IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 6, NOVEMBER 2003
875
Indirect Stator Flux-Oriented Output Feedback
Control of a Doubly Fed Induction Machine
Sergei Peresada, Andrea Tilli, and Alberto Tonielli, Associate Member, IEEE
Abstract—A new indirect stator flux field-oriented output feedback control for Doubly Fed Induction Machine is presented. It
assures global exponential torque tracking and stabilization of the
stator-side power factor at unity level, provided that electric machine physical constraints are satisfied. Based on the inner torque
control system, a speed tracking controller, with load torque compensation is designed using passivity approach. In contrast to existing solutions, the stator voltage vector oriented reference frame
is adopted in order to improve robustness properties with respect to
induction machine parameters variation. To achieve smooth connection of electric machine to the line grid a synchronization algorithm is developed for excitation stage of the Doubly Fed Induction
Machine operation. The solution proposed requires measurements
of line voltages, rotor currents, rotor position and speed. Intensive
experimental studies demonstrate high dynamic performance capabilities of the control algorithm proposed.
Index Terms—AC generators, AC motor drives, electric machines, Lyapunov-based control, power control, torque control,
velocity control.
I. INTRODUCTION
M
ODERN induction motor drives are the most widely
used industrial electromechanical systems. During the
last several decades, a significant research activity has been
concentrated on the control development for squirrel-cage
induction motor drives [1]. From a control point of view, they
represent a complex, multivariable, nonlinear output feedback
problem with parameter uncertainties [2]. Significantly less
attention has been paid to the control development of so-called
Doubly Fed Induction Machine (DFIM). The DFIM stator
windings are directly connected to the line grid, while windings
of the wound rotor are controlled by means of a bi-directional
power converter. The typical connection scheme of a DFIM
is shown in Fig. 1. A vector controlled DFIM is an attractive
solution for high performance, restricted speed range drives and
energy generation applications [3]. For limited speed variations
around the synchronous speed of the induction machine, the
Manuscript received November 13, 2001; revised February 3, 2003. Manuscript received in final form May 27, 2003. Recommended by Associate Editor
J. Chiasson. This work was supported in part by Project MIUR-PRSIN-2001
1093788_004 “Innovative Methodologies and Tools for the Design of Mechatronic Systems”.
S. Peresada is with the Department of Electrical Engineering, National Technical University of Ukraine, “Kiev Polytechnic Institute,” Kiev 252056, Ukraine
(e-mail: peresada@i.com.ua).
A. Tilli and A. Tonielli are with Center for Research on Complex Automated
Systems “G. Evangelisti” (CASY), Department of Electronics, Computer Science and Systems (DEIS), University of Bologna, 40136 Bologna, Italy (e-mail:
atilli@deis.unibo.it; atonielli@deis.unibo.it).
Digital Object Identifier 10.1109/TCST.2003.819590
Fig. 1. Typical connection scheme of a DFIM.
power handled by the converter on the rotor side is a small
fraction (depending on slip) of the overall converted power.
In variable speed drives during motor operating condition,
the rotor slip power is regenerated to the line grid by the rotor
power supply, resulting in efficient energy conversion. In variable speed energy generation applications, the asynchronous nature of the DFIM allows to produce constant-frequency electric
power from a prime mover whose speed varies within a slip
range (sub and super) of the DFIM synchronous speed. Variable-speed energy generation systems have several advantages
when compared with fixed-speed synchronous and induction
generation. In diesel engine and hydroelectric generation systems, they increase the energy efficiency up to 10%. In wind
energy generation systems, the adjustment of the shaft speed
as a function of the wind speed permits higher energy capture
by maximizing the turbine efficiency. Reduction of the torque
ripple in the drive train due to torsional mode resonance can be
achieved with variable speed operation [4].
In both motor and generator applications, the DFIM is able to
provide torque production together with stator side power factor
control. Moreover, if suitably controlled AC/AC converter is
used to supply the rotor side of the DFIM, the power components of the overall system can be controlled with low harmonic
distortion in the stator and rotor sides.
The fundamentals of DFIM vector control are presented in
[3] and [5] and widely used in different developments [6]–[9].
The concept of field-orientation (stator or air-gap flux) as a
torque-flux decoupling technique applied to induction motor
control, is the background for the results reported in [3], [5]–[9].
