Decision Making for the Design of Solar Cars and Basis for Driving Strategy

Decision making for the design of solar cars and basis for driving strategy

General estimation of recommended mean speed

for solar cars

Main Subject area: Computer Engineering Author: Isac Sélea, Håkan Thorleifsson Supervisor: Rickard Nyberg JÖNKÖPING 2021 February

This final thesis has been carried out at the School of Engineering at Jönköping University within Computer Engineering. The authors are responsible for the presented opinions, conclusions, and results.

Examiner: Rachid Oucheikh Supervisor: Rickard Ninde Scope: 15 hp (first-cycle education) Date: 2021-08-07

Abstract The global interest in green vehicles has been growing since it is letting out less pollution than normal internal combustion engines (ICE) and many people want to get into the ecological-friendly alternative mode of transport. The solar car is one of these types of green vehicles, which is powered by renewable energy with zero emissions. The solar car makes use of its solar panel that uses photovoltaic cells to convert sunlight into electricity to the batteries and to also power the electric motor. The state of solar cars is that it is almost exclusively for competition and when competing a strategy is needed to get the best placement. Having knowledge about how the car is behaving is a good basis for building a driving strategy. Therefore, a case study is made on World Solar Challenge (WSC) focused on the cars of JU Solar team with the use of datasets such as topographical data and solar irradiation. An optimization model is made that inputs these datasets and simulates a time period (an hour) and checks the set battery discharge rate (BDR or C rating). It is concluded that a safe BDR is between 8 to 9 % per hour (i.e. 0.08 to 0.09 C), relative to the full capacity of the battery. Results shows an improved mean speeds of the solar cars and improved finish times. The model also works very well for solar cars that are not meant for racing. Since it keeps a relatively stable state of charge for long term driving, that ensures battery longevity. With these results JU Solar team can use this model to improve their driving strategy but could also be used for economical driving for the future of commercial solar cars. This paper recommends to follow a simple procedure, to keep the BDR on 9% as long as the sun irradiation stays above 800 W/m2, and lower the BDR to 8% if irradiation goes below 800 W/m. Adjustments to increase the BDR for the end of the race is also recommended for optimal driving strategy.

Keywords: solar car, world solar challenge, energy model, MATLAB, driving strategy

Table of content

Abstract ...... ii

Table of content ...... iii

1 Introduction ...... 5

1.1 SOLAR CARS ...... 5

1.2 JÖNKÖPING UNIVERSITY SOLAR TEAM ...... 7

1.3 PROBLEM STATEMENT ...... 7

1.4 PURPOSE AND RESEARCH QUESTIONS ...... 8

1.6 DISPOSITION ...... 8

2 Method and implementation ...... 9

2.1 DATA COLLECTION ...... 9

2.2 DATA ANALYSIS ...... 10

2.2.1 Power consumption ...... 10

2.2.2 Sun irradiation data ...... 12

2.3 THE OPTIMIZATION MODEL ...... 12

2.3.1 Sun data interpolation ...... 12

2.3.2 Simulation model ...... 13

2.4 VALIDITY AND RELIABILITY ...... 15

2.5 CONSIDERATIONS ...... 15

3 Theoretical framework ...... 16

3.1 DRIVING STRATEGY IN PREVIOUS WORK ...... 16

3.1.1 Undulating roads ...... 16

3.1.2 Clouds ...... 16

3.1.3 Other Solar Car Teams ...... 16

3.2 FORMULAS ...... 17

4 Results ...... 19

iii

4.1 THE CARS OF JU SOLAR TEAM ...... 19

4.1.1 Axelent (2019) ...... 19

4.1.2 Solveig (2017) ...... 21

4.1.3 Solbritt (2015) ...... 21

4.1.4 Magic (2013) ...... 21

4.2 ANALYSIS...... 21

5 Discussion ...... 23

5.1 RESULT DISCUSSION ...... 23

5.2 METHOD DISCUSSION ...... 24

6 Conclusions and further research ...... 26

6.1 CONCLUSIONS ...... 26

6.1.1 Practical implications ...... 26

6.1.2 Scientific implication ...... 26

6.2 FURTHER RESEARCH ...... 27

7 References ...... 28

8 Appendixes ...... 30

1 Introduction The global interest in green vehicles has been growing since it is letting out less pollution than normal internal combustion engines (ICE) and many people want to get into the ecological-friendly alternative mode of transport. The world is moving into that direction because many countries have announced plans to ban the sales of ICE vehicles after 2040. The policy has the aim to reduce air pollution and greenhouse gas emissions (Fulton et al., 2019).

