Low-Cost Variable Speed Drive Based on a Brushless Doubly-Fed Motor and a Fractional Unidirectional Converter

Abstract

The paper presents a low-cost variable-speed drive system comprising a brushless doubly-fed motor (BDFM) and a fractionally rated unidirectional frequency converter. A simple control algorithm is proposed for regulating the drive's speed and torque. A method of starting the BDFM in the cascade mode is presented and the starting performance is analyzed. The efficiency of the BDFM is discussed and the dynamic performance of the drive is verified by experimental results obtained from a 180 frame-size BDFM. Index Terms—Brushless doubly-fed motor (BDFM), dynamic performance, phase angle controller, unidirectional converter.

Full text

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012 317
Low-Cost Variable Speed Drive Based on a Brushless
Doubly-Fed Motor and a Fractional
Unidirectional Converter
Shiyi Shao, Ehsan Abdi, and Richard McMahon
Abstract—The paper presents a low-cost variable-speed drive
system comprising a brushless doubly-fed motor (BDFM) and a
fractionally rated unidirectional frequency converter. A simple
control algorithm is proposed for regulating the drive’s speed and
torque. A method of starting the BDFM in the cascade mode is
presented and the starting performance is analyzed. The efficiency
of the BDFM is discussed and the dynamic performance of the
drive is verified by experimental results obtained from a 180
frame-size BDFM.
Index Terms—Brushless doubly-fed motor (BDFM), dynamic
performance, phase angle controller, unidirectional converter.
I. INTRODUCTION
THE brushless doubly-fed machine (BDFM) offers an at-
tractive approach to variable-speed drive (VSD) applica-
tions requiring only a moderate range of operating speeds, an
example being water pumping where significant energy savings
can be achieved [1], [2]. As well as drive applications, the
BDFM has been proposed as a generator for wind power [3]
and also appears suited to small-scale hydropower [4].
In contrast to the majority of contemporary VSDs which
comprise a cage rotor induction motor with a fully rated uni-
directional frequency converter, the BDFM only needs a frac-
tionally rated converter. Cost savings are likely to be greatest
in medium–high-power applications, such as water pumping,
as the higher cost of manufacturing small BDFMs, under for
example 10 kW, may well outweigh the savings in the converter
cost. However, to become a practical drive, the dynamic and
steady-state performance of the BDFM drive, such as starting
characteristics, torque, and speed responses and efficiency, have
to be carefully considered.
The contemporary BDFM is a single-frame induction ma-
chine with two three-phase stator windings of different pole
numbers and a special rotor design. Typically, one stator wind-
ing (the power winding, PW) is connected directly to the ac
supply and the other (the control winding, CW) is supplied
with variable voltage at variable frequency from a converter [5].
Manuscript received September 15, 2010; revised January 14, 2011 and
March 10, 2011; accepted March 11, 2011. Date of publication April 5, 2011;
date of current version October 4, 2011.
The authors are with the Department of Engineering, University of
Cambridge, CB3 0FA Cambridge, U.K., and also with Wind Technologies
Limited, CB4 0WS Cambridge, U.K. (e-mail: ss656@cam.ac.uk; ea257@cam.
ac.uk; ram1@cam.ac.uk).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIE.2011.2138672
The drive operates in a synchronous mode, so variable-speed
operation is achieved by regulating the frequency of the CW
supply.
The majority of power is supplied to the BDFM directly from
the mains and only a proportion, dependent on the fractional
deviation from the natural (base) speed, is processed by the
converter. Above natural speed, power flows into the control
winding but the direction of power flow reverses below natural
speed [5]. It is attractive from a cost-saving perspective to
exploit the speed range from natural speed upwards, so only
a unidirectional converter is needed. However, this poses diffi-
culties for starting.
To overcome this, a starting procedure is presented in this
paper which is a further development of the method proposed
in [6]. By shorting the CW, the BDFM behaves as a self-
cascaded machine and accelerates toward the cascade synchro-
nous speed, equal to the natural speed of the BDFM. The
machine then makes a transition to the synchronous (doubly-
fed) mode.
The BDFM is not stable in the open loop over its required
operating speed range [7], so a controller is required to stabilize
the machine and to achieve the required dynamic and steady-
state performance. A number of control methods involving var-
ious degrees of sophistication have been applied to the BDFM.
