Two-level and Multilevel Converters for Wind Energy Systems: A Comparative Study

R. Melício*, V. M. F. Mendes† and J. P. S. Catalão*

* University of Beira Interior, Covilha, Portugal, e-mail: ruimelicio@gmail.com; catalao@ubi.pt † Instituto Superior de Engenharia de Lisboa, Lisbon, Portugal, e-mail: vfmendes@isel.pt

Abstract—This paper is concerned with modeling and simulation of a wind energy system with different topologies for the power converters, namely a two-level converter and a multilevel converter. Pulse modulation by space vector modulation associated with sliding mode is used for controlling the converters, and power factor control is introduced at the output of the converters. Finally, a case study is presented, showing the electric behavior of the power and the current at the output of the converters and the direct voltage at the multilevel converter.

Keywords—Multilevel converters, sliding mode control, wind energy.

I. INTRODUCTION

Electricity restructuring has offered additional flexibility at both levels of generation and consumption. Also, since restructuring has strike the power system sector, developments in distributed generation technologies opened new perspectives for generating companies [1], in order to consider their energy supply portfolio with adequacy and advantage. Adequacy and advantage due to a better generation mix, concerning not only the traditional economic perspective, but also politic developments with strong social impact in power systems, imposing the internalization of costs formerly externalized.

Distributed generation technology is said to offer a clean emission-free energy source with fast ramp capability, and it goes on penetrating more and more power systems. Distributed generation technology includes, for instances, arrays of solar photovoltaic panels, wind farms, hydroelectric, biomass and tidal power plants. Among distributed generation technology, wind farms are the most commonly viewed on power systems, even envisaged as competing with the traditional fossil-fuelled thermal power plants in the near future.

The European Commission concerned with the climate change, due to the emission of greenhouse gases, put forward a set of proposals to create a new Energy Policy for Europe, cutting its own CO2 emissions by at least 20% by 2020 and 50% until 2050, increasing the share of renewable energy sources in the overall generation mix.

Hence, it is expected that wind energy will turn out to be an important part of the future Energy Policy for Europe. In Portugal, the total installed wind power capacity reached 2037 MW in September 2007, and continues growing.

The increasing share of wind in power generation will change considerably the dynamic behavior of the power system [2], and may lead to a reduction of power system

frequency regulation capabilities [3]. In addition, network operators have to ensure that consumer power quality is not compromised [4]. Hence, new technical challenges emerge due to the increase in wind power penetration: dynamic stability and power quality. These challenges imply research of more realistic physical models for wind energy systems.

Power electronic converters have been developed for integrating wind power with the electric grid. The use of power electronic converters allows for variable speed operation of the wind turbine, and enhanced power extraction. In variable speed operation, a control method designed to extract maximum power from the turbine and provide constant grid voltage and frequency is required [5].

This paper is concerned with modeling and simulation of a wind energy system with different topologies for the power converters, namely a two-level converter and a multilevel converter. Pulse modulation by space vector modulation associated with sliding mode is used for controlling the converters, and power factor control is introduced at the output of the converters. Finally, a case study is presented, showing the electric behavior for the two types of converters.

II. MODELING

A. Turbine and Electric Machine The mechanical power of the turbine is given by

pm cuAP 3

21 ρ= , (1)

where mP is the power extracted from the airflow, ρ is the air density, A is the area covered by the rotor, u is the wind speed upstream of the rotor, and pc is the performance coefficient or power coefficient.

The power coefficient is a function of the pitch angle of rotor blades θ , and of the tip speed ratio λ , which is the ratio between blade tip speed and wind speed upstream of the rotor. The computation of the power coefficient requires knowledge of issues like: blade element theory and blade geometry. These issues are considered in this paper using the numerical approximation developed in [6]. Hence, in this paper the power coefficient is given by

iiec ipλ

−λ=

4.18

73.0 , (2)

where iλ and iiλ are respectively given by 1682

978-1-4244-1742-1/08/$25.00 c© 2008 IEEE

2.13002.058.0151 14.2 −θ−θ−λ

=λii

i , (3)

)1(003.0

)02.0(1

1

3 +θ−

θ−λ

=λii . (4)

The maximum power coefficient is given for a null pitch angle and is equal to

4412.0max =pc , (5)

where the optimum tip speed ratio is equal to

057.7=λopt . (6)

The mechanical power extracted from the wind is modeled by (1) to (4).