The torque (active power) or speed regulation problems together
with the stator side reactive power regulation are typically considered depending on application. All of the reported results
are based on the following assumptions: a) information about
flux vector are available in order to provide field oriented coordinate transformation; b) rotor current-fed condition of DFIM
1063-6536/03$17.00 © 2003 IEEE
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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 6, NOVEMBER 2003
operation; c) stator resistance is negligible. Under such conditions, reduced order torque and stator-side reactive power control problem is transferred to the rotor current control problem
if the rotor currents are defined in the field-oriented reference
frame. Assumption of negligible stator resistance is needed in
order to establish the condition of DFIM operation with constant
stator flux modulus. Direct field-orientation is considered on
the base of the flux vector information, which can be computed
from the stator and rotor current measurements or obtained from
the integration of the stator voltage differential equations.
The structure of standard DFIM controllers considered in
[3], [5]–[9] includes two-axis rotor current control loops with
high-gain PI current controllers, implemented in flux oriented
reference frame. Two rotor current references serve as scaled
references for torque and reactive power. Speed and reactive
power outer control loops can be added [3], [5]. In [10], a state
feedback linearization technique has been applied to solve
DFIM control problem. The rotor current-fed assumption is
used with an additional first order filter in the control loop.
The comparison of the power control dynamics in the field
oriented and rotor oriented coordinate frames is given in [11].
Position sensorless solutions have been considered in [7], [9],
[12]. A number of publications report results on the successful
experimental testing of vector controlled DFIM. The general
idea behind all direct field oriented control strategies is that
stator (or air-gap) flux is available from indirect measurements.
Since in DFIM both stator and rotor currents are available from
measurements, the flux vectors (stator, air-gap or rotor) can
be computed using flux current static equations. Nevertheless,
the flux vector computation involves the transformation of one
current vector into stationary or rotor-oriented reference frame,
using high precision position information. Moreover, the static
flux-current relation is dependent on the electric machine
inductances. The saturation effect should be considered in the
flux computation from the measured stator and rotor currents,
since DFIM with power factor control operates with the varying
flux amplitude, dependent on the produced torque. Open loop
integration of the stator voltage equations in order to get stator
fluxes has obvious and well-known practical limitations due to
variation of stator resistance and open loop integration drift.
In [13], the authors introduced an alternative approach for
vector control of DFIM. For the first time the full order control problem, with no assumption of negligible stator resistance,
has been considered. A torque—stator-side reactive power controller has been developed in a line-voltage oriented reference
frame. Since the line voltage can be easily measured with negligible errors, this reference frame is independent of the parameters of the DFIM in contrast with the field-oriented frame. Moreover, information about line voltage is typically needed to perform soft connection of the DFIM to the line grid during the preliminary excitation-synchronization stage. The controller proposed in [13] guarantees global asymptotic torque tracking and
unity stator-side power factor stabilization during steady state.
In [14], the approach of [13] is extended to speed tracking at
stator-side power factor stabilization control problem under assumption of rotor current fed conditions. Both controllers [13]
and [14] are based on the measurement of rotor currents and
rotor speed/position only, and consequently can be classified
as output feedback controllers. The output feedback problem
of DFIM appears even more complex as compared with the
squirrel cage induction machine control. In contrast to vector
control of a standard induction machine, where output variables
to be controlled are torque and rotor flux modulus, torque and
stator flux angle need to be controlled in order to achieve the
stator side reactive power control of DFIM.
The aim of this paper is to present a new output feedback control of the DFIM. The solution proposed provides Indirect Stator
Flux Orientation (ISFO), which corresponds, in principle, to Indirect Rotor Flux Orientation (IRFO) for squirrel-cage induction motor, but it must be emphasized that the control design
path adopted is substantially different with respect to the case
of classical induction motor controllers based on IRFO.
Specifically, the torque tracking, stator-side unity power
factor control problem is considered first, with the requirement
to achieve global exponentially stable rotor current and stator
flux error dynamics, independently of speed behavior. It is
demonstrated that conditions of stator flux field orientation and
line voltage orientation are equivalent if the stator side power
factor is controlled at unity level. Under such a condition, the
stator flux modulus is not a free output variable, but rather it is
a function of the produced electromagnetic torque.
The torque tracking is then extended to the speed tracking
problem in the presence of an unknown constant load torque,
using a passivity-based approach. It is shown that exponential
speed tracking and stator-side power factor stabilization is
locally achievable, provided that the speed references and
their time derivatives, as well as load torque, are properly
bounded. The proposed controller decomposes the original
DFIM dynamics in two interconnected subsystems: mechanical
and electrical, providing asymptotic linearization of the speed
(mechanical) subsystem. As far as the authors know, it is a first
solution of the full order speed tracking problem for this class
of electric machine. An intensive experimental study shows
that high performance torque tracking is achievable while
keeping the stator side power factor at unity during the energy
generation regime. For drive application, high precision speed
tracking is experimentally demonstrated.
