Lorenz Solar Collector
May 30 2013
Talk Outline
• Solar energy overview
• Description of my invention
• Overview of pros/cons
• Progress to date
• Future work
Solar Energy overview
Main types of solar energy collection:
Heating
Solar cells
-Not useful for electricity
generation
-Expensive, but getting
cheaper fast
-Good for distributed
production of power
Concentrated solar power
-Least expensive for
generating electricity
-Good for centralized
production of power
Concentrated Solar Power
used to generate electricity
Dish Collector
Best concentration possible
Best efficiency possible
Expensive
Power Tower
High concentration possible
More practical - cheaper
Linear collector
Much lower concentration
Least expensive to date
Most plants built are linear
Linear collectors – parabolic trough
The only kind of linear collector in widespread use
Basic schematic
Side view
Economy of scale
Parabolic trough – schematic of plant
The linear receiver is where my novel
idea occurs.
Parabolic trough – Existing design – SEGS
• Largest solar plant in the world
• Built in Arizona by Luz corporation
between 1984 and 1990
• 1800 acres, 354 Megawatts
• Estimated cost per kWh is 14¢
• 4.6¢ due to maintenance
• Rest due to initial construction
costs
• In 2010, 1.5 billion dollar loan given
by US DOE to build parabolic trough
power plant.
My idea - Outline
• Observation 1 – Geometric fact about circles
• Resulting invention – fixed mirror collector from 70’s
• Observation 2 - Property of slightly curved mirrors
• Resulting invention – my idea, fixed mirrors that flex
My Idea - Geometric Observation
C2
Take any two
points A and B on
a circle.
C1
θ1
Connect to third
point C. Consider
the angle formed.
Try several
different points for
C.
How do these
angles relate?
θ2
θ3
A
B
C3 All the same!
θ1=θ2=θ3
My Idea - Geometric Observation
C
θ
Consider sunlight
shining from above.
Put mirrors at A and
B so that light is
reflected to point C.
Fix points A and B,
and pick some C.
A
B
My Idea - Geometric Observation
C’
θ
A
B
Suppose light shines from a
different direction. Where do
A and B reflect the light to?
Geometry dictates that they
reflect to another point on the
circle!
Geometric Observation – Fixed mirror solar collector
In 1972 a new design of solar collector was Pivot arm
invented, (Deplomb, Russell Patent #3868823)
utilizing this geometrical idea.
Absorber
Absorber
Pivot arm
Pivot
As before, just use several
mirrors instead of 2. Choose
so they all focus at C when
sun is above.
These mirrors stay fixed. As
incoming sunlight direction
changes, rotate absorber
about pivot.
C
C’
A1
A5
A2
A
A4
Fixed mirror solar collector-3D view
Pivot
Pivot arm
Absorber
Fixed mirror solar collector-pros/cons
Pros: Fixed mirror means
• Smaller motors
• Less structure
• Less wind damage
So potentially less installation cost
and less maintenance cost
Cons:
• Lower concentration ratio, maybe 40 suns
• Shading losses get severe at wide angles
• Many small mirrors, construction costs are large
Other fixed mirror solar collectors
Solar bowl
Compound parabolic concentrator
Sounds quite tasty
Low concentration ratio
Costly, poor concentration ratio
Useful as a secondary reflector
My Idea – Observation about slightly curved mirrors
Parabolas reflect parallel light to single point
A small portion of parabolic
mirror is almost circular
It concentrates light on axis very well
Slightly curved mirrors
Even off-axis, not that bad. But gets worse
as amount light is off-axis increases.
D
D
d
D
d
d
𝐷
𝑑
is concentration ratio
My idea slide 1 (of 4)
C
As before, put mirrors at A and B
so that sunlight from above hits
point C.
Connect these two mirrors with a
(slightly) curved mirror.
This then concentrates sun well
from above
A
B
My idea, slide 2
Place pivot at center of circle.
With pivot arm pointing up, sun
from above will be collected at
point C.
Pivot arm
θ
Absorber
C
C’
Pivot
2θ
If sun comes in at angle θ,
pivot arm must be rotated 2θ.
Note there is some error in how
the light focuses.
A
B
My idea, slide 3
If mirror is appropriately bent,
this error can be mostly corrected
for.
C’
Split mirror in two.
Bend mirrors slightly in correct
direction.
Smile as the light is focused oh so
much better!
A
B
My idea, slide 4
As in similar designs, we must
track the sun.
In addition we must
simultaneously bend the mirrors.
