The use of doubly fed reluctance machines for large pumps and wind turbines
ABSTRACT Brushless doublyfed induction machines (BDFIMs) have been extensively researched over the last 15 years because of the possibility of using a partially rated inverter in many applications with limited speed variations. However, the special cage rotor construction and substantial rotor losses is one of the key deficiencies of these machines. A similar and extremely interesting machine, the brushless doublyfed reluctance machine (BDFRM), has been largely ignored in comparison. This was mainly due to the fact that reluctance rotor designs were not capable of generating saliency ratios large enough to make the BDFRM competitive with other machines. However recent developments in reluctance rotors, spurred on by research into synchronous reluctance machines, have resulted in high saliency ratio cageless rotors that are economic to build. This, together with the promise of higher efficiency and simpler control compared to the BDFIM, means that further investigation of the BDFRM is warranted. This paper presents a comparative theoretical analysis of the important control properties and related machine performance/inverter size tradeoffs for the BDFRM in the light of its most likely applicationslarge pump type adjustable speed drives and variable speed constant frequency wind power generation systems.

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ABSTRACT: The objective of this paper is to present a series of novel doubly salient electromagnetic generator (DSEG) with multiple rotor poles for direct driven wind turbine. The 6k/4kpole DSEGs are restricted in direct drive wind power application for the constraint between stator pole number and rotor pole number. Recent work by the authors shows a series of DSEG which the rotor pole number is more than the stator pole number. 2D finite element analysis software for DSEG was developed and the obtained results verify the rationality of new structures and also show that the new structures have many attractive advantages, such as cogging torque, external characteristic, power density and efficiency.Electrical Machines and Systems (ICEMS), 2011 International Conference on; 01/2011 
Conference Paper: Design principles for brushless doubly fed reluctance machines
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ABSTRACT: This paper aims to provide the background theory and design methodology required for the effective design of brushless doubly fed reluctance machines. Reviewing existing theory, a new mean synchronous speed reference frame is presented to aid the understanding of the design requirements for an effective machine. Design equations are presented and an example design is developed. The example design indicates that the machine is capable of high torque density at low speeds.IECON 2011  37th Annual Conference on IEEE Industrial Electronics Society; 01/2011 
Conference Paper: Issues with the design of brushless doublyfed reluctance machines: Unbalanced magnetic pull, skew and iron losses
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ABSTRACT: In this paper some fundamental design issues concerning the brushless doublyfed reluctance machine are addressed. The literature has several examples of electrical machines with different pole number. It has become apparent that a radiallylaminated ducted rotor is a better option. In this paper it is illustrated that the pole number combination should not have pole pair number varying by one, otherwise unbalanced magnetic pull occurs. In addition, it is shown that to reduce voltage ripple due to the interaction of the slotting between the stator slots and rotor ducts, two axial rotor sections can be used with a small degree of skew between them. The example machine design is a 2 MW design as used previously, this has 48 stator slots. The machine results are couched in terms of a 4/8 pole and a 4/6 pole combination (for UMP calculation). Finite element analysis and analytical algorithms are used in the paper.Electric Machines & Drives Conference (IEMDC), 2011 IEEE International; 01/2011
Page 1
The use of doubly fed reluctance machines for
large pumps and wind turbines
M. G. Jovanovi´ c, Member, IEEE, R. E. Betz, Member, IEEE, and J. Yu
Abstract— Brushless doublyfed induction machines (BDFIMs) have
been extensively researched over the last 15 years because of the possi
bility of using a partially rated inverter in many applications with limited
speed variations. However, the special cage rotor construction and sub
stantial rotor losses is one of the key deficiencies of these machines. A
similar and extremely interesting machine, the brushless doublyfed re
luctance machine (BDFRM), has been largely ignored in comparison. This
was mainly due to the fact that reluctance rotor designs were not capable
of generating saliency ratios large enough to make the BDFRM competi
tive with other machines. However recent developments in reluctance ro
tors, spurred on by research into synchronous reluctance machines, have
resulted in high saliency ratio cageless rotors that are economic to build.
This, together with the promise of higher efficiency and simpler control
compared to the BDFIM, means that further investigation of the BD
FRM is warranted. This paper presents a comparative theoretical analysis
and aspects of practical implementation of the important control strate
gies and associated machine performance/inverter size tradeoffs for the
BDFRM in the light of its most likely applications  large pump type ad
justable speed drives and variable speed constant frequency wind power
generation systems.
Keywords—brushless doublyfed machine, self cascade machine, reluc
tance machine, electric machine control.
