In the past few years, the electric vehicle industry has truly boomed as countless brands use this new technology. The widespread adoption of electric vehicles (EVs) is not only a matter of technology but also the infrastructure for using them, so it requires investment and support from car manufacturers as well as from governments. Furthermore, by switching to electric vehicles, each country’s electricity consumption will increase, putting pressure on the power grid, especially in big cities.

Although the construction of charging stations is being promoted to meet market demand, the remaining problem is vehicle charging time. Each charging post takes hours to fully charge an EV, and other EVs that need to charge either do not have a parking space or cannot wait that long for their turn. In emerging markets, electric vehicle companies all offer different charging standards with proprietary connectors to compete, leading to charging stations that are not compatible with other brands’ vehicles. Although common connection standards for each market have been introduced as a common standard that car manufacturers must follow, such as the European standard BS ISO 23274-1, there are still too many charging port types that confuse users when they choose their vehicle and charging port. According to a J. D. Power report [1], “Up to 20.8% of electric vehicle users experienced charging problems when they used public charging stations, including hardware and software problems as of Q4 2023.” This leads to a major hurdle, as users not only worry about battery life but also the stability of vehicle charging systems. In addition to compatibility, there are also charging station issues related to operation. Although charging stations are technically functional, they aren’t always usable. Payment problems and slow or unstable charging also make users feel uncomfortable in the process of charging their vehicles.

To solve these problems, car manufacturers have conducted futuristic projects for “next-generation electric vehicles” [2], where cars can charge themselves with integrated solar panels placed on the vehicle without relying on external charging stations. The goal is to generate enough energy for an electric vehicle to run a distance equivalent to the average trip distance of a car (29.5 km) [3], Although there are many doubts about the feasibility of solar vehicles with inherent disadvantages such as the influence of temperature on solar cell performance, solar panels all have a temperature coefficient, and most manufacturers’ declared maximum performance is carried out in a laboratory environment (25 ℃) and typical solar cells output losses of approximately 0.2–0.5% are expected for each degree above 25 ℃. In summer working conditions in Korea, temperatures can reach up to 40 ℃ under direct sunlight, and efficiency can decrease from 4% to 10%. Another factor to consider is that solar panels are sensitive to shade since the cells in a solar panel are often connected in a series. Therefore, if just one cell of the solar cells in that series of arrays is shaded, the performance of the whole system will be significantly reduced. In addition, installing solar panels on a car makes the car less attractive.

Despite these drawbacks, research has gradually addressed each problem to provide a clear and viable future for this new technology [4]. Manufacturers not only invest in new solar cell technologies such as improving solar panel efficiency with new materials and structure [5], but they also focus on optical design, such as static photovoltaic concentrators, to maximize the power generated from sunlight [6] or maximize the area of solar cells mounted around the vehicle. Improving the efficiency of solar cells is an idea pursued by many electric vehicle manufacturing companies due to its high applicability and virtually no change to the vehicle structure [7].

New generations of solar cells are continuously being introduced to increase conversion efficiency. Currently, these solar cells focus on multilayer structures to improve the performance of single-material cells. The layers have materials with different band gaps to broaden the solar energy absorption spectrum, thereby providing better performance.

However, this new battery technology also encounters many difficulties. In the case of structures based on InGaAs material, they have high stability, a long life similar to silicon solar cells, and continuously improved performance. Recent studies with this cell structure have shown a performance of 45%, which will get higher in the near future, and commercial products using it have 40% efficiency. However, the high price of solar cells with this material prevents car manufacturers from pursuing research on it. A new type of material with great potential in solar cells for electric vehicle applications is perovskite material. This material structure is much more affordable and has a recorded efficiency of up to 33.9% [8]. The main disadvantage of this material is its short lifespan, and so it requires more time to commercialization.