1.1 Solar Cars The solar car is one of these types of green vehicles, which is powered by renewable energy with zero emissions. The solar car makes use of its solar panel that uses photovoltaic cells to convert sunlight into electricity to the batteries and to also power the electric motor.

Figure 1. Axelent, Jönköping University Solar Teams 2019 solar car General Motors showcased in 1958 the first solar car that a human could drive. Larry Perkins and Hans Tholstrup in 1982 made the first long distance travel in a solar car, from Perth to Sydney, Australia in 20 days. Later, a race was organized by Hans Tholstrup in Australia called the World Solar Challenge (WSC) to bring more publicity and interest in research of solar cars (Babalola & Atiba, 2021). General Motors won the event and in a response of their victory they partnered with US Department of Energy to organize a solar race in north America. These are the two most notable races of solar car racing but there are many others around the world. The interest of solar cars was in the beginning fueled by research but now it is being referred to as a “brain sport”, with the sole purpose to develop new solar cars for competition and not production. Solar car racing was made to promote interest in the vehicles and demonstrate a proof of concept. Still today it remains a sport for students but continue to improve valuable technologies that could be applied to electric vehicles to provide more efficient and cleaner alternatives over ICE vehicles.

An applied example is the technology in an ICE vehicle can make use of a solar panel that gives energy to a battery. This will put a load off the engine and make less of an environment impact (Connors, 2007). In 2006 a company named Venturi announced the first production solar car called Astrolab, (see figure 2). The projected range was only 110 kilometers (Astrolab - Venturi Automobiles, 2021).

Figure 2. Venturi’s Astrolab solar car In 2019 the Lightyear One (see figure 3). was announced with production expected to start in 2021 with a range of 725 kilometers. The solar panel design came out of the Solar Team Eindhoven's solar car that competed at the WSC (Vijayenthiran, 2019).

Figure 3. The Lightyear One solar car

1.2 Jönköping University Solar Team The solar car racing competition teams are mostly made up of students from different universities around the world. Jönköping University has its own team called Jönköping University Solar Team (JU Solar Team) where students create a solar car that will race at the solar car race in Australia. WSC is an international solar car race that start in Darwin and goes all the way to Adelaide which spans little over 3000 km (see figure 4). They race between 8:00 and 17:00 and usually last for 4-5 days with a number of control stops the teams have to stop at for 30 minutes. This happens every two years and JU Solar Team has been competing in this race four times with last race in 2019 finishing 10th and having the mean speed of 64.6 km/h.

Figure 4. World solar challenge route with all the control stops.

1.3 Problem statement The state of solar cars is that it is almost exclusively for competition. A crucial thing when going racing in solar cars is to have a driving strategy. When teams leave the start line the new energy coming in is only from the sun and that is not always predictable as filling up on fuel. To have the knowledge on how the solar car performs in the race with the changes in solar input is a huge advantage. JU Solar Team currently does not have a proper driving strategy, the team has made simulations of the coefficient of aerodynamic drag (퐶푑퐴) and lift force because of the lack of a wind tunnel. But has not used any pre-race simulation when it comes to driving strategy. This means when the team goes racing, they have no simulation data on how the solar car is going to perform with the changes in both sun irradiation and topographical data. The team has then no clue of how they are going to up the mean

speed of the race to get a better placement than previous year. That is why a simulation software is relevant, so the JU Solar Team can be able to put their solar car in a race simulation to maximize their knowledge about how the car is behaving to be able to use that knowledge to build a driving strategy even before racing events. What JU Solar Team wants from this research is a model that could provide a simulation of optimal mean speeds for changes in sun irradiance, with the possibility to simulate different solar cars with their different properties. Also, to test the precision and accuracy of the model by comparing the results to real life results of historic races.

1.4 Purpose and research questions The purpose of this study is to develop a simple energy model in MATLAB that calculates an optimal mean speed for solar cars, therefore be able to make it from A to B before power runs out. The model must be able to investigate how much the estimated mean speed varies with the different changes in sun irradiation and topographical data. Hence the research questions are: 1. What is the optimal mean speed for different solar car models? 2. How much does the estimated mean speed vary in relation to fluctuations in sun irradiation for different solar car models? 3. With what precision and accuracy can the model estimate the mean speed with the turn-out from the results of earlier solar cars and their properties?