I. INTRODUCTION
T
gether with the classical Cascaded Induction Machine (CIM),
the traditional Double Excited Slip Ring Induction Machine
(DESRIM) and the Brushless Doubly Fed Induction Machine
(BDFIM)1. A common property of all the machines from this
group is that if the operational speed range is restricted a con
verter, which is normally supplying one of the windings, can
be fractionally rated the specific rating being determined by the
magnitude of the speed range around a “synchronous” speed2.
In order to achieve the enhanced control and operational mode
flexibility and improved power quality a bidirectional PWM
converter should be used. The cost, switching losses and line
harmonic content of this configuration would be substantially
reduced by the lower kVA requirement. As far as the machine
is concerned, it turns out that with the same torque as an in
duction machine or an equivalent synchronous reluctance ma
chine (Syncrel), a larger BDFIM/RM is required [2]. There
fore the use of a BDFIM/RM allows a tradeoff between the
size of the converter and machine. For classes of large, limited
HE BrushlessDoublyFedReluctanceMachine(BDFRM)
belongs to a group of slip power recovery machines to
M.G.Jovanovi´ c is with the School of Engineering and Technology,
Northumbria University, Newcastle upon Tyne NE1 8ST, UK. Email: mi
lutin.jovanovic@unn.ac.uk
R.E. Betz is with the School of Electrical Engineering and Com
puter Science, University of Newcastle, NSW 2308, Australia.
reb@ee.newcastle.edu.au
J.Yu is with the School of Engineering and Technology, Northumbria Uni
versity, Newcastle upon Tyne NE1 8ST, UK. Email: jian.yu@unn.ac.uk
1A good review of the BDFRM/IM historical evolution is presented in [1].
2This is half the speed of a conventional synchronous machine having the
same number of rotor poles. It corresponds to the situation when the inverter
fed winding of the BDFRM/IM is DC supplied.
Email:
range variable speed systems3, the overall system cost could be
significantly lower compared to applications with fullyrated
converters despite the somewhat increased cost of the ma
chine itself4[1]. The previous advantages can be also accom
plished using static Kramer or Scherbius cascades based on a
DESRIM. However, the BDFRM/IM’s brushless, and therefore
maintenancefree, structure offers improved reliability to these
systems. For these reasons, BDFRM/IM based drive technol
ogy may be an ideal brushless solution for such areas as Vari
able Speed Constant Frequency (VSCF) hydro and wind power
generation [3–5], commercial Heating, Ventilation and Air
Conditioning (HVAC), large pumptype drives (pumps [6,7],
fans, blowers, compressors etc.) as well as turbo machinery
(where the rugged nature of the rotor and the synchronous ma
chine mode of operation can be exploited [8]).
The BDFIM/RM has two stator windings of different pole
numbers and generally different applied frequencies (Fig. 1)
 the primary (power) winding is grid connected and the sec
ondary (control) winding is converterfed. Magnetic coupling
between the windings, a prerequisite for torque to be produced
from the machines, is provided via the rotor having half the
total number of stator poles5. In the BDFIM case, the rotor
is of special cage construction composed of nested loops [9]
whereastheBDFRMcanuseanyoftheSyncrel’srotordesigns.
In many respects the BDFRM and the BDFIM are obviously
similar, however the BDFRM has the following important ad
vantages:
• It is potentially more efficient6(since the ‘cold’ rotor losses
are much smaller than with the BDFIM), and should be able to
operate at higher speeds because the cageless rotor can be more
robustly constructed.
• It is considerably easier to model and control as the BDFIM
has an additional winding on the rotor.
• In contrast to the BDFIM, the BDFRM allows inherently
decoupled control of torque and primary reactive power (so
does the DESRIM) which further facilitates its vector control
schemes [11]. For the BDFIM, complicated decoupling algo
rithms are required to achieve the same objective [12].
• It can operate stably and reliably over the entire speed range
(at sub and supersynchronous speeds) in both motoring and
generating modes. The BDFIM, on the other hand, has sta
bility problems around the zerotorque operating point at syn
chronous speed of the gridconnected winding field [13].
3For a speed range of 2:1, that is typical for pumps and wind turbines, the
converter real power rating can be reduced to about 25% of the machine rating.
4Note that in small power applications, the cost benefits would not be that
pronounced due to relatively low market prices of associated power electronic
hardware.
5Unlike a conventional machine, the BDFRM/IM’s rotor pole number can be
odd (for 4/2pole stator windings). The most common design reported in the
literature is however with a 6/2pole stator and a 4pole rotor.
6It has been experimentally verified in [10] that this is the case if the ma
chines are inverter driven but not for dead online operation.
Page 2
Fig. 1. A schematic of a BDFRM based drive system with closedloop scalar
control
This paper will consequently limit its scope to the BDFRM.
