1. Introduction
PV modules have been widely used to collect solar energy to generate clean renewable electricity, and solar farms have become one of the primary solutions to climate change. The China Photovoltaic Industry Association (CPIA) reported the latest 2021–2022 China PV Industry Development Roadmap [
1], providing the latest initial full investment cost of China’s ground-mounted solar farms. In the United States, the Solar Energy Industries Association (SEIA) and Wood Mackenzie reported the Q2 2022 US Solar Market Insight Executive Summary [
2] and provided the full investment cost for different types of solar farms, including utility fixed-tilt and tracking solar farms.
Table 1 compares the investment cost percentages of the fixed-tilt solar farms in the two countries. The results showed that PV modules and their supporting systems account for more than 55% of the investment cost of the entire solar farm. Support systems are key components of solar farms and directly affect the safety of PV modules and construction investment. The wind load is the control load of the PV systems. Therefore, the optimal design of wind-resistant PV modules and their supporting systems has always been a hot topic in the fields of wind, PV, and transportation engineering [
3].
Most PV modules are supported by fixed structures, as illustrated in
Figure 1. To accurately assess wind loads on PV modules, since the 1980s, many researchers have studied wind loads on fixed supporting structures for PV modules. Radu et al. [
4] described the wind loads on PV module arrays on top of residential buildings via wind tunnel testing and observed that the average wind load of the rear modules markedly decreased owing to the shielding effect of the building and windward PV modules. Wood et al. [
5] described the influence of the position of PV modules on the wind loads on both flat roofs and PV modules via wind tunnel testing. Warsido et al. [
6] investigated the effects of array spacing on the shielding effect of the wind load on rooftop PV modules. Radu et al. [
7] studied the effect of roof parapets on the wind load on roof PV modules. In recent years, Pratt and Kopp [
8], Cao et al. [
9], Banks [
10], and Stathopoulos et al. [
11,
12] investigated wind loads on PV arrays with different aspect ratios on flat roofs and showed that wind loads on PV modules are primarily affected by the width of the building. Alrawashdeh and Stathopoulos [
13] studied the influence of the geometric scale of roof PV modules on the wind pressure distribution and concluded that the geometric scale has a significant influence on the wind load of PV modules.
For wind loads on ground-mounted PV modules, Bitsuamlak et al. [
14] found that the wind load on leeward PV modules was 30% lower than that on the windward row through full-scale measurements and computational fluid dynamics (CFD) numerical simulations. In addition, they found that the CFD numerical simulation yielded similar wind pressure distribution rules to the full-scale measurement, but the pressure coefficients of the simulation results were smaller than those of the full-scale measurement. Shademan and Hangan [
15] and Shademan et al. [
16,
17] studied the influence of distance and spacing from the ground on the wind loads on PV modules and showed that increasing the distance between the modules produced stronger vortex shedding, resulting in a greater average and fluctuating wind loads. When two adjacent PV modules reach a certain distance, the drag coefficient of the leeward PV modules decreases to a minimum. Aly and Bitsuamlak [
18] and Aly [
19] studied the wind load of ground-mounted PV modules via wind tunnel tests and CFD numerical simulations under different model scales and wind field characteristics. Their results showed that the geometric scale of the model and the characteristics of the wind field had little effect on the average wind pressure coefficient but markedly affected the peak pressure coefficient. Abiola-Ogedengbe et al. [
20] studied the wind pressure field and loads of ground-mounted PV modules via CFD simulations and showed that the interpanel gap and tilt angle affect the surface pressure. Mammar et al. [
21] studied the influence of column height and estimated steady and unsteady wind loads on heliostats through a wind tunnel test. The results show that an increase in column height produces larger steady and unsteady pressure wind loads, stronger vortex shedding, and higher shedding frequencies. Geurts and Steenbergen [
22], Erwin et al. [
23], Geurts and Blackmore [
24], and Bender et al. [
25] conducted field measurements of the wind loads on PV modules.
