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International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015
ANALYSIS OF PMSG BASED WIND ENERGY
CONVERSION SYSTEM OPERATING UNDER
DIFFERENT GRID FAULT
Kaki shanmukesh1, Mr.D.V.N.Ananth2 (PH.D)
PG Scholar, Dept of EEE, VITAM Engineering College, Anandapuram, Visakhapatnam (Dt), A.P, India.
2
Assistant Professor, Dept of EEE, VITAM Engineering College, Anandapuram, Visakhapatnam (Dt), A.P, India.
1
ABSTRACT----- In the field of renewable energy
generation has been observed wind energy. Where the
technology is more rapid growth. It attracts attention
as one of the most effective ways in terms of the cost
of generating electricity from renewable energy
sources. Voltage of the wind generator permanent
magnet synchronous generator (PMSG) is directly
driven by a variable due to the sporadic nature of
wind energy. Voltage fluctuation and power of major
concern in the connected network systems generate
electricity using a wind converter list. Inverter is
essential for interaction of from wind sources with Ac
network. Synchronous generators used a variable
speed the permanent magnet to extract the utmost of
energy from wind energy conversion system. The is
suggested common strategy for power control the
permanent magnet synchronous generator a system
based on wind energy conversion (WECS) operating
under different the network conditions A unified
power control strategy is proposed for the permanent
magnet synchronous generator-based wind energy
conversion system (WECS) operating under different
grid conditions. In the strategy, the generator-side
converter is used to control the dc-link voltage and
the grid-side converter is responsible for the control
of power flow injected into the grid. The generatorside controller has inherent damping capability of the
torsional oscillations caused by drive-train
characteristics. The grid-side control is utilized to
satisfy the active and reactive current (power)
requirements defined in the grid codes, and at the
same time mitigates the current distortions even with
unsymmetrical grid fault. During grid faults, the
generator-side converter automatically reduces the
generator current to maintain the dc voltage and the
resultant generator acceleration is counteracted by
pitch regulation. Compared with the conventional
strategy, the with and without dc chopper, which is
intended to assist the fault ride through of the WECS,
can be eliminated if the proposed scheme is
employed., the proposed strategy has quicker and
more precise power responses, which is beneficial to
the grid recovery The simulation results CHECK the
effectiveness of proposed strategies. the power output
of the permanent magnet synchronous generator
(PMSG) of wind turbine systems.
Index Terms—Active damping, grid fault,
permanent magnetic synchronous generator
(PMSG), power control, unbalanced voltage,
wind energy conversion system (WECS).
I. INTRODUCTION
DURING the last decades, wind energy has grown
rapidly and becomes the most competitive form of
renewable energy. Among all kinds of wind energy
conversion systems (WECSs), a variable speed
wind turbine (WT) equipped with a multi pole
permanent magnet synchronous generator (PMSG)
is found to be very attractive and suitable for
application in large wind farms [1], [2]. With
gearless construction, such PMSG concept requires
low maintenance, reduced losses and costs, and at
the same time has high efficiency and good
controllability. Currently, the PMSG-based WECS
has been commercialized
Fig. 1. Configuration of the PMSG-based WECS.
By some WT manufactures, such as Siemens
Power Generation and GE Energy, and its capacity
can be as high as 3 MW.
A typical configuration of the direct driven
MW class PMSG based WECS is illustrated in Fig.
1 [3]–[5]. It consists of the mechanical system
(aerodynamics, gearless drive train, and pitch angle
control) and the electrical system (multi pole
PMSG, full scale converter, and its control). The
modelling and control of such a WECS have been
widely discussed in the bibliography. Usually, the
generator-side converter controls the power flow
produced by the PMSG while the grid-side
converter maintains the dc-link voltage to balance
the input and output power [2]. Field-oriented
control (FOC) and direct torque control are the
most dominant strategies used in the generator side.