The paper is organized as follows. In Section II the DFIM
model and control problem statement are presented. Torque
tracking controller and speed tracking controller, together
with the stator-side unity power factor stabilizing controller,
are designed in Sections III and IV correspondingly. System
initialization procedure is given in Section V. Results of the
experimental tests are presented in Section VI.
II. DFIM MODEL AND CONTROL PROBLEM STATEMENT
A. DFIM Model
The equivalent two-phase model of the symmetrical DFIM,
under the assumptions of linear magnetic circuits and balanced
operating conditions, is represented in an arbitrary rotating (d-q)
reference frame as [3]
(1)
PERESADA et al.: INDIRECT STATOR FLUX-ORIENTED OUTPUT FEEDBACK CONTROL
(2)
(3)
877
with the squirrel cage induction machine (where
) this
allows one to achieve the main control objectives of electromechanical energy conversion together with the optimization of
energy efficiency, using the additional degree of freedom in the
control.
The parameters of the electric machine are defined as follows:
B. Output Feedback Control Objectives
Referring to the general machine model (1), (2), (5), consider
the DFIM model represented in terms of stator fluxes and rotor
currents as
where
, are stator/rotor resistances and inducis the mutual inductance,
is 4 4 inductance
tances,
J is the total rotor inertia, is the
matrix
viscous friction coefficient. One pole pair is assumed without
loss of generality.
Subscripts 1, 2 are used to indicate stator and rotor variables
respectively; subscripts d,q indicate vector components in the
are the rotor
rotating (d-q) reference frame. Variables
is an external load torque,
angle position and speed,
are stator and rotor voltage and current vectors. The
is the angular position of the (d-q) reference frame
variable
with respect to a fixed stator reference frame (a-b). Variables in
the rotating reference frame are related to their corresponding
in the stator and rotor reference frames as follows:
(6)
where
.
The generated torque is equal to
(7)
.
where
Two main classes of DFIM applications are considered.
in the first
When the DFIM is used as generator, the torque
equation of (6) is a mechanical input torque, generated by a
prime mover, and used to stabilize the mechanical system, as
follows:
(4)
where
represents two phase
equivalent voltage, current, flux vectors; superscript (dr, qr) denotes vectors in a reference frame fixed to the rotor.
Flux linkages and currents are related by
(5)
.
where
According to (1) and (2), the electric machine has two control
. When
inputs given by stator and rotor voltage vectors
the DFIM connected to the line is considered, the stator voltage
vector is fixed by
where
are the (constant) amplitude and angular frequency of the line voltage, generated by an ideal voltage source
.
of infinite power;
The line voltage source can be viewed as an additional (not
controlled) excitation input of the DFIM, providing redundancy
. As compared
for the joined action of the two controls
(8)
is the speed controller gain of the prime mover
where
is the prime mover’s speed reference. The elecand
tromagnetic torque T of the DFIM is the load torque for the
mechanical system (8) of the prime energy converter. The main
control objective of the DFIM operating as a generator is to proindependent of .
duce the desired generated torque
In electrical drive applications, the DFIM torque T is the electromagnetically produced torque that controls the speed of the
is an external load torque. A speed
mechanical system and
control objective is typically defined for such applications.
For the abovementioned tasks, the following output feedback
control objectives are defined. Consider the DFIM model, given
by (6) and (7) and assume the following:
A1) the stator voltage amplitude and frequency are constant
(the stator windings are directly connected to the line
grid);
A2) rotor position and speed, stator voltages, and rotor currents are available from the measurements;
A3) DFIM parameters are known and constant.
Under these conditions, it is required to design an output feed) which
back control algorithm (rotor voltage vector
guarantees the following.
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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 6, NOVEMBER 2003
1) For Energy Generation Systems: O.1–1 Global asymptotic torque tracking under condition of stator flux field-orientation, i.e., with
where
is the q-axis flux reference trajectory and
is the
, the torque-flux
reference for stator flux modulus
error dynamics can be written as
(9.a)
(9.b)
is a bounded torque reference
where is the torque error and
trajectory with bounded first and second derivatives.
O.1–2 A smooth transient-free connection of the stator windings to the line grid during the start-up procedure.
2) For the Electric Drives Application: O.2–1 Asymptotic
speed tracking together with the condition of asymptotic stator
flux field-orientation under the condition of constant bounded
load torque, i.e.,
(14)
Assuming the rotor current-fed condition, the following
torque-flux control algorithm is constructed.
