Height-Dependent Inter-Array Temperature Difference and Position-Dependent Intra-Array Temperature Gradient

Abstract

This study investigates the influence of array height, irradiance, and wind speed on temperature difference and thermal gradients in photovoltaic (PV) arrays operating in hot, arid conditions. A field experiment was conducted in Mesa, Arizona (latitude 33° N), using two fixed-tilt PV module arrays installed at different elevations—one at 1 m and the other at 2 m above ground level. Each array comprised seven monocrystalline PV modules arranged in a single row with an 18° tilt angle optimized for summer performance. Data were collected between June and September 2025, and the analysis was restricted to 10:00–13:00 h to avoid shading and ensure uniform irradiance exposure on both arrays. Measurements included module backsheet temperatures at the center and edge modules, ambient temperature, plane-of-array (POA) irradiance, and wind speed. By maintaining identical orientation, tilt, and exposure conditions across all PV configurations, the influence of array height was isolated by comparing module operating temperatures between the 1-m and 2-m installations (inter-array comparison). Under the same controlled conditions, the setup also enabled an examination of how the intra-array comparison affects temperature gradients along the PV modules themselves, thereby revealing edge-center thermal non-uniformities. Results indicate that the 2 m array consistently operated 1–3 °C cooler than the 1 m array, confirming the positive impact of elevation on convective cooling. This reduction corresponds to a 0.4–0.9% improvement in module efficiency or power based on standard temperature coefficients of crystalline silicon modules. The 1 m array exhibited a mean edge–center intra-array temperature gradient of −1.54 °C, while the 2 m array showed −2.47 °C, indicating stronger edge cooling in the elevated configuration. The 1 m array displayed a broader temperature range (−7 °C to +3 °C) compared to the 2 m array (−5 °C to +2 °C), reflecting greater variability and weaker convective uniformity near ground level. The intra-array temperature gradient became more negative as irradiance increased, signifying intensified edge cooling under higher solar loading. Conversely, wind speed inversely affected ΔT, mitigating thermal gradients at higher airflow velocities. These findings highlight the importance of array height (inter-array), string length (intra-array), irradiance, and wind conditions in optimizing PV system thermal and electrical performance.

1. Introduction

The operating temperature of photovoltaic (PV) modules is one of the most influential factors affecting system efficiency, energy yield, and long-term reliability. While the electrical design of a PV system determines its output potential, the thermal environment defines how closely that potential can be achieved in the field. Among the many site-specific parameters governing PV module temperature, array height and string length play particularly critical roles, as they directly influence convective heat exchange between the modules and surrounding air. Understanding the thermal impact of array geometry is therefore essential for modern PV array and plant design, especially in hot and low-wind climates where cooling is predominantly governed by natural convection. Array height determines the extent of air circulation beneath and around modules; higher elevations promote stronger airflow and turbulence, which enhance convective heat removal, reduce operating temperature, and improve conversion efficiency. Conversely, low-mounted systems—such as those installed close to the ground on short supports—experience reduced ventilation, higher heat retention, and larger thermal gradients. These differences not only affect instantaneous efficiency but also contribute to accelerated material aging, potential-induced degradation (PID), and other temperature-related performance losses. A clear understanding of the influence of array height on convective cooling [1], row spacing and its technoeconomic implications for thermal management [2], and module arrangement effects on airflow and heat transfer within PV arrays [3] enables system designers to optimize racking structures, ground clearance, and layout, while mounting dimensions and detailed temperature distribution studies further demonstrate how local geometry governs module thermal behavior and long-term durability [4,5]. The present work advances the literature by simultaneously resolving height-dependent inter-array temperature differences and position-dependent intra-array thermal gradients under controlled, real-world field conditions in a hot-arid climate. Unlike earlier studies that primarily focus on mean module temperatures, array-level performance, or modeled airflow behavior, this study explicitly quantifies edge–center temperature non-uniformities along a single-row array and demonstrates how these gradients systematically vary with array height, irradiance, and wind speed. By employing two otherwise identical fixed-tilt arrays that differ only in elevation and by isolating mid-day, shade-free operating conditions, the analysis provides a clear separation between inter-array and intra-array thermal effects. This dual-scale thermal characterization offers new insight into how array height influences not only overall cooling but also thermal uniformity along long strings—an aspect that is increasingly relevant for modern PV systems with extended string lengths due to higher system voltages and reliability-driven design considerations.

