Andrea Pirisi, G. Gruosso, Riccardo E. Zich Politecnico di ... · Andrea Pirisi, G. Gruosso,...

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 .