Adaptive Control Pmsg
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Transcript of Adaptive Control Pmsg
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1446 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 29, NO. 3, MAY 2014
An Adaptive Control Strategy for a Wind Energy
Conversion System Based on PWM-CSC and PMSGEduardo Giraldo, Member, IEEE, and Alejandro Garces, Member, IEEE
AbstractThis paper proposes a new adaptive control strategy
for a wind energy conversion system based on a permanent
magnet synchronous generator and a pulse-width modulated cur-
rent source converter. Most of the studies on wind farms are based
on double fed induction technology. Nevertheless, the proposed
conversion system is a good alternative due to its high efciency
and reliability. Electrolytic capacitors are not required in this
type of converter and the voltage in the DC-link as well as the
generated reactive power can be dynamically modied according
to the wind velocity, being even negative if required. However, it is
challenging from the control and stability standpoint. Capacitive
lters placed on the AC side, which are required for safe commu-
tation, can create resonances with the power grid. Reactive power
is generated according to the capacity of the converter, the wind
velocity and the load prole. The adaptive control strategy uses an
adaptive PI which is self-tuned based on a linear approximation
of the power system calculated at each sample time. A model ref-
erence is also proposed in order to reduce the post-fault voltages.
Simulation results demonstrate the advantages of the proposed
control.
Index TermsAdaptive control, permanent magnet generators,
pulse-width modulated current source converter, reference model,
wind energy.
NOMENCLATURE
Mechanical power.
Wind velocity.
Area swept by the blades.
Air density.
Tip ratio.
Pitch angle.
Coefcient of power.
Rotational speed.
Stator phase resistance of the machine.
Armature inductance.
Inductance in the PWM-CSC.
Voltage in the output of the diode rectier.
Manuscript received May 03, 2013; revised August 15, 2013; accepted
September 25, 2013. Date of publication October 08, 2013; date of current
version April 16, 2014. Paper no. TPWRS-00521-2013.
The authors are with the Department of Electrical Engineering, Universidad
Tecnolgica de Pereira, Pereira, Colombia (e-mail: [email protected]; ale-
Color versions of one or more of the gures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identier 10.1109/TPWRS.2013.2283804
Current in the DC link.
Voltage in the input of the PWM-CSC (DC side).
Voltage in the output of the PWM-CSC (AC side).
Modulation index.
Angle of the modulated current.
I. INTRODUCTION
M ODERN wind power applications require efcient andexible technologies that adapt to changes in load andgeneration. These challenges can be met by a combination of
non-conventional energy conversion systems and improved
adaptive control strategies.
In terms of the energy conversion system, most of the wind
turbines for on-land emplacements use double fed induction
generators due to their economic advantages (i.e., high ef-
ciency, improved controllability and reduced rating of the
converter [1]). Nevertheless, other energy conversion sys-
tems and generator technologies have been proposed recently
[2][4]. One of the most promising of them is the permanent
magnet synchronous generator (PMSG) which has clear ad-
vantages in terms of efciency and power density. Integration
into the grid of this type of generators requires a full rated
AC/AC converter which, in most cases, is based on the voltage
source converter technology (VSC). Another possible type of
converter is the pulse-width modulated current source con-
verter (PWM-CSC) which has potentially more advantages for
medium size wind turbines [5]. It is capable of controlling the
DC current according to the wind velocity independently of
the DC voltage. This characteristic is exploited in this paper
to create an adaptive control which does not require measure
of the rotational speed. In addition, it permits the use of a full
bridge diode rectier in the side of the machine and hence,
efciency and reliability are improved.
Adaptive control allows the integration of wind resources as
plug-and-play devices in electric power systems. As a result,
this type of control is a key technology in smart-grids and elec-
tric energy systems with non-dispatchable generating sources
[6].