As photovoltaic architectures evolve from traditional 600 V legacy strings to today’s 1500 V commercial standards—and toward 2000 V future configurations—the number of modules per string has increased substantially [6,7,8]. These extended strings form longer continuous arrays, which inherently restrict airflow through central sections and elevate internal thermal coupling between adjacent modules. The result is a higher effective thermal mass and reduced convective exchange, especially in glass/glass PV modules that already possess lower heat dissipation rates. Under low-wind or stagnant air conditions, these factors cause persistent temperature gradients between the center and edge modules, where edge regions benefit from lateral cooling while the inner modules retain heat for longer durations. Such non-uniform thermal profiles can exacerbate mismatch losses, accelerate thermomechanical stress, and amplify degradation rates over time. As system voltages and string lengths continue to grow, quantifying and mitigating these intra-array temperature gradients has become an important step toward thermally robust PV plant design.

In our previous work, long-term thermal mapping of PV modules and plants revealed significant temperature non-uniformities both within modules and across arrays. Center cells within a module typically operated at higher temperatures than edge cells, while centrally located arrays within a PV plant tended to run hotter than edge or corner arrays [9]. Building on these findings, the present study examines temperature variations between arrays of different mounting heights (inter-array comparison) and evaluates the temperature gradients between center and edge modules within each array (intra-array comparison). This study does not include datasets or analyses related to thermal gradients between edge and center modules for arrays of differing string lengths. The study focuses on how irradiance, wind speed, array height, and string length jointly influence module temperature distributions and their resulting impact on performance. The field experiment was conducted under actual desert conditions in Mesa, Arizona, providing high-fidelity data for hot-climate PV operation. This work isolates the geometric and aerodynamic effects of array configuration using identical modules, orientation, and operating conditions by systematically quantifying height- and string length-induced temperature differences.

2. Methodology

2.1. Experimental Setup

The field experiment was conducted in Mesa, Arizona (latitude 33° N), where two fixed-tilt photovoltaic module arrays were installed at different heights—one at 1 m and the other at 2 m above ground level (Figure 1). Each array consisted of seven monocrystalline PV modules arranged in a single row, with an 18° tilt angle optimized for summer production and thermal evaluation. The longitudinal (north–south) separation between the two arrays was maintained at 0.2 m to ensure identical irradiance exposure while minimizing mutual shading. The site was selected to ensure unobstructed sunlight throughout the day during the four-month test period.

The experiments were conducted from June 2025 through September 2025, capturing the summer operating conditions most representative of high-temperature PV performance in hot, arid climates. To measure the thermal distribution on the back surface of the PV modules, type-K thermocouples were securely attached to the center of the middle module and the center of an edge module in each array (Figure 1). This configuration allowed for simultaneous monitoring of both inter-array (1 m vs. 2 m) temperature differences and intra-array (edge–center) temperature gradients under identical environmental conditions.

2.2. Instrumentation and Data Acquisition

Incident solar irradiance on the array plane was measured using a plane-of-array (POA) irradiance sensor. Wind speed and ambient temperature were recorded using meteorological sensors positioned near the arrays. All instruments were connected to a data acquisition (DAQ) system programmed to record data at 1- or 2-min intervals, depending on the parameter. The following parameters were continuously monitored and stored with time stamps: backsheet temperature, ambient temperature, wind speed, and POA irradiance.

The performance and thermal characteristics of the modules used in this study are provided in

Table 1. Performance and Thermal Characteristics of the Test Modules.

Parameter	Symbol	Value
Maximum power at STC	Pmax	320 Wp
Open circuit voltage at STC	VOC	45.9 V
Short circuit current at STC	Isc	9.41 A
Nominal Operating Cell Temperature	NOCT	46 °C
Temperature coefficient of Isc	$T_{\mathrm{C},{\mathrm{I}}_{\mathrm{S}\mathrm{C}}}$	0.042% °C−1
Temperature coefficient of Voc	$T_{\mathrm{C},V_{\mathrm{O}\mathrm{C}}}$	−0.304% °C−1
Temperature coefficient of Pmax	$T_{\mathrm{C},P_{\mathrm{m}\mathrm{a}\mathrm{x}}}$	−0.43% °C−1

.

