40220140502003

International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 5, Issue 2, February (2014), pp. 26-43 © IAEME
26
ANALYTICAL STUDY AND CONTROL OF A BRUSHLESS DOUBLY FED
RELUCTANCE MACHINE PERFORMANCE
Dr. Maher Faeq Mohammed
Electronic and control engineering department, technical collage Kirkuk/Iraq
ABSTRACT
In this paper, dynamic performance analysis and control technique for a brushless doubly fed
reluctance machine (BDFRM) with extensive simulation results is presented. The transient and
steady-state governing equations are presented with appropriate assumptions. A speed control
scheme based on field orientation control strategy is presented, and start-up behavior of the machine
are studied extensively via digital simulation. Moreover, effects of both voltage and frequency of the
control winding on the machine performance are studied. Machine performance simulation studies
have been carried out using the proposed method of analysis.
Keyword: brushless motor, doubly fed motor, reluctance motor.
1. INTRODUCTION
Brushless doubly-fed machines (BDFMs) have been extensively researched over the past last
few years because they allow the use of partially rated inverter in many variable speed applications
[1–17]. This machine uses a special type of rotor and a double wound stator with dissimilar number
of poles. The brushless doubly-fed induction machine (BDFIM) has received more attention from the
researchers over the last few years [6–10]. However, a BDFRM was ignored until the early 1990s [3,
4].The motivation for considering the BDFRM as compared to the BDFIM is that it offers the
potential of higher efficiency, lower cost, simpler and more reliable structure, and lower rating of the
power electronic inverter than a comparably rated BDFIM. Therefore, the utilization of the BDFRM
in adjustable speed drives (ASD) system and variable speed generator (VSG) has been recently
proposed [11–13].
One nice and interesting feature of the BDFRM is that it can operate in various modes of
operation depending on the excitation of the control stator winding. This means that with controlled
AC source fed to the control winding, the machine can operate either in the synchronous,
subsynchronous or supersynchronous modes permitting large speed operational range. Therefore,
INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING &
TECHNOLOGY (IJEET)
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 5, Issue 2, February (2014), pp. 26-43
© IAEME: www.iaeme.com/ijeet.asp
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IJEET
© I A E M E

27
much work has to be carried out on the analysis, design, control and experimental testing of this
machine before the trade-offs in inverter size versus machine size and the subsequent cost issues can
be quantified.
The main objective of this article is to:
• Predict the dynamic and steady-state performances of the BDFRM.
• Demonstrate the important aspects of the machine behavior in various modes of operation.
• Study the start-up and synchronization process of the BDFRM under V/F control.
• Develop a control technique by which the machine can be successfully controlled over a wide
range of speeds.
2. MACHINE STRUCTURE
The stator configuration of the BDFRM has conventional laminations with 36 uniformly
distributed semi-open slots. The rotor, however, is constructed with reluctance saliency. The stator
has two separate stationary windings, each one of the windings having a different pole numbers, so
that the windings are not magnetically coupled, and the magnetic mutual coupling between the two
sets of stator windings is realized through the rotor. Thus, the rotor structure basically determines the
magnetic coupling between the two stator windings, which, in turn, determines the machine
behavior. Furthermore, to avoid unbalanced magnetic pull on the rotor, the difference between the
pole pairs of the two stator windings must be greater than one [7, 11]. Also, the number of salient
rotor poles must equal the sum of the number pole pairs in the stator windings. The saliency on the
rotor serves only to provide magnetic coupling between the two stator windings. The rotor speed is a
function of the frequency of the secondary winding currents. The basic structure of the BDFRM is
shown in Figure 1. As can be seen, the primary winding has 2p-pole, and is connected to the main
supply, while the secondary (control) winding has 2q-pole, and is connected to an inverter.
Figure 1. Schematic diagram of the brushless doubly fed reluctance machine (BDFRM)
3. THE MACHINE MODELING
3.1. Dynamic Model
The analysis presented here is based on representing the machine in terms of equivalent
rotating reference frame fitted along the d- and q-axes and rotates with rotor speed. The following
assumptions are considered:

28
• The two stator windings are assumed to have sinusoidally distributed windings having equal turns
per phase.
• The iron of both stator and rotor has infinite permeability.
• Effects of magnetic saturation and core losses are ignored.
• Effects of stator slots are neglected.
Assuming balanced operating conditions, the voltage equations of the BDFRM in the rotor
reference frame can be written in a simplified form as follows [4]:
‫ݒ‬௤ௗ ൌ ‫ݖ‬௤ௗ ݅௤ௗ (1)
The electromagnetic torque is
ܶ௘ ൌ ‫ܯ݌‬ଵ൫݅௤ଵ݅ௗ௥ െ ݅ௗଵ݅௤௥൯ ൅ ‫ܯݍ‬ଶሺ݅௤ଶ݅ௗ௥ െ ݅ௗଶ݅௤௥ሻ (2)
which can be written in terms of primary winding parameters as:
ܶ௘ ൌ
ଷ
ଶ
ሺ‫݌‬ ൅ ‫ݍ‬ሻሺߣௗଵ݅௤ଵ െ ߣ௤ଵሻ (3)
The dynamic equation is given by
ܶ௘ ൌ ‫ܬ‬
ௗఠೝ
ௗ௧
൅ ‫߱ܤ‬௥ ൅ ܶ௅ (4)
The subscripts “1,” “2,” and “r” refer to the quantities associated with the primary, the
secondary windings and the rotor circuit, respectively. M1 is the mutual inductance between the
primary winding and rotor circuit, M2 is the mutual inductance between the secondary winding and
rotor circuit, M12 is the mutual inductance between the primary and secondary windings. ωr , J , B,
and TL are the rotor angular speed, motor inertia, friction coefficient, and load torque, respectively.
ܼ௤ௗ ൌ
‫ۏ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ێ‬
‫ۍ‬‫ݎ‬ଵ ൅ ‫ܮ‬ଵ
ௗ
ௗ௧
‫ܮ݌‬ଵ߱௥ ‫ܯ‬ଵଶ
ௗ
ௗ௧
െ‫ܯ݌‬ଵଶ߱௥ ‫ܯ‬ଵ
ௗ
ௗ௧
‫ܯ݌‬ଵ߱௥
െ‫ܮ݌‬ଵ߱௥ െ‫ݎ‬ଵ ൅ ‫ܮ‬ଵ
ௗ
ௗ௧
െ‫ܯ݌‬ଵଶ߱௥ െ‫ܯ‬ଵଶ
ௗ
ௗ௧
‫ܯ݌‬ଵ߱௥ ‫ܯ‬ଵ
ௗ
ௗ௧
‫ܯ‬ଵଶ
ௗ
ௗ௧
െ‫ܯݍ‬ଵଶ߱௥ ‫ݎ‬ଶ ൅ ‫ܮ‬ଶ
ௗ
ௗ௧
‫ܮݍ‬ଶ߱௥ െ‫ܯ‬ଶ
ௗ
ௗ௧
‫ܯݍ‬ଶ߱௥
െ‫ܯݍ‬ଵଶ߱௥ െ‫ܯ‬ଵଶ
ௗ
ௗ௧
െ‫ܮݍ‬ଶ߱௥ ‫ݎ‬௥ ൅ ‫ܮ‬௥
ௗ
ௗ௧
‫ܯݍ‬ଶ߱௥ െ‫ܯ‬ଶ
ௗ
ௗ௧
‫ܯ‬ଵ
ௗ
ௗ௧
0 െ‫ܯ‬ଶ
ௗ
ௗ௧
0 ‫ݎ‬௥ ൅ ‫ܮ‬௥
ௗ
ௗ௧
0
0 ‫ܯ‬ଵ
ௗ
ௗ௧
0 ‫ܯ‬ଶ
ௗ
ௗ௧
0 ‫ݎ‬௥ ൅ ‫ܮ‬௥
ௗ
ௗ௧‫ے‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ۑ‬
‫ې‬
(5)
‫ݒ‬௤ௗ ൌ ሾ‫ݒ‬௤ଵ ‫ݒ‬ௗଵ ‫ݒ‬௤ଶ ‫ݒ‬ௗଶ ‫ݒ‬௤௥ ‫ݒ‬ௗ௥ሿ்
݅௤ௗ ൌ ሾ݅௤ଵ ݅ௗଵ ݅௤ଶ ݅ௗଶ ݅௤௥ ݅ௗ௥ሿ்
3.2. Steady-State Model
The steady-state analysis can be obtained by assuming that the machine is synchronized so
that the frequencies of the windings in the two axes are constrained by (7), allowing either positive or
negative sequence secondary (control) voltage. Maintaining this constraint enables power to flow
from one winding to another through the rotor circuit. In response to the stator fields, rotor currents

