© R. Moruno et al., Published by EDP Sciences, 2026

1 Introduction

The growing share of electric vehicles (EVs) in the global automotive fleet [1] highlights the need to address new challenges in mobility, such as an increase in the electric grid demand, battery life cycle optimization and vehicle autonomy. The concept of using the vehicle's surface to generate electricity by incorporating photovoltaic modules, known as Vehicle Integrated Photovoltaics (VIPV), has gained increasing interest in recent years. The current state of the art positions this technology as a viable option to help to address several emerging challenges in electric mobility. Some of the reported benefits of VIPV in EVs include extending the driving range by up to 30 km with the current technology [2], increasing the battery lifespan by 19% [3] and reducing the charging time and frequency by up to 16% [4], thereby easing the burden on the power grid. Other more optimistic studies — such as that of Carr et al. [5] — suggest that conventional passenger vehicles equipped with integrated photovoltaic modules could reduce their overall energy demand by 35–50%, depending on daily mileage and geographical location, with sunnier regions offering the greatest potential benefits. VIPV can also provide a source of power in scenarios such as catastrophes or remote areas where the grid may be inaccessible [6], as well as in new applications as Vehicle to Grid (V2G) [7]. However, integrating PV technology into vehicle surfaces introduces unique challenges due to the requirements and the operating conditions of the modules installed on vehicles. Passenger vehicles often feature complex three-dimensional (3D) curvatures for aerodynamic and aesthetic purposes, while the limited surface area restricts the space for PV installation. Such curvatures lead to significant irradiance non-uniformity across the module [8], altering its IV curve shape and reducing the output power by 10% or more compared to a flat module, depending on the curvature [9]. Furthermore, the complex shading patterns cast upon vehicles on urban environments pose additional difficulties inaccurately estimating output power and energy yield.

A common approach to evaluate the on-road solar resource is the installation of pyranometers on the vehicle body, as demonstrated by Wetzel et al. [10,11]. Their experiments revealed how seasonal variations, tree foliage, and weather conditions influence on-road irradiance, with differences between sunny and cloudy days ranging from 30 W/m² in autumn to 640 W/m² in summer. Most irradiance fluctuations occurred below 5 Hz (98%), suggesting relatively slow dynamics, though their setup could not capture the spatial distribution of shadows. Salomon et al. [12] also employed pyranometers to define MPPT response requirements, concluding that 97% of the available energy can be extracted at a 10 Hz tracking frequency, compatible with current MPPT hardware. Araki et al. [9,13] expanded on this work by linking urban morphology to performance, showing 25% and 50% annual irradiation reductions in moderate and dense urban areas, respectively, compared to open environments.

Celi et al. [14] advanced this analysis through on-board IV curve tracing, capturing a full IV scan every 0.5 s (with a 100 ms acquisition time). This allowed a detailed study of dynamic partial shading and its effects on electrical parameters. Despite challenges caused by non-uniform illumination at higher urban speeds (∼50 km/h), which led to a 14% reduction in usable data, the method enabled precise insight into VIPV operation under motion. Results showed low temperature differences (∼4 °C) across the module and stable V_MP but strongly fluctuating I_SC. MPPT evaluation revealed that the classical Perturb and Observe (P&O) algorithm [15,16] maintains high efficiency (97–98%) under steady conditions but drops to 83–84% under rapidly changing irradiance. A hybrid algorithm combining fast IV scanning with localized P&O control achieved up to 99% global efficiency and 90% in dynamic sections, underscoring the value of high-speed IV tracing for improving MPPT adaptation in real-world VIPV conditions.

The on-road irradiance measurements revealed high fluctuations across different environments. This effect, combined with the severe VIPV module spatial constraints and the rarely optimal module-to-sun orientation incentivizes the use of densely packed high efficiency cells. Although not a new approach, originating in the 1960s [17], shingle interconnection offers significant advantages for VIPV applications compared to conventional front to back interconnection using copper ribbons. The active area of the cell is increased by removing the busbars from the front. Electrical conduction is achieved through electrically conductive adhesives or solder that connect the front of one cell to the rear of the next. Shingled disposition presents high efficiency and surface coverage, delivering up to 12% more power output than conventional modules of the same area [18]. The active surface improvement is reflected on the cell to module (CTM) ratio, with values over 90% [19,20]. Moreover, shingled cell modules have demonstrated significantly improved energy output (up to nearly 50% higher) under partial shading situations [21]. However, in [22] reports that a shingled cell module dissipate more energy as heat (up to 70%) under certain partial shading scenarios leading to reverse bias. This drawback can be mitigated using bypass diodes, whose design and placement must be carefully considered.

Beyond the PV cell type, the interconnection between cells plays a vital role in the performance of VIPV modules. Studies have shown that a high number of bypass diodes improved performance in the presence of partial shading. Macías et al. [23] performed a comparison on the energy yield of a vehicle's roof with 160 PV cells with different cell interconnections under a wide range of irradiance profiles. It showed that a similar power output could be achieved with parallel branches and a reduced number of bypass diodes (8, one per string vs 160, one per cell), offering a more practical and cost-effective approach to mitigate partial shading. Other studies have explored the Total-Cross-Tied (TCT) interconnection under partial shading [24], showing up to 12% less drop in power output under equivalent shading conditions to those of a Series-Parallel module.

A distributed modules strategy may also improve the overall energy yield in VIPV [25], as mismatch losses are expected to decrease on smaller modules, and DC/DC converter performance may be optimized by individually tracking the Maximum Power Point (MPP) of each device [26]. The company Lightyear showed this approach on its Lightyear 0 model [27], incorporating hundreds of cells distributed across dozens of individual modules, each one with independent tracking.

