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Application of Real-Time Rotor Current

Measurements Using Bluetooth Wireless

Technology in Study of the Brushless Doubly-Fed

(Induction) Machine (BDFM)

Ehsan Abdi-Jalebi (ea257@cam.ac.uk) and Richard McMahon

Engineering Department, University of Cambridge, Cambridge, United Kingdom

Abstract— The Brushless Doubly-Fed Machine (BDFM) shows

commercial promise as a variable speed drive or generator.

However, for this promise to be realised, the design of the machine

must be improved. Accurate machine modelling is therefore

required for design optimisation. The measurement of rotor bar

currents is of considerable beneﬁt in the process of developing

an accurate machine model. The authors present a system of

measuring rotor bar currents in real time using a Rogowski

coil to transduce the signal and recently available Bluetooth

technology to transmit the data from the moving rotor to a

standard PC. A coupled-circuit model has been developed for

the BDFM to predict its dynamic and stead-state performance.

The model has been veriﬁed using the proposed measurement

system. The experiments were carried out on a frame size 180

BDFM with a nested-loop rotor design.

I. INTRODUCTION

Potential applications for the BDFM have been the subject

of research over the last decade. The machine has attracted

attention as a variable speed drive [1] and as a generator [2] in

applications where the prime mover speed is variable, such as

in wind turbines. The rating of the inverter need only be a frac-

tion of rating of the machine so there are potential savings in

system cost. In wind turbines, the BDFM is being considered

as an alternative to the doubly fed induction generator as using

the BDFM eliminates the problems associated with brush gear,

making the BDFM particularly attractive for offshore wind

turbines.

The BDFM comprises two stators wound for different, non-

coupling, pole numbers. The rotor is designed to couple both

ﬁelds. In the normal mode of operation, one stator is connected

to a source of ﬁxed frequency, normally the mains or grid,

and the other is fed with variable voltage at variable frequency

from a converter. The machine operates in a synchronous mode

and the shaft speed has a ﬁxed relationship to the two supply

frequencies. Details of machine construction and operation can

be found in [3].

The design of the rotor is critical to good performance [4].

The nested loop type of rotor is the most widely used but the

analysis of its performance is not straightforward. The ability

to make direct measurements of rotor currents would help to

build conﬁdence in predictions from theory. Measurements of

rotor currents would also facilitate the acquisition of parameter

values for the equivalent circuit of the machine. In previous

work, parameters have been obtained from terminal measure-

ments at the two stators but it was not possible to obtain

explicit values for all inductances [5]. The availability of rotor

quantities in principle allows separation of these inductances.

Furthermore, Roberts et. al. [6] presented a control strategy

which requires knowledge of the rotor bar currents in real-

time, so monitoring these currents during operation is of

considerable advantage.

Rotor bar currents are difﬁcult to measure. The design of a

system to measure these currents is complicated because the

rotor is moving and because of strong electro-magnetic ﬁelds

in the machine air gap and end region. In the case of the

BDFM, one winding will normally be fed from an inverter

and this will introduce interference at frequencies related to

the switching frequency of the inverter. Apart from the obvious

difﬁculty of extracting data signals from a moving rotor, the

centripetal acceleration acting on the transducer is around

1000m/s2at 1000rpm.

The authors have developed a system of measuring rotor

bar currents directly with Rogowski coils, using the Bluetooth

wireless technology to transmit the signal from the moving

rotor back to a computer for logging and analysis [7], [8].

Bluetooth is one of a range of recently introduced protocols

developed for the transmission of digital data. Measurements

of rotor currents have been made to conﬁrm predictions of

rotor currents from the coupled-circuit model of the BDFM

[9].

Table I gives the physical data for the machine used

throughout this and the work described in [3]–[9]. The BDFM

is shown in ﬁg. 1 in the experimental rig.

II. MEASUREMENT SYSTEM DESIGN AND SPECIFICATION

The measurement system comprises the sections shown

diagrammatically in ﬁg. 2. Full details are given in [7].