The equations for modeling rotor motion are given by

)(1elasamdmm

m

m TTTTJdt

d −−−=ω , (7)

)(1eaedeelas

e

e TTTTJdt

d −−−=ω , (8)

where mω is the rotor speed of turbine, mJ is the turbine moment of inertia, mT is the mechanical torque, dmT is the resistant torque in the turbine bearing, amT is the resistant torque in the hub and blades due to the viscosity of the airflow, elasT is the torque of the torsional stiffness,

eω is the rotor speed of the electric machine, eJ is the electric machine moment of inertia, deT is the resistant torque in the electric machine bearing, aeT is the resistant torque due to the viscosity of the airflow in the electric machine, and eT is the electric torque.

The equations for modeling a permanent magnetic synchronous machine, PMSM, can be easily found in the literature; using the motor machine convention, the following set of equations [7] is considered

)(1ddqqed

d

d iRiLpuLdt

di −ω+= , (9)

])([1qqfddeq

q

q iRiMiLpuLdt

di−+ω−= , (10)

where fi is the equivalent rotor current, M is the mutual inductance, p is the number of pairs of poles; and where in dq axes, di and qi are the stator currents, dL and qLare the stator inductances, dR and qR are the stator resistances, du and qu are the stator voltages. A unity power factor is imposed to the electric machine in order to minimize power losses, implying a null reactive electric power, 0=eQ . The electric power eP is given by

Tfqdfqde iiiuuuP ][][= . (11)

The output power P and Q injected in the electric network in βα axes [8] is given by

−=

β

α

αβ

βα

ii

uuuu

QP

, (12)

where in βα axes, αi and βi are the phase currents, αuand βu are the phase voltages. The apparent output power [8] is

21222 )( HQPS ++= , (13)

where H is the harmonic power.

B. Two-level Converter The two-level converter is an AC/DC/AC converter,

with six unidirectional commanded IGBT's ikS used as a rectifier, and with the same number of unidirectional commanded IGBT's used as an inverter.

The rectifier is connected between an electric machine and a capacity bank. The inverter is connected between this capacity bank and a filter, which in turn is connected to an electric network. In this paper, a three-phase symmetrical circuit in series models the electric network. The groups of two IGBT’s linked to the same phase constitute a leg k of the converter. The configuration of the wind energy system with two-level converter that will be simulated is shown in Fig. 1.

Fig. 1. Wind energy system with two-level converter.

2008 13th International Power Electronics and Motion Control Conference (EPE-PEMC 2008) 1683

For the two-level converter modeling it is assumed that: 1) The IGBT’s are ideal and unidirectional, and they will never be subject to inverse voltages, being this situation guaranteed by the arrangement of connection in anti-parallel diodes; 2) The diodes are ideal: in conduction it is null the voltage between its terminals and in blockade it is null the current that passes through it; 3) The voltage in the exit of the rectifier should always be 0>dcv ; 4) Each leg k of the converter should always have one IGBT on conduction state.

For the switching function of each IGBT, the switching variable kγ is used to identify the state of the IGBT i in the leg k of the converter. The index i with }2,1{∈iidentifies the IGBT. The index k with }3,2,1{∈kidentifies the leg for the rectifier and }6,5,4{∈k identifies the leg for the inverter. The two valid conditions [9] for the switching variable of each leg k are as follows

==

=γ1,01,1

ik

ikk S

S for }2,1{∈i and }6,...,1{∈k . (14)

The topological restriction for the leg k is given by

==

2

11

iikS }6,...,1{∈k . (15)

Hence, each switching variable depends on the conduction and blockade states of the IGBT’s. The phase currents injected in the electric network are modeled by the state equation

)()(

1skkck

fc

k uiRuLLdt

di −−+

= . (16)

The output continuous voltage of the rectifier is modeled by the state equation

)(1 6

4

3

1 ==γ−γ=

kkk

kkk

dc iiCdt

dv. (17)

The two-level converter is modeled by (14) to (17).

