Available online at www.sciencedirect.com
Electric Power Systems Research 78 (2008) 399–408
A systematic approach to design and operation
of a doubly fed induction generator
Chad Abbey ∗ , Géza Joós 1
Department of Electrical and Computer Engineering at McGill University, Canada
Received 7 November 2006; received in revised form 21 March 2007; accepted 23 March 2007
Available online 7 May 2007
Abstract
The doubly fed induction generator (DFIG) is currently one of the most common topologies employed for wind turbine generators (WTGs).
The system has the benefit of a back-to-back voltage sourced converter (VSC) of reduced rating, due to its connection to the rotor windings. This
paper considers the impact of mechanical and electrical parameters on the kVA requirements of the two VSCs, which together with the dc link
capacitor serve as the rotor winding’s power supply. This topology is contrasted with alternatives utilizing a diode rectifier-voltage sourced inverter
pair and a set of design curves are generated. In addition to steady-state analysis, an operating strategy for reactive power allocation management
is proposed. The theoretical considerations are validated with results obtained from representation of the system in an electromagnetic transient
program.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Power electronics; Reactive power; Wind energy; Doubly fed induction generator
1. Introduction
The growth of wind energy has continued during the past
decade and renewed focus on alternative sources of energy has
contributed to its further development worldwide. In some cases,
the amount of wind generation has approached that of conventional technologies and the impact of wind on system stability,
operation and power quality can no longer be neglected. New
recommendations and utility standards require that wind parks
aid in voltage support and that turbines remain connected during
system disturbances [1,2]. This implies the need for advanced
control schemes requiring coordination of the wind park output
power and reactive power for support of the system voltage.
Amongst the types of large capacity WTGs, wound rotor
induction machines represent an important percentage. Here, the
back-to-back voltage sourced converters (VSCs) are connected
between the supply and the rotor windings. This facilitates inde∗ Corresponding author at: Department of Electrical and Computer Engineering, 3480 University Street, Rm. 633 McConnell Engineering Bldg., Montreal,
Quebec, Canada H3A 2A7. Tel.: +1 514 398 4667; fax: +1 514 398 4470.
E-mail addresses: chad.abbey@mail.mcgill.ca (C. Abbey),
geza.joos@mcgill.ca (G. Joós).
1 Tel.: +1 514 398 4667; fax: +1 514 398 4470.
0378-7796/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.epsr.2007.03.013
pendent control of the direct and quadrature components of the
stator current through the rotor-side, while realizing a reduction
in the ratings of the IGBT converters, as only a fraction of the
power produced by the machine circulates through this path.
Many researchers have demonstrated that this topology can be
effectively used to separately control the generator’s speed and
the delivered reactive power [3–9].
This paper considers the operating range of a doubly fed
induction generator (DFIG), applied as a WTG, with emphasis on the impact of operating strategy and design parameters
on the converter ratings, considered in part in Ref. [10]. The
wind characteristic, speed range, gearbox ratio and allocation of
reactive current between the two converters are considered, first
from the steady-state point of view. We discuss the operating
procedures for normal and transient modes and the implication
of grid code requirements on the converter rating. Validation of
the theory is performed using the representation of the system
in electromagnetic transient programming software.
2. Wound rotor induction generator
The wound rotor induction generator, through its slip rings,
allows access to the rotor windings, which can be connected
to external resistors or may be fed from a variety of converter
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its slip. In a truly optimized system, maximum rotor power will
in fact occur for two operating points: (1) maximum speed and
rated power and (2) lower output power but a larger magnitude
of slip, as will be demonstrated. The requirement for delivery
of reactive power adds an additional dimension to the problem.
The issues of speed range and reactive power allocation are each
treated in turn in what follows.
