Space solar power station is a novel renewable energy equipment in space to provide the earth with abundant and continuous power. The Orb-shaped Membrane Energy Gathering Array, one of the alternative construction schemes in China, is promising for collecting space sunlight with a large-scale spherical concentrator. Both the structural and optical performances such as root mean square deformation, natural frequency, system mass, and sunlight blocking rate have significant influences on the system property of the concentrator. Considering the comprehensive performance of structure and optic, this paper proposes a novel mesh grid based on normal polyhedron projection and spherical arc bisection for the supporting structure to deal with the challenge of the large-scale structural modular design. For both achieving low system mass and high surface precision, a multi-layer and multi-objective optimization model is proposed by classifying the supporting structure into different categories and optimizing their internal and external diameters. The Particle Swarm Optimization algorithm is adopted to find optimal sectional dimensions of the different kinds of supporting structure. The infinite model is also established and structural analysis is carried out, which are expected to provide a certain reference for the subsequent detailed structural design. The numerical results indicate that the spherical concentrator designed by the novel mesh grid would obtain as high as 94.37% sunlight collection efficiency. The supporting structure constructed with the multiple layers would reduce the system quality by 6.92%, sunlight blocking rate by 28.54%, maximum deformation by 41.50%, and root mean square by 9.48% to the traditional single layer, respectively.

A clean and renewable energy platform can be truly established only when energy is driven by solar power. However, ground-based solar energy is small in scale and low in efficiency because it is greatly affected by climate, geography, and other factors. Space solar power station (SSPS) has demonstrated an exclusive advantage, where the power density is 1367 W/m^{2}, much higher than that of ground-based solar energy (about 300 W/m^{2}) [

The SECS is the frontend of the SSPS, the size of which would reach km level and the performance of which would directly affect the overall performance of the SSPS. The conceptual design of the SECS is greatly important and several classical schemes have been proposed until now. Classical schemes can be classified by focus mode into three types, such as non-focusing mode, point-focusing mode, and distribution-focusing mode.

The original SSPS, the reference model, and the tethered SSPS capture sunlight by the non-focusing mode [

Focusing technology can decrease the area of the cell array whilst increasing the photovoltaic conversion efficiency. The Integrated Symmetrical Concentrator (ISC) utilizes parabolic point-focusing mode but complicated control strategies and thermal problems on the sandwich structure restrict its realization [

To improve the performance presented above, the Chinese research team proposed the OMEGA (Orb-shaped Membrane Energy Gathering Array) concept [_{c}/2 along the Z_{1}-axis, where _{c} is the radius of the concentrator. The concentrator is connected to the microwave transmitting antenna via long cables. Because the curvature of the ideal sphere is equal everywhere, the photovoltaic array moves around the geometric center of the concentrator in a circle with a period of 24 h, which can theoretically ensure the stability of the light collection efficiency.

For the concentrator for the space solar power station, Yang et al. [

For the optimization algorithms for the space solar power station, Meng et al. [

The concentrator of the 2 GW-output OMEGA is as large as km level which undertakes the function of structural support and energy collection. According to the conceptual design, the radius is about 1,500 m [

Considering the topology design of the supporting structure of the spherical concentrator, this paper mainly deals with the mesh grid of the spherical concentrator and its optimization. At first, a novel topology grid scheme of the super large-scale spherical concentrator is proposed. Optical simulation via the ray-tracing method evaluates the efficiency of the concentrator with the novel topology. Second, the connection relationship between the long truss cables and the concentrator is evaluated. Third, a multi-layer and multi-objective optimization model is proposed to improve both the optical and structural performance. Finally, the PSO algorithm is adopted to achieve optimal numerical results. Furthermore, the structural analysis is conducted and modal shape is discussed to provide a detailed reference to the further research.

For the OMEGA scheme, the spherical concentrator would be constructed with supporting structure and thin-film elements and should meet the requirements of high collection rate, small fluctuation of energy of collection, and small grid distortion for small structural deformation. To meet the previous requirements, the grid design criterion based on the idea of normal polyhedron projection and spherical arc bisection is established. Then, the shape and node of sub-array mesh, and splicing modules are determined based on the design criteria. Finally, the topological grid, that is the connection relationship of supporting structure is designed.

Shown in _{1}-X_{1}Y_{1}Z_{1} is established for the PV cell array. O_{1} is a boundary point of the PV cell array. X_{1}-axis points to O_{1} and Y_{1}-axis is opposite to tangent to the trajectory.

