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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 6, JUNE 2013 2477
Generalized Vector Control for Brushless Doubly Fed
Machines With Nested-Loop Rotor
Farhad Barati, Richard McMahon, Shiyi Shao, Ehsan Abdi, Member, IEEE, and Hashem Oraee
Abstract—This paper presents a generalized vector control
system for a generic brushless doubly fed (induction) machine
(BDFM) with nested-loop type rotor. The generic BDFM consists
of p1/p2pole-pair stator windings and a nested-loop rotor with
N number of loops per nest. The vector control system is derived
based on the basic BDFM equation in the synchronous mode
accompanied with an appropriate synchronization approach to
the grid. An analysis is performed for the vector control sys-
tem using the generic BDFM vector model. The analysis proves
the efficacy of the proposed approach in BDFM electromagnetic
torque and rotor flux control. In fact, in the proposed vector
control system, the BDFM torque can be controlled very effectively
promising a high-performance BDFM shaft speed control system.
A closed-loop shaft speed control system is composed based on the
presented vector control system whose performance is examined
both in simulations and experiments. The results confirm the
high performance of the proposed approach in BDFM shaft speed
control as well as a very close agreement between the simulations
and experiments. Tests are performed on a 180-frame prototype
BDFM.
Index Terms—Brushless doubly fed machine (BDFM), general-
ized vector control, generalized vector model, shaft speed control,
wind power generation.
NOMENCLATURE
Ms1r, M s2rMutual inductance matrix for stator1-rotor and
stator2-rotor.
J, B Rotor moment of inertia and friction
coefficient.
p1,p
2Pole-pairs of stator1 and stator2 windings.
θs1,θ
s2,ϕ
rArbitrary functions of time in stator1, stator2,
and rotor transformations.
ωs1,ω
s2Time derivatives of θs1,θ
s2.
Vs1, Is1,Λs1Stator1 voltage, current, and flux vectors.
Vs2, Is2,Λs2Stator2 voltage, current, and flux vectors.
Vr, Ir,ΛrRotor voltage, current, and flux vectors.
Manuscript received February 1, 2012; revised April 25, 2012, July 2,
2012, and September 20, 2012; accepted October 2, 2012. Date of publication
October 24, 2012; date of current version February 6, 2013.
F. Barati is with the Department of Electrical Engineering, University of
South Carolina, Columbia, SC 29208 USA (e-mail: baratif@cec.sc.edu).
R. McMahon and E. Abdi are with the Department of Engineering, Univer-
sity of Cambridge, Cambridge CB3 0FA, U.K. They are also with the Wind
Technologies Ltd, St Johns Innovation Center, Cambridge CB4 0WS, U.K.
(e-mail: ram1@cam.ac.uk; ea257@cam.ac.uk; ehsan.abdi@windtechs.com).
S. Shao is with the Department of Engineering, University of Cambridge,
Cambridge CB3 0FA, U.K. (e-mail: ss656@cam.ac.uk).
H. Oraee is with the Department of Electrical Engineering, Sharif University
of Technology, 11365-9363 Tehran, Iran (e-mail: oraee@sharif.edu).
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.2012.2226415
Fig. 1. Nested-loop rotor in the prototype BDFM.
Re{} Real part of a complex number.
Z∗Complex conjugate of Z.
ZtTranspose of Z.
I. INTRODUCTION
THE BRUSHLESS doubly fed machine (BDFM) promises
significant advantages for use both in variable speed drives
and wind power generation [1]. The reduced system cost due
to fractional size of the converter is an encouragement to
electric drive manufacturers to utilize the BDFM. The brushless
operation and thereby reduced manufacturing and operational
costs as well as improved reliability have led to interests in the
BDFM as a replacement for the doubly fed (slip-ring) induction
generator which is currently widely used in the wind power
industry.
The BDFM is a single-frame induction machine with two
three-phase stator windings of different pole numbers and a
special rotor design. The nested-loop type rotor is the most
well-known one consisting of nests equally spaced around the
circumference as shown in Fig. 1 for a prototype BDFM. The
number of nests equals to the sum of stator windings pole-
pairs [1]. The prototype BDFM consists of 2/4 pole-pair stator
windings; hence, there are six nests in the rotor circuit. Each
nest can contain several concentric loops, as there are three
loops in each nest of the prototype BDFM.
