Andrea Pirisi, G. Gruosso, Riccardo E. Zich

Politecnico di Milano

2Outline of Today

Novel Modeling Design of Three Phase Tubular

Permanent Magnet Linear Generator for Marine

Applications

1 Introduction

2 System Definition and Analysis

3 Simulations & Results

4 Conclusions

31. Introduction: why marine energy

With respect to wind and photovoltaic, the energy associated tosea waves is more concentrated and consistent

- it is related to a fluid significantly denser than air

- it is caused by a phenomenon more intense than solar radiation

41. Introduction: why tubular generator

In recent years linear generators have been proposed in severalmarine applications

they seems to be a well-suited technology for power generationsuch as power buoys

51. Introduction: why tubular generator

- no transmission: no crank shaft, rod and rotary parts

WindingsSlider

Stator

TPM-LiG features:

- no boundary dissipation of magnetic field

- well-suited for energy convertion in power buoys

- versatile design and performances

Buoy

Sealed Chamber

Wave

TPM-LiG

61. Introduction: Aim of the work

Buoy

Sealed Chamber

Wave

TPM-LiG

- TPM-LiG is analyzed to supply small electronic devices such assensorial buoys with energy scavenging

Since energy harvesting techniques are able to overcomebattery life limitations

Aim of the work:

72. System Definition and Analysis

3phase tubular permanent magnet linear generator (TPM-LiG)machine equipped with a modular stator winding

Buoy

Sealed Chamber

Wave

TPM-LiG

WindingsSlider

Stator

- three winding slots (fill factor is assumed to be closed to 0.8)

- winding air gap slot is ignored in the simulation model

- slider is moved by 0.5m/s peak square wave

0.5

0 0.5 1 t [s]

[m/s] sz

-0.5

82. System Definition and Analysis

The core and the spacers are considered to be realized by usingpure iron with nonlinear B-H curve

The slider consists of

- a hollowed shaft and ironed spacers which separate PMs

- permanent magnets (grade N42: hc = 955kA/m, br = 1.32T)

axially magnetized and mounted alternately on the shaft

92. System Definition and Analysis

- harvesting systems for electronic power supplying: maximize theenergy conversion from mechanical source to electrical load

Since the available energy Wm depends on the time-integral ofpower pm, the waveform of power is a crucial variable

T

s

PM

s

sm idz

d

dz

Ldp ][

][][

Our objective

r

PMs

dz

de

][0 electromotive force, no load connected

T

m iep ][][ 0

102. System Definition and Analysis

- harvesting systems for electronic power supplying: maximize theenergy conversion from mechanical source to electrical load

Our objective

Find out a convenient peak values and waveforms of slider’svelocity as well as derivatives of PMs’ fluxes.

To simplify the structure of the electronic converter:

- particular set-up of TPM-LiG geometrical parameters

- under the hypothesis of a quasi-impulsive slider’s acceleration- neglecting cogging force

This is possible:

11

The analysis has been developed along the radial direction andalong the axial direction separately, with respect to thesymmetry of the system.

VARIABLE NAME VALUE [mm]

Axial Parameters

Pole pitch PP 18.8

Magnet height Mg_H Mg_H _pu * PP/2

Slider tooth height SlT_H SlT_H_pu * PP/2

Stator core height StC_H StC_H_pu * PP/3

Stator tooth height StT_H StT_H_pu * PP/3

Radial Parameters

Stator outer radius St_r 20

Air gap Ag 1

Slider outer radius Sl_r Sl_r_pu * (St_r - Ag_t/2)

Shaft outer radius Sh_r Sh_r_pu * Sl_r

Slider core thickness SlC_t SlC_t_pu * Sl_r

Slider tooth thickness SlT_t SlT_t_pu * Sl_r

Stator tooth thickness StT_t StT_t_pu * St_t

Winding thickness Wn_t Wn_t _pu * St_t

Stator armour thickness Ar_t Ar_t _pu * St_t

2. System Definition and Analysis

12

2 per-unit systems, 1 base unit quantity for each direction:

VARIABLE NAME VALUE [mm]

Axial Parameters

Pole pitch PP 18.8

Magnet height Mg_H Mg_H _pu * PP/2

Slider tooth height SlT_H SlT_H_pu * PP/2

Stator core height StC_H StC_H_pu * PP/3

Stator tooth height StT_H StT_H_pu * PP/3

Radial Parameters

Stator outer radius St_r 20

Air gap Ag 1

Slider outer radius Sl_r Sl_r_pu * (St_r - Ag_t/2)

