# Measurement and Modeling of 3D Solar Irradiance for Vehicle-Integrated Photovoltaic

^{1}

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## Abstract

**:**

## Featured Application

**This technology is expected to be applied to vehicle-integrated photovoltaic.**

## Abstract

## 1. Introduction

^{2}, temperature loss is 9%, Maximum power point tracking (MPPT) loss is 5%, DC-to-DC converter (DC is direct current) loss is 10%, battery charging and discharging loss is 5%, Electronic Control Unit (ECU) loss is 0.12 kWh/day, mileage is 12.5 km/kWh for electric vehicles (EVs), 10 km/kWh for plug-in hybrid vehicles (PHVs), and the battery size is 40 kWh to EVs and 10 kWh to PHVs. Then, the requirement of the car roof PV is 1 kW. As a result, 70% of cars (runs less than 30 km/day) are expected to run by solar energy [2,3,4]. When we multiply 71 million vehicles (annual sales in 2017), the expected sales are 50 GW/year (50,000,000 kW/year) [5]. The above calculations assume that the solar cells are stabilized with no or negligible degradation. However, some solar cells degrade with time, and this should be considered, in case such type of solar cells such as, amorphous Si [6], perovskite [7], crystalline Si [8], and Si module [9] are used. The photovoltaic is also useful for auxiliary powers and range-extension of other low-carbon energies, like hybrid vehicles [10], electric vehicles [11], as well as researches on innovation of the usage of solar energy [12] like, auxiliary power [13], charging [14], and support for fuel cells [15].

## 2. Model

- Greater chance of shading by objects around the car (trees and buildings)
- Curved surface
- The orientation angle randomly varies
- Mismatching loss by partial shading

#### 2.1. Shading Probability

#### 2.2. 3D Irradiance Model

#### 2.3. Relation to the Conventional Solar Irradiance Model

_{roof}is the irradiance onto the car roof. Q

_{side}is the averaged irradiance of the car sides. Since the orientation of the car is independent of the sun’s orientation, the side irradiation may be regarded as the averaged value from four car sides. Φ is the main angle of the solar beam onto the car roof. Q

_{th}is the threshold of the effective measurement value of the irradiance. It must be greater than zero (non-zero value). NaN represents a missing or faulted value. D is the discriminant of the non-shaded condition. False (= 0) if the car roof is shaded. The function if(condition, x, y) returns x if the condition is true (non-zero), y otherwise. The function max(A, B, C, ...) returns the largest value from A, B, C, ... The function min(A, B, C, ...) returns the smallest value from A, B, C, ... Note that Equation (10) contains a two-dimensional vector calculation, and Equation (11) contains the Boolean algebra.

_{1}, Qs

_{2}, ax

_{1}, and ax

_{2}are parameters calculated by Equations (12)–(15) and are used in Equation (16). G is the orientation angle of the main solar beam. Dir is the orientation angle of the car. The function max2nd(A, B, C, ...) returns the second largest value from A, B, C, ... The function mod(x, y) returns the remainder on dividing x by y (x modulo y). The result has the same sign as x. The function sign(x) returns 0 if x = 0, 1 if x > 0, and −1 otherwise. Note that Equations (14)–(16) contain Boolean algebra.

#### 2.4. Angular Distribution Model

#### 2.5. Curve Correction Model

#### 2.5.1. Why the Curved PV Modules are Often Overestimated in Efficiency Measurements

^{2}and uniform in the entire area of the aperture area $A$. For the standard flat PV module, the aperture area $A$ is the same as the module active area. However, this definition is not applied to the curved PV module because the aperture area is defined as the window of the flat plane, and not the curved surface.

#### 2.5.2. Examples of the Curve-Correction Calculations

_{1}is the coving factor, or in another way, geometrical curve correction factor corresponding to the ratio of the projected area by surface area, f

_{2}is the irradiance ratio due to the local cosine loss and self-shading loss, in other words, optical curve correction factor. The parameter f

_{1}may represent the overall shape of the curved surface.

#### 2.5.3. Curve-Correction Calculation Based on Ray-Tracing Simulation

_{1}dominates it, but the optical curve correction also decreases by the increase of the curvature as well. However, the optical influence depends on the surface shape, and it is essential to calculate its factor to every curve surface.

