Permanent Magnet Wind Generator Technology for Battery Charging Wind … · 2018. 10. 5. ·...

Permanent Magnet Wind Generator Technologyfor Battery Charging Wind Energy Systems

Casper J. J. Labuschagne, Maarten J. Kamper

Electrical Machines LaboratoryDept of Electrical and Electronic Engineering

Stellenbosch University

September 2018

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Outline

Outline

1 Introduction

2 Wind Turbine Battery Charging System

3 Steady-State FE Simulation Method

4 Optimisation

5 Simulation Results

6 Optimisation Results

7 Conclusions

8 Extras

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Introduction

Introduction

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Introduction

Active Battery Charging System

I

V

Active

EZ

LC Load

synchronous

rectifier

Figure 1: Single line diagram of PM wind generator connected to active battery chargingsystem with actively synchronous rectifier.

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Introduction

Passive Battery Charging System

Load

EZ

I

V

Diode rectifier

Figure 2: Single line diagram of PM wind generator connected to passive batterycharging system with uncontrolled diode rectifier.

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Introduction

PMSG

Permanent magnetsynchronous generatorDirect-driveLow cogging torqueRelatively large internalsynchronous inductance

Figure 3: Cross section of theradial flux outer rotor PMSGconfiguration with surface mountedPMs

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Introduction

Passive Battery Charging System

Load

EZ Zext

I

V

Diode rectifier

Figure 4: Single line diagram of PM wind generator connected to passive batterycharging system with uncontrolled diode rectifier.

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Introduction

Passive Battery Charging System

Load

EZ Zext

I

V

αDiode rectifier

VI

E

Figure 5: Single line diagram of PM wind generator connected to passive batterycharging system with uncontrolled diode rectifier.

Static FEA method is proposed to achieve maximum power pointmatching for a turbine-specific design using an external inductance.

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Introduction

Active Battery Charging System

I

V

Active

EZ

LC Load

synchronous

rectifier

Figure 6: Single line diagram of PM wind generator connected to active battery chargingsystem with actively synchronous rectifier.

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Wind Turbine Battery Charging System

Wind Turbine Battery Charging System

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Wind Turbine Battery Charging System

Power Matching

0 100 200 300 400 500 6000

1

2

3

4

5

6

7

13 m/s

12 m/s

11 m/s

10 m/s9 m/s

8 m/s

Turbine speed (r/min)

Powe

r(k

W)

Passive

Figure 7: Wind turbine power versus turbine speed curves with wind speed a parameter,and operating power curves for passive and active systems.

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Wind Turbine Battery Charging System

Power Matching

0 100 200 300 400 500 6000

1

2

3

4

5

6

7

13 m/s

12 m/s

11 m/s

10 m/s9 m/s

8 m/s

Turbine speed (r/min)

Powe

r(k

W)

Passive

Optimum

Figure 7: Wind turbine power versus turbine speed curves with wind speed a parameter,and operating power curves for passive and active systems.

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Wind Turbine Battery Charging System

Power Matching

0 100 200 300 400 500 6000

1

2

3

4

5

6

7

nc

13 m/s

12 m/s

11 m/s

10 m/s9 m/s

8 m/s

Turbine speed (r/min)

Powe

r(k

W)

Passive

Optimum

Figure 7: Wind turbine power versus turbine speed curves with wind speed a parameter,and operating power curves for passive and active systems.

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Wind Turbine Battery Charging System

Power Matching

0 100 200 300 400 500 6000

1

2

3

4

5

6

7

nr

nc

13 m/s

12 m/s

11 m/s

10 m/s9 m/s

8 m/s

Turbine speed (r/min)

Powe

r(k

W)

Passive

Optimum

Figure 7: Wind turbine power versus turbine speed curves with wind speed a parameter,and operating power curves for passive and active systems.