Nominal Operating Cell Temperature (NOCT) is defined in IEC 61215:2005 as the equilibrium temperature reached by a photovoltaic (PV) module operating under open-circuit conditions when exposed to a total irradiance of 800 W/m², an ambient air temperature of 20 °C, and a wind speed of 1 m/s, with the rear surface freely ventilated [10]. The experimental setup specified in the standard requires that the test modules be surrounded by non-operating (dummy) modules to replicate the thermal environment of a real PV array and minimize edge-cooling effects. Temperature sensors are affixed to the back of representative cells, and measurements taken over several weeks are extensively processed to obtain the eventual NOCT value. The NOCT test characterizes the module’s thermal behavior under standardized, yet realistic, field conditions and provides a reference for estimating operating temperatures in system performance models. The manufacturer-reported NOCT value of 46 °C aligns closely with the average NOCT of approximately 46 °C reported for glass/backsheet photovoltaic modules in the California Energy Commission (CEC) equipment open-source database listing about 20,000 modules [11]. This consistency indicates that the tested modules exhibit typical thermal behavior for conventional crystalline silicon glass/backsheet constructions, supporting the representativeness of this module for use in thermal analyses of the industry.

2.3. Data Filtering and Analysis

To ensure data quality and avoid shading effects from nearby structures or between the two arrays, only the data collected between 10:00 h and 13:00 h were used for analysis. This time window corresponds to near-solar-noon conditions when the sun’s position minimizes the risk of shading on the 1 m array caused by the adjacent 2 m array’s edge. Raw data were screened to remove outliers resulting from sensor noise, cloud transients, or data gaps. The processed dataset was analyzed to evaluate both inter-array and intra-array thermal behavior, focusing on three main aspects:

• Temperature difference between arrays with different heights (see Section 3.1): The difference in module backsheet temperature between the 1 m and 2 m arrays was statistically evaluated as a function of irradiance, wind speed, month, and time of day.
• Temperature gradient within each array (see Section 3.2): The edge–center temperature gradient (ΔT_edge-center) was computed and statistically analyzed for both arrays to assess spatial temperature variation and compare gradient magnitudes.
• Combined effects of weather parameters (see Section 3.3): A summary on the combined effects of irradiance, wind speed, and ambient temperature on the inter-array and intra-array ΔT values is provided.

3. Results and Discussion

3.1. Temperature Difference Between 1 m and 2 m PV Arrays

3.1.1. Results

This section examines the thermal behavior of photovoltaic (PV) arrays installed at two different heights—1 m and 2 m above ground level, based on time-series and statistical analyses of module temperature differences. The two plots presented below—a smoothed ΔT time series (Figure 2) and a histogram of temperature differences (Figure 3) provide complementary insights into the cooling effects of array elevation on module performance and temperature uniformity. The temperature difference (ΔT) is defined as the mean module temperature at 2 m minus that at 1 m; thus, negative values indicate that the 2 m array operates at lower temperatures. Both datasets cover the summer season (June–October), when solar irradiance and ambient temperatures are highest, and convective cooling plays a significant role in module thermal behavior.

Temporal Evolution and Seasonal Behavior: The smoothed ΔT versus time plot shown in Figure 2 includes a ±1σ confidence band to represent short-term variability. This time-series plot illustrates the seasonal variation in ΔT. Throughout most of the period, ΔT remains negative, confirming that the 2 m array consistently operates cooler than the 1 m array. The fluctuations reflect changes in irradiance, wind speed, and ambient temperature. Peaks in ΔT magnitude occur during high irradiance periods (late June, mid-August, late September), when the difference in convective heat transfer between the two configurations becomes most evident.

Statistical Characteristics and Distribution of ΔT: The histogram of ΔT shown in Figure 3 provides a quantitative trend on the ΔT distribution. The mean ΔT is −1.71 °C and the mode is −2.10 °C, indicating that most temperature differences cluster between −3 °C and −1 °C. This distribution is slightly right-skewed, suggesting that occasional low-wind or cloudy periods produce smaller temperature differences. Nevertheless, the consistent negative mean demonstrates that the 2 m configuration maintains a cooler operating condition across all environmental variations.

