Impact of Additional PV Weight on the Energy Consumption of Electric Vehicles With Onboard PV

Photovoltaics (PV) in onboard vehicle applications adds weight to an electric vehicle (EV), increasing the overall energy consumption. Although the added PV system weight is small compared with the vehicle weight, the power generated by PV is also very small compared with the power needed to propel an EV, making the effect of additional PV system weight on energy consumption a nontrivial topic to analyze. We present a method to study the impact of the vehicle onboard PV weight on the energy balance of EVs for different vehicle-added PV and vehicle-integrated PV configurations. The results are expressed through a newly introduced parameter called “onboard PV yield factor,” where positive values indicate a net energy gain and negative values indicate a net energy loss of the onboard PV system. Simulations are carried out to highlight the methodology for the driving phase of a medium and large passenger electric car with onboard PV for a selection of trips. Our method calculates the energy consumption attributable to the added PV system weight and PV energy yield for the selected trips. Our results for these sample simulations for the driving phase show a large range of yield factors, indicating the importance of systematically studying the impact of onboard vehicle PV weight.

Impact of Additional PV Weight on the Energy Consumption of Electric Vehicles With Onboard PV Neel Patel , Karsten Bittkau , Bart Elger Pieters , Evgenii Sovetkin , Kaining Ding , and Angèle Reinders Abstract-Photovoltaics (PV) in onboard vehicle applications adds weight to an electric vehicle (EV), increasing the overall energy consumption.Although the added PV system weight is small compared with the vehicle weight, the power generated by PV is also very small compared with the power needed to propel an EV, making the effect of additional PV system weight on energy consumption a nontrivial topic to analyze.We present a method to study the impact of the vehicle onboard PV weight on the energy balance of EVs for different vehicle-added PV and vehicleintegrated PV configurations.The results are expressed through a newly introduced parameter called "onboard PV yield factor," where positive values indicate a net energy gain and negative values indicate a net energy loss of the onboard PV system.Simulations are carried out to highlight the methodology for the driving phase of a medium and large passenger electric car with onboard PV for a selection of trips.Our method calculates the energy consumption attributable to the added PV system weight and PV energy yield for the selected trips.Our results for these sample simulations for the driving phase show a large range of yield factors, indicating the importance of systematically studying the impact of onboard vehicle PV weight.

I. INTRODUCTION
R ECENTLY, the number of prototypes and products for onboard vehicle photovoltaics (PV) has increased [1], [2].Research work has also been ongoing in various aspects of onboard vehicle PV.PV module-specific research focuses on module curvature [3], aesthetic [4], interconnection [5], and integration [6], to name a few.In terms of control electronics, studies have been conducted to determine the required response times for onboard PV maximum power point trackers (MPPTs) [7] and the design of dc-dc circuits [8].Various approaches to model the energy yield for onboard PV applications have also been published in [9], [10], [11], and [12].Measurement campaigns to estimate the PV resource for onboard PV have been reported and are ongoing [13], [14], [15].Since vehicle onboard PV has to adhere to various automotive standards, some draft standards have been proposed [16].Innovative designs for PVpowered electric mobility concepts have been published in [17].Social acceptance and sustainability analysis of onboard PV applications have been reported in [18] and [19], respectively.Regarding the weight of PV technologies, some products and approaches have been proposed in [20] and [21], respectively.
Onboard PV is a unique application where the PV system is moving.It is vital to estimate how much energy is required to enable that motion and whether the energy yield of onboard PV is sufficient to satisfy that demand.Despite the progress in multiple research themes for onboard PV technologies, the impact of the additional weight of onboard PV systems, covering PV modules and (control) electronics, has yet to be studied or reported.However, the weight of the vehicle onboard PV system for electric cars, in the range of 1.5-40 kg (scaled specific weights in kg/m 2 of different PV technologies to the roof area of medium to large passenger electric cars), is small compared with the weight of an electric vehicle (EV) in the 1500-2200 kg range (weight for medium to large passenger electric cars).Moreover, the power produced by the onboard vehicle PV in the 55-700 W range (scaled specific power in W/m 2 for different PV technologies to the roof area of medium to large passenger electric cars) is insignificant compared with the power needed to propel the vehicle up to 80-285 kW (motor power for medium to large passenger EVs).This differential nature of the weight and power of onboard PV and the car makes the impact of the weight of onboard PV a nontrivial issue.The question now is whether the added weight and power produced by vehicle-added PV (VAPV) and the vehicle-integrated PV (VIPV) configurations positively affect the energy balance of the EVs.A positive effect implies that the onboard PV system produces more energy after accounting for the additional energy required to propel its weight.In contrast, a negative effect implies that additional energy is required from the EV battery to propel the onboard PV system weight.The prime focus of this study is the impact of onboard PV, assuming that the combined total weight of the vehicle and onboard passengers (except PV system weight) is constant throughout.
Analyzing the effects of weight on the energy consumption of passenger vehicles is a standard procedure in the automotive industry.Doing so for onboard PV weight and coupling it with the PV system's energy yield gives more understanding to the automotive and the PV industry of how additional weight will influence the design of small, medium, and large passenger cars with onboard PV configurations.Therefore, the results of this study have implications for selecting proper onboard PV technology considering different PV technologies' efficiency, cost, weight, and degradation rates.
The rest of this article is organized as follows.Section II describes the tools and input parameters needed to perform the analysis along with the defined scenarios and introduces the onboard PV yield factor to study the weight impact.Section III describes a set of special case parameters used as an example to highlight the functioning of the methodology.Section IV describes the results of this special case.Finally, Section V concludes this article.