1.5 Scope and limitations There are several factors that can affect the power consumption that will be hard to simulate and will be out of the scope. In a real-world example, road traffic must be considered, that involves traffic jams, overtaking etc. Environmental factors, like rain, wind, tree shades, dust accumulating on the solar panels and temperature also affects the performance on the car. Wind is outside of the scope because the limitations of getting accurate data and making accurate readings of how the wind is behaving on the solar car.

1.6 Disposition In chapter 2 the method is explained and the who the data is collected and analyzed is shown. In chapter 3 driving strategy in previous work is presented and context is given on standard formulas that are used in this study. In chapter 4 results the results are given. Chapter 5 is the discussion of the results of the findings and discuss about the chosen method. Chapter 6 are where conclusions are made of the research and what can be built upon this. In Chapter 7 the references collected for this study in APA system. In Chapter 8 all the figures from the result of the study are here.

2 Method and implementation This study will use quantitative research, and experimental studies to develop a model that estimates the mean speed based on sun irradiation and topographical data. With the collaboration of JU Solar Team this will be combined with the properties of the different solar car models that the team has raced with. The sun irradiation and topographical data are based on where WSC race is held i.e., the route from Darwin to Adelaide in Australia. Earlier work is based on MATLAB code by alumni from prior JU Solar Teams, together with research papers published from other solar car teams. However, no prior research paper in this area has been published by JU Solar Team on this matter. The code provided by alumni of JU Solar Team calculates the power consumption throughout the whole distance by determining the gradient between the points after a down sample to smooth out the calculated gradient of the road. The power consumption is compared to real life topographical data, applying the gradient to the energy equation and presenting it in a graph parallel to the topographic data to the user. MATLAB will be used as the main platform for the simulation. Existing code that has been provided by a JU Solar Team alumni currently only presents a very rough energy consumption estimation, based only on the topographical data. The code will be further developed to include the different aerodynamic properties of the vehicles; combine these aerodynamic properties with imported historical sun data and adding regenerative braking in downhill slopes and at the control stops to make a more realistic simulation of the energy consumption, to be able to answer the research questions. All collected data, e.g. the properties of a certain solar car, will be run through a simulation which will be paired with the solar irradiation data i.e. a simulated race will be run in different types of solar irradiation intensities, that has been historically recorded in the race, with different mean speeds, and present them in figures that will help us identify what the optimal strategy would be for each solar car. 2.1 Data collection Collected data in this paper is elevation data that is based on the route of World Solar Challenge in Australia and has been provided by JU Solar Team. This data describes the elevation changes from Darwin to Adelaide. Figure 5 presents the topographical data as a visual aid. The topographical data is used to calculate the slope angle, it can also be used for hill anticipation as described by Pudney (2000). The slope angle may also be used in calculating the angle of solar panel in relation to the sun, but because of time constraints this is not included in this model. Other collected data includes historical data which consists of sun data from Darwin

and Adelaide provided by Solcast. From JU Solar Team data has also been collected of the solar car, the properties of the car as aerodynamic characteristics like aerodynamic drag coefficient (퐶푑퐴), vehicle weight, electrical properties like motor effect and efficiency, solar panel effect and battery capacity.

Figure 5. The topographic layout the WSC race in Australia, control stops included. The data provided by Solcast consist of a table with different variables (see table 1), the two following variables below are chosen to be used for this simulation (Solar Resource and Weather Data in Time Series, Typical Meteorological Year (TMY) and Monthly Averages, 2021). • GHI Global Horizontal Irradiance, one hour periods. Total irradiance on horizontal surface W/m2, used for solar charge effect • Period Start Start of the period the data was collected UTC Start.

2.2 Data analysis The data that is being analyzed is used to calculate power consumption of the solar car with the properties of the solar car and sun irradiation.