To satisfy the previous requirements, the authors divide the sphere with the process of the sphere–subarrays–modules. The grid design criteria are as follows:

The OMEGA would operate in the geosynchronous (GEO) orbit and the PV cell array would be rotated around the geometric center of the spherical concentrator in a two-dimensional plane. Using the symmetry of a regular polyhedron can guarantee the stability of light collection in principle. By projecting a regular polyhedron onto its external sphere, several groups of basic subarrays are obtained.

To avoid the problems such as poor equal-area property and a large number of modules caused by plane mapping in traditional methods [

The sunrays paralleling the Y-axis are reflected by the reflector. Based on the previous criteria, the spherical mesh grid can be obtained as follows:

As is shown in

Meshing the subarray Δ

where _{c} is the radius of the sphere, φ_{j} and _{i} are azimuth and elevation, calculated as:

where _{0} and _{1} are the number of segments in longitudinal and latitudinal direction, respectively.

3. Mirroring the nodes and connecting the adjacent nodes, the grid for the subarray Δ

Ray tracing technique is one of the important methods to analyze the optical performance for complicated system geometries [_{ref}, _{inc} and

The collection efficiency of the splicing concentrator _{c} can be calculated as follows:

where _{j,k} is the power of a single sampling ray, _{r} is the area of sunlight irradiating to the aperture of the splicing sphere, _{0} is the solar constant at a value of 1367 W/m^{2}. _{j} are the number of subsections and the number of sun rays reflected in the _{th} subsection.

Considering the proposed topological grid, the specific grid is determined by the number of segments in the longitudinal and latitudinal directions. To evaluate the influence of the mesh grid on the collection efficiency, the authors analyze the optical performance in the different number of segments in the longitudinal and latitudinal directions with the previous ray-trace method. To reduce grid distortion, the number of segments in the longitudinal and latitudinal directions are set to be equal in the simulation progress. To precisely track incident sunlight, the transmittance and the reflectance of the concentrator modules are all assumed to be 100%. The results are indicated in

Segments | Module number | Normalized efficiency _{c}(%) |
---|---|---|

Ideal sphere | — | 100 |

17 | 366 | 80.82 |

20 | 511 | 85.54 |

22 | 615 | 87.70 |

25 | 824 | 91.47 |

27 | 968 | 92.19 |

30 | 1,196 | 94.37 |

As seen in

The size of the spherical concentrator is in km scale and it is likely to be a large flexible structure. It is necessary to analyze the structural characteristics.

In terms of the topology connection relationship, key points are obtained and the pipe beams can be connected. Additionally, the membrane elements are generated by key points. Based on the connection relationship, the vertex of the thin-film modules and the ends of the beams have common key points. The three-dimensional beam element and three-dimensional shell element are selected for the beams and thin-film elements. As the fixed devices are locked, a rigid connection between the beams is taken into account. According to the system transmission efficiency of the 2GW-output OMEGA project, the diameter of the microwave power transmission antenna and the spherical concentrator are 1 and 3 km, respectively [

Structure | Material | ^{3}) |
||
---|---|---|---|---|

Circular pipe beams | Reinforced carbon fiber | 1940 | 588.0 | 0.307 |

Thin-film elements | Polyimide | 1400 | 2.9 | 0.370 |

MPT antenna elements | Titanium alloy | 75 | 150.0 | 0.340 |

Steel cables | Stainless steel | 7850 | 200.0 | 0.300 |

According to the original design of the OMEGA, the MPT antenna will be connected to the spherical concentrator with eight steel cables. The static analysis and modal analysis with different connection positions are conducted, as is shown in

Nevertheless, the pipe beams can block the incident sun rays. As presented in _{b}, is defined as:

where _{e}_{,i} is the external radius of a circular beam, (_{s,i}, _{s,i}) and (_{t,i}, _{t,i}) are the coordinates of its start point and end point in aperture surface.