For the operation of BDFM, one stator winding, called the
power winding (PW), is connected to the mains, while the other
winding, called the control winding (CW), is supplied through
a fractional converter as shown in Fig. 2.
In order to realize its commercial adoption, the BDFM must
have predictable and robust dynamic performance. Since the
BDFM is not stable over the operating speed range, a controller
is required to stabilize the machine as well as meeting other
dynamic and steady-state performance requirements. Vector
0278-0046/$31.00 © 2012 IEEE
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2478 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 6, JUNE 2013
Fig. 2. BDFM operation.
control methods, also known as field oriented control, have
been examined for the BDFM control in [2]–[5].
In order to understand the requirements for a controller, an
appropriate mathematical model is required to describe the
machine’s dynamic performance; this model then forms the
basis for the controller design and analysis. Vector models are
known to provide effective tools for both analysis and control
of electrical machines as employed for the BDFM in [6]. In
fact, the vector model presented in [6] was a significant contri-
bution toward a dynamic model for the BDFM based on which
successful vector control schemes were presented in [3]–[5].
This vector model considered a single-loop per nest rotor, but it
provided guidelines for a multiple-loop per nest rotor as well.
The approach proposed in [6] for a multiple-loop per nest rotor
was based on an approximate equivalent loop for each nest.
The approximate equivalent loop approach provides significant
reductions in the model complexity; however, it trades off the
model accuracy. An accurate model, although some complexity
involved, provides a valuable tool for control synthesis whose
performance is reliable and predictable.
In [7]–[10], significant contributions on the steady-state
model development for the BDFM were presented. These mod-
els, which were experimentally validated, are suitable for the
BDFM steady-state analysis and design. In [11], a low-cost
BDFM-based variable speed drive is presented along with its
performance validations both in simulations and experiments.
It utilized a phase-angle scalar control for the BDFM. In [12], a
low voltage ride-through capability enhancement and analysis
are presented for the BDFM which utilized the vector control
system in [5], presented an analysis of BDFM ride-through,
and proposed techniques to improve the machine ride-through
capability. Validating simulation and experimental results are
presented for the techniques proposed.
In [13], [14], a vector model as well as a vector control
were derived for the dual stator induction machine (DSIM).
The DSIM, similar to the BDFM, consists of two three-phase
windings in the stator, but its rotor is of the squirrel cage type.
In [15], a vector control was derived for the cascade doubly
fed machine (CDFM). The CDFM consists of two wound-
rotor induction machines which are both mechanically and
electrically coupled through the rotor. The CDFM has similar
operating characteristics to the BDFM, but it suffers from a
non-compact structure compared to the BDFM.
In [16], [17], a vector model was derived for the proto-
type BDFM considering the effects of all loops in each nest
which was employed for the BDFM performance simulations
and analysis in [18]. The approach presented in [16], [17] is
generalized for a generic BDFM with p1/p2pole-pair stator
windings and Nloops per nest in [19]. It is confirmed in [19]
that the generalized BDFM vector model behaves accurately in
predicting the machine performance under different operating
conditions. In [20], a vector control structure is presented for
the prototype BDFM which was designed and analyzed using
the vector model presented in [16]. A comprehensive extension
to the approach in [20] is presented in this paper.
In this paper, a generalized vector control system is presented
for a generic BDFM with nested-loop rotor. The generalized
vector control system is based on the basic BDFM equation
in the synchronous mode accompanied with an appropriate
synchronization to the grid. Using the generalized vector model
in [19], an analysis is performed for the generalized vector
control system proving the efficacy of the proposed approach
in the BDFM electromagnetic torque and rotor flux control.
In this paper, based on the generalized vector control sys-
tem proposed, a high-performance BDFM shaft speed control
system is presented which is examined both in simulations and
experiments.