Several design procedures for control of power systems are
well known for cases in which the resulting control system is
time invariant. However, these procedures require a detailed
knowledge of the process dynamics and must be redesigned
if the process is time varying [7]. On the other hand, adaptive
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GIRALDO AND GARCES: ADAPTIVE CONTROL STRATEGY FOR A WIND ENERGY CONVERSION SYSTEM 1447
control techniques that perform identication and control of dy-
namic systems can be adapted to highly-complex dynamic sys-
tems in order to auto-adjust the controller parameters. However,
thesemethods require an adequate initialization of the controller
parameters and detailed system data [8].
Specically, PI controls has been widely used for control of
power systems, but the tuning of these controllers is a highly
demanding task when the parameters of the controlled process
either are poorly known or vary during normal operation [9].
An adaptive PI control can be designed in order to achieve
high-performance control systems [10]. However, during
normal operation where the controlled process are almost time
invariant, a xed PI control may have similar performance in
terms of reference tracking. Additionally, since the process is
nonlinear, by using linear estimators it is possible to obtain
a time varying linear approximation which can be used to
self-tune the controller.
This paper proposes a new adaptive control strategy for a
wind energy conversion system based on a permanent magnet
synchronous generator and a pulse-width modulated current
source converter. The proposed conversion system is a good
alternative due to its high efciency and reliability. The control
strategy uses an adaptive PI which is self-tuned based on a
linear approximation of the power system and a desired closed
loop response.
The paper is organized as follows: In Section II the energy
conversion system is presented. Advantages of each component
are also described. Next, in Section III the proposed adaptive
control is deduced. After that, simulation results are presented.
Finally, conclusions are presented in Section V.
II. ENERGY CONVERSION SYSTEM
The proposed energy conversion system is based on PMSG.
This type of machine has three main features which are rele-
vant for wind power applications: there are no signicant losses
generated in the rotor; magnetization provided by the perma-
nent magnets allows soft start; and there is no consumption of
reactive power. The rst characteristic implies an improvement
in efciency while the second and third effect the power elec-
tronic converter which does not require bidirectional power ca-
pability. Hence, a full bridge diode rectier is enough for the
AC/DC conversion. In addition, PMSGs allow smaller, exible
and lighter designs as well as lower maintenance and operating
costs. A gear box is not required if it is designed appropriately
with a high number of poles.
A PMSG requires a full rated converter which is usually a
back-to-back conguration with voltage source converters as
shown in Fig. 1(a). This type of converter is efcient for in-
tegrating induction generators since it controls reactive power
in the rectier as well as in the inverter. However, a PMSG
does not require reactive power and hence the rectier can be
replaced by a diode rectier [11]. Nevertheless, the DC voltage
in a VSC must remain within certain limits in order to maintain
stability. As a consequence of this, a DC/DC boost converter
is required for controlling the power in the electric machine as
depicted in Fig. 1(b). The use of a three-phase diode rectier
improves the efciency and reliability of the energy conversion
system but the boost converter could have an opposite effect.
Fig. 1. Three possible congurations for PMSG integration: (a) back to
back converter with VSCs, (b) diode-bridge rectier and boost converter, and
(c) proposed energy conversion system with PWM-CSC.
Any power electronic converter based on forced commutations
has two types of losses: conduction losses and switching losses.
Conduction losses depend mainly on the collector current while
switching losses are mainly related to the switching frequency.
Usually converters are designed in such a way that conduction
and switching losses are equal. A full-bridge can be considered
as a device with only conduction losses since switching occurs
only once during each cycle.
A third option is to integrate the PMSG to the main grid
through a diode rectier and a PWM-CSC as given in Fig. 1(c).
Variation on the DC voltage is not a limitation on the PWM-
CSC; hence the power can be controlled directly by the inverter.
In addition, a PWM-CSC does not require an electrolytic capac-
itor as the VSC. This impacts the reliability of the systems since
30% of failures on AC converters are related to the electrolytic
capacitor [12].
PWM-CSC technology has been applied successfully in a
wide range of applications such as motor drives [13], power
quality conditioners [14] and HVDC transmission for offshore
wind generation [15][17]. Unlike the line commutated con-
verter a PWM-CSC is based on forced commutation and con-
sequently it is able to control active and reactive power. In ad-
dition, it has an inherent short-circuit protection capability [18].