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Wind Turbine Battery Charging System

System Requirements

Table 1: Wind generator operating points for passive battery charging system

nc nr

Wind speed 3 m/s 12 m/sTurbine speed 100 r/min 320 r/minPower 0 kW 4.2 kW

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Steady-State FE Simulation Method

Steady-State FE Simulation Method

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Steady-State FE Simulation Method

Steady-State FE Simulation Method

State of the PMSG? (α = ∆)

External Inductance Lext?

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Steady-State FE Simulation Method

Static FEA Iterations

q

dIs

Vs

(α 6= ∆)

1st Iteration

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Steady-State FE Simulation Method

Static FEA Iterations

q

dIs

Vs

(α 6= ∆)

1st Iteration

q

d

IsVs

(α 6= ∆)

2nd Iteration

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Steady-State FE Simulation Method

Static FEA Iterations

q

dIs

Vs

(α 6= ∆)

1st Iteration

q

d

IsVs

(α 6= ∆)

2nd Iteration

q

d

Is

Vs

(α ≈ ∆)

3rd Iteration

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Steady-State FE Simulation Method

External Inductance Calculation

External Inductance LextLext = L1 Lext = L2 Lext = L3

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Steady-State FE Simulation Method

External Inductance Calculation

y

f2(y)Pg(L1)

L1

Figure 8: Second degree polynomial obtained from curve fitting of the static FEAsolutions, and calculating Lext from the rated power Pg.

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Steady-State FE Simulation Method

External Inductance Calculation

y

f2(y)Pg(L1)

L1

Pg(L2)

L2

Figure 8: Second degree polynomial obtained from curve fitting of the static FEAsolutions, and calculating Lext from the rated power Pg.

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Steady-State FE Simulation Method

External Inductance Calculation

y

f2(y)Pg(L1)

L1

Pg(L2)

L2

Pg(L3)

L3

Figure 8: Second degree polynomial obtained from curve fitting of the static FEAsolutions, and calculating Lext from the rated power Pg.

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Steady-State FE Simulation Method

External Inductance Calculation

y

f2(y)Pg(L1)

L1

Pg(L2)

L2

Pg(L3)

L3

Figure 8: Second degree polynomial obtained from curve fitting of the static FEAsolutions, and calculating Lext from the rated power Pg.

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Steady-State FE Simulation Method

External Inductance Calculation

y

f2(y)Pg(L1)

L1

Pg(L2)

L2

Pg(L3)

L3Lext

4.2 kW

Figure 8: Second degree polynomial obtained from curve fitting of the static FEAsolutions, and calculating Lext from the rated power Pg.

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Steady-State FE Simulation Method

Static FEA method

Design for cut-in point. (1)Solve for Lext = L1. (3)Solve for Lext = L2. (3)Solve for Lext = L3. (3)Determine actual Lext.Solve PMSG. (3)Evaluate final performance.

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Optimisation

Optimisation

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Optimisation

Figure 9: Cross section of the double layernon-overlap winding PMSG indicating the relevantdimensions for design and optimisation.

X =

do

hrotor

hmag

θmag

hslot

wtooth

hstator

l

(1)

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Optimisation

Non-dominated Sorting Genetic Algorithm II

Performance constraints

U =

Pgen

η

J

=

4.2kW≥ 90%

≤ 6A/mm2

Objective function

minimise F(X) =

Mactive(X)MPM (X)

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Simulation Results

Simulation Results

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Simulation Results

Simulation ResultsEffect of Lext on power point matchingEffect of number of polesEffect of generator sizeStatic FEA performance

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Simulation Results

Effect of Lext on Power Point Matching

0 100 200 300 400 500 6000

1

2

3

4

5

6

7

13 m/s

12 m/s

11 m/s

10 m/s9 m/s

8 m/s

Turbine speed (r/min)

Powe

r(k

W)

Lext = 0 mH (G1)

Figure 10: Power matching of the 28/30 wind generator (G1 and G∗1) with Lext a

parameter.

