In snowy winter regions, the combined action of wind and snow loads is a critical factor in the structural design of photovoltaic (PV) support systems. The accurate assessment of this combined environmental action is essential for ensuring the structural reliability and economic efficiency of solar power installations. However, there is a notable lack of research specifically focused on the combination factors for wind and snow loads applicable to photovoltaic structures. Current international load codes and standards, as well as national PV support structure design specifications, typically adopt combination factors derived for general buildings, which may lead to overly conservative or inadequately optimized designs for the distinct structural characteristics of solar panel arrays.
This paper addresses this gap by investigating the wind-snow load combination factor for solar panels in Harbin, a representative city in a cold, snowy region of China. The study employs a comprehensive methodology that integrates meteorological analysis, probabilistic hazard modeling, and structural response evaluation. The primary objective is to establish a rational combination factor based on the joint probabilistic characteristics of wind and snow hazards, rather than applying general building codes directly. The research focuses on a single-axis solar panel tracker system, a common configuration known for its vulnerability to combined wind-snow action due to its relatively flexible and slender structural form.
The methodology begins with the reconstruction of historical ground snow pressure data. Since direct long-term measurements of snow pressure are often unavailable, a physically based multi-layer snowmelt model is utilized. This model simulates the accumulation, densification, and melting processes of snowpack on the ground using standard meteorological inputs such as precipitation, air temperature, wind speed, and relative humidity. For Harbin, daily meteorological data from 1951 to 2016 are processed into hourly inputs and fed into the model to generate time series of ground snow pressure for each winter season. This provides a robust dataset of the snow load hazard.
Subsequently, different methods are explored to pair wind speed observations with corresponding ground snow pressure values, forming “data pairs” that represent potential concurrent or associated wind-snow events. Four pairing methods are investigated:
- Method 1: Maximum ground snow pressure between two consecutive snowfall events paired with the maximum wind speed during that same interval.
- Method 2: Maximum ground snow pressure between snowfall events paired with the maximum wind speed occurring within three days after the preceding snowfall event (considering snow stabilization time).
- Method 3: Maximum ground snow pressure during an entire snow cover season paired with the maximum wind speed during that same season.
- Method 4: Annual maximum ground snow pressure paired with the annual maximum wind speed.
For the wind speed and ground snow pressure samples extracted via each method, statistical analysis is performed to identify their optimal probability distributions. Three candidate distributions are fitted: Gumbel (Extreme Value Type I), Lognormal, and Generalized Extreme Value (GEV). Parameters are estimated using methods like Maximum Likelihood Estimation (MLE) and Method of Moments (MOM). The goodness-of-fit is evaluated using the Kolmogorov-Smirnov (K-S) test and the Akaike Information Criterion (AIC) to select the best model for each dataset.
The joint hazard analysis is then conducted. Linear regression analysis reveals that the correlation between wind speed and ground snow pressure samples is very weak (coefficient of determination, R² < 0.24) for all four pairing methods. Therefore, the two hazards are treated as independent. The joint exceedance probability for independent events is given by:
$$P(V > v, S > s) = [1 – F_V(v)] \cdot [1 – F_S(s)]$$
where $F_V(v)$ and $F_S(s)$ are the cumulative distribution functions (CDFs) for wind speed and ground snow pressure, respectively. The joint return period $T$ is:
$$T = \frac{1}{P(V > v, S > s)} = \frac{1}{[1 – F_V(v)] \cdot [1 – F_S(s)]}$$
By fixing a target return period (e.g., 25 years, which is the typical design working life for solar panel support structures), one can solve for all combinations of $(v, s)$ that satisfy the equation, thereby constructing joint hazard contours.
The next phase involves translating these hazard contours into structural loads and evaluating the load effects on a representative solar panel support structure. A finite element model of a 100-meter long single-axis tracking solar panel array with a 30-degree tilt angle is developed. The structure consists of a main torque tube (beam) supported by columns spaced at 8 meters.
Wind load on the solar panel is calculated according to the standard format: $w_k = \beta_z \mu_z \mu_s w_0$, where $w_0 = 0.5 \rho v_0^2$ is the basic wind pressure based on the wind speed $v_0$ from the hazard contour. The shape coefficients $\mu_s$ for the tilted solar panel are derived from codes for monopitch roofs. The trapezoidal distribution of wind pressure across the panel width is considered, which results in a uniform load and a torsional moment on the main beam. Snow load on the solar panel is calculated as $s_k = \mu_r s_0$, where $s_0$ is the ground snow pressure from the hazard contour and $\mu_r$ is the snow distribution coefficient, taken as 0.85 for a 30-degree slope.