3.1.2. Discussion

The cooler operation of the 2 m array is primarily attributed to enhanced natural convection and air turbulence. At 2 m height, air circulation beneath and around the modules is more effective, reducing the boundary layer thickness and increasing the convective heat transfer coefficient. In contrast, the 1 m array experiences limited airflow and partial stagnation within the ground boundary layer, leading to reduced heat dissipation and higher overall module temperatures. This aligns with theoretical expectations from convective heat-transfer models, where the Nusselt number increases with both wind speed and free-air exposure. From a performance standpoint, cooler operation at 2 m translates into improved electrical efficiency. For crystalline silicon PV modules, every 1 °C decrease in operating temperature typically increases conversion efficiency by about 0.36–0.45%. Thus, a consistent 1–2 °C reduction in temperature yields roughly a 0.4–0.9% gain in power output. This estimated power gain is theoretically inferred from industry standards, databases, and published literature, and is not derived from direct I–V measurements of the individual modules investigated in this study. Lower operating temperatures also reduce thermomechanical stress and material degradation over time, especially solder bond degradation [12,13]. The 1 m configuration, while more compact and cost-efficient structurally, sacrifices some performance and thermal efficiency due to constrained airflow. In this study, a single ground surface and albedo condition were considered; however, variations in ground properties may influence module thermal behavior at a secondary level and warrant further investigation.

3.2. Temperature Gradient Between Edge and Center Modules

3.2.1. Results

The following discussion analyzes the (Edge–Center) ΔT distributions for the 1 m and 2 m height photovoltaic (PV) arrays. Each histogram shown in Figure 4 and Figure 5 represents the temperature difference between the module edge and its center, with negative values indicating that the edges are cooler due to convective air movement. The plots include overlaid kernel density estimate (KDE) curves, mean (black dashed line), and mode (red dotted line) indicators to illustrate key trends in the thermal distribution.

The 1 m array shown in Figure 4 exhibits a mean ΔT of −1.54 °C and a mode of −0.26 °C, while the 2 m array shown in Figure 5 indicates a mean of −2.47 °C and a mode of −3.22 °C. These differences reveal that modules elevated to 2 m experience stronger convective cooling at the edges due to enhanced airflow. In contrast, the 1 m array, being closer to the ground, encounters restricted airflow, resulting in reduced edge cooling and warmer overall module temperatures. The 1 m array’s distribution spans approximately −7 °C to +3 °C, indicating greater variability and a broader spread. This suggests less stable thermal behavior influenced by fluctuating ground-level airflow and boundary-layer effects. The 2 m array’s narrower range, centered between −5 °C and +2 °C, implies more consistent convective cooling. The mean–mode differences (−1.27 °C for 1 m and +0.75 °C for 2 m) indicate skewness: the 1 m array leans toward smaller gradients, while the 2 m array exhibits more strongly negative ΔT values, confirming improved cooling efficiency. Since the degradation rates of most PV module failure mechanisms increase exponentially with temperature, the center modules in a series-connected string—being the hottest—are expected to determine the end-of-life of the entire string.

To assess the statistical relevance of the observed temperature differences, the full distributions of ΔT were analyzed in addition to their mean and mode values. The results show consistent and systematic shifts in both the inter-array (1 m vs. 2 m) and intra-array (edge–center) temperature distributions, with limited overlap and clear separation relative to the spread of the data. These distributional characteristics indicate that the observed differences are statistically meaningful and not attributable to random variability or measurement uncertainty. Because field-measured thermal data exhibit non-Gaussian behavior, emphasis was placed on distributional analysis and comparative confidence intervals rather than parametric hypothesis testing. The persistence of the observed trends across the test samples supports the conclusion that array height and module position exert a significant influence on module operating temperature and thermal gradients under hot-arid conditions.

3.2.2. Discussion

Figure 6 and Figure 7 show that the (Edge–Center) ΔT generally becomes more negative with increasing irradiance, indicating that the panel edges tend to cool more effectively than the center under higher thermal loading. Across most irradiance bins, ΔT remains slightly below zero, reflecting preferential convective heat removal at the boundaries where airflow is less restricted. The variability in ΔT widens at higher irradiance levels, suggesting that localized cooling effectiveness becomes increasingly sensitive to moment-to-moment wind conditions as the modules heat up. The accompanying wind-speed trends highlight that sharper decreases in ΔT often coincide with periods of enhanced air movement, reinforcing that (Edge–Center) temperature differences are strongly governed by the interplay between irradiance-driven heating and wind-driven convective cooling.