2.1. Reactive power considerations
Through proper division of the reactive power between the
two converters the overall rating of the two converters can be
minimized. In order to facilitate the discussion, the parameter,
K, will be defined here as the rotor-side converter compensation
constant, representing the proportion of compensation supplied
from the rotor-side converter and will be given by:
K=
Qr
Qr
+ Qgrid
(1)
where Qr and Qgrid are defined as the equivalent1 reactive power
injected into the machine from the rotor-side, and the reactive
power supplied by the grid-side converter, respectively, Fig. 2:
Fig. 1. Converter topologies for a wound-rotor induction generator and associated speed ranges.
options, Fig. 1. Depending on the converter topology implemented this may restrict the generator speed range, due to the
direction of flow of power from the rotor terminal. Diode rectifier front-ends (Fig. 1, top) and slip energy recovery drives
(Fig. 1, bottom) will be limited to sub- and supersynchronous
speeds, respectively. However, the bidirectional converter, using
two IGBT voltage sourced converters (VSCs), has the flexibility
to operate either above or below synchronous speed, at the cost
of a second forced-commutated converter.
For the latter arrangement, the reactive power compensation
can be accomplished from the grid-side, the rotor-side converter
or a combination of the two, Fig. 2. The choice of how to divide
the compensation has an effect on the rms current, and consequently the kVA of the two converters.
Equally important in determination of the kVA requirements
of the converters is the speed range of the machine; the power
carried across the bridge is a function of the generator power and
Qr =
Qr
s
(2)
In the majority of the literature, the rotor-side converter supplies all of the reactive power compensation since the reactive
power injected is amplified by a factor of s−1 . In the present
work, the possibility of supplying some reactive power from the
grid-side converter is considered. In steady-state operation this
could have the benefit of reducing the overall kVA requirements
of the converters. Transient effects related to realization of the
low voltage ride through (LVRT) requirement are also important,
and will be discussed in subsequent sections.
In order to translate these features into the optimal allocation
of reactive power, one needs to consider how the performance of
the system varies with the compensation constant. The compensation constant will be chosen in order to minimize the complex
power of the rotor-side and grid-side converters, at the peak
rotor power points. Transient behavior and analysis of the other
operating points will then be considered in the development of
an operating strategy that aims to minimize the apparent power
of the two converters and improve transient response following
disturbances.
2.2. Equivalent circuit model
The wound-rotor induction machine steady-state equivalent
circuit model, Fig. 3, can be used, together with the steadystate models of the other components of the system to obtain
information regarding the kVA ratings of both the grid-side and
rotor-side converters. The equivalent circuit model can be used
1
Fig. 2. Reactive power sources in the doubly fed induction generator.
Equivalent refers to the fact that the injected rotor converter reactive power,
as seen from the machine, is multiplied by the inverse of the slip, as given by
Eq. (2).
C. Abbey, G. Joós / Electric Power Systems Research 78 (2008) 399–408
401
Fig. 3. Steady-state equivalent circuit model of wound-rotor induction machine.
to derive equations that describe the relationship between the
stator and rotor currents. Thus, for a desired stator current (which
is dictated by the complex power and the stator voltage) the
corresponding rotor-side current can be calculated. The matrix
equation below is used to describe this relationship:
⎡
⎤⎡
⎤ ⎡
⎤
1 Rs + jXs
Vm
Vs ∠0◦
0
⎢
⎥⎢
⎥ ⎢
⎥
0
(Rr /s) + jXr ⎦ ⎣ Is ⎦ = ⎣ (Vr /s)∠δr ⎦ (3)
⎣1
1
jXm
jXm
Ir
0
In the case of a wind generator, the real power, which is a
function of the mechanical input torque, follows from the wind
speed. However, reactive power can be easily controlled and is
related to the imaginary current of the magnetizing branch and
the contribution from the rotor-side converter:
isq = imq − irq
(4)
Therefore, it can be noted that the stator reactive power can
be reduced by supplying a greater proportion of the magnetizing current from the rotor-side. The source of isq must also be
considered, noting that it can be supplied from either the grid
or from the grid-side converter in the form of igrid,q . The point
to extract from the discussion is that the reactive power compensation can be applied from two sources: (i) rotor-side using
irq or (ii) grid-side using igrid,q. How this is supplied will affect
the converter currents, which are also related to the real power
flows, which is considered in the following section.
