Pushing the limits of
beam-steering lens arrays

Håkon Jarand Dugstad Johnsen1, Astrid Aksnes2, Jan Torgersen1
1Department of Mechanical and Industrial Engineering, NTNU
2Department of Electronic Systems, NTNU

Solar tracking

Tracking integration

Beam-steering
lens arrays

How?

Why?

  • No rotation
  • Small physical footprint
  • Low power, fast, accurate tracking


Old news?

  • Johnsen, 2018
  • Lin, 2012

What's new?

Improving the
optical performance

Outline

• Objectives
η, θmax, $
• Design method

@numba.njit
def trace_single_ray(surfaces,ray):
  for surface in surfaces:
    surface_normal = (surfacemodel
                     .intersect(surface,ray))
    aperture.vignett_ray(surface,ray)
    ...
• Results

Objectives

• Maximize efficiency
↑ η
• Minimize divergence
↓ θmax
• Minimize cost & complexity
↓ $

Maximize efficiency

Choose an orientation

Inspired by Ito et al.
Ito, A., Sato, D. and Yamada, N., “Optical design and demonstration of microtracking CPV module with bi-convex aspheric lens array,” Opt. Express, OE 26(18), A879–A891 (2018).

Angular distribution of sunlight

Average yearly efficiency

Objectives

• Maximize average yearly efficiency
↑ η
• Minimize divergence
↓ θmax
• Minimize cost & complexity
↓ $

Minimize divergence

Minimize divergence

Objectives

• Maximize average yearly efficiency
↑ η
• Minimize permitted divergence
↓ θmax
• Minimize cost & complexity
↓ $

Minimize cost & complexity

  • Difficult to quantify
  • Try a few different configurations:
1
2
3
4

Design method

  • Numerical optimization
    • Scalarizing by fixing $\theta_{max}$
    • Memetic programming
  • Ray-tracing simulations
    • Custom ray-tracer, Python & Numba
    • Material: PMMA
    • Google Compute Engine
$$\min\,\mathbf{f}\left(\mathbf{x},\theta_{max}\right)=\left(1-\overline{\eta}\left(\mathbf{x},\theta_{max}\right),\theta_{max}\right)^{T}\\\text{such that}\,\,g_{j}\left(\mathbf{x}\right)\le0,$$

Optimization results

Selected example 1

Average yearly efficiency:74.4%
Permitted divergence: 1°
(Concentration limit $\frac{1}{\left(\sin 1^{\circ}\right)^2}$:≈3300x)

Optimization results

Selected example 2

Average yearly efficiency:74.6%
Permitted divergence: 2.2°
(Concentration limit $\frac{1}{\left(\sin 2.2^{\circ}\right)^2}$:≈680x)

Benefits

  • Reduced physical footprint
  • Low-power, high-accuracy, high-speed tracking

Drawbacks

  • Cosine projection effect

Outlook

  • More configurations & orientations
  • Alignment tolerances
  • New proof-of-concept

Conclusions

  • New and promising configurations
  • Comparison framework
  • Design method
Interested?
hakon.j.d.johnsen@ntnu.no