II. BDFM S YNCHRONOUS OPERATION
The main operating mode of BDFM is the synchronous
mode, at which the PW and CW are cross-coupled through the
rotor circuit. The shaft speed in this mode only depends on
the supply frequencies to the two stator windings, i.e., it only
depends on the variable output frequency from the converter if
one stator winding is supplied from the mains [1]. The rotor
shaft speed in rad/s is given by
ωm=ω1+ω2
p1+p2
(1)
where, ω1and ω2are the angular frequencies of the supplies to
stator1 and stator2 windings, respectively.
The BDFM is characterized by the so-called natural speed at
which the stator winding connected to the converter is supplied
by DC. For the prototype 2/4 pole-pair BDFM with the PW
connected to the 50 Hz grid, the natural speed is 500 r/min. A
positive frequency, positive sequence voltage, is required for the
CW for the operation of BDFM above the natural speed, while
a negative frequency voltage feeding the CW reduces the shaft
speed below the natural speed.
III. BDFM G ENERIC VECTOR MODEL
A generic vector model for a p1/p2pole-pair BDFM with a
nested-loop rotor with Nloops per nest is derived in [19]. The
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BARATI et al.: GENERALIZED VECTOR CONTROL FOR BRUSHLESS DOUBLY FED MACHINES WITH NESTED-LOOP ROTOR 2479
Fig. 3. Proposed vector control structure for generic BDFM.
generic vector model equations are summarized as follows:
Vs1=R1Is1+dΛs1
dt −jωs1Λs1(2)
Vs2=R2Is2+dΛs2
dt −jωs2Λs2(3)
0=Vr=RrIr+dΛr
dt −jp1
dϕr
dt Λr(4)
R1and R2are the winding phase resistances of stator1 and
stator2, respectively. Rr∈RN×Nis the nest resistance matrix.
The flux vector equations are as follows:
Λs1=Ll1+3
2L1Is1+3Ms1re−jη Ir(5)
Λs2=Ll2+3
2L2Is2+3Ms2rejγ I∗
r(6)
Λr=(Lr−Mr)Ir+3
2Mt
s1rejηIs1+3
2Mt
s2rejγI∗
s2(7)
where L1and L2are self-inductances and Ll1and Ll2are leak-
age inductances of stator1 and stator2 phase windings, respec-
tively. Ms1r∈R1×Nand Ms2r∈R1×Nare stator1-rotor and
stator2-rotor mutual inductance matrixes, respectively. Lr∈
RN×Nis the nest inductance matrix which comprises the
self- and mutual inductances of the loops within one nest.
Mr∈RN×Nis the nest-nest mutual inductance matrix which
comprises the mutual inductance terms between the loops of
two different nests. The angles ηand γare given as
η=p1ϕr−θs1−p1θr(8)
γ=p1ϕr+θs2+p2(θr−ζ)(9)
θris the rotor position angle, and ζis the physical displacement
angle between the two stator windings in the stator core. The
BDFM electromagnetic torque Tecan then be expressed as
Te=9
2p1Ms1rreal IrI∗
s1ej(π
2−η)
+9
2p2Ms2rreal IrI∗
s2ej(π
2+γ).(10)
The generic vector model predicts both dynamic and steady-
state performances of BDFM accurately. Its predictions are
examined against the coupled-circuit model as well as the
experimental data in [19]. The reduced-order vector model,
however, behaves poorly in predicting the BDFM dynamic
performance [21].
IV. PROPOSED VECTOR CONTROL STRUCTURE
FOR THE BDFM
The proposed vector control scheme for the BDFM is shown
in Fig. 3. As seen in Fig. 3, the stator1 is regarded as the PW,
fed directly from the grid and stator2 as the CW connected to
a voltage source inverter (VSI). The VSI is run in the current
regulation mode to provide current control inputs for the control
system [22].
A. CW Current Regulation Loop
The VSI is run in the current regulation mode using a
hysteresis current regulator. The hysteresis controller keeps
the actual CW currents around the reference ones within the
hysteresis band. High response speed and robust performance
to the machine parameters are among the main advantages
that can be achieved by employing the hysteresis controller
[22], [23].