Recently, CSPSs have become popular because they save land resources and are cost-effective. Baumgartner et al. [
26] first proposed a CSPS in their study; a sketch of the structure is shown in
Figure 2. The CSPS has broad application prospects because of its light weight, few pile foundations, short construction period, good heat dissipation performance, large span, reduced land use, increased space utilization, and applicability to complex terrains [
26,
27,
28]. Thus, the CSPS is an alternative solution that overcomes the drawbacks of conventional fixed-mounted PV systems. However, the original CSPS has high settlement because only two supporting cables bear self-weight, static wind loads, and/or snow loads. Reducing the settlement requires a higher pretension and larger cables. Moreover, the original CSPS is prone to strong wind-induced vibrations (WIV) because of its high flexibility.
Recently, the authors proposed a new CSPS [
30], as shown in
Figure 3, and verified its wind resistance capability [
31]. A single element of the new CSPS consisted of three cables, four triangular brackets, and several lateral connectors. The upper two cables support the PV modules, and the lower cable supports the two upper cables in the four sections through triangular brackets. The new CSPS has a larger span and smaller deflection. The lateral connectors enhance the wind resistance of the CSPS.
Compared with the traditional fixed-tilt PV support system, the new CSPS saves 10–15 tons of steel and 100–180 pile foundations per MW [
31]. Therefore, the new CSPS has great potential for wide applications. Over the past three years, more than 20 new cable-supported solar farms have been built in China with a total capacity of more than 1 GW. In addition, an increasing number of CSPS solar farms will be built in the coming years.
To date, only China and Japan have published specifications [
32,
33] for the structural design of ground-mounted PV modules. As previously reported by Browne et al. [
34], “Despite the current understanding of wind effects on ground-mounted multirow solar arrays, there is no comprehensive method in any building code/standard that provides appropriate guidance to practitioners designing these types of structures. Although numerous commercial wind loading studies on ground-mounted solar arrays have been carried out by wind tunnel laboratories worldwide, these data remain largely proprietary in nature and thus are not available in the public domain. Consequently, there is a need to establish a new design method for ground-mounted multi-row solar arrays…” The study on the design method of CSPVs is rare [
34,
35,
36].
The cable design of the CSPVs mainly refers to JGJ 257-2012 (2012), JG/T 200-2007 (2007), ASCE/SEI 19-16 (2016), and BS EN 1993-1-11:2006 (2006) [
37,
38,
39,
40]. The wind load of the CSPS mainly refers to building load codes, such as GB50009-2012 (2012), ASCE 7-16 (2016), and AS/NZS 1170.2-2011 (2011) [
41,
42,
43]. These codes were drafted to build the structures. Therefore, a design method for the CSPS is required for a better application of the new structure. The present study investigated the failure models and bearing capacity of the primary structures of the new CSPS using the FEM method and proposed a design procedure for the new structure based on the limit state design method. The effectiveness of the proposed design procedure was verified using a solar farm project.
3. Bearing Capacity and Failure Modes
To investigate the bearing capacity and failure modes of the CSPS, the equivalent static wind load was increased from 0 to 2.0 kN/m2 according to the Chinese wind environment. Theoretically, the design structure changes according to the wind load, . The required design parameters of the structure can be calculated for each wind load. In fact, the required design parameters are the minimum values at which the structure meets the structural internal force, stress, and deformation, which are curves that change dynamically with the calculated wind load. In this section, the internal force, stress, and deformation of the CSPS were calculated under different wind pressures using the basic model. The bearing capacity and failure modes are discussed below.
3.1. Bearing Capacity
The internal forces of cables 1, 2, and 3 are calculated when the wind load varies from 0 to 2.0 kN/m2 in the two control cases. The cross-sectional areas of the cables changed as the wind load increased. The internal forces of cables 1, 2, and 3 are also considered in relation to the required breaking forces of cables 1, 2, and 3 to ensure structural safety and are referred to as and , respectively.