The cross-sectional area of the irradiating surface, _{r}, can be calculated as:

With _{s}, can be calculated with:

Assuming that the beams have the same outer radius and considering that if the blocking rate cannot exceed 3%, the maximum outer radius of the beams for the 2GW-output OMEGA should not be over 0.692 m. According to the technology development planning route of the SSPS, the sunlight concentrator is about 1,500 t [

Cables | Position | RMS (m) | Maximum deformation (m) | Natural frequency (Hz) |
---|---|---|---|---|

C1∼C8 | Case I (1, 6, 7, 12, 13, 18, 19, 24) | 0.0774 | 0.2941 | 0.00774 |

Case II (2, 5, 8, 11, 14, 17, 20, 23) | 0.0617 | 0.2008 | 0.00774 | |

Case III (3, 4, 9, 10, 15, 16, 21, 22) | 0.0300 | 0.1864 | 0.00774 |

The structural deformation would make an influence on the solar energy collection efficiency. According to the numerical results in

As mentioned, light collection efficiency, system quality, surface accuracy, and fundamental frequency are the key characteristic parameters of a super large-scale light collection system. The size of the GW level concentrator will reach km level, and the system will have a large mass and low dynamic stiffness. As a supporting structure, the structural characteristics of the concentrator framework directly affect the overall performance of the system. The topological connection form of the supporting structure has been obtained in the previous work in this paper, and the mesh density can be controlled by adjusting the number of segments in the longitudinal and latitudinal direction directions. Illustrated in

The structural deformation is evaluated by RMS, which has been defined with _{j} is the material density, _{j} and _{j} are the external and internal radius of different categories of the circular beams. (_{s,i}, _{s,i}, _{s,i}) and (_{t,i}, _{t,i}, _{t,i}) are the coordinates of its start point and end point in aperture surface.

For its super large scale, the concentrator is expected to reduce system mass whilst reducing the structural deformation. Therefore, a multi-objective function is established as:_{1} and _{2} are weighting coefficients, and _{1} + _{2} = 1.

To prevent numerical issues, two different dimensions of the objective function are translated into a unified dimensionless as follows:_{min} and _{max} are the minimum and maximum mass, _{min} and _{max} are the minimum and maximum RMS.

Based on the multi-layer construction method and multi-objective function, a multi-layer and multi-objective optimization model is established and optimal design is to find the optimum internal and external diameters of the three categories of the supporting structure. The optimization model can be described as follows:_{min} are the eigenfrequency and its constraint. _{s} and _{s}_{max} are blocking rate and its constraint, _{s} can be calculated with _{max} are the system mass and its constraint.

PSO is a population-based heuristic, which is motivated by social behaviors such as bird flocking. Knowledge is optimized by social interaction in the population, which is called a swarm. PSO has the characteristics of a simple algorithm, fewer computational resources, and high convergence speed.

The PSO algorithm starts with a randomly allocated population in the search space. Each solution within the swarm is a particle, described by a vector

where _{th} particle at the _{th} iteration of the evolutionary process, and _{1} and _{2} are cognitive and social factors, respectively. _{th} particle and _{max}, i.e.,

To test the proposed optimization model, the authors utilize the PSO algorithm to obtain optimal results. Three models are compared:

Model I: the initial conceptual design in

Model II: the objective function and constraints are the same as the optimization model in

Model III: the proposed optimization model in

Comprehensively considering calculation time and accuracy, the generation number is 200 and the population size is 100. The inertia weight _{1} and _{2} are set to 2.0. During the simulation, _{min}, _{s}_{max} and _{max} are set to 0.005 Hz, 5%, and 2,000 t, respectively. To take account of the system mass and RMS, the weighting coefficients _{1} and _{2} are set to 0.5.

The variation of objective function and performance properties with iterations are shown in

Model | Categories | RMS (m) | Max. deformation (m) | Natural frequency (Hz) | Mass (t) | Blocking rate (%) | ||
---|---|---|---|---|---|---|---|---|

Model I | – | 0.6920 | 0.6870 | 0.0300 | 0.1864 | 0.00774 | 1,682 | 3.0000 |

Model II | – | 0.4999 | 0.4948 | 0.0327 | 0.1523 | 0.00558 | 1,214 | 2.1672 |

Model III | Category 1 | 0.2450 | 0.2397 | 0.0296 | 0.0891 | 0.00561 | 1,130 | 1.5487 |

Category 2 | 0.3998 | 0.3977 | ||||||

Category 3 | 0.5000 | 0.4882 |

As is illustrated in

Comparing the results of Model I and Model III in detail, the natural frequency of Model III is decreased from 0.00774 to 0.00561 Hz. However, the RMS and maximum deformation are decreased by 1.33% and 52.20%, respectively. The system mass is reduced by 32.82% and the blocking rate is also decreased by 48.38%.