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Simulation Results

Effect of Lext on Power Point Matching

0 100 200 300 400 500 6000

1

2

3

4

5

6

7

13 m/s

12 m/s

11 m/s

10 m/s9 m/s

8 m/s

Turbine speed (r/min)

Powe

r(k

W)

Lext = 0 mH (G1)Lext = 2.84 mH (G1)

Figure 10: Power matching of the 28/30 wind generator (G1 and G∗1) with Lext a

parameter.

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Simulation Results

Effect of Lext on Power Point Matching

0 100 200 300 400 500 6000

1

2

3

4

5

6

7

13 m/s

12 m/s

11 m/s

10 m/s9 m/s

8 m/s

Turbine speed (r/min)

Powe

r(k

W)

Lext = 3.86 mH (G∗1)

Lext = 2.84 mH (G1)Lext = 0 mH (G1)

Figure 10: Power matching of the 28/30 wind generator (G1 and G∗1) with Lext a

parameter.

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Simulation Results

Table 2: Static FEA results for 28/30 pole PMSG.

G1 G2 G∗1

Pg , kW 4.22 4.25 3.86fs, Hz 74.67 74.67 116.67Turns per winding, Ns 14 10 14Vrms 23.5 23.6 23.65J , A/mm2 4.67 3.29 4.37α 54.4◦ 54.4◦ 68.8◦

η, % 90.4 92.4 88.6Xs, p.u. 0.58 0.46 0.83Xext, p.u. 1.88 1.99 3.59Lext, mH 2.84 3.06 3.74Xext/Xs 3.26 4.33 4.32Outer Diameter, mm 384 384 384Axial Length, mm 70.55 100 70.55Mactive 22.08 32.1 22.7MP M 2.77 3.72 2.63

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Optimisation Results

Optimisation Results

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Optimisation Results

0 0.5 1 1.5 2 2.5 30

5

10

15

20

25

30

35

PM Mass (kg)

Activ

eM

ass

(kg)

PassiveActive

Optimum

Figure 11: Pareto fronts of PM mass versus active mass of the PMSGs for the passiveand acive systems, with the chosen optimal design points indicated.

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Optimisation Results

Table 3: Design optimisation results and component ratios

Parameters Passive Active Pas:Act

Outer diameter, do (mm) 384 350 1:0.91Stator height, hrotor (mm) 6.8 4.74 1:0.70Magnet height, hmag (mm) 6.2 3 1:0.48Magnet pitch, θmag (%) 0.7 0.7 1:1Slot height, hslot (mm) 35.1 31.6 1:0.90Tooth width, wtooth (mm) 12 8 1:0.67Rotor height, hstator (mm) 5.8 4.125 1:0.71Axial length, l (mm) 70.55 50 1:0.71Active iron mass (kg) 14.24 6.41 1:0.45Copper mass (kg) 5.07 3.76 1:0.74PM mass (kg) 2.77 0.88 1:0.32Total active mass (kg) 22.08 11.05 1:0.50External reactance, Xext (p.u.) 1.88 -Current density, (A/mm2) 4.67 6.0Current angle, α (degrees) 54.4 0Rated power, Pg (kW) 4.22 4.26Efficiency, η (%) 90.4 90

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Optimisation Results

Figure 12: To scale representation of the optimised PMSGs in Table 3 for (a) passiveand (b) active systems.

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Conclusions

Conclusions

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Conclusions

Conclusions

Static FE Simulation MethodPassive charging systems have poor power matching with no externalinductance.The proposed method is accurate and not computationally expensive.For maximum power point matching using non-overlap windingmachines, Xext/Xs is about a factor 4.Higher frequency generators require a much reduced externalinductance, although slightly less efficiency.The proposed calculation method can be used excellently to do awind site specific design optimization of the system, maximizingannual wind energy harvesting and minimizing generator and externalinductance sizes.

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Conclusions

Conclusions

Optimal DesignThe passive system’s generator active mass is almost twice that of theactive system’s generator active mass.The active system generator also outperforms the passive systemgenerator in terms of PM mass, where it is found that the activesystem generator’s PM mass is three times less.The passive system PMSG is more expensive to manufacture and thewind tower structure will most likely also be more expensive. Alsorequires large Lext.The active system requires an LC filter and an expensive rectifier withcomplex position-sensorless control.