2.3. WTG relationships
When considering the effect of the WTG generator power on
the power that must be carried across the dc link one must take
into account the actual WTG power characteristic, as well as the
influence of the gearbox ratio on the generator speed range, and
consequently its slip. The output power of a wind generator is
given by:
Pm = CP (λ, β)
ρA 3
ν
2 wind
(5)
where Pm is the mechanical output power of turbine; Cp the
performance coefficient of the turbine; ρ the air density (kg/m3 );
A the turbine sweep area (m2 ); vwind the wind speed (m/s); λ the
tip-speed ratio (rotor blade tip speed divided by the wind speed);
and β is the blade pitch angle.
A typical WTG output power versus wind speed characteristic is shown in Fig. 4. For WTGs there are three modes of
operation: (i) maximum power point tracking (MPPT), where
Fig. 4. Generator power vs. wind speed, corresponding turbine speed and the
effect of the gearbox ratio on the operating range of the generator. Operation at
maximum power point tracking, pitch regulated power beyond vrated .
the speed is set to the optimum tip-speed ratio, λopt ; (ii) constant
speed region, usually above rated nominal wind speed and (iii)
WTG shut down, which occurs for wind speeds below cut-in
wind speed, vcut-in , or above the upper wind speed limit (not
shown in the figure, typically 20–25 m/s).
Fig. 4 also shows how changing the gearbox ratio, nGB , affects
the location of synchronous speed on the characteristic. For all
three topologies in Fig. 1 it is essential to consider this parameter.
With regards to the bidirectional topology, the choice of nGB will
affect the amount of power that flows to or from the rotor. The
following sections propose a methodology for selection of this
parameter.
3. Converter rating minimization
Conventionally, the reactive power compensation in a DFIG
is supplied from only one of the converters, namely the rotorside converter. This is done for reasons of simplicity and since
the reactive power supplied by the rotor converter is effectively
amplified by a factor of s−1 . However, this may not be the optimal method since the kVA needs of the rotor-side converter can
be greater than the grid-side converter. More specifically, when
the speed of the generator deviates greatly from synchronous
speed or when the output power approaches or reaches the rating of the machine, there is likely justification for deviating from
this operating approach. Under these circumstances it may be
desirable to supply some of the reactive power from the grid-side
converter, relaxing the demand on the rotor-side device.
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This section addresses the minimization of the kVA requirements of the converters by considering the division of reactive
power and the installed gearbox ratio and their relationship to
the overall rotor apparent power requirements. The problem is
formally developed and optimality conditions are determined.
A design example is used to aid in illustration of the concepts.
3.1. Problem formulation
min Srating (K, nGB )
(6)
K,nGB
Subject to:
0≤K≤1
(7)
nGB,min ≤ nGB ≤ nGB,max
(8)
ωtur,min ≤ ωtur ≤ ωtur,max
(9)
where the turbine speed is related to the generator speed by:
(10)
Srating can be expressed by:
Srating = || S r
S grid ||∞
(11)
Sr and Sgrid are the vectors of the apparent power magnitudes
for the rotor and grid-side converters, respectively, evaluated at
all wind speeds from vcut-in to vrated , and over the entire range
of reactive power values. These quantities are evaluated using
the equivalent circuit model (3) together with the wind speed
characteristic (5).
3.2. Problem reduction
As Eq. (11) implies, the search space constitutes all compensation constants and possible gearbox ratios, across the entire
operating range of the WTG. Although the problem is still comparatively small in terms of dimensionality, both reduction of
the search space and an operating strategy for K result if the
converters are assumed to be lossless.
Neglecting converter losses implies that the kVAs will be
equal for a given operating point if the reactive powers of both
converters are also equal. This taken together with Eqs. (1) and
(2) gives the following relationship for K:
K=
Qr /s
Qr /s + Qr
Radius, R (m)
vwind,nom (m/s)
vcut-in (m/s)
λopt
37.5
12
5
6.3
Table 2
Generator data
The greater of the two converter ratings was chosen as the
minimizing function, which intuitively suggests that this should
result in the same rating for each converter following optimization. The reasoning for this choice is that generally in practice,
the kVA ratings of back-to-back converters should be matched
in order minimize cost. Matched converters are typically standard and thus, a reduction in cost is possible if they are chosen
to be equal.