The results of previous studies indicate that the
and
have different trends when the wind load is in the range of 0.15~2.0 kN/m
2. The static wind load is supported by three cables in Case 0°, whereas only cables 1 and 2 bear the static wind load when the wind load is greater than 0.238 kN/m
2 in Case 180°. In addition, the required breaking force of cables 1 and 2 in Case 0° (
) is always smaller than that in Case 180° (
). In contrast, the required breaking force of cable 3 in Case 0° (
) is larger than that in Case 180° (
), which means that Case 180° is the controlling condition of cables 1 and 2, and Case 0° is the controlling condition of cable 3 when the wind
is in the range of 0 to 2.0 kN/m
2 [
31].
To ensure the structural safety of a given CSPS, the required breaking force should be lower than the cable resistance force. The load-bearing capacity was determined by the resistance forces of cables 1, 2, and 3. In Case 180°, the bearing capacity of the CSPS () is calculated by setting the resistance force of cables 1 and 2 equal to , and setting the resistance force of cable 3 to be higher than . In Case 0°, the load-bearing capacity of the CSPS () was calculated by setting the resistance force of cable 3 equal to , and setting the resistance force of cables 1 and 2 to be higher than . The load capacity of the CSPS was the minimum between and .
Figure 5 shows the vertical deformation at the midspan of the structure as the wind load increased in the two cases. The vertical deformation in Case 0° was downwards, and that in Case 180° was upward. In both cases, the midspan vertical deformation increased nonlinearly with increasing wind load, and the deformation increment decreased when the wind load increased. These results indicate that the vertical stiffness of the PV system increased with increasing deformation. When the wind load increases from 0.3 to 2.0 kN/m
2, the midspan vertical deformation increased by 226.5% and 190%, respectively. The midspan vertical deformation in Case 180° was always greater than that in Case 0° when the wind load was higher than 0.238 kN/m
2.
3.2. Failures of Cables
A given CSPS fails when the wind load continues to increase. Generally, the new CSPS fails owing to the failure of columns, beams, cables, triangle brackets, fasteners, or modules. Because columns, beams, fasteners, and modules are traditional components in normal arrangements, and their failure modes have been studied in detail, this subsection primarily focuses on the failures of cables and triangle brackets. A cable breaks when its internal force exceeds its resistance force. For the stainless-steel strand used in the proposed CSPS support system, the resistance force of the cables,
, was calculated using Equation (2), as recommended by [
38].
where
is the strength reduction factor,
is the sectional area (m
2), and
is the tensile strength (MPa).
Based on Equation (2), the required resistance force is transformed into the required sectional area
S when only the control cases are considered.
Figure 6 shows the required cross-sectional areas of cables 1 and 2 (
), and cable 3 (
) as the wind load increases. The results show that
and
increase with increasing wind load. When the wind load
is between 0 and 2.0 kN/m
2, the curves of
and
separate the required cross-sectional area space into two areas. Under a given wind load, if the cross-sectional area is smaller than the required cross-sectional area, the structure fails under the corresponding control condition. Consequently, the failure modes of the CSPS are summarized as follows: (1) when the cross-sectional areas of cables 1 and 2 are smaller than
and the cross-sectional area of cable 3 is larger than
, the structure is prone to failure in Case 180°; (2) when the cross-sectional areas of cables 1 and 2 are larger than
and that of cable 3 is smaller than
, the structure is prone to failure in Case 0°; and (3) when the cross-sectional areas of cables 1, 2, and 3 are smaller than the required cross-sectional area, the structure is prone to failure in both cases 180° and 0°.
3.3. Failure of Triangle Brackets
Triangle brackets are analyzed in this subsection, and lateral connectors are not considered because they only enhance lateral stability. In Case 180°, the axial force of the lateral connectors and the triangular brackets are close to 0 when the wind load is greater than 0.238 kN/m2 because cable 3 no longer works; in Case 0°, the axial force of the lateral connectors is much smaller than that of the triangular brackets. Normally, the lateral connectors are set the same as those of the triangular brackets. Case 0° was the controlling case for the triangle brackets, and the axial forces of all triangle brackets in Case 0° were investigated in detail.