A. Rogowski Transducers

A Rogowski coil is a low noise, air-cored current transducer.

The Rogowski current transducer was chosen for the following

reasons [7]:

1-4244-0365-0/06/$20.00 (c) 2006 IEEE

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TAB LE I

PROTOTYPE MACHINE SPECIFICATIONS

Parameter Value

Frame size D180

Stator 1 pole-pairs 2

Stator 2 pole-pairs 4

Stator slots 48

Rotor slots 36

Rotor design

‘Nested-loop’ design consisting of 6 ‘nests’ of 3

concentric loops of pitch 5/36,3/36 and 1/36

of the rotor circumference. Each nest offset by

1/6of the circumference, for the details see [10].

Fig. 1. Prototype BDFM machine (left) on test rig with torque transducer

and DC load machine (right)

•It is air-cored and therefore, a small cross-section is

possible. This is necessary as the coil is to be wrapped

around a rotor bar.

•It can easily be made in an openable form, so it can be

retro-ﬁtted to a bar.

•Linear characteristic over a wide measuring range.

•High level of immunity to electromagnetic interferences.

High-performance, low-cost Rogowski transducers were

constructed using the technique described in [11]. Fig. 3 shows

the Rogowski coils installed on the rotor.

B. Bluetooth Wireless Technology

Bluetooth wireless standard was used for data communi-

cation between the instrumentation system installed on the

rotor and a computer. It uses a 2.4GHz radio link for short-

range connections. Bluetooth was chosen for this application,

in preference to other wireless standards, because of its high

Integrator Filter A/D Bluetooth

I

PC

Bluetooth

Fig. 2. Functional block diagram of the rotor instrumentation system

Fig. 3. Rogowski coils installed on the nested-loop prototype rotor to measure

end-ring currents

interference immunity, low cost, and ease of implementation

[7]. BlueCoreTM RS232 cable replacement modules from

Cambridge Silicon Radio (CSR) were used.

C. Electronic Circuitry

The circuitry is shown in ﬁg. 4. The system is supplied by

three rechargeable AA cells. Recharging in situ is possible via

connections brought out through a hole in the shaft.

D. System Speciﬁcation

The instrumentation system was constructed to measure

rotor bar currents for the BDFM. The measurement setup

was designed to measure bar currents up to 3000Apeak-to-

peak, with a resolution of 0.5A, from 1Hz to 100Hz.This

frequency range is required for the BDFM as the machine

runs with a wide range of slips in normal operation, unlike

a standard induction motor. A high signal to noise ratio

(SNR) of 50dB was achieved due to careful design and

construction of the transducer and its accompanying circuitry

Fig. 4. Two electronic boards constructed for instrumenting the BDFM

rotor. Left: Electronic circuitry mounted on the rotor shaft. Right: Electronic

circuitry designed for logging data

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i3l

i2

l

i1l

i1r

i2r

i3r

i4r

Fig. 5. End-ring and bar currents in a nested-loop rotor design

[11]. In practice, data rates of about 115.2Kbps were rou-

tinely achieved between the rotor mounted transmitter and the

receiver, approximately 5mdistant.

The nested-loop rotor consists of 36 slots, and as the

prototype machine has stator windings with p1=2and p2=4

poles respectively, the rotor has S=p1+p2=6nests

terminated with a common end ring at one end only [4]. Each

nest is allocated 6 slots. Therefore, three concentric loops are

housed within each nest.

The Rogowski coils were installed to measure the end-ring

currents as shown in ﬁg. 3. Seven coils were used to acquire six

loop currents in two consecutive nests and the current ﬂowing

between those nests. The relationship between the end-ring

and loop currents may be simply derived from ﬁg. 5, and is

given by

il1=ir1−ir2

il2=ir2−ir3

il3=ir3−ir4

(1)

III. BDFM COUPLED-CIRCUIT MODEL

A generalised coupled-circuit model for a wide class of

BDFM was developed by Roberts in [9]. The model can

accurately predict the transient performance of the machine.