29
are induced at frequencies of ωpr and ωsr . The rotor field can induce emfs in the primary winding at
frequency ωp and in the secondary winding at frequency ωs only when ωpr = ωsr . Where
߱௣௥ ൌ ߱௣ െ ‫߱݌‬௥ and ߱௦௥ ൌ ߱௦ା
ି
൅ ‫߱ݍ‬௥ (6)
Equating both sides of Eq. (6), one obtains the motor speed as:
߱௥ ൌ
ఠ೛ ఠೞశ
ష
௣ା௤
(7)
Negative sign (−) is used for the motor speed below the synchronous speed and the positive
sign (+) is used for the motor speed above the synchronous speed. The steady-state voltage equations
can be obtained by replacing d/dt by jω in Eq. (5). The qd variables become phasors and these
phasors are related to symmetrical positive and negative sequence components [8–11]. Hence, the
steady-state equations may be written as
ܸଵ ൌ ሺܴଵ ൅ ݆ܺଵሻ‫ܫ‬ଵ ൅ ݆ܺଵଶ‫ܫ‬ଶ
‫כ‬
൅ ݆ܺଵ௥‫ܫ‬௥ (8)
௩మ
‫כ‬
ௌ
ൌ ቀ
ோమ
ௌ
൅ ݆ܺଶቁ ‫ܫ‬ଶ
‫כ‬
൅ ݆ܺଵଶ‫ܫ‬ଵ ൅ ݆ܺଶ௥‫ܫ‬௥ (9)
0 ൌ ൬
ோೝ
ௌ೛
൅ ݆ܺ௥൰ ‫ܫ‬௥ ൅ ݆ܺଵ௥‫ܫ‬ଵ ൅ ݆ܺଶ௥‫ܫ‬ଶ
‫כ‬
(10)
ܶ௘ ൌ
ଷ
ଶ
ܴ௘൫݆‫ܯ݌‬ଵሺ‫ܫ‬ଵ
‫כ‬
‫ܫ‬௥ሻ െ ݆‫ܯݍ‬ଶሺ‫ܫ‬ଶ‫ܫ‬௥ሻ ൅ 2݆ሺ‫݌‬ ൅ ‫ݍ‬ሻ‫ܯ‬ଵଶሺ‫ܫ‬ଵ
‫כ‬
‫ܫ‬ଶ
‫כ‬ሻ൯ (11)
The electromagnetic torque of Eq. (11) consists of three components:
• The first component is due to the interaction between the rotor circuit and the primary stator
windings.
• The second component is due to the interaction between the rotor circuit and the secondary stator
windings.
• The third component is due to the interaction between the two stator windings (namely the
synchronous torque).
Equation (11) is valid only for the BDFRM with cage rotor, but in case of cageless rotor, the
first and second components disappear.
Using the power winding voltage as a reference, the equivalent circuit voltages can be written
as:
ܸതଵ ൌ ට
ଷ
ଶ
ܸଵ݁௝଴
and ܸതଶ ൌ ට
ଷ
ଶ
ܸଶ݁௝ఉ
(12)
where V1 and V2 are the magnitudes of the actual power and control winding phase voltages. β is the
angle between the power and control winding voltages.
4. MODES OF OPERATION OF THE BDFRM
The modes of operation of the BDFRM may be classified according to the excitation of the
control winding into three modes of operation as follows.