A PWM-CSC requires semiconductor devices with reverse
voltage blocking capability. This can be added to a standard in-
sulated-gate bipolar transistor (IGBT) using a diode connected
in series as shown in Fig. 2. Another alternative is the new
type of semiconductor devices such as reverse blocking IGBTs
(RB-IGBT) or integrated gate commutated thyristors (IGCTs).
The latter alternative is promising for PWM-CSCs [19].
The DC current is directly controlled by the converter. This
feature is specially important for low wind velocities when
voltage in the machine is greatly reduced. While a voltage
source converter requires a constant voltage on the DC side, a
PWM-CSC is able to adapt its voltage according to the wind
velocity. Efciency is improved due to this capability.
The unity power factor is achieved by the modulation itself.
This is done by using space vector modulation [5]. In addition,
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1448 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 29, NO. 3, MAY 2014
Fig. 2. Pulse-width modulated current source converter.
output voltage presents low harmonic distortion and the perfor-
mance for weak grids is guaranteed.
Nevertheless, PWM-CSC has some challenges related to the
control of the converter [20]. The lter placed in the AC side
can create resonances with the grid so that active damping tech-
niques are required. However, these techniques reduce the band
width of the control [21]. In addition, the voltage on the DC
side must be controlled according to the wind velocity in order
to improve efciency and guarantee stability.
III. PROPOSED ADAPTIVE CONTROL FOR PWM-CSC
A hierarchical control is proposed for integration of the wind
turbine into the grid as depicted in Fig. 4. First, the maximum
tracking point algorithm is modied in terms of the DC cur-
rent in the PWM-CSC. Therefore, the reference for this current
is modied dynamically according to the wind velocity. Next,
an adaptive PI control is designed in order to track this refer-
ence. Finally, a model reference control is included in order to
reduce the over-voltages resulting from a fault in the grid. Space
vector modulation (SVM) is used to modulate the current of the
converter.
A. Maximum Tracking Point
The power generated by a wind turbine is proportional to the
cube of the wind velocity as given in (1):
(1)
Maximum power transference is achieved by an optimal
value of . Consequently the rotational speed must be
proportional to the wind velocity and hence, power must be
proportional to the cube of the rotational speed as given in (2):
(2)
On the other hand, the PMSG is modeled on the rotor refer-
ence frame as follows:
(3)
(4)
Fig. 3. Reference for using a maximum tracking point algorithm.
The voltage on the diode rectier (see Fig. 2) is propor-
tional to the voltage in the terminals of the machine which in
turn is given by (5) where is a proportional constant:
(5)
This expression was obtained by replacing (2) in the model
of the PMSG in stationary state and ignoring the voltage drop
in the inductance. This approximation will be demonstrated nu-
merically on Section IV. A speed sensor is not required when
using this expression since the voltage is measured.
The generated power is given by (PMSG losses
are ignored). As a result, the optimal to achieve maximum
tracking is given by (6):
(6)
where is a proportional value which can be approximated as
follows:
(7)
This equation establishes a set point for current as given
in Fig. 3. A low pass digital lter (LPF) is required to smooth
voltage . The cut-off frequency is set below commutation
frequency.
On the other hand, the dynamics of depends on the in-
ductance as follows:
(8)
Each element in this equation is given in Fig. 2. The modula-
tion of the converter depends on the current which varies
according to the wind velocity but cannot be zero. Therefore,
(8) can be written in terms of power as given in (9):
(9)
where is the power delivered by the converter which in turn
depends on the modulation index as follows:
(10)
where is the angle of the output current. This angle must be
equal to the angle of the grid voltage in order to achieve a unity
power factor. A phase locked loop is required as illustrated in
Fig. 4. Therefore, the only control variable is as given in (11):
(11)
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GIRALDO AND GARCES: ADAPTIVE CONTROL STRATEGY FOR A WIND ENERGY CONVERSION SYSTEM 1449
Fig. 4. Proposed hierarchical strategy for adaptive control of the energy conversion system based on a pulse-width modulated current source converter.
Fig. 5. Adaptive control and identier.