The primary target applications of the BDFRM are envis
aged to be large pumps [6] and VSCF wind turbine generators
[3]. In these systems the shaft power is approximately varying
with the speed cube. This paper will attempt to answer how
the BDFRM should be controlled to achieve optimum theoret
ical performance under this condition. Control properties to
be investigated include: maximum torque per inverter ampere,
maximum power factor (at the mains supply side) and mini
mum inverter VA for a given torque. Tradeoffs associated with
these control strategies shall be examined, and correlations of
the BDFRM parameters with those of its singlefed counter
part, the Syncrel, shall be made where appropriate. The ma
chine ability of primary reactive power control for minimum
copper losses in the machine shall be also considered. Basic
principles of scalar and vector control of the machine will be
also established. Most of this analysis is carried out using inde
pendent normalised modelling techniques for an ideal machine
(no saturation and with sinusoidal windings).
II. MAIN APPLICATIONS
This section is a brief review of the above mentioned most
likely applications of the BDFRM  wind turbines and large
pumps.
The majority of wind turbine installations use grid
connected cageinductiongeneratorsbecausetheyarerelatively
cheap, reliable and reasonably efficient. The generator is nor
mally mechanically coupled to a turbine rotor shaft through a
stepup gearbox. This configuration is of fixed speed type since
the generator is operated slightly above the synchronous speed
in order to have small absolute slips and therefore better effi
ciency. The most serious limitation of such a system is that the
available wind power is not adequately utilised and the maxi
mum energy extraction can be achieved only at a single wind
speed (or in a very narrow range). It is mainly for this reason
that Variable Speed Constant Frequency Generation (VSCFG)
has been recently becoming very popular.
Apart from the possibility of maximum wind power cap
ture at all allowable wind speeds, which is certainly the main
Fig. 2. Power curve of a typical Danish 600kW wind turbine (Courtesy of
Danish Wind Turbine Manufacturers Association)
virtue of VSCFG, variable speed turbines have many other ad
vantages over fixed speed ones: considerably improved power
quality, reduced mechanical stresses on a drive train and lower
noise impact at low wind speeds (more details about this and
related issues can be found in [4]). However, if the generator
is interfaced to the supply grid using a fullyrated power elec
tronics, these advantages can be offset by the high system cost.
The use of BDFRM with a small bidirectional PWM converter
would be therefore a costeffective and reliable brushless7de
sign solution for VSCFG. Furthermore, an additional degree
of control freedom relative to singlyfed machines and conse
quent possibility of reactive power compensation (i.e. power
factor regulation) and/or efficiency optimisation [4,5] in addi
tion to torque (real power) control, are undoubtedly the other
attractive BDFRM features that can be of particular interest to
this and similar applications.
The maximum power output of a typical wind turbine can be
represented as [4,5]:
Ptmax=1
8· π · ρ · Cp(λopt,β) · D2· v3
(1)
where ρ is the air density (specific mass), Cpis the power coef
ficient (i.e. turbine efficiency), λopt= Dωt/2v is the optimum
tip speed ratio (ωtis the turbine rotor angular velocity), β is
the blade pitch, D is the blade (rotor) diameter and v is the
wind speed. Therefore, by varying the turbine speed so that
the tip speed ratio is kept constant at its optimum value for a
given wind speed in the base speed region (between the mini
mum ‘cutin’ speed and the rated speed) the turbine efficiency
is then maximised. At higher wind speeds, the power must
be restricted to a rated level to avoid generator overloading as
shown in Fig. 2.
In large pump applications, the BDFRM based adjustable
speed drive can be used instead of a wound rotor induction ma
chine as a maintenancefree brushless alternative [6]. With a
partially rated converter, the payback periods can be substan
7In this respect the BDFRM is superior to a wound rotor synchronous ma
chine which can also serve as a wind power generator (multipole designs are
often used as direct i.e. gearless drives).
Page 3
d
q
ds
dp
qs
qp
is
ip
ωs
ωp
θpf
θsf
θs
θp
αs
αp
Fig. 3. The reference frames and current angles for BDFRM modeling
tially reduced which, given all the performance benefits of vari
able speed pumping in terms of energy savings, would make
the BDFRM preferable to uncontrolled constant speed induc
tion machines in these systems.