II. METHOD
We propose a method to study the impact of additional PV weight on the energy balance of vehicles, which combines two existing simulation tools, namely the future automotive systems technology simulator (FASTSim) [22] tool developed by the National Renewable Energy Laboratory (NREL) and PVWatts [23].FASTSim is used to calculate EV energy consumption, while the PVWatts model is applied to determine the onboard PV energy yield.Based on the simulations, an onboard PV yield factor (from here on yield factor) will be determined, see the following equation: where F y = onboard PV yield factor (%); E y = energy yield (Wh/km); ΔE a = additional consumption (Wh/km).
The yield factor is calculated for a set of trips conducted during a period, for instance, a few months.Mean values of energy yields (Wh/km) and additional consumptions (Wh/km) for a set of trips are used to calculate the yield factor.A balanced set of day-time and night-time trips representing realistic drive profiles leads to a balanced yield factor calculation.Considering only night-time trips will lead to a negative infinity yield factor as the energy yield during the night is zero, and considering only day-time trips will lead to an overestimated yield factor.A positive yield factor indicates a net energy gain, while a negative yield factor indicates a net energy loss due to the onboard PV system.Equation ( 1) is used to calculate the yield factor during the driving phase of the vehicle.
Since parking time is also a part of the operation of a vehicle with onboard PV, it is essential to calculate the yield factor during parking.During parking, the vehicle will have zero additional consumption due to onboard vehicle PV weight and positive energy yield during the daytime.Assuming the yield factor during the parking phase as 1, we introduce the total yield factor as a simple weighted sum of the driving and parking phases, as shown in (2).It is important to note that since night-time parking has no additional consumption or energy yield, it is not considered a part of the operation and is omitted from the total time (t t ) where F yt = total yield factor (%); F yd = driving phase yield factor (%); t t = driving fraction of the total time.
Below, detailed information is provided on how the EV energy consumption (see Section II-A) and PV energy yield (see Section II-B) are calculated for various scenarios (see Section II-C).