The output power beyond the capacitive lter is approxi-
mately equal to . Usually, the control in current source con-
verters is made in two stages, one controlling the active power
and the other controlling the voltage in the AC side. This ap-
proach directly controls the active power and the reactive power
is maintained by the modulation itself. Therefore, the possible
resonances on the controls are reduced. The resulting nonlinear
system requires an adaptive control as will be demonstrated in
the next subsection.
B. Adaptive Control
This paper means by adaptive control any control strategy
which uses parameter estimation of the plant in real time by
using recursive identication. The adaptive controller to be de-
signed is based on the certainty equivalence principle: design
the controller as long as the plant parameters are known. How-
ever, since these are unknown at time , they are replaced by
an estimate given by an online identier [22].
This adaptive controller is easy to implement, since for the
controlled plant, only the output signal is needed for feedback.
An adaptive PI control is designed where the plant parameters
are estimated by an online identier, as shown in Fig. 5.
In continuous time, a PI controller can be dened as
(12)
being the control signal, and the error signal (repre-
sented by the difference between the reference and the output
signals). In this case, these variables are given as follows:
(13)
(14)
In discrete time, the PI controller can be dened as
(15)
(16)
being the sample time , and the error
and the integral error at time respectively, and the
integral error at time . By dening a delay operator
such as . Equation (15) can be rewritten as
follows:
(17)
(18)
(19)
Therefore, the control signal at time can be expressed as
(20)
(21)
(22)
(23)
Obtaining the following expression for the PI controller in dis-
crete time
(24)
where the parameters and of the PI controller in con-
tinuous time can be related to the controller in discrete time, as
follows:
(25)
(26)
Since the process to be identied is nonlinear, the identied
model is a linear approximation of the nonlinear model at time
instant . A simplied rst order model is selected, described
by a discrete transfer function, as
(27)
where the unknown parameters to be estimated are and .
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1450 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 29, NO. 3, MAY 2014
Fig. 6. Diagram block using transformation.
Equations (24) and (27) can be rewritten by using the trans-
formation as follows:
(28)
and
(29)
By using (28) and (29) it is possible to formulate the block
diagram of Fig. 6. From this gure it is possible to obtain the
closed loop transfer function, as follows:
(30)
(31)
(32)
(33)
If dening desired closed loop poles, given by
(34)
where and are the discrete time roots of (34), which can
be related to the continuous time roots and by using
(35)
(36)
It is possible to obtain the controller parameters by comparing
the closed loop poles with the desired closed loop poles of (34)
as follows:
(37)
(38)
(39)
(40)
Therefore, the controller parameters can be obtained from
(34) as
(41)
(42)
where it is evident that and are related to the linear ap-
proximation model of the nonlinear process, represented by the
discrete transfer function (29).
In order to estimate the plant parameters (29), a simplied
identication algorithm, known as projection algorithm, de-
scribed in [22] is proposed. When the projection algorithm is
applied in (29) for the estimation of and , the following
actualization rule is obtained:
(43)
(44)
(45)
where and are the estimated parameters at time
, and and are the estimated parameters at
time .
Since the controller parameters are dependent on and
according to (41), a time varying parameters for each can be
obtained as follows:
(46)
(47)
where and are automatically tuned according to
the desired closed loop poles.
Finally, the controller parameters and can be calcu-
lated from (25) by
(48)
(49)
Therefore, the resultant controller is an adaptive PI controller
calculated for each . The behavior of the controller can be
determined by the selection of the desired closed loop poles of
(34) and the sample time , according to (35).
C. Model Reference Adaptive Control
Reference current is modied during a short circuit in
order to improve the short circuit behavior of the converter. A
slightly different current in which the desired output is gen-
erated by a linear reference model is proposed. The reference
model can be selected with an order less than or equal to the
order of the process. In this work, a zero order model is used in
pre-fault , no control during the fault
and a rst order model after the fault as follows:
(50)
(51)
where must be selected as a stable root , where
it is clear that the reference model must be selected as a stable
model with unitary gain. However, the selection of the reference
model and the pole placement technique are separate problems,
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GIRALDO AND GARCES: ADAPTIVE CONTROL STRATEGY FOR A WIND ENERGY CONVERSION SYSTEM 1451
Fig. 7. Simulated primary feeder with the proposed energy conversion system.