The two strategies have similar dynamic responses
and both of them allow separate control of the
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reactive and active current components (or flux and
torque) of the generator [6]. In order to extract
more power from the wind, the active current
component (torque) is regulated so that the WECS
tracks the maximum power point (MPP). The
reactive current component can be controlled to
zero in order to achieve the unity power factor
operation of the PMSG. Alternatively, it can be
regulated to maintain the stator voltage [7] or
minimize the power loss of the generator [2]. The
grid-side converter can also be controlled with
FOC, in which the dq reference frame is usually
aligned with the grid voltage vector [8]. Besides dc
link voltage control, the grid-side converter can
provide parts of reactive current (power) to the grid
[9].
With increasing penetration of wind energy into the
grid, the power system enforces more regulations
on the grid integration of the WECSs [10]–[14].
These codes require the WECSs to behave more
and more as the conventional power plants in the
power system. One important rule is that the
WECS should be able to stay operating during grid
disturbances or faults and provide ancillary services
in order to support the utility.
In order to be compliant with the grid codes,
additional measure, such as the dc chopper, is
required to assist the system operation during grid
disturbances [4], [15].With no more control effort,
the dc chopper can dissipate the unbalanced power
between the generator and the grid when grid fault
happens. Considering the worst scenario (the grid
voltage drops to zero), the power rating of the dc
chopper should be full scale (in MW class) [15].
Such a strategy can hardly satisfy the requirements
of some grid codes as will be shown in this paper.
For the sake of eliminating the dc chopper, a
variable structured controller is designed in [16]
and [17]. Such controller varies the generator-side
power control from the MPP tracking to the
reduced power output when the grid fault is
detected. Nevertheless, the controller cannot
provide enough torsional damping for the WECS in
some instances as denoted in [18]. To reserve the
fault ride through (FRT) capability while obtaining
enough torsional damping, a novel control strategy
is proposed in [3] and [19]. Instead of controlling
the active power flow, the generator-side converter
is utilized to maintain the dc-link voltage while the
grid-side converter is controlling the active power
to the grid. Besides the power controller, additional
active damping loop, consisting of a notch filter
and a phase compensator, is designed to ensure a
positive damping for the torsional vibration. As
verified by the simulations in [19], such a strategy
can successfully assist the FRT of the WECS
during symmetrical grid faults. However, the
strategy is complex and its performance relies on
the system parameters. Moreover, such a solution
can hardly be adaptive to the unsymmetrical grid
faults scenario that is much more common in the
power system. This paper proposes a unified power
control strategy for the MW class PMSG based
WECS operating under different grid conditions,
including unsymmetrical grid faults. In the strategy,
the generator side converter maintains the dc-link
voltage, while providing inherent damping for the
torsional oscillations. Compared with the
conventional strategy, in the proposed strategy, the
dc chopper can be eliminated. In comparison with
the variable-structured control scheme, the
proposed strategy can provide enough torsional
damping for the WECS and has a quicker and more
precise current (power) response during grid faults.
Compared with the scheme in [19], no system
parameter is required for the proposed strategy,
which results in the simple implementation and
good robustness. Moreover, the distortions of the
current injected into the grid can be mitigated with
the strategy so that the power quality is improved
when unsymmetrical grid fault occurs. The
simulation results verify the analyses and the
effectiveness of the proposed strategy.
