EUROPEAN TRANSACTIONS ON ELECTRICAL POWER

Euro. Trans. Electr. Power 2011; 21:954–972

Published online 25 August 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/etep.488

PMSG-based variable speed wind energy conversion system

using Vienna rectifier

Amir Hossein Rajaei, Mustafa Mohamadian*,y,

Seyed Mohamad Dehghan and Ali Yazdian
Department of Electrical Engineering, Tarbiat Modares University, Tehran 14115-111, Iran

SUMMARY
In this paper, a new variable-speed wind energy conversion system (WECS) with permanent magnet
synchronous generator (PMSG), Vienna rectifier and three-level neutral point clamped (NPC) inverter is
proposed. Vienna rectifier is used for flux vector control of PMSG, maximum power point tracking (MPPT)
of wind turbine, PMSG efficiency optimization, and balancing of two rectified DC voltages. As power
conditioner, a three-level NPC inverter is used to deliver energy to the grid. Vector control of the inverter
provides the ability to regulate power factor to any desired value. The results of two simulations (for back-to-
back inverter and the proposed topology) are presented and compared. The results verify improved efficiency
of the proposed WECS compared to WECS using back-to-back inverter. Copyright # 2010 John Wiley &
Sons, Ltd.

key words: wind energy, permanent magnet synchronous generator, Vienna rectifier, three-level NPC
inverter, maximum power point tracking

1. INTRODUCTION

Wind energy is known as one of the main renewable energy resources due to its cost effectiveness and
high reliability, compared to other types of green resources. A conventional wind energy conversion
system (WECS) consists of three basic parts: wind turbine, electric generator, and power conditioning
system. As electric generator, permanent magnet synchronous generator (PMSG) has received wide
interest in WECSs, due to its high efficiency and reliability. Other benefits are low weight and volume.
These are achieved mainly because of eliminating external excitation and therefore conduction losses.
Obtaining maximum power under different wind conditions needs variable speed operation of wind
turbine. In order to achieve this, mechanical gearbox systems are recently replaced by power electronic
modules. The system mainly comprises two parts: generator-side converter (rectifies the output voltage
of the generator) and grid-side (load-side) converter (delivers input power to a load or a grid)
(Figure 1).
Three-phase diode rectifier [1], and three-phase PWM rectifier [2] are traditionally two main
topologies utilized as generator-side converter in WECSs. Two main disadvantages of employing
diode rectifier are: no control on generator power factor (which affects generator efficiency), and high
harmonic distortion currents in generator (which affects efficiency and produces torque oscillations)
[2]. In configurations using diode rectifier, DC bus voltage is used to control PMSG speed [3]. In order
to control this voltage and maintain the DC input voltage of inverter constant, a DC/DC converter [4,5]
or a z-source inverter [3] is employed. Current control of generator is achieved using three-phase PWM

*Correspondence to: Mustafa Mohamadian, Department of Electrical Engineering, Tarbiat Modares University, Tehran
14115-111, Iran.
y
E-mail: mohamadian@modares.ac.ir

Copyright # 2010 John Wiley & Sons, Ltd.

 PMSG-BASED WIND ENERGY CONVERSION SYSTEM 955

Figure 1. Connection of wind power generation system to grid through conventional back-to-back inverter.

rectifier. This obviously shows a better performance for speed control of PMSG. But this increases
considerably manufacturing cost because of employing six switches.
In this paper, PWM rectifier is replaced by Vienna rectifier (Figure 2(a)) [6]. This three-switch active
rectifier provides current control; it also builds two equal DC voltages and has cost advantage because
of utilizing only three switches in the structure. In addition, no dead time consideration is required.
This dead time introduces dead time effect harmonics and increase total harmonic distortion (THD) in
conventional three-phase PWM rectifier which is undesirable. The block diagram of the proposed
system is illustrated in Figure 2(b).
The main advantages of multilevel inverters are listed as: higher output power quality because of
smaller output voltage steps, reduction of current spark on the load, smaller voltage stress on the
switches. Due to these advantages multilevel inverter can be used as power conditioner in a WECS [7].
In this paper, a three-level neutral point clamped (NPC) inverter is used to deliver power to the grid.
Since Vienna rectifier provides two balanced DC voltages, there is a better opportunity to use three-
level NPC inverter. However, it is optional.
This paper is organized as follows. The Vienna rectifier characteristics are described in Section 2.
Control systems of generator side and grid side converters for the proposed system are explained in
Section 3 and 4, respectively. The results of simulations for conventional back-to-back inverter and the
proposed system and the comparison are presented in Section 5.