• Torque control algorithm
(15)
• Flux level (q-axis) control algorithm
(16)
(10)
is a bounded speed
where is the speed tracking error and
reference trajectory with bounded first, second and third time
derivatives.
It is important to note that speed control objective is required
also for some energy generation systems such as wind power
plants when turbine efficiency control is applied [8].
In the next section, it is shown that the condition of
guarantees that
stator flux orientation
during steady-state condition
with constant torque, i.e., stator reactive power asymptotically
tends to zero when the torque reference is constant.
The torque-tracking problem is solved first to provide global
exponential asymptotic properties for the DFIM electric subsystem. Then the speed tracking and load compensation controller is designed for the outer speed control loop.
III. DESIGN OF THE TORQUE-TRACKING CONTROLLER
In [13], the authors first proposed the use of a stator voltage
vector oriented reference frame, instead of a stator flux oriented
frame, for the control of a DFIM. The line voltage-vector angle
can be easily measured with negligible errors thus avoiding any
stator current measurements.
The stator voltage oriented coordinate transformation is defined by setting in (3) and (4)
(11)
Under such transformation stator flux dynamics (6) becomes
(12)
Defining the flux errors as
(13)
with the q-axis flux reference manifold given by
(17)
The torque-flux error dynamics, generated by the control algorithm (15) to (17) is
(18)
The solution
(19)
is a globally exponentially stable equilibrium point of the
system (18) which has linear time invariant dynamics with
. From (19) it foleigenvalues
lows that requirements (9) of stator flux field-orientation
and torque control objectives are
achieved.
computed from (17) and (15) is
The q-axis flux reference
equal to
(20)
Remark 1: The q-axis flux reference is negative according to
the particular choice of the reference frame.
Remark 2: Equation (20) establishes the physical limitation
of the DFIM torque production with unity power factor at the
stator side during motor operation.
From (19) and (20) it can be concluded that in the steady
and
constant),
state (with
(see (16)), which implies that
(see
(5)), and operation with zero stator-side reactive power
is
achieved.
Remark 3: According to previous consideration, the flux orientation (9.b) imposed by the proposed algorithm is sufficient to
guarantee zero reactive power at stator side in steady-state. It is
PERESADA et al.: INDIRECT STATOR FLUX-ORIENTED OUTPUT FEEDBACK CONTROL
worth noting that (9.b) is also necessary for the above condition
about stator reactive power. In fact, considering the stator equations in terms of stator fluxes and currents in the line voltage
reference frame
879
From (25) it follows that for any
there exist
such that
, therefore, the equilibrium point
(26)
is globally exponentially stable, i.e.,
(27)
it results that
is necessary to guarantee
in
steady-state
.
Remark 4: Since conditions of the stator flux field-orientation are achieved without flux measurement (computation or estimation) the proposed approach can be viewed as an indirect
stator field-orientation, based on passivity of the electric machine stator circuit.
In an actual DFIM, the rotor currents are not available as conin
trol inputs and the torque-flux controller outputs
(15) and (16) can only represent desired trajectories
for the real currents
. The rotor voltage vector
is the only physically available control input of
DFIM. The current loop control algorithm should be designed
to guarantee that current tracking errors
(21)
asymptotically decay to zero.
The rotor current dynamics is given by fourth and fifth equa. By defining the current
tions in (6), with
controllers control algorithm as
(22)
the stator-flux rotor-current error dynamics becomes
(23)
is the current controller proportional gain and
where
the derivative of the current references are computed from the
torque-flux controller (15), (16) with real currents replaced by
their references. To show that the current tracking control objective is achieved, consider the following Lyapunov function:
(24)
.
which is positive definite if
The time derivative of V along the trajectories of (23) is equal
to
(25)
Global stator flux field orientation and current tracking is
achieved according to (27) with bounded internal signals provided that DFIM physical constraint
in (20) is satisfied. The torque error equation from (14) and
(21) is given by
(28)
and torque-tracking objective directly follows from condition
(27).
The resulting torque-flux-current error dynamics is given by
(23), (28). The torque-flux controllers equations are given by
replaced with
, (20) and the rotor
(15), (16) with
current controllers (22).
Remark 5: According to the results proposed by the authors
in [13], an integral action can be added in the current controller
(22). From the application view point, high gains in the proportional and integral feedback actions allow to remove the feedforward actions in (22) preserving “practical stability”, owing
to time scale separation between rotor current and stator flux
dynamics.