Therefore, the premise is to attempt to limit the installed
kVA of the two converters, using the free variables K and nGB .
Therefore, the objective becomes:
ωgen = nGB ωtur
Table 1
Wind turbine data
(12)
Sbase (MVA)
Vbase (V)
Poles
Xs (p.u)
Rs (p.u)
Xr (p.u)
Rr (p.u)
Xm (p.u)
2
690
4
0.117
0.00621
0.1136
0.00627
3.28
which reduces to:
K=
1
1 + |s|
(13)
The constrained optimization problem can then be simplified
using this condition by calculating the allocation constant for any
given operating point. Furthermore, Eq. (13) forms the optimal
operating strategy for selection of K.
3.3. Design example
The outlined problem was then solved using data for a typical
WTG utilizing the DFIG topology. Tables 1–3 provide the characteristics of the wind turbine, generator data and constraints.
The characteristics curve, Cp , for the wind turbine used was that
given in Ref. [11]. Here no upper or lower bounds were set for
the generator slip, but the methodology could easily incorporate
these values in order to respect mechanical limitations or other
constraints.
The emphasis was to develop an analytical model for optimally choosing the gearbox ratio. This could then be used to
quickly determine the effect of different parameters that influence the optimal design parameter as well as the rated value of
the two converters. In the following section, a graphical approach
is taken; essentially mapping out the solution process performed
by the optimization tool. This validates the solution but also provides valuable insight into the variation of the apparent power
flow through the converters for changes in operating modes.
Table 4 shows the results of the optimization process performed using the numerical method and using the graphical
method in the following section. Both provide approximately
Table 3
Electrical and mechanical operating ranges
Qdfig lead/lag (p.u.)
ωtur,min (rpm)
ωtur,max (rpm)
nGB,min
nGB,max
0.5
9
21
94
224
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403
Table 4
Optimal gearbox ratio and converter ratings
Solution method
nGB
Srating
Analytical
Graphical
118
116.5
0.2878
0.28–0.29
the same result, the advantage of the analytical method being the
speed and precision once the solution method has been outlined,
yet lacking the intuitive insight that the graphical procedure
offers.
4. Parametric analysis
Using the induction machine equivalent circuit a number of
curves were obtained in order to gain an understanding of the
dependence of the apparent power demands of the two converters on the gearbox ratio, as well as on the compensation
constant. While the optimal values were determined in the previous section, it is informative to consider the variation of these
parameters, particularly for the alternate converter topologies
presented in Fig. 1.
4.1. Gearbox selection
Here the effect of the gearbox ratio was investigated by calculating the infinite norm of the two converter ratings for different
values of nGB . The full reactive power range was considered and
easily enough one can arrive at the somewhat obvious conclusion that the limiting case is for full leading reactive power (as
the internal requirements must be provided in addition to that
supplied to the grid). Reactive power was allocated using the
operational strategy defined by Eq. (13).
Fig. 5 shows the results of the calculation, performed for different pole numbers. We note that as the number of poles is
increased, the optimum gearbox ratio decreases, as expected.
For the 4 pole machine the optimum gearbox ratio was found
Fig. 5. Variation of required kVA rating vs. gearbox ratio, given for different
poles, operation at Qdfig = 0.5 p.u., Kopt .
Fig. 6. Calculated converter kVA vs. wind speed for (a) optimal nGB (116.5), Kopt
and for two alternate WRIM topologies; and (b) for optimal nGB and different
values of K.
to be about 116.5, which balances the rotor apparent power carried at rated power with the rotor power needs at low speed
operation—near zero real power production but high rotor power
due to large values of slip.
Next, the kVA requirements were calculated for the nGB,opt ,
over the wind speed range to demonstrate how the kVA changes
for different operating points, Fig. 6. As can be noted, the
kVA requirements starts from a first peak at 5 m/s (low power
but high slip), decreases to zero at synchronous speed and
then reaches the maximum value again at rated wind speed.
This confirms the result from Fig. 5 and the previous section, showing that the gearbox value is optimum for the given
constraints. The kVA requirements for the alternate converter
topologies are also given, assuming MPPT operation, along with
the effect of using a constant value for the compensation constant
(1 and 0.5).