2. CONFIGURATIONS, SPECIFICATIONS, AND BASIC OPERATION PRINCIPLES OF

VIENNA RECTIFIER

Combination of a boost DC/DC converter series with a three-phase rectifier provides a topology called
Vienna rectifier (Figure 3).

Figure 2. Schematic diagram of (a) Vienna rectifier and (b) the proposed grid-interface configuration for
PMSG wind turbines.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
956 A. H. RAJAEI ET AL.

Figure 3. Vienna rectifier.

Vienna rectifier is a unidirectional active AC/DC converter therefore power flows in just one
direction from AC to DC side. Lack of regeneration is the main drawback of this rectifier, which limits
its application. On the other hand, various advantages of the rectifier such as low manufacturing cost
due to usage of only three switches, higher efficiency, boosting ability, production of two equal DC
voltages, and no dead time makes it a good choice in the applications that regeneration process is not
required.
State of the switch (ON/OFF) and the polarity of the line current in each phase determine the rectifier
pole voltages (VAM, VBM, VCM) at any instant of operation. In order to discuss operation principles of
the rectifier, here Phase A is explained. Phase B and C have the same behavior. If the line current is
positive, and the switch Ta is off, the current flows through diode D11, and the voltage between the
converter pole A and the DC-bus midpoint M (i.e. VAM) is Vdc/2. The conduction path for this case is
illustrated in Figure 4(a). If the polarity of the line current is positive, and the switch Ta is on, the
voltage VAM is 0, in which the conduction path is illustrated in Figure 4(b). Similarly, the voltage VAM
can be determined in other states as illustrated in Figure 4(c) and (d). This operating principle also can
apply to Phase B and C to determine VBM and VCM.
Several approaches have been proposed to extract switching commands from reference waveforms.
The initial applications proposed the use of hysteresis current controller [6]. Although, this technique
has the benefit of simplicity and fast dynamic response, it injects rather high frequency harmonics to
the mains and suffers from variable switching frequency. In order to keep switching frequency

Figure 4. Conduction paths for phase-leg A when (a) the line current is positive, and the controlled switch is
off; (b) the line current is positive, and the controlled switch is on; (c) the line current is negative, and the
controlled switch is off; and (d) the line current is negative, and the controlled switch is on.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
 PMSG-BASED WIND ENERGY CONVERSION SYSTEM 957

Figure 5. Mechanical power versus rotor speed with the wind speed as parameter.

constant, ramp comparison technique is used which compares the current error with a fixed frequency
carrier signal to generate control signals [8].

3. CONTROL OF GENERATOR SIDE CONVERTER (VIENNA RECTIFIER)

The mechanical power delivered by a wind turbine is expressed as:

1
Pm ¼ rACp Vw3 (1)
2

where r is the air density, A is the area swept out by the turbine blades, Vw is the wind velocity, and
Cp is the power coefficient defined as the ratio of turbine power to wind power and depends on the
aerodynamic characteristics of blades. Figure 5 represents the relation between generator speed and
output power for different wind speeds. It is observed that the maximum power output occurs at
different generator speeds for different wind velocities.
Since, WECS use PMSG, active power always flows from generator side (AC side of rectifier) to the
gird side, and lack of regeneration in Vienna rectifier does not affect system performance.
Control system for Vienna rectifier in a WECS contains three crucial parts: maximum power point
tracking (MPPT) control of wind turbine according to instantaneous wind speed, minimizing power
loss, and balancing two output DC voltages.

3.1. MPPT control of wind turbine

Maximum output power of wind turbine is obtained in different speed of wind turbine (Figure 5)
according to wind speed. MPPT algorithm should adjust WECS operating point to achieve this optimal
speed. Speed control of PMSG is achieved by controlling generator currents.
Recently, several MPPT methods are proposed [9,10], which require wind energy (WG) optimal
power characteristic and instantaneous wind speed information; both of which are undesirable. WG
optimal power characteristic cannot be extracted accurately and wind speed measurement increases
cost of the system and control system complexity. Thus neural network-based [11] and fuzzy-logic-
based [12,13] control systems are presented. An algorithm is proposed in [14] to estimate wind speed
based on the theory of support-vector regression (SVR). All of these increase control system
complexity.
Perturb and observe (P&O) algorithm [15–17] is the most commonly used method employed to
obtain maximum power point (MPP). This is due to ease of implementation and not requiring feedback
from wind velocity and system characteristics. It is based just on monitoring output electrical power of
PMSG. In this paper, P&O algorithm is employed to obtain MPP.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
958 A. H. RAJAEI ET AL.