Several scalar control algorithms have been developed for the
BDFM, such as open-loop control [8], closed-loop frequency
control [9], and phase angle control [6].
These controllers are suitable for applications such as pumps
which do not require fast dynamic response. Vector control
methods, also known as field-oriented control, have been shown
to give fast and robust performance for the BDFM [10], [11].
Direct torque control (DTC) algorithms have also been pro-
posed for the BDFM in simulation [12], [13]. However, vector
control and DTC methods are more complex to implement.
This paper reports the implementation and performance of a
VSD based on a frame size 180 4/8-pole BDFM and a fraction-
ally rated unidirectional converter. A phase angle controller has
been adopted which uses a measurement of the shaft speed with
a moderate pulse-per-revolution rate provided by an encoder.
II. BDFM OPERATION AND MODELLING
The BDFM is normally operated in the synchronous mode
where the shaft speed only depends on the supply frequencies
of the two stator windings, i.e., the variable output frequency
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318 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012
Fig. 1. Per-phase referred equivalent circuit for the BDFM.
from the converter if the PW is supplied from the mains. The
shaft speed is given by
Nr=60
f1+f2
p1+p2
.(1)
p1and p2are the pole pair numbers of the two windings, and
f1and f2are the mains and converter output frequencies, re-
spectively. The BDFM is characterized by the so-called natural
speed Nnobtained by setting f2zero
Nn=60 f1
p1+p2
.(2)
The BDFM has also asynchronous modes of operation where
the shaft speed is dependent on the loading of the machine, as
well as the supply frequency. As described in Section IV, by
shorting the CW, a BDFM operates as a self-cascaded induction
machine, behaving as an induction machine with p1+p2pole
pairs. This form of operation is known as the cascade mode.
Dynamic and steady-state models have been developed for
the BDFM in order to design and study the drive system. The
equivalent circuit model shown in Fig. 1 is used to represent
steady-state operation [14]. R1and R2are the resistances of
the stator windings and Rris the rotor resistance. L1and
L2are the stator leakage inductances. Lm1and Lm2are the
stator magnetizing inductances and Lris the rotor inductance.
All the quantities are referred to stator 1 (PW), and the use
of the modifier “” denotes that the quantity is referred. Iron
losses and saturation of the iron circuit are neglected. The
equivalent circuit parameters for the prototype BDFM are given
in Appendix I.
The slips s1and s2are defined as [14]
s1=ω1−p1ωr
ω1
(3)
s2=ω2−p2ωr
ω2
.(4)
The dynamic model is based on the coupled-circuit approach
as described in [6] and can be derived from the general electri-
cal machine coupled-circuit equation
v=Ri +ωr
dM
dθr
i+Mdi
dt (5)
where vand iare the voltage and current vectors, respectively,
and Rand Mare the resistance and inductance matrices, re-
spectively. ωrand θrare the rotor angular velocity and position,
respectively.
In the BDFM, it is convenient to partition vand iinto stator 1
(PW), stator 2 (CW), and rotor quantities, noting that the rotor
voltage will always be zero. The mutual inductance between
Fig. 2. BDFM coupled-circuit model implementation in Simulink.
the two stator windings is zero because the stator pole numbers
and winding configurations are chosen so that by design, the
PW and CW do not couple to each other. The BDFM coupled-
circuit equations can therefore be written as
d
dt ⎡
⎣
is1
is2
ir⎤
⎦=⎡
⎣
Ms10Ms1r
0Ms2Ms2r
MT
s1rMT
s2rMr⎤
⎦
−1⎧
⎨
⎩−⎛
⎝⎡
⎣
Rs100
0Rs20
00Rr⎤
⎦
+ωr⎡
⎢
⎣
00
dMs1r
dθr
00
dMs2r
dθr
dMT
s1r
dθr
dMT
s2r
dθr0
⎤
⎥
⎦⎞
⎟
⎠⎡
⎣
is1
is2
ir⎤
⎦+⎡
⎣
vs1
vs2
0⎤
⎦⎫
⎪
⎬
⎪
⎭
.(6)
The resistance and inductance matrices in (6) can be calcu-
lated from the machine’s geometrical dimensions. The mechan-
ical differential equations are
Jdωr
dt =Te−Tl(7)
dθr
dt =ωr(8)
where Tlis the load torque and Teis the BDFM torque
Te=1
2iTdM
dθr
i=iT
s1iT
s2dMs1r
dθr
dMs2r
dθr[ir].(9)
Equations (6)–(9) form the dynamic model for the BDFM.