Remark 6: The indirect stator field orientation provided by
the proposed controller is based on the strict passivity of the
DFIM stator circuit. The structure of flux and current error dynamics is similar to rotor flux and stator current error dynamics
obtained when indirect rotor flux field-oriented control is applied to squirrel cage Induction Motor (IM) [16]. Nevertheless,
the physics of indirect field-orientation is different for the two
cases. Amplitude of the rotor flux vector can be arbitrary controlled (according to saturation bounds) in standard IM drives,
while angle position of the rotor flux vector is not a degree of
freedom for the field-oriented controller. In the case of DFIM,
the space position of the synchronous reference frame is given
by the stator line voltage vector and angle position of the stator
flux vector (orthogonal to line voltage vector) is controlled by
specifying its amplitude as a function of the produced torque.
IV. SPEED TRACKING CONTROLLER DESIGN
In this section, the speed-tracking and load compensation algorithm is designed on the basis of the inner torque tracking subsystem developed in Section III. The property of global asymptotic exponential stability of the electrical subsystem is used to
specify the desired dynamics of the electric drive mechanical
subsystem. The approach adopted here is similar to the one considered in [15] for squirrel cage IM control and based on passivity theory.
in (27) exSince the norm of the electrical variables
ponentially decays to zero independently of the motor speed, the
torque error converges to zero if flux and current references in
(28) do not grow faster than the exponential function.
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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 6, NOVEMBER 2003
The speed error dynamics can be computed using the first
equation in (6), as follows:
ence
straint
in (20) is bounded according to physical DFIM con-
(34)
(29)
is the estimation of the constant
where is defined in (28),
and the load torque estimation
load torque component
.
error is defined as
Define the desired torque trajectory, generated by the speed
controller, as
(30)
(31)
are proportional and integral gains of the
where
speed controller and is the speed filter time constant. Substituting (30) and (31) in (29) the speed error dynamics becomes
Condition (34) takes into account the effect of the voltage drop
on stator circuit resistance in DFIM stator-side power balance
equation. Such condition exists for all energy converters connected to ac line source. For standard IM, stator resistance is
is sufficiently higher than the motor maxquite small and
. As a result, during physical operating
imum torque
conditions of DFIM inside of motor and converter current and
voltage limits inequality (34) is always satisfied and the torque
production capabilities of the electrical machine are completely
utilized.
During closed-loop speed operation the torque reference is
generated by the speed controller according to (30) and, in general, condition (34) can be violated. Consequently, the speed reference trajectory, the controller initialization as well as the sequence of motor operation must be properly specified in order
not to violate the physical constraint (34) on the motor operation. To specify the speed reference trajectory and load conditions, rewrite (30) as
(35)
(32)
of the speed subsystem is
The nominal dynamics
linear and can be designed to achieve the desired transient perof the PI speed controller
formance by selection of gains
and time constant of the speed filter. Note that a second-order
filter has been inserted in order to generate the reference traand , required for the computation of the flux
jectory for
derivative reference trajectories in (16), (20) and current reference derivatives in (22).
The speed controller design, according to (29) to (32), introduces additional speed filter dynamics, which can be designed
arbitrary fast with small enough in order to be negligible as
compared to basic nominal speed error dynamics given by the
)
reduced order system (with
should be only one part of
The “external” torque reference
. The system initialization procedure
the maximum torque
should guarantee that the “dynamic” part of the torque reference
satisfies condition
. Additionally, limiting the output of the speed controller protects the motor-converter system from over-current conditions. The current limiting
procedure is given by
(36)
If during undesirable transients the speed controller output is
saturated according to (36), then the speed tracking performance
is lost while the torque-flux subsystem remains asymptotically
stable.
In the following stability analysis, it is assumed that conditions (34) is satisfied. The flux reference (20) can be presented
as
(33)
The total error dynamics of the mechanical and electrical subsystems is given by (32) and (18) for rotor current-fed DFIM
and by (23), (28), (32) for the full order case.
Before proceeding to the investigation of stability properties
of the full order error dynamics it is worth considering the following remark.
Remark 7: The torque tracking control algorithm is globally
asymptotically exponentially stable provided that torque refer-
(37)
it follows that
Since by assumption
there exist two constants such that
and
(38)
PERESADA et al.: INDIRECT STATOR FLUX-ORIENTED OUTPUT FEEDBACK CONTROL
881
the total system error dynamics (32), (41), and (23) can be presented as a feedback interconnection of the mechanical and electrical subsystems, whose general form is
The property of exponential stability of the electrical
subsystem has been given in Section III. Conditions 2) and
3) follows from the structure of the torque regulation error
(41). Since bounds
are based on conditions (34),
(37)(38)(39)–(40), the stability is local in general sense.
