The parking dilemma for solar-powered vehicles

Abstract

Parking a solar electric car in the sunshine will help charge its battery, increasing its driving range. On the other hand, it will also raise its indoor temperature, leading to the need to switch on the air conditioning to make it comfortable when driving, increasing the driving load and reducing the vehicle range. Thus, one may wonder if the solar-extended range is somehow reduced or even eliminated by the increasing demand due to air conditioning. To address this “parking dilemma”, we have characterized the thermal properties of a passenger car for typical summer conditions in a moderate latitude temperate location (Lisbon, Portugal) to be able to explore the vehicle's thermal performance when parked in the sun. Results show that effective solar charging depends critically on the onboard installed PV capacity. For the specific conditions tested and a 0.5 kWp PV system, the critical parking time below which the parking session does not contribute to net charging is around 2 h. For systems with more than 0.8 kWp installed capacity, parking in the sun always provides a positive impact on the vehicle's driving range.

1. Introduction

Solar-powered electric vehicles (EV) are a promising approach to decreasing the use of fossil fuels and lowering CO2 emissions [1,2], extending the daily range of EVs [3] and reducing the frequency of charging events thus decoupling, or at least mitigating, the electrification of mobility from the investment in the charging infrastructure [4].

The solar-extended driving range due to the integration of photovoltaics (PV) in EVs will depend on the installed capacity, which may range from 200 to 1200 Wp [5], and the available solar resource which, of course, will depend on the location, the time of the day and time of the year [6] as well as local shading [7,8]. The typical solar-extended driving range has been estimated to be of the order of 10–20 km/day for a wide variety of conditions [9,10].

The "parking dilemma" in the context of solar-powered vehicles is defined as resulting from the trade-off between charging the vehicle's battery by parking it in the sun and the increase in the indoor temperature of the vehicle, requiring air conditioning. On one hand, parking the vehicle in the sun allows the solar modules to generate electricity and charge the battery, thereby increasing the range of the vehicle. On the other hand, solar radiation also heats up the interior of the vehicle, making it uncomfortable for the occupants [11]. Temperatures as high as 76 °C can be reached inside a vehicle for an outdoor temperature of 41 °C and a solar irradiance of about 800 W/m² on a hot summer day [12]. To cool down the interior of the vehicle, the air conditioning system is used [13], drawing energy from the charged battery. This creates a "parking dilemma" for the owner of the solar-powered vehicle, as the decision to park in the sun to charge the battery also increases the cooling load and reduces the range of the vehicle.

Air conditioning is an important feature in EVs as it provides a comfortable driving experience translated into a cabin temperature setpoint of about 20 °C in the summer [14]. The use of air conditioning in EVs can have a significant impact on the vehicle's operation range, where several developments can take place to improve the energy efficiency of the system itself, while the optimization of local flow and glazing schemes can reduce energy consumption to meet cabin thermal requirements [15,16].

The air conditioning system in an EV is powered by the vehicle's battery, which means that it draws energy from the same source that powers the vehicle's propulsion system [17], and thus leads to a reduction in the vehicle's range. Regardless of technological advances employing effective energy-saving strategies, the impact of air conditioning on the range of an EV can be quite significant with some studies reporting its reduction of up to 50% due to cabin cooling requirements during a hot season [18] although other studies using newer EVs driven at speeds close to 100 km/h show range losses below 20% for outside temperatures close to 40 °C [19]. On the other hand, a climatization system operated in cooling mode may only represent 14% of the load of an EV during an urban driving cycle in a mild summer country [20]. The air conditioning systems in light-duty EV cars in the US can have an average annual energy consumption range of 1300–2300 kWh per vehicle [21]. The thermal management system used to maintain the optimal battery operation conditions seems to have a lower consumption when compared to air conditioning, with the other auxiliaries showing the lowest energy consumption shares [22].

To explore the parking dilemma for solar cars, the study presents a simplified thermal model (section 2) used to experimentally characterize the thermal properties of a passenger car for typical summer conditions in a moderate latitude temperate location (section 3). Then, the model is used to analyse the vehicle's thermal performance when parked in the sun (section 4), exploring the concept of critical parking time (section 4.1) and discussing the limitations of the method (section 4.2). Section 5 concludes, aiming to provide insights into the trade-off between solar charging and air conditioning and to identify strategies to optimize the range of solar EVs.

