Slide 1

Material 
Patent Pending

Constant Voltage Permanent Magnet 

Wind Generator

Andrew Hirzel

LE Incorporated

October 14, 2003

andy@lightengineering.com

Slide 2

Material 
Patent Pending

Overview

•

Problem Description (3)

•

Geometry Construction (8)

•

Propose Solution (9)

•

Review Solution

•

Power, Voltage, Efficiency (6)

•

BEMF waveform (2)

•

Cogging (6)

•

Rotor Losses (3)

•

Axial Force (1)

Slide 3

Material 
Patent Pending

Project Definition

•

Speed range: 1000 – 2000 rpm

•

Voltage range: 410 – 480 Vrms (line)

•

Machine Efficiency:  

•

90% min at lightest load

•

95% min at maximum power

•

Passive Rectification to DC

•

Power Output Proportional to Rotor-Speed

3

•

Power Output 100 kW at 2000 rpm

Slide 4

Material 
Patent Pending

Wind Generator Goal 

Power Output and Terminal Voltage

250

300

350

400

450

500

900

1400

1900

2400

Speed, RPM

Voltage

0

20

40

60

80

100

120

kW Power

Output Voltage, max 
Output Voltage, nom 
Output Voltage, min
Target Power ~ Rotor Speed Cubed

•Power ~ rotor-speed

3

•Voltage > 410 Vrms
•Voltage < 480 Vrms

Slide 5

Material 
Patent Pending

Wind Generator Goal 

Power Output and Machine Efficiency

85%

87%

89%

91%

93%

95%

97%

99%

900

1400

1900

2400

Speed, RPM

Percent

0

20

40

60

80

100

120

kW Power

Target Efficiency

Target Power

Slide 6

Material 
Patent Pending

Axial Airgap Stator: 

Example with 12 slots

Maxwell 3D Magnetostatic

•One stator shown

•Single wound 
amorphous metal 
ribbon, followed by 
slot cutting

Slide 7

Material 
Patent Pending

Stator shown with Phase Coils

Maxwell 3D Magnetostatic

•0.5 slots/phase/pole

•Discrete coils 

•Wired A-B-C-A-B-C

C

A

B

B

C

A

Slide 8

Material 
Patent Pending

Axial-Gap Rotor and Shaft: 8 Poles

Maxwell 3D Magnetostatic

•Surface magnets 
(thru rotor)

•North red

•South blue

•Shaft and rotor 
shown for clarity

Slide 9

Material 
Patent Pending

Complete Axial-Gap Machine: 12 Slots

Maxwell 3D Magnetostatic

•One rotor assembly

•Two stator assemblies

•Housing not shown

Slide 10

Material 
Patent Pending

Minimum Machine for EM Analysis

•Shaft and disk not 
needed for analysis

•Actual airgap 2.5 mm

Maxwell 3D Magnetostatic

A

C

B

Slide 11

Material 
Patent Pending

Boundary and Planar Entities: 12 Slots

Maxwell 3D Magnetostatic

•Master-slave boundaries

•Current sources (not 
shown)

•Analysis surfaces; 
orthogonal grid

•Tangent/normal 
boundaries

Slide 12

Material 
Patent Pending

Actual Sized Machine to meet 

Project Specifications

•466 cm diameter

•13 cm axial length

•72 Slots

•24 Pole Pairs

Maxwell 3D Magnetostatic

Slide 13

Material 
Patent Pending

Maxwell 3D Macro

•

1200 lines main code; 400 lines post processor code

•

Performs following:

•

Allows direct change to all parameters

•

Draws geometry

•

Assigns materials

•

Assigns boundaries

•

Defines solver options

•

Runs solver

•

Runs post processor macro

•

Writes inputs/outputs and writes to a .txt file

•

Iterates all of the above, on any variable

“Homegrown” Optimetrics

Slide 14

Material 
Patent Pending

Variation in Flux Density Inside Coils

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1

2

3

4

5

6

7

8

Rotor Position

Tesla

A phase

B phase

C phase

Analysis for 1/6 
of synchronous 
cycle, i.e. 1/6 of 
pole-pair angle.

Observation of 
symmetry 
concludes that 
this is all the 
analysis needed.