This study investigates strategies to address dynamic shading in VIPV, focusing on the effects of cell orientation, interconnection topology, and evaluate the potential benefits of a distributed modules architecture. Eight cases are evaluated, comparing energy yield and MPPT efficiency under different VIPV configurations: series vs. TCT interconnection, vertical vs. horizontal cell orientation, and a single large module with centralized MPPT vs. six smaller modules with distributed MPPT. For this purpose, real urban shading patterns were captured using a roof-mounted camera during vehicle operation. The roof of the vehicle was selected since it is the surface with a highest energy yield potential, since experimental measurements indicate that the roof receives 2.5-3 times more irradiance than the sides [11,28]. These images are used as an input to reproduce shadows in electrical simulations of the modules. To address the localized nature of the findings the surroundings of the route have been classified into different categories, according to density and height of buildings and trees, as well as road width. In addition, a systematic classification of the obtained shadow patterns is proposed, according to their distribution over the PV surface. This paper is organized as follows: Section 2 presents the methodology for obtaining the images of shadows, performing the electrical simulation of the modules and simulating the MPPT algorithms. Section 3 reports the results on energy yield and MPPT performance of the simulated cases. Section 4 summarizes the main conclusions of the study.

2 Material and methods

The methodology employed in this study is based on an established and validated framework [29]. The workflow consists of a sequence of interconnected steps:

• Environment classification: Categorization of vehicle surroundings in the route according to environmental characteristics (trees, buildings, etc.).

• High-frequency image acquisition: Capturing dynamic shadows cast on the roof of a vehicle during urban driving under real-world conditions.

• Advanced image processing: Extraction of accurate shading profiles from the captured images.

• Electrical simulation: The electrical performance of a module integrated in the roof of a vehicle is simulated under the previously obtained shading profiles.

• MPPT algorithm evaluation: Analysis of algorithm behaviour to estimate the power that an ideal DC/DC converter (lossless) would deliver during simulated urban driving.

• Shading profile classification: Classification of the shadows obtained in the images according to their shape.

2.1 Environment classification

The classification of the route environment was carried out following the Local Climate Zone (LCZ) framework proposed by Stewart and Oke [30]. This approach analyses the building and land cover typologies, according to a qualitative and quantitative analysis. The qualitative analysis was based on Google Earth imagery, considering building and vegetation density as the main visual indicators. Complementarily, quantitative parameters, such as building height and street width were obtained using Madrid's Geoportal online tool [31].

To estimate how shading varies over a vehicle in each zone, a simplified 2D static shading analysis was performed. For simplicity, a straight road was considered, assuming infinitely long shading objects and neglecting shape details (e.g., tree leaves). The schematic in Figure 1 defines key parameters: object heights (H₁ and H₂), distances from the road (W₁ and W₂), lane width (L = 3.5 m per [32]), car roof width (W_c= 1.2 m) and height (H_c = 1.4m) and parking lane width (L_p), which might not be present. The values of the parameters affecting the analysis are listed on Table A1, in the Appendix A section, based on the values suggested in [30] for each LCZ.

From this analysis, three shading conditions can be identified: full shading, partial shading, and total illumination. Full shading occurs when the entire roof width is covered by shadows, while partial shading begins when the shadow edge reaches the roof and ends when it is either fully shaded or fully exposed. The shadow projections of the right and left obstacles are described by equations (1) and (2), respectively, where Az_sun and El_sun correspond to the azimuth and elevation angles of the Sun. Az_right and Az_left correspond to the azimuth of the obstacles. For illustration, Az_right = 90° would mean that the right obstacle is located to the east.

$$L_{ShadeRight}=\frac{H_1-H_c}{\tan \left(E{l}_{sun}\right)}\cos \left(A{z}_{sun}-A{z}_{right}\right)$$(1)

$$L_{ShadeLeft}=\frac{H_2-H_c}{\tan \left(E{l}_{sun}\right)}\cos \left(A{z}_{sun}-A{z}_{left}\right).$$(2)

Positive values indicate shadows cast onto the road, while negative values correspond to shadows cast away from it. To capture seasonal variations, the analysis is conducted for solar positions at the summer and winter solstices, as well as on the experimental day.

Fig. 1 Static shading case of study schematics. The black car icon indicates the parking lane, whereas the blue car represents the subject of this analysis.

2.2 High-frequency image acquisition

The set-up used to acquired images is based on a camera and a flat white board over the roof of the vehicle to properly identify shadow patterns (Fig. 2a). The camera utilized for this study was a DJI Osmo Action 4 camera, with the capability of acquiring HD video (1920 × 1080 px) at high framerate (240 fps) with stabilization function. The board was fixed to the vehicle roof through using magnets, and the camera was fixed through a suction cup (Fig. 2b). The use of the flat white board eases the image processing for separating shadowed areas from the sunny ones significantly.

The studied route was performed on May 23^rd, 2025, beginning at 9:58 in the morning, with Madrid's time zone, with a total duration of 17 min and 20 s and a 5.6 km extension (Fig. 2c). The average speed of the vehicle was 19.4 km/h, and a top speed of 45 km/h (Fig. 2d). The Sun's position was considered to remain constant during the experiment duration.

The experiment was carried out on a day with a clear sky, under a Global Horizontal Irradiance (GHI) of 360 W/m² and a Diffuse Horizontal Irradiance (DHI) of 43 W/m². The reduced weight of DHI in the overall irradiance ensures that there are not fast irradiance fluctuations, associated to days with a stronger diffuse component. In addition, the clear day condition ensures that the differences in irradiance between shaded and unshaded areas are maximized, allowing to isolate mismatch effects caused by shading. The mismatch on cloudy days is expected to be much less challenging for VIPV modules and converters, according to the findings of Chambion et al. [33].

Fig. 2 a) Experimental setup: a white board in the vehicle roof and camera in a support structure. b) Sketch of setup, showing the flat board and camera with the structures that fix them to the vehicle. c) Route map. The blue sign indicates the start and end of the route. d) Speed profile of the vehicle during the experiment.

