IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
1
Sensorless Frequency and Voltage Control in
Stand-Alone DFIG-DC System
Gil D. Marques, Senior Member, IEEE and Matteo F. Iacchetti, Member IEEE

x
*
Subscripts
0
dc
d,q
s,R
,
Abstract—A sensorless stand-alone control scheme of a DFIGDC system is investigated in this paper. In this layout, the stator
voltage is rectified by a diode bridge that is directly connected to
a dc bus. The rotor side Voltage Source Inverter (VSI) is the only
controlled converter required in this system and is directly
powered by the same dc-bus created by the stator-side rectifier.
Dc voltage and stator frequency are regulated by two
independent PI regulators that give the references for inner
current controllers implementing field oriented control. As it is
capable of creating a stable and regulated dc-bus, this system can
be conveniently adopted to supply dc loads or to form a dc grid.
Due to the constraint imposed by the stator diode bridge, the
DFIG has to operate under a constant stator voltage, and the
conventional stator field oriented control implemented in standalone ac DFIG must be modified. The paper presents the control
structure and the theoretical framework for the controller
synthesis. Simulation and experimental validations on a smallscale rig are included.
space vector quantity
set point value
quiescent point in the small-signal analysis
dc side
oriented frame axes
stator, rotor in the  equivalent circuit
stationary axes
I. INTRODUCTION
Wind power capacity is experiencing a massive growth in
recent years, with a record in 2015 when new installations
amounted to 51 GW [1]. Middle-term forecasts predict that
wind energy might contribute up to 18% of the global
electricity production by 2050 [2]. The increasing penetration
of wind energy into the power system brings new challenges,
which need to be addressed through appropriate power
conversion and control layouts. DC-networks are seen as
potentially highly-beneficial to achieve an efficient integration
of renewables into power systems, particularly for off-shore
plants [3]-[4]. Minimizing the number of conversion stages
and paralleling constraints make dc micro-grids attractive for
supplying energy to final users [5]-[7]. The available variety of
generators and power electronics converters allows a wide
range of interface solutions for variable-speed wind turbines
[8]-[9]. In spite of their relatively low cost, induction
generators need to be connected to a dc-link via a fully-rated
and fully controllable voltage source inverter (VSI) which also
provides the necessary magnetizing current [10], [11].
Permanent-magnet synchronous generators can replace the
VSI with a diode bridge and fully-rated dc-dc converter [12],
but at the price of a low dynamics in the power control.
Wound field synchronous generators (WFSGs) may
theoretically implement the cheapest power electronics, which
might reduce to a simple diode bridge and to a low-power
chopper handling the excitation current [12]. However, the
variable-speed, constant-voltage operation required by the
connection to a constant voltage dc-grid is critical for the
WFSG and causes the generator to be oversized proportionally
to the max/min speed ratio.
The doubly fed induction generator (DFIG) has been deeply
studied for ac wind power generation [13] as an effective way
to reduce the cost of power electronics, by preserving highperformance regulation via either field-oriented control or
direct-power control. Stand-alone DFIGs with frequency and
voltage regulation have also been considered [14]-[17], for
Index Terms—Dc grid, Dc-link, Doubly-fed induction machine,
Field oriented control, Rectifier.
NOMENCLATURE
is , iR
stator, rotor (-model) current (p.u.)
idc1 , idc2 diode bridge, inverter dc current (p.u.)
k
inductance ratio Ls/M
Ls , M
stator, magnetizing inductance (p.u.)
rs , rr
stator, rotor resistance (p.u.)
TC
closed-loop rotor current time constant (s)
TL , T'
dc-bus time constants (s)
TiV , Ti dc-voltage, frequency PI controller time constant (s)
UL
inner dc-load voltage (p.u.)
udc , us
dc-bus, stator voltage (p.u.)
s ,m, sr stator flux, mechanical, slip angles (electr. rad)
s
stator flux linkage magnitude (p.u.)
b
rated (base) stator angular frequency (rad/s)
s, sr, m stator frequency, slip speed, rotor speed (p.u.)
Superscripts
Manuscript received March 14, 2016; revised May 23 and Sept. 9;
accepted October 11, 2016. This work was supported by national funds
through Fundação para a Ciência e a Tecnologia (FCT), with reference
UID/CEC/50021/2013.
G. D. Marques is with the INESC-ID, Instituto Superior Técnico (IST),
Universidade de Lisboa, Av. Rovisco Pais, no 1, 1049-001 Lisbon, Portugal
(e-mail: [email protected]).
M. F. Iacchetti is with the School of Electrical and Electronic Engineering, at
the
University
of