II. SYSTEM MODELING AND ANALYSIS
MW class multi pole PMSG-based WECS has
relatively soft shafts [3]. The eigen frequency of
the drive train is rather low and within the
bandwidth that is normally taken into account in
power system dynamic simulations [3], [20]. A
multi mass model representation of the drive train
is, therefore, essential in order to properly illustrate
the dynamic impact of WTs on the grid. Although
the three- or higher mass model can be used in the
transient performance study of the WECS, the twomass model is accurate enough to yield acceptable
results [20]. Because of no inherent damper in the
conventional PMSG, the damping factor of the
shaft is neglected. The mechanical system of the
WECS can be expressed as follows [3], [21], [22]:
where, ωh, ωg are the rotational speed of theWT
and the generator; Jh, Jg are the turbine inertia and
generator inertia, respectively; θ is the electrical
angle of the shaft; K is the stiffness of the shaft;
and Twt is the mechanical torque that can be
expressed as
Twt = KwCq v2
(2)
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The PMSG model can be expressed in the
synchronous frame as follows, in which the d-axis
is aligned to the generator rotor frame and the
corresponding q-axis is 90◦ leading [23]
ids =1/Ld vds – Rs/Ld ids + Lq/Lid npωg iqs
iqs =1/Lq vqs − Rs/Lq iqs − Ld/Lq npωg ids –
ψrnpωg/Lq
Tg =1.5np [ψr iqs + (Ld − Lq ) ids iqs]
(3)
where Ld, Lq are d-, q-axis inductances,
respectively; Rs is the resistance of the stator
windings; vds, vqs, and ids, iqs are d-, q-axis
voltages and currents, respectively ;ψr is the
amplitude of the flux induced by the permanent
magnets of the rotor in the stator phases; and np is
the number of pole pairs. If the PMSG is assumed
to have equal d-, q-axis inductances (Ld ≈ Lq ), the
generator torque Tg is proportional to the q-axis
current iqs.
Because of huge inertias of the generator and
turbine, the mechanical dynamics is much slower
than the electrical ones. In the case, the electrical
system can be simply modelled as follows:
where Tg, T* g are the generator electrical torque
and its reference; Xdc = 12 V 2 dc, Cdc, Vdc are the
dc-link capacitance and voltage; Pout, P∗ out are
the output power and its reference from the gridside converter; ts, t_ s is the equivalent time
constants of the generator torque and grid side
converter.
By implementing the control structure in [2] and
[19], the performance of the whole system can be
evaluated based on its small-signal model deduced
from (1), (2), and (4) [18]. As concluded in [18],
resonance can be excited by mechanical or
electrical load changes with either control structure,
which will result in torsional vibrations and system
instability. Strategies in [2] cannot provide enough
damping for the WECS when the constant or
smoothed power production is required. The active
damping scheme presented in [3] needs to know the
shaft resonant frequency and it is non effective if
the WECS operates at power smoothing mode [18].
From the FRT capability point of view, the
control structure in [19] is preferred because the
active and reactive power in the grid side can be
directly controlled. As a result, not only
symmetrical, as in [19], but also unsymmetrical
fault can be handled by the grid-side converter. The
dc chopper can be substantially derated or
eliminated and it is unnecessary to vary the
controller structures when grid fault occurs. This
results in a unified structure for the power control
of the WECS.
III. DESIGN OF THE UNIFIED POWER
CONTROL FOR THE MW CLASS PMSGBASED WECS
The increasing penetration of wind power in the
utility leads to a continuous evolution of grid
interconnection requirements. Basically, the
WECSs are requested to operate robustly in
different grid situations and to provide ancillary
services in order to behave as a conventional power
plant.
The unified power control scheme for the MW
class PMSG based WECS is designed to satisfy the
grid requirements explained in this section. In the
scheme, the generator-side converter is controlled
to maintain a constant dc-link voltage and actively
damp the torsional oscillation. The grid-side
converter can regulate the positive- and negativesequence output power as required by the power
system operator (PSO) under different grid
conditions. If a grid fault happens, to keep the dclink voltage constant, the generator side converter
control starts to reduce the generator power and
thus the power flow to the dc link, by decreasing
the stator current. The power surplus is buffered in
kinetic energy of the large rotating masses and is
reflected in the acceleration of the generator. The
acceleration can be counteracted by the pitch
control when the generator speed increases above
its rated value.