To reduce the cost of solar systems on electric vehicles, integrated optical structures that reduce solar cell area while maintaining overall efficiency have been rapidly developed recently, typically static photovoltaic concentrator systems. Applying static concentrator photovoltaic technology without using a sun-tracking system has many benefits and outstanding advantages compared to high-concentrator photovoltaic systems (HCPV) that require a very accurate sun-tracking structure. Firstly, these systems have a thin and light structure. Their thickness is only a few centimeters, so they are suitable for applications with strict space and stability requirements [9]. Secondly, because they do not use a sun tracking system to maintain a very tight acceptance angle, they only need simple maintenance such as cleaning the surface, similar to PV flat panel solar cells, so operations will be easier and less expensive. Thirdly, static concentrated photovoltaic (CPV) systems with a concentrator ratio (C_R) normally less than 10× work in a less harsh environment than HCPV systems with a C_R of up to 1,000×, so optical components can be made at a cheaper cost without worrying about material degradation in an HCPV environment.

Furthermore, HCPV systems are mostly only effective with direct sunlight, whereas static CPV systems easily operate with both direct and diffuse sunlight. Therefore, static CPV systems can be applied to more weather conditions and have better environmental adaptability. For example, a CPV system with a C_R of 200× [9], when applied in a place with direct sunlight accounting for 80% of the total radiation, will have an efficiency of 34.5%. However, when applied to conditions where direct sunlight accounts for 50% of total radiation, the efficiency is 21.5%, a reduction of 37.7%. When applied under similar conditions, a static CPV with a C_R of 4×, achieves efficiency of 26.7% and 25.15%, respectively, with a difference of only 5.8% [10]. This gives outstanding advantages to static CPV in applications that require high stability, such as rooftop solar collectors in EV applications. A case study of a static CPV applied to an EV was introduced by Sato et al. [11], using aspherical lenses with a concentrator ratio of 3.5× connected to high-performance solar cells to capture light with an incident angle of 60°. This structure is also very flexible due to the use of many separate parts connected together to meet the requirements of the non-planar structures of EVs [12]. However, this structure only allows about 50% of direct sunlight to be collected by high-performance solar cells, and the remaining radiation is collected by low-efficiency panels placed below.

To increase the amount of solar radiation reaching multi-junction solar cells, the use of CPCs is an optimal solution [13]. The typical CPC is a combination of two parabolic mirrors with axes of symmetry tilted [14]. We can obtain the relationship between the concentration ratio and the acceptance angle by the folowing fomula:

where the C_R is the concentrator of the CPC and is calculated by dividing the area of the input surface of the CPC (d_in) by the output surface of the CPC (d_out).

Divergent light with an incidence angle less than or equal to Ɵ will exit at the output of the CPC (d_out), while divergent light with an incidence angle greater than Ɵ will be reflected at the edges of the CPC and then reflected back to the aperture (d_in) [15]. This process is shown in Fig. 1. To reduce light loss when their incident angle is greater than the acceptance angle of CPC, we use a solid CPC with the same structure as a mirror CPC but filled with dielectric material such as glass or acrylic [16]. This will lead to a significant advantage: When light has an angle of incidence greater than the acceptance angle of the CPC, it will not be completely reflected at the surface of the CPC and return to d_in. Instead, it will refract between the two environments and leak out of the solid CPC toward the bottom surface, where a Si cell absorbs them. Filling the CPC with dielectric material also allows the acceptance angle of the CPC to be increased, for example, when using a CPC with a C_R of 4×. According to Eq. (1), the acceptance angle of the mirror CPC will be 30°, but for solid CPCs with a refractive index of 1.49, their acceptance angle will increase to 44.7° according to Snell’s law. A specific description of this phenomenon is shown in Fig. 2.

Figure 1. Structure and working principle of a mirror compound parabolic concentrator (CPC) with different incidence angles: (a) Equal to Ɵ, (b) less than Ɵ, and (c) greater than Ɵ.

Figure 2. A static solar system under light rays with (a) an incidence angle less than Ɵ of the compound parabolic concentrator (CPC), (b) incidence angle greater than Ɵ, and passing though the CPC wall to the Si cell.