30
4.1. Asynchronous Mode
This mode takes place when the primary winding is excited from the main supply with a
frequency fp, and the secondary winding is either open circuited or short-circuited. If the secondary
winding is short-circuited, currents are induced and these currents interact with the primary flux
producing a torque in the rotor. The frequency of these induced currents decreases from fp when the
rotor at standstill to zero at the synchronous speed of Ns = 60fp/(p + q).
4.2. Synchronous Mode
This mode takes place when the primary winding is fed from the main supply and the
secondary winding is connected to a DC supply. For a DC excitation, the common and practical
connection of two phases in parallel and one phase in series is used. Also, this mode can take place
when the two sets of the stator winding are excited from two separate sources of different
frequencies. Synchronous operation is established when the frequencies of the induced current in the
rotor produced by the two rotating fields of the stator windings become identical. Once synchronous
operation is established, shaft speed becomes independent of load conditions unless a serve
disturbance occurs. Synchronization can also be achieved if a set of low frequency, negative
sequence AC voltage is applied to the 2-pole winding. In this case, the 2-pole frequency is slowly
ramped up, with the 2-pole voltage. The voltage is applied in such a way that a constant V/Hz ratio is
maintained. Once the machine is running synchronously, the applied voltage on the 2-pole winding
can be reduced to a substantially lower level without losing synchronism. This is a practical
importance in certain applications since reducing the excitation voltage means reducing the rating
requirements of the power inverter and hence the cost.
4.3. Supersynchronous Mode
This mode can be defined as the speed above the synchronous speed of the 6-pole winding
field. This mode takes place when the primary winding is connected to the main source and the
secondary winding is fed from an inverter with inverting the phase sequence of the secondary
winding current.
5. SPEED CONTROL
Unfortunately, speed control of the BDFRM did not receive more attention from the
researchers . Speed control of the BDFRM can be successfully achieved using field oriented control
(FOC) technique which can be applied to either a 6-pole winding or a 2-pole winding depending on
the selection of the transformation [22]. The reference frame used for vector control is ω = ω1. Under
this condition the primary equation is in the frame ω1, and the secondary equation is in the frame ω2.
The electromagnetic torque can be re-written in the following form [17]:
ܶ௘ ൌ
ଷ
ଶ
ሺ‫݌‬ ൅ ‫ݍ‬ሻ
ெభమ
௅భ
൫ߣௗଵ݅௤ଶ ൅ ߣ௤ଶ݅ௗଶ൯ (13)
where p, q are the pole pair number of the two stator windings, respectively. Hence, one can
further manipulate Eq. (13) to get an expression in terms of the primary fluxes and secondary
currents. This expression is particularly useful since the secondary currents are the variables one has
control over using an inverter, and the primary fluxes are fixed by the voltage and frequency of the
main supply. Equation (13) can be further refined by using the frame ω1 and aligning the primary
reference frame so that it lies along the primary flux vector. The primary flux vector can be written
as

31
ߣଵ ൌ ߣௗଵ ൅ ݆ߣ௤ଵ (14)
Equation (14) means that we have defined away the λq1 flux component and therefore Eq.
(13) can be simplified to:
ܶ௘ ൌ
ଷ
ଶ
ሺ‫݌‬ ൅ ‫ݍ‬ሻ
ெభమ
௅భ
൫ߣଵ݅௤ଶ൯ (15)
where λ1 is the magnitude of the primary flux vector. Equation (15) forms the basis for vector
control of the BDFRM. It could be observed that the torque can be controlled by ݅௤ଶ, while λ1 is a
constant related to the main supply conditions. Therefore, it has independent control of the torque. It
should be noted that the secondary currents are measured relative to the primary reference frame.
Therefore, ݅௤ଶ is the q-axis component of the secondary winding current. The block diagram of the
implemented FOC is given in Figure 2. The scheme consists of an outer speed feedback loop and an
inner current loop. The control signals ݅ௗଶ
‫כ‬
and ݅௤ଶ
‫כ‬
are proportional to the flux and torque commands,
respectively. Consequently, ݅ௗଶ
‫כ‬
is the field component of the control winding, while ݅௤ଶ
‫כ‬
is
Figure 2. Block diagram of the implemented FOC.
the torque component of the control winding current. The unit vectors cos θ2 and sin θ2 are calculated
from the information of rotor position as: θ2 = θ1−(p+q)θr , where θ2 is the secondary current angle,
θ1 is the primary flux angle, and θr is the rotor angle. The flux component of current is determined as

32
a function of the desired rotor flux and is maintained constant. The torque component of current is
derived from the speed control loop. The actual motor currents are compared with its reference
waveforms in a hysteresis controller. The output of the hysteresis controller is used to control the
inverter switching devices such that the error between the motor actual and reference is acceptable.
The indirect vector control gives the advantage of fast transient response because of the linear
relation between the torque and iq2. These facilitate the design of the drive for four-quadrant
operation.
The machine can be started according to the following four steps:
1) The machine is freely accelerated close to the synchronous speed of the primary winding;
2) The inverter is switched into the secondary windings;
3) Speed control is applied to bring the machine to the desired (below or above synchronous) speed;
and
4) Once the rotor speed is close to the synchronous speed, the speed control loop is activated.
6. SIMULATION RESULTS
Simulation results were obtained using available software package of Matlab/Simulink.
6.1. Run-Up Responses
Figure 3 shows the simulated responses of speed and stator currents during free acceleration
for the BDFRM when the 6-pole is connected to the main supply, while the 2-pole winding was
short-circuited. It can be noted that the responses of the BDFRM are similar to those of conventional
8-pole induction motor runs up to a steady state speed, which is less than 1000 rpm.
(a)
(b) (c)
Figure 3. Run-up responses when the 6-pole winding is connected to the main source and the 2-pole
is short-circuited. (a) speed versus time; (b) primary current versus; and (c) secondary current time
versus time