2.3 Advanced image processing

The frames of the video are extracted, processed and translated into shadowing profiles. Each frame is used to simulate the irradiance pattern over the module under study and therefore obtain the IV curve of VIPV module under real conditions. For the video processing, the corners of a rectangular area on the flat board are selected (Fig. 3a), delimiting the same area in all the frames in the entire video. The next step uses the 4 marked corner points of the selected area for undoing the perspective effects and trim the image leaving only the rectangle of interest (Fig. 3b). Regarding image processing, a local Laplacian filter and a contrast adjustment is performed [34] to obtained a binarized image that enhance sunny and shadowed areas (Fig. 3c). A suitable threshold value of 0.91 is employed to binarize the pixels (0 for shadowed, 1 for sunny) [35]. The threshold is the mean of thresholds upon a 1000 images sample distributed uniformly over the entire sequence, employing the Otsu method [36] to obtain the values. A grid is then projected upon the image, each cell representing one of the photovoltaic module's cells. For this study, two cell orientations have been considered: Vertical (V) (Fig. 3d) and Horizontal (H) (Fig. 3e), ensuring identic surface coverage on both cases. The number of black and white pixels on each cell is counted and then used to obtain the shading factor (SF) [37] of each cell. A value of 1 represents a fully shaded cell and a value of 0 represents a fully illuminated cell. To obtain the effective irradiance in each cell, the shaded area of the cell is only under diffuse light, whereas the unshaded area is under both the direct and the diffuse light. The used values of GHI and DHI values are the ones provided by the meteorological station at the campus near the driving route. Reflected light is not considered in this work, as the study focuses on the mismatch caused by shading, and it is unlikely that reflections can increase brightness on a shaded area with enough intensity to consider it illuminated. However, its potential impact on power output has been noted in previous studies [38].

Fig. 3 a) Video frame with projected rectangular grid. b) Extracted rectangular area from the video, after angular transformations. c) Binarized area in black and white. d) Black and white area with grid representing vertical cell orientation. e) Black and white area with grid representing horizontal cell orientation.

2.4 Electrical simulation

The effective irradiance patterns obtained from image processing are used to simulate the electrical response of the PV surface. An effective irradiance value is assigned to each cell for every video frame, resulting in a temporal sequence of IV curves. The electrical simulation of each cell is based on the two-diode model [39] of a silicon cell, in which the generated current is adjusted according to the effective irradiance of each cell. (see Tab. A2 of the Appendix A).

2.4.1 Module's architecture

The total active area of the simulated VIPV surface is 126 cm x 63 cm (∼0.8 m²), and it incorporates a total of 216 cells shingled photovoltaic cells of 3.5 cm x 10.5 cm, each with a defined 1:3 form factor. The photovoltaic surface is modelled with radius of curvatures of 5 meters and 6 meters in the longitudinal and transversal directions, respectively. The effect of the curved shape has been considered by calculating the normal vectors of each cell, consequently calculating the non-uniform irradiance pattern due to cosine losses.

However, in this work, incidence angle modifier (IAM) related losses, the vehicle's position along the route, and the sun's position at each evaluated time step, which would also affect the irradiance pattern on the vehicle's roof, are not considered. The module's temperature has been considered constant at 25°C, without using a thermal model.

In this study, the Single Large Module (SLM) that occupies the entire surface is compared against 6 mini-modules (6 MM) on a 2 × 3 disposition.to implement the distributed MPPT technique [25].

Figure 4 illustrates the SLM module architecture. The SLM layout with vertical cells is shown in Figure 4a (TCT interconnection) and Figure 4b (series interconnection). Figure 4c represents the TCT configuration with vertical cells, and Figure 5d the series configuration with vertical cells. For series interconnection, the only distinction between SLM-Series-V and SLM-Series-H is the number of bypass diodes (12 vs 6). The increased number of bypass diodes is expected to improve performance under partial shading for the V case. Series-connected SLM configurations yield high voltages, exceeding the 60 V low-voltage limit for electric vehicles specified in ISO 6469-3:2021 [40]. In contrast, TCT interconnection remains below this limit, though its higher currents require consideration due to increased ohmic losses and DC/DC converter range of operation.

Figure 5 illustrates the mini-module module architecture. Each mini-module contains 36 cells covering the same surface area, regardless of orientation. The MM layout with vertical cells is shown in Figure 5a (TCT interconnection) and Figure 5b (series interconnection). Figure 5c represents the TCT configuration with vertical cells, and Figure 6d the series configuration with vertical cells. Figures 5e and 5f represent the distribution and numeration of the mini-modules, with horizontal and vertical cells, respectively. The reduced size of each mini-module makes the 6 MM architecture compatible with the 60 V threshold indicated by the norm in every case.

Table 1 summarizes the electric characteristics of each architecture. For series connection, both V_OC and I_SC remain unchanged; however, the 6 MM-Series-H case (Fig. 5d) has fewer bypass diodes, which is expected to reduce performance under partial shading compared to 6 MM-Series-V (Fig. 5b). In the TCT configurations—6 MM-TCT-V (Fig. 5a) and 6 MM-TCT-H (Fig. 5c)—the higher currents in vertical orientation are expected to increase ohmic losses.

Fig. 4 Single Large Module architecture summary. The negative and positive terminals are represented by the red and blue circles, respectively. The cells are represented by the red grid elements. a) SLM-TCT-V. b) SLM-Series-V. c) SLM-TCT-H d) SLM-Series-V.

Fig. 5 Mini-module architecture summary. The negative and positive terminals are represented by the red and blue circles, respectively. The cells are represented by the red grid elements. a) MM-TCT-V. b) MM −Series-V. c) MM −TCT-H d) MM −Series-V. e) Distribution of mini-modules on the active PV surface with horizontal cells, including numeration. f) Distribution of mini-modules on the active PV surface with vertical cells, including numeration.

Fig. 6 a) Processed frame with shadow only crossing horizontally. b) Processed frame with shadow only crossing vertically. c) Processed frame with shadow crossing both horizontally and vertically. d) Processed frame with shadow not crossing either vertically or horizontally. e) MM distribution schematic, with indexed mini-module rows (R1 and R2) and columns (C1, C2 and C3).

2.5 MPPT algorithm evaluation

The perturb and observe (P&O) Maximum Power Point Tracking (MPPT) algorithm [15] is simulated considering the IV curves generated by the VIPV module while the vehicle is driven. The P&O algorithm is a classical MPPT algorithm in conventional PV systems used to extract the maximum power by fixing the DC/DC converter's voltage, setting the I-V curve's working point as it evolves over time.