A. Controller Design of the Generator-Side
Converter
In the WECS, usually Jh >> Jg >> max(ts, t’s,
Cdc), so the dynamic responses of the WECS can
be classified into three time scales. Based on the
singular perturbation theory, the slow and fast
dynamics will not affect each other as they have
different response time scale [24]. Therefore, the
fast dynamic is supposed to be fast enough to
converge to its steady state instantaneously when
discussing the slow dynamic. Similarly, the slow
dynamic is neglected in the study of fast dynamic.
As a result, the control of the WECS can be
designed based on the following three sub models:
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International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015
Dynamic model (9) will be stable if kh > 0.
In (7), responses of Tg and Xdc are independent. Tg
responses stably with a positive ts . Substituting (8)
into (7) and ignoring the high-order items, if z = X*
dc − Xdc, we have
Dynamic model (10) is stable if kp > tski .
Fig. 2. Torque characteristics of the WT.
Based on the perturbation theory, the whole
system can be stabilized by controller (8) if all the
subsystems are stable or (11) holds true. The
proposed scheme has inherent oscillation damping
capability since the damping torque is provided
with the generator speed feed forward
in which X*dc = 1/2V *2dc , V * dc is the reference
of the dc-link voltage and the symbols with
superscript “-” represent the quasi-steady value of
the state variables. Design the reference of the
generator torque as
T*g = kh (t) ωg
(8)
where kh (t) = _kp + ki _ _ (X*dc − Xdc) and kp, ki
are the proportional and integral coefficients.
The slowest model (5) behaves as a first-order
system. Fig. 2 shows the typical torque
characteristics of the WT. Considering the
generator torque as Tg1 , the WECS has two
possible steady operation points, in which point
“B” is stable and “C” is unstable. Regarding ωg =
￣ωg = ωh in (8), dynamics model (5) is stable if
kh > ∂Twt/∂ωh . The conclusion can also be
identified from the fact that there is unique cross
point “B” between torque characteristic and line
OB in Fig. 2.
Model (6) is a second-order system and its
transfer function with the control input (8) is as
follows:
Fig. 3. Control diagram of the generator-side
converter.
In order to behave as the first-order dynamic, the
PMSG is controlled with vector control techniques
[3]. By aligning the d-axis of the rotating reference
frame on the rotor flux, the control of the generator
torque and stator voltage can be decoupled. The
control diagram of the generator-side converter is
depicted in Fig. 3. The PI regulator of the dc-link
voltage controller has upper and lower limits in
order to satisfy (11). Equation (8) is the input of the
vector controller and i* ds can be set to zero to
avoid demagnetization of the permanent magnetic.
The rotor flux angle θr for the frame transformation
and the generator speed _ωg in (8) can be estimated
based on the back electromotive force of the
PMSG, which results in the sensor less
implementation of the proposed scheme [25].
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B. Controller Design of the Grid-Side Converter
As the generator and grid are decoupled by the
back-to-back converter, the grid disturbances
would not affect the operation of the generator-side
converter. The grid side converter should take the
responsibility to keep the WECS running properly
even with grid faults. In order to extract the
symmetrical sinusoid currents from the WECS and
improve the power quality during unsymmetrical
grid faults,
where · represents the dot product and × denotes
the cross product; the symbols with superscript “+”
represent the positive sequence variables.
Since only positive-sequence powers are
controlled in such a strategy, the currents injected
into the grid only contain positive sequence
components so that the current distortions are
mitigated [27].
C. Design of the Pitch Controller
Fig. 4. Control diagram of the grid-side converter.
the positive-sequence active and reactive power are
regulated in the proposed strategy. The control
diagram is illustrated in Fig. 4. The control of the
grid-side converter is also based on the vector
control techniques, in which the rotating reference
frame is aligned to the positive sequence grid
voltage vector. The positive- and negativesequence components of the grid voltage can be
separated with the second-order generalized
integrator-based phase locked loop [26]. The angle
of the positive-sequence grid voltage vector θ+ is
then applied to the frame transformation and
control. With such a strategy, the positive-sequence
active and reactive powers of the grid-side
converter, Pout,pos ,Qout,pos, can be controlled
independently by the d-, q-axis currents id,g , iq,g.