C. Multilevel Converter The multilevel converter is an AC/DC/AC converter,

with twelve unidirectional commanded IGBT’s ikS used

as a rectifier, and with the same number of unidirectional commanded IGBT’s used as an inverter.

The rectifier is connected between an electric machine and a capacity bank. The inverter is connected between this capacity bank and a filter, which in turn is connected to an electric network. In this paper, a three-phase symmetrical circuit in series models the electric network. The groups of four IGBT’s linked to the same phase constitute a leg k of the converter. The configuration of the wind energy system with multilevel converter that will be simulated is shown in Fig. 2.

For the multilevel converter modeling it is also assumed that: 1) The IGBT’s are ideal and unidirectional, and they will never be subject to inverse voltages, being this situation guaranteed by the arrangement of connection in anti-parallel diodes; 2) The diodes are ideal: in conduction it is null the voltage between its terminals and in blockade it is null the current that passes through it; 3) The voltage in the exit of the rectifier should always be 0>dcv ; 4) Each leg k of the converter should always have two IGBT’s on conduction state.

For the switching function of each IGBT, the switching variable kγ is used to identify the state of the IGBT i in the leg k of the converter. The index i with }4,3,2,1{∈iidentifies the IGBT. The index k with }3,2,1{∈kidentifies the leg for the rectifier and }6,5,4{∈k identifies the leg for the inverter. The three valid conditions [9] for the switching variable of each leg k are as follows

=−==

=γ1)and(,11)and(,01)and(,1

43

32

21

kk

kk

kk

k

SSSSSS

}6,...,1{∈k . (18)

The topological restriction for the leg k is given by

1).().().( 433221 =++ kkkkkk SSSSSS }6,...,1{∈k . (19)

With the two upper IGBT’s in each leg k ( kS1 and kS2 )of the converters it is associated a switching variable k1Γand also for the two lower IGBT’s ( kS3 and kS4 ) it is associated a variable k2Γ , respectively given by

2)1(

1kk

kγ+γ=Γ ;

2)1(

2kk

kγ−γ=Γ }6,...,1{∈k . (20)

Fig. 2. Wind energy system with multilevel converter.

1684 2008 13th International Power Electronics and Motion Control Conference (EPE-PEMC 2008)

Hence, each switching variable depends on the conduction and blockade states of the IGBT’s.

The phase currents injected in the electric network are modeled by the state equation

)(1kfkcfk

c

fk uiRuLdt

di−−= }6,5,4{=k . (21)

The output continuous voltage of the rectifier is the sum of the voltages in the capacity banks 1C and 2C , modeled by the state equation

+Γ−Γ===

)(1 6

41

3

11

1 kkk

kkk

dc iiCdt

dv

==Γ−Γ+

6

42

3

12

2)(1

kkk

kkk ii

C, (22)

where (18) to (22) model the neutral point clamped multilevel converter for high voltage and high power applications [9]-[11].

III. CONTROL METHOD

Pulse modulation by space vector modulation associated with sliding mode is used for controlling the converters. The controllers used in the converters are PI controllers.

The output voltage vectors in the βα axes for the two-level converter are shown in the Fig. 3.

↑ β

→α

3

1

↑ 0,7

5

2

6

4

↑ β

→α

3

1

↑ 0,7

5

2

6

4

↑ β

→α

3

1

↑ 0,7

5

2

6

4

↑ β

→α

3

1

↑ 0,7

5

2

6

4

↑ β

→α

3

1

↑ 0,7

5

2

6

4

Fig. 3. Output voltage vectors for the two-level converter.

The output voltage vectors in the βα axes for the multilevel converter are shown in the Fig. 4.

↑ β

→α

31621

20

19

24

25 12 7

8

42,1517,22

18,23

13,26 6,11

5,10

1,14,27

Fig. 4. Output voltage vectors for the multilevel converter.

The converters are variable structure, because of the on/off switching of their IGBT’s. Hence, using the sliding mode control is due to be of fundamental importance for controlling the converters, guaranteeing the choice of the most appropriate space vectors.