The P&O algorithm behaviour is governed by two parameters: perturbation step and period [32]. They define the magnitude and frequency of the perturbation, directly impacting the VIPV system performance. In this study, the MPPT performance is evaluated for different combinations of these two parameters to define the optimum one for each case. This way, the efficiency, defined as the ratio of energy extracted by the converter vs the maximum deliver energy by the module [41] can be compared in the all of the proposed cases.

The main advantage of distributed MPPT (DMPPT) lies in its ability to effectively mitigate mismatch losses. Under partial shading, several individual mini-modules can operate at different points of the IV curve, without affecting each other. This way, various MPPT algorithms can extract the maximum power effectively without getting trapped in local maxima. This is particularly relevant for VIPVs due to the highly dynamic, localized, and unpredictable nature of urban shading.

2.6 Shading profile classification and distribution

To gain a better understanding on the performance of each configuration and algorithm under different shading conditions, a shading profile classification method is proposed.

The first step in the shading image analysis is the identification of partial shading events. For each frame, the average SF of the module is calculated. To prevent misclassification of minor fluctuations, a 1% tolerance is applied. Frames with SF ≥ 0.99 will be classified as fully shaded, those with SF ≤ 0.01 as fully illuminated, and the remaining as partially shaded.

The next step involves categorizing partial shading events by shape and assessing their potential impact on the module's electrical performance. Since module strings may be arranged either horizontally or vertically, partial shading frames were categorized accordingly:

• Only crosses width (Fig. 6a). A frame is classified in this category if there is a continuous path of shaded cells (SF on cell >0.01) starting on the left edge and ending on the right edge, and there is not a continuous path of shaded cells from the top edge to the bottom edge.

• Only crosses length (Fig. 6b). A frame is classified in this category if there is a continuous path of shaded starting on the top edge and ending on the bottom edge, and there is not a continuous path of shaded cells from the left edge to the right edge.

• Crosses both width and length (Fig. 6c). There is a continuous path of shaded cells from the left to the right edges and from the top to the bottom edges.

• Does not cross (Fig. 6d). There is no continuous path of shaded cells from any edge to the opposite.

The third step of this classification involves a detailed analysis of shadow distribution across the studied surface for each category. For this purpose, the average SF of each mini-module is computed over all frames within the category. Additionally, the SF range—defined as the difference between the highest and lowest SF among mini-modules per frame—is averaged. This parameter reflects the non-uniformity of shading across the surface, which is particularly relevant given the dynamic movement of shadows, typically shifting from the top to the bottom edge.

The results are analysed at three levels: globally (MM1–MM6), by rows (R1 = MM1–MM3, R2 = MM4–MM6), and by columns (C1 = MM1 and MM4, C2 = MM2 and MM5, C3 = MM3 and MM6), as illustrated in Figure 6e. The combination of the average SF and average SF range allows identifying whether shadows are primarily horizontal (low row range, high column range), vertical (high row range, low column range), or diagonal (similar row and column ranges, high global range), and whether specific areas of the module are more frequently shaded than others.

Finally, to evaluate the overall performance of each PV system configuration, the available irradiation, module energy and MPPT extracted energy will be compared across the different illumination conditions.

3 Results

The surroundings along the route were analysed and classified into different environment types based on their physical characteristics. A simplified two-dimensional static shading model was then evaluated using typical obstacle heights and road widths representative of these environments, providing a general understanding of the expected shading conditions in each zone.

After studying the shading conditions, eight VIPV scenarios—combining cell orientation (vertical/horizontal), layout (SLM/6MM), and interconnection (series/TCT)—are evaluated under them. First, the maximum available energy is quantified for each case. Then, a bi-parametric sweep of the P&O algorithm's step size and period identifies the optimal settings for maximum energy extraction.

Shading profile images were categorized into full illumination, partial shading, and total shading. Partial shading frames were further divided into four typologies according to the continuity of the shaded areas. Their overall relevance to the route's energy-harvesting potential was assessed by comparing the duration of each category with the irradiance incident on the module. Finally, the average SF and average SF range among mini-modules were analysed for each subcategory. This comparison across different mini-module combinations helped identify the characteristic shadow patterns associated with each shading condition.

3.1 Environment assessment

On a first assessment, the route segments (Fig. 7a) were categorized into three distinct LCZ classes after visual inspection: the vast majority corresponds to “open midrise” (88%) (Fig. 7b), with a lesser appearance of “scattered trees” (9%) (Fig. 7c) and “dense trees” (3%) (Fig. 7d). Subsequently, building height, street width, and pavement width were analysed for each zone type. The average values of these parameters, along with their dispersion, are presented in Table 2.

Next, a simplified two-dimensional static shading simulation was conducted to obtain a general understanding of common shading scenarios. The simulation parameters were based on both the measured data and the reference values suggested in [30] (see Tab. A2 in the Appendix). Note that the usual distance to the trees' trunks from the edge of the road is notably smaller than the width of the pavement. Figure 8 illustrates examples of the distribution of partial shading events—represented by colour stripes—for each zone type under different solar trajectories. The winter and summer solstices (dashed lines) indicate yearly variations, while the experiment day (23 May 2025, continuous line) provides a reference for daily conditions. Figure 8a shows the results for a vehicle in the left lane, and Figure 8b for one in the right lane.

In the “dense trees” case, a symmetrical shading pattern is observed between Figures 8a and 8b, while the “scattered trees” case shows asymmetry due to the presence of a parking lane. This contrast is even more pronounced in the “open midrise” zone, where the model assumes a 20 m building on one side of the road and a 6 m tree on the other. This configuration reflects the central elongated roundabout along the route, bordered by buildings on one side and trees on the opposite side.