In P&O method, power deviation at speed of maximum power is as shown in Figure 5 given by:
8
dP <
> 0v < vMPP
¼ 0v ¼ vMPP (2)
dv :
< 0v < vMPP
Where, P and v are turbine output power and speed, respectively. vMPP is turbine speed at MPP.
The conventional P&O algorithm is based on the following criteria: control system makes a certain
change in PMSG speed, if electrical power increases, direction of change is correct and during next
step a similar change is applied; if power decreases, the speed is reduced during next step. Con-
ventionally, the amount of speed change is constant. The rule is given as:
dvn ¼ C
signðdvn1 Þ
signðPn  Pn1 Þ (3)
Where dvn, Pn, dvn-1, and Pn-1 are step change in speed and PMSG output power at nth and (n1)th
step, respectively. C is the value of change in speed reference. The function sign(x) is defined as


1ifx  0
signðxÞ ¼ (4)
1ifx < 0

The main drawback of conventional P&O algorithm is oscillations around the operating point at
steady state (Figure 6). The smaller the value of dvn in each step, the smaller oscillation around MPP,
but this increases significantly the time for converging to MPP (Figure 6(a)), especially at presence
of large transients. On the other hand, large dvn in PMSG speed improves transient response time

Figure 6. Principle of adaptive P&O-based MPPT. (a) Conventional P&O algorithm with small value of C.
(b) Conventional P&O algorithm with a large value for C. (c) Adaptive P&Oalgorithm with two different C
values.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
 PMSG-BASED WIND ENERGY CONVERSION SYSTEM 959

but large oscillation at MPP in steady state condition (Figure 6(b)) decreases maximum wind power
extraction. In Reference [17], a method is proposed to adapt value of C, considering dP in any step. The
value of C is proportion to dP and dv in previous step. This improves transient response time and
decreases oscillations around MPP.
In this paper, C has two different values C1 and C2 to improve transient response and reduce
oscillation around MPP. Considering C1 > C2, in transient condition, C has value of C1. In this
condition, any change in PMSG speed leads to a large variation (positive or negative) in output power.
C2 is chosen in steady state condition (Figure 6(c)). Equation (5) formulates the above rules. Consider
that k1 > k2.
8
>
> C1 if jðPn  Pn1 Þj > k1 and C ¼ C1 at ðn  1Þth step
<
C2 if jðPn  Pn1 Þj > k1 and C ¼ C1 at ðn  1Þth step
C¼ (5)
>
> C1 if jðPn  Pn1 Þj > k2 andC ¼ C2 atðn  1Þthstep
:
C2 if jðPn  Pn1 Þj > k2 andC ¼ C2 atðn  1Þthstep

The P&O-based MPPT determines a speed reference value vref for PMSG speed controller. Speed
error gives a reference value for electromagnetic torque t
by a Proportional–Integral (PI) controller as
shown in Figure 7. Reference value of Quadrature-axis (q-axis) current component of PMSG i
q is given
by Equation (7) in rotor reference frame.
t
e
i
q ¼ (6)
ð3=2ÞðP=2Þlf
Where, p is PMSG pole pairs and lf is PMSG flux induced by magnets.

3.2. Efficiency optimization by reactive power control

Q-axis current component of PMSG is controlled to generate maximum active power and direct-axis
current component of PMSG (id) is controlled to achieve maximum efficiency. Zero id minimize

Figure 7. Block diagram of proposed WECS control system.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
960 A. H. RAJAEI ET AL.

Figure 8. Block diagram of control system for balancing output DC voltages of rectifiers.

Table I. Parameters of PMSG.