2.2.1 Power consumption The power consumption is calculated minute by minute: 퐸 퐸 퐸 = 퐸 + 푖푛 + 표푢푡 푡표푡 푐푢푟푟푒푛푡 60 60

Where 퐸푐푢푟푟푒푛푡 is the current charge of the battery in Watt hours (Wh), 퐸 푖푛 is the energy from the solar panel and the regenerative brake of the electrical motor, 60 divided by 60 to get the total Wh produced for that minute. 퐸 표푢푡 is the energy to the motor divided by 60 to get the total Wh produced during that 60 minute. Regenerative braking runs at every control stop where the car brakes to a full stop. 푀 ( ∗ (푣2)) 퐸 = 2 ∗ 휇 푅푒푔푒푛 3600 Where 푀 is the mass of the car in kg, 푣2 is the initial speed of the car, and 휇 is the efficiency coefficient of the regenerative braking system. The dynamic regenerative braking is used when a certain slope angle is reached, and in this case, based on Mocking, (2006) the angle is 1°. The formula used in to calculate the regenerated energy in Wh: 푚𝑔ℎ 퐸 = ∗ 휇 퐷푦푛푅푒푔푒푛 3600 Where 푚𝑔ℎ is the potential energy of the car, and ℎ is the difference in elevation the car has traveled during that minute, and 휇 is the efficiency coefficient of the regenerative braking system. Figure 6 shows an example on how the battery charge may vary during a 24-hour period during the race with the following car properties (see table 2):

Figure 6. Total energy and distance traveled during a 24-hour period

Solar panel area 4 m2

퐶푑퐴 0,089

Solar panel efficiency 20%

Weight 200 kg

Wheels 4

Battery capacity 6300 Wh

Battery voltage 115.2V

Average speed in race 64.6km/h

Table 2. car properties of Axelent (2019)

2.2.2 Sun irradiation data The global horizontal coefficient (퐺퐻퐼) will be used from the sun irradiation dataset to calculate the charge from the solar panel. The charging effect, in watts, of the solar panel is calculated:

퐸푆표푙푎푟퐶푎푟푔푒 = 퐴 ∗ 퐺퐻퐼 ∗ 휇 Where 퐴 is the total area of the solar panel, 퐺퐻퐼 is the global horizontal coefficient and 휇 is the total efficiency coefficient of the solar panel. 퐺퐻퐼 represents sunlight on a horizontal plane, which is what the solar panel of the car will be during the race.

2.3 The Optimization Model

2.3.1 Sun data interpolation The data provided by Solcast has a resolution of one hour between each datapoint, but to ensure that the data will work better with our simulation and provide a more realistic result, interpolation will be utilized. The interpolation will increase the resolution from hourly data points to minute-by-minute basis (see figure 7). The method used for interpolation is a modified variant of the Akima interpolation method Akima (1970), provided by Matlab (Modified Akima Piecewise Cubic Hermite Interpolation - MATLAB Makima, 2019). The modified Akima (makima) method

should be more pessimistic and avoid overshoots more, compared to other interpolation methods

Figure 7. Example of sun GHI data, before and after makima interpolation

2.3.2 Simulation model Figure 8 shows an overview of the flow of the simulation where sun data is imported and interpolated. Topographical data and properties of the solar car is imported and put into the optimization model.

Figure 8. Overview flow of the simulation model

Figure 9 is an overview of the optimization model, data is appended into the model. Data, as described in figure 8, is appended to a dataset that is used to simulate a set time period. In this case intervals of 1 hour are used for each period. The simulation begins testing with a default car speed of 130 km/h, which is in general the highest legal speed on highways in Australia. After each period the battery state of charge (SOC) is checked whether it does not go under a certain set value, which is a percentage of the solar car’s total battery capacity. If the SOC is below the threshold, or the SOC goes below a certain safety region, the speed of the car is lowered by, in this case 1 km/h. This is repeated until a desired SOC is kept and the simulation continues the next hour, again starting with the default car speed of 130 km/h.

Figure 9. A more detailed view of the optimization model

2.4 Validity and reliability To ensure the reliability of the data we have used standard equations that will be presented in this paper, the study also uses other proven methods in another research e.g. as Baldissera & Delprete (2017), that describes the rolling resistance depending on the number of wheels. Sun Irradiation data is provided by Solcast, which provides hourly data back to 2007. To ensure validity and reliability both datasets have the data from the same location e.g., Darwin, Australia, that they are synchronized and merged and that the correct time zone is applied to the datasets, since they originally are in UTC format. The sun irradiation data will be interpolated to a minute by minute basis to emulate a more frequent change in irradiation (Solar Resource and Weather Data in Time Series, Typical Meteorological Year (TMY) and Monthly Averages, 2021). This data will be used to compare the results of the previous cars in competition of JU Solar Team to assess the accuracy of the simulation, thus establishing validity and reliability of the results.