The reference values for the CW current regulation loop,
is2,ref , are provided by the 2/3 transformation as the following:
is2,ref =Re1e−J2π
3e−j4π
3te−jθs2,ref Is2,ref(11)
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2480 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 6, JUNE 2013
where, θs2,ref is the reference angle and Is2,ref is the CW
reference current vector defined as
Is2,ref =Ids2,ref +jI qs2,ref .(12)
B. Calculation of the Reference Angle
In the proposed vector control scheme, the reference angle
is determined based on the principle equation of the BDFM
operation in the synchronous mode, i.e., (1). Based on (1),
the following relation can be derived between the CW angular
frequency, PW angular frequency, and the rotor shaft speed
in rad/s:
ω2=(p1+p2)ωm−ω1.(13)
Based on the 2/3 transformation, it can be shown that the
following relation between ωs2,ref and ω2holds:
ωs2,ref =−ω2(14)
where, ωs2,ref is the time derivation of the reference angle, i.e.,
ωs2,ref =d(θs2,ref )/dt.
Substituting (14) into (13) and integrating over the both sides,
the following relation can be derived for the reference angle:
θs2,ref =ω1dt −(p1+p2)θm(15)
where, θmis the rotor shaft position in rad measured by the
shaft encoder and ω1is the grid fixed frequency in rad/s.
C. Synchronization Between the PW and CW
The PW and CW variables must be appropriately synchro-
nized for the proper operation of the BDFM vector control
scheme. In the proposed vector control system, the synchro-
nization is achieved using the following procedure.
To synchronize the PW and CW, the integrator in (15) must
provide the instantaneous phase angle of PW phase “a” voltage.
For this purpose, the PW voltage is measured using which the
sign of phase “a” voltage is to detect the end of each voltage
cycle. The integrator in (15), or in Fig. 3, is then reset by the end
of each PW phase “a” voltage cycle. Such synchronization ap-
proach is preferred to the commonly used phase-locked loop ap-
proach, as it involves less required computations and provides
higher response speed. Also, practical experiences show that it
behaves well under real line voltages; however, an appropriate
input filter is recommended if the machine is connected to a low
quality grid in order to remove voltage ripples or fluctuations
before its utilizations in the synchronization procedure.
The grid fixed frequency is used for calculating the refer-
ence angle in the proposed vector control scheme. The grid
frequency may have small variations, e.g., ±2%, from the nom-
inal frequency. Using the synchronization approach discussed,
errors introduced in θs2,ref at the result of deviating the grid
frequency from the nominal one are reset by the end of each PW
voltage cycle, i.e., after 0.02 s in a 50 Hz grid. Hence, it can be
concluded that deviations of grid frequency from the nominal
Fig. 4. Synchronous reference frames with respect to the stationary frame.
frequency have no significant effects on the performance of the
proposed scheme as far as the BDFM shaft speed control is
under considerations.
V. A NALYSIS OF THE PROPOSED VECTOR
CONTROL STRUCTURE
The analysis of the proposed vector control structure is
performed using the BDFM generic vector model as the
followings.
A. Synchronous Reference Frames
The generic vector model described by (2)–(10) has three
free parameters corresponding to the three vector transforma-
tions employed for stator1, stator2, and rotor quantities, i.e.,
θs1,θs2, and ϕr, respectively. In principle, any arbitrary values
can be assigned to these free parameters. However, they must be
assigned appropriately according to the specific application of
the vector model [19]. For the specific purpose of the proposed
vector control structure analysis, the most appropriate approach
is to make the time-varying mutual inductance terms constants.
This can be achieved by setting η=γ=0in the vector model.
We assign θs2as
θs2=θs2,ref =ω1t−(p1+p2)θm.(16)
Using η=γ=0, the following relations are derived
θs1=−ω1t+p2ζ−(p1+p2)c(17)
ϕr=1
p1
[−ω1t+p2(ζ−c)] + θm(18)
where, c=θr−θmis a constant for a specific installation of
the shaft encoder.