It includes the effect of all space-harmonic components of

inductance parameters. The proposed model is straightforward

to implement on a computer, and allows a general interface

for different machine windings or rotor designs.

The general electrical machine coupled-circuit equation is

v=Ri +ωr

dM

dθr

i+Mdi

dt (2)

where vand iare the voltage and current vectors, and Rand

Mare the resistance and inductance matrices. ωrand θrare

respectively the rotor angular speed and position.

The torque generated by an electrical machine can be

determined by considering instantaneous power transfer in the

system [12] and is given by

Te=1

2iTdM

dθr

i(3)

The mechanical differential equation is

Jdωr

dt =Te−Tl(4)

where Jis the combined moment of inertia of the machine

and load, and Tlis load torque.

The full dynamic equations may therefore be written as

d

dt

i

θr

ωr

=

−M−1Ri +ωr

dM

dθri

ωr

1

2JiTdM

dθri

+

M−1v

0

−Tl

J

(5)

In the BDFM, it is convenient to partition vand iinto stator

1, stator 2, and rotor quantities, noting that the rotor voltage

will always be zero. The BDFM coupled-circuit equations can

be therefore written as

vs1

vs2

0

=

Rs100

0Rs20

00Rr

+ωr

00

dMs1r

dθr

00

dMs2r

dθr

dMT

s1r

dθr

dMT

s2r

dθr0

is1

is2

ir

+

Ms10Ms1r

0Ms2Ms2r

MT

s1rMT

s2rMr

d

dt

is1

is2

ir

(6)

The torque equation from (3) and (6) is

Te=iT

s1iT

s2dMs1r

dθr

dMs2r

dθr[ir](7)

vs1,is1,vs2,is2∈R3×1are stator 1, stator 2 voltage and

current vectors. iris the rotor current vector. For the nested-

loop rotor with Nnests of Sloops, ir∈RNS×1.Rs1,

Rs2and Rrare respectively stator 1, stator 2 and rotor

resistance matrices. The calculation of resistance matrices is

straightforward and is presented in, for example [9].

The mutual inductance matrices Ms1,Ms2and Mrare all

constant as they link circuits which are not moving relative

to one another. The position varying parameters Ms1rand

Ms2rare rotor-stator 1 and rotor-stator 2 mutual inductance

matrices. For ease of implementation and to maximise running

speed, the position dependent parameters Ms1rand Ms2rand

their derivatives were computed off-line at one degree intervals

and then values interpolated online.

A generalised method of calculating the mutual inductance

matrices for the BDFM is presented in [9]. The method ﬁrst

calculates the ﬂux density due to unit current ﬂowing in a

single coil. It then uses this result to determine the mutual

inductance between any two coils in the machine. Since the

machine is made up of interconnected groups of coils, the self

and mutual inductance of the stator windings and rotor circuits

may be derived by summing the single coil elements.

The authors have therefore developed a coupled-circuit

model for the BDFM with a nested-loop design rotor. The

inductance and resistance matrices were calculated using MAT-

LAB. The model has been implemented in Simulink. A block

diagram of the implemented model is shown in ﬁg. 6.

IV. EXPERIMENTAL VERIFICATIONS

The coupled-circuit model can predict the actual waveforms

of voltages and currents in the BDFM, allowing both the

dynamic and steady-state performance to be considered. The

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Fig. 6. The BDFM coupled-circuit model implementation in Simulink

measurement system similarly enables the actual waveforms

of rotor bar currents to be observed. Comparisons are made

between predicted and measured current waveforms and fur-

ther comparisons are made in steady-state operation between

the magnitudes of predicted and measured currents. The tests

were performed at relatively low supply voltages in order to

avoid saturating the iron circuit.

A. Comparison of current waveforms

Experimental tests were carried out in the synchronous

mode of operation, the normal running mode and the one

for which the design of the machine is to be optimised

[3]. The machine 4-pole and 8-pole stator windings were

supplied at 90Vand 50Hz, and 170Vand 30Hz respectively.