3.3. Combined Parameter Influence—Summary

Temperature difference between two array heights: The 2 m array consistently exhibits more negative mean ΔT values than the 1 m array, confirming stronger convective cooling at greater elevation. At 2 m, air circulation beneath and around the modules is less obstructed by ground interference, promoting higher convective heat transfer. Conversely, the 1 m array operates closer to the ground boundary layer, where airflow stagnation reduces convective efficiency. At high irradiance levels (900–1100 W/m²), the mean ΔT of the 2 m array is approximately 1 °C more negative than that of the 1 m configuration, underscoring the benefit of increased elevation for thermal management.

Temperature gradient between modules within an array: Both 1 m and 2 m arrays with identical string length display increasingly negative ΔT values with rising irradiance, particularly beyond 500 W/m². This trend reflects the greater edge–center thermal contrast as solar heating intensifies. Under higher irradiance, module centers retain heat more efficiently due to limited exposure to airflow, while the edges, being more exposed, dissipate heat faster through convection. At irradiance levels above 800 W/m², broader ΔT distributions emerge, indicating increased variability caused by increased string length, fluctuations in ambient airflow and wind turbulence.

Combined influence of weather parameters: Wind speed serves as a crucial moderating factor. At low irradiance (<400 W/m²), higher wind speeds coincide with smaller ΔT magnitudes, as stronger convection minimizes temperature gradients across the module surface. As wind speed increases, the ΔT magnitude tends to decrease. This inverse relationship shows that wind promotes thermal uniformity and counteracts radiative heating. In both arrays, when wind speeds drop below approximately 2 m/s, the ΔT magnitude increases sharply—most notably within the 800–900 W/m² range, where radiative effects dominate. The combined effects of irradiance and wind speed can be interpreted through convective and radiative heat transfer mechanisms. Higher irradiance increases absorbed solar energy, raising module temperature and enhancing buoyancy-driven flow. The 2 m array benefits from higher Reynolds number (higher turbulent flow) and Nusselt number (higher convective heat transfer) due to stronger air motion, yielding greater convective efficiency. By contrast, the 1 m array resides within the near-ground boundary layer, where reduced turbulence limits heat exchange. These physical mechanisms collectively explain the observed differences in ΔT and reinforce the importance of module height in promoting convective cooling.

In this study, the thermal analysis focuses on ambient temperature, plane-of-array irradiance, and wind speed, which are widely recognized as the dominant environmental parameters governing PV module operating temperature in established thermal models. Factors such as wind direction, turbulence intensity, and atmospheric humidity were not explicitly included, as their influence on module temperature is generally considered secondary under typical outdoor operating conditions. Nevertheless, these variables may contribute second-order effects to convective cooling and thermal uniformity, and their role warrants further investigation in future studies incorporating detailed airflow measurements or numerical modeling.

4. Conclusions

The inter-array temperature comparison results presented in this study show that the 2 m array consistently operated 1–3 °C cooler than the 1 m array, confirming the beneficial influence of elevation on convective heat dissipation. The increased mounting height allowed for greater air circulation and turbulence beneath and around the modules, enhancing convective heat removal. This cooling effect translates into measurable gains in performance and long-term reliability for photovoltaic (PV) systems.

Intra-array temperature analysis revealed distinct temperature gradients between the edge and center modules, demonstrating the role of localized convection in shaping module temperature profiles. The 1 m array exhibited a mean edge–center temperature gradient of −1.54 °C, while the 2 m array showed −2.47 °C, indicating stronger edge cooling in the elevated configuration due to improved airflow exposure. Because the center modules in a series-connected string typically operate at higher temperatures, they are more susceptible to accelerated degradation and are therefore expected to dictate the end-of-life of the entire string.

The study also examined the combined effects of irradiance and wind speed on temperature gradients. The gradient became increasingly negative with higher irradiance, suggesting intensified edge cooling under stronger solar loading. Conversely, wind speed exhibited an inverse relationship with ΔT, as higher airflow velocities reduced temperature differentials by promoting convective uniformity across the module surface.

Overall, the findings highlight the importance of array height and module position within an array as key design parameters for enhancing module cooling, improving thermal uniformity, and increasing both energy yield and reliability in crystalline silicon PV installations, particularly in hot and arid climates. The analysis framework and observed trends are also applicable to other existing and emerging PV technologies, including perovskite and cadmium telluride modules. While the present study is based on a limited number of modules and a single tilt angle, future work should extend the investigation to a statistically significant number of arrays with long strings, additional seasons, and multiple sites in order to fully quantify and generalize configurational, seasonal, and site-specific variability in thermal differences and gradients.