2. Vehicle thermal model

The simplified thermal model of the vehicle can be described by equation (1).

$$G-H\left(T-T_a\right)=mC\frac{dT}{dt}$$ (1)

In this equation, $G$ [W] is the solar gain, $H$ [W/°C] represents the thermal losses, $T$ [°C] is the indoor temperature whilst $T_a$ [°C] is the ambient outdoor temperature. On the right side of equation (1), $mC$ [Wh/°C] represents the thermal mass of the vehicle. Fig. 1 schematically represents the energy balance of the vehicle.

Fig. 1.

Schematically representation of the energy balance of the vehicle.

All of these variables refer to effective values for the vehicle as a whole, as it is composed of many different materials (with different mass and heat capacities) with different optical and thermal properties, such as the transparent windshields and the opaque rooftop or hood. The solar gain $G$ will depend on the solar irradiance but also the sun elevation and azimuth and the parking orientation of the vehicle and its geometry.

For constant solar gain, the solution to the thermal balance of the vehicle is equation (2), where we have imposed the initial condition $T\left(t=0\right)=T_a$.

$$T\left(t\right)=T_a+\frac{G}{H}\left(1-e^{-\frac{H}{mC}t}\right)$$ (2)

Thus, in an experiment where the vehicle at ambient temperature is placed in the sunshine, the time constant allows the estimation of $H/mC$ whilst the final temperature is a measure of $G/H$.

It should be noted that the solar gain $G$ increases with the incident irradiance on the horizontal plane ($GHI$) but it is not known a priori because it depends on many factors, including the effective area of transparent windows, the orientation of the vehicle relative to the position of the sun in the sky or the thermal conduction of the opaque surfaces.

In a second experiment, the vehicle is parked in the shade and heated using an electric heater (whose heat output is known or can be measured). In this case, $G$ refers to the heat gain (here represented as $q$). For low $T$, we can neglect the thermal losses $H$ and therefore the solution is as shown in equation (3).

$$T\left(t\right)=T_a+\frac{q}{mC}t$$ (3)

Experimental data leads to the estimation of $q/mC$ which, combined with the results of the first experiment, allows the unequivocal determination of $mC$, $G$ and $H$.

3. Vehicle thermal characteristics

The sample vehicle is a mid-sized car (Alfa Romeo 156, Fig. 2a), light grey with a black leather interior. The experiments were conducted in Lisbon, Portugal. Solar irradiation was measured on the rooftop of the vehicle using a Jinie 1.0 (a calibrated custom-made solar irradiance measurement instrument based on the short-circuit current of a silicon solar cell) while the indoor ambient temperatures were measured using an infrared thermometer DeltaTRAK 20901 mounted on the gear shift console (Fig. 2b), avoiding direct irradiance during the experiments.

Fig. 2.

Illustration of the experimental setup, including (a) rooftop solar irradiance measurement and (b) indoor temperature measurement.

Experiment I was conducted for a diversity of solar conditions, where the car was initially parked in the shade from the day before, and then moved to the sunshine at a time before peak solar irradiation takes place. The experiments were carried out with the car's front side oriented 20° towards the southeast (south: 0°). Experimental results for Experiment I are illustrated in Fig. 3, featuring the solar irradiance (blue line) and the indoor and outdoor temperatures (red and orange lines, respectively) as a function of the local time (UTC+1). For this particular experimental run, one can observe that the vehicle was parked in the shade until about 12:30, before being parked in the sunshine. Solar irradiance peaked at about 2:00 p.m., a little earlier than the outdoor temperature peak. The indoor temperature peaked at about 5 p.m.

Fig. 3.

Experimental results for one particular day: indoor and outdoor temperature (red and orange lines, respectively), solar irradiance (blue dots) and numerical fit to indoor temperature (black line) using equation (2).

For the numerical fit to the indoor temperature using equation (2), only data between 12:30 and 3:00 p.m. are considered due to the restriction of ‘constant’ solar gain. This approximation neglects the 10% variation (between 700 and 770 W/m²) of the irradiance in the horizontal plane in that period and the change in solar gain due to the change in the angle of incidence associated with the apparent movement of the sun in the sky.