Compared with the optimal case the maximum value of each
of the alternatives is consistently higher. However, it is interesting to note that the variable speed drive topology requires
a rating which is only twice that of the full converter topology with optimal operation. The higher apparent power and
increased harmonic injection would be somewhat offset by the
reduced converter cost, whereas the slip recovery drives does not
appear to be competitive. Nonetheless, the operating strategy of
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C. Abbey, G. Joós / Electric Power Systems Research 78 (2008) 399–408
Fig. 7. Calculated kVA for rotor-side and grid-side converters as a function of
K. Calculated for operation at wind speed of 5 m/s and for different values of
Qdfig . Optimal operating K is given by the dotted vertical line.
these topologies will certainly differ and lack other beneficial
characteristics that the full converter is able to provide.
Although the main focus has been the impact of these design
parameters on the converter rating, for completion the relationship between the gearbox ratio and the size of the machine is
now considered. We can consider the relation for the mechanical
torque of the machine:
τm ∝ |φr ||φs | sin δ
(14)
which is related to the mechanical power by the speed of the
machine:
Pm = τm ωr
(15)
Therefore, as the gearbox ratio is increased, the electrical
speed of the generator will also increase, and consequently the
size of the machine required to meet the same power rating
decreases. So, a tradeoff needs to be established between the
machine design and that of the converter; however this discussion is deferred to another work.
4.2. Compensation constant
Using the gearbox ratio of 116.5, the converter kVA requirements were obtained for different values of WTG reactive power,
at different values of K. The results were obtained for the two
peaks given in Fig. 6, corresponding to wind speeds of 5 and
12 m/s, Figs. 7 and 8, respectively. This provides a detailed
understanding of the influence of the different parameters and
validates the expression in Eq. (13).
Here the kVA needs of the grid-side and rotor-side converters
are given for operation at 0.5 and 0.25 leading VArs and unity
power factor operation. The omission of lagging VArs is justified
by the fact that smaller reactive power is required in these cases,
due to the internal requirements of the generator. As can be noted
the optimal K, as given by the intersection of the curves for the
rotor and grid-side converters agrees with that predicted by Eq.
(13), which is shown by the vertical line.
Fig. 8. Calculated kVA for rotor-side and grid-side converters as a function of
K. Calculated for operation at wind speed of 12 m/s and for different values of
Qdfig . Optimal operating K is given by the dotted vertical line.
It can be noted that the majority of the compensation is supplied from the rotor-side converter (70–85%) however, a small
percentage should come from the grid-side converter in order to
minimize the maximum rating of the two VSC’s, which is given
by the point of intersection. The optimum point is a function of
the operating slip only and corresponds with the value predicted
by Eq. (13). Note that the actual reactive power supplied by each
converter is equal; however, the reflected rotor reactive power
represents the majority of the contribution.
In summary, either a rigorous optimization method or a set
of design curves can be used to determine the optimal parameters for minimization of the converter ratings. While the latter
provides greater insight into the sensitivity with respect to the
different parameters involved, the former will be favored where
the intent is design focused. It is interesting to note that Kopt is
independent of the machine and turbine characteristic, whereas
the gearbox ratio is sensitive to the wind turbine characteristic
curve.
4.3. Machine turns ratio
Some mention should be made to the actual rotor current
magnitude. In wound-rotor induction machines, the turns ratio
between the stator side and rotor-side is typically not equal to 1.
Here, by plotting the current in the rotor, considering the power
curve and generator speeds given in Fig. 4, for decreasing values
of turns ratio, one can determine the ratio for which the current in
the grid-side and rotor-side converters becomes equal. Assuming
again our objective is to equate the two ratings – both in terms
of power and current – the optimum turns ratio falls close to 0.3,
Fig. 9. Note here that the power transformation is not affected
by this parameter, like for a transformer, and therefore, previous
developments still hold.
4.4. Speed and power factor range
The dependence of the converter rating on parameters related
to the design of the WTG is also of interest, namely the upper
C. Abbey, G. Joós / Electric Power Systems Research 78 (2008) 399–408
405
ing. This results in a nearly linear increase in converter rating,
doubling for a change in pF from 0.99 to 0.85.