Manchester,
Manchester,
U.K.
(e-mail:
[email protected]).
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supplying ac loads in remote areas or in ac microgrids.
The DFIG has been recently recognized as potentially able
to be interfaced to a dc system, bringing a significant reduction
of the power electronics cost as it does in ordinary ac-grid
connected DFIGs. A layout with two VSIs rated to half the
global power has been proposed in [18]: the VSIs work in
regenerative mode and their dc-links are directly paralleled to
the dc grid. An alternative solution called DFIG-DC system
has been investigated in [19]-[22], where a unique de-rated
VSI and a fully-rated diode bridge are used to interface the
DFIG to the dc grid. Being in a DFIG the stator frequency
independent of speed, the DFIG is well-suited to operate at
variable speed and constant stator voltage, as demanded when
the stator diode bridge is connected to a constant voltage dclink or grid. This is the major advantage for using a DFIG: the
max/min speed ratio does not affect the machine sizing, and
the DFIG also allows the optimization of the stator frequency
as a function of power, to maximize efficiency [22]. Similar
benefits can be achieved with dual-stator induction generators
[23]. Relevant applications for the DFIG-DC system range
from dc micro-grids to on-board dc generation and off-shore
wind turbines, where the DFIG-DC system may directly feed a
voltage boost and insulation stage [3].
In the DFIG-DC system, the instantaneous torque regulation
achievable by the Field Oriented Control (FOC) through the
rotor VSI is potentially able to compensate for the main torque
ripple component produced by the diode commutation [24].
This however requires the implementation of resonant or
multiple-frame PI current controllers [25]-[26]. Torque ripple
can also be conveniently mitigated with multi-pulse rectifiers.
The control developed in [19] drives the air-gap reference
flux-linkage at constant speed and adjusts the magnitude to
control power. Schemes in [20] and [21] are based on the fact
that in DFIG-DC systems the product flux × frequency is
almost constant, making the frequency controllable through the
d-axis rotor current.
Existing studies on the DFIG-DC system only consider the
operation under torque reference control, because the dc
voltage is assumed to be controlled by another voltage source.
Although such a scenario is relevant to a dc-grid connected
system, voltage control is desirable to participate to the voltage
regulation and properly share the generated power with other
units [27]. Dc-voltage regulation is obviously necessary for
stand-alone operation. Therefore, dc-voltage control must be
implemented in the DFIG-DC system in order to achieve fullycontrollable, variable-speed, constant-voltage generation.
Control techniques for ac stand-alone DFIGs, such as open[14] or closed-loop [17] schemes with the stator angle (simply
obtained as integral of the reference frequency) do not take
into account the peculiarity of the DFIG-DC system, where daxis rotor current, rather than the q- one, is the most relevant
control variable for frequency regulation.
A first proposal of stand-alone control for the DFIG-DC
system has been made in [28] using a proportional-integral
(PI) voltage controller to directly set the reference torque
value, via the q-axis rotor current. However, [28] only
discusses a basic design approach narrowly focusing on the
operation with a well-defined dc-load, and only reporting
introductory simulation results.
Unlike [28], this paper presents extensive study and
experimental investigations on the stand-alone DFIG-DC
system. The paper derives a comprehensive small-signal model
of the system, which allows the controller design to be
addressed for generic operating conditions. A sensorless
implementation is adopted to achieve field orientation and
regulate stator frequency and dc voltage with a reduced
number of sensors. Experimental responses to reference
frequency, dc voltage and load changes are reported, also
showing the start-up capability.
The paper is organized as follows. Section II introduces the
system layout and the necessary modeling background. Section
III reports the control scheme for voltage and frequency
control, derives the complete small-signal model of the system
and discusses the control synthesis. Sections IV and V validate
the theory with simulations and experimental results.
II. SYSTEM TOPOLOGY AND MODELING
Fig. 1 shows the system investigated in this paper. A generic
dc active load is considered in this study: it might represent
either a stand-alone load or even a weak dc-grid.
Fig. 1 DFIG-DC system feeding a stand-alone dc load.
This paper considers a control scheme with fast rotorcurrent controllers. Thus, for frequency and voltage control