Parameter Value
Rs (Stator Resistance) 0.05 V
Lq (Inductance) 0.795 mH
Ld (Inductance) 0.795 mH
P (pole pairs) 4
J (Inertia) 0.011 Kg m2
Flux induced by magnets 0.192 Kg m2
Ref. and Actual Values of PMSG Speed (rpm)

1150
(a)
1100
Ref. BValue
1050

1000 Actual Value

950

900

850

800
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75
Time (s)
Ref. and Actual Values of PMSG Speed (rpm)

1150
(b)
1100

1050

1000 Actual Value

950

900
Ref. Value
850

800
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75
Time (s)

Figure 9. Reference and instantaneous values of PMSG speed. (a) Conventional P&O-based MPPT. (b)
Adaptive P&O-based MPPT.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
 PMSG-BASED WIND ENERGY CONVERSION SYSTEM 961

resistive loss PCu [18], but considering Equation (7), id can be used to reduce stator flux. This will
decrease iron loss PFe; therefore Equation (8) should be evaluated to minimize overall PMSG loss [2].
Stator flux is determined as follows [2].
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ls ¼ ðLs iq Þ2 þ ðlf þ Ls id Þ2 (7)

Where, Ls and ls are PMSG stator reactance and stator flux respectively. id is the flux producing
component of the stator current [2].
X
minð Ploss Þ ¼ minðPFe þ PCu þ Pmec þ Prect Þ (8)

Where, Ploss is overall loss of WECS. Pmec and Prect are mechanical and rectifier power losses,
respectively. Optimal value of id is determined according to WECS characteristics.

3.3. Balancing two output DC voltages

Balancing voltage of two output capacitors is needed to prevent excessive voltage stress on
semiconductors. This is simply implemented by adding a DC component to the PMSG reference
currents as illustrated in Figure 8.

(a) 12

11.5
Wind Speed (m/s)

11

10.5

10

9.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Time (s)
(b) 0.9
0.85
Wind Turbine Power(pu)

0.8

0.75

0.7
Max. Power
0.65

0.6

0.55 Delivered Power

0.5
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Time (s)

Figure 10. a) Wind speed variation. b) Extracted power.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
962 A. H. RAJAEI ET AL.

4. CONTROL OF GRID-SIDE CONVERTER (THREE-PHASE THREE-LEVEL NPC

INVERTER)

The relations for active and reactive power delivered to the grid are given by Reference [2]:
3 
Pgrid ¼ Vdgrid :idgrid þ Vqgrid :iqgrid (9)
2

3 
Qgrid ¼ Vqgrid :idgrid  Vdgrid :iqgrid (10)
2
Where, Pgrid and Qgrid are active and reactive power delivered to the grid, respectively. V is grid voltage
and i is the current to the grid. The subscripts ‘dgrid’ and ‘qgrid’ stand for D-axis and Q-axis components.
For a balanced grid voltage, Vqgrid equals to zero in synchronous reference frame. Therefore active and
reactive power equations simplifies as:
3
Pgrid ¼ ðVdgrid :idgrid Þ (11)
2

3
Qgrid ¼  ðVdgrid :iqgrid Þ (12)
2
Considering Equations (11) and (12), active and reactive power is controlled by id and iq, respectively.
The error of DC bus voltage generates reference value of iq (i
qgrid ) using a PI controller. This
automatically delivers all extracted power to the grid.

(a) 50

Ref. VAlue
id of PMSG (A)

Actual Value

-50
0.2 0.21 0.22 0.23 0.24 0.25
Time (s)

(b) 0

-20

Actual Value
iq of PMSG (A)

-40

-60

-80 Ref. Value

-100
0.2 0.21 0.22 0.23 0.24 0.25
Time (s)

Figure 11. D-axis and Q-axis current components of PMSG in synchronous reference frame (a) id and (b) iq.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
 PMSG-BASED WIND ENERGY CONVERSION SYSTEM 963

The reference value of capacitor voltage VC is given by active and reactive power delivered to the
grid as follows [2].

 2 pffiffiffi 2
2 VG 2 3VG MVC
Pgrid þ Qgrid þ ¼ p ffiffi
ffi (13)
X 2 2X

Where, X is the grid reactance, VG is the line-to-line voltage of the grid, M is the modulation index and
VC is the DC input voltage of inverter. Assuming unity power factor, reactive power is zero, thus above
equation is simplified to:

pffiffiffi 2
2 VG 4 3VG MVC
Pgrid þ 2 ¼ pffiffiffi (14)
X 2 2X

The reference value of id (i
dgrid ) is determined by required reactive power.