_{2}, significantly vary by the site conditions, including latitude, climate pattern, and shading environment (urban zone or rural zone). This is because of the difference in the distribution of the incident angle onto the curved surface (Figure 10).

#### 2.6. Partial and Dynamic Shading Model

- In the sun
- Full shade
- Partial shade

**SF**(n, Nstrings) is a function that generates a vector containing the number of shaded cells in each string. n is a scalar parameter of the number of cells in a string. Nstrings is a scalar parameter of the number of strings in a module.

**floor**(z) is a function that returns the greatest integer ≤ z.

**rnd**(x) is a function that returns a uniformly distributed random number between 0 and x.

**if**(cond, x, y) is a function that returns x if cond is true (nonzero), y otherwise.

**stack**(A, B, C, ...) is a function that returns an array formed by placing A, B, C, ... top to bottom.

**submatrix**(

**A**, ir, jr, ic, jc) is a function that returns the matrix consisting of rows ir through jr and columns ic through jc of array

**A**.

**Ir**in Equation (22) is an array that contains solar irradiance of each cell in the module affected by partial shadings. STI is a scalar parameter of the diffused sunlight onto the module plane.

**Scn**is a vector that contains a number of the unshaded cells in each string in the module.

**Snp**is a vector that contains a number of partially shaded cells in strings.

**runif**(m, a, b) is a function that returns a vector of m random numbers with uniform distribution, and m is a scalar of real values, a ≤ m ≤ b. To allow integration and other operations over this argument, values outside of the stated range are allowed, but they produce a 0 result. a and b are real numbers, a < b. DTI is a scalar parameter of the direct sunlight onto the module plane. TIS is a scalar parameter of the total sunlight onto the module plane.

## 3. Results

#### 3.1. 3D Measurement by Multiple Pyranometer Array

_{x+}, Q

_{x−}, Q

_{y+}, Q

_{y−}, and Q

_{z}are defined, as shown in Figure 12. One pyranometer is placed horizontally on the car roof (Q

_{z}), and four pyranometers are placed vertically facing each side of the car (Q

_{x+}, Q

_{x−}, Q

_{y+}, Q

_{y−}). The global irradiance onto the car roof (I

_{z}) is measured using a pyranometer Q

_{z}. The global irradiance onto the side of the car (I

_{x+}, I

_{x−}, I

_{y+}, I

_{y−}) is measured using pyranometers Q

_{x+}, Q

_{x−}, Q

_{y+}, Q

_{y−}. The direction of the moving car is equal to that of Q

_{y+}. An ambient temperature meter (Pt 100 temperature sensor) is also placed on the car roof. The GPS is incorporated into the data logger, and data are recorded in 1 s intervals. The total number of hours of sun radiation (more than 10 W/m

^{2}in I

_{z}) received over the year was 3374 h, while the number of hours the car was running was approximately 6% of this.

#### 3.2. Measurement Example of the Solar Irradiance on the Car Roof and Car Side

#### 3.3. Validation of the Solar Irradiation Model around the Car (Intensity)

#### 3.4. Validation of the Solar Irradiation Model around the Car (Angle)

## 4. Discussion

#### 4.1. Simplified Rating Method of VIPV Considering 3D Solar Irradiance

- Measure the PV performance in five directions (see Figure 2).
- The rating of the total performance in the specific area can be weighted by the normalized solar resources using Equation (23) and the values in Table 2, namely,$$P=a{P}_{z}+b\left({P}_{x+}+{P}_{x-}\right)+c\left({P}_{y+}+{P}_{y-}\right)$$
_{z}is the measured power output by the illumination on the car roof. P_{x+}, P_{x−}, P_{y+}, and P_{y1}are the measured power outputs by the illumination on the car sides in the direction defined in Figure 1. a, b, and c are weighting coefficients given by Table 2. Note that the coefficients a, b, and c in our measurement in Miyazaki, Japan are 0.925, 0.395, and 0.435, respectively. Equation (21) gives a total energy output of the entire PV system on the vehicle considering 3D solar irradiance around the vehicle comparable to GHI.