Referring to the reference frames theory, it can be shown that
PW and rotor quantities are in dq1reference frame and CW
quantities are in dq2reference frame as shown in Fig. 4. The
dq1and dq2reference frames rotate at ω1and ((p1+p2)ωm−
ω1)=ω2speeds, respectively, with respect to the stationary
reference frame αβ. They can, therefore, be considered as the
synchronous reference frames rotating at ω1and ω2speeds.
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BARATI et al.: GENERALIZED VECTOR CONTROL FOR BRUSHLESS DOUBLY FED MACHINES WITH NESTED-LOOP ROTOR 2481
B. BDFM Rotor Flux and Torque Control
The PW in BDFM is supplied from the grid which is assumed
as a balanced three-phase source, so the PW voltage vector is
as follows:
Vs1=Vm1ej(θs1+ω1t)(19)
where, Vm1is the amplitude of the PW phase voltage. Note that,
in the above equation, the initial phase angle of PW phase “a”
voltage is considered to be zero. By substituting (17) into (19)
Vs1=Vm1ej(p2ζ−(p1+p2)c)=Vds1+jV qs1(20)
where, Vds1and Vqs1are constants.
To avoid complexity in the vector analysis, it is common to
neglect the PW resistance and assume dΛs1/dt =0[4], [5].
Hence,
Λs1=Vs1
jω1
=Vqs1
ω1−jVds1
ω1
.(21)
Using the rotor flux equation, the rotor current vector can be
calculated as
Ir=(Lr−Mr)−1Λr−3
2Mt
s1rIs1−3
2Mt
s2rI∗
s2.(22)
By substituting (22) into the stator1 flux equation, the PW
current vector can be derived as the following:
Is1=1
LΛs1−3Ms1r(Lr−Mr)−1Λr
+9
2Ms1r(Lr−Mr)−1Mt
s2rI∗
s2(23)
where,
L=Ll1+3
2L1−9
2Ms1r(Lr−Mr)−1Mt
s1r.(24)
The rotor flux vector is divided into Λr1and Λr2parts with the
following differential equations:
Λr= Λr1+ Λr2(25)
dΛr1
dt +AΛr1=B1Vqs1+B2Ids2(26)
dΛr2
dt +A−j(p1ωr−ω1)IN×NΛr2−
j(p1ωr−ω1)Λr1=−j(B1Vds1+B2Iqs2)(27)
where, A∈RN×N,B1∈RN×1and B2∈RN×1are given as
the following:
A=Rr(Lr−Mr)−1
×IN×N+9Mt
s1rMs1r(Lr−Mr)−1
2L(28)
B1=3
2ω1LRr(Lr−Mr)−1Mt
s1r(29)
B2=Rr(Lr−Mr)−1
×3
2Mt
s2r+27
4LMt
s1rMs1r(Lr−Mr)−1Mt
s2r.(30)
As can be seen from (26) and (27), Λr1is controllable since it
can be regulated using Ids2, while Λr2is uncontrollable and, in
general terms, time varying.
For a constant Ids2, the steady-state value of Λr1can be
calculated as
Λr1(∞)=A−1(B1Vqs1+B2Ids2).(31)
Finally, the BDFM electromagnetic torque can be written as
the following:
Te=GIqs2+Td(32)
where
G=9
2−9
2p1Ms1rD1D2+p2Ms2rD1−9
LD2Λds1
+27
LD2Ms1rD1(33)
D1=(Lr−Mr)−1Λr1(∞)(34)
D2=Ms1r(Lr−Mr)−1Mt
s2r(35)
Tdis regarded as the disturbance torque in the closed-loop shaft
speed control system design and analysis.
The relationship established between the control input and
the BDFM electromagnetic torque, as in (32), promises a high-
performance closed-loop shaft speed control system synthe-
sized based on the proposed vector control system. It also
confirms the versatility of the generalized vector model in
analyzing the proposed vector control scheme resulting in a
linear pure gain relation.
VI. PROPOSED VECTOR CONTROL SYSTEM
PERFORMANCE VERIFICATIONS
The performance of the proposed vector control system is
verified both in simulations and experiments in this section.
