equal to the accomplished in Fig. 10 by having a separate excitation bus power bus voltage. When the thyristor switches are on, the to supply the SRM's excitation through the IGBT switches diodes keep the excitation bus from discharging into the and a separate power bus the SRM generates into through lower voltage power bus. Note that the combined current the diodes. Thus the machine's excitation comes from a rating of an upper diode-thyristor pair is the same as that of separate source that does not depend on the SRG's output a lower diode. Note too that the thyristor switches must and thus on load faults. Calculations show that the amount support reverse voltage as well as forward voltage and they of excitation power that must be supplied to excite the SRM must turn off when their current goes to zero like a diode. is typically about 30% of the power going to the load at Under normal circuit operation the thyristors commutate off rated load. The reason the excitation power is this large is naturally. If during a fault a thyristor does not commutate that during each electrical cycle energy is delivered to the SRM from the excitation source through the IGBT switches
Power BusExcitation Bus
Vvpower150 Fig. 11 SRM generating system that generates its own excitation during normal operation. 100
Power BusExcitation Bus50
000.010.020.030.040.050.06s CexFig. 13 Simulated excitation and power voltages for the circuit in Fig 9 Ph1Ph2Ph3Cpwrincluding start up, a load fault, and normal operation. Load
vexcite300 Fig. 12 SRM generating system that generates its own excitation during vpower250load faults. 200off naturally, it will be forced off when its corresponding V,lower IGBT switch turns on. A150The simulated excitation bus voltage and power bus
voltage for the circuit in Fig. 12 are shown in Fig. 13. The 100starting source value is 50V and the load is 442m，;(？，；. phase currents / 3The commanded output voltage is stepped from 0 to 270V 50at 5ms, then at 23ms a 20m， fault is applied to the SRG's
output until 48ms when the fault is removed. As required, 00.06640.06660.06680.0670the excitation bus voltage is greater than the power bus svoltage and its average value remains constant right through 132the load fault. An expanded view of the simulated Fig. 14 Simulated excitation voltage, power voltage, and phase currents excitation voltage, power voltage, and phase currents (divided by 3) during normal operation. during normal operation are shown in Fig. 14. The control sequence for each phase is to turn on both IGBT switches
during the time interval labeled 1 in Fig. 14 to excite the V. SWITCHED RELUCTANCE GENERATOR CONTROL ISSUES. SRM. Then both IGBTs are turned off, turning on both
diodes for the time interval labeled 2. Both diodes remain Because of the SRM's significant incremental phase on until their corresponding thyristor is turned on. When the inductance and the fact that its excitation is controlled on a thyristor is turned on it turns off its upper diode. The cycle by cycle basis, the SRG behaves more like a current thyristor is not turned on until the excitation voltage has source than a voltage source . The upper plot in Fig. 15, reached its commanded value (320V in Figs. 13 and 14) for a varying commanded excitation, illustrates the current and then remains on during the time period labeled 3 in Fig. into the voltage bus in Fig. 2. The average generated current 14. The thyristor naturally commutates off when its current can only be changed once per output cycle. This suggests and thus the phase current go to zero. The SRM phase the SRM, power electronics, and switch state control can all current is similar to the phase current in a single bus voltage be modeled as a controlled current source whose value in SRG with the addition of a change in slope when the any time interval is equal to the average current generated thyristors turn on. This change in slope occurs because the by a phase during that time interval as illustrated by the phase voltage steps from the higher excitation voltage value lower plot in Fig. 12 .
to the lower power voltage value when the thyristor turns Because the SRG behaves more like a current source, on. The circuit in Fig. 12 has the disadvantage that the output voltage feedback is required to keep the SRG's combined capacitance value of the excitation bus capacitor output voltage constant as the load and speed vary. To and the power bus capacitor is of the order of twice the analyze the stability of the SRG system the simplified value of the single bus capacitor in Fig. 2. The circuit in Fig. average model in Fig. 16 may be used . The SRG is a 12 can be generalized to generate AC. This generalized first order system and thus it is typically controlled using circuit has been named the switched reluctance proportional-integral control. The output of this controller is cycloconverter (SRC) [13,15]. a current command whose value is ideally equal to the
average current generated by the SRG. This current 20
command is the input to the SRG's switch state control
One way to control the average current generated by 15
the SRG is to vary its excitation time . A typical plot of
the computed ratio of the incremental change in the average
generated current to the incremental change in mechanical Gain10
t015102025303540Angular duration of excitation, mechanical degrees Fig. 17 Gain of the SRM during generating in Amp per degree of rotor iin5rotation. i4i 3i2i1
VI. CONCLUSIONS t2TnT3T4TT5T0This paper has described the fundamental SRM Fig. 15 Illustration of the average SRG model concept. Shown are the generating characteristics that make its operation unique actual converter bus current and the bus current used in the average model. compared to other machine types. Though these
characteristics are driven by the structure of the machine, +LoadCthey impact the power converter and system control. It was
Vshown that the phase current waveforms during generating out
are the mirror images of the phase currents during motoring
mirrored about the rotor's unaligned position. It was also -
shown that the excitation of the SRM is accomplished by -having its windings excite the machine for part of the time Icomerrorand deliver power to the load part of the time. Thus the Control+conventional SRG cannot clear a load fault or recover from +refone. Because the conventional SRG is unable to clear load faults alternative SRG circuit topologies were presented Fig. 16 Simplified average model of the SRG.