Experiment II consisted of heating the car cabin using an electric heater coupled to a fan, with the car parked in the shade. The heater was installed on top of the car's dashboard and turned backwards to homogeneously spread the heat in the cabin. With all doors/windows closed, the experiment was conducted for about an hour, with the heater set to an average power $q$ = 500 W. The initial car cabin and outside temperatures were 21.5 °C. A linear increase of the cabin temperature over time was verified, as shown in Fig. 4, where a total of 390 Wh were used to raise the cabin temperature by 3 °C. After fitting the data points, a slope of approximately 4 °C/h was obtained for the current experimental conditions.

Fig. 4.

Experimental results for the car cabin temperature as the function of the heater switch on time (blue dots). The dashed line is the linear fit to the data points.

Fitting the experimental results for Experiments I and II, using equations (1), (2)), respectively, allows the determination of the relevant parameters, shown in Table 1. It may be noticed that the solar gain (1800 W) is about 2.5 times the solar irradiance on the horizontal plane (730 W/m²) due to the effect of the aperture area of the windshield and the body of the car, considering the angle of incidence and the total effective area of the vehicle.

Table 1.

Experimental estimation of thermal characteristics of the vehicle.

Experimental conditions	Variable	Value	Units
$GHI=$ 800 W/m2 $T_a=$ 20 °C	$G$	1800	W
	$H$	60	W/°C
	$mC$	125	Wh/°C

It should be noted that the purpose of these experiments and the lumped-parameter thermal model, is only to estimate the order of magnitude of the thermal characteristics of a typical vehicle, to allow for the exploration of the ‘parking dilemma’. The detailed thermal modelling of the vehicle would require a more extensive set of experiments under changing solar/geometry conditions.

4. Parking dilemma

4.1. Critical parking time

When the car is parked in the sunshine, its indoor temperature will increase as described by equation (2). If a car ride starts at a given time $t$, the energy $Q$ required to bring the indoor temperature to a comfortable range (assumed to be the ambient temperature since we are assessing the impact of the extra cooling load due to the parking) may be approximated by equation (4), where equation (1) was used to describe the difference between the indoor and the ambient temperatures and $COP$ is the coefficient of performance of the air conditioning heat pump, assumed to be $COP=$ 2.3 [18].

$$Q=\frac{mC}{COP}\left(T\left(t\right)-T_a\right)=\frac{mC}{COP}\left(\frac{G}{H}\left(1-e^{-\frac{H}{mC}t}\right)\right)$$ (4)

On the other hand, the accumulated solar energy during the parking period $t$ is given by equation 5

$$E=\eta AGHIt$$ (5)

where $\eta$ is the PV efficiency, $A$ is the effective area of the PV system and $GHI$ the global horizontal irradiation. As usual, the installed PV capacity [kWp] is defined as $P_i=\eta A\times 1$ kW/m².

Fig. 5 shows the extra cooling load (orange line) and PV-generated electricity (blue dashed line) for the particular case of $P_i=$ 0.5 kWp. One can observe that for parking periods below 2h, the extra cooling load exceeds the generated electricity and therefore parking the vehicle in the sunshine leads to an effective loss of range. For parking periods above 2h, the generated electricity exceeds the extra cooling load; therefore, it is beneficial to park the car in the sunshine. For the case of 1 kWp of installed PV capacity (blue solid line), the generated electricity always exceeds the extra cooling load and it is always adequate to park the vehicle in the sunshine (if the battery is not already full).

Fig. 5.

Extra cooling load (orange) and solar-generated electricity for 0.5 kWp (blue dashed line) and 1 kWp (blue solid line) PV capacity.

Nevertheless, it should be pointed out that the effective solar charge after a 3h parking period for a 1 kWp is about half of what would be estimated if the AC load was not taken into consideration. This effect is even more relevant for low PV installed capacities.

It can also be noted that both the extra cooling load (equation (4)) and the PV generation (equation (5)) are proportional to the irradiation and therefore the results are independent of the irradiance level.