III. PRELIMINARIES
Before considering the control related issues in detail it may
be beneficial to briefly review the fundamental properties and
key spacevector equations of the BDFRM. It is beyond the
scope of this paper to develop the complete dynamic model
of the BDFRM, and relevant expressions will simply be stated
[14,15] :
up= Rpip+dλp
dt
+ jωpλp
(2)
us= Rsis+dλs
dt
+ j(ωr− ωp)λs
(3)
λp= Lpip+ Lpsi∗
λs= Lsis+ Lpsi∗
s= λp(λpq= 0)
(4)
(5)
p
where Lp,s,psare the constant self and mutual 3phase induc
tances of the primary and secondary windings (their definitions
can be found in [2,16]). In steadystate, the machine develops
useful torque if [15,17]:
ωr= prωrm= ωp+ωs⇐⇒ θrf= prθrmf= θpf+θsf(6)
where ωrm = dθrmf/dt is the rotor mechanical angular ve
locity (rad/s), pris the number of rotor poles equal to the sum
of the windings polepairs (not poles), ωp,s = dθp,s/dt are
the applied frequencies (rad/s) to the windings and θr,p,sfare
the reference frame (not vectors) angular positions relative to
a stationary dq frame as illustrated in Fig. 3 (the rotor frame
not shown). The above reference frame relationship serves as a
basis for field oriented control of the machine as will be shown
in the following section.
Remark 1: One of the most distinguishing features of the
space vector model for the BDFRM is that the primary (sub
script ’p’) and secondary (subscript ’s’) equations are in two
different reference frames  one rotating at ωpand “naturally”
chosen to be aligned with the primary flux λp(as this is of fixed
frequency and approximately constant magnitude due to the
windinggridconnection)andtheotherrotatingatωr−ωp= ωs
(Fig. 3).
Remark 2: The i∗
conjugates of the ‘coupled’ current vectors from the secondary
to the primary winding and vice versa and they rotate at ωp
and ωsrespectively. These two terms are the original current
vectors referred to their complementary winding side but in a
frequency (not traditional turns ratio) sense. This frequency
transformation results from the modulation process (similar to
that in a communication mixer) of the stator mmf waveforms
via the rotor, and represents the basic mechanism behind mag
netic coupling and torque production in the machine [17].
sand i∗
pterms in (4) and (5) are the complex
Remark 3: It is interesting that despite the existence of two
separate frames and the fundamentally different operating prin
ciples, the above equations are virtually identical in form to
those for the DESRIM. The fact that there is such a close model
similarity of the two machines means that the existing control
schemes for the DESRIM can be essentially applied to the BD
FRM [18,19].
Remark 4: It should be noted that the dynamics of the BD
FRM are not as fast as those of the DESRIM because of the
relatively high leakage inductances of the BDFRM. This limi
tation is not that important for the applications considered here
(especially not for pumps) as very quick transient response is
not required.
Remark 5: From a control viewpoint, another important im
plication of the above currentmapping is that the secondary to
primary flux coupling term Lpsi∗
trolled by the secondary currents supplied from an inverter.
How this is achieved is discussed next.
sin (4) can be directly con
IV. CONTROL ASPECTS
A. Relevant Expressions
In order to make the development of analytical expressions
ofimportanceforcontrolfeasible, themachineisassumedloss
less. This approximation should have little effect on the accu
racy of the analysis to be performed in the following sections.
In addition, motoring convention has been adopted as a refer
ence.
Substituting for (2)(5) into the general expression for com
plex electrical power – Pp+ jQp=3
derive the normalised expressions8in a form suitable for pri
mary flux oriented control of the BDFRM:
2(upi∗
p+ usi∗
s), one can
8The base values used for normalisations are [14]:
TB=3
4pr
λ2
Lp; PB=2ωB
p
pr
TB; iB=λB
LB
=λp
Lp
where VBand ωB= ωp= 2πfBare the grid supply voltage and frequency.
Page 4
Ppn=1
2Tn=Lps
Lp
isnsinαs
(7)
Psn=ωsn
2
Tn= ωsnPpn= −sPpn=
ωsn
1 + ωsnPn
(8)
Pn= Ppn+ Psn=1 + ωsn
2
Tn= ωrnTn
(9)
Tn= 2Lps
Lp
isqn= 2ζisnsinαs
(10)
Qpn= 1 − ζisdn= 1 −
Tn
2tanαs
(11)
Qsn=
ωsnTn
4tan2αs
?
Tn(1
k2
ps
− 1)(tan2αs+ 1) + 2tanαs
?
(12)
ipn=
sinαs
sin(αp+ αs)=
?
(2tanαs− Tn)2+ T2
ntan2αs
2tanαs
(13)
isn=
sinαp
ζ sin(αp+ αs)=Tn
?
2ζ tanαs
1 + tan2αs
(14)
λpn= ipdn+ ζisdn= 1
ipqn− ζisqn= 0
?