The model has been implemented in Simulink and a block
diagram of the model is shown in Fig. 2.
III. CONTROLLER DESIGN
A. Phase Angle Control Theory
In order to describe the theory for the design of the phase
angle controller, the BDFM torque is expressed in terms of the
stator winding voltages and the load angle associated with the
machine’s synchronous operation. The torque generated by a
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SHAO et al.: LOW-COST VSD BASED ON BDFMMOTOR AND FRACTIONAL UNIDIRECTIONAL CONVERTER 319
lossless BDFM (neglecting all resistances and stator leakage
inductances in Fig. 1) is given by [5]
Te=3(p1+p2)|V1||V
2|
ω1ω2L
r
sin δ(10)
where V1is the PW voltage and V
2is the referred CW voltage.
δis the load angle which can be expressed as [15]
δ=θ2(t)+ζ−(p1+p2)θ
r.(11)
θ
ris the rotor shaft position referred to the rotor reference
frame, and θ2(t)is the phase angle of the CW voltage. ζis a
fixed angle determined by the physical location of the stator
windings
ζ=p1β1+p2β2.(12)
β1and β2are related to the orientation of the PW and CW in
the stator frame. From (10) and (11), the relationship between
Teand θ2can be expressed as
Te=3(p1+p2)|V1||V2|
ω1ω2L
r
sin (θ2+β−(p1+p2)θ
r).(13)
From (13), Tecan be controlled by varying the free variable θ2.
For small changes in θ2at a steady-state operating speed, it can
be shown from (13) that ΔTe∝Δθ2, since sin(Δθ2)≈Δθ2.
Therefore, the torque can be directly controlled by controlling
the phase of the CW voltage, hence stabilizing the machine.
This is shown in the following by linearizing (13) about a
suitable equilibrium point.
At an equilibrium point under steady-state conditions, and
considering that the mechanical dynamic system has a much
larger time constant than the electromagnetic dynamic system,
it can be assumed that the rotor position remains constant in
the rotor reference frame when a small variation in the control
variable Δθ2occurs. For small Δθ2, (13) can be approximated
by its first-order Taylor Series expansion as
Te(θ2E+Δθ2)=Te(θ2E)+dTe
dθ2
Δθ2.(14)
“E” indicates equilibrium status. From (13) and (14)
ΔTe=3(p1+p2)|V1||V2|
ω1ω2L
r
×cos (θ2E+β−(p1+p2)θ
rE)Δθ2.(15)
Equation (15) shows a linear relationship between Teand θ2.
Now, substituting (13) in (7)
dωr
dt =Te−Tl
J
=3(p1+p2)|V1||V2|
Jω1ω2L
r
sin (θ2+β−(p1+p2)θ
r)−Tl
J.(16)
At equilibrium when dωr/dt =0, from (16)
θ
rE =−arcsin Tlω1ω2L
r
3(p1+p2)|V1||V2|+β+θ2E
p1+p2
.(17)
Fig. 3. Schematic of the phase angle controller.
Hence, a linearized transfer function from θ2to θ
rfor small
changes in θ2is established. Noting that cos(−arcsin x)=
√1−x2, (15) can be expressed as
ΔTe=⎛
⎝3(p1+p2)|V1||V2|
ω1ω2L
r2
−T2
l⎞
⎠Δθ2.(18)
From (18), the following condition must be satisfied:
Tl<3(p1+p2)|V1||V2|
ω1ω2L
r
.(19)
The right-hand side of (19) is the BDFM pull-out torque which
can be derived from (10) when δ=90
◦.
In (18), it can be seen that at high load torques Tlor at
low ratios of CW excitation |V2|to CW frequency ω2,the
linearized gain between ΔTeand Δθ2decreases, degrading the
dynamic response of the controller and its stability. Therefore,
the stability region of the BDFM with a phase angle controller
depends on the operating point, i.e., load conditions, rotor
speed, and CW excitation. In practice, stable operation between
a speed 50% below the natural speed to 50% above the natural
speed has been demonstrated. It appears possible to extend this
range, particularly if the rate of change of the reference speed
can be restricted to improve stability.
The above theory has been presented for a lossless BDFM
which can only produce a synchronous torque. In a practical
BDFM, the torque has also asynchronous components but
these component are substantially smaller than the synchronous
torque in normal operation [5].