To implement this prototype, we used an evaluation of the static CPV design that we referenced in a previous study [10]. The evaluated CPCs have a C_R of 2.25×, 4×, and 6.25×, according to which C_R of 4× has a half-acceptance angle of 44.7° and can work effectively for 8 hours per day. Detailed parameters of the evaluated CPV are shown in Table 1. We selected the 8-hours-per-day condition because it is best suited for car roof applications, in accordance with [17] shown most users will leave their car in a parking lot for an average time of 7.9 hours per day. Other sizes of CPCs are decided based on commercial multi-junction solar cells. We chose a rotational symmetry and solid CPC design with a C_R of 4×; the CPC is constructed of acrylic material with a refractive index of 1.49, and the bottom of the CPC is circular in shape with a diameter of 1 cm to suit the multi-junction solar cell [18]. The overall design consists of nine CPCs coupled with nine solar cells; The PV panels are placed below with a size of 6 × 6 cm, as shown in Fig. 3.

Figure 3. A 3D rendering of a static concentrator photovoltaic module.

TABLE 1. Main parameters of the static concentrator photovoltaic module.

Specifications
Concentration Ratio	4×
Module Thickness (mm)	25
Half-angle of Acceptance (°)	44.7
Module Size (cm)	6 × 6
CPC Material	Acrylic
CPV Cell	Triple-junction with the Size of 1 cm × 1 cm
Efficiency of the CPV Cell (%)	30
Efficiency of the PV Cell (%)	18

Figure 4 shows the fabricated static CPV with nine CPCs arranged in a 3 × 3 array (left-hand side of the figure). The CPCs are coupled with multi-junction solar cells and are connected to each other by serial connection. A flat Si panel is placed below the CPV structures, and all components are attached together with clear epoxy [19]. The CPC array was made with acrylic with a geometrical concentration ratio C_R of 4× (CPC aperture diameter: 20 mm; bottom diameter: 10 mm).

Figure 4. Fabrication of static concentrator photovoltaic modules.

3.1. Evaluation of the Acceptance Angle of the Module

To evaluate the effectiveness of the design, we conducted simulations of the module’s acceptance angle and compared the simulation with experiment results. The acceptance angle is defined as the incident angle of the light ray at which the light received at the output of the CPC reaches 90% of the light incident at the input of the CPC. The combined optical performance of the module was also evaluated. Because the module consists of two collectors, we evaluated the optical performance individually for each component.

We conducted the simulation using LightTools^TM software. The light source has a power of 1 W, a divergence angle of 0.26° similar to the sun, and has a spectrum taken from terrestrial solar spectrum data with a range of 200 nm–2,000 nm [20]. Because the CPCs have a rotationally symmetric structure, the light source will change the angle in one direction from 0 to 70° and thereby simulate the output energy of the CPC and the energy reaching the Si cell surface. In the experiment, we used the same conditions with an LED light source with a collimation angle of ±0.5° and a radiation of 848 W/m², as shown in Fig. 5. The experimental optical efficiency of CPC is calculated by dividing the short-circuit current obtained on the solar cell with a CPC attached by four times the short-circuit current on the solar cell without a CPC. The efficiency of the flat Si cell is calculated by dividing the short-circuit current obtained on the Si cell with a CPC on top by the short-circuit current of the Si cell not integrated with the CPC structure.

Figure 5. Experimental setup showing the irradiation of the LED in the workplace, and the module with different angles of incident light.

The simulation and experimental results are shown in Fig. 6, where there are negligible differences with light with an incident angle varying from 0 to 55°. When the incident angle of the light source changes from 0 to 40°, the optical efficiency of the CPC structure will be stable at 78% and the optical efficiency of flat Si cell is 19%. When the incident angle of the light source is greater than 40°, the optical efficiency of the CPC gradually decreases, and the optical efficiency of the flat Si cell gradually increases because the incident light escapes from the CPC and reaches the Si cell surface. The acceptance angle of the module is 43° and the average optical efficiency of the module within the acceptance angle range is 96.7%. When the incident light is greater than 55%, there is a difference between simulation and experiment because the experimental light source is not a perfectly collimated light source like the simulation, and also includes light with a divergence angle greater than 0.5°, which affects the experimental results at large incidence angles.

Figure 6. A comparison of simulation and experiment data of the dependence between incidence angle to optical efficiency for each solar cell.