Nevertheless, full demagnetization of the DFIM due to stator
resistance voltage drop is physically not possible under limited
currents and supply rotor voltages (specifically for DFIM
operation with restricted speed range and strictly limited rotor
side voltage). Therefore practical stability should be guaranteed
by applying appropriate selection of speed references and
initialization of system as discussed above.
Speed tracking directly follows from asymptotic stability of
the system (43). Stator flux field-orientation is achieved according to (27) independently of speed control. Additionally,
, operation
when the system is in steady state with
with zero reactive power at the stator side is guaranteed.
The overall system error dynamics, whose general form is
given by (43), has important properties.
1) The mechanical and electrical dynamics are asymptotis an
ically decoupled, namely, the manifold
asymptotically stable invariant, with a dynamics given by
(indicated as nominal error dynamics of me, the mechanical
chanical-part). Moreover, if
dynamics can be viewed as the sum of the nominal dynamics and a vanishing perturbation, generated by electrical subsystem.
2) Asymptotic linearization of the mechanical subsystem is
achieved since its error dynamics asymptotically tends to
the nominal linear one. Standard optimization techniques
for linear systems can be applied to design the system
of the nominal dynamics of (32).
matrix
The complete equations of the proposed output feedback controller are as follows.
Stator flux vector controller
(43)
(44)
From (37) and (38) it follows that
(39)
and the flux reference derivative
(40)
is bounded.
is also bounded if
Using (30), (31), (37), and (40) the torque tracking error (28)
can be written as
(41)
By using (41) and defining the state space vectors of mechanical
and electrical subsystems as
(42)
Using result reported in [16] it can be proven that the equilibof system (43) is asymptotically exrium point
ponentially stable since the following conditions hold:
is glob1) the subsystem given by the state space vector
ally asymptotically exponentially stable for every trajecsuch that condition (34) is satisfied
tory of
2)
Torque controller
(45)
Rotor current controllers
(46)
Speed controller
3)
Note that with respect [16], the matrix
depends explicitly
on , but, owing to (39), condition 3) reported above holds and
the result of [16] can be applied.
(47)
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Fig. 2.
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 6, NOVEMBER 2003
Block diagram of the speed controller based on inner controller of torque and stator reactive power.
where current reference derivatives are computed using (44),
(45) and (47). Physical rotor voltages are
(48)
are the tuning parameters of the
The coefficients
is the tuning gain of the proportional
speed controller and
rotor current controllers. The block diagram of the proposed
controller is shown in Fig. 2.
trol unit starts the proposed control algorithm with a zero torque
reference (machine “connection”). At this point the torque reference can be applied.
The control algorithm during the excitation stage is constructed as follows. The machine model with open stator
, represented in stator
obtained from (2) with
voltage oriented frame is
(49)
V. SYSTEM INITIALIZATION PROCEDURE
In contrast to squirrel cage IM, the DFIM is supplied from
both stator and rotor sides. A special initialization procedure is
required in order not to violate the physics of the electric machine operation and to ensure that rotor/stator currents as well
as the required rotor voltages are inside the given limits.
The adopted starting sequence for DFIM generator is the following. The prime mover is started first, with the DFIM not actuated. When the mechanical speed is sufficiently close to the
synchronous speed, the control unit (acting on the rotor voltages) imposes currents in the rotor in order to produce on open
stator windings an induced stator voltage vector which is opposite with the line-voltage one (machine “excitation”). During
this stage the excitation control algorithm acts to synchronize
the stator EMF vector to the line voltage vector (both amplitude
and phase). When synchronization is achieved, the stator circuit
is connected to the line grid ensuring soft transient. The con-
with the EMF vector generated by rotor currents in open stator
circuits given by
(50)
The rotor current control algorithm is constructed first as
(51)
PERESADA et al.: INDIRECT STATOR FLUX-ORIENTED OUTPUT FEEDBACK CONTROL
883
Fig. 3. Experimental setup.
where
are the proportional and integral gains of the
PI current controllers.
For constant current references the EMF equations and the
error dynamics of rotor currents during excitation becomes
(52)
(53)
The rotor current subsystem is globally asymptotically stable
. To define the EMF reference it can be noted
for all
that the voltage line vector is aligned with the d-axis, therefore
EMF references are
(54)
Consequently, the references for rotor current are
(55)
From (52) and (53) it can be concluded that synchronization is
achieved with transient performance defined by the dynamics
of the rotor current subsystem (53). Note that: a) the current
references given by (55) are the same as in (15), (16), (20), with
; and b) the structure of the current controller (51)
is a part of the general current controller (22), with additional
integral actions.