2.5 Considerations The project aims to simulate using historical data, not to gather live data. The solar panel will not be orthogonal to the sun during control stops and when the race stops for the day as it would be in a real-life scenario. Things that will not be included in the simulation are unplanned stops, that were caused by various reasons like equipment failure, road accidents, ineffective planning etc. But they will be considered in the text when the results are compared. The simulation will simulate speeds between 50 and 130 km/h, but will not take local speed limits into account.

Regarding 퐶푑퐴, JU solar team obtained the drag coefficient through simulations of the model of the car’s body, thus a discrepancy between the provided 퐶푑퐴 and real life 퐶푑퐴 must be considered.

3 Theoretical framework

3.1 Driving strategy in previous work Driving strategy has been researched in the past and one of the earliest and most referenced work is in Pudney’s thesis. In Pudney (2000), he first concludes that the most efficient way for a solar car to cover a flat road with no wind is to hold one constant speed.

3.1.1 Undulating roads In the case for undulating roads Pudney (2000) proposes that the optimal strategy is anticipating hills. When the solar car is approaching an uphill slope, it should accelerate to reach its maximum speed at the bottom of the hill then decelerate while climbing. Once back on level ground the solar car should accelerate back to its cruising speed. For the case of downhill slopes, the solar car should decrease its speed in anticipation of the descending hill and then coast, making gravity accelerate the car and then at flat ground go back to the cruising speed. Daniels & Kumar (1997) analyzed this scenario as well in the American solar challenge (ASC) and comes to similar conclusions.

3.1.2 Clouds For the case of cloudy areas there has been research made in the paper by Shimizu et al. (1998) here they took three different strategies and compared them. First was cruising with a constant power, during sunny period the speed increased and during cloudy periods the speed decreased. Second one was cruising at a constant speed from start to finish. Third one was increasing speed during cloudy periods and decreasing speed during sunny periods. The third alternative was the most effective racing strategy for the car to generate as much solar energy as possible. By extending the periods through the sunny areas and going through cloudy areas in the shortest amount of time possible (Pudney, 2000). Pudney (2000) reaches similar conclusions of dealing with cloudy weather. Daniels & Kumar (1997) suggest the opposite of that concluding that it is more beneficial to use the power instead of storing it. The different conclusion can be a result of them using an inefficient battery.

3.1.3 Other Solar Car Teams Solar Team Twente has also published a study on their solar car SolUTra. They used a strategy program called PALLAS which was able to determine constant speed strategies. This strategy is divided into separated sub-categories that are long term strategy over the entire race and then day to day strategy. Gradient-based optimization is then made to optimize these strategies. In the study it is also mentioned about safety regions on battery range. In the paper Mocking takes safety regions of 10% and 90% of

the battery capacity. These zones guard the occurrence of unfavorable situations. The conclusions were that it was able to predict long term average power consumption to develop a race strategy and to show if the team was able to maintain the schedule. But still the strategy program had shortcomings in the form of a relative low accuracy of the measurement (Mocking, 2006). Istanbul Technical University Solar Car Team proposed a heuristic approach. Yesil et al. (2013) uses a strategy that is based on the formation of the universe called Big Bang Big Crunch optimization. The model had something called speed reference which means it could make a desired average speed in a segment, but this was limited between 40 and 90 km/h. Then through the iterations the total race time went down until it remained constant and could see how many hours the race would last in their optimal speed profile. Experimental validation is missing but expert commented on the implementation saying it has a satisfactory outcome. Solar forecasting is important to get an accurate impact on the power consumption of the solar car. Shao et al. (2016) demonstrate three elements of solar forecasting for two different races WSC and ASC using machine learning. The first element is solar irradiance per hour, the second is a visualization of cloud coverage as a layer over the calculations. The third element is a sky camera that was put on a car that drove 1-2 hours ahead of the solar car. It showcased to aid in decision making to maximize solar irradiance, also gives a glimpse of percentile forecasts to potentially make the strategist assess risk in different case scenarios. The sky camera that they used came into good use to validate data in real time. Betancur et al., (2017) developed another heuristic optimization for race strategy for the EPM-EAFIT Solar Car in 2015. The cases to find optimal speeds was first a clear sky race and a second case, a race with one cloudy day diminishing the entire day irradiance to 60%. Results was that the second case took almost an additional 2 hours with optimal speed between 75 and 84 km/h and clear sky between 78 and 83 km/h.