Comparing the results of Model II and Model III in detail, the support skeleton constructed with three types of trusses could reduce the system quality by 6.92%, light blocking rate by 28.54%, maximum deformation by 41.50%, and RMS by 9.48%, respectively. Furthermore, the fundamental frequency is raised by 0.54%.

As is stated, Model III has better performance on both structural and optical properties than Model I and Model II. The large-scale spherical concentrator optimized with the multi-layer and multi-objective optimization model could have the characteristics of lightweight, high surface precision, and high sunlight collection efficiency.

To further evaluate the dynamic properties of Model III, model analysis is also conducted and the natural frequency and corresponding modal shape are summarized in

Order | Natural frequency (Hz) | Modal shape |
---|---|---|

1 | 0.00561 | Respiratory vibration of the whole structure |

2 | 0.00591 | Staggered respiratory vibration of the upper and lower parts of the structure |

3 | 0.00609 | Symmetric mode of the order 1 |

4 | 0.00635 | Symmetric mode of the order 2 |

5 | 0.00665 | Parallel movement of the whole structure |

6 | 0.00666 | Symmetric mode of the order 5 |

7 | 0.00799 | Torsional vibration of the whole structure |

8 | 0.00800 | Symmetric mode of the order 7 |

9 | 0.00967 | Respiratory vibration and parallel movement of the whole structure |

10 | 0.01182 | Respiratory vibration and torsional vibration of the whole structure |

Due to the large scale of the system and the material properties at the current state, the natural frequency is low, the fundamental frequency of the supporting structure is 0.00561 Hz. From the 1st order to the 10th order, the modal shapes appear as respiratory vibration, parallel movement, and torsional vibration in different directions. In addition, there exists a corresponding symmetrical mode with different orders of torsion.

Considering the construction strategy, the regular polyhedron is utilized and mesh generation based on symmetrical sub-array was conducted in

Considering the SSPS-OMEGA concept, modular design and multi-layer and multi-objective optimization design of supporting structure of large-scale spherical solar concentrator were calculated. A novel spherical grid meshed with the equatorial circles, declination circles, and meridian circles was proposed. The optical performance was also evaluated by the ray-tracing method and the collection efficiency is as high as 95%. The finite element model for the spherical concentrator was established. Structural analysis and modal analysis were performed to give a preliminary investigation of the structural static and dynamic characteristics. A multi-layer and multi-objective optimization model was proposed by a comprehensive consideration of the structural and optical properties. The numerical results by PSO have indicated better structural and optical performance such as system mass, structural deformation, natural frequency, and sunlight blocking rate. Compared to the traditional single layer, the proposed multiple layers would reduce the system mass by 6.92%, blocking rate by 28.54%, maximum deformation by 41.50%, and RMS by 9.48%, respectively. Furthermore, the fundamental frequency is also raised by 0.42%.

Although better structural and optical properties were obtained, only sunlight blocking was involved in the proposed optimization model and better sunlight collection efficiency was achieved. For further study, the sunlight efficiency loss and the variation of energy distribution on the cell array caused by the structural deformation should be evaluated. Furthermore, the thermal vibration and thermal deformation should be also considered and an optical, mechanical, electrical, thermal coupled-field simulation analysis of the SSPS would be established.

_{b}

blocking area of supporting structure (m^{2})

_{r}

sunlight irradiating area (m^{2})

_{min}

eigenfrequency and its constraint (Hz)

_{1},

_{2}

cognitive and social factors

_{j,k}

power of a single sampling ray (W)

elastic modulus (GPa)

_{0}

solar constant (W/m^{2})

_{max}

system mass and its constraint (t)

_{0},

_{1}

number of segments in longitudinal and latitudinal direction

number of subsections

unit vector along the normal

_{j}

number of sun rays reflected in a single subsection

pbest and gbest

radius of the ideal spherical concentrator (m)

_{e}

_{,i}

external radius of a circular beam (m)

_{inc}

unit vector of an incident ray

_{ref}

unit vector of its reflected ray

random numbers distributed uniformly on the interval [0, 1]

inner and outer radius of the three categories of the pipe beams (m)

velocity vector

position vector

incident angle (°)

_{c}

collection efficiency

_{s},

_{s}

_{max}

blocking rate and its constraint (%)

_{i}, φ

_{j}

elevation and azimuth angle (rad)

density (kg/m^{3})

poisson ratio

_{1},

_{2}

weighting coefficients