Overall, this simplified analysis provides a qualitative overview of the expected shading conditions for each zone throughout the year. According to the results in Figures 8a and 8b, the scattered trees zone is most likely to experience full illumination during the experiment, regardless of obstacle orientation or vehicle direction. In contrast, the dense trees zone tends toward full shading, as the tree canopies are tall enough to cast shadows across the entire road at the given solar elevation. Meanwhile, the open midrise zone exhibits high variability in illumination, as shading conditions depend strongly on building height, distance from the road, and vehicle direction. It is important to note that real shadows cast by tree canopies are not uniform but consist of irregular shade patterns that evolve over the year. Moreover, actual spacing between shading objects can introduce additional partial shading and intermittent illumination, effects not captured by this simplified model—making the simulated scenario more pessimistic than real-world conditions.

Fig. 7 a) Map indicating the driving route of the experiment. The blue marker on the top right corner indicates the start and end of the route. The colour bar indicates the height of the building. The majority of the route corresponds to an “Open Midrise” category. The green patch corresponds to a “Scattered Trees” category and the red one to “Dense Trees”. b) Google Earth image of a section of the route categorized as “Open Midrise”, corresponding to May. c) Google Earth image of a section of the route categorized as “Scattered Trees”, corresponding to June. d) Google Earth image of a section of the route categorized as “Dense Trees”, corresponding to May. e) Speed of the vehicle over the experiment's timelapse.

Fig. 8 Sun trajectories for the winter and summer solstice (dashed lines) and the experiment day (continuous line). The partial shading events on different zone typologies are indicated with coloured stripes, as indicated in the legend. The solar positions between two patches of the same colour correspond to full illumination. The solar positions below the patches correspond to full shading. The yellow dot indicates the actual sun's position for the experimental route. a) Shading events with car on the left lane. b) Shading events with car on the right lane.

3.2 Energy yield assessment

In this section, the maximum available energy during the route is compared for the different scenarios. This is calculated by summing the maximum power of each IV curve, weighed by the time interval between them (4.16ms), thus obtaining the total route energy yield. As shown in Figure 9, the configuration with 6mini‑modules exhibits a slightly higher energy harvest potential (+1.17 to +2.25%) than the single large module. In all scenarios, the TCT interconnection performs notably better than the series connection (+5.8 to +7.6%). For both the SLM and 6MM layouts, the vertical cell orientation shows a modest advantage over the horizontal one, mostly due to bypass diodes. These improvements range from +0.6% to +1.1% with SLM and from 0.4% to 2.1% with 6 MM.

The mismatch losses, as indicated by the numbers above the red and blue bars on Figure 9 represent the average value between both SLM and TCT configurations. These values have been obtained after discounting the effect of SF, SVF and IAM. Curvature proved to have a lesser impact in the overall energy distribution, and the low ambient temperature even enhanced energy output, though minimally (+0.14%) These results align with the initial expectation that TCT interconnection enhances module performance under partial shading by allowing electrical current to bypass shaded cells more effectively.

The energy distribution across the six mini‑modules is presented on Figure 10a. The numeration of the mini-modules corresponds to the one indicated on Figure 10b. It becomes evident that the individual energy outputs of all 6 modules are very similar, as long as they share the same interconnections and cell orientations. This energetic resemblance among the six mini-modules of the same configuration stems from the movement of shading patterns. Figure 10b reveals the average SF on each cell of the module obtained during the route, with an average value of 0.24 and a standard deviation of 0.006, which indicates a high consistency in the shading distribution over the module. This analysis has been done for vertical cells but can also be extrapolated to horizontal. As the vehicle moves, shadows shift from front to rear, causing identical shading profiles to affect different modules with a slight time delay. This explains the close match in IV curves between front and rear modules at different instants [42]. The shape and distribution of shadows will be analysed in detail in Section 3.4, complementing these results.

The relative differences between configurations (Series-H, Series-V, TCT-H and TCT-V) on MM1 are found on the rest of the mini-modules, following a consistent trend. The TCT-V interconnection offers the highest energy yield, although the TCT-H offers almost identical results (0.4% less energy yield). Conversely, when the modules are connected in series, orientation plays a more significant role, with the vertical arrangement consistently achieving slightly higher energy yields than the horizontal one.

The higher energy output for the 6 MM-Series-V configuration compared to 6 MM-Series-H can be explained by the cell interconnection of each mini-module, affecting the IV curves' shape under partial shading. Despite sharing the same characteristic values of I_SC and V_OC in STC, the number of bypass diodes is superior on the V-Series case. This allows reaching higher current values on the IV curves under partial shading (Fig. 11b) with V orientation, as less cells present a current limited by the shading profile (Fig. 11a).

Fig. 9 Performance Ratio (PR) on the route with every configuration, with red bars representing the energy of SLM layout and blue bars representing the energy of 6 MM layout. The 100% corresponds to an unshaded module of similar characteristics at 25°C under a uniform GHI during the same period. The rectangles on each bar illustrate the cell orientation and module layout, with the small red grid showing the first row or column of cells, depending on the orientation. The numbers above the bars indicate the average mismatch associated losses. The dashed lines indicate the losses due to SF (green), SVF (yellow) and IAM (teal), with the corresponding coloured numbers expressing the values.

Fig. 10 a) Distribution of available energy across the 6 mini-modules in every scenario. b) Average shading factor on each cell during the route. The average value of SF among cells is 0.24, and the standard deviation is 0.006. The blue rectangles delimitate each submodule. The numbers above and below the graph indicate the MM number.

Fig. 11 a) IV curves of the MM1 with different cell interconnections and configurations under the partial shading situation shown on b), with the dots and numbers representing the maximum power point of the IV curve. The colours in both numbers and lines represent different configurations: Red, MM1-TCT-V; green, MM1-TCT-H; orange,MM1-Series-V and blue, MM1-Series-H. b) Shading pattern over the module with the blue rectangles showing the location and numeration of the 6 MM. MM1 is emphasized in bright green.

3.3 P&O efficiency

To evaluate the MPPT algorithm in VIPV, a sweep of perturbation frequencies and step sizes was conducted across the eight scenarios under study. Since the IV curves for each configuration differ in shape, particularly in V_OC and I_SC values (see Tab. 1), the step size was defined as a percentage of V_MP under STC conditions. The results indicate that the six mini‑modules display nearly identical performance when subjected to the same perturbation frequency and step size. Consequently, the efficiency patterns observed for MM1 in Figure 12 are almost identical for the other mini-modules as well (see Fig. A1 in the Appendix A for the MM2 case).