Note that the BDFM vector model, as well as the proposed
vector control structure, is implemented in Matlab/Simulink for
simulation purposes. The tests are carried out on the 180-frame
prototype BDFM in which the four-pole winding is connected
to the 240 V, 50 Hz grid, and eight-pole winding is fed from
the VSI. A DC machine equipped with a commercial DC Drive
(DCS800 from ABB) is mechanically coupled to the BDFM to
provide the required load torque, and a torque transducer is used
between the BDFM and the DC machine to monitor the torque.
The experimental test rig is shown in Fig. 5.
The proposed vector control algorithm is implemented in
Matlab/Simulink based on the xPC Toolbox. In this scheme,
the target PC reads signals from sensors including voltage and
current sensors of stator windings, rotor position, and speed
from an incremental encoder with a resolution of 2500 pulses
per revolution. The target PC provides reference signals for
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2482 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 6, JUNE 2013
Fig. 5. Experimental test rig.
an FPGA-based pulse width modulator generating switching
signals for the VSI based on the measured signals and the vector
control algorithm implemented. Further details of the hardware
can be found in [24].
Based on the proposed vector control structure, in [21], a
well-designed linear shaft speed controller is presented for
the prototype BDFM. Based on which, the closed-loop shaft
speed control system has the gain margin (GM) of 23 dB
and phase margin (PM) of 52◦.Also,Ids2,ref has been set to
zero for the closed-loop control system synthesis. The closed-
loop shaft speed control system performance is evaluated in
several different operating conditions both in simulations and
experiments as the followings.
A. Response to Step Change in the Reference Speed at
No-Load
Two tests have been carried out in which the response to step
changes in the reference speed has been investigated which are
as follows.
First Test: In this test, a step change in the reference speed
from the natural speed 500 to 400 r/min has been applied.
The performance results are shown in Fig. 6. As can be seen
in Fig. 6, the shaft speed follows the speed command with
undershoot of about 5.5%, rise time of 1 s, and settling time
of 7 s. As clear from Fig. 6, the CW actual currents track
the reference ones closely confirming the proper operation of
current control loop. Note that, the performance of the current
control loop with the hysteresis controller is robust to BDFM
parameter changes, so its performance in practice is guaranteed
under any operating conditions [22], [23].
For the current control loop, the hysteresis band is set to
0.5 allowing ±0.25 A of actual currents variation around the
reference ones. These variations are of high-frequency and low
amplitude nature compared to the fundamental current. Such
variations in CW currents result in variations in PW currents
as well. This is due to the cross-coupling effect between the
stator windings in the BDFM. Also, variations in CW and PW
currents result in BDFM electromagnetic torque pulsations, but
they do not have noticeable effects on the shaft speed because
of the rotor moment of inertia.
Second Test: The second test investigates the closed-loop
control system performance when a step change in the speed
reference is applied from 500 to 600 r/min. The results from
experiments and simulations are shown in Fig. 7. As can be
seen from Fig. 7, the shaft speed follows the reference speed
with overshoot of about 13%, rise time of 1.1 s, and settling
time of 7 s. It is also clear that the CW actual current follows
the reference one closely.
In both tests, as can be seen in Figs. 6 and 7, close
agreement has been achieved between the experimental re-
sults and simulation predictions which validates the accuracy
of the implemented vector model and control algorithm in
Matlab/Simulink. There are, however, slight differences be-
tween the steady-state values of the control input in simulations
and experiments which are due to the friction coefficient of the
test rig including the BDFM, torque transducer, DC machine,
and the mechanical couplings between them which cannot be
accurately determined. Note that, the BDFM electromagnetic
torque at steady-state and under no-load condition equals to the
friction torque.
In the above, the dynamic performance of the closed-loop
control system with GM =23dB and PM =52degrees has
been investigated. It should be noted that such performance can
even be improved in terms of rise time and settling time, but this
will compromise the closed-loop system stability. Hence, an ap-
propriate tradeoff must be considered between the closed-loop
system response time and stability conditions in the selection of
controller’s gains [21].
