Performance Characterisation of Brushless Doubly-Fed Generator

Abstract

This paper presents the steady-state performance of the brushless doubly-fed machine operating as a generator. The performance characterization includes the generator efficiency, power factor and output power. The equivalent circuit model is used to represent the performance and the predictions are verified experimentally. The experimental results shown in this paper were carried out on a 180 frame size BDFM with a nested-loop rotor.

Full text

Performance Characterisation of Brushless
Doubly-Fed Generator
Ehsan Abdi, Xiaoyan Wang, Shiyi Shao and Richard McMahon
Engineering Department, Cambridge University
9 JJ Thomson Avenue, Cambridge CB3 0DS, United Kingdom
Email: ea257@cam.ac.uk
Peter Tavner
School of Engineering, Durham University
South Road, Durham, DH1 3LE, United Kingdom
Abstract - This paper presents the steady-state performance of
the Brushless Doubly-Fed Machine operating as a generator. The
performance characterization includes the generator efficiency,
power factor and output power. The equivalent circuit model is
used to represent the performance and the predictions are veri-
fied experimentally. The experimental results shown in this paper
were carried out on a 180 frame size BDFM with a nested-loop
rotor.
Keywords - BDFM, Improved design, Equivalent circuit, Parameter
extraction, Performance characterisation.
I. INTRODUCTION
The Brushless Doubly-Fed Machine (BDFM) shows com-
mercial promise as both a variable speed drive and generator.
As a generator, it is particularly attractive for wind power gen-
eration as a replacement for doubly-fed slip-ring generators. A
wind turbine incorporating a BDFM will have higher reliabili-
ty and lower maintenance costs by virtue of the absence of
brush-gear. Studies have shown that problems with brush-gear
are a significant issue in wind turbine operation and reliability,
and that the problem will be more severe in machines de-
ployed offshore where there are stronger winds and accessibil-
ity is impaired. In addition, the BDFM offers a key advantage
as a variable speed drive in that it requires only a fractionally
rated converter.
The contemporary BDFM is a single frame induction ma-
chine with two 3-phase stator windings of different pole num-
bers, and a special rotor design. Typically one stator winding
(the power winding) is connected to the grid and the other (the
control winding) is supplied with variable voltage at variable
frequency from a converter [1,2]. Recent research on the
BDFM has led to significant improvements in the design of
the machine and hence better performance in terms of output
power, torque density and other steady-state measures for a
machine of given frame size [3,4]. Considerable research has
also been directed towards the control of the machine which is
important as the machine is not stable in open loop at all
speeds. Several control methods have been proposed involv-
ing various degrees of sophistication [5-9].
To date, no BDFMs are in commercial service. It is, there-
fore, desirable for machine manufacturers to have a quantita-
tive assessment of the performance of the new technology and
to understand the economic benefits. Relatively little attention
has been paid to assessing the performance of the machine in
terms of output power, efficiency and power factor as few
prototype machines have been constructed.
The authors have devised an improved design for the rotor
which has been fitted into a 180 frame size BDFM to give it
increased torque capability. This paper presents the perform-
ance characterisation of the machine with regards to its output
power, torque density and efficiency. The experimental results
are compared with the predictions from the equivalent circuit
model for which parameters were extracted experimentally.
The parameters for the equivalent circuit were also calculated
from the machine geometry.
II. BDFM OPERATION
The BDFM normally operates in the synchronous mode
[2]. The shaft speed is independent of the machine torque and
only depends on the supply frequencies to the two stators, i.e.
the variable output frequency from the converter if one stator
is supplied from the mains. The shaft speed in rpm is given by:
21
21
60 pp
ff
N+
+
= (1)
Where p1 and p2 are the pole pair numbers of the two
windings and f1 and f2 are the grid and converter output fre-
quencies respectively. The BDFM is characterized by the so-
called natural speed obtained by setting f2 zero.