⇔ tanαp=
Tntanαs
2tanαs− Tn
(15)
where ζ = Lps/Lp, kps= Lps/?LpLsis the coupling coeffi
cient between the windings, and (15) represents the fundamen
tal relationship (this corresponds to the primary flux/reference
frame alignment conditions contained in (4)) between the pri
mary and secondary current angles αp,sdefined as shown in
Fig. 3 (0 ≤ αs ≤ π for motoring and π ≤ αs ≤ 2π for
generating). The previous equations are developed in terms of
the secondary current vector magnitude and angle (as the sec
ondary current dsqscomponents are directly controllable via
the inverter) for a given torque value.
B. Vector Control
The BDFRM can be configured into a drive system9of the
form of Fig. 4 employing vector control techniques based on
the above expressions [11]. It should be noted that the ref
erence frame position for the secondary winding (θsf) can be
determined using the primary frame position θpf(both the pri
mary flux angle and magnitude can be estimated from the mea
sured grid voltages10), rotor position measurement θrmfand
(6). Once θsfis known one can implement current control of
the secondary dsqscomponents (and thus torque and primary
reactive power) in a conventional way as shown in the same
figure.
Thedesiredvaluesoftorqueandreactivepower(T∗
in Fig. 4, corresponding to (10) and (11) respectively, depend
on the control strategy to be implemented (related aspects are
eandQ∗
p)
9Fig. 4 does not show the circuitry required for starting. If a partially rated
inverter is used then an auxiliary contactor is usually needed to short the sec
ondary terminals directly or through external resistors. This allows the BD
FRM to start as an induction machine. Once the machine is near the syn
chronous speed the contactors are opened and the inverter is connected.
10Estimation errors can occur due to the presence of the primary winding
resistance, but in most cases these are negligible because of the dominant back
emf effect.
BDFRM
BiDir
Inverter
Grid Supply
e
js
− θ
ejs
θ
Flux
Calc
Sec.
Frame
Calc.
θrm
θp
θs
θs
θs
ia
ib
isd
isq
va
vb
Current
Ctrller
Torque &
Reactive
Power
Ctrl
isd
*
isq
*
Te
*
Qp
*
λp
Fig. 4. A simplified block diagram of a BDFRM control system
discussed in the following). In the case of a wind turbine gen
erator, the torque command should generally follow a power
profile in Fig. 2 and in the base speed region, according to (1),
it can be formulated as :
T∗
e=Ptmax
ωrm
=π · ρ · Cpmax· D5
λ3
opt· g3
·ω2
rm= Cbdfrm·ω2
rm(16)
where g = ωrm/ωtis the gear ratio, Cbdfrmshould be known
for a particular turbine and the remaining parameters have al
ready been defined. For vector controlled drives, the torque
setpoint is the output of a speed loop.
C. Scalar Control
Inpumptypeapplications[6], simplescalarcontrolwithlow
cost microprocessor implementation appears to be an appro
priate solution as high dynamic performance is not required
and speed variations are relatively limited. Some preliminary
results generated using Simulink, illustrating the machine re
sponse to step changes of speed and load torque under open
and closedloop constant V/f control11(Fig.1), are presented in
Figs. 5 and 6 respectively. A 6/2pole machine (whose data
have been taken from [11] for simulation purposes) has been
started with the shorted secondary winding to a speed close to
synchronous (750rpm) when the inverter is connected and the
control enabled. It can be seen that the machine performance
is much better with the lower speed oscillations and faster re
sponse under closedloop control as expected. This should be
11Keeping the secondary flux at its approximately rated value is by no means
optimal for the BDFRM. This approach has been chosen simply for testing the
control schemes.
Page 5
0123456789 10
−200
0
200
400
600
800
1000
1200
Time[s]
Speed[rpm]
Fig. 5.BDFRM response under openloop V/f speed control (speed step
change at 2s and load torque step change at 5s)
012345678910
−200
0
200
400
600
800
1000
Time [s]
Speed [rpm]
Fig. 6. BDFRM speed with closedloop V/f control (speed step change at 2s
followed by load torque step change at 5s)
attributed to the smoothing action of the PI controller (the ‘sta
biliser’ block in Fig. 1). The openloop algorithm has been
experiencing stability problems in case of larger step changes
of command secondary frequency (ω∗
s).
V. OPERATING MODES
As a member of the doublyfed family of machines, one of
the BDFRM’s main virtues is the operational flexibility. The
secondary power expression (8) indicates the BDFRM’s abil
ity to emulate the DESRIM in slippower recovery systems
as the supply inverter only has to handle the amount of real
power proportional to the degree of slip s = −ωs/ωp= −ωsn.