B. Control Structure
A phase angle controller has been designed and developed
as shown in Fig. 3. The controller receives the speed reference
and speed feedback and provides the required switching signals
to the converter. The rate of change of the reference speed is
restricted (block A) to maintain stability. θ2, the CW phase
angle, is regulated by a conventional Proportional-Integral con-
troller (block B). The CW frequency, ω2, is determined from the
principle of doubly-fed operation given by (1) (block C). The
magnitude of the CW voltage is adjusted using a conventional
V/f (voltage-versus-frequency) algorithm [16] (block D),
hence keeping the CW magnetic flux at an appropriate level.
The pattern used is shown in Fig. 4. Voltage boosting is pro-
vided at low frequencies to compensate for the voltage drop
across the CW resistance. Therefore, for frequencies less than
|flow|, a constant voltage |Vlow |is applied to the CW.
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320 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012
Fig. 4. V/f (voltage-versus-frequency) control pattern.
Once the phase, frequency, and magnitude of the CW exci-
tation are determined, a pulsewidth modulation (PWM) signal
generator (block E) produces the gate switching signals for the
machine-side inverter (block F).
As can be seen from Fig. 3, the proposed controller uses
simple conventional control algorithms. In addition, it only
incorporates a speed feedback (block G) and no further mea-
surements are required. The control system can therefore be
implemented using simple and low-cost hardware. Although
the controller does not require any currents to be sensed, in
practice, current sensors may be used for protection purposes
but they need only have limited resolution and bandwidth.
IV. STA RT IN G PROCEDURE
A. Starting Torque and Current
The BDFM is started in the cascade mode with the CW
shorted by switching on the IGBTs in the upper legs of the
motor-side inverter and leaving those in the bottom legs off. The
cascade torque and current can be calculated from the equiva-
lent circuit shown in Fig. 1, assuming the CW is shorted. Ne-
glecting the effect of Lm1and Lm2and applying the principle
of power conservation, the cascade torque can be calculated as
Te=3
ωrR1+1
s1
R
r+s2
s1
R
2|I1|2−(R1+R
r+R
2)|I1|2

=3p1
ω1(1 −s1)|I1|21
s1−1R
r+s2
s1−1R
2.
(20)
The power winding current is
|I1|=|V1|
R1+1
s1R
r+s2
s1R
22+ω2
1(L1+L
r+L
2)2
.
(21)
The starting current and torque can be calculated from (20) and
(21) and assuming ωr=0
|I1|(ωr=0) =|V1|
(R1+R
r+R
2)2+ω2
1(L1+L
r+L
2)2(22)
Te(ωr=0) =
3p1|V1|2R
r+p1+p2
p1R
2
ω1!(R1+R
r+R
2)2+ω2
1(L1+L
r+L
2)2".(23)
Fig. 5. Cascade torque-speed profile with different external resistances in-
serted into the CW.
The maximum starting torque is achieved when
∂Te(ωr=0)
∂R
2
=0
R
2=1
3# (3 R1+2R
r)2+9ω2
1(L1+L
r+L
2)2−R
r
$.(24)
Fig. 5 shows the predicted torque-speed characteristics of
the authors’ BDFM in the cascade mode, showing a starting
torque of about 30% of rated synchronous torque. As with
conventional induction motors, the starting torque can be
increased by connecting external resistances to the CW, as seen
in Fig. 5. Alternatively, as starting only takes a short time, slip
power could be recovered and absorbed in a modestly rated
dump resistor across the dc link of the inverter.
B. Synchronization Procedure With a
Unidirectional Converter
The rotor accelerates due to the cascade torque and reaches a
speed just below the BDFM natural speed, the precise speed be-
ing determined by the load exerted on the shaft. The transition
to the synchronous mode can now take place. However, special
care must be taken in managing the CW power flow to avoid
unwanted regeneration.
The relationship between the real power in the CW and PW
in a lossless BDFM is given by [5]
P2=P1
ω2
ω1
=P1ωr
ωn−1.(25)
The above equation shows that there will be power flowing out
of the control winding once the transition to the synchronous
mode is made. However, in a real machine, there are copper
and iron losses. If the power generated in the CW is less than
the losses in that winding, then regeneration can be avoided.