A. EV Energy Consumption
The power needed at any given instant to propel an EV is a summation of multiple power demands of subsystems and the various physical forces the vehicle has to overcome.A simplified version of this power demand and expanded weight-dependent powers are shown in (3)- (6).A detailed explanation of each of the terms in (3) can be found in [24] and [25] P T = P w + P d + P x Weight independent + P a + P s + P r − P b Weight dependent (3) where P T = total power demand (W); P w = power to overcome rotational inertia of wheels and transmission (W); P d = power to overcome wind drag (W); P x = auxiliary power consumption (W); P a = acceleration power needed (W); P s = power to overcome road slope (grade) (W); P r = power to overcome tire rolling resistance (W); P b = regenerative braking power (W).
The weight-dependent variables can be further expanded to where m = total mass of the vehicle (kg); a = vehicle acceleration (m/s 2 ); g = gravitational acceleration (m/s 2 ); α = road slope (grade); C r = coefficient of rolling resistance.
Regenerative braking power P b is also a weight-dependent variable not defined by a specific relationship but rather a regenerative strategy dependent on the vehicle speed and is limited by the battery power, battery state of charge, and motor capacity.The regenerative braking strategy deployed in FASTSim is described in [22].
Ambient weather conditions, such as high wind speed and extreme temperatures, can impact vehicles' energy consumption.High ambient wind speeds can create resultant drag force, increasing or decreasing energy consumption.Extreme ambient temperatures can significantly affect the battery performance of an EV, requiring more energy consumption to maintain the battery at an optimum temperature.However, it is essential to note that not all power demand terms depend on the system's weight.The weight-dependent power demand terms are highlighted in the equation.Since ambient wind and temperature are weight-independent external variables, their impact has been assumed constant for all simulations in this study.Passenger and cargo weight also affect the energy consumption of the vehicle.Since our focus is to study the weight impact of onboard PV only, passenger and cargo weight is assumed to be 136 kg for all simulations constantly.
For this study, we use the open-source energy consumption model implemented in the FASTSim tool developed by NREL [22], version 0.1.0,implemented in Python.FASTSim calculations result in an EVs energy consumption in Wh/km for different drive cycles and weight scenarios.
FASTSim is a high-level tool for rapid simulation of efficiency, performance, cost, and battery life of various vehicle categories, including EVs.The vehicle is represented by its various components, simulated through speed-versus-time drive cycles.At each time step, FASTSim accounts for drag, acceleration, ascent, rolling resistance, each powertrain component's efficiency and power limits, and regenerative braking [22].It offers the best accuracy with the lower complexity of operation, thanks to its ability to run on the most critical vehicle parameters publicly available.It also provides a set of vehicles in the form of an included database with parameters necessary to execute energy consumption simulations.
A subset of the parameters of two such electric cars used in this study is mentioned in Table I.These sets of vehicles and the overall models within FASTSim have been extensively validated, whose results can be found in their validation report [26].The energy consumption model validation is done using the highway fuel economy test (HWFET) and urban dynamometer driving schedule (UDDS) standard driving cycles recommended by the United States of America's (USA) Environmental Protection Agency (EPA).The FASTSim simulated energy consumption numbers for these standard drive cycles are then compared with the EPAs so-called window sticker values.FASTSim requires a set of other input variables to execute the energy consumption simulations of different vehicle types.The drive cycle is one such input that comprises a timestep (s), vehicle speed (m/s), and road grade (%).Road grade determines the slope of the road on which the vehicle is traveling and is calculated using the method adapted from [27].Road grade is calculated outside of FASTSim by smoothing the global positioning system (GPS) elevation data and taking the differential between consecutive GPS points of a trajectory.The two most important variables influencing a vehicle's additional energy consumption due to the added weight are vehicle speed and road grade values.Vehicle specifications, such as curb weight, drag coefficient, frontal area, battery and motor capacities, and efficiencies, are taken directly from the FASTSim database and used without modifications.More details about which drive cycles and vehicle models are used in this study are mentioned in Section III.

B. PV Energy Yield
The energy yield of the onboard PV system is calculated using the PVWatts model described in [23] and implemented in PVLIB-Python [28], version 0.9.3.The result of this calculation is an electrical power time series in W generated by an onboard PV system for a given drive cycle, which we integrate and divide by the distance of that particular drive cycle to determine the energy yield of the PV system in Wh/km.
PVWatts calculates the dc power generated by the PV system, given all the input variables and a system loss factor to consider various system losses.Calculating a total system loss factor from various individual losses is also described in [23].For onboard PV applications, mismatch, wiring, parasitic consumption, and curvature losses are the most important contributors to the total system loss factor.Since it is challenging to determine concrete system loss factors for onboard PV, given that only a little measurement data has been published, we are assuming a range of values, respectively, 5%, 25%, and 40%, in this study.It is important to note that shading loss is not deducted as a loss factor but is already incorporated in the POA irradiance used to calculate the yield.