Slide 15

Material 
Patent Pending

“Assembled” Variation in Flux Density

•Assembly of 
synchronous 
cycle from 1/6 
analysis

•Makes macro 
code much 
faster and much 
easier to write

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1

7

13

19

25

31

37

43

49

55

Rotor Position

Tesla

A phase

B phase

C phase

Slide 16

Material 
Patent Pending

Results from Macro

•

Cogging

•

Ripple

•

Flux in core and backiron

•

Flux variation in magnet – demagnetization potential

•

Axial Forces

•

Limited by your code

Slide 17

Material 
Patent Pending

On to the Solution

•

Need…

•

Constant Voltage plus

•

Increasing Speed plus

•

Increasing Power plus

•

Permanent magnet equals

•

….

•

Not possible (?)

Slide 18

Material 
Patent Pending

Stators In-line

Standard stator 
arrangement:  Both 
stators are 
physically in-line, 
causing series 
connected voltage 
to add to 2X single-
side voltage.

Maxwell 3D Magnetostatic

Slide 19

Material 
Patent Pending

Stator Shifting: Method of EMF Control by 

Relative Rotation about Z-axis

Upper stator section is kept 
fixed relative to the rotation 
about z-axis of the lower 
section.

Previously in-phase coils 
are taken out of phase.  
Series connection causes 
additive resulting sine-
wave voltage.

Maxwell 3D Magnetostatic

Slide 20

Material 
Patent Pending

Stator Movement: Method of EMF Control by 

Relative Rotation

Maxwell 3D Magnetostatic

Amount of relative 
rotation …

never greater than …  

1 pole pitch; in this 
example 1 pole pitch 
~30 mm.  

Slide 21

Material 
Patent Pending

How much movement?

•

1 Pole Pitch = 7.5 degrees

•

1 Pole Pitch ~ 30mm circumferentially

•

1 Slot Pitch = 2/3 Pole Pitch

Slide 22

Material 
Patent Pending

Stators Shifted by 25% Pole Pitch with Serial 

Addition of Waveforms

•No load

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Rotor Position

Tesla

Stator fixed

Stator shift 25%

Series stators

Best Fit Series

•THD=2%

Slide 23

Material 
Patent Pending

Stators Shifted by 25% Pole Pitch with Serial 

Addition of Waveforms

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Rotor Position

Tesla

Stator fixed

Stator shift 25%

Series stators

Best Fit Series

•Rated load

•THD=4%

Slide 24

Material 
Patent Pending

Stators Shifted by 66% Pole Pitch with Serial 

Addition of Waveforms

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Rotor Position

Tesla

Stator fixed

Stator shift 66%

Series stators

Best Fit Series

•No load

•THD=7%

Slide 25

Material 
Patent Pending

Stators Shifted by 66% Pole Pitch with Serial 

Addition of Waveforms

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Rotor Position

Tesla

Stator fixed

Stator shift 66%

Series stators

Best Fit Series

•Rated load

•THD=20%

Slide 26

Material 
Patent Pending

Stators Shifted by 66% Pole Pitch with Serial 

Line-Line Waveform

•Rated load

•THD=6%

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Rotor Position

Tesla

Phase A

Phase B

Line A-B

Best Fit

Slide 27

Material 
Patent Pending

How is this all useful?