These losses can also be artificially increased by increasing the
CW excitation voltage to give greater CW currents and thus
higher copper losses. Therefore, if the CW is excited at or above
a certain voltage level to produce enough losses to consume
the regenerated power, then synchronization can be performed
a little below the natural speed. Clearly, the minimum CW
excitation voltage VCWmin is when the generated power is equal
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SHAO et al.: LOW-COST VSD BASED ON BDFMMOTOR AND FRACTIONAL UNIDIRECTIONAL CONVERTER 321
Fig. 6. Minimum excitation voltage for the CW to enable zero power flow in
the converter for operation below the natural speed.
Fig. 7. CW excitation during synchronization. (a) Two excitation strategies;
(b) optimal CW excitation.
to the losses, i.e., the power flow between the the CW and
converter is zero. It should be noted that the intentional increase
in the CW power losses during the synchronization process
would not cause any efficiency concerns as this process is of
short duration.
The minimum CW excitation VCWmin required to avoid
regeneration has been found using the equivalent circuit model
and is plotted for the authors’ BDFM in Fig. 6. It is compared
in Fig. 7(a) with the excitation voltage from the V/f control
method VV/f, which would have been applied if a bidirectional
converter had been used. With a unidirectional converter, the
CW excitation below natural speed will need to be either
VCWmin or VV/f, whichever is the larger, as shown in Fig. 7(b).
To avoid excessive rise of the dc link from regeneration during
Fig. 8. Torque-speed operating region for the prototype BDFM drive.
Fig. 9. Prototype BDFM machine (left) on test rig with torque transducer and
dc load machine (right).
braking, starting, or when a fault occurs during transfer to the
synchronous mode, a standard arrangement of an appropriately
sized chopper-fed braking resistor can be employed.
V. T ORQUE-SPEED OPERATING REGIONS
Once in the synchronous mode, the capabilities of the drive
at or above the natural speed are dependent on the rating of the
converter. Fig. 8 shows the operating regions for the prototype
BDFM drive including the cascade mode (region I) for starting
and synchronous mode (region II) for variable-speed opera-
tion. It also shows the maximum torque envelope of the drive
(region III) which is calculated from the equivalent circuit
assuming constant flux on the PW and CW through applying
rated voltage levels to the windings and allowing the load angle
to rise to 90◦. Extended operation in region III is not allowed to
prevent overheating the machine windings.
VI. EXPERIMENTAL PERFORMANCE VERIFICATION
A. Experimental Rig and Simulation Setup
An experimental setup was established in order to evalu-
ate the performance of the proposed drive, incorporating the
180-frame BDFM detailed in Appendix I. A dc machine
equipped with a commercial dc drive (ABB DCS800) is me-
chanically coupled to the BDFM in order to provide the re-
quired load torque, sensed by a Magtrol torque transducer
TMB312. The test rig is shown in Fig. 9 and a schematic
drawing of its constituent parts is provided in Fig. 10. The PW is
connected in delta and fed from an autotransformer at 240 Vrms
and 50 Hz. The CW is supplied by a unidirectional converter
made by Semikron. An incremental encoder with 10 000 pulses
per revolution is used to measure the shaft rotational speed.
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322 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012
Fig. 10. Schematic of the BDFM drive laboratory rig. (a) BDFM rig and
(b) converter and control system.
TAB L E I
V/f CONTROLLER PARAMETERS (SEE FIG.4)
The voltages and currents of each stator phase are measured by
LEM LV 25-p and LEM LTA 100-p transducers, respectively.
The control algorithm was implemented in MATLAB
Simulink and is based on an xPC Target computer which re-
ceives and processes all the signals stated above. The sampling
time of the control loop is 0.4 ms. The controller parameters in-
cluding the proportional and integral gains of the Proportional-
Integral module have been refined through experimental tests
and are shown in Table I. The Target PC calculates the required
parameters for the CW excitation voltage including magnitude,
phase, and frequency and sends them to an FPGA-based PWM
signal generator. The FPGA board then generates six PWM
switching signals to drive the IGBT switches in the machine-
side converter.
A simulation setup was developed in MATLAB including
the coupled-circuit model and the proposed controller. The
predictions from simulation are compared with experimental
measurements in the following sections.
B. Starting Management
As described in Section IV, the BDFM is started in the
cascade mode by shorting the CW using the converter. Once the
rotor accelerates and reaches an appropriate steady-state speed
near the natural speed, the synchronization procedure will take
place, allowing operation above the natural speed with torque
and speed control capabilities.