C. Scenarios
After quantifying the additional EV energy consumption and PV energy yield for PV technologies in the VAPV and VIPV scenarios, the onboard PV yield factor, according to (1), is determined to estimate the impact of the added weight of each PV technology.The PV technologies used in the VAPV and VIPV scenarios are different in terms of the added weight.
EV energy consumption calculations have been executed with FASTSim for the following three configurations: reference, VAPV, and VIPV, see below, using a set of drive cycles, as described in Section III.According to the configuration and the PV technology used, the additional weight of the onboard PV system is directly added to the curb weight of considered vehicles.
Reference: This configuration represents no added PV or control electronics weight.Energy consumption numbers from this case will be subtracted from other configurations to calculate the additional consumption.For the considered weight scenarios, there will be an addition of the control electronics weight (except for the reference scenario).Control electronics are assumed to consist of an MPPT and a dc-dc boost converter that feeds the PV power directly to the traction battery of the vehicle system.After considering the onboard PV system combinations for VAPV and VIPV configurations, simulations are run for the considered vehicles and drive cycles.Fig. 1 visualizes the flow of data and calculations performed.Additional consumption for each scenario is estimated by subtracting results from each weight class with the reference configuration.These give additional consumption due to PV technology in the VAPV and VIPV configurations.

III. INPUT DATA
To show the functioning of the presented methodology in Section II, a special case of parameters is selected and simulated to estimate the weight impact of onboard vehicle PV.For this, two EVs, a set of drive cycles derived from measurement data (during daytime only), and various PV technologies are selected.However, the method itself is generalized enough to calculate the weight impact of onboard vehicle PV for different types of vehicles, drive cycles (consisting of day-time and night-time trips as well as parking time), and PV technologies, and is not limited to the input data selected in this special case study.
Information about the EV models used in this study is mentioned in Section III-A, measurement data, and drive cycles used for simulations using FASTSim and PVWatts are mentioned in Section III-B, and the considered PV technologies in VAPV and VIPV configuration are mentioned in Section III-C.

A. Vehicle Specifications
This study uses the 2016 Nissan Leaf and 2016 Tesla Model S EVs for simulations.The vehicle specifications are taken from the FASTSim database as is.It is assumed that onboard PV is located only on each vehicle's roof area, with 1.8 m 2 for the Leaf and 2.5 m 2 for the Tesla Model S [29].Some of the vehicle specifications are shown in Table I.

B. Drive Cycles
The drive cycles used for EV energy consumption are derived from data from measurement campaigns described in [13] and [14].These campaigns took place in 2021 around Germany's Jülich and Hannover regions.The variables used in this study are the timestamps (s), GPS vehicle speed (m/s), GPS elevation (m), roof irradiance (W/m 2 ), and roof cell temperature (°C).It is important to note that we only consider the scenarios when the vehicle is driving.The datasets have an average measurement frequency of 0.5-1 Hz and were measured from March to October 2021.For rare cases when collected data are fragmented, i.e., during a trip, certain parts are not recorded due to GPS errors or some other externality; such trips are excluded from this study.In total, we use data from 260 completed trips in this study.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.We deliberately avoid using standard drive cycles, such as the UDDS, HWFET, New European Driving Cycle, and worldwide harmonized light vehicles test procedure to conduct our analysis as estimating or measuring irradiance data for the standard drive cycles would be difficult since these drive cycles have no associated location data.Since we already have comprehensive measured data suited for this analysis, we opt to use it rather than generate synthetic datasets based on the standard drive cycles.
Measurement data from the Jülich campaign mentioned in [14] are open source and available for download at [30].