TABLE I
PARAMETERS OF THE SYSTEM
so it is evident that by using a reference model the exibility of
the control system in the assignment of the closed loop poles is
increased. The fault condition is detected using the voltage .
IV. RESULTS
A detailed switching model of the proposed energy conver-
sion system was simulated using Matlab-Simulink. The system
consists of a 13.2-kV distribution feeder with a 2-MWwind tur-
bine as shown in Fig. 7. Parameters of this system are shown in
Table I.
The discrete time roots were selected in order to
achieve steady state in 20 ms. On the other hand, the reference
model for short circuit condition was calculated for 400 ms.
Wind velocity for 15-s simulation is depicted in Fig. 8. Base
wind velocity is 12 m/s. A gust is simulated in order to demon-
strate the maximum tracking point capability of the proposed
control. Wind velocity prole was created using a detailed
model which considers stochastic behavior [23]. Rotational
speed and voltage are plotted in Fig. 8. These two vari-
ables are proportional as expected. Fig. 9 shows voltage
with respect to rotational speed for the aforementioned simu-
lation. The linear approximation given in (5) is more accurate
for low wind velocities. At high wind velocities, the generated
power increases the current and hence, the voltage drop on the
inductance inuences the generated voltage. Nevertheless, the
linear approximation is accurate enough from a practical point
Fig. 8. Wind velocity, rotational speed and DC voltage.
Fig. 9. Voltage versus rotational speed.
Fig. 10. Generated power in the point of common coupling.
of view and maximum tracking is achieved as shown in Fig. 10.
High inertia of the set turbine-generator produces a delay in
the rotational-speed tracking capability but also a smoothing
effect. This is expected in almost all type of controls for wind
energy.
Generated power is shown in Fig. 10. Wind velocity is again
shown in this gure. An almost perfect tracking characteristic
is achieved in as illustrated in Fig. 11.
The control strategy changes dynamically according to the
wind conditions as shown in Fig. 12. If a time invariant PI con-
trol is used the performance could be similar at least at nominal
wind velocity. In that case, the proposed algorithm can be used
as a tuning technique.
Three-phase voltages and currents in the PWM-CSC are
shown in Fig. 13. Small harmonic distortions are present in
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1452 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 29, NO. 3, MAY 2014
Fig. 11. DC current and reference .
Fig. 12. Values of the adaptive controls and .
Fig. 13. Three-phase voltages and currents on the PWM-CSC.
three-phase voltages due to the commutation process. They
are attenuated by the transformer and hence, the voltage
in the point of common coupling is completely sinusoidal.
A smoother waveform can be achieved by increasing the
switching frequency at the expense of higher switching losses.
Transient behavior of the proposed control was also tested
in the same distribution feeder. Wind velocity was maintained
constant in 12 m/s. A three-phase short circuit at Node 3 was
simulated in (see Fig. 7). Results are shown in Fig. 14.
The voltage on the grid dropped to almost zero [Fig. 14(a)]. Cur-
rent increased due to the drop on the grid voltage in Node
3. The converter still worked in this condition maintaining the
unity power factor. The reference model enter into operation
by maintaining . This allows for energy storage in
Fig. 14. Response for a three-phase fault in the grid. (a) Grid voltages. (b)Mod-
ulation index and DC current. (c) Control variables. (d) Voltages at the primary
of the transformer. (e) Output currents.
the inductance during a fault. The reference for changes
smoothly since it depends on the wind velocity. The modula-
tion index increases up to the point of over-modulation. Conse-
quently, the parameters of the control decreases. These parame-
ters return to their normal values after the fault is cleared. Notice
that the voltages and currents after the fault are within the max-
imum limits due to the introduction of the reference model.
V. CONCLUSIONS
An adaptive control for a PWM-CSC-based energy conver-
sion system particularly designed for wind power applications