Therefore, ifthemachinewasrequiredtooperateatsmallabso
lute slips i.e. in a narrow speed range around the synchronous
speed ωsyn = ωp/pr = 0.5pu (which is, for instance, the
situation in pump drives [6] and wind turbines [4]), then a frac
tionally rated inverter would be sufficient (Fig. 7). From Fig. 7
one can also see that at supersynchronous speeds (ωrn> 0.5)
the power flow in both windings is to the machine when oper
0 0.1 0.20.3 0.40.50.60.7 0.8 0.91
−0.2
0
0.2
0.4
0.6
0.8
1
1.2
Speed [PU]
Real Power [PU]
Primary
Secondary
Total
Fig. 7. Real power share between the BDFRM windings operating as a motor
at Tn= ω2
rn
ated as a motor (and to the grid for a generator). At 1pu speed,
when the secondary is supplied with the mains frequency, the
two windings evenly share the machine real power loading and
the inverter has to handle half the machine power in this case.
At synchronous speed (ωsn= s = 0) the secondary is DC
fed and the BDFRM behaves as a classical field controlled 2pr
pole synchronous turbomachine with αseffectively becoming
the torque angle [8]. The inverter does not contribute to any
power under this condition (Fig. 7) but only covers the sec
ondary resistive losses. In this operating mode the BDFRM
could be used as a high frequency alternator in automotive in
dustry where, apart from the low cost, its terminal voltage reg
ulation property would be an additional advantage over per
manent magnet machines. Furthermore, supplying the primary
from another converter, a brushless variable speed synchronous
motor suitable for high speed field weakened traction and spin
dle applications could be realised but at the expense of a higher
cost.
If ωsn< 0 (which means the opposite phase sequence of the
secondary to the primary), then Psn < 0 as follows from (8)
and the primary power being taken from the grid is circulat
ing through the machine to be returned back to the supply via
the secondary winding (for a generator, the real power flow is
completely reversed). In this operating region, the machine is
running at subsynchronous speeds (ωrn< 0.5) and a fully re
generative inverter would be required for sustained operation.
Under this condition, the lineside converter should be appro
priately controlled (not shown in Fig. 4) to maintain real power
balance thus preserving the DC link voltage stability (it acts as
a DC voltage regulator in this case) [20]. However, if this mode
is only used for starting (the machine is at standstill for unity
slip i.e. s = −ωsn= 1) then resistive dumping could be an op
tion. A more common solution is short the secondary winding,
either directly or via external resistors, and start the BDFRM as
an induction machine. The possibility of induction motor op
eration is an important ‘failsafe’ mode of the BDFRM in case
of inverter failure.
Page 6
VI. OPTIMAL CONTROL STRATEGIES
This section is concerned with different control methodolo
gies for the BDFRM having a square torquespeed characteris
tic (in normalised terms Tn= ω2
in the following correspond to the motoring mode (for gener
ating they are very similar) and have been generated assuming
that the secondary winding has twice the number of primary ef
fective phase turns per pole (ns= 2np) which is equivalent to
Ls= 4Lpi.e. kps= Lps/?LpLs= ζ/2 = 7/9 (the BDFRM
rotor, when used in a Syncrel, has the typical saliency ratio of
ξ = 8) [2,16]. It has been shown in [2] that under these con
ditions the BDFRM is a larger machine than the Syncrel for a
given torque.
rn). The plots to be presented
A. Maximum Power Factor
The equations (10) and (11) demonstrate one of the most
salient properties of the BDFRM  the inherently decoupled
control of torque and primary reactive power. The torque is
controlled via the qsaxis secondary current (as λp = const.)
isqn and the reactive power through the dsaxis component
isdn. This is a significant control simplification as there is
no need for special decoupling algorithms that are normally
present with vector control techniques for other more conven
tional machines (except for the DESRIM having the same ad
vantage [20]).
Therefore, regardless of the BDFRM’s constant primary flux
operation, one can regulate torque and primary power factor
simultaneously and independently (see Fig. 4) [11] this being
clearly impossible with singleexcited machines. For a given
torque, the maximum power factor (MaxPF) i.e. Qpn = 0 is
obtained at the secondary current angle of :
αsMaxPF= tan−1Tn
2
(17)
One can easily conclude from (15) that the corresponding pri
mary current vector is in quadrature with the respective flux
(remember that this lies along the dpaxis in Fig.
αpMaxPF= π/2 as expected for zero reactive power condition.
The secondary winding is entirely responsible for the machine
magnetization and αsangles are small in this case (Fig. 8).
The inverter current rating should be increased appropriately
(more than three times for the machine operation around the
synchronous speed) if this control strategy is desired as shown
in Fig. 9.
It is also notable from Fig. 9 that under MaxPF conditions,
due to λp= const and dominant reactive (daxis) component,
the secondary current (isn) variations are insignificant espe
cially at lower speeds (and torques) where isnis almost con
stant. The primary current, on the other hand, is low as this is
nothing else but a coupled torque producing isqncurrent since
ipdn= 0.