33
Figure 4 shows the simulated run-up responses of speed for the BDFRM when the 6-pole
winding is connected to a 60 V, 50 Hz power supply and the 2-pole winding was open-circuited. It
can be seen from the results that the use of rotor cage winding with the BDFRM improves the run-up
response and this makes the machine self-starting. The synchronous speed of the 6-pole winding is
approximately fixed (1000 rpm) by the current frequency in the 6-pole main winding. The responses
are similar to those of conventional 6-pole induction motor runs up to a steady-state speed of 1000
rpm.
Figure 5 shows the simulated run-up responses of the motor during DC synchronization.
Initially the machine is running steadily in the singly fed induction mode. Synchronization begins
when a set of DC voltage (18 V DC) was applied to the initially short-circuited 2-pole winding. It
can be noted from the results that the motor can pull into synchronism quickly and runs steadily at
750 rpm, yielding a good synchronization process. The responses are similar to those of a
conventional 8-pole synchronous motor.
Figure 6 shows the simulated speed-time response when the motor is running in the
Supersynchronous mode. It is clear from the figure that the motor speed
Figure 4. Run-up speed responses when the 6-pole winding is connected to the main source and the
secondary winding is open circuited
increases with increasing the secondary current frequency. This can be achieved when the two stator
windings having the same sequence.
Figure 7 shows the simulated speed-time response when the motor is singly-fed from the 6-
pole winding under (V/Hz) control. In such a case, the 2-pole winding was left open. Base voltage
and frequency are taken to be 60 V and 50 Hz, respectively. When the conventional PWM inverter
drives the line-start BDFRM, the terminal voltage can be changed easily for high efficiency
operation.
Figure 8 shows the simulated speed-time response when the motor is singly-fed from the 2-
pole winding under (V/Hz) control. Base voltage and frequency are chosen to be 120 V and 16.67
Hz, respectively. In this case, the 6-pole winding is left open. It is noticed from Figure 9 that motor
speed reached 1000 rpm, while if the base frequency was chosen to be 50 Hz, then the speed will
reach 3000 rpm.

34
Figure 5. Run-up speed responses for a synchronous mode of operation
Figure 6. Run-up responses for a Supersynchronous mode of operation
Figure 7. Run-up speed response for the 6-pole winding under (V/Hz) control when the 2-pole
winding is open-circuited

35
Figure 8. Run-up speed response for the 2-pole winding under (V/Hz) control at secondary current
frequency 16.67 Hz and the 6-pole winding is left open
Figure 9 shows the rotor speed response when the drive is subjected to a step increase in the
reference speed from 1000 rpm to 1500, 1800, and then 2400 rpm, respectively. It can be seen from
the results that the actual speed of the machine overlaps the command speed, showing a perfect
speed tracking. For Supersynchronous speeds, the sequence of the secondary winding must be
inverted with increasing the input command of the 2-pole winding. Therefore, any desired speed can
be achieved by increasing the step in reference speed.
Figure 9. Speed versus time response to step increase in the reference speed
Figure 10 shows the speed and secondary current responses when the drive is subjected to a
step decrease in the reference speed from 1500 rpm to 1200, 900, 600, and then 300 rpm,
respectively. It is clear from the results that the actual speed of the machine follows the command
speed showing a good speed tracking.

36
Figure 10. Speed versus time response to step decrease in the reference speed.
Figure 11 shows the simulated speed and secondary current responses of the drive system
when a step change in the load occurs while the machine was running at a steady speed of 600 rpm.
It can be noticed from the figure that the speed response increased and then decreased so that it could
be returned back to its steady-state value after removing the load. On the other hand, the secondary
current is decreased to the no-load value. In general, the proposed controller exhibits a good transient
response and high control accuracy with the BDFRM. The controller also provides convenience for
tuning control parameters.
Figure 11. Speed and secondary current responses during a sudden change in the load.
(a) speed versus time; (b ) secondary current versus time.