purpose only the stator equations are relevant for the machine.
Using per unit (p.u.) quantities except for time and considering
the stator field oriented frame d-q, the stator equations are
usd  rsisd 
1 d s
b dt
, usq  rsisq  ss
(1)
The base frequency b (in rad/s) appears in (1) as time t is
still in seconds. The stator frequency s is the derivative of the
stator flux angle s: then the right-hand side equation in (1)
remains unchanged at steady state, where s is simply
constant.
The DFIG -model is used throughout this paper. Hence
rotor currents (subscript “r”) are transformed with the
inductance ratio k=Ls/M to obtain the -model values
(subscript “R”).
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rectifier gives
iRd  ird k
,
iRq  irq k , with
k  Ls M .
(2)
u dcidc1 
Flux-current relations under field-oriented conditions are
then
 s  Ls  isd  iRd 
,
0  i sq  i Rq .
(6)
with iˆs  isq = iRq, due to the negligible phase shift and to (3).
Then,
(3)
The p. u. torque, in generator convention, is given by:
te   siRq
3 ˆ
3
uˆ i  u iˆ
2 s s  dc s
i dc1 
3
i
 Rq
(7)
(4)
In this paper the same base values for ac and dc variables
are adopted. Thus, (5) and (7) hold also in p.u. variables.
Since the diode bridge is connected to bulk capacitors in the
dc-side, stator current and voltage are distorted. Nevertheless,
as discussed in [12] and [29], an average model in terms of
first harmonics is adequate for control purposes. This is
because the amount of power delivered through the diode
bridge is mostly related to first harmonic components. The
diode-bridge average model is then established according to
the simplified phasor-diagram in Fig. 2, where phasors
represent first harmonics. Fig. 2 also shows reference frames
and angles involved in the control algorithm.
III. CONTROL SCHEME
A. General principle
The main requirement in a stand-alone DFIG-DC system is
monitoring and controlling the dc voltage across the bulk
capacitor. Being the stator feeding a diode bridge only, the
stator frequency does not need to be strictly regulated at a
precise value. The only constraint is that the stator flux does
not exceed the machine rated value, to avoid saturation. This
feature would allow the flux to be regulated to minimize losses
[22], but this possibility is not considered in this paper, and a
simple frequency regulation is implemented.
Sensorless vector control based on stator flux linkage is
adopted to achieve a satisfactory decoupling between dcvoltage (torque) and stator frequency.
As shown in [20], the diode bridge imposes an almost
constant stator voltage to the machine. Being the stator
resistance negligible in usual DFIGs, the machine operates
under a constant flux × frequency product at the stator side. As
a consequence, the natural control variable for the frequency is
the stator flux, namely the d-axis rotor current, in the fieldoriented d-q reference frame. This is quite different from what
happens in conventional stand-alone ac DFIGs, where
frequency is controlled via the q-axis rotor current.
The constraint flux × frequency  constant induces a further
important difference with ac stand-alone systems, because it
indirectly affects the stator flux position (integral of
frequency). This makes possible to achieve the field
orientation by setting the estimated slip angle in the reference
frame transformations, rather than by driving the reference
frame with a reference stator angle (integral of the reference
frequency). This is of course possible as long as the diode
bridge is conducting. By contrast, in a stand-alone ac DFIG the
stator flux needs to be permanently driven by using a reference
stator angle in the frame transformations.
The dc voltage across the capacitor is mainly affected by the
active power flow through the stator and load. Thus, the dcvoltage is regulated through the q-axis rotor current: the
voltage error is delivered to a proportional-integral (PI)
regulator, which sets the q-axis reference current.
Fig. 3 reports the resulting control scheme: detailed
explanations of the main subsystems are provided in the next
Fig. 2 Simplified steady-state phasor diagram with first-harmonic
components: es=ss is the stator electromotive force.
The phase shift between stator (terminal) voltage and
current phasors has been proved to be less than 13° [21], and
is then neglected. Additionally, the ratio between average dc
voltage and first-harmonic stator voltage amplitude is rather
constant and close to the theoretical limit 2/0.64.
The average-model technique for the diode bridge treats udc
and idc1 as slowly-varying, ripple-free variables, and
approximates stator-side space vector quantities with their
first-harmonics. For this reason, capital letters for first
harmonics will not be used anymore.
The dc-voltage and peak value of the stator voltage are
related by
2
uˆ s  u dc
(5)