#### 4.2. Estimation of the Practical Solar Resource to VIPV in Other Regions

#### 4.3. Partial Shading Issue

#### 4.4. Limitation of the Model

#### 4.5. Feasibility of the VIPV Based on Our Measurement and Modeling

#### 4.6. Future Works

- Improvement of the shading model. The current model is useful but too simplified, especially in the urban area. Note that more than 45° of the average shading height is not allowed, because the maximum height becomes more than 90°. Even in the area of Miyazaki, the average height of 15.5° means that the maximum height should be 31°. However, there are many buildings of more than 31°. Possibly, we need to develop a curved trend, namely the two parameters model.
- Modeling of partial shading validated to the measured data. To do this, we need to start monitoring the partial shading on the car roof and car body.
- Validation of energy yield using the real curved PV module.
- Validation of the shading model by several areas with different shading height and shading density.
- Development of the spectrum model for predicting energy yield by multi-junction solar cells on the car roof and car body.

## 5. Conclusions

_{2}on a well-to-wheel basis. The typical approach is an electric vehicle (EV) [47] charged by the electricity generated by renewable energy like solar power [48]. The primary energy should be renewable energy; otherwise, a significant reduction of the greenhouse gas emission will not be expected [49]. However, this approach relies on the infrastructure of the distribution of clean electricity (PV power station installation, grid construction and connection, distribution of the clean electricity, and installation and operation of the EV charging station). It is much more convenient that the car collects solar energy and runs by it (or at least extending the range of mileage supported by its PV modules to reduce the frequency of charging).

- A simple shading model to VIPV was developed and validated by one-year monitoring on the solar irradiation on the car roof and car body in five axes.
- The curve-correction model of the curved surface of VIPV was developed.
- A mismatching model using Monte Carlo simulation was developed to analyze the partial shading of VIPV.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of the segmented annular region for modeling distribution of the shading objects around the photovoltaic (PV) panel.

**Figure 3.**Three-dimensional irradiance around the car body [1].

**Figure 4.**Illustration of the underestimation of the input energy in the measurement of the curved PV module.

**Figure 6.**Illustration of the multiple definitions of the module area: (

**a**) principle ray direction in testing, although the illumination by the typical solar simulators is not collimated, and the field of view is typically ±10° to ±45°; (

**b**) principle ray direction in the outdoor operation. The outdoor illumination is the mixture of the collimated light (direct sunlight) and diffused sunlight (illumination from the sky and reflection by surroundings). The ratio of the collimated and diffused light varies by climate; (

**c**) example of the distribution level in the outdoor operation calculated by the ray-tracing simulation. The light-green arrow lines correspond to the direct sunlight. The blue arrow lines correspond to the scattered sunlight. The color gladiation on the curved surface indicates the non-uniformity of the irradiance on the curved surface. The darker color indicates lower irradiance.

**Figure 7.**Geometrical relation between the curved PV panel (curved detector, opaque gray surface) and light source (corresponding to the projected area, semi-transparent light-blue area). The line segment around the light source (semi-transparent light-blue area) corresponds to the rays emitted from the light source. The short line segments correspond to the ray that does not reach the curved surface. The longer line segments correspond to the one that hits the curved PV panel (curved opaque gray surface), namely the ray that is absorbed by the PV. Note that rays just above the module do not always hit the module due to its curvature [1].

**Figure 8.**Curve correction factor vs. representative curve shape parameter (coving factor as f

_{1}).

**Figure 10.**Correction factor vs. representative curve shape parameter (coving factor as f

_{1}) in two extreme cases. One is the urban zone in Bangkok (N 13.7° and 4.87 kWh/m

^{2}/day global horizontal irradiance, GHI), drawn by a blue line, and the other is a rural zone of Omsk (N 54.9° and 3.34 kWh/m

^{2}/day GHI) drawn in an orange line: (

**a**) curve-correction factor f; (

**b**) optical curve correction factor f

_{2}.

**Figure 11.**Solar irradiance distribution on the curved surface of the PV panel. The light-green arrow lines correspond to the direct sunlight. The blue arrow lines correspond to the scattered sunlight. The color gladiation on the curved surface indicates the non-uniformity of the irradiance on the curved surface. The darker color indicates the lower irradiance.