5. Operating considerations
The converter ratings are defined for normal operation but
certain concessions may need to be made for transient conditions, and as well, the compensation may need to be adjusted for
different operating conditions. These issues are treated here in
brief.
5.1. Steady-state
Fig. 9. Magnitude of rotor and grid-side (in bold) converter currents over speed
range for different machine turns ratios. Operation at rated leading reactive
power (Qdfig = 0.5 p.u.).
Table 5
Dependence of converter rating on maximum machine speed
ωe,max
kVA (p.u.)
nGB
1.05
1.15
1.25
0.328
0.310
0.292
98
107
116
speed limit and the reactive power capability of the generator.
Utilizing the developed methodology, the influence of these two
parameters was determined, Table 5 and Fig. 10.
With regards to the upper speed limit, we can note that as
long as the generator’s electrical speed is allowed to vary up to
25% greater than synchronous speed, the optimal gearbox ratio
and minimum converter rating can be achieved. As we further
restrict the speed range, we ultimately reduce to the specific case
of the variable speed drive topology, only that the flexibility to
delivery reactive power from the grid-side converter is retained.
The reactive power range of the WTG will be dictated by the
grid code requirement in most cases. Fig. 10 shows the impact
of imposing greater reactive power capability (expressed as the
leading power factor at rated real power) on the converter rat-
Fig. 10. Effect of power factor range (leading/lagging power factor capability at
rated power, as dictated by interconnection standards) on converter kVA rating.
As was alluded to in previous sections the same equation used
to determine the compensation constant at the limiting operating points can form the basis for an operating strategy, Fig. 11.
In this way, the kVA requirements of both converters can be
equalized during normal operating. It should be noted that this
is complicated by certain practical logistics. Most notably, it
requires calculation of the rotor reactive power, and the internal
magnetizing current will change slightly for different operating
points.
In the calculations performed this issue was addressed in two
ways. One can assume a magnetizing current by taking the internal voltage to be 1 per unit. Stator and converter reactive powers
then follow from this assumption and all other quantities are
calculated. The compensation constant is then recalculated at
the end. Alternatively, an iterative method can be used to determine the stator and supply converter contributions for a given
K and wind speed. Either method works fine for generation of
the curves; however, on-line operation requires further consideration. An open-loop approach (resembling the former case)
can be used, relinquishing the benefit of exactly controlling
the compensation constant to its optimum value. Opting for a
look-up table is likely the simplest and most practical approach
and should yield compensation constants that are close to the
optimum value if a significant number of points are charted
offline.
Fig. 11. Operational strategy for selection of K as a function of slip.
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C. Abbey, G. Joós / Electric Power Systems Research 78 (2008) 399–408
Fig. 12. Active crowbar protection for low voltage ride through in the DFIG.
5.2. Transient control
Low voltage events on the grid, most often caused by faults
on the transmission network or adjacent feeders, require special
consideration for the control of the WTG but also in the hardware
components required. Most utilities now demand that a WTG
meet a low voltage ride through (LVRT) requirement, meaning
that they must remain connected for all normally cleared contingencies [1,2]. While the LVRT characteristic itself is somewhat
subjective, the implication is that the WTG must be able to operate during low voltage events; in extreme cases operation for zero
voltage events is required.
The most commonly cited LVRT solution for the DFIG is the
active crowbar, whereby the rotor windings are short-circuited
[12]. The consequence is that the rotor converter is not able to
provide reactive current during and immediately following the
fault (Fig. 12). As a result, the proposal here is that, regardless
of the prefault compensation constant, it should be immediately
set to zero upon activation of the crowbar, as is discussed in Ref.
[13], shifting compensation entirely to the grid-side converter.
Following recovery of the voltage, the normal operating conditions can then once again dictate the necessary compensation
constant. This is easily implemented in the control algorithm
using a logic signal that automatically sets the compensation
constant to 0 should the rotor winding be short-circuited.