The BDFM also has asynchronous modes of operation
where the shaft speed is dependent on the loading of the ma-
chine, as well as the supply frequency. The machine can be
operated as a self-cascaded induction machine by exciting
stator 1 or stator 2 and shorting the other winding. A cascade
induction machine formed from p1 and p2 pole pair induction
machines has characteristics which resemble an induction ma-
chine with p1 + p2 pole pairs. This mode will be referred to as
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the cascade mode and can be used for estimating the machine
parameters using curve-fitting methods [10-11]. It can also be
used for starting the machine as a motor to avoid the need to
use a bi-directional converter for the control winding [12].
III. EQUIVALENT CIRCUIT MODEL
The equivalent circuit model is a simple method of
representing the steady-state performance of the BDFM [10].
Since the meaning of the parameters has a clear physical inter-
pretation, the model can be very helpful for understanding the
design and optimisation of the machine. The equivalent circuit
model offers a straightforward way of calculating the efficien-
cy, power factor and other steady-state measures of the ma-
chine to a practical accuracy.
One form of the equivalent circuit for the BDFM is shown
in figure 2 where all the parameters are referred to the power
winding [10]. The equivalent circuit shown in figure 2 does
not include the harmonics effects and iron losses. s1 and s2 are
the power and control windings slips and are defined as:
1
11
1
ω
ω
ω
r
p
s−
∆ (2)
2
22
2
ω
ω
ω
r
p
s−
∆ (3)
where
ω
1 and
ω
2 are angular frequencies of the supplies to the
power and control windings respectively, and
ω
r is the rotor
mechanical angular velocity.
Figure 1. BDFM operation
I1R1j
ω
1L1
j
ω
1Lm1
V1
,
ω
1
j
ω
1Lrj
ω
1L2
Rr/s1R2
s2
s1I2
s2
s12
VV 1
rV2
rj
ω
1Lm2
Ir
Figure 2. Equival ent circuit model for the BDFM
The parameters of the equivalent circuit model can be cal-
culated from the machine geometry using the method pre-
sented in [9]. A coupled-circuit model was presented by [9]
for a general class of BDFMs. The parameter values were cal-
culated from the machine physical dimensions. The coupled-
circuit model was transformed into the d-q reference frame
and then into symmetrical sequence components, in order to
derive the equivalent circuit model. The major contribution
made by [9] was to propose a technique of reducing the order
of the rotor states, hence representing the equivalent circuit for
the BDFM in a simple form. The technique was implemented
on a nested-loop design rotor and shown to have good accura-
cy.
The accuracy of these calculations depends on having good
physical data for the machine. There are particular problems
with the accurate measurement of the air-gap, which directly
affects the mutual couplings in the models. In addition, it is
hard to obtain precise estimates of certain parameters such as
the leakage reactances of end-windings.
The equivalent circuit parameters can also be extracted
from experimental tests using curve-fitting methods as de-
scribed in [10, 11]. Using the parameter values estimated from
experimental tests has led to more accurate predictions [11].
IV. DESIGN IMPROVEMENTS
The authors have recently incorporated a new nested-loop
rotor with improved design. In the new design, special care
has been taken into account in optimising the electric and
magnetic loadings of the machine. In previous work by the
authors [2,10], the effects of magnetic saturation were evident
considerably below the nominal stator voltages. There were
significant saturation effects when the machine was operating
at nominal voltages on the power and control windings includ-
ing excessive magnetising currents and reduced efficiency. In
the previous rotor, iron saturation appears in the rotor teeth
well before the stator teeth (above a magnetic den sity ( B) of
0.35T).
The configuration of the rotor loops in the new nested-loop
rotor is the same as the previous design [2], but the slot and
tooth areas are re-balanced to improve the magnetic loading to
commercially available levels whilst keeping sufficient elec-
tric loading to match that of the stator [13]. The optimisation
was performed for the generating operation. The 4-pole
winding was used as the power winding with a fixed voltage
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of 240 Vrms. The objective in the optimisation was to obtain
maximum power output at 750 rpm.