•

Find a machine solution, passive rectification  using 

basic phasor diagrams and algebra

•

Solve at lowest speed, 0% shift

•

Solve at increasing speed, while increasing the stator 

shift to keep terminal voltage near constant

•

Solution:  73% pole pitch shift needed = 22 mm 

movement circumferentially

Slide 28

Material 
Patent Pending

Results Voltage vs. Target Voltage

300

350

400

450

500

550

600

900

1400

1900

2400

Speed, RPM

Voltage

V @ max power

V @ min power

target V nominal

Slide 29

Material 
Patent Pending

300

350

400

450

500

550

600

900

1400

1900

2400

Speed, RPM

Voltage

0

20

40

60

80

100

120

kW Power

target V nominal

Target Power

max power

min power

Results Power vs. Target Power

Voltage would be exceeded
So power cannot be maintained

Slide 30

Material 
Patent Pending

85%

87%

89%

91%

93%

95%

97%

99%

900

1400

1900

2400

Speed, RPM

Percent

Eff @ max power

Eff @ min power

Target Efficiency

Results Efficiency vs. Target Efficiency

Voltage would be exceeded
So current must increase

Slide 31

Material 
Patent Pending

Resulting needed Stator Movement

0.0

5.0

10.0

15.0

20.0

25.0

0

1000

2000

3000

Speed, RPM

mm

circum movement
for max power

circum movement
for min power

Ref:
30 mm=pole pitch
20 mm=slot pitch

Voltage would be exceeded

Slide 32

Material 
Patent Pending

Speed and Power vs. Stator Position

0

500

1000

1500

2000

2500

3000

0.0

10.0

20.0

30.0

movement, mm

speed, RPM

0

20

40

60

80

100

120

Power, kW

spd @ max power

spd @ min power

max power

min power

Voltage would be exceeded

Slide 33

Material 
Patent Pending

Speed and Voltage vs. Stator Position

0

500

1000

1500

2000

2500

3000

0.0

10.0

20.0

30.0

movement, mm

speed, RPM

0

50

100

150

200

250

300

350

400

450

500

Voltage

spd @ max power

spd @ min power

V @ max power

V @ min power

Voltage would be exceeded

Slide 34

Material 
Patent Pending

Other items of interest: 

Flux Density in Backiron

Discontinuity is 
not real, it’s a 
function of 
solver accuracy

-1.5

-1

-0.5

0

0.5

1

1.5

Rotor Position

Tesla

no load B in
backiron

load B in backiron

Slide 35

Material 
Patent Pending

Cogging Controlled via 3D Optimized 

Magnet Spacing

Maxwell 3D Magnetostatic

Typical approach to 
design minimal 
cogging into 
machine is via 3D 
analysis and 
variation of magnet 
spacing.

Slide 36

Material 
Patent Pending

Stator Shifting and Effect on Cogging

-8

-6

-4

-2

0

2

4

6

8

0

2

4

6

8

10

12

14

16

18

Rotor Position

N-m

Pole Pitch 0% - Slot Pitch 0%

Pole Pitch 25% - Slot Pitch 38%

Pole Pitch 33% - Slot Pitch 50%

Pole Pitch 40% - Slot Pitch 60%

Pole Pitch 67% - Slot Pitch 100%

Slide 37

Material 
Patent Pending

Unfortunately, Axial Forces Increase with 

amount of Stator Shift

0

1000

2000

3000

4000

5000

6000

0%

10%

20%

30%

40%

50%

60%

70%

Pole Pitch Percent

Axial Force, N

Slide 38

Material 
Patent Pending

No Load; 

Review Flux Density in Magnet Grid

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0

5

10

15

Rotor Position

Tesla

Leading OR

Central OR

Trailing OR

Leading R

Central R

Trailing R

Leading IR

Central IR

Trailing IR

Slide 39

Material 
Patent Pending

Rated Load; 

Review Flux Density in Magnet Grid

0.4

0.5

0.6

0.7

0.8

0.9

1

0

5

10

15

Rotor Position

Tesla

Leading OR

Central OR

Trailing OR

Leading R

Central R

Trailing R

Leading IR

Central IR

Trailing IR

Slide 40

Material 
Patent Pending

3X Rated Load; All current in D-axis 
Review Flux Density in Magnet Grid

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0

5

10

15

Rotor Position

Tesla

Leading OR

Central OR

Trailing OR

Leading R

Central R

Trailing R

Leading IR

Central IR

Trailing IR

De-magnetization 
is a real concern!

Slide 41

Material 
Patent Pending

A Plug for Maxwell 2D:  AC Ohmic Loss

Maxwell 2D Transient Solver

•2D transient analysis

•Determines AC losses

•Due to proximity effects

•+/-20% error vs. test

Slide 42

Material 
Patent Pending

Solution Results

á

Power =  98kW at 2000 rpm

á

Power follows rotor-speed

3

for 2X speed range

á

Voltage stays within 410 – 480 Vrms range

á

Efficiency > 94%

â

Harmonic content increases (changes) with Stator 
Shift

â

Axial force increases with Stator Shift