If supplied from a dualbridge PWM converter, the BDFRM
(as well as the DESRIM) has another feature that can be of
extreme importance for the considered applications  it can op
erate as a reactive power compensator with minimum copper
losses [20]. It has been demonstrated in the authors’ recent
work [16] that it is possible to minimise total copper losses in
themachine (andthusfurtherimprove itsefficiency) foragiven
3) i.e.
0 0.10.20.30.40.50.6 0.70.80.91
0
20
40
60
80
100
120
Speed [PU]
Current angles [degs]
αs at MaxPF = αp at MTPSA
αs at MinVA
αp at MinVA
Fig. 8. Current angles for different control strategies and Tn= ω2
rn
0 0.10.20.30.40.50.6 0.70.80.91
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Speed [PU]
Current [PU]
ipn for MaxPF
ipn for MinVA
isn for MaxPF
isn for MinVA
isn for MTPSA
Fig. 9. Optimal currents under pump loading conditions
torque by controlling isdnand hence Qpnas this is isdndepen
dent considering (11). The unity overall power factor control is
achieved by supplying the reactive power required by the pri
mary not from the grid but using the PWM rectifier (Qg = 0
and Ql= Qpin Fig. 1).
B. Maximum Torque per Inverter Ampere
In terms of reducing the converter size needed to supply the
machine, another performance index of interest to be optimised
is the secondary winding current. The maximum torque per
secondary ampere (MTPSA) strategy should provide the mini
mum inverter current (Fig. 9) for a given torque. As indicated
by (10) the optimum secondary current angle for this condition
to be satisfied is αsMTPSA= π/2
The same equation also points out the general improvement
of torque per ampere with increasing the ζ = Lps/Lpratio.
This suggests that it would be desirable to design a machine
with both ns/np and the rotor saliency ratio (ξ = Ld/Lq)
as higher as possible [2]. It has been shown in [2] that with
ns = np, the same amount of active material and equal cop
Page 7
per losses the BDFRM has inferior MTPSA compared to the
Syncrel. However, due to the lower inductances the BDFRM
can attain much higher speeds and develop more power using
the same inverter than the Syncrel. Its maximum power out
put per inverter ampere and efficiency are consequently better
under the above conditions.
C. Minimum Inverter VA
This control strategy allows one to minimise the inverter size
required for a machine. The minimum inverter VA (MinVA)
for a lossless machine occurs for Qsn = 0 i.e. at the unity
secondary power factor and the control angle of :
αsMinV A= tan−1−
?
1 − T2
n(
1
ps− 1)2− 1
k2
Tn(
1
ps− 1)
k2
>π
2
(18)
Note that the MinVA angles, though close, are greater than
π/2 (as these are defined with respect to the primary and not
secondary flux oriented reference frame) indicating the demag
netising effect of isnon the primary flux (Fig. 8). A large flux
producing primary current is therefore required to maintain λp
constant (Fig. 9) which conforms with the lower values of αp
angles in Fig. 8. It can be seen from Fig. 9 that the MinVA
primary current waveform is quite similar in shape to that of
isnunder MaxPF conditions.
Another important observation from (12) is that the bet
ter magnetic coupling between the windings (the higher kps)
the lower both reactive power (Qsn) and inverter VA (=
?P2
chine in this respect because of the unusual operating principle
where one of the flux side bands is torque producing and the
main fundamental flux and other sideband are leakage compo
nents [17]. As a consequence, even with an axiallylaminated
rotor which allows high saliency ratios and coupling coeffi
cients [21], kpsvalues are relatively modest (0.78 under the
assumptions adopted) resulting in compromised torque perfor
mance for the machine [2].
The MinVA and MTPSA control strategies are closely re
lated and the corresponding setpoints virtually coincide over
the entire speed range (Figs. 8  11). One can see from Fig. 11
that the MTPSA secondary power factor (cosφs) is near unity
the change of sign occuring at synchronous speed (0.5pu) as
a reflection of the secondary real power profile in Fig. 7. A
reversible power flow at the secondary winding side allows the
BDFRM operation at both sub and supersynchronous speeds
in motoring as well as in generating mode. The actual operat
ing regime of the machine is determined by the electrical power
flow in the primary winding.
Notice from Fig. 10 that for the MaxPF strategy the sec
ondarykVAneededismuchlargercomparedtotheotherstrate
gies, which is consistent with the results in Fig. 9. The corre
spondingpowerfactorislaggingastheinverterissupplyingthe
reactive power for the machine magnetisation under the MaxPF
conditions.
sn+ Q2
sn). Unfortunately, the BDFRM is not a good ma
VII. EXPERIMENTAL RESULTS
At this stage the experimental results have not been com
piled. Therefore this section will outline the progress made so
far toward the generation of these results.