The power semiconductors present physical limitations that have to be considered during design phase and during simulation. Particularly, they cannot switch at infinite frequency. Also, for a finite value of the switching frequency, an error αβe will exist between the reference value and the control value. In order to guarantee that the system slides along the sliding surface ),( teS αβ , it has been proven that it is necessary to ensure the state trajectory near the surfaces verifies the stability conditions [9], given by

0),(

),( <αβαβ dt

tedSteS . (23)

As power semiconductors can switch only at finite frequency, in simulation practice a small error 0>ε for

),( teS αβ is allowed. Consequently, a switching strategy is considered, given by

ε+<<ε− αβ ),( teS . (24)

A practical implementation of the switching strategy considered in (24) could be accomplished by using hysteresis comparators at the simulation level.

IV. SIMULATION

The mathematical models of the two-level and multilevel converters were implemented with Matlab/Simulink block system coding, because it is not yet available enough facilities in SimPowerSystem application for simulation of the model proposed in this paper.

The data used is for a wind energy system of 900 kW, a ramp wind speed upstream of the rotor with a speed between 4.5 and 25 m/s and a time horizon of 3.5 s.

Fig. 5 shows the behavior for the mechanical power of the turbine and the electric power of the electric machine. Also, it shows the difference between the two powers, i.e., the accelerating power.

0 0.5 1 1.5 2 2.5 3 3.50

2

4

6

8

10x 10

5

Time (s)

Pow

er (

W)

← Pe

P →m

↓ P − Pm e

Fig. 5. Mechanical power and electric power.

2008 13th International Power Electronics and Motion Control Conference (EPE-PEMC 2008) 1685

The output power performance for the two-level converter is shown in Fig. 6, while the current injected in the electric network is shown in Fig. 7.

0 0.5 1 1.5 2 2.5 3 3.50

1

2

3

4

5

6

7

8

9

10x 10

5

Time (s)

Q (

VA

r)

P (

W)

S

(VA

) ↓ S

↑ P

↑ Q

Fig. 6. Output power for the two-level converter.

0 0.5 1 1.5 2 2.5 3 3.50

100

200

300

400

500

Time (s)

Cur

rent

(A

)

Fig. 7. Output current for the two-level converter.

The output power performance for the multilevel converter is shown in Fig. 8, while the current injected in the electric network is shown in Fig. 9.

0 0.5 1 1.5 2 2.5 3 3.50

1

2

3

4

5

6

7

8

9

10x 10

5

Time (s)

Q (

VA

r)

P (

W)

S

(VA

)

↓ S

↓ P

↓ Q

Fig. 8. Output power for the multilevel converter.

0 0.5 1 1.5 2 2.5 3 3.50

100

200

300

400

500

Time (s)

Cur

rent

(A

)

Fig. 9. Output current for the multilevel converter.

The output voltage dcv , the voltages 1Cv and 2Cv for the multilevel converter are shown in Fig. 10.

0 0.5 1 1.5 2 2.5 3 3.50

500

1000

1500

2000

2500

3000

3500

Time (s)

Vol

tage

(V

)

↓ v dc

↓ v C1

↑ v C2

Fig. 10. Output voltages for the multilevel converter.

Hence, it is concluded that the multilevel converter presents a better behavior for the electric power and the electric current relatively to the two-level converter.

V. CONCLUSIONS

The increased wind power penetration leads to new technical challenges, dynamic stability and power quality, implying research of more realistic physical models for modeling the wind energy systems behavior. This paper presents a more realistic modeling, considering a more accurate dynamic of the wind turbine, rotor, generator, converter and filter connecting the system to the electric network. A case study using the proposed modeling is presented for two power converter topologies: two-level and multilevel converters. Pulse modulation by space vector modulation associated with sliding mode is used for controlling the converters, and power factor control is used at the output of the converters. The results show that the multilevel converter has an enhanced behavior comparatively to the two-level converter. Although more complex, this modulation strategy presents more accurate results, which are necessary for facing the new technical challenges.

1686 2008 13th International Power Electronics and Motion Control Conference (EPE-PEMC 2008)

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