C. PV Technologies
The PV technologies considered in our case study are PERC, IBC, SHJ, CdTe, CIGS, Micromorph (MM), and OPV, with a specific power range of 22-249 W/m 2 (see Table II).Their efficiency ranges from 2.1% to 24.9%, with silicon technologies, such as PERC, IBC, and SHJ being dominant.As per our considered configurations, we classify the weights of different technologies in terms of VAPV and VIPV.To study the impact of the weight of these technologies on energy consumption, we consider the specific weight in kg/m 2 scaled to the roof size of considered vehicles.Table II presents the specific weights for VAPV technologies that are calculated from the specification sheets of various commercial products.Since no flexible commercial modules are available for CdTe technology, we are considering the glass-glass utility-scale product [31].The PV weights assumed here are examples, and the weights in real applications can vary dramatically.This consideration of the CdTe module also highlights the drawback of using a glassglass module for onboard PV applications.The specific weights of VIPV technologies consist of the weight of the PV active material only consisting of cell material, interconnects, and a single layer of encapsulant (ethylene-vinyl acetate) weighing about 150 gm/m 2 .The weights of active materials of different PV technologies and the encapsulant are taken from [32].It is assumed that the PV cells are sandwiched with the vehicle roof glass sheets at the back and the front sides.This sandwich structure provides structural and mechanical durability to PV cells and protection against humidity.
The energy yield of the considered PV technologies is computed using the specific power in W/m 2 scaled to the roof size of the considered vehicles.The energy yield of the considered PV technologies is calculated using the specific power in W/m 2 scaled to the roof size of the considered vehicles.We assume

TABLE II LIST OF PV TECHNOLOGIES AND THEIR SPECIFIC WEIGHT, POWER, AND TEMPERATURE COEFFICIENTS OF POWER
the same power of the VAPV and VIPV configurations for simplification.The specific power is calculated using the total area and rated power values mentioned in the specification sheets (cf.Table II).We are not considering the aperture area or designated illuminated area but the total area defined in [33] to calculate the specific power.
The temperature coefficients of power are taken from the specification sheets or literature with the exact sources, as mentioned in Table II.The considered PV technologies and their specification sheets are from commercially available onboard PV products and not the state-of-the-art of each technology.
Since it is difficult to find commercial offerings of the control electronics to track the onboard PV output and feed it into the high-voltage traction battery, we assume their weight based on the generic ones available for the automotive sector.For example, a dc-dc converter for an automotive application can weigh around 2.5 kg, as seen in some examples [34], [35].Typically, these converters are rated in the ranges of several kW, and onboard PV for passenger cars will almost certainly be in the range of a few hundred to a thousand watts; the assumed control electronics weight in this study could be an overestimation for most cases.To address this uncertainty, we are assuming the weight of the control electronics consisting of MPPT, dc-dc converters, and wiring as three scenarios of 1, 2.5, and 5 kg.