The negligible angle between stator voltage and current
makes the stator power to be well approximated by 3uˆsiˆs / 2 .
Thanks to (5), the power balance across the ideal diode
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sections. Fast current PI controllers are designed according to
usual rules: as shown in [30], a reasonable bandwidth is 300
Hz.
Fig. 5 PLL scheme for the stator frequency detection [21].
C. Small-signal model for voltage and frequency control
design
The small-signal flux-frequency relationship in the DFIGDC has been derived in [20] for the case of constant dc
voltage. The frequency perturbation is given by
s 

B. Sensorless field oriented control and frequency regulation
The sensorless field-oriented control used in this paper has
been firstly proposed in [21] for a grid-connected DFIG-DC
system, namely where the DC-link voltage was externally set
and regulated. The slip angle estimation in [20] exploits the
diode bridge property of imposing almost zero phase-shift
between stator current and voltage first harmonics. This leads
to the following definition of the generalized error

(9)
The disturbance es includes the minor effect of the voltage
drop across stator resistance, which makes the stator voltage
slightly differ from the stator electromotive force (EMF). In
the stand-alone DFIG-DC system considered in this paper, es
must also incorporate a further contribution due to any change
of the dc voltage in compliance with Fig. 1, (1) and (5):
Fig. 3 FOC scheme for the dc voltage and stator frequency regulation.


1
es  s 0  s
 s0
 s0
es  rs isq 
2
udc

(10)
The small signal model of the voltage loop is derived
treating currents idc2 and iL as disturbances, with
idis  idc2  iL .

M ˆ
M
i  is 
i cos ˆ sr  i R sin ˆ sr  i s . (8)
Ls Rq
Ls R
(11)
Then, the p. u. dc voltage varies according to
Cdc
The self-sensing scheme is shown in Fig. 4 and comprises a
PI controller (parameters kp FOC and ki FOC) which forces the
error (8) to zero and provides the slip angle after integration.
No flux estimation is needed for this scheme.
1 dudc
 idc1  idc2  iL  idc1  idis
b dt
(12)
Using (7), the perturbation of (12) and the Laplace
transform yields
u dc 
b
sC dc
3

 i Rq  i dis 


(13)
For control synthesis purpose, (13) is rewritten as follows
u dc 
1
sT
C
3

 i Rq  i dis  , T  dc

b


.
(14)
The small signal model resulting from (9)-(14) is
represented in the block diagram of Fig. 6, which comprises
the frequency and voltage PI controllers and the PLL transfer
function. Simplified first-order transfer functions representing
current loops in field oriented conditions are also included: the
time constant TC is the reciprocal of the current loop
bandwidth. The reference voltage is processed by a low-pass
filter with time constant Td =TiV to reduce voltage overshoots
at the start-up. For the derivation of the PLL transfer function,
Fig. 4 Self-sensing scheme to estimate the slip angle [21].
The frequency is estimated by a PLL (see Fig. 5) which
tracks the stator voltage space-vector. A low-pass filter is used
to reduce the ripple inherently affecting the stator frequency
because of the distorted stator voltages [31]. The small signal
model and design criteria for the PLL are thoroughly explained
in [21].
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the reader is referred to [21]. The transfer function is given by
PLL s  
a0 
k pll
T f2
,
a0
(15)
s  a2 s  a1s  a0
3
2
a1 
1
T f2
,
D. Synthesis of the dc voltage controller
The symmetry criterion for designing PI controllers can be
used in this case, due to the structure of the voltage loop in the
block diagram of Fig. 6. The constant representing the diode
bridge can be eliminated defining a new time constant T':
a2 
2
.
Tf
(16)
T '