The rated operating conditions at 750 rpm of the optimised
generator are shown in table 1 [13]. The machine performance
is predicted by the equivalent circuit [2]. B is the air gap spe-
cific magnetic loading, 1
J and 2
J are stator 1, stator 2 specific
electric loadings, and r
J is the rated current density of rotor
bars.
The new rotor design has enabled the machine to operate at
a higher torque density with greater efficiency and power fac-
tor. The performance of the machine is presented in the fol-
lowing section. The rotor is shown in figure 3.
Table I. Rated operating conditions for the optimised D180 BDFM at 750 rpm
B
(T)
1
J
(kA/m)
2
J
(kA/m)
r
J
(A/mm2)
T
(Nm)
Pout
(kW)
η
(%)
0.62 13.3 19 5.4 112 7.6 85
Figure 3. The new nested-loop rotor with improved design
Figure 4. Protot ype BDFM machine (left) on test rig with torque
transducer and DC load machine (right)
Table II. Prototype machine specifications
Parameter Value
Frame size
Stator 1 pole-pair s
Stator 2 pole-pair s
Stator 1 rated current
Stator 2 rated current
Rotor design
D180
2
4
8A
8A
‘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 1/6 of
the circumference, for details see [2].
V. PERFORMANCE CHARACTERISATION
Table 2 gives the physical data for the BDFM used
throughout this and the work described in [2-4,9-12]. The ma-
chine is shown in figure 3 in the experimental rig.
A DC machine is mechanically coupled to the BDFM in
order to provide required test conditions for operation in gene-
rating, or motoring, modes.
A. Magnetising Characteristics
Figure 5 shows the magnetisation characteristics obtained
by running the BDFM as an induction machine with no-load.
To minimise the error in the no-load test arising from the rotor
currents, the DC machine was used to run the machine at syn-
chronous speed. As can be seen in the figure, there is no sign
of undue saturation up to normal working flux density. The air
gap flux density when either power or control winding is ex-
cited at 400 Vrms is about 0.52 T. Note that in the induction
mode of operation, the air gap magnetic field only couples the
power or the control winding field.
The magnetic field in the machine is complex, being estab-
lished by the balance of the MMFs in the power and control
windings and the induced MMF in the special rotor winding.
In [2], it has been shown that the specific magnetic loading of
the BDFM can be approximated by the following:
2
2
2
1pp BBB += (4)
where 1p
B and 2p
B are calculated using the conventional
definition for the specific magnetic loading given by:
rms
pp BB 11
22
π
= (5)
rms
pp BB 22
22
π
= (6)
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B. Parameter Estimation
In order to extract machine parameters, experimental tests
were performed in the cascade and induction modes of opera-
tion [2] and the parameters were obtained using a curve-fitting
method [10,11]. The tests were performed at two voltage le-
vels of 120V and 240V in order to assess the effects of iron
saturation on the machine parameters.
The algorithm applies the curve fitting optimisation to
measured quantities including torque, speed, stator and rotor
currents, and power fact ors obtained from the tests, and ex-
tracts one set of parameters [10,11]. The stator winding resis-
tances were obtained from DC measurements at working tem-
perature.
Table III. Equivalent circuit parameters
Calculated
from geometry
Experimentally
extracted at 120V
Experimentally
extracted at 240V
R12.31Ω 2.42 Ω 2.42 Ω
L1 4.5mH 4.9mH 4.7mH
Lm1 345mH 390mH 380mH
R23.89 Ω 4.04 Ω 4.04 Ω
L2 11.6mH 12.5mH 11.5mH
Lm2 350mH 420mH 400mH
Rrҁ1.64Ω 1.8Ω 1.8Ω
Lrҁ37.1mH 40mH 38mH
N1/N2 0.718 0.724 0.724
Figur e 5. Magnetising characteristics of the machi ne
The estimated parameter values are shown in table 3 and
are compared with the values calculated from the machine
geometry [9]. The estimated parameter values at 120V and
240V are in close agreement. This confirms the fact that the
saturation effects are not significant over the operating voltage
range.