IV. RESULTS AND DISCUSSION
We present simulation results for the special case parameters, as described in Section III: two electric cars fitted with different PV technologies in two different configurations, assuming different electronics' weights and system loss factors.Fig. 4 shows the additional consumption in Wh/km attributable to the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.onboard VAPV weight as simulated using FASTSim.Additional consumption is calculated by subtracting the consumption of a reference case (without onboard PV) from the consumption with various onboard PV scenarios.The boxplot shows results for considered PV technologies in the VAPV configuration for the 260 trips.Each box plot represents the additional energy consumption of individual trips attributable to respective PV system weights.The variations in the boxplot for each technology are attributable to the different vehicle speeds and driving terrain for the simulated trips.Although the outliers are not shown for each boxplot for clarity, the mean and median values already incorporate them.Similar additional consumption results for the VIPV configuration are shown in Fig. 5, which highlights that the weight of electronics will have more impact on the additional consumption, it being considerably higher than the PV weight itself for most cases.For the VAPV configuration, the average additional consumption is in the 0.06-1.4Wh/km range for the considered technologies.For most VAPV technologies, the impact from assumed electronics' weights is not significantly high as the PV weights are also high.Similarly, for VIPV configuration, the additional consumption is in the average range of 0.05-0.26Wh/km.For VIPV technologies, the impact from assumed electronics' weights is relatively higher as the PV weights are low.However, the additional consumption in all cases is still lower than the VAPV configuration for the respective technologies.
Fig. 6 shows the energy yields calculated for the different PV technologies using the PVWatts model.Three boxplots for each PV technology represent variations in the assumed system loss factors.The variations in energy yields of each PV technology are attributable to the fact that the irradiance measurements for these trips were carried out for different times of day, Fig. 6.Energy yield for different PV technologies in Wh/km.The lighter shade represents a loss factor of 40%, the medium shade is 25%, and the darker shade is 5%.Fig. 7. Yield factors for VAPV configuration.The heatmap represents yield factors for nine combinations of electronics weight and system loss factors for eight VAPV technologies.The VAPV weights are the same as in Fig. 4. The columns are broadly divided according to the electronics weight ranges of 1, 2.5, and 5 kg, with each column representing the respective loss factors in the range of 5%, 25%, and 40%.The best-case scenario is on the left of the respective figures with an electronics weight of 1 kg and a loss factor of 5%.The worst-case scenario is on the right, with an electronics weight of 5 kg and a loss factor of 40%.
weather, and surroundings.The energy yields during the trips are converted to Wh/km for uniform comparison with additional consumption.
We assume that the energy yields are the same for the VAPV and VIPV configurations.The energy yields for the considered PV technologies average in the 0.12-3.12Wh/km range.Some boxplot values are close to zero, representing driving scenarios during early morning and late evening when the available irradiance is low.
Simulated additional consumption and energy yields enable us to calculate the yield factor, see (1), to determine the impact of the weight of each PV technology in the VAPV and VIPV configurations.
A yield factor of 100% would indicate that the onboard PV weight has zero impact on the vehicle's energy balance.A yield factor of 0% indicates that the total energy yield compensates for the consumption attributable to additional weight.A negative yield factor suggests that the car consumes more additional energy than it can generate due to the onboard PV.We calculated the yield factor for each PV technology in VAPV and VIPV configuration, using the results, as shown in Figs.4-6, for nine combinations of assumed electronics weight (three variations) and system loss factors (three variations).We calculate the yield factors using the mean values for each PV technology in the boxplots of Figs   The specific PV weights are in the 0.25-10 kg/m 2 range, which are scaled to the respective car roof area, and an electronics weight of 2.5 kg is added.These composite system weights are shown on the X-axis.The efficiencies are in the 5%-25% range, reducing performance by a system loss factor of 25%.The similarly calculated composite weights of different VAPV technologies (except CdTe and OPV) are annotated on the contour plot.configuration.This large range of yield factors for the PV technologies in VAPV or VIPV configurations indicates that the weight of the vehicle onboard PV technologies is a nontrivial aspect, especially when energy yield during parking time is not considered.
Since the PV technologies for onboard applications vary in weight and efficiency, it is essential to know how the yield factor is impacted beyond the PV technologies we have considered in the VAPV and VIPV configurations.To address this, we calculate the yield factor for the same set of trips and vehicles for a range of weight values from 0.25 to 10 kg/m 2 and efficiencies of 5%-25%, irrespective of the PV technology.The results of this calculation are presented as a contour plot and show how different PV weight and efficiency values impact the yield factor for onboard PV applications.
Since we do not consider any specific PV technology in this case, the temperature coefficient of power is neglected for energy yield calculations.The results are shown in Fig. 9 as a contour plot.The PV technologies considered in the VAPV scenario are annotated on the contour plot for reference.The contour plot can help determine the performance of other PV technologies in terms of weight.
It can be seen in the yield factors presented for various scenarios that VAPV configuration has more impact than VIPV.It is important to note that the yield factors we calculated consider the energy yield during the driving phase only, which is a worst-case scenario.There is also a bias stemming from the time of day of the considered trips.The trips are in the daytime, with no trips occurring at night when the onboard PV energy yield is zero.Including night-time trips will decrease the magnitude of yield factors.On the other hand, considering the energy yield during the day-time parking phase would increase the yield factors for all scenarios.
The yield factors presented here are not meant to rate different PV technologies concretely.To reach such ratings, the trips used to calculate these yield factors must be more comprehensive, consisting of day-time and night-time trips and parking time data.In addition, the PV technologies used are only sometimes state-of-the-art.Instead, our emphasis is on the method to quantify the ratings of PV technologies in terms of weight.Such methodology can also be applied to commercial vehicles, such as vans and trucks, where weight is even more significant.
One aspect that needs to be added to the current study is the inclusion of PV on the sides of the vehicle.We estimate that the weight of PV on the sides of the vehicle will be even more critical as the energy yield from the sides will be significantly lower due to the nonoptimal angle of incidences.