T
3
(19)
Once a proper damping V for the voltage loop is chosen,
the parameters of the voltage PI controllers are
TiV   2TC
, k pV 
T'
TC
,
with
  1  2V
(20)
IV. SIMULATION RESULTS
A. Model and control parameters.
A Simulink model representing all the details according to
the descriptions above is built and used to study this system.
DFIG data are those of the experimental rig (see Appendix).
According to Section III, the parameters of the frequency
controller were set at: kp= 0.07 p.u., ki=70 p.u., kpll=0.75
p.u., Tf = 1.4ms, kpFOC =16 p.u. and kiFOC =0.15 p.u.. The dclink voltage controller was synthesized for =3, using (19) and
(20), giving TiV = 0.027 s, kpV =9.4 p.u., kiV =209 p.u.. A filter
on the voltage reference is implemented using a time constant
equal to TiV. The dc load is emulated using a controlled current
source, and simulations are carried out at constant speed.
Fig. 6 Small signal model of the stand-alone DFIG-DC system
The coupling of the frequency loop with the dc-voltage loop
is not a concern in this system, as there are no strict
requirements in terms of frequency control. In addition, one of
the two contributions to this coupling is inherently weak,
because of the negligible value of rs. However, the gain s0/s0
in the frequency chain strongly depends on the quiescent
operating point and affects the frequency controller design.
This is particular relevant during the starting transient, when
the dc voltage experiences a variation over a wide range. This
issue was not considered in the implementation of the
sensorless frequency control proposed in [21], because the
operation connected to a stable dc grid was investigated, and
all the tests only referred to constant frequency operation.
In this paper, a compensation gain is introduced in the
frequency loop before the frequency controller, in order to
address the issues of large dc-voltage and frequency variations.
The compensation gain can be expressed in terms of the stator
flux magnitude or stator frequency using (1) and neglecting rs:
2
 s0  s0
1


s 0
us
u s 2s 0
B. Response of the stator frequency controller.
Fig. 7 shows the response of the system when the reference
of the frequency is changed from 1 p. u. to 1.5 p. u..
(17)
Equation (17) can be used for practical implementation.
From Fig. 6, the closed-loop transfer function for frequency is
 s
*s

L s k p 1  sTi 
sTi 1  sTC   L s k p 1  sTi PLL s 
(18)
Fig. 7 Response of the stator frequency controller.
As the stator frequency increases and the dc-link voltage is
maintained constant, the stator flux, and consequently the d5
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
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axis rotor current, decreases. Since the dc load is maintained at
the same level during this transient and the dc voltage is
constant, the final load power does not change, and because
the speed is constant, the average torque must be roughly
constant too. Then, according to (4) the q-axis rotor current
should increase to compensate for the flux reduction and
achieve constant average torque: this can be seen in Fig. 7.
The transient on the frequency has some impact on the dcvoltage control loop because of the disturbance term idis in
(13), due to the slight increase in the magnitude of the rotor
current absorbed by the inverter.
A. Description of the laboratory setup.
In order to validate the theory and the implementation of the
two control loops, tests have been conducted on the laboratory
rig shown in Fig. 9: the parameters are reported in the
Appendix. Because the machine was not sized for this purpose,
it was decided to set the maximum stator flux level at 0.67
p.u., in order to allow an appropriate range for the rotor
current component producing torque. Additionally, a step
down transformer was used on the stator circuits to correct the
stator/rotor turns ratio. This transformer increases the
equivalent leakage impedance of the machine by 10% of its
original value. The clamp dc voltage source ucl is adjusted to
230 V (1.15 p.u. in the dc-voltage base) and used as protection
just in case of voltage overshoots. It was obtained using the dc
network of the laboratory (40 kW dc machine driven by a
cage-rotor induction machine). A similar way was used to
implement the starting voltage source ust =100 V needed to
provide initial excitation to the inverter. The dc load was
implemented by a load resistor. To minimize the number of
sensors, the dc voltage is estimated by the modulus of the
stator ac voltage using (5).
C. Response of the DC voltage controller
Fig. 8 shows the resulting waveforms of the response to a
step on the dc-link voltage reference at t=25 ms from 0.9 p.u.
to 1 p.u followed by a step on the load current at t=250 ms
from 0.2 to 0.5 p.u.. The transient frequency perturbation
immediately after t=25 ms and t=250 ms is due to the coupling
between voltage and frequency loops via the gain 2/(s0), as
pointed out in Fig. 6. Notice that idc1 and irq have an almost
identical trend, which validates (7). Slow components of rotor
current reference commands are properly tracked. The ripple
at 300 Hz is produced by the diode commutation and is not
entirely compensated for by the current control. However,
improving the tracking capability of current control can be
interesting only when compensation strategies for the torque
ripple are implemented using a suitably distorted reference
command irq*. In that scenario, PI controllers should be
replaced by multi-frame PI or resonant controllers [25]-[26].
Fig. 9 Experimental test rig.
The voltage source inverter was controlled by a low cost
fixed point dsPIC30F4011 produced by Microchip. To obtain
results in real time, four 30 kHz PWM output channels were
used feeding low-pass RC filters whose bandwidth was set at
270 Hz. The DFIG-DC system is connected to a separately
excited dc motor whose armature voltage is adjusted using a
simple three-phase variac and diode bridge. This results in
small rotor speed variations depending on the load. No
decoupling term -idis for the voltage loop has been
implemented, to avoid the additional current sensor for the dc
load current.
Fig. 8 Response of the dc-link controller.
B. Response to the reference in the frequency chain
Fig. 10 shows the response to a step from 1 to 1.4 p.u. on
the reference of the frequency chain.
The frequency increases as predicted. This can be seen also
in the sine of the estimated stator flux position sins. The rotor
current components behave as expected and described in
simulations. The dc-link voltage is only slightly affected by the
frequency transient because of the change in the rotor current
and then in disturbance idis (11) affecting (13) (see Fig. 6).