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Thank you

Thank you.

Contact: Casper LabuschagneE-mail: 17539455@sun.ac.za

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Extras

Effect of Number of Poles

(a) (b)

Figure 13: Different pole-slot configurations for PMSG where (a) 28/30 pole-slotcombination and (b) 56/60 pole-slot combination.

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Extras

Table 4: Static FEA results for 28/30 pole PMSG and 56/60 pole PMSGs.

G1 G2 G∗1 G3 G4

Pg , kW 4.22 4.25 3.86 4.20 4.25fs, Hz 74.67 74.67 116.67 149.33 149.33Turns per winding, Ns 14 10 14 7 5Vrms 23.5 23.6 23.65 24.0 24.0J , A/mm2 4.67 3.29 4.37 4.58 3.15α 54.4◦ 54.4◦ 68.8◦ 54.6◦ 54.7◦

η, % 90.4 92.4 88.6 89.62 90.46Xs, p.u. 0.58 0.46 0.83 0.571 0.449Xext, p.u. 1.88 1.99 3.59 1.87 1.96Lext, mH 2.84 3.06 3.74 1.47 1.61Xext/Xs 3.26 4.33 4.32 3.27 4.37Outer Diameter, mm 384 384 384 384 384Axial Length, mm 70.55 100 70.55 70.55 100Mactive 22.08 32.1 22.7 22.08 32.1MP M 2.77 3.72 2.63 2.77 3.72

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Extras

Table 4: Static FEA results for 28/30 pole PMSG and 56/60 pole PMSGs.

G1 G2 G∗1 G3 G4

Pg , kW 4.22 4.25 3.86 4.20 4.25fs, Hz 74.67 74.67 116.67 149.33 149.33Turns per winding, Ns 14 10 14 7 5Vrms 23.5 23.6 23.65 24.0 24.0J , A/mm2 4.67 3.29 4.37 4.58 3.15α 54.4◦ 54.4◦ 68.8◦ 54.6◦ 54.7◦

η, % 90.4 92.4 88.6 89.62 90.46Xs, p.u. 0.58 0.46 0.83 0.571 0.449Xext, p.u. 1.88 1.99 3.59 1.87 1.96Lext, mH 2.84 3.06 3.74 1.47 1.61Xext/Xs 3.26 4.33 4.32 3.27 4.37Outer Diameter, mm 384 384 384 384 384Axial Length, mm 70.55 100 70.55 70.55 100Mactive 22.08 32.1 22.7 22.08 32.1MP M 2.77 3.72 2.63 2.77 3.72

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Extras

Effect of Generator Size

Geometric dimensions held constant.

Axial Length

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Extras

Table 5: Static FEA results for 28/30 pole PMSG and 56/60 pole PMSGs.

G1 G2 G∗1 G3 G4

Pg , kW 4.22 4.25 3.86 4.20 4.25fs, Hz 74.67 74.67 116.67 149.33 149.33Turns per winding, Ns 14 10 14 7 5Vrms 23.5 23.6 23.65 24.0 24.0J , A/mm2 4.67 3.29 4.37 4.58 3.15α 54.4◦ 54.4◦ 68.8◦ 54.6◦ 54.7◦

η, % 90.4 92.4 88.6 89.62 90.46Xs, p.u. 0.58 0.46 0.83 0.571 0.449Xext, p.u. 1.88 1.99 3.59 1.87 1.96Lext, mH 2.84 3.06 3.74 1.47 1.61Xext/Xs 3.26 4.33 4.32 3.27 4.37Outer Diameter, mm 384 384 384 384 384Axial Length, mm 70.55 100 70.55 70.55 100Mactive 22.08 32.1 22.7 22.08 32.1MP M 2.77 3.72 2.63 2.77 3.72

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Extras

Table 5: Static FEA results for 28/30 pole PMSG and 56/60 pole PMSGs.