Notice that left mirror bended
down, and right mirror up.
Absorber
Pivot arm
Pivot
Cable
Cable
We connect these two motions
using wire/twine. As pivot is
moved, mirrors automatically
bend correctly.
(left mirror must have been under tension)
3D model of invention (patent pending)
Absorber
Pivot arm
Absorber
Pivot arms
Pivot
Pivot
Left mirror
A
Left mirror
B
Right mirror
Right mirror
Benefits/Drawbacks
(My idea versus parabolic trough)
vs
The red dimension is small for early prototypes but will be large in practice.
Similarities
(My idea versus parabolic trough)
1. Both reflectors are designed with the
same overall plant design in mind.
Similarities
(My idea versus parabolic trough)
The linear receiver type is the only place
where plants differ.
Similarities
(My idea versus parabolic trough)
2. Both reflectors are linear, a low cost
design.
Benefits
Drawbacks
1. Less expensive components
1. Not proven
2. Less maintenance costs
2. Restricted incidence angle
3. Good concentration ratio
4. High land use efficiency
5. Highly scalable
Benefit – Less expensive components
A. Flatter, thinner mirrors
B. Smaller motor to control
C. Less structure needed
Benefit – Less expensive components
A. Flatter, thinner mirrors
≈23⁰
Mirror itself can be
thin coating on
aluminum flashing
≈45⁰
Smaller angle here
at focus (CPV)
Lower mirror support
constructed from
single piece of material
≥70⁰
≈180⁰
Flatter
Incidence
mirror
angle
potentially
onto
reflector
works
forcan
well
easier
contruction
CPV
Mirror
not
subject
windallows
forces,
bewith
very
thin.
–(concentrated
of mirror as well
photovoltaics).
as supports.
Benefit – Less expensive components
A. Flatter, thinner mirrors
B. Smaller motor to control
C. Less structure needed
Benefit – Less expensive components
2. Smaller motor to control
Cross-section
Wind
Wind
Cross-section
smaller cross-section => smaller forces => smaller motor needed
Benefit – Less expensive components
A. Flatter, thinner mirrors
B. Smaller motor to control
C. Less structure needed
Benefit – Less expensive components
C. Less structure needed
Moving parts
Structure
Base
smaller, lighter moving parts => smaller forces => less structure needed
Plus, mirror support doubles as a wide base!
Benefits
1. Less expensive components
2. Less maintenance costs
3. Good concentration ratio
4. High land use efficiency
5. Highly scalable
Benefit – Less maintenance costs
A. Less mirrors lost to wind damage
B. Mirrors lower – easier to replace/clean(?)
Benefits
1. Less expensive components
2. Less maintenance costs
3. Good concentration ratio
4. High land use efficiency
5. Highly scalable
Good concentration ratio – theoretical
Concentration ratio key design parameter
Angle of incidence α
Concentration ratio
0
82.6
±15
77.8
±30
51.6
±45
20.6
Bold these as we animate drawing on the right
Good concentration ratio – theoretical
Concentration ratio key design parameter
Angle of
incidence α
Concentration ratio
Conc. Ratio for
perfectly parabolic
0
82.6
106.5
±15
77.8
94.7
±30
51.6
84.0
±45
20.6
72.8
Good concentration ratio – theoretical
Angle of
incidence α
Concentration ratio
Conc. Ratio w
secondary collector
0
82.6
94.0
±15
77.8
94.5
±30
51.6
76.1
±45
20.6
53.9
2 cables
4 cables
vs
Benefits
1. Less expensive components
2. Less maintenance costs
3. Good concentration ratio
4. High land use efficiency
5. Highly scalable
High land use efficiency
We must choose a range of incidence angles to accept.
Sunlight
α= -70°
Incidence angle α = 0°
Suppose we choose a range of -70 ≤ α ≤ 70.
Consider standard parabolic trough.
α = 70°
Land use efficiency – parabolic troughs
How far apart to space in order to avoid shading?
70°
This portion shaded
Min spacing to avoid shading
Land use efficiency – parabolic troughs
How far apart to space in order to avoid shading?
70°
w = d cos 70°
≈ 0.342d
w
70°
d
Min spacing to avoid shading
Land use efficiency – parabolic troughs
Land use efficiency = w/d
= d cos 70°/d
= cos 70°
≈ 0.342
w
w-d
d
Land use efficiency – novel collector
Land use efficiency is close to 100%
Land use efficiency – novel collector
Land use efficiency is close to 100%