V. EXPERIMENTAL RESULTS
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level (being ss  (2/)udc). At the same time, the q-axis rotor
current slightly increases in order to provide more generating
torque and then the required active power at the stator side.
However, part of the increase in the torque is also achieved
through the increase in the stator flux. Fig. 11 includes the
reference rotor current traces, confirming the reasonable
tracking capability of current controllers already discussed in
Sec. IV-C. Finally, the stator frequency exhibits a very small
perturbation due to the coupling terms shown in Fig. 6.
D. Response to changes on the load
The response shown in Fig. 12 was obtained increasing the
dc-load from 25% to 50% at a rotor speed close to the
synchronous speed. However, unlike the test in Fig. 10, the
reference values of the dc-voltage and stator frequency were
set to 1 p.u. and were not changed during the test. As a result,
the stator flux magnitude remains almost constant and the
increase in the torque is entirely produced by the q-axis rotor
current. This is clearly visible in Fig. 12, where the q-axis
rotor current is almost doubled after the transient.
Fig. 10 Response to a step on the frequency reference set-point.
C. Response to the reference in the voltage chain
Fig. 11 shows the response of the system to a step on the dclink reference voltage from 0.8 p.u. to 1 p.u.. The references
were calculated in order to obtain a steady state dc voltage
equal to 200 V (approximately 1 p.u. in the dc voltage base).
Obviously, the dc-link voltage signal is characterized by ripple
at 6s due to the diode bridge operation.
Fig. 12 Response to a step on the load.
E. Starting transient
In Fig. 13 a starting transient is shown.
Fig. 11 Response to a step on the reference. Using stator voltage for dc link
measurement.
The q-axis rotor current rises to produce more active power
needed to increase the dc-link capacitor voltage. As already
shown in simulations and according to (7), idc1 and irq have the
identical trend. The d-axis rotor current increases because the
reference frequency is maintained constant and then the flux
needs to increase in order to match with the new dc-voltage
Fig. 13 Starting transient.
The voltage source for starting transients was set at ust =100
V. However, the voltage in Fig. 13 starts from zero because it
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is calculated using the stator voltage: initially the stator voltage
is zero (no excitation in the rotor) and the diode bridge is not
conducting. The q-axis rotor current increases very fast to the
maximum current and next decreases when the voltage is
adjusted. The initial dc voltage variation over a large range
causes an overshoot in the stator frequency, because of the
cross-coupling term and the high initial gain 2/(s0) (the
stator flux is proportional to iRd and starts from zero).
Nevertheless, the frequency and dc voltage quickly stabilize to
the prescribed set-point values.
current loops [24]. Air-gap power has a ripple of about 0.12
peak to peak, again due to the distortion of stator current and
EMF. The error in the estimated slip position is less than 5
deg. As discussed in [21], the error in the estimated slip
position depends mainly on the ratio k (2). The dc current idc1
coming from the diode bridge is distorted due to the diode
commutation, but the dc voltage is quite smooth, thanks to the
dc capacitor.
F. Variable-speed results