Two primary load cases are considered for the solar panel:
1. Load Case 1: Both wind and snow act as pressure on the solar panel surface.
2. Load Case 2: Wind acts as suction (uplift) while snow acts as pressure.
For Load Case 1, the combined load effects are significant. A series of wind-snow load pairs from the 25-year joint hazard contour are applied to the finite element model. Key structural responses are monitored: the maximum column axial force ($P_{max}$), the maximum main beam bending moment ($M_{max}$), and the maximum main beam torque ($T_{max}$). The analysis identifies the combination of wind and snow loads that produces the maximum load effect $S_m$ (e.g., the most negative axial force or the largest bending moment). This maximum combined effect is then compared to the sum of the load effects caused by the 25-year wind load alone ($S_{w,25}$) and the 25-year snow load alone ($S_{s,25}$).
The wind-snow load combination factor $\psi$ is defined as the ratio needed to scale down the sum of the individual extreme load effects to match the maximum combined effect observed from the joint hazard analysis:
$$S_m = \psi (S_{w,25} + S_{s,25})$$
$$\psi = \frac{S_m}{S_{w,25} + S_{s,25}}$$
This factor, by definition, will be less than or equal to 1.0.
For Load Case 2, since wind suction and snow pressure oppose each other, their load effects tend to counteract. The critical design condition for the solar panel support is often governed by either the maximum wind suction (with little or no snow) or the maximum snow load (with little or no wind suction). Therefore, a combination factor for this opposing action case is generally not required for strength design, as considering them simultaneously is not the worst-case scenario.
The results from the probabilistic analysis for Harbin are summarized below. Table 1 shows the optimal probability models selected for wind speed and ground snow pressure samples under the four different data pairing methods, based on K-S test and AIC criteria.
| Data Pairing Method | Optimal Model for Wind Speed | Optimal Model for Ground Snow Pressure |
|---|---|---|
| Method 1 | GEV (MLE) | GEV (MLE) |
| Method 2 | GEV (MLE) | GEV (MLE) |
| Method 3 | Lognormal (MLE) | Lognormal (MLE) |
| Method 4 | Lognormal (MLE) | GEV (MLE) |
Using these optimal models and treating the hazards as independent, the joint wind-snow hazard contours for return periods of 10, 25, 50, and 100 years are constructed. The 25-year contour is of primary interest for design. The analysis of the finite element model under Load Case 1 yields the maximum combined load effects and the corresponding individual effects. The calculated combination factors for column axial force ($\psi_P$) and main beam bending moment ($\psi_M$) are presented in Table 2.
| Data Pairing Method | $\psi_P$ (Axial Force) | $\psi_M$ (Bending Moment) |
|---|---|---|
| Method 1 | 0.7 | 0.6 |
| Method 2 | 0.7 | 0.7 |
| Method 3 | 0.6 | 0.6 |
| Method 4 | 0.6 | 0.7 |
| Average | 0.7 | 0.7 |
The analysis reveals several key findings. Firstly, the joint probability analysis confirms the weak correlation between extreme wind speeds and extreme ground snow pressures in Harbin, justifying the assumption of independence for hazard modeling. Secondly, the structural response analysis for the solar panel array clearly shows that when both wind and snow loads act as pressure (Load Case 1), their combined effect is less than the simple sum of their individual 25-year return period effects. The degree of reduction is quantified by the combination factor $\psi$. For the primary load effects considered in the design of the solar panel support—namely, the column axial force and the main beam bending moment—the calculated combination factor averages to approximately 0.7 based on the four hazard pairing methods. This suggests that using a factor of 0.7 for combining the characteristic wind and snow pressure loads on the solar panel is appropriate for this location and structural system.
Conversely, for Load Case 2 (wind suction with snow pressure), the analysis indicates that the governing design condition is not the simultaneous occurrence of both at their respective 25-year levels. Therefore, a combination factor less than 1.0 is not warranted for this load case in strength design; the design should be checked for the 25-year wind suction alone and the 25-year snow load alone. The torque on the main beam of the solar panel is found to be governed solely by wind load, as the assumed uniformly distributed snow load does not induce torsion. Hence, no combination with snow load is necessary for torsional design checks.
In conclusion, this study presents a framework for determining region-specific wind-snow load combination factors for photovoltaic structures based on joint hazard analysis. Applying this framework to Harbin, it is recommended that for the design of single-axis solar panel tracker supports, a combination factor of 0.7 be used when considering the concurrent pressure from both wind and snow loads and when the critical load effects are the column axial force and main beam bending moment. This value, derived from the probabilistic characteristics of the local climate and the specific structural response, offers a more rational basis for design compared to the adoption of generic building code values. This research provides a methodological foundation and a specific recommendation that can inform future revisions of codes and standards dedicated to photovoltaic structure design, ultimately contributing to safer and more cost-effective solar power infrastructure in snowy regions. Future work could extend this methodology to other climatic regions, different solar panel configurations (e.g., fixed-tilt, dual-axis), and incorporate more complex effects such as wind-induced snow drift redistribution on and around the solar panel arrays.