Fig. 13. Variation of the kVA ratings of the rotor and grid-side converters as a
function of K for operation at 5 m/s, slip = 0.45, Qdfig = 0.5 (validation of Fig. 7).
optimum compensation constants and the minimum kVA match
well with those values determined in the previous sections.
6.2. Allocation implementation
The most straightforward method for implementation of the
allocation strategy is offline calculation of the internal magnetizing requirements of the machine, which could then be
incorporated into the control using a look-up table. This would
avoid the use of major modifications to the control structure,
circumventing the need for additional compensation blocks.
Alternatively, the two reactive current loops could potentially
be combined; however, it is not clear how equal contribution
from each converter could be guaranteed, or how the control
loop might respond during transients. Potential merits of this
approach might include a simpler control structure; however
further investigation is required.
6. EMTP validation
In order to support the theory developed in the previous section and to investigate the behavior of the system in response to
various disturbances, the WTG was represented in a commercial electromagnetic transient programming package and various
simulations were performed. The objective was to reproduce the
theoretical predictions and therefore, demonstrate the validity
of the installed rating. This serves not only as mutual validation for the different representations of the system but also to
address how the allocation strategy could be executed in the
control scheme.
6.1. Steady-state performance
The kVA requirements were obtained for the same operating conditions as for the curves generated using the equivalent
circuit model. Again operation for wind speeds of 5 and 12 m/s
was considered, Figs. 13 and 14. The compensation constant
was slowly varied from 1 to 0 and the results were plotted. The
Fig. 14. Variation of the kVA ratings of the rotor and grid-side converters as a
function of K for operation at 12 m/s, slip = −0.25, Qdfig = 0.5 p.u. (validation of
Fig. 8).
C. Abbey, G. Joós / Electric Power Systems Research 78 (2008) 399–408
7. Conclusions
This paper has discussed the parameters affecting the converter kVA requirements and reactive power management in a
doubly fed induction machine. Steady-state analysis of the system for determining the impact of gearbox ratio and choice of
operating point on the reactive power flow on the converter rating
was performed. A methodology was proposed and demonstrated
for minimization of the converter ratings and allocation of reactive power, considering these parameters. Based on this analysis,
operating strategies were proposed for overall minimization of
kVA flow on the rotor-side. Implementing optimal allocation
of reactive power results in a 15% reduction in converter rating compared with full delivery from the rotor-side, whereas an
almost 50% reduction is realized when compared with the less
expensive diode-front-end converter topology.
Appendix A. List of symbols
A
Cp
imq
irq
isq
Igrid,q
Ir
Is
K
Kopt
nGB
nGB,max
nGB,min
nGB,opt
Pm
Qdfig
Qgrid
Qr
Qr
Rr
Rs
s
Sgrid
Sr
Srating
vcut,in
vrated
vwind
Vm
Vr
Vs
Xm
Xr
Xs
turbine sweep area
performance coefficient of the turbine
quadrature component of the magnetizing current
quadrature component of the rotor current
quadrature component of the stator current
quadrature component of the grid side converter’s current
rotor current
stator current
compensation constant
optimum compensation constant
induction machine turns ratio
maximum induction machine turns ratio
minimum induction machine turns ratio
optimum induction machine turns ratio
mechanical output power of turbine
reactive power delivered from the DFIG generator system
reactive power delivered from grid-side converter
reactive power delivered from rotor-side converter
reactive power delivered from rotor-side expressed on
stator side
rotor resistance expressed on stator side
stator resistance
generator slip
grid-side converter kVA rating
rotor-side converter kVA rating
power electronic converter kVA rating
wind turbine generator cut-in wind speed
wind turbine generator rated wind speed
wind speed
voltage across magnetizing branch
rotor voltage
stator voltage
magnitizing reactance
rotor reactance expressed on stator side
stator reactance
407
Greek letters
β
blade pitch angle
δ
angle between the stator and rotor flux vectors
angle of rotor-side voltage expressed relative to stator
δr
voltage
λ
tip-speed ratio of the rotor blade tip speed to the wind
speed
ρ
air density
ωgen
generator angular speed
ωtur
wind turbine angular speed
ωtur,max maximum wind turbine angular speed
ωtur,min minimum wind turbine angular speed
References
[1] S.M. Bolik, Grid requirements challenges for wind turbines, in: Proceedings of the Fourth International Workshop on Large Scale Integration
of Wind Power and Transmission Networks for Offshore Wind Farms,
2003.