Fig. 14 shows the rotor speed, slip speed, cosine of the slip
position, stator frequency and dc voltage during a lowacceleration transient obtained by increasing the speed of the
dc motor within the usual range 0.66 pu - 1.33 pu. The dc load
is set at 0.33 p.u.. The control system is able to maintain both
reference stator frequency and dc voltage at the set-point
values. The dc voltage exhibits no significant perturbations.
Fig. 15 Steady-state waveforms.
The harmonic content for stator current, dc voltage and diodebridge dc current is given in Table I. No significant harmonics
are detected in the dc-voltage.
TABLE I
HARMONICS IN THE THE STEADY-STATE STATOR CURRENT, DC VOLTAGE
AND BRIDGE CURRENT (NORMALIZED TO THE FUNDAMENTAL COMPONENTS)
Fig. 14 Behavior during low-acceleration transient crossing synchronism.
G. Steady-state results
In Fig. 15 steady state results obtained at 1500 r/min are
shown: the dc load is about 0.33 p.u..
Fig. 15 includes p. u. stator phase voltages us and current is
(-component in the stator frame), electromagnetic torque te,
airgap power pg, slip angle error , diode-bridge dc current idc1
(see Fig. 1) and dc voltage udc. The slip angle error  is defined
as the difference between the actual slip angle (computed offline using a stator flux estimator and the encoder signal) and
the estimated slip position ̂ sr given by the block scheme in
Fig. 4 and used to control the DFIG.
As stated, the phase displacement imposed by the diode bridge
on the stator is small. The torque has a 6th-order harmonic due
to the distorted flux and current. The torque ripple amplitude is
about 0.15 p.u. and aligned to values reported in literature for
grid-connected DC-DFIG systems [19]-[20] and can be
reduced using several technologies such as multi-pulse
rectifier arrangements or resonant controllers for the rotor
Harm.
is
udc
idc1
5
6
7
11
12
13
17
18
0.141
0.017 0.017 - 0.014 0.001 <10-3
- <10-3 - <10-3
-
0.091
-
-
0.041
-
-
0.004
19
THD
<10-3
16.3%
-
1.3%
-
10.4%
VI. CONCLUSION
A sensorless field-oriented control of the DFIG-DC system
operating in stand-alone mode has been developed in this
paper. Dc voltage and stator frequency regulations have been
implemented by acting on the q- and d-axis rotor current in the
stator field-oriented reference frame. A small-signal model for
the system under field-oriented control has been derived,
addressing the design of the controllers. A sensorless
implementation avoiding encoder and dc-voltage sensing has
been adopted in simulations and experimental tests to validate
the proposed control. The system has been proved to be
capable of delivering appropriate voltage and frequency
8
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
9
[19] M. F. Iacchetti, G. D. Marques, R. Perini, “A Scheme for the Power
Control in a DFIG Connected to a DC-Bus via a Diode Rectifier,” IEEE
Trans. Power Electron., vol. 30, no. 3, pp. 1286-1296, March 2015.
[20] G. D. Marques, M. F. Iacchetti, “Stator Frequency Regulation in a Field
Oriented Controlled DFIG Connected to a DC Link,” IEEE Trans. Ind.
Electron., vol. 61, no. 11, pp. 5930-5939, Nov. 2014.
[21] G. D. Marques, M. F. Iacchetti, "A Self-Sensing Stator-Current-Based
Control System of a DFIG Connected to a DC-Link," IEEE Trans. Ind.
Electron., vol.62, no.10, pp.6140-6150, Oct. 2015.
[22] G. D. Marques, M. F. Iacchetti, “Field Weakening Control for
Efficiency Optimization in a DFIG Connected to a dc-link,” IEEE
Trans. Ind. Electron., vol. 63, no. 6, pp. 3409-3419, Jun 2016.