As discussed in Section 1, a three-level NPC inverter is used as grid-side converter. Employing three-
level NPC inverter is optional. A tradeoff between cost and power quality helps to make a decision
between two-level and three-level inverter. Here, Vienna rectifier balanced output voltages helps keep
the NPC inverter DC bus center point fluctuations limited.
The block diagram of control systems for generator-side and grid-side inverters are shown in Figure 7.

(a) 50 14
Actual Value
40
id Injected to the Grid (A)

12
30
Ref. Value
10
20 0.21 0.211 0.212 0.213 0.214 0.215

10

0
0.2 0.21 0.22 0.23 0.24 0.25
Time (s)

(b) 15
0.5
Actual Value

10
iq Injected to the Grid (A)

5 Ref. Value
-0.5
0.21 0.211 0.212 0.213 0.214 0.215

-5
0.2 0.21 0.22 0.23 0.24 0.25
Time (s)

Figure 12. D-axis and Q-axis current components of WECS grid current in synchronous reference frame
(a) idgrid and (b) iqgrid.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
964 A. H. RAJAEI ET AL.

5. SIMULATION RESULTS

To verify the performance of the proposed WECS, several simulation tests are performed. The
simulated PMSG parameters are listed in Table I.

5.1. Evaluation of P&O-based MPPT

In order to evaluate the performance of MPPT algorithm, wind speed is assumed to have a constant
value of 10 m/s with a step of 2 m/s at t ¼ 0.5 seconds.
As described before by vMPP varies with changes in wind speed. Figure 9 illustrates that P&O-based
MPPT converges to vMPP (vMPP ¼ 900 rpm for wind speed ¼ 10 m/s and vMPP ¼ 1080 for wind

(a) 750
DC-link Voltage (v)

700

650
0.15 0.2 0.25 0.3 0.35 0.4
Time (s)

(b) 400
First Capacitor Voltage (v)

380

360

340

320

300
0.15 0.2 0.25 0.3 0.35 0.4
Time (s)

(c) 400
Second Capacitor Voltage (v)

380

360

340

320

300
0.15 0.2 0.25 0.3 0.35 0.4
Time (s)

Figure 13. Output voltage of Vienna rectifier. (a) DC-link voltage. (b) Upper capacitor voltage. (c) Lower
capacitor voltage.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
 PMSG-BASED WIND ENERGY CONVERSION SYSTEM 965

speed ¼ 12 m/s). When adaptive MPPT is used, C has values of 30 and 10 in transient and steady state
conditions, respectively. A constant value of C ¼ 20 is selected for execution of traditional MPPT and a
sampling rate of 64 samples per second is used for both MPPTs. As illustrated in Figure 9, adaptive
MPPT provides better transient and steady state responses.
In Figure 10(a), wind speed is changed randomly. Figure 10(b) shows maximum obtainable
mechanical power and mechanical power extracted by wind turbine; as illustrated, MPPT algorithm
can follow MPP.

(a) 80

60
PMSG Output Current (A)

40

20

-20

-40

-60

-80
0.5 0.505 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55
Time (s)

(b) 80

60
PMSG Output Current (A)

40

20

-20

-40

-60

-80
0.5 0.505 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55
Time (s)

(c) 80

60
PMSG Output Current (A)

40

20

-20

-40

-60

-80
0.5 0.505 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55
Time (s)

Figure 14. Output current of PMSG. (a) Conventional back-to-back inverter. (b) Vienna rectifier and two-
level inverter. (c) Vienna rectifier and three-level NPC inverter.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
966 A. H. RAJAEI ET AL.

In the rest of this paper simulations are performed with a constant wind speed of 11 m/s.

5.2. D-axis and Q-axis current components of the WEC

iq, id (current components of PMSG in synchronous reference frame), also idgrid and iqgrid (components
of current delivered to the grid in synchronous reference frame) are shown in Figure 11 and Figure 12,
respectively. Reference value of id is zero.