37
7.2. Steady-State Performance
Steady-state performance predictions can be obtained using the steady-state model presented
in Section 3.2. In order to examine the validity of the model, simulation of the steady-state
performance of a 0.75 hp, 6/2-pole stator with a 4-pole reluctance rotor machine was used. The self
and mutual inductances of the BDFRM can be determined analytically in standstill condition of the
machine as [17]:
‫ܮ‬ଵ ൌ ඥሺܸଵ ‫ܫ‬ଵ⁄ ሻଶ െ ሺܴଵሻଶ /߱ଵ (16)
‫ܯ‬ଵଶ ൌ ቀ
௏మ೚
ூభ
ቁ ߱ଵൗ (17)
where V1 and I1 are the phase voltage and current are applied to the 2p-pole winding, and
V2o is the measured open-circuit phase voltage of the 2q-pole winding.
In a similar way, the self-inductance L2 and mutual inductance M21 can be determined. It
should be noted that the self-inductance and mutual inductance are dependent on the rotor position.
Figure 12 shows the measured self-inductance and mutual-inductance curves versus the rotor
position angle of the BDFRM. For the sake of clarity, only the inductance of one phase for the 6-pole
winding and one phase for the 2-pole winding is displayed. The results show that the self-inductance
and mutual inductance of the primary and secondary windings do not have much difference.
Figure 13 shows the variation of the primary winding power factor angle as a function of the
control voltage at different values of the secondary current frequency. It can be seen from Figure 14
that the machine has the ability to control the primary power factor from leading to lagging via the
secondary voltage and its frequency
Figure 14 shows the variation of the primary power factor as a function of the control voltage
at different values of the secondary current frequency. The results show that the power factor can be
improved by varying the secondary voltage. Notice that the primary power factor improves reaching
its maximum value at Vs = 40 V when the secondary winding becomes fully responsible for the flux
production. Behind this value, the power factor decreases towards zero as the primary winding is
generating large amounts of reactive power into the grid, this being taken by the secondary winding
from the inverter.
Figures 15 and 16 show the variations of primary and secondary stator currents as a function
of the secondary control voltage at different values for the 2-pole winding current frequency. It is
noticed that the secondary winding currents increase with increasing the control voltage. However, it
is observed that the primary stator current of a BDFRM exhibits a characteristic of a V curve when
the control voltage is increased. This unique feature can be used successfully to improve the power
factor of the BDFRM. The minimum power winding currents, which correspond to the highest power
factors possible, is evident. The similarity between the V curves of a BDFRM and those of a
conventional synchronous motor is observed.

38
Figure 12. variation of inductances with rotor position angle

39
Figure 13: variation of the primary winding power factor angle with control voltage
Figure 14: variation of the primary power factor with control voltage

40
Figure 17 shows the variation of the overall power factor of the machine as a function of the
control voltage at different values of the secondary current frequency. The results show that the
overall power factor of the BDFRM improves reaching its maximum value at Vs < 20 V when the
primary and secondary windings are responsible for the flux production.
Figure 15. Variation of the primary winding current with control voltage
Figure 16. Variation of the secondary winding current with control voltage

41
Figure 18 shows the variation of the efficiency as a function of the control voltage at different
values of the secondary current frequency. It can be noticed that the efficiency of the BDFRM
improves with increasing of both control voltage and secondary current frequency.
The symbols shown in Figures 14 through 19 are related as:
+ for
௙ೞ
௙೛
ൌ 0.01 * for
௙ೞ
௙೛
ൌ 0.1 - for
௙ೞ
௙೛
ൌ 0.15
Figure 17. Variation of the overall power factor with control voltage
Figure 18. Variation of the efficiency with control voltage

42
8. CONCLUSION
A successful analytical design of a BDFRM has been developed and tested in different modes
of operation. It is designed to operate at both line and variable frequencies. Moreover, performance
analysis of such a machine has been given. A comprehensive set of results for the digital simulation
of the run-up and steady-state performances of such type of motors has been extensively presented.
the results showed that the BDFRM has performance characteristics similar to those of a non-salient
pole synchronous machine. Effects of both voltage and frequency of the control winding on the
machine performance have been investigated. It was noticed that the rating of the control winding
and the inverter is a function of the required operating conditions of speed and power factor of the
power winding. Simulation results have been illustrated improved system performance under V/Hz
control.
A speed control method for the BDFRM was developed and successfully tested. The main
advantage of the proposed drive is its improving capability to operate at any desired speed including
standstill condition. The proposed controller exhibits a good transient response and high control
accuracy with the BDFRM. The controller also provides convenience for tuning control parameters.
A This article conclusively proves that the BDFRM still needs a lot of research and
improvement for the practical use. Therefore, additional analysis to account for core and stray load
losses in the BDFRM is being under taken.
REFERENCES
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