Andrea Pirisi, G. Gruosso, Riccardo E. Zich
Politecnico di Milano
Outline 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
2
1. Introduction: why marine energy
3
With respect to wind and photovoltaic, the energy associated to
sea 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
1. Introduction: why tubular generator
4
In recent years linear generators have been proposed in several
marine applications
they seems to be a well-suited technology for power generation
such as power buoys
5
1. Introduction: why tubular generator
TPM-LiG features:
- no transmission: no crank shaft, rod and rotary parts
- no boundary dissipation of magnetic field
- well-suited for energy convertion in power buoys
- versatile design and performances
Buoy
Wave
Sealed Chamber
TPM-LiG
Stator
Slider
Windings
1. Introduction: Aim of the work
6
Since energy harvesting techniques are able to overcome
battery life limitations
Aim of the work:
- TPM-LiG is analyzed to supply small electronic devices such as
sensorial buoys with energy scavenging
Buoy
Wave
Sealed Chamber
TPM-LiG
7
2. System Definition and Analysis
3phase tubular permanent magnet linear generator (TPM-LiG)
machine equipped with a modular stator winding
- 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
zs [m/s]
0.5
0
Buoy
0.5
-0.5
Wave
Sealed Chamber
TPM-LiG
Stator
Slider
Windings
1
t [s]
2. System Definition and Analysis
8
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
The core and the spacers are considered to be realized by using
pure iron with nonlinear B-H curve
9
2. System Definition and Analysis
Our objective
- harvesting systems for electronic power supplying: maximize the
energy conversion from mechanical source to electrical load
Since the available energy Wm depends on the time-integral of
power pm, the waveform of power is a crucial variable
pm
e0
[e0 ] [i]T
s
d [ PM ]
dz r
pm
s
d [ L]
dz s
d [ PM ]
[i ]T
dz s
electromotive force, no load connected
2. System Definition and Analysis
10
Our objective
- harvesting systems for electronic power supplying: maximize the
energy conversion from mechanical source to electrical load
To simplify the structure of the electronic converter:
Find out a convenient peak values and waveforms of slider’s
velocity as well as derivatives of PMs’ fluxes.
This is possible:
- particular set-up of TPM-LiG geometrical parameters
- under the hypothesis of a quasi-impulsive slider’s acceleration
- neglecting cogging force
2. System Definition and Analysis
11
The analysis has been developed along the radial direction and
along the axial direction separately, with respect to the
symmetry 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:
- pole pitch (PP) [mm]: base unit quantity - axial direction
- stator outer radius (St_r) [mm]: base unit q.ty - radial 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
2. System Definition and Analysis
13
Axial direction, examples:
- height of the magnets (Mg_H): as a p.u. of the half of the PP
- height of the slider iron core (SlC_H) : is its complementary
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
Radial direction, examples:
- slider outer radius (Sl_r) : as a p.u. fraction of the St_r
- thickness of the stator (St_T): is its complementary
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
14
3. Simulations & Results
15
A parametric analysis
By using simulation tool:
- move the slider, step by step
- measure the PMs’ fluxes in the stator armour behind each
winding
- plot the diagram of PMs’ fluxes in
function of slider position
3. Simulations & Results
16
Results along the axial direction (most significative)
- Height of stator iron core: in the interval [0.1, 0.35] stator
core height determines a 100% increase of peak value
without any variation of the waveform; outside interval:
negligible variation of peak value
3. Simulations & Results
17
Results along the axial direction (most significant)
- Height of the stator tooth: a variation of 40% of its value
determines a negligible variation in peak value with a 10%
translation of the waveform along the “slider position” axis.
3. Simulations & Results
18
Results along the radial direction (most significant)
- Slider core thickness: a variation of 60% of its value
determines a variation up to 40% of peak value and no
modification of the waveform
3. Simulations & Results
19
Results along the radial direction (most significant)
- Stator armour thickness: in the interval [0.05, 0.125] this
parameter yields a negligible variation of peak value but
causes a considerable modification of the waveform from a
squared shape to a triangular one; in the interval [0.125,
0.2] there is no variation of peak value and of the waveform
4. Conclusions
20
By selecting the values of geometrical parameters it is possible
to reach a first optimization of TPM-LiG in order to:
- 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
4. Conclusions
21
A possible application of tubular generator is proposed as well
as the system definition is presented and analyzed.
A parametric evaluation of the machine is done to enforce a
finite element model.
A parametric approach is adopted to perform a first
optimization of TPM-LiG electromagnetic behavior, and the
specified features are achieved .