The start-up of the DFIM during motor operating conditions
are typically achieved with additional rotor resistances [3] or
using semiconductor soft-starter. When induction machine
speed is inside the controllable slip range (according to rotor
voltage limits), the speed control algorithm can be actuated,
setting the initial condition for speed reference equal to actual
rotor speed.
VI. EXPERIMENTAL RESULTS
Both torque tracking and speed tracking control algorithms
have been experimentally tested using 1 kW wound rotor induction machine, whose rated data are listed in Appendix. The
experimental tests were curried out using an experimental setup,
whose block diagram is shown in Fig. 3. The experimental setup
includes the following.
1) A wound rotor induction machine supplied by a 30 A
matrix converter, operating at 5 kHz switching frequency,
with dead-time equal to 4 s.
2) A current (speed) controlled dc motor, used to provide
the load torque to the DFIM, during drive operation, or to
stabilize the speed of the rotor shaft, when the DFIM is
used as a generator.
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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 6, NOVEMBER 2003
(a)
(b)
Fig. 4.
Transient performance during torque tracking (generator mode).
3) A DSP-based, real-time controller implemented using
dSPACE DS1102 control board (TMS320C31) directly
connected to PC bus. The sampling time for control
implementation has been set to 200 s, the visualization
PERESADA et al.: INDIRECT STATOR FLUX-ORIENTED OUTPUT FEEDBACK CONTROL
885
Fig. 5. Transients during compensation of speed perturbation (generator mode).
and acquisition system of DS1102 were used for real
time tracing of selected variables and data storage.
4) LEM current and voltage sensors for measuring all of the
analog signals. Analog filters with a cut-off frequency of
2 kHz have been adopted for filtering of all analog signals.
5) An incremental encoder with 5000 p/r, used to measure
rotor position and speed.
6) A personal computer, acting as operator interface for programming, debugging, program downloading, virtual oscilloscope and automation functions during the experiments.
The proportional gain of the rotor current controllers in (46)
. The speed controller proportional and
have been set at
integral gains have been selected equal to
,
ms. All programs
with the time constant of the speed filter
for controller implementation have been written using C++ language. The discrete-time version of the algorithm proposed has
been obtained applying simple Euler derivative discretization
method.
A first set of experiments, reported in Fig. 4(a) and (b), was
performed to investigate system behavior during torque tracking
in “generator mode”. The sequence of operation during this test
is shown in Fig. 4(a). The DFIM, already connected to the line
grid, is required to track a trapezoidal torque reference, which
s from zero initial value and reaches the rated
starts at
Nm at
s. Note that flux value, required
value of
886
Fig. 6.
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 6, NOVEMBER 2003
DFIM control system behavior during complete sequence of operating conditions.
to track torque trajectory with unity power factor at stator side
is not a constant, as it is usually assumed neglecting stator resistance in standard field oriented solutions. Fig. 4(b) reports
transients of DFIM variables during torque tracking. Rotor current errors are controlled at zero level. The reactive component
of the stator current is almost null during all the time (a nonzero
value is theoretically admissible only when the torque reference
derivative is not null). As result, the stator phase current, reported in Fig. 4(b), has a phase angle opposite to the line voltage
one.
Fig. 5 shows the dynamic response of the torque controller
for speed perturbation under condition of constant (rated value)
torque production. During this test, the speed of the prime mover
has been controlled below and above the DFIM synchronous
speed (104 rad/s). From the reaction of stator and rotor currents
it can be concluded that perfect compensation of the speed perturbation is achieved. The full test history of the energy conversion system behavior is shown in Fig. 6. It includes: prime
mover start-up; DFIM excitation and synchronization started at
s; connection to the line grid at
s; torque production starting from
s; prime mover speed reduction
to the region below synchronous speed, started at
s.
The transients of the complete test show that high quality of the
synchronization between the EMF, generated by the controlled
DFIM, and the line voltage vector is achieved using excitation
algorithm given by (51). It ensures smooth transient-less connection of the DFIM stator windings to the line grid.
The experimental results reported in Fig. 7 demonstrate the
dynamic performance during speed trajectory tracking (“drive
mode”). During this test the rotor speed has been preliminary
set to 110 rad/s by means of the DC motor and a start-up procedure similar to the case of “generator mode” has been adopted.