[23] Feifei Bu, Yuwen Hu, Wenxin Huang, Shenglun Zhuang, Kai Shi,
“Wide-speed-range-operation dual stator-winding induction generating
system for wind power applications,” IEEE Trans. Power. Electron.,
vol. 30, no. 2, pp. 561-573 Feb. 2015.
[24] M. F. Iacchetti, G. D. Marques and R. Perini "Torque Ripple Reduction
in a DFIG-DC System by Resonant Current Controllers," IEEE Trans.
Pow. Electron., vol. 30, no. 8, pp. 4244-4254. 2015.
[25] Van-Tung Phan, Hong-Hee Lee, ”Control strategy for harmonic
elimination in stand-alone DFIG applications with nonlinear loads,”
IEEE Trans. Pow. Electron, vol. 26, no. 9, Sept. 2011, pp. 2662-2675.
[26] C. Liu, F. Blaabjerg,W. Chen, and D. Xu, “Stator current harmonic
control with resonant controller for doubly fed induction generator,”
IEEE Trans. Power Electron., vol. 27, no. 7, pp. 3207–3220, July 2012.
[27] S.Anand, B. G. Fernandes, M. Guerrero, "Distributed Control to Ensure
Proportional Load Sharing and Improve Voltage Regulation in LowVoltage DC Microgrids," IEEE Trans. on Pow. Electron., vol.28, no.4,
pp.1900-1913, Apr. 2013.
[28] G. D. Marques, M. F. Iacchetti "Voltage control in a DFIG-DC system
connected to a stand-alone dc load," Compatibility and Power
Electronics (CPE), 2015 9th International Conference on, pp.323-328,
Caparica (PT), 24-26 June 2015.
[29] J. T. Alt, S. D. Sudhoff, B. E. Ladd, “Analysis and average-value
modeling of an inductorless synchronous machine load commutated
converter system,” IEEE Trans. Energy Convers., vol. 14, no. 1, pp. 3743, Mar. 1999.
[30] A. Petersson, “Analysis, modeling and control of doubly-fed induction
generators for wind turbines,” Ph.D. dissertation, Chalmers Univ.
Technol. Gothenburg, Sweden, 2005, page 49.
[31] Saeed Golestan, Mohammad Monfared, Francisco D. Freijedo, “DesignOriented Study of Advanced Synchronous Reference Frame PhaseLocked Loops” IEEE Trans. Power Electron., vol. 28. no. 3, pp. 765778, Feb. 2013.
regulation against load variation in the dc-link and can be used
in stand-alone and grid-connected units when inherent dcvoltage regulation capability is required.
APPENDIX
Parameters of the wound-rotor machine
Stator 380 V, 50 Hz, 8.1 A, rotor 110 V, 19 A, 3.2 kW, four
poles, 1400 rpm, Ls = 1.5 p.u., M = 1.13 p.u., rs = 0.06 p.u.,
rr = 0.05 p.u..
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G. D. Marques (M’95-SM’12) was born in
Benedita, Portugal, on March 24, 1958. He
received the Dipl. Ing. and Ph.D. degrees in
electrical engineering from the Technical
University of Lisbon, Lisbon, Portugal in 1981
and 1988, respectively.
Since 1981, he has been with the Instituto
Superior Técnico, University of Lisbon, where he
involves in teaching power systems in the
Department of Electrical and Computer
Engineering. He has been an Associate Professor since 2000. He is
also a Researcher at INESC-ID. His current research interests include
electrical machines, static power conversion, variable-speed drive and
generator systems, harmonic compensation systems and distribution
systems.
Matteo F. Iacchetti (M’10) received the Ph.D.
in electrical engineering from the Politecnico di
Milano, Milano, in 2008. From 2009 to 2014, he
has been a PostdoctoralResearcher with the
Dipartimento di Energia, Politecnico di Milano.
He is currently a Lecturer with the School of
Electrical and Electronic Engineering, at the
University of Manchester, Manchester, U.K. His
main research interests include design,
modelling, and control of electrical machines and electrical drives for
power conversion.
9