ANALYSIS OF PMSG BASED WIND ENERGY...

International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015

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ISSN: 2278 – 7798 All Rights Reserved © 2015 IJSETR

ANALYSIS OF PMSG BASED WIND ENERGY

CONVERSION SYSTEM OPERATING UNDER

DIFFERENT GRID FAULT

Kaki shanmukesh1, Mr.D.V.N.Ananth

2 (PH.D)

1PG Scholar, Dept of EEE, VITAM Engineering College, Anandapuram, Visakhapatnam (Dt), A.P, India.

2Assistant Professor, Dept of EEE, VITAM Engineering College, Anandapuram, Visakhapatnam (Dt), A.P, India.

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 generator-

side 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 two-

mass 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 grid-

side 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 PMSG-

BASED 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 negative-

sequence output power as required by the power

system operator (PSO) under different grid

conditions. If a grid fault happens, to keep the dc-link 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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Fig. 2. Torque characteristics of the WT.

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:

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 .

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

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,

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 negative-

sequence 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:

Fig. 5. Control diagram of the pitch angle.

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

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 1-

kHz switching frequency and 10-kHz sampling

frequency. Parameters of the WECS for the simulations are listed in the Appendix.


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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 grid-

side 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

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. 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. 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 full-

scale 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

chopper

Fig. 10.1 PMSG speed, torque and stator

current parameters for TLG fault


chopper

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

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.10.4 DC capacitor voltage waveforms with

and without chopper circuit with TLG fault

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

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 phase-

phase short circuit is applied on the transmission

line at t = 1 s, which results in 85% positive-

sequence 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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chopper


current parameters for SLG fault

Conventional technique with chopper and

without chopper

Fig. 10.7 DC link capacitor voltage during SLG

fault


without chopper


without chopper


current parameters for DLG fault


without chopper

Fig 10.9 DC link capacitor voltage during SLG

fault


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Proposed Control Scheme Without & With

Chopper

Fig.11 generator parameters like speed, torque

and current output waveforms withand without

chopper circuit with SLG fault

Fig.11.1 Mechanical torque output waveforms

with and without chopper circuit with SLG fault

Fig.11.2 DC capacitor voltage waveforms with

and 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


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Fig.11.4 generator parameters like speed,

torque and current output waveforms withand

without chopper circuit with SLG fault

Fig11.5 DC capacitor voltage waveforms with

and without chopper circuit with DLG fault

Fig.11.6 stator three phase voltage & current

output 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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