# The use of doubly fed reluctance machines for large pumps and wind turbines

**ABSTRACT** Brushless doubly-fed 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 doubly-fed 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 trade-offs for the BDFRM in the light of its most likely applications-large pump type adjustable speed drives and variable speed constant frequency wind power generation systems.

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**ABSTRACT:**A novel shaft-position sensorless algorithm for decoupled control of torque and reactive power (TRPC) of doubly fed machines, such as the classical wound-rotor induction machine (DFIM) and the emerging brushless reluctance machine (BDFRM), has been discussed and experimentally verified in this paper. The underlying control concept is derived from first principles of magnetization and torque production in the machines. For control purposes, only the grid-connected winding measurements and rough knowledge of its resistance value are required. Such a weak parameter dependence makes the TRPC inherently robust, structurally simple, and fast to execute even on low-cost DSPs. A variety of applications are possible including drive and generator systems with limited variable speed ranges (e.g., large pumps and wind turbines), where cost savings of using partially rated power electronics are significant. Two custom-designed and built BDFRM prototypes have served as case studies to evaluate the controller performance by computer simulations and through laboratory experiments.IEEE Transactions on Power Electronics 01/2012; 27(1):113-121. · 4.08 Impact Factor -
##### Conference Paper: Brushless doubly-fed reluctance machine rotor design

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**ABSTRACT:**This paper investigates the rotor design factors that impact the performance of brushless doubly-fed reluctance machines (BDFRMs). The performance of the BDFRM relies on the ability of the rotor structure to modulate stator magnetic fields so that magnetic coupling occurs between stator windings that do not otherwise interact. This paper investigates those factors that create the desired magnetic coupling and those that can cause undesirable magnetic performance. Theoretical analysis is compared to test results from an early prototype BDFRM and then applied to the design of a new BDFRM. New designs are explored using Finite Element Analysis. A prototype, based on these investigations is under construction.Energy Conversion Congress and Exposition (ECCE), 2012 IEEE; 01/2012 - SourceAvailable from: R.E. Betz[Show abstract] [Hide abstract]

**ABSTRACT:**Brushless doubly fed reluctance machines (BDFRMs) are a class of machines that may be controlled using a power converter that has a rating lower than the total power rating of the machine. The attractive properties of these machines have, in the past, been offset by low power density and efficiency when compared to other types of machines. Recent advances have shown that, when well designed, these machines are, in fact, capable of operation at high torque density and efficiency. However, little guidance on how to design these machines is available in the literature. This paper presents analytical approaches to design a BDFRM with desirable qualities and the use of time-stepped finite-element analysis to validate the results of the design process.IEEE Transactions on Industry Applications 01/2013; 49(1):50-58. · 1.67 Impact Factor

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 doubly-fed 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 doubly-fed 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 trade-offs 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 doubly-fed 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 bi-directional 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 trade-off 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. E-mail: 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. E-mail: 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.

E-mail:

range variable speed systems3, the overall system cost could be

significantly lower compared to applications with fully-rated

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

maintenance-free, 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 pump-type 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 converter-fed. Magnetic coupling

between the windings, a pre-requisite 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 super-synchronous speeds) in both motoring and

generating modes. The BDFIM, on the other hand, has sta-

bility problems around the zero-torque operating point at syn-

chronous speed of the grid-connected 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 4/2-pole stator windings). The most common design reported in the

literature is however with a 6/2-pole stator and a 4-pole rotor.

6It has been experimentally verified in [10] that this is the case if the ma-

chines are inverter driven but not for dead on-line operation.

Page 2

Fig. 1. A schematic of a BDFRM based drive system with closed-loop 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. Trade-offs associated with

these control strategies shall be examined, and correlations of

the BDFRM parameters with those of its single-fed 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

step-up 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 600-kW 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 fully-rated power elec-

tronics, these advantages can be offset by the high system cost.

The use of BDFRM with a small bi-directional PWM converter

would be therefore a cost-effective and reliable brushless7de-

sign solution for VSCFG. Furthermore, an additional degree

of control freedom relative to singly-fed 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 ‘cut-in’ 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 maintenance-free 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 space-vector 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 3-phase induc-

tances of the primary and secondary windings (their definitions

can be found in [2,16]). In steady-state, 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 pole-pairs (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 d-q 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

Bi-Dir

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

set-point is the output of a speed loop.

C. Scalar Control

Inpump-typeapplications[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 closed-loop constant V/f control11(Fig.1), are presented in

Figs. 5 and 6 respectively. A 6/2-pole 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 (750-rpm) 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 closed-loop 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 open-loop V/f speed control (speed step

change at 2-s and load torque step change at 5-s)

012345678910

−200

0

200

400

600

800

1000

Time [s]

Speed [rpm]

Fig. 6. BDFRM speed with closed-loop V/f control (speed step change at 2-s

followed by load torque step change at 5-s)

attributed to the smoothing action of the PI controller (the ‘sta-

biliser’ block in Fig. 1). The open-loop 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 doubly-fed 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 slip-power 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 = 0.5-pu (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 super-synchronous 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 1-pu 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 turbo-machine 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 sub-synchronous speeds (ωrn< 0.5) and a fully re-

generative inverter would be required for sustained operation.

Under this condition, the line-side 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 ‘fail-safe’ 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 torque-speed 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 qs-axis secondary current (as λp = const.)

isqn and the reactive power through the ds-axis 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 single-excited 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 dp-axis 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 (d-axis) 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 dual-bridge 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 axially-laminated

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 set-points 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 (0.5-pu) 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 super-synchronous 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 10-kW induction machine

frame and an axially laminated 4-pole 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 trade-offs 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, real-time operating systems, and

industrial electronics. A/Professor Betz was a Senior

Research Fellow at the University of Glasgow, Scot-

land (1990-91), 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 doubly-fed reluctance machines. His main inter-

ests are electric drives, power electronics and wind

power generation. Jian Yu is an associate IEE mem-

ber.