that separate the machine's excitation from it load. These
degrees of rotor rotation during the excitation time is shown circuit topologies allow the SRG to clear faults. Finally the in Fig. 17. This incremental gain was computed for the modeling and design issues associated with regulating the experimental SRG the data in Figs. 6 and 8 is from. It is output voltage of the SRG were addressed. Experimental
data and simulation results were used to demonstrate the apparent that not only must the control stabilize an
fundamental results. inherently unstable SRG, it must do so with a widely
varying gain. In addition, this gain can be quite large, as
large as about 16 A/degree with a 150A load at the 270V VII. REFERENCES
rated voltage. Thus if the rotor's position can be measured  M. R. Harris, A. Hughes, and P. J. Lawrenson, "Static torque to an accuracy of 0.3 degrees, there will be an error in the prediction in saturated doubly-salient machines," Proc. IEEE, Vol.112, No. 10, pp 1121-1127, 1975 generated current of 4.8A. This corresponds to a 3.2% error  P. J. Lawrenson, J. M. Stephenson, P. T. Blenkinsop, J. Corda and in the average generated current and the output voltage. N. N. Fulton, "Variable-speed switched reluctance motors," IEE An alternative strategy to control the average current Proc., pt. B, vol. 127, no. 4, pp. 253-265, July, 1980. generated by the SRG is to turn on the IGBT switches at an  T.J. E. Miller, "Switched reluctance motor drives, a reference book of collected papers," Intertec Communications Inc., 1988. appropriate rotor position for generating while turning them  J Faiz and J. W. Finch, "Aspects of design optimization for off when the SRM phase current reaches a commanded switched reluctance motors," IEEE Transactions on Energy value [10,14-16]. Now the average generated current is Conversion, Vol. 8, No. 4, pp 704-713, Dec. 1993 controlled more directly. The open loop system (it now has  T. J. E. Miller, "Switched reluctance motor drives and their control," Clarendon Press Oxford, 1993. current feedback) is now stable since the IGBT switch turn  A. V. Radun, "High power density switched reluctance motor on and turn off angles are no longer fixed. In addition the drive for aerospace applications," IEEE Transactions on Industry gain is smaller and more nearly constant, resulting in a Applications, Vol: 28, pp 113-119, Jan-Feb 1992. design whose stability depends much less on the SRGs  C. M. Stephens, "Fault detection and management system for fault tolerant switched reluctance motor drives," Conf. Record IEEE operating point. Industry Applications Society Annual Meeting, Sept. 1989, pp. 574- 578.  E. Richter, "Application considerations for integral gas turbine starter/generator revisited," SAE Paper 892252, Aerospace
Technology Conf. and Exposition, Anaheim, CA, Sept. 1989 and Aerspace Atlantic, 1990.  S. R. MaMinn and W. D. Jones, "A very high speed switched reluctance starter-generator for aircraft engine applications," Proc. NAECON 89 (Dayton, OH), May 22-26, 1989.  S. R. MacMinn and J. W. Sember, "Control of a switched reluctance aircraft engine starter-generator over a wide speed range," Proc. IECEC 89,(Washington, DC), Aug. 6-11, 1989.  Cameron, D. E. & Lang, J. H., "the Control Of High-Speed Variable-Reluctance Generators In Electric Power Systems," Proc. of APEC March 1992  A. V. Radun, J. A. Rulison, and P. Sanza,., "Switched reluctance starter/generator," Trans. SAE, J. Aerosp., v 101, n Sect 1, 1992, p 1771.  A. V. Radun, "Generating with the switched reluctance motor," Proceedings of the Ninth Annual Applied Power Electronics Conference and Exposition, Vol 1 pg. 41, 1994.  R. Rockwell and A. Radun, "Preliminary design results for the thswitched reluctance cycloconverter," 34 Intersociety Energy Conversion Engineering Conference (IECEC), August 1-5, 1999, Vancouver, British Columbia, Canada.  A. V. Radun., C. A. Ferreira, and E. Richter, "Two channel switched reluctance starter/generator results," IEEE Transactions On Industry Applications, vol. 34, n. 5, pp. 1026-1034, September/October 1998.  A.V. Radun, and Y. Q. Xiang, "Switched reluctance starter/generator system modeling results," Trans. SAE, J. Aerosp., vol. 104, sec. 1, pp. 257-266, 1995.