[2] G. Joos, Grid code review, Integration of Renewable Energy Sources
and Distributed Energy Resources Conference, Brussels, December 1–3,
2004.
[3] R. Pena, J.C. Clare, G.M. Asher, Doubly fed induction generator using
back-to-back PWM converters and its application to variable-speed windenergy generation, J. Proc.-Electr. Power Appl. 43 (3) (1996).
[4] R. Datta, V.T. Ranganathan, Direct power control of grid-connected wound
rotor induction machine without rotor position sensors, J. IEEE Trans.
Power Electr. 16 (3) (2001).
[5] J.B. Ekanayake, L. Holdsworth, X. Wu, N. Jenkins, Dynamic modeling
of doubly fed induction wind turbines, J. IEEE Trans. Power Syst. 8 (2)
(2003).
[6] H. Akagi, H. Sato, Control and performance of a doubly-fed induction
machine intended for a flywheel energy storage system, J. IEEE Trans.
Power Electr. 17 (1.) (2002).
[7] R. Datta, V.T. Ranganathan, A simple position-sensorless algorithm for
rotor-side field-oriented control of wound-rotor induction machine, J. IEEE
Trans. Ind. Electr. 48 (4) (2001).
[8] R. Datta, V.T. Ranganathan, A method of tracking the peak power points
for a variable speed wind energy conversion system, J. IEEE Trans. Power
Electr. 16 (3) (2001).
[9] L. Morel, H. Godfroid, A. Mirzaian, J.M. Kauffmann, Double-fed induction
machine: converter optimization and field-oriented control without position
sensor, J. IEE Proc.-Electr. Power Appl. 145 (4) (1998).
[10] B. Rabelo, W. Hofmann, Optimal active and reactive power control with
the doubly-fed induction generator in the MW-class wind-turbines, Proc.
IEEE Conf. Power Electr. Drive Syst. 1 (2001) 53–58.
[11] L. Ran, J.R. Bumby, P.J. Tavner, Use of turbine inertia for power smoothing
of wind turbines with a DFIG, in: Proceedings of the 11th International
Conference on Harmonics and Quality of Power, 2004, pp. 106–111.
[12] J. Niiranen, Voltage ride through of a doubly-fed generator equipped with
an active crowbar, in: Proceedings of the Nordic Wind Power Conference,
Chalmers University of Technology, 2004.
[13] V. Akhmatov, Variable-speed wind turbines with doubly-fed induction
generators. Part IV. Uninterrupted operation features at grid faults with
converter control coordination, Wind Eng. 27 (6) (2003) 519–529.
Chad Abbey received his degree in electrical engineering from the University
of Alberta in 2002. In 2004, he graduated with an M.Eng. degree from McGill
University, in Montréal where he is currently pursuing his Ph.D. He is presently
working with CANMET Energy Technology Centre, in Varennes, Québec where
he is a Research Engineer and coordinates a research program on the modeling
and integration of distributed generation. His current research interests include
wind energy, distributed generation and their integration to the grid.
Géza Joós graduated from McGill University, Montreal, Canada, with an M.Eng.
and Ph.D. He is a Professor with McGill University, Montreal, Canada, since
408
C. Abbey, G. Joós / Electric Power Systems Research 78 (2008) 399–408
2001. He is involved in fundamental and applied research related to the application of high-power electronics to power conversion, including distributed
generation, and power systems. He has published extensively and presented
numerous papers and tutorials on these topics. His employment experience also
includes ABB, the University of Quebec and Concordia University. He has been
involved in consulting activities in Power Electronics and Power Systems, and
with CEA Technologies as Technology Coordinator of the Power Systems Planning and Operations Interest Group. He is active in a number of IEEE Industry
Applications Society committees and in IEEE Power Engineering Society and
CIGRE activities and working groups dealing with Power Electronics and applications to Distributed Resources. He is a Fellow of the Canadian Academy of
Engineering.