Compared to the results presented for the same test rig, the
settling time for a step change in the reference speed is more
than 40 s in [5]. It is also confirmed in [5] that attempts to
increase in the system response speed, by increasing in the
controller gains, will result in the system instability.
B. Response to Step Change in the Load Torque
In order to evaluate the performance of closed-loop control
system in disturbance torque rejection, a number of consecutive
step changes in the load torque have been applied to the BDFM
shaft. The shaft reference speed is set to 550 r/min during
the test. The closed-loop control system performance both for
simulations and experiments are shown in Fig. 8.
Starting from no-load, each increment in the load torque
is a step of 5 N.m. The applied torque is in the direction of
speed, i.e., a generating torque, causing a transient increase in
shaft speed. As clear from Fig. 8, the control input increases
accordingly after the load torque is applied. Note that, increas-
ing in iqs2,ref provides higher BDFM electromagnetic torque
compensating for the increment in load torque. It should also
be noted that the BDFM electromagnetic torque is able to
compensate for the load torque as far as the control input has not
reached its limits. For the prototype BDFM with the rated CW
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BARATI et al.: GENERALIZED VECTOR CONTROL FOR BRUSHLESS DOUBLY FED MACHINES WITH NESTED-LOOP ROTOR 2483
Fig. 6. Simulation and experimental results for a speed change from 500 to 400 r/min (1.0 to 0.8 p.u.). (a) experimental speed; (b) experimental CW current;
(c) experimental control input; (d) experimental PW current; (e) simulated speed; (f) simulated CW current; (g) simulated control input; (h) simulated PW
current.
Fig. 7. Simulation and experimental results for a speed change from 500 to 600 r/min (1.0 to 1.2 p.u.). (a) Experimental speed; (b) experimental CW current;
(c) experimental control input; (d) experimental PW current; (e) simulated speed; (f) simulated CW current; (g) simulated control input; (h) simulated PW
current.
Fig. 8. Simulated and experimental results of the BDFM performance under changes in the load torque. (a) Load torque change; (b) rotor shaft speed; (c) control
input iqs2,ref .
current of 7 A (rms), assuming Ids2,ref set to zero, the control
input limits are ±7√2A.
As can be seen from Fig. 8, by applying a step change in the
load torque, a transient increase occurs in the shaft speed whose
peak value is less than 10%. It can also be seen in Fig. 8 that
the settling time for transient increase in the shaft speed is about
13 s. Note that, the settling time as well as the transient increase
peak value can be reduced by increasing in the controller gains,
but this trades off the stability of the closed-loop system [21].
C. Steady-State Performance Analysis
The steady-state performance of the proposed closed-loop
shaft speed control system in terms of harmonic contents of
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2484 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 6, JUNE 2013
Fig. 9. Harmonic analysis of the PW and CW currents under steady-state condition. (a) Experimental PW current; (b) experimental CW current; (c) harmonic
content of the PW current; (d) power spectral density of CW current.
the PW and CW currents is investigated in this section. By an-
alyzing the harmonic contents of the CW current, the harmonic
contents of the PW current can be investigated based on the
cross-coupling effect existing between the CW and PW in the
BDFM.
The steady-state operation of the prototype BDFM at
400 r/min and under no-load condition is presented in Fig. 9.
In Fig. 9, the experimental PW and CW currents and their
harmonic contents are shown. It can be seen from Fig. 9(b)
that, the CW current contains significant amount of harmonic
components due to the hysteresis controller. The power spectral
density of the CW current is shown in Fig. 9(d). As clear from
Fig. 9(d), the CW current fundamental component is at 10 Hz,
as expected for the prototype BDFM connected to the 50 Hz
grid and working at 400 r/min, and its high-frequency contents
centered at 700 Hz.
Due to the cross-coupling effect between the PW and CW,
the high-frequency contents of CW current induce harmonics
in the PW whose frequency can be calculated according to (1).
Using this equation, it can be shown that the induced signif-
icant harmonic in the PW due to CW harmonic contents has
the frequency of 650 Hz, i.e., 13th order. This fact is clear
from Fig. 9(c). As can be seen, the PW current has the most
significant harmonics component at the 13th harmonics.