C. Steady-State Characteristics
The stator power (4-pole) winding is supplied from a con-
stant voltage and frequency supply at 240V (phase) and 50Hz.
The stator control (8-pole) winding is fed with a variable vol-
tage, variable frequency inverter. The machine is controlled
using a closed-loop phase angle control algorithm.
In order to characterise the generator performance, the
BDFM was run at a speed of 550rpm with the prime mover
torque changing from no-load to just under the full load. The
control system aimed at keeping the power factor at a desired
level for a wide range of input torque. The experiments were
carried out at power factors of 0.72 and 0.8 lagging. The gene-
rator efficiency and the power winding power factor are plot-
ted in figure 6 and 7. Results are shown from experiments
overlaid with predictions from the equivalent circuit.
D. Discussion
-The rated torque of the optimised BDFM is 112 Nm as
shown in table 1. This is equivalent to about 80% of the
rated torque of a 4-pole induction machine with the same
frame size. It is believed that this is the first BDFM design
that has achieved an output torque consistent with the theo-
retical predictions in [2] and is comparable with a commer-
cial induction machine.
-The efficiency of the optimised BDFM is in the order of 75-
80%. This is approaching with the efficiency of induction
machines of this size (typically 85-90%). It should be noted
that the stator winding has not been fully optimised.
-As can be seen in figures 6 and 7, efficiency falls with im-
proving power factor, as expected from [2]. This is due to
the fact that the power factor is improved by increasing the
excitation on the control winding which introduces greater
losses in the control winding and therefore reduced effi-
ciency.
-The predictions for the efficiency from the equivalent cir-
cuit are higher than obtained from the experiments. This is
most likely due to the iron and other mechanical and win-
dage and, harmonics losses being neglected by the equiva-
lent circuit model. In addition, the limitations of the mea-
surement apparatus contribute to the discrepancies.
-Optimisation has been performed based on the existing sta-
tor lamination geometry and air gap diameter. However, a
further increase in power output may be achieved if the air
gap diameter was allowed to vary. To match the given elec-
tric and magnetic loadings of the stator, the volume of the
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nested-loop rotor can generally be smaller than induction
rotors. This may, at least in part, compensate for the penalty
of the machine rating [13].
-BDFMs are relatively slow-speed machines. Nevertheless,
both 4/8 and 2/6 BDFMs with natural speeds of 500 and
750 rpm promise significant application as a replacement
for doubly-fed slip-ring induction generators (DFIGs) in
wind turbine applications. The BDFM offers a significant
advantage of brushless operation whilst still being doubly-
fed, eliminating the need for brush gear. In addition, the
BDFM requires a gearbox with lower gear ratio as com-
pared to the DFIG, enabling the use of a two-stage rather
than a three-stage gearbox as used by the DFIG. Both these
effects increase the reliability of the gearbox and generator
and reduce the cost and weight of the gearbox.
Figure 6. Efficiency and power factor of the BDFM against variation
in shaft torque when running at 550rpm as a generator. The control
system aims to keep the power factor at 0.8 for a wide range of shaft
torque.
Figure 7. Efficiency and power factor of the BDFM against variation
in shaft torque when running at 550rpm as a generator. The control
system aims to keep the power factor at 0.72 for a wide range of shaft
torque.
VI. CONCLUSIONS
The steady-state performance of a D180 frame size BDFM
with an optimised nested loop rotor operating as a generator
has been presented. The new rotor allows the machine to pro-
duce a torque of up to 110 Nm at 550 rpm compared to the 65
Nm reported in [2], representing a major advance in the design
of the BDFM. The experimental results are compared with
predictions from an equivalent circuit with satisfactory agree-
ment.
The authors’ intention is to study the machine losses in a
greater detail to be able to quantify the discrepancies between
the theoretical predictions and experimental tests. Moreover, a
larger BDFM is being built intended for fitting in a 20kW
wind turbine.
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