V. CONCLUSION
We presented a method to study the impact of vehicle onboard PV weight on the energy balance of EVs.Simulation results for a special case of two EVs, a selection of measured trip data, and different PV technologies in VAPV and VIPV configurations were presented as a newly introduced yield factor to highlight the methodology.It is important to note that the PV technologies assumed in this study are randomly selected to get a weight estimate to demonstrate the methodology.For this special case in VAPV configuration, the yield factors range from −69.1% to 86.9% for the worst-case scenario and 47.6% to 96.5% for the combined best-case scenario for both vehicles.Given the lightweight of the VIPV technologies, the yield factors are relatively better, with 77.2%-89.7% in the worst-case scenario and 94.5%-98.2% in the best-case scenario for both vehicles combined.The presented yield factors only account for the driving phase without considering the parking state.Even though our simulations were performed on a limited set of trips for two specific EVs and are not suitable to concretely rate PV technologies in terms of weight, they show that the impact of PV weight for onboard applications is nontrivial, especially for VAPV configuration.Furthermore, combined with comprehensive trip and parking state data, this method can determine which technology makes more sense in onboard PV applications from a weight perspective.

Fig. 1 .
Fig.1.Representation of the data flow and calculations executed to determine the yield factors for various scenarios.Various inputs and outputs are marked with their respective units.X, P, V, V 0 , L, and E represent the variables changed in a loop to execute simulations for all scenarios mentioned.X is the individual trip/parking, P represents the different PV technologies (in both VAPV and VIPV configuration), V represents the considered vehicles in either VAPV or VIPV configuration, V 0 is the vehicle in reference configuration, L is the PV system loss factor with values of 5%, 25%, and 40%, and E is the electronics weight with values of 1, 2.5, and 5 kg.

Fig. 2 .
Fig. 2. GPS trajectories for the Jülich (left) and Hannover (right) datasets.The Jülich trips are more spread out compared with the commuting pattern of the Hannover trips.Trips at both locations were mostly on flat terrains.

Fig. 3 .
Fig. 3. Histograms of distance, vehicle speed, road grade, and roof irradiance from the combined Jülich and Hannover datasets.

Fig. 4 .
Fig. 4. Additional consumption for VAPV configuration in Wh/km.The left image shows results for the Nissan leaf and the right for the Tesla model S (This is true for the rest of the figures as well).The green triangles indicate the mean, and the red lines indicate the median.The PV technologies considered (MM stands for micromorph) are shown with the weight of each system in kg scaled to the respective car roof area (1.8 m 2 for Nissan leaf and 2.5 m 2 for Tesla Model S).On top of the PV weight, three different electronics' weights are added for each technology, which can be seen as three separate boxplots.The lighter shade represents an electronics weight of 1 kg, the medium shade is 2.5 kg, and the darker shade is 5 kg.

Fig. 5 .
Fig. 5.Additional consumption for VIPV configuration in Wh/km.The PV technologies considered are shown with the weight of each system in kg scaled to the respective car roof area (MM and OPV technologies are not considered).On top of the PV weight, three different electronics' weights are added for each technology, which can be seen as three separate boxplots.The lighter shade represents an electronics weight of 1 kg, the medium shade is 2.5 kg, and the darker shade is 5 kg.
. 4-6 to avoid skewed yield factors for cases when the energy yield for the trips that occur very early in the morning or late evening have close to zero value.The yield factors for the nine combinations of electronics' weights and loss factors are shown as a heatmap in Figs.7 and 8 for VAPV and VIPV configurations, respectively.The VIPV technologies are already lightweight compared with VAPV technologies, so their yield factors for the worst-case scenario are relatively much better.CdTe in the VIPV configuration performs significantly better considering the lightweight option than in the VAPV Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

Fig. 8 .
Fig. 8. Yield factors for VIPV configuration.The results are represented in the same manner as in Fig. 7, except that MM and OPV technologies are not considered.

Fig. 9 .
Fig. 9. Contour plot for various PV weight and efficiency ranges.The color and different levels show the yield factors for considered weights and efficiencies.The specific PV weights are in the 0.25-10 kg/m 2 range, which are scaled to the respective car roof area, and an electronics weight of 2.5 kg is added.These composite system weights are shown on the X-axis.The efficiencies are in the 5%-25% range, reducing performance by a system loss factor of 25%.The similarly calculated composite weights of different VAPV technologies (except CdTe and OPV) are annotated on the contour plot.

TABLE I VEHICLE
SPECIFICATIONS ARE TAKEN FROM THE FASTSIM DATABASE