Moreover, all configurations follow a similar trend, in which shorter perturbation periods yield the highest efficiencies. Regarding the step size, the efficiency maps exhibit nearly horizontal contours at the optimum frequency for all orientations and interconnection types. However, the TCT configuration consistently shows slightly lower efficiencies for perturbation steps over 8% in both the H and V orientations (Figs.12a and 12c). This reduction is attributed to the steeper IV curves associated with TCT connections, characterized by high I_SC and low V_OC values. Under these conditions, a large perturbation size induces a more pronounced power fluctuation due to the greater current variation, in contrast to the behaviour observed in series connected IV curves (Fig. 11a).

Similarly, the SLM layout achieves efficiency levels comparable to those of the 6MM configuration in all scenarios and exhibits trends in efficiency variation consistent with those observed for MM1. Nevertheless, the efficiency drop with increasing perturbation period is slightly more pronounced in the series connection (Figs. 13b and 13d). Consequently, the narrower optimal parameter range could complicate tuning a real MPPT device.

Fig. 12 Efficiency of mini-module 1 (MM1) over the entire dataset with different configurations, indicated above each graph. The Y axis indicates the perturbation period in seconds, and the X axis indicates the perturbation size, expressed as a percentage of VMP of the module in STC (1000 W/m2, 25°C).

Fig. 13 Efficiency of SLM over the entire dataset with different configurations, indicated above each graph. The Y axis indicates the perturbation period in seconds, and the X axis indicates the perturbation size, expressed as a percentage of VMP of the module in STC (1000 W/m2, 25°C).

3.4 Dynamic shading image analysis

This section summarizes the results obtained from the systematic analysis of dynamic shading patterns. The first subsection examines the frequency and morphology of the shading events, while the second assesses their impact on the photovoltaic module and algorithm performance.

3.4.1 Shading classification

The extracted images were categorized into three main illumination classes according to the tolerances described in Section 2.4: full illumination (62.00% of time), partial shading (30.80% of time), and total shading (7.20% of time). Partial shading events were further divided into four subcategories:

• Only crosses width (OCW): 8.38% of total route time.

• Only crosses length (OCL): 0.46% of total route time.

• Crosses both width and length (CWL): 15.71% of total route time.

• Does not cross (DNC): 6.25% of total route time.

OCL events are notably infrequent, confirming that shading situations in which horizontal strings with vertically oriented cells will be more affected by shades than vertical strings with horizontal cells are uncommon. Together, OCW and CWL account for approximately three-quarters of all partial shading events, consistent with shading mainly originating from roadside obstacles located on the side of the road while the vehicle moves forward.

To characterize shading distribution, the average SF (Tab. 3) and average SF range (Tab. 4) were calculated for different groups of submodules. These parameters describe both shading intensity and spatial variability across the surface. Since all mini-modules have identical surface area and cell count, cell orientation does not affect comparability.

For the entire set of partial shading events, results show a uniform average SF ≈0.54–0.55 across all rows and columns. The average SF range is ≈0.2 per row/column, increasing to ≈0.4 across all six mini-modules, indicating diagonal shadow patterns that shift gradually over time—consistent with their dominance (≈50% of total partial shading events).

OCW events show a homogeneous average SF ≈0.4 across all rows and columns. However, the row range (≈0.2) is lower than the column range (≈0.35), suggesting horizontal stripes moving longitudinally along the roof. These are likely caused by traffic lights or tall tree trunks.

OCL events exhibit a global and row-wise SF ≈ 0.35, increasing from left to right columns (C1: 0.2; C2: 0.3; C3: 0.5). The row range is high (≈0.6), while the column range remains lower (≈0.2). This indicates vertical shadow bands primarily affecting the right side of the roof, consistent with asymmetric roadside geometry and objects close to the vehicle's right-hand side such as short trees or distant obstructions casting narrow edge shadows. It is worth noting that this can be tied to the driving orientation, as in Spain, vehicles circulate on the right lane. The column SF progression could change in a country where vehicles move on the left lane.

CWL events present a high average SF≈ 0.8 with row and column ranges ≈0.2 and a global range ≈0.35, indicating dense, scattered shadow patterns. These are likely associated with tree crown shading.

Finally, DNC events show a very low average SF (0.05–0.08), with the central column (C2) being the most illuminated. The row and column ranges remain low (0.10–0.15) and even lower for C2 (≈0.08), suggesting small, isolated shadows near the longitudinal edges of the roof without a defined pattern.

These shapes explain the uniform distribution on energy yield among the 6 mini-modules found on Figure 10a, in Section 3.2. OCL events were infrequent, whereas OCW conditions produced stripe-shaped shadows and CWL cases generated dense shading over the entire module. In DNC situations, the shading factor (SF) was particularly low. Modules arranged in different rows exhibited similar shading patterns at different times, resulting in delayed yet comparable I–V curve profiles.

3.4.2 Shading impact on PV performance

The performance of the analysed module configurations and MPPT algorithms under different shading conditions is summarized in Table 5. Three main illumination states were considered: full illumination, full shading, and partial shading. The “Energy fraction” parameter quantifies the proportion of the maximum available module energy corresponding to each lighting condition.

For all configurations, most of the harvested energy was obtained during fully illuminated periods (84–87%), exceeding the proportion of time that these conditions represent. This value also surpasses the total irradiation percentage (78.89%), indicating the presence of mismatch losses under shading conditions.

The MPPT efficiencies were evaluated for a converter operating at 20 Hz (83 ms) and a 4% V_MP-STC perturbation size, representative of an average commercial P&O device. Under full illumination, efficiencies were comparable to those reported for static applications. In contrast, efficiency decreased notably under full shading (66–69%), although the energetic contribution of these periods was negligible due to their limited duration and irradiance share.

In partially shaded conditions, the modules still accounted for a significant portion of the total available irradiation, yet exhibited lower MPPT efficiency (69–82%). For the SLM configuration, TCT achieved higher performance under partial shading, with a 2% increase in energy fraction and about 12% higher algorithm efficiency (η) compared to Series. Differences between SLM-V-TCT and SLM-H-TCT were negligible, while SLM-V-Series showed slightly greater resilience than SLM-H-Series (≈1% higher energy fraction).