(a) 10000
PMSG Output Power
8000

6000
Power (W)

4000

2000 Power Delivered to Grid

0
0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6
Time (s)

(b) 10000

PMSG Output Power

8000

6000
Power (W)

4000

Power Delivered to Grid

2000

0
0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58
Time (s)

(c) 10000
PMSG Output Power
8000
Power (W)

6000

4000
Power Delivered to Grid

2000

0
0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6
Time (s)

Figure 15. PMSG output power and power delivered to the grid. (a) Conventional back-to-back inverter. (b)
Vienna rectifier and two-level inverter. (c) Vienna rectifier and three-level NPC inverter.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
 PMSG-BASED WIND ENERGY CONVERSION SYSTEM 967

5.3. Capacitor voltage

As described in Section 3, the control system of Vienna rectifier is modified to balance two DC-link
capacitor voltages. Figure 13 shows DC-link voltage and capacitor voltages. It is seen that the voltages
are balanced and DC-link voltage is controlled at 700 V.

5.4. Comparison of the Vienna and back-to-back generator side converter

In order to evaluate the performance of proposed system and compare it with conventional back-to-
back system, three simulations were performed. First simulation was performed for a conventional
back-to-back inverter. In the second simulation, Vienna rectifier is used to rectify PMSG output and a
two-level inverter delivers power to the grid and finally two-level inverter was replaced with a three-
level NPC inverter in the third simulation. Switching frequency of 15 kHz is selected for all
simulations.

5.4.1. PMSG current. Figure 14 shows output current of PMSG, which are similar in three cases.
The variations in magnitude of the currents are related to the variations in reference speed of PMSG
speed controller.

5.4.2. Power and efficiency. Input power of generator-side converter and output power of grid-side
converter for three simulated systems are shown in Figure 15. Obviously the difference shows
switching power loss of converters. It is seen that Vienna rectifier and three-level NPC inverter has a
lower power loss. This would improve WECS efficiency.

Figure 16. Efficiency comparison for three simulated systems.

80

60
PMSG Output Current (A)

40

20

-20

-40

-60

-80
0.3 0.305 0.31 0.315 0.32 0.325 0.33 0.335 0.34 0.345 0.35
Time (s)

Figure 17. Output current of PMSG with a conventional PWM rectifier and a dead time of 4 ms.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
968 A. H. RAJAEI ET AL.

For various wind speeds, input and output average power of WECS are calculated in three cases.
WECS efficiency is defined as:
Pgrid
h% ¼  100 (15)
PWT
Where, PWT is the power output of wind turbine. The relationship between PWT and Pgrid is given by:

PWT ¼ Pgrid þ PlossPMSG þ Prect þ Pinv (16)

Where PlossPMSG, Prect, and Pinv are the PMSG, rectifier, and inverter loss, respectively. The loss model
used for switches is expressed in [19].
Figure 16 shows the efficiency of three simulated systems in different wind speeds.
As seen in Figure 16, conventional back-to-back inverter has higher efficiency component to other
topologies. This is due to lower voltage across Vienna rectifier switches (350 V for Vienna rectifier and
700 V for back-to-back inverter) and lower voltage across NPC inverter.

5.4.3. THD and power quality. A certain dead time should be considered for conventional PWM
rectifiers in switching of two switches at any leg to prevent short circuit. This dead time introduces dead
time effect harmonics and THD is increased consequently, which is undesirable. On the other hand,
Vienna rectifier does not need any dead time according to the topology. Also, three-level output voltage
of NPC inverter decreases current harmonics injected to the grid. A dead time of 4 ms was used in
generating switching commands. Output current of PMSG is shown in Figure 17. In Figure 18,
harmonic spectrum of PMSG output current using PWM rectifier and Vienna rectifier are shown.
Output current of WECS and its harmonic spectrum using two-level inverter and three-level NPC
inverter are illustrated in Figure 19.
Table II shows THD of PMSG current and current injected to the grid for three simulated systems.

Figure 18. Harmonic spectrum of PMSG output current using (a) PWM rectifier and (b) Vienna rectifier.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
 PMSG-BASED WIND ENERGY CONVERSION SYSTEM 969

Figure 19. Output current of WECS and its harmonic spectrum. (a) Current using two-level inverter. (b)
Current using three-level inverter. (c) Current harmonic spectrum using two-level inverter. (d) Current
harmonic spectrum using three-level NPC inverter.

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
970 A. H. RAJAEI ET AL.

Table II. Current THD comparison.