As calculated in Fig. 9(c), the total harmonic distortion
(THD) of the PW current is 9%. Note that, the THD of PW
current decreases as the BDFM load torque increases [1].
Hence, for the normal operation of BDFM which often contains
some amounts of load torque, a better quality for the PW current
is expected.
VII. CONCLUSION AND FUTURE WORKS
A generalized vector control system is proposed for a generic
BDFM along with its analysis, simulation, and experimental
validations. The analysis is performed using the generic BDFM
vector model showing the efficacy of the vector control scheme
in establishing proper relations between the vector control
inputs and the machine electromagnetic torque and rotor flux.
In fact, as the analysis confirms, the BDFM electromagnetic
torque is controlled very effectively. Also, the simulation and
experimental results confirm the efficacy of the proposed vector
control system in composing a high-performance BDFM shaft
speed control system. Thus, the proposed vector control system
is liable to be employed for BDFM in wind power industry.
Moreover, the proven accuracy of BDFM vector model and
control system implemented in Matlab/Simulink makes it a
valuable tool for different BDFM studies under any operating
conditions.
The presented vector control scheme has also the capabilities
to be utilized for either BDFM drive performance optimizations
or reactive power regulation using Ids2,ref which can be con-
sidered as the future works. The loss minimizations or torque
capability maximizations are among the objective functions
for the BDFM drive performance optimizations. It can also be
shown that there exists a relationship between the rotor flux and
the PW reactive power. Hence, alternatively, the PW reactive
power can be regulated in the proposed vector control system.
The total BDFM reactive power which includes the reactive
powers of PW and grid side converter (GSC) can be regulated
using both of the GSC and machine side converter in a bi-
directional converter.
APPENDIX
TAB L E I
PROTOTYP E BDFM SPECIFICATIONS
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Farhad Barati received the B.Sc. degree in elec-
trical engineering from Malek-Ashtar University of
Technology, Isfahan, Iran, in 2002. He then received
the M.Sc. and Ph.D. degrees in electrical engineering
from Sharif University of Technology, Tehran, Iran,
in 2005 and 2010, respectively.
Currently, he is a Postdoctoral Fellow at the Uni-
versity of South Carolina, Columbia, US. His main
research interests include electric machines, power
electronics, and industrial applications of control
theory.
Richard McMahon received the B.A. degree in
electrical sciences and the Ph.D. degree from the
University of Cambridge, Cambridge, U.K., in 1976
and 1980, respectively.
He has been with the Department of Engineering,
University of Cambridge, Cambridge, where he was
appointed the University Lecturer in electrical en-
gineering in 1989, following his postdoctoral work
on semiconductor device processing, and became a
Senior Lecturer in 2000.
His research interests include electrical drives,
power electronics, and semiconductor materials.
Shiyi Shao received the B.Eng. degree and
M.Phil. degree from Shanghai Jiao Tong University,
Shanghai, China, in 2003 and 2006, respectively. He
also received M.Phil. and Ph.D. degrees in electri-
cal engineering from the University of Cambridge,
Cambridge, U.K. in 2008 and 2010, respectively.
Currently, he is with the 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 (M’06) received the B.Sc. degree from
the Sharif University of Technology, Tehran, Iran, in
2002, and the M.Phil. and Ph.D. degrees from the
University of Cambridge, Cambridge, U.K., in 2003
and 2006, respectively, all in electrical engineering.
Currently, he is the Managing Director of Wind
Technologies Ltd where he has been involved with
commercial exploitation of the brushless doubly
fed induction generator technology for wind power
applications. His main research interests include
electrical machines and drives, renewable power
generation, and electrical measurements and instrumentation.
Hashem Oraee received the B.Eng. degree in elec-
trical and electronic engineering from the University
of Wales, Cardiff, U.K. in 1980 and the Ph.D. de-
gree in electrical engineering from the University of
Cambridge, U.K. in 1984.
Currently, he is a Professor of electrical engi-
neering at Sharif University of Technology, Tehran,
Iran. His research interests include electrical energy
conversion and power quality.
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