The 6 MM case presents higher energy yields than their SLM homologues in every case. However, the P&O efficiency drop with 6 MM-Series connection compared to 6 MM-TCT is reduced compared to the SLM case (∼5% less efficiency), thanks to the independent tracking.

These trends are explained by the shading distribution and bypass diode configuration. The scenarios in which H series connection is expected to improve performance (OCL) are very rare (0.46% of total route time). Given the high SF (0.8) found on the dominant case CWL, the potential for energy production will be limited, even though it represents the highest share of the partial shading events. TCT interconnections are expected to be more efficient under CWL shading events, thanks to their capability to allow current to flow between strings more freely. The most productive shading types are OCW and DNC. In OCW, V-Series connection performed better than H-Series thanks to its string disposition, which is best for shadows shaped as horizontal stripes. In DNC, the higher number of bypass diodes improves performance under circumstances that cover small numbers of cells, which is likely to occur given the low average SF found (0.08).

4 Conclusion

This study compares different cell and module configurations for VIPV under real-world urban shading, proposing a method to classify shadows by their shape and discussing the performance of each configuration according to each described category. The environment surrounding the car during the experiment was analysed according to a methodology designed to identify local climate zones, which provided relevant information on the evolution of shading events over the year on different area topologies. This analysis opens the door for future, detailed environmental classification that enhances the precision of VIPV performance on different locations.

Six small independent modules (6 MM) were compared with a single large module (SLM). In all cases, the yield improvement ranged between 1.1 and 2.2%. This small difference is likely due to minimal surface curvature and uniform angles of incidence during the route, as the vehicle makes several turns, lacking a predominant directionality during the route. The Distributed Module strategy presents other advantages, such as keeping system voltage below the 60 V safety threshold. Using a large module with TCT connection also keeps the voltage below the safety limit but produces high currents which can result in severe ohmic losses (I²R). It could also increase the cost of the hardware required for its operation, as the DC-DC converter should be operational under a broader range of currents.

Shadow movement across the vehicle surface produces similar yields and MPPT behaviour among all six mini-modules. No specific zone remains shaded more often, due to the moving nature of shadows and changes in vehicle direction. In general, urban shadows affect all areas comparably but at different instants, with most patterns moving front-to-back, allowing DMPPT to maintain more cells at peak output. The shadow shape analysis confirmed the similarity between mini-module energy output, revealing that a significant fraction of partial shadows presents either horizontal stripes shapes or covers an irregular large fraction of the PV surface, reaching both vertical and horizontal edges.

Across the mini-modules, energy output is moderately affected by cell orientation and interconnection, with TCT being the most productive, irrespective of cell orientation (vertical or horizontal). Series connection, however, presents a slightly better performance with vertical cell orientation. Rather than the impact of shading patterns on orientation, the increased number of bypass diodes per mini-module (6 vs 2) explains the differences on IV curves and the improved energy yield potential.

In terms of algorithm performance, in the eight cases presented in this study, the P&O reached high values of efficiency (∼99%) under the considered algorithm parameters, matching results found by other studies. The efficiency distribution across the studied combinations of perturbation size and period follows a similar trend across all configurations, orientations and layouts, with the lowest perturbation periods presenting the highest efficiency and decreasing towards higher periods. The single module layout resulted to be slightly more sensitive towards this increase in period than the small modules. Besides, the TCT case, independent of orientation or layout, showed a slight dependence on perturbation size, with values over 8% presenting moderately reduced efficiencies. This is due to steeper IV curve shape. As the TCT interconnection presents a higher I_SC and lower V_OC, a small fluctuation in tension produces a greater change in current, affecting power output significantly. Despite the similar algorithm behaviour, the horizontal cell orientation presents lower current values than the vertical, which might be helpful to reduce ohmic losses. Nevertheless, applying these low perturbation periods (4.16 ms) on a real device might prove impractical, so future research on alternative MPPT methods is encouraged.

This study also evaluated, for each of the 8 studied configurations, the fraction of the total available energy and P&O algorithm efficiency on total illumination, total shading and partial shading events. These results revealed a significant advantage of TCT connectivity in terms of algorithm performance. The TCT connection ability to extract energy under partial shading was significantly higher than the series connectivity for the SLM case, but not as much in the 6 MM case. In the latter, the granularity of the module distribution and the high number of bypass diodes proved their resilience.

The innovative shadow shape classification with a parametrized environment proposed in this study opens the door for future research and shadow parametrization on different areas. This approach allowed to identify the most critical shadow typologies for VIPV operation, providing a significant breakthrough on VIPV design parameters optimization. Regarding the configurations, the Distributed Module strategy showed better energy yield potential (1-2%), with TCT connection achieving the best results and 6 MM-V-Series showing good resilience to partial shading too, thanks to the high number of bypass diodes. Nevertheless, the losses associated with the extra electronic components should be assessed. However, drawing such conclusions requires more comprehensive simulations that account for different environments at different times of the year and sharper curvatures. Despite these limitations, the use of several smaller modules inherently lowers the maximum voltage of the IV curves, representing a potentially valuable contribution to the advancement of VIPV technology.

Funding

The authors gratefully acknowledge the DETEC-PV project, Grant PID2021-128853OB-I00, funded by MCIN/AEI/10.13039/501100011033 and “ERDF A way of making Europe.”

R. Moruno thanks his grant “PID2021-128853OB-I00” funded by MCIN/AEI/ 10.13039/501100011033 and by “ERDF A way of making Europe”.

Conflicts of interest

Ricardo Moruno certifies that he or she has no financial conflicts of interest (eg., consultancies, stock ownership, equity interest, patent/licensing arrangements, etc.) in connection with this article. The authors have nothing to disclose.

Data availability statement

Data will be provided on request.