The load considered for this test is a pump-type load with the
following characteristic:
Tl=0.0146 ×ω2.(26)
The pump with the above torque profile exerts the rated torque
of 90 Nm (1 p.u.) on the BDFM shaft at the rated speed of
750 r/min (1.5 p.u.). The load was emulated by the dc drive.
The performance of the drive during the starting procedure is
shown in Fig. 11. The machine accelerates rapidly and reaches
470 rpm (0.94 p.u.) in about than 1 s. The pump torque is 35 Nm
(0.4 p.u.) at this speed. Then, at time 4.5 s, the BDFM makes
a transition to the synchronous mode and shortly after that, it
reaches a pre-set speed of 550 r/min (1.1 p.u.). In this case,
with the transition to the synchronous mode was deliberately
delayed for clarity, the whole starting process took about 7 s,
but this could be reduced to as little as 2.5 s.
The following comments can be made about the performance
observed in Fig. 11
• The maximum starting currents in the PW and CW are
14 A (1.85 p.u.) and 10 A (1.3 p.u.), respectively. Given
the fact that the acceleration time is relatively short, the
transient overload is acceptable, but since the CW current
passes through the machine-side converter, the current
rating of the IGBTs has to be adequate.
• Torque ripples can be observed in the measured and sim-
ulated data. The ripples are most likely due to cogging
effects arising from the combination of a 48-slot stator and
a 36-slot rotor and the harmonic content of the air gap flux
produced by the nested loop rotor.
• The power flow is controlled to be from the converter
to the CW during the synchronization process when the
shaft speed is below the natural speed. This was managed
by controlling the CW excitation voltage as described in
Section IV.
• The phase sequence of the CW voltage and current
changes when the shaft speed passes the natural speed.
This effectively provides a negative sign for the CW
frequency given by (1).
C. Dynamic Performance
The dynamic performance of the BDFM drive in the syn-
chronous mode is presented in this section. Fig. 12 shows
the measured and simulated performance of the drive when a
rapid change is made in 0.2 s in the speed reference from 1 to
1.24 p.u. The machine is driving a constant 0.5-p.u. load torque.
The behavior of the drive under a step change in the load torque
from no load to 0.9 p.u. is shown in Fig. 13. The shaft speed is
kept constant at 1.1 p.u.
A discussion of the results shown in Figs. 12 and 13 follows.
• The shaft speed follows the reference speed very closely
and the overshoot is almost negligible. The rate of change
of the reference speed could be increased, but this would
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SHAO et al.: LOW-COST VSD BASED ON BDFMMOTOR AND FRACTIONAL UNIDIRECTIONAL CONVERTER 323
Fig. 11. Experimental and simulated results for starting and synchronizing the BDFM drive. (a) Measured speed; (b) measured torque; (c) measured CW voltage;
(d) measured currents; (e) simulated speed; (f) simulated torque; (g) simulated CW voltage; and (h) simulated currents.
Fig. 12. BDFM dynamic performance for change in speed reference. (a) Measured speed; (b) measured torque; (c) measured currents; (d) measured load angle;
(e) simulated speed; (f) simulated torque; (g) simulated currents; and (h) simulated load angle.
Fig. 13. BDFM dynamic performance for change in load torque. (a) Measured speed; (b) measured torque; (c) measured currents; (d) measured load angle;
(e) simulated speed; (f) simulated torque; (g) simulated currents; and (h) simulated load angle.
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324 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012
Fig. 14. Efficiency of BDFM drive at different torque and speed operation. (a) Shaft speed 550 r/min; (b) shaft speed 600 r/min; (c) shaft speed 650 r/min;
and (d) shaft speed 700 r/min.
lead to an increased overshoot and reduced stability. How-
ever, in many drive applications, such as water pumps
and gas compressors, a moderate dynamic response is
acceptable.
• The load angle changes slightly as a result of the speed
change, as shown in Fig. 12. However, from (10), the load
angle is expected to be constant since V/f for both PW
and CW is kept fixed over the speed change. The small
change in the load angle is due to the fact that the BDFM
torque has also an induction component (10).
• The drive performs very well in response to a large change
of 0.9 p.u. in the load torque. The transient change in the
shaft speed is small and within an acceptable range. The
stator currents increase to provide the increased mechani-
cal output power.