G1 G2 G∗1 G3 G4

Pg , kW 4.22 4.25 3.86 4.20 4.25fs, Hz 74.67 74.67 116.67 149.33 149.33Turns per winding, Ns 14 10 14 7 5Vrms 23.5 23.6 23.65 24.0 24.0J , A/mm2 4.67 3.29 4.37 4.58 3.15α 54.4◦ 54.4◦ 68.8◦ 54.6◦ 54.7◦

η, % 90.4 92.4 88.6 89.62 90.46Xs, p.u. 0.58 0.46 0.83 0.571 0.449Xext, p.u. 1.88 1.99 3.59 1.87 1.96Lext, mH 2.84 3.06 3.74 1.47 1.61Xext/Xs 3.26 4.33 4.32 3.27 4.37Outer Diameter, mm 384 384 384 384 384Axial Length, mm 70.55 100 70.55 70.55 100Mactive 22.08 32.1 22.7 22.08 32.1MP M 2.77 3.72 2.63 2.77 3.72

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Extras

Table 5: Static FEA results for 28/30 pole PMSG and 56/60 pole PMSGs.

G1 G2 G∗1 G3 G4

Pg , kW 4.22 4.25 3.86 4.20 4.25fs, Hz 74.67 74.67 116.67 149.33 149.33Turns per winding, Ns 14 10 14 7 5Vrms 23.5 23.6 23.65 24.0 24.0J , A/mm2 4.67 3.29 4.37 4.58 3.15α 54.4◦ 54.4◦ 68.8◦ 54.6◦ 54.7◦

η, % 90.4 92.4 88.6 89.62 90.46Xs, p.u. 0.58 0.46 0.83 0.571 0.449Xext, p.u. 1.88 1.99 3.59 1.87 1.96Lext, mH 2.84 3.06 3.74 1.47 1.61Xext/Xs 3.26 4.33 4.32 3.27 4.37Outer Diameter, mm 384 384 384 384 384Axial Length, mm 70.55 100 70.55 70.55 100Mactive 22.08 32.1 22.7 22.08 32.1MP M 2.77 3.72 2.63 2.77 3.72

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Extras

Table 5: Static FEA results for 28/30 pole PMSG and 56/60 pole PMSGs.

G1 G2 G∗1 G3 G4

Pg , kW 4.22 4.25 3.86 4.20 4.25fs, Hz 74.67 74.67 116.67 149.33 149.33Turns per winding, Ns 14 10 14 7 5Vrms 23.5 23.6 23.65 24.0 24.0J , A/mm2 4.67 3.29 4.37 4.58 3.15α 54.4◦ 54.4◦ 68.8◦ 54.6◦ 54.7◦

η, % 90.4 92.4 88.6 89.62 90.46Xs, p.u. 0.58 0.46 0.83 0.571 0.449Xext, p.u. 1.88 1.99 3.59 1.87 1.96Lext, mH 2.84 3.06 3.74 1.47 1.61Xext/Xs 3.26 4.33 4.32 3.27 4.37Outer Diameter, mm 384 384 384 384 384Axial Length, mm 70.55 100 70.55 70.55 100Mactive 22.08 32.1 22.7 22.08 32.1MP M 2.77 3.72 2.63 2.77 3.72

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Extras

Static FEA Performance

Table 6: General performance of the static FEA simulations

G1 G3

Mesh Elements 17731 18241FEA iterations 13 13Total simulation time, s 28.8 33.7

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Extras

Static FEA Performance

Table 6: General performance of the static FEA simulations

G1 G3

Mesh Elements 17731 18241FEA iterations 13 13Total simulation time, s 28.8 33.7

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Extras

Verification

0 5 10 15 20100

125

150

Mechanical rotation (deg)

Torq

ue(N

m)

TransientStatic

Figure 14: Developed torque versus mechanical rotation obtained from transient(ANSYS Maxwell) and static (SEMFEM) solutions.

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