The machine was operating at its synchronous speed, that is

800rpm. The mechanical torque applied to the machine shaft

was 30Nm.

Fig. 7 and 8 show the measured rotor loop currents with

the simulation results from the coupled-circuit model overlaid.

The currents in all loops of a nest have the same phase (see

ﬁg. 7). The loop currents of two consecutive nests have 2π

3

phase difference (see ﬁg. 8). This is in agreement with the

consideration of the nested-loop rotor with Nsets of Sloops

as NS-phase systems.

B. Comparison of current magnitudes in steady-state opera-

tion

The BDFM was run in steady state in the normal syn-

chronous mode and also in the cascade mode which is used

for parameter extraction purposes. A description of BDFM

operating modes is given in [3].

1) Synchronous operation: The machine 4-pole stator

winding was supplied from a constant voltage and frequency

supply at 90Vand 50Hz. The machine 8-pole stator winding

was fed with a variable voltage, variable frequency inverter.

However, the 8-pole supply frequency was ﬁxed to 30Hz

0 0.05 0.1 0.15 0.2 0.25

−800

−600

−400

−200

0

200

400

600

800

Time (s)

Rotor currents (A)

Experiments

Predictions

Fig. 7. Middle and inner loop currents within one nest for the nested-loop

rotor. The middle loop current clearly has a greater amplitude.

Fig. 8. Outer loop currents for two consecutive nests of the nested-loop

rotor.

throughout the experiment and therefore the synchronous

speed was 800rpm. The test was performed at a constant

torque of 30Nm. Fig. 9 shows the predictions made by the

coupled-circuit model overlaid with the experimental results.

2) Cascade operation: Two cascade tests over a wide speed

range were carried out: one with 4-pole winding supplied with

a constant 90Vrms, and 8-pole winding shorted, and one with

8-pole winding excited by a constant 110Vrms supply, and

4-pole winding shorted. All tests were performed at 50Hz

supply frequency. In order to limit currents to acceptable

values throughout the range of the machine rating, reduced

supply voltages were applied. The outer loop currents are

plotted against the rotor speed in ﬁg. 10.

V. C ONCLUSIONS

The paper presents the design and evaluation of the real time

rotor bar current measurement system which uses a Rogowski

coil as a current transducer and a Bluetooth wireless link to

transmit data back to the bench. The measurement system has

high accuracy, good immunity to noise, and low power con-

sumption. By using commercially available Bluetooth modules

the cost is moderate.

1560

60 80 100 120 140 160 180

0

100

200

300

400

500

600

8−pole stator supply (V)

Rotor loop currents (A)

Outer loop

Middle loop

Inner loop

Fig. 9. The rotor loop currents at synchronous mode of operation. Solid

lines are the coupled-circuit predictions and marks indicate the experimental

results.

The application to the BDFM shows the feasibility of the

approach, which may ﬁnd application in the wider ﬁeld of

electrical machines. The approach can also be used when

electrical isolation is required, as in high voltage machines.

Applying the system to the BDFM allows the rotor current

to be monitored. This is valuable both in verifying theoretical

predictions and in obtaining machine parameters for equivalent

circuits. The system has the potential to be part of a control

system of the type proposed in [6].

The measurement system was used to verify predictions of

rotor bar currents in the BDFM in the machine’s synchronous

and cascade modes of operation. The agreement between the

experimental and predicted results was good and within the

limitations of measurement accuracy.

ACKNOWLEDGMENT

The authors would like to thank Cambridge Silicon Radio

for their support and their kind provision of the Bluetooth

modules.

REFERENCES

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number combinations for brushless doubly fed machines as applied to

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0 500 1000 1500

0

100

200

300

400

500

600

Speed (rpm)

Outer loop current (A)

Experiments

Coupled−circuit

0 500 1000 1500

0

50

100

150

200

250

300

350

400

450

Speed (rpm)

Outer loop current (A)

Experiments

Coupled−circuit

Fig. 10. Rotor outer-loop current in the cascade mode of operation.

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