**Figure 14.**Monitored the result of the solar irradiance on the car roof and car sides in the driving route in Figure 13.

**Figure 15.**Monthly-based comparison between the measured solar irradiance around the car (bar-chart) and modeled (typical year from the METPV-11 solar database, namely, MEteorological Test data for PhotoVoltaic system) solar irradiance on the car (line-chart): (

**a**) car roof irradiance; (

**b**) car side irradiance.

**Figure 16.**Daily-based comparison between the measured solar irradiance around the car (blue dots) and modeled (typical year from the METPV-11 solar database) solar irradiance on the car (orange dots): (

**a**) car roof irradiance; (

**b**) car side irradiance.

**Figure 19.**Map of the effective solar irradiance for the car roof: (

**a**) curve-correction factor in a typical car roof; (

**b**) effective solar resource to the car roof normalized to GHI, including the loss by the curved surface; (

**c**) correlations between latitude (related to the sun height) and the curve correction factor; (

**d**) correlations between latitude (related to sun height) and the effective solar resource to the car roof normalized to GHI, including the loss by the curved surface.

**Figure 20.**Distribution of the normalized efficiency of some design of the car roof PV affected by synthesized partial shading given by the Monte Carlo simulation. Note 1/6 or more cut is recommended for suppressing partial-shading loss to <10%.

Section | Distribution | Type | Range |
---|---|---|---|

Date (day number) ^{1} | Uniform distribution | Integer | 0–364 (day) |

Time ^{1} | Uniform distribution | Integer | 0–23 (h) |

Number of cells partially shaded ^{2} | Uniform distribution | Integer | 0 (Number of cells in the string) |

Number of cells fully shaded ^{2} | Uniform distribution | Integer | 0 (Number of cells in the string) |

Shading ratio of each partially-shaded cell ^{3} | Uniform distribution | Real | 0–1 |

Car orientation ^{4} | Uniform distribution | Real | 0°–360° |

Isc of each cell | Normal distribution | Real | -- |

Voc of each cell | Normal distribution | Real | -- |

Diode ideality ^{5} | Normal distribution | Real | Greater than 1 |

^{1}Repeat throwing a dice until the horizontal global sunlight given by the database is more than 1 Wh/m

^{2}to avoid the inclusion of the trial in the nighttime. The bissextile day is removed.

^{2}Random numbers are given to each string. The number of partial and fully shaded cells must be less than the number in the strings.

^{3}The ratio of the partial shading (0 to 1).

^{4}Assuming that the car always parks or runs on the horizontal plane.

^{5}Representing the shape of the I–V curve.

**Table 2.**Comparison of model and measurement (relative to GHI) by one-year monitoring of a passenger’s car.

Measured | Model by Rough Physical Measurement | Modeled by Parameter Fit (Average Height of Shading Objects and Reflectance of the Road) ^{1} | |
---|---|---|---|

Car roof | 0.925 | 0.929 | 0.925 |

Car side (x-direction) | 0.395 | 0.412 | 0.395 |

Car side (y-direction) | 0.435 | 0.435 |

^{1}The degree of freedom and the number of fit parameters are the same (= 3).

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**MDPI and ACS Style**

Araki, K.; Ota, Y.; Yamaguchi, M. Measurement and Modeling of 3D Solar Irradiance for Vehicle-Integrated Photovoltaic. *Appl. Sci.* **2020**, *10*, 872.
https://doi.org/10.3390/app10030872

**AMA Style**

Araki K, Ota Y, Yamaguchi M. Measurement and Modeling of 3D Solar Irradiance for Vehicle-Integrated Photovoltaic. *Applied Sciences*. 2020; 10(3):872.
https://doi.org/10.3390/app10030872

**Chicago/Turabian Style**

Araki, Kenji, Yasuyuki Ota, and Masafumi Yamaguchi. 2020. "Measurement and Modeling of 3D Solar Irradiance for Vehicle-Integrated Photovoltaic" *Applied Sciences* 10, no. 3: 872.
https://doi.org/10.3390/app10030872