In Fig. 4, Pout,pos, Qout,pos, can be calculated
with the following equations:
The pitch control is activated once the generator
speed increases above its rated value and the power
extracted from the wind energy subsequently
reduces.
Due to the nonlinear aerodynamic characteristics
of the WT, pitch angle control is quite difficult.
Conventional linear controller cannot provide
satisfactory performance in a wide wind speed
range [28]. Controller with gain scheduling may be
effective but the gains are hard to tune. In [28] and
[29], the authors proposed a robust pitch controller
based on inverse-system theory. The controller is
simple to implement and is robust to the system
parameter deviations. Fig. 5 shows its control
diagram. It consists of an inverse-system based
control block for the nominal system control and a
robust compensator to mitigate the control error
caused by the parameter deviations [28]. The
controller is employed in the paper and the details
can be found in [28].
IV. SIMULATION RESULTS
The simulations are carried out in MATLAB/
Simulink to verify the aforementioned analysis and
the effectiveness of the proposed strategy. The
models of the MW class PMSG-based WECS
shown in Fig. 1 are included in the simulations.
The drive train is modelled as two-mass
mechanical system as described in (1). The
converter is modelled as a digital system with 1kHz switching frequency and 10-kHz sampling
frequency. Parameters of the WECS for the
simulations are listed in the Appendix.
Fig. 5. Control diagram of the pitch angle.
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its dynamic will affect the reactive current response
once the converter rating is reached. The active
current control of strategy A is not as flexible as the
other strategies since the generator-side converter
always operates at the MPP. As a result, it cannot
provide the reduced iq defined in
Fig. 9 after t = 1.5 s, in contrast to the capability.
Fig. 6. Wind speed profile.
4.1 Operation in Normal Grid situation
Two control strategies, one is the conventional
scheme in [2] and the other is the proposed scheme,
are compared through simulations when the grid is
normal. In both strategies, the grid side converter is
controlled to operate at the unity power factor
mode and output smoothed active power. A random
wind with the profile shown in Fig. 6 is utilized in
the simulation. The responses in terms of the gridside active and reactive power, dc-link voltage,
generator torque, turbine, and generator speed are
presented in Fig. 7. As shown in Fig. 7(a), the
generator speed is oscillating at 2.01 Hz and the
system tends to be unstable with the conventional
scheme. In accordance with [18], the conventional
scheme cannot provide enough damping for the
WECS when the smoothed or constant power is
produced. In contrast, the proposed scheme can
actively damp the speed or power oscillations to
improve the system stability.
4.2 Operation with Symmetrical Grid Faults
The FRT capabilities of the following three control
schemes during symmetrical grid voltage sags are
compared in this section.
Strategy A: the conventional scheme with and
without dc chopper [2].
Strategy C: the proposed scheme without dc
chopper scheme with and without dc chopper [17].
The “E-On Netz” voltage dip profile, shown in
Fig. 8, is employed in the simulations. As
requested, reactive current must be provided if the
voltage dip is more than 10% of the rated value and
no active current should be injected to the grid for
voltage fewer than 0.5 per unit (pu) [11]. The
resultant active and reactive current support during
the fault is defined in Fig. 9. The wind speed
remains 12 m/s during the fault and the simulation
results are illustrated in Fig. 10.
As shown in Fig. 10(a), the grid-side active and
reactive current (iq , id ) controlled with the
proposed strategy can track the profile defined in
Fig. 9 very well. In contrast, strategies A and B can
hardly provide satisfactory results because the
active current (power) is indirectly controlled and
Fig. 7. System responses under normal grid
condition. (a) Conventional scheme. (b)
Proposed scheme
Fig. 8. Voltage drop profile from E-On Netz.