3.2. System Performance in an Outdoor Test

The daily power generation performance of the static CPV module was evaluated by performing actual outdoor experiments. Figure 7 shows the experimental setup conducted under clear skies conditions on May 25, 2023, at the campus of Myongji University in Yongin City, Korea. Before testing, the module was calibrated by exposing it to sunlight for 30 minutes to equilibrate the temperature, prevent sudden changes during the evaluation, and avoid affecting the photoelectric conversion result [21]. Main parameters of the static CPV module is shown in Table 1. Accordingly, the temperature measured on the surface of the solar cell was 36 ℃, because the panels were bonded by epoxy and calibrated, which can be considered the temperature of the entire module during the test. The test was evaluated for 6 hours from 10 am to 4 pm and data was collected every 15 minutes using the PROVA 1011 solar system analyzer (PROVA Instruments Inc., New Taipei City, Taiwan). The device measured the current-voltage (I–V) characteristics of the solar cell and calculated the peak power generation in that case. We did not test the module with chargers and inverters so that we could obtain P_max data to perform a comparison with our previous simulation.

Figure 7. Configuration of static concentrated photovoltaic (CPV) performance test.

Because solar cell modules will usually be installed permanently on the vehicle’s roof and parallel to the ground the module’s power generation efficiency was compared with global horizontal irradiance (GHI), which is the total irradiance from the sun on the horizontal surface of the Earth. GHI is the sum of the diffuse horizontal irradiance (DNI) (after accounting for the solar zenith angle of the sun (z)) and DHI:

The experiment collected the GHI and the maximum power generated from the solar cells and then compared them to evaluate the module’s performance, as shown in Fig. 8.

Figure 8. Power generation of the module with a C_R of 4× in an outdoor test environment.

The results show that the module with a C_R of 4× has an overall efficiency of 22.85%, in which the efficiency of the multi-junction (MJ) solar cell and SI cell are 21.67% and 1.18%, respectively. During the test period from 10:00 AM to 4 PM (six hours), the efficiency of the two solar cell modules remained virtually unchanged, as shown in Table 2. Compared to the calculation in a previous report [10], the average daily power generation of the module decreased by approximately 2.3%, from 22.85% to 25.15%. This result can be explained by several factors: Using solar cells with lower efficiency than calculated, setup factors such as CPC quality, loss due to CPC coupling with solar cells, and dust on the surface of the CPC.

TABLE 2. Performance of static concentrated photovoltaic (CPV) module in an outdoor test environment.

Parameter	Value
Total Radiation (Wh)	4,208
Power Generation by CPV Cells (Wh)	912
Power Generation by PV Cells (Wh)	50.7
Daily Module Efficiency (%)	22.85

In this study, a static CPV module was designed, and the basic characteristics of the prototype were measured. The structure of the module included CPCs, multi-junction solar cells, and a Si cell panel. Acceptance angle measurements showed that the module has a wide acceptance angle of approximately 43° and that the module also allows the collection of diffuse sunlight to improve overall performance. Outdoor experiments also showed that the module works very effectively in a low-concentration environment with a concentrator ratio of 4×. The system has an average efficiency of 22.85% during the day. With a typical electric vehicle having an average consumption of 132 Wh/km [22], a module with an area of 2 m² can provide electricity to help vehicles run an additional 14.6 km/day, although the measurement was made in Korea, which represents a northern hemisphere climate with approximately 50% direct irradiation.

Nguyen Van Nhat was funded by Vingroup JSC and supported by the Master, PhD Scholarship Programme of the Vingroup Innovation Foundation (VINIF), Institute of Big Data, code VI-NIF.2021.ThS.31.

This work was supported under the framework of international cooperation program managed by the National Research Foundation of Korea (Grant no. NRF-2022K2A9A1A06092471) and by the Vietnam Academy of Science and Technology (Grant no. NVCC04.04/22-23); Nguyen Van Nhat was funded by Vingroup JSC and supported by the Master, PhD Scholarship Programme of Vingroup Innovation Foundation (VINIF), Institute of Big Data, code VI-NIF.2021.ThS.31.

The authors declare no conflicts of interest.

Data underlying the results presented in this paper are not publicly available at this time, but may be obtained from the authors upon reasonable request.