Each triangular bracket is composed of three slender steel pipes that bear only axial forces. The failure modes of the triangular brackets were either yielding or buckling. When the internal force of the steel pipes is larger than their yielding strength or buckling strength, the steel pipes fail and the CSPS breaks.
The internal forces of the triangular brackets at the 1/5 and 2/5 spans, as shown in
Figure 7, were calculated when the wind load
varied from 0 to 2.0 kN/m
2. The results for Case 0° are shown in
Figure 8. Rods 1, 3, 4, and 6 are in compression, whereas rods 2 and 5 are in tension. The maximum compressive force appears in rod 3, whereas the maximum tensile force appears in rod 2; the compression force is much higher than the tensile force. The internal forces of the rods increased with the wind load.
The internal forces in rods 1–6 are considered in relation to the load capacity of the rods to ensure the structural safety of the proposed system and are referred to as
through
, respectively. The rods should have sufficient cross-sectional area to withstand the required internal forces. The load capacity of the rod,
, was calculated using Equation (3) while considering the yield strength of the rod. In addition, according to Euler’s formula, the load capacity of a slender compression rod,
, which is hinged at both ends, is calculated using Equation (4) while considering the buckling strength. The required load capacity of the rods is the minimum of
and
:
where
is the elastic modulus of the rod,
is the minimum inertia moment of the cross section,
is the calculation length,
is the yielding strength, and
and
are the outer and inner diameters, respectively. In this study,
is set equal to 0.01 m, and the required load capacity
and outer diameter
are calculated as follows:
Using Equation (6), the internal forces in
Figure 8 were transformed into the required outer diameters.
Figure 9 shows the required outer diameters of rods 1–6 (
to
) as the wind load increases. Rod 6 had the maximum required outer diameter, and rods 2 and 5 had the minimum required outer diameter. Wind strongly affects the required outer diameters of the compression rods but has little effect on the tensile rods. The required outer diameters of the compression rods increased nonlinearly as the wind load increased.
Triangle brackets exhibit two different types of failure: yielding and buckling. Considering rod 6 as an example, the required outer diameter is calculated separately under the yielding and buckling conditions, and referred to as
and
, respectively. The calculation results are shown in
Figure 10. Both
and
increase with increasing wind load, and
is much higher than
, which indicates that rod 6 is more prone to buckling than to yielding. The curves of
and
separate the figure into three areas, which indicate three possible states of the triangular brackets: (1) when the outer diameter area of rod 6 is smaller than
, the structure is prone to yielding or buckling failure; (2) when the outer diameter area of rod 6 is higher than
but lower than
, the structure is prone to yielding failure; and (3) when the outer diameter area of rod 6 is higher than
, the structure is safe under the given wind pressure.
5. Conclusions
In this study, the bearing capacity and failure modes of the primary structures of a new CSPS were investigated in detail using FEM. A design method for a new structure was proposed based on the limit state design method. The primary conclusions of this study are as follows.
(1) The proposed structure exhibited a strong load-bearing capacity. Case 180° is the controlling condition of cables 1 and 2, and Case 0° is the controlling condition of cable 3. When the internal forces of the three cables are equal to their resistance force, the wind load is supported by all three cables in Case 0°, whereas only cables 1 and 2 bear the wind load when the wind load is greater than a certain critical value in Case 180°.
(2) The failures of the cables and triangle brackets are the two primary types of failures of the primary structure. The cross-sectional area of the cables is the most important factor affecting the load-bearing capacity of the structure and directly affecting the failure modes of the PV system. Case 0° is the controlling condition of the triangular brackets, the buckling or yielding of which is closely related to the outer diameter of the rods.
(3) The proposed limit state design method was shown to be cost-effective, and the designed structure had less steel consumption and a strong load capacity.