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Fig. 10.1 PMSG speed, torque and stator
current parameters for TLG fault
Conventional
technique
with
and
without
chopper
Fig. 9. Active and reactive current support in
the event of grid fault defined in E.on code.
strategies Aand B. In the generator side, strategy A
outputs a constant maximal power while strategies
B and C reduce the power extraction during the
fault. The active power of PMSG (Pg ) responds
quicker with strategy B in comparison with C
because it is directly controlled. In contrast to
strategy B, strategy C controls the dc-link voltage
Vdc with the generator-side converter. Usually, the
generator side has larger time constant than grid
side. Due to this, slower response and larger
fluctuations can be found in the dc-link voltage
when strategy C is employed. In Fig. 10.2, the fullscale dc chopper is activated during the fault to
consume the generator power in strategy A. The
chopper can be eliminated in strategies A and C
since the output power of the PMSG is actively
reduced by the strategies during grid fault. The
surplus power in the turbine is buffered in the
rotating masses and the resultant generator
acceleration is counteracted by the pitch control
Conventional technique with and without
Fig. 10.2 DC link capacitor voltage during DLG
fault
In Figure above shows plots of the power produced
from the PMSG, , and the real and reactive power
injected into the utility grid, and .
chopper
Conventional
technique
with
and
without
chopper
However, the average model provides significant
savings in computational time com-pared to the
other models.
Proposed with chopper and without chopper
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Fig.10.3 generator parameters like speed, torque
and current output waveforms with and without
chopper circuit with TLG fault
.proposed with chopper and without chopper
In Fig 10.5 above, the full-scale dc chopper is
activated during the fault to consume the generator
power in strategy A.
Fig.10.5 stator three phase voltage & current
output waveforms with and without chopper
circuit with TLG fault
Hence the output power of the PMSG is
actively reduced by the strategies during grid fault.
The surplus power in the turbine is buffered in the
rotating masses and the resultant generator
acceleration is counteracted by the pitch control
4.3 Operation With Unsymmetrical Grid Faults
Fig.10.4 DC capacitor voltage waveforms with
and without chopper circuit with TLG fault
Usually, unsymmetrical grid fault happens more
often than the symmetrical faults. During
unsymmetrical voltage sags, the negative-sequence
voltage can lead to second-order harmonics in the
injected currents. In addition to handling the
overvoltage of the dc capacitor during the fault,
additional efforts should be spent on mitigation of
current harmonics. With the three strategies, the
system responses during unsymmetrical grid faults
are illustrated in Fig. 11. In the simulation, the
wind speed remains at 12 m/s and a 150 ms phasephase short circuit is applied on the transmission
line at t = 1 s, which results in 85% positivesequence voltage sags and 50% negativesequence
voltage jump at the connection point of the WECS.
The WECS is requested to produce 1 pu reactive
currents and no active currents during the fault.
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Conventional
technique
with
and
without
chopper
Conventional technique with chopper and
without chopper
Fig. 10.8 PMSG speed, torque and stator
current parameters for DLG fault
Fig. 10.6 PMSG speed, torque and stator
current parameters for SLG fault
Conventional technique with chopper and
without chopper
Fig. 10.7 DC link capacitor voltage during SLG
fault
Conventional technique with chopper and
without chopper
Conventional technique with chopper and
without chopper
Fig 10.9 DC link capacitor voltage during SLG
fault
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Proposed Control Scheme Without & With
Chopper
Fig.11.2 DC capacitor voltage waveforms with
and without chopper circuit with SLG fault
Fig.11 generator parameters like speed, torque
and current output waveforms withand without
chopper circuit with SLG fault
Fig.11.3 Grid terminal three phase voltage &
current output waveforms with and without
chopper circuit with SLG fault
Fig.11.1 Mechanical torque output waveforms
with and without chopper circuit with SLG fault
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International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015
Fig.11.4 generator parameters like speed,
torque and current output waveforms withand
without chopper circuit with SLG fault
Fig.11.6 stator three phase voltage & current
output waveforms with and without chopper
circuit with DLG fault
Fig11.5 DC capacitor voltage waveforms with
and without chopper circuit with DLG fault
Fig 11.7 Grid terminal three phase voltage &
current output waveforms with and without
chopper circuit with DLG fault
The direct and quadrature axis current waveforms
without and with chopper are shown in Fig. 7.14.
As denoted, the positive- and negative-sequence
components Vabcg,pos, Vabcg,neg in the grid
voltage Vabc,g can be separated successfully with
the presented scheme. Because the power control is
not designed on the positive-sequence synchronous
frame, the output currents with strategies A and B
are highly distorted in Fig.8.14. In contrast,
strategy C results in sinusoidal and symmetrical
grid currents even with the unsymmetrical grid
fault.
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CONCLUSION
The converter-based WECS has the potential to
improve the transient stability of the power system
because of its quickpower response. However, the
rating of power devices limits its applications. In
order to make maximal use of such systems,
advanced control technique should be developed to
satisfy the requirements of the power systems. The
conventional control strategy for the PMSG-based
WECSis mainly designed to promise the proper
operation of the generator. In the strategy, the
generator torque (power) is directly controlled
while the grid side power is indirectly regulated.
The disturbance at the generator side will aggravate
the power responses
at the grid side, which is not desired by the PSO.
The basic idea of the proposed strategy is to first
satisfy the power system requirements under
different grid conditions. In the strategy, the
active/reactive current (power) is directly regulated
through the grid-side converter. In order to provide
enough oscillation damping, additional active
damping loop is integrated into the generator-side
controller. Compared with the conventional or
variable-structured control strategies, the proposed
one has the quickest and most precise grid-side
current(power) responses. During grid fault, no dc
chopper or controller switching is necessary with
the strategy and the current distortions can be
mitigated when the unsymmetrical grid fault
occurs. Moreover, the proposed strategy requires
no system parameters and is simple to implement,
which makes it attractive for the engineering
practice. However, such a strategies sacrifices the
response of the generator-side variables and leads
to the fluctuation of the dc-link voltage. It is
believed that a large dc-link capacitor can be
helpful to improve the system performance if the
proposed strategy is employed.
APPENDIX
PARAMETERS OF THE PMSG-BASED WECS
Parameters of the WECS in the simulations are
converted to a pu system and the real values can be
derived by multiplying each pu value and the base
value. The system base values are defined as
follows [30]:
where the variables with subscript “b” represent the
base values; P, V, I, f are the power, voltage,
current, and electrical frequency, respectively;
Z,L,C are the impedance, inductance, and
capacitance, respectively; ω,Ω are the electrical and
mechanical angular frequencies, respectively; T is
the torque; J,K are the inertia and stiffness,
respectively; np is the pole pairs of PMSG; and ψr
is the amplitude of the flux induced by the
permanent magnets of the rotor.
Base power Pb (MVA)
1.5
Base voltage Vb (V )
690/√3
Base frequency fb (Hz)
11.5
Pole pairs of PMSG np
40
Nominal WT mechanical power (pu)
1.1
Nominal WT speed (pu)
1.2
WT inertia constant (pu)
4.8
PMSG inertia constant (pu)
0.5
Shaft stiffness (pu)
2
Rated generator torque (pu)
1
Rated generator power (pu)
1
Rated generator line voltage (pu)
1
Rated generator speed (pu)
1
Generator inductance in the d frame (pu)
0.7
Generator inductance in the q frame (pu)
0.7
Generator stator resistance (pu)
0.01
Flux of the permanent magnets (pu)
0.9
DC-link capacitance (pu)
1
Line inductance (pu)
0.1
Rate wind speed (m/s)
12
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