• The load angle increases as a result of increasing the
torque as shown in Fig. 13. It settles at a relatively low
value (i.e., less than 15◦) even at a high load torque of
0.9 p.u. This shows that the system has a high stability
margin which is desirable for practical applications.
• There is good agreement between the experimental mea-
surements and the predictions from simulation. The small
disagreements are most likely due to limitations of the
measurement system and the approximations made in cal-
culating the machine parameters used in the simulations.
D. Efficiency of the BDFM
The efficiency of electrical machines is important and is the
subject of regulatory requirements [17]. The efficiency of the
BDFM has been measured at different speed and load condi-
tions using the torque transducer and encoder for the output
power and voltage and current sensors for the input power. The
efficiency has also been predicted from the equivalent circuit.
The measured and calculated efficiencies are shown in Fig. 14.
The efficiency of the BDFM is in the range of 75%–80%
which is approaching the efficiency of commercial induc-
tion machines of this size (typically 80%–90%). However,
the BDFM is a laboratory prototype and the design can be
optimized to improve efficiency. The predictions from the
equivalent circuit suggest higher efficiencies than the measured
figures but the equivalent circuit does not take into account iron
losses, friction, and windage. The prediction of iron loss is not
straightforward due to the complex distribution of the magnetic
field in the machine [5], [18]. A finite element approach is
therefore required for accurate prediction of iron losses [18].
The efficiency of the BDFM can be improved by control of
excitation but other performance aspects such as the dynamic
response will be affected [11]. The controller proposed in this
paper incorporates a conventional V/f algorithm for the CW
excitation voltage as discussed in Section III. However, it can be
modified using an efficiency estimator based on the equivalent
circuit to vary the excitation voltage with the aim of optimizing
efficiency at any operating point; implementation of such a
scheme is expected to be straightforward.
VII. CONCLUSION
This paper shows that it is practical to implement a BDFM-
based drive using a fractionally rated unidirectional converter.
It is possible to start the machine in the cascade mode and
then make the transition to the synchronous mode just below
the natural speed. However, the cascade mode does not offer
full starting torque, so if this is a requirement, either means
for absorbing a limited amount of regenerated power during
starting can be provided or external resistances can be switched
in and out. The efficiency of the drive is currently limited by
the performance of the prototype BDFM; research is underway
to improve the machine’s performance. Finally, the simple
phase angle controller approach has been shown to stabilize
the BDFM satisfactorily. Work is also underway to understand
better the origin of the torque ripples and to reduce their
amplitudes.
APPENDIX I
PROTOTYPE BDFM SPECIFICATIONS
Table II provides the design specifications of the prototype
BDFM.
TAB L E I I
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SHAO et al.: LOW-COST VSD BASED ON BDFMMOTOR AND FRACTIONAL UNIDIRECTIONAL CONVERTER 325
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Shiyi Shao received the B.Eng. and M.Phil. de-
grees from Shanghai Jiao Tong University, Shanghai,
China, in 2003 and 2006, respectively, and the
M.Phil. and Ph.D. degrees in electrical engineering
from Cambridge University, Cambridge, U.K., in
2008 and 2010, respectively.
He is currently with Wind Technologies,
Cambridge, involved in electrical system design and
machine control. He is also working as a Research
Collaborator at Cambridge University in the field of
electrical machines, machine drive, and control.
Ehsan Abdi received the B.Sc. degree in electrical
engineering from Sharif University of Technology,
Tehran, Iran, in 2002, and the M.Phil and Ph.D.
degrees in electrical engineering from Cambridge
University, Cambridge, U.K., in 2003 and 2006,
respectively.
He is currently with Wind Technologies,
Cambridge, aiming at exploiting the Brushless
Doubly-Fed Machine for commecial applications.
He is also an Embedded Researcher at Cambridge
University Electrical Engineering Division and his
main research interests include electrical machines and drives, renewable
power generation, and electrical measurements and instrumentation.
Richard McMahon received the degrees of B.A.
in electrical sciences and the Ph.D. degree from
Cambridge University, Cambridge, U.K., in 1976
and 1980, respectively.
Following postdoctoral work on semiconductor
device processing he was appointed University Lec-
turer in Electrical Engineering at Cambridge Univer-
sity Engineering Department in 1989 and became
a Senior Lecturer in 2000. His research interests
include electrical machines and power electronics,
particularly for wind and wave power systems.
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