3.2 Formulas These are the standard equations used in the model. The cars power consumption is summed from its aerodynamic resistance, rolling resistance and its gradient resistance. The aerodynamic resistance is calculated by the standard drag formula: 1 퐹 = 휌푣2퐶 퐴 퐷 2 퐷

Where 퐶퐷 is the drag coefficient, and A is the frontal area of the car. 푣 is the speed of the car.

In conclusion, 퐶퐷퐴 is the drag area of the vehicle.

The rolling resistance is calculated by the standard rolling resistance equation:

퐹푅 = 퐶푟푟푁

Where 푁 is the normal force and, 퐶푟푟 is the rolling resistance coefficient and is calculated by this formula, as (Baldissera & Delprete, 2017) described in their paper:

푛 1 퐶 = ∙ ∑(퐶 ∙ 푃 ) 푟푟 푃 푟푟,푖 푖 푖=1

Where 푃 is the overall weight of the vehicle, 푛 is the number of wheels, 퐶푟푟,푖 is the rolling resistance of each wheel and 푃푖 is the load on each wheel.

According to Baldissera & Delprete (2017) 푃푖 is independent from 퐶푟푟,푖 on cars and trucks since the load is equally distributed on each wheel, as it is in our case. 푃 So we can conclude that 푃푖 = ⁄푛 where 푛 is the number of wheels.

The gradient resistance is calculated:

퐹퐺푟 = 푚𝑔 ∗ sin 훼 Where 훼 is the angle of the slope derived from the topographic data. The power is then calculated by multiplying the speed of the car with the sum of the three forces 퐹퐷, 퐹푅 and 퐹퐺푟, multiplying it with the speed of the car, while taking the efficiency of the electrical system in to consideration to get a good estimation of the power produced by the car.

퐸퐶표푛푠푢푚푝푡푖표푛 = (퐹퐷 + 퐹푅 + 퐹퐺푟) ∙ 푣 ∙ 휇 Where 푣 is the speed of the car in m/s.

4 Results

4.1 The cars of JU Solar Team In the following passages, the simulated results of the different solar cars of JU Solar Teams are presented (see Appendix tables 3 to 5 for their properties). Appendix G to I shows the sun irradiation during the different race periods.

4.1.1 Axelent (2019) The result from the first simulation was run on the JU Solar Team 2019 car, Axelent. (as shown in figure 1). The optimal mean speed of Axelent would be 78.4 km/h, with a maximum speed of 85 km/h and a minimum speed of 76 km/h. With this mean speed, the battery discharge will be at a maximum of 9% of the total battery capacity per hour (which is equivalent to 0.09C). The total simulated race time is 44 hours. Figure 10 shows the simulation result of Axelent during its 2019 race. The top graph shows the battery SOC with its discharge over time. There is a clear upwards curve when the car is stationary, showing that the solar panel provides charge from the sun. The increase in charge corresponds with the second graph that shows total distance over time. When the line is flat, the car does not move, and the longer flat areas is when the car is stopped during the night hence no charging from the solar panels occurs. The third graph shows the speed the solar car has at that moment, and it varies between each simulation period. Stops, as in control stops and night stops are depicted as blank areas in the graph since the speed is 0 km/h. When simulating Axelent in the 2017 race conditions Axelent completed the race in 48 hours, with a battery discharge rate of 0.08C. Mean speed of 68.3 km/h with a maximum of 78 km/h and a minimum of 63 km/h. (see Appendix D)

Likewise, simulating the in the 2015 conditions a battery discharge rate of 0.08C was used. A total race time of 47 hours, with a mean speed of 69.9 km/h, with 83 km/h maximum and 63 km/h minimum. (see Appendix E)

In 2013 conditions Axelent completed the race in 47 hours, with a battery discharge rate of 0.09C. A mean speed of 64.2 km/h, with a maximum of 85 km/h and a minimum of 62 km/h. (see Appendix F)

The 2019 WSC race, Axelent came in 10th place with a mean speed of 64.6km/h. With the result of the simulation the solar car would finish at third place (Dekker, 2019).