00.10.20.3 0.40.50.60.70.80.91
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Speed [PU]
Secondary VA [PU]
MaxPF
MinVA
MTPSA
Fig. 10. Inverter VA requirements for various control strategies
00.10.2 0.30.40.50.60.70.8 0.91
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Speed [PU]
Power Factor
cosφp at MinVA
cosφs at MaxPF
cosφs at MTPSA
cosφp at MTPSA
Fig. 11. Power factor performance for control strategies investigated
A BDFRM prototype, based on a 10kW induction machine
frame and an axially laminated 4pole reluctance rotor, is being
constructed. The rotor is complete, and appears in Fig. 12.
The parallel path windings have been designed, and are being
checked via a finite element (FE) analysis. This will allow the
torque of the machine to be calculated, and more importantly
the flux levels in the back iron and teeth of the machine to be
accurately determined. Because of the unusual structure of the
BDFRMthenormalquartermachinesymmetrycannotbeused,
and instead a half machine model has to be developed. Fig. 13
shows the FE model.
The power electronics and control computer for the experi
mental system already exist. The controller is based on a high
performance TMS6701 floating point digital signal processor.
Several custom designed Altera EPLDs are used to control the
sampling system and the firing of the inverter power devices.
Figs. 14 and 15 show the power electronics and the control
board.
The machine to be tested will be mounted on a dynamome
ter (Fig. 16) so that precise reading of torque, output power and
Page 8
Fig. 12. The axially laminated rotor of the BDFRM
Fig. 13. Finite element model of the BDFRM
input power can be made and therefore the machine efficiency
determined. In addition the performance of the scalar and vec
tor control strategies will be evaluated using this rig, and the
results compared with the theory.
VIII. CONCLUSIONS
The paper has investigated different control strategies and
aspects of both vector and scalar control of the BDFRM in
the light of its potential applications  wind turbines and large
pumps. While the work presented is largely theoretical in na
ture and has considered an ideal machine, a number of impor
tant relationships and preliminary results, that can serve as a
basis for control development and implementation in real ma
chines, have been derived.
Another significant contribution of the paper lies in the dis
cussion of tradeoffs between the machine performance and
size of the supply inverter. It is expected that the economic
benefits of these compromises will ultimately decide the BD
FRM’s future.
The development of two BDFRM prototypes and the corre
sponding test systems for experimental verification of the con
sidered control strategies is currently in progress at the Univer
sity of Newcastle, Australia and the University of Northumbria
at Newcastle, UK. The main components of the former drive
system have been described in the paper.
ACKNOWLEDGMENT
The authors would like to acknowledge the financial support
of the Engineering and Physical Sciences Research Council
Fig. 14. The power electronics for the experimental system
(GR/N34550) and the Australian Research Council.
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Milutin G. Jovanovi´ c received the Dipl.Eng and
M.E.E. degrees from University of Belgrade, Yu
goslavia, in 1987 and 1991 respectively, and the
Ph.D. degree from the University of Newcastle, Aus
tralia, in 1997.He is currently a Senior Lec
turer in the School of Engineering and Technology,
Northumbria University, Newcastle upon Tyne, UK.
His main interests are in the areas of electrical ma
chines and drives, power electronics and renewable
energy systems. Dr. Jovanovi´ c is a member of the
Industrial Drives Committee, and the Electric Ma
chines Committee of the IEEE Industry Applications Society.
Robert E. Betz received the B.E., M.E. and Ph.D.
Degrees from the University of Newcastle, Australia
in 1979, 1982 and 1984 respectively. He is currently
an Associate Professor and Head of the School of
Electrical Engineering and Computer Science, Uni
versity of Newcastle. His major interests are electri
cal machine drives, realtime operating systems, and
industrial electronics. A/Professor Betz was a Senior
Research Fellow at the University of Glasgow, Scot
land (199091), andtheDanfoss Visiting Professor at
Aalborg University, Denmark (1998). He is a mem
ber of the Industrial Drives Committee, and the Electric Machines Committee
of the IEEE Industry Applications Society.
Jian Yu received his B.E. and M.Sc. degrees from
the Harbin Institute of Technology, China and New
castle University, UK in 1998 and 2000 respectively.
He is currently a PhD research student in the School
of Engineering and Technology, Northumbria Uni
versity, UK where he is working on control of brush
less doublyfed reluctance machines. His main inter
ests are electric drives, power electronics and wind
power generation. Jian Yu is an associate IEE mem
ber.