Shaft outer radius Sh_r Sh_r_pu * Sl_r

Slider core thickness SlC_t SlC_t_pu * Sl_r

Slider tooth thickness SlT_t SlT_t_pu * Sl_r

Stator tooth thickness StT_t StT_t_pu * St_t

Winding thickness Wn_t Wn_t _pu * St_t

Stator armour thickness Ar_t Ar_t _pu * St_t

- pole pitch (PP) [mm]: base unit quantity - axial direction

- stator outer radius (St_r) [mm]: base unit q.ty - radial direction

2. System Definition and Analysis

13

Axial direction, examples:

VARIABLE NAME VALUE [mm]

Axial Parameters

Pole pitch PP 18.8

Magnet height Mg_H Mg_H _pu * PP/2

Slider tooth height SlT_H SlT_H_pu * PP/2

Stator core height StC_H StC_H_pu * PP/3

Stator tooth height StT_H StT_H_pu * PP/3

Radial Parameters

Stator outer radius St_r 20

Air gap Ag 1

Slider outer radius Sl_r Sl_r_pu * (St_r - Ag_t/2)

Shaft outer radius Sh_r Sh_r_pu * Sl_r

Slider core thickness SlC_t SlC_t_pu * Sl_r

Slider tooth thickness SlT_t SlT_t_pu * Sl_r

Stator tooth thickness StT_t StT_t_pu * St_t

Winding thickness Wn_t Wn_t _pu * St_t

Stator armour thickness Ar_t Ar_t _pu * St_t

- height of the slider iron core (SlC_H) : is its complementary

2. System Definition and Analysis

- height of the magnets (Mg_H): as a p.u. of the half of the PP

14

Radial direction, examples:

VARIABLE NAME VALUE [mm]

Axial Parameters

Pole pitch PP 18.8

Magnet height Mg_H Mg_H _pu * PP/2

Slider tooth height SlT_H SlT_H_pu * PP/2

Stator core height StC_H StC_H_pu * PP/3

Stator tooth height StT_H StT_H_pu * PP/3

Radial Parameters

Stator outer radius St_r 20

Air gap Ag 1

Slider outer radius Sl_r Sl_r_pu * (St_r - Ag_t/2)

Shaft outer radius Sh_r Sh_r_pu * Sl_r

Slider core thickness SlC_t SlC_t_pu * Sl_r

Slider tooth thickness SlT_t SlT_t_pu * Sl_r

Stator tooth thickness StT_t StT_t_pu * St_t

Winding thickness Wn_t Wn_t _pu * St_t

Stator armour thickness Ar_t Ar_t _pu * St_t

- thickness of the stator (St_T): is its complementary

2. System Definition and Analysis

- slider outer radius (Sl_r) : as a p.u. fraction of the St_r

15

A parametric analysis

- move the slider, step by step

- plot the diagram of PMs’ fluxes infunction of slider position

3. Simulations & Results

- measure the PMs’ fluxes in the stator armour behind each winding

By using simulation tool:

163. Simulations & Results

Results along the axial direction (most significative)

- Height of stator iron core: in the interval [0.1, 0.35] statorcore height determines a 100% increase of peak valuewithout any variation of the waveform; outside interval:negligible variation of peak value

173. Simulations & Results

Results along the axial direction (most significant)

- Height of the stator tooth: a variation of 40% of its valuedetermines a negligible variation in peak value with a 10%translation of the waveform along the “slider position” axis.

183. Simulations & Results

- Slider core thickness: a variation of 60% of its valuedetermines a variation up to 40% of peak value and nomodification of the waveform

Results along the radial direction (most significant)

193. Simulations & Results

- Stator armour thickness: in the interval [0.05, 0.125] thisparameter yields a negligible variation of peak value butcauses a considerable modification of the waveform from asquared shape to a triangular one; in the interval [0.125,0.2] there is no variation of peak value and of the waveform

Results along the radial direction (most significant)

20

By selecting the values of geometrical parameters it is possibleto reach a first optimization of TPM-LiG in order to:

4. Conclusions

- Find out a convenient peak values and waveforms of PMs’ fluxes and electromotive force

- simplify the structure of the electronic converter

- maximize the energy conversion from mechanical source to electrical load

214. Conclusions

A possible application of tubular generator is proposed as wellas the system definition is presented and analyzed.

A parametric evaluation of the machine is done to enforce afinite element model.

A parametric approach is adopted to perform a firstoptimization of TPM-LiG electromagnetic behavior, and thespecified features are achieved .