The critical parking time, which may be defined as the minimum parking time required for the PV generation to exceed the AC load, will thus depend on the installed PV capacity. Fig. 6 shows how the critical parking time depends on the onboard installed PV capacity. We can observe that, for the tested conditions, a PV capacity exceeding 0.8 kWp always allows parking in the sunshine whilst for lower installed capacities only long-duration parking is beneficial.

Fig. 6.

Critical parking time as a function of onboard installed PV capacity.

4.2. Limitations

The thermal model used in this analysis is a simplified version of the actual complexity of the problem. In reality, there are various routes through which heat is transferred from the vehicle, including heat conduction to the road, convection to the air which is affected by wind speed, and heat radiation losses to the environment due to the varying emissivity of different materials at different temperatures. This suggests that a more complex solution, featuring multiple time constants, would be more accurate than the presented single time constant model. Examples of this approach include more sophisticated lumped-parameter models such as the work of Marcos et al. [23] modelling a vehicle cabin considering two thermal inertia elements, or 3D computational-fluid-dynamics modelling as reported by Moon et al. [24]. For a thorough review of thermal models see the work of Alahmer et al. [25].

Defining the indoor temperature within the vehicle cabin is not a simple task as it requires taking into account not just the air temperature but also the temperature of various cabin components (such as seats and dashboard) and the heat fluxes between them.

User behaviour can also play a relevant role in the extended range of a parked solar car. For example, the use of a sunshade on the windshield has been shown to halve the increase in indoor temperature [26], which would significantly reduce the air conditioning load, thus extending the solar range. Similarly, opening the windows of the vehicle at the start of a trip to allow for the rapid replacement of hot air with cooler outside air or, to a lesser extent, free cooling i.e. using the ventilation system to bring cooler air from the outside, also reduces the load on the air conditioning system.

On the opposite side, if the EV battery is almost fully charged before the parking session, the PV contribution to the driving range will be less relevant whilst the increased AC load will be the same, and therefore the critical parking time is going to be even shorter. This is known as the full-battery effect [27]. In addition, the increase in temperature resulting from the prolonged parking periods in the sun can lead to a decrease in the car's battery performance and shorter life or even an increase in system energy consumption as the battery pack should be kept within the 15 to 35 °C range [28,29].

It should also be pointed out that the results are only illustrative of the order of magnitude of the energy balance for the parking dilemma as they were estimated for a specific vehicle in particular environmental conditions. The critical parking time will depend on the characteristics of the vehicle (for example, a white-painted vehicle with a small windshield will feature lower solar gains), the environmental conditions (including wind conditions or the parking orientation with respect to the solar azimuth and/or elevation) as well as the efficiencies of the air conditioning and/or the PV system.

The impacts of the diversity of environmental conditions and user behaviour on the parking dilemma for solar cars are worth exploring in detail as solar-powered vehicles enter the market in the next few years.

5. Conclusions

This study examines the solar cars’ parking dilemma, the trade-off between charging the battery by parking the vehicle in the sun and the increased energy usage from the air conditioning system, which results from the higher temperatures inside the vehicle.

A simplified thermal model for the car was created using data from experiments conducted in a location with high solar irradiance and moderate latitudes. The model was then used to evaluate the impact of parking in the sun on the vehicle's PV generation and air conditioning load.

It is found that the effect on the air conditioning load is considerable for vehicles with a low PV installed capacity. Additionally, the "critical parking time" is defined as the minimum amount of time needed for the PV generation to surpass the extra air conditioning load due to the parking session. For the specific conditions tested, the critical parking time is around 2 h for a 0.5 kWp PV system.

For systems with more than 0.8 kWp installed capacity, parking in the sun always provides a positive impact on the vehicle's driving range.

Data availability statement

Data will be made available on request.

CRediT authorship contribution statement

Guilherme Gaspar: Writing – review & editing, Writing – original draft, Visualization, Supervision, Investigation, Formal analysis, Data curation, Conceptualization. Ivo Costa: Writing – review & editing, Writing – original draft, Supervision, Investigation, Formal analysis, Conceptualization. Miguel Centeno Brito: Writing – review & editing, Writing – original draft, Supervision, Resources, Project administration, Methodology, Investigation, Formal analysis, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.