This solution is not suitable for industrial plants since the rotor
must be moved by the DFIM also during start-up procedure.
It has been applied for the experimental tests of Fig. 7, since
the available set-up was not provided with additional hardware
(like rotor resistors or semiconductor soft-starter) to perform autonomous moving from zero speed. At
s, as shown in
Fig. 7, the speed reference trajectory is applied, requiring the
unloaded motor to operate above and below the synchronous
speed. The adopted speed trajectory requires a dynamic torque
that is about 80% of the rated value. High-quality speed tracking
capabilities, together with the stabilization of the stator side reactive power on zero level, are observed from the oscillograms.
VII. CONCLUSION
A full-order output-feedback control for Doubly Fed Induction Machine has been presented. This solution is based
on the measurements of line voltages, rotor currents, rotor
position and speed, while no information on stator currents is
required. The algorithm proposed guarantees global exponential torque tracking and stator-side power factor stabilization
during steady state, provided that torque reference amplitude
satisfies the DFIM physical constraints on torque production
(34). The torque tracking problem has also been extended for
speed tracking under condition of constant load torque. The
control development is based on line voltage vector oriented
reference frame, which is more robust with respect to direct
stator-flux oriented one. It has been shown that, under condition
of unity power factor at stator side, the two reference frames
are equivalent during steady state. Experimental tests show
high performance torque and speed tracking during generator
and electric drive operation modes. Soft connection of the
DFIM stator windings to the line grid during excitation-synchronization stage is also achieved. The controller proposed is
suitable for both high-performance generator and electric drive
applications with restricted speed range.
PERESADA et al.: INDIRECT STATOR FLUX-ORIENTED OUTPUT FEEDBACK CONTROL
Fig. 7. Transient behavior during speed tracking.
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APPENDIX
RATED DATA OF THE ADOPTED DFIM
REFERENCES
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Sergei Peresada was born in Donetsk, Ukraine, on
January 14, 1952. He received the Diploma degree
in electrical engineering from Donetsk Polytechnical
Institute in 1974 and the Candidate of Sciences degree in electrical engineering from the Kiev Polytechnical Institute, Kiev, Ukraine, in 1983.
From 1974 to 1977, he was a Research Engineer
in the Department of Electrical Engineering, Donetsk
Polytechnical Institute. Since 1977, he has been with
the Department of Electrical Engineering, Kiev Polytechnical Institute, where he is currently Professor.
From 1985 to 1986, he was a Visiting Professor in the Department of Electrical
and Computer Engineering, University of Illinois at Urbana, Champaign.
His research interests include applications of modern control theory (nonlinear control, adaptation, VSS control) in electromechanical systems, model
development, and control of electrical drives and internal combustion engines.
Andrea Tilli was born in Bologna, Italy, on April 4,
1971. He received the “Laurea” degree in electronic
engineering from the University of Bologna, Italy, in
1996. On February 29, 2000, he received the Ph.D.
degree in system science and engineering from the
same university with a thesis about nonlinear control of standard and special asynchronous electric machines.
Since 1997, he has been with the Department of
Electronics, Computer and System Science (DEIS) of
the University of Bologna. In July 2000, he won a research grant from the above department about the modeling and control of complex electromechanical systems. Since October 1, 2001, he has been a Research
Associate at DEIS. His current research interests include applied nonlinear control techniques, adaptive observers, variable structure systems, electric drives,
automotive systems, active power filters, and DSP-based control architectures
Dr. Tilli is a Member of the Center for Research on Complex Automated
Systems “G. Evangelisti” (CASY).
Alberto Tonielli (A’92) was born in Tossignano,
Bologna, Italy, on April 1, 1949. He received the
Dr.Ing. degree in electronic engineering from the
University of Bologna, Italy, in 1974.
In 1975, he joined the Department of Electronics,
Computer and System Science (DEIS) of the University of Bologna, with a grant from the Ministry of
Public Instruction. In 1979, he started teaching as an
Assistant Professor. In 1980, he became Permanent
Researcher. In 1981, he spent two quarters at the University of Florida, Gainesville, as Visiting Associate
Professor. In 1985, he became an Associate Professor of Control System Technologies at the University of Bologna. Currently, he is a Professor of Automatic
Control at the same university. His current research interests are in the fields of
nonlinear and sliding mode control for electric machines, nonlinear observers,
robotics, and DSP-based control architectures.
Dr. Tonielli is a Member of the Center for Research on Complex Automated
Systems “G. Evangelisti” (CASY).