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 .