Author contribution statement

The authors of this article have contributed in the following way:

Conceptualization:

Methodology: R. Moruno, L. San José, R. Núñez, R. Herrero

Software: R. Moruno, L. San José, R. Núñez

Validation: R. Moruno, R. Núñez

Formal Analysis: R. Moruno, R. Herrero

Investigation: R. Moruno, L. San José, R. Herrero

Resources: R. Moruno, L. San José

Data curation: R. Moruno, L. San José, R. Núñez

Writing − Original Draft Preparation: R. Moruno, L. San José, R. Núñez

Writing − Review & Editing: R. Núñez, L. San José, R. Herrero

Visualization: R. Moruno

Supervision: L. San José, R. Núñez, R. Herrero, I. Antón Hernández

Project Administration: R. Núñez, R. Herrero, I. Antón Hernández

Funding Acquisition: R. Núñez, R. Herrero, I. Antón Hernández.

References

Appendix

Fig. A1 Efficiency of mini-module 2 (MM2) over the entire dataset with different configurations, indicated above each graph. The Y axis indicates the perturbation period in seconds, and the X axis indicates the perturbation size, expressed as a percentage of VMP of the module in STC (1000 W/m2, 25°C).

All Tables

All Figures

	Fig. 1 Static shading case of study schematics. The black car icon indicates the parking lane, whereas the blue car represents the subject of this analysis.
In the text

	Fig. 2 a) Experimental setup: a white board in the vehicle roof and camera in a support structure. b) Sketch of setup, showing the flat board and camera with the structures that fix them to the vehicle. c) Route map. The blue sign indicates the start and end of the route. d) Speed profile of the vehicle during the experiment.
In the text

	Fig. 3 a) Video frame with projected rectangular grid. b) Extracted rectangular area from the video, after angular transformations. c) Binarized area in black and white. d) Black and white area with grid representing vertical cell orientation. e) Black and white area with grid representing horizontal cell orientation.
In the text

	Fig. 4 Single Large Module architecture summary. The negative and positive terminals are represented by the red and blue circles, respectively. The cells are represented by the red grid elements. a) SLM-TCT-V. b) SLM-Series-V. c) SLM-TCT-H d) SLM-Series-V.
In the text

Fig. 5 Mini-module architecture summary. The negative and positive terminals are represented by the red and blue circles, respectively. The cells are represented by the red grid elements. a) MM-TCT-V. b) MM −Series-V. c) MM −TCT-H d) MM −Series-V. e) Distribution of mini-modules on the active PV surface with horizontal cells, including numeration. f) Distribution of mini-modules on the active PV surface with vertical cells, including numeration.

In the text

	Fig. 6 a) Processed frame with shadow only crossing horizontally. b) Processed frame with shadow only crossing vertically. c) Processed frame with shadow crossing both horizontally and vertically. d) Processed frame with shadow not crossing either vertically or horizontally. e) MM distribution schematic, with indexed mini-module rows (R1 and R2) and columns (C1, C2 and C3).
In the text

Fig. 7 a) Map indicating the driving route of the experiment. The blue marker on the top right corner indicates the start and end of the route. The colour bar indicates the height of the building. The majority of the route corresponds to an “Open Midrise” category. The green patch corresponds to a “Scattered Trees” category and the red one to “Dense Trees”. b) Google Earth image of a section of the route categorized as “Open Midrise”, corresponding to May. c) Google Earth image of a section of the route categorized as “Scattered Trees”, corresponding to June. d) Google Earth image of a section of the route categorized as “Dense Trees”, corresponding to May. e) Speed of the vehicle over the experiment's timelapse.

In the text

Fig. 8 Sun trajectories for the winter and summer solstice (dashed lines) and the experiment day (continuous line). The partial shading events on different zone typologies are indicated with coloured stripes, as indicated in the legend. The solar positions between two patches of the same colour correspond to full illumination. The solar positions below the patches correspond to full shading. The yellow dot indicates the actual sun's position for the experimental route. a) Shading events with car on the left lane. b) Shading events with car on the right lane.

In the text

Fig. 9 Performance Ratio (PR) on the route with every configuration, with red bars representing the energy of SLM layout and blue bars representing the energy of 6 MM layout. The 100% corresponds to an unshaded module of similar characteristics at 25°C under a uniform GHI during the same period. The rectangles on each bar illustrate the cell orientation and module layout, with the small red grid showing the first row or column of cells, depending on the orientation. The numbers above the bars indicate the average mismatch associated losses. The dashed lines indicate the losses due to SF (green), SVF (yellow) and IAM (teal), with the corresponding coloured numbers expressing the values.

In the text

	Fig. 10 a) Distribution of available energy across the 6 mini-modules in every scenario. b) Average shading factor on each cell during the route. The average value of SF among cells is 0.24, and the standard deviation is 0.006. The blue rectangles delimitate each submodule. The numbers above and below the graph indicate the MM number.
In the text

Fig. 11 a) IV curves of the MM1 with different cell interconnections and configurations under the partial shading situation shown on b), with the dots and numbers representing the maximum power point of the IV curve. The colours in both numbers and lines represent different configurations: Red, MM1-TCT-V; green, MM1-TCT-H; orange,MM1-Series-V and blue, MM1-Series-H. b) Shading pattern over the module with the blue rectangles showing the location and numeration of the 6 MM. MM1 is emphasized in bright green.

In the text

	Fig. 12 Efficiency of mini-module 1 (MM1) over the entire dataset with different configurations, indicated above each graph. The Y axis indicates the perturbation period in seconds, and the X axis indicates the perturbation size, expressed as a percentage of VMP of the module in STC (1000 W/m2, 25°C).
In the text

	Fig. 13 Efficiency of SLM over the entire dataset with different configurations, indicated above each graph. The Y axis indicates the perturbation period in seconds, and the X axis indicates the perturbation size, expressed as a percentage of VMP of the module in STC (1000 W/m2, 25°C).
In the text

	Fig. A1 Efficiency of mini-module 2 (MM2) over the entire dataset with different configurations, indicated above each graph. The Y axis indicates the perturbation period in seconds, and the X axis indicates the perturbation size, expressed as a percentage of VMP of the module in STC (1000 W/m2, 25°C).
In the text