Figure 10. Simulation results for Axelent (2019)

4.1.2 Solveig (2017) The optimal mean speed for Solveig is 67.7 km/h with a maximum speed of 78 km/h and a minimum speed of 63 km/h. The battery discharge rate will be a maximum of 0.08C, and a total race time of 49 hours. (see Appendix A) A thing to note, battery discharge rate is lowered to 0.08C due to the relatively low sun irradiation during the 2017 race. The 2017 WSC race Solveig came in 8th place with a mean speed of 59.7 km/h. With the result of the simulation the solar car would finish at 6th place (World Solar Challenge 2017, n.d.).

4.1.3 Solbritt (2015) For Solbritt the mean speed is also 79.6 km/h with a maximum speed of 87 km/h and a minimum speed of 63 km/h. A battery discharger rate of 0.09C per hour. and a total race time 42 h. (see Appendix B) The 2015 WSC race Solbritt came in 15th place with a mean speed of 66.4km/h. With the result of the simulation the solar car would finish at seventh place (Challenger Class Outright Results 2015, 2015).

4.1.4 Magic (2013) Magic never finished the race in 2013, but it went through the simulation to see what driving strategy was needed in order to complete the race. The mean speed of Magic would be 71.3 km/h, with a maximum 92 km/h, and minimum 65 km/h. With a total race time of 43 hours and a battery discharge rate of 0.09C (See Appendix C). With the result of the simulation the solar car would have got a 7th place finish. However, the way mean speed was calculated in 2013 differs from the later races. As of, 2013 the mean speed included the duration the cars stood still during control stops. Without taking this into consideration, the characteristics of the simulation results deviates from the results from the later race simulations. But after taking the time standing still during control stops, the results are consistent with the 2013 results (Challenger Class 2013, 2013).

4.2 Analysis A clear trend that was noticed throughout the simulations was that a battery discharge rate of 0.08-0.09C was a perfect rate to use, since the simulations showed promising results. A general rule that was learned was that the default battery discharge rate per hour would be 0.09C, and then lowered to 0.08C if the sun irradiation were not high enough, possibly aiming for a rate somewhere between 0.08C and 0.09C for the most optimal result.

Comparing the results from simulating Axelent in earlier races Axelent performs better compared to Solveig. Where it completed the race 1 hour faster, with a mean speed higher by 0.7 km/h. However, both Solbritt and Magic performed better than Axelent where Solbritt had a mean speed higher by 9.5 km/h and finished the race 5 hours earlier. Magic finished 4 hours earlier and had a mean speed of 7.1 km/h more than Axelent. Another take away from the race simulation is a peak in speed in the beginning of the race. And in general, the lowest speed occurs mid race, with an increase in speed during the end of the race. This explains why the SOC rises in the second half of the race, instead of keeping a steady level. Analyzing the result of the simulation, the long-term strategy does not take regard to the short-term strategy that the model needs for the second half of the race. The goal is to end with battery being at close to zero percent to know the team has pushed everything to finish as quickly as possible. The model shows all solar cars not using up the entire battery. This however can be used in advantage for non-race cars where the goal is to drive economically. Studying the battery SOC in the graphs presented in appendix A to F the battery charge increased during the second half of the race. As described by Wang et al. (2011) minimizing the depth of discharge (DOD) of a battery increases its longevity. Wang et al. (2011) states that a battery’s lifespan depends mainly on its full charge/discharge cycle when the C rates are low (<0.5C) i.e., a DOD of 100%. E.g., if a battery has a lifespan of 2000 cycles, but the DOD is only at 50% then it theoretically should last for 4000 cycles since only a 100% DOD cycle counts as a complete one. When studying the SOC curves in Appendix A to F the DOD is low, in some cases having a SOC with more than 50% in the end of the race, thus lowering the DOD compared to a model focused on racing where the goal is to expend all the charge at the finish line. Wang et al. (2011) states that the lower the DOD the less wear on the battery, thus results show that the model is good for non-race solar cars. When comparing the results from the simulation to the historic results, there is clearly an increase in mean speed and shorter race times, this is mainly caused by unplanned stops during the race, but other factors like local shading from i.e., clouds, buildings and trees. In short, the factors mentioned in 2.4 affects the accuracy of the results.

5 Discussion Compared to earlier work this study explored a novel method that uses a relatively simple model. Inspiration was found in Pudneys study of driving strategy on undulating roads where hill anticipation was presented (Pudney, 2000). In our work regenerative braking is used on downhill slopes where 1° is reached as mentioned in 2.2.1.

5.1 Result discussion Studying the SOC in Charge over time in the results (see Figure 9 and Appendix A to F), there was an excessive charge left in the battery at the end of the race. Race time can be improved if this is considered by comparing current SOC to remaining distance. A pattern that was observed was the battery discharge rate, which is how much energy relative to the maximum capacity of the battery was used each hour. A safe battery discharge rate Wang et al. (2011) was between 0.08C to 0.09C, depending on the conditions. Even though this C rating was not optimized for racing, decent results are still achievable. The model provides a good basis of driving strategy, so the accuracy will be improved with better and more datasets, like more localized sun irradiation datasets, local shading from clouds, buildings and foliage. Similar to Yesil et al. (2013) that also used time segments to get a desired mean speed, this model also used this approach, but each segment was specified to 1 hour. Betancur et al (2017) also utilized sun irradiation data like this model, but then changes optimal mean speeds between every control stop. The purpose of this study was to develop a simple energy model to be able to answer the research questions. The first question is answered respectively to each solar car in the results. The second question is answered in the analysis part of the result as well as the third question. RQ1: What is the optimal mean speed for different solar car models? The mean speed for each solar car is: Axelent (2019): 78.4 km/h Solveig (2017): 67.7 km/h Solbritt (2015): 79.6 km/h Magic (2013): 71.3 km/h RQ2: How much does the estimated mean speed vary in relation to fluctuations in sun irradiation for different solar car models? Note that only Axelent was compared to the other cars. Including the other cars in different race conditions were concluded to be redundant, since JU Solar Team compares their 2022 car with the results from Axelent and its properties.

Axelent’s 2017 performance compared to Solveig was 0.7 km/h lower than Solveig and finished 1 hour later. This is mainly because of Solveig being a lighter car of only 186 kg compared to Axelent which weighs 200 kg (see Table 3). Axelent’s 2015 performance had a mean speed compared to Solbritt that was 9.5 km/h faster and finished 5 hours earlier than Solbritt. The higher performance of Axelent can be attributed to Axelent being 37 kg lighter than Solbritt (see Table 4). Axelent’s 2013 performance had a mean speed compared to Magic that 7.1 km/h lower than Magic and finished 4 hours later. Magic outperforms Axelent because of its lower weight of 190 kg and a larger area of the solar panel, which is 6 m2 compared to Axelent’s 4 m2 (see Table 5). RQ3: With what precision and accuracy can the model estimate the mean speed with the turn-out from the results of earlier solar cars and their properties? The model has not the accuracy to simulate the real-world example of WSC races but provides enough data to give an insight on how the solar cars behave in the race with the changes in sun irradiation and car properties. But studying the calculated mean speeds from the simulations and comparing them to the real world examples a discrepancy can be noticed. This is however due to unplanned stops during the real- world races, and everything mentioned in 2.5, which affects the real world mean speed negatively. However, the model has a high precision because unless the input data changes the results of the simulation stays the same. Also, no deviations to any of the simulations is found which shows that the model is precise. The simulation provides good general aid to optimize the cars power consumption. This research concludes that in good conditions a C rating of 0.09 works well for safe driving, and it can be lowered to a C rating of 0.08 if the sun irradiation is lower (conditions comparable to Appendix G and H). As mentioned, accuracy may be improved with more accurate and additional datasets. That may include more localized sun data, and weather data with high granularity. Future solar teams may collect live weather data from the race with the use of sensors on the car to get an even more accurate dataset that may improve the accuracy of the results.

5.2 Method discussion The strengths with this model are the relative simplicity of how it calculates the results, the model is also easily customizable to different datasets. These sets are e.g., sun irradiation, topographical data of any road and location, properties of the solar cars. Another important feature that is a strength is the power conservative nature of this model, that is applicable to general solar cars in non-race situations. Which provides

minimal strain on the battery pack and lower energy consumption for general driving as mentioned in 4.2 (Wang et al., 2011