PMSG current Injected current
Conventional back-to-back Inverter 4.25% 3.91%
Vienna rectifier and two-level inverter 3.52% 3.88%
Vienna rectifier and three-level inverter 3.47% 2.01%

Table III. Demand TSDP for PWM and Vienna rectifiers.

TSDP Type
529200 PWM rectifier
352800 Vienna rectifier
191100 Three-level NPC inverter
163800 Two-level inverter

5.4.4. Total switching device power. The total switching device power (TSDP) is a useful tool for
comparison of rating of converters. TSDP is calculated as:
X
N
TSDP ¼ Cj Vsj Isj (17)
j¼1

Where, N is the number of semiconductor devices. Vsj and Isj are the voltage stress and current stress of
device, respectively. Cj is the cost factor and is defined as one for semiconductor switch and half for
diode.
The steady-state torque equation of PMSG is given by:
T ¼ Kt Ia (18)
Where, Ia and T are the stator current and torque, respectively. Kt is a constant determined by PMSG
characteristics. Isj is given by Equation (19).
Tmax
Is ¼ Iamax ¼ (19)
Kt

Tmax is related to the cut off (furling) wind speed. Here, furling wind speed is 13.5 m/s. Vsj is equal to
VC for PWM rectifier and VC/2 for Vienna rectifier. Table III shows TSDP for PWM rectifier, Vienna
rectifier, two-level inverter, and three-level NPC inverter.

6. CONCLUSION

In this paper, a Vienna rectifier was used as PMSG generator side converter to rectify AC output voltage
of PMSG wind generator and to build two equal DC voltages. MPPT technique is utilized to produce
maximum instantaneous power. Two equal DC voltages were used as input of a three-level NPC
inverter to deliver power to grid. The presented simulation results verified higher efficiency and better
output characteristics such as better THD compared to conventional back-to-back WECS with a two-
level inverter. Also it was shown that TSDP of the conventional back-to-back converter is higher
compared to Vienna rectifier.

7. APPENDICES

7.1. Nomenclature
A the area swept out by the turbine blades
C value of change in speed reference

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
 PMSG-BASED WIND ENERGY CONVERSION SYSTEM 971

cp the power coefficient defined as the ratio of turbine power to wind power
Ia PMSG stator current
i current to the grid
ia Line current in phase A
id direct-axis current component of PMSG
idqrid Direct-axis component of current to grid
iqgrid Quadrature-axis component of current to grid


i dgrid Reference value for Direct-axis component of current to grid


iq Reference value of Quadrature-axis current component of PMSG


i qgrid Reference value for Quadrature-axis component of current to grid
Isj current stress of device
Kt a constant determined by PMSG characteristics
Ls PMSG stator reactance
MPP Maximum Power Point
MPPT Maximum Power Point Tracking
N number of semiconductor devices
NPC Neutral Point Clamped
P turbine output power
P&O Perturb and Observe
PI Proportional-Integral
PCu Generator resistive loss
PFe iron loss
Pgrid active power delivered to the grid
Ploss overall loss of WECS
Pm Mechanical power delivered by a wind turbine
Pmec mechanical loss
Pn step change in PMSG output power at (n-1)th step
Pn-1 step change in PMSG output power at nth step
Prect rectifier power loss
PMSG Permanent Magnet Synchronous Generator
PWM Pulse Width Modulation
q-axis Quadrature-axis
Qgrid reactive power delivered to the grid
SVR Support-Vector Regression
T PMSG torque
Ta Vienna rectifier switch in phase A
THD Total Harmonic Distortion
Tmax Maximum PMSG torque
TSDP total switching device power
v grid voltage
VAM rectifier pole voltage in phase A
VBM rectifier pole voltage in phase B
VC reference value of capacitor voltage
VCM rectifier pole voltage in phase C
Vdc dc-bus voltage
vqgrid Quadrature-axis component of grid voltage
Vsj voltage stress device
WECS Wind Energy Conversion System
WG Wind Energy
r air density
vw the wind velocity
v turbine speed
vMPP turbine speed at MPP
dvn step change in speed at nth step

Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep
972 A. H. RAJAEI ET AL.

dvn-1 step change in speed at (n-1)th step

vref Generator speed reference value


t reference value for generator electromagnetic torque
lf PMSG flux induced by magnets
lS PMSG stator flux

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Copyright # 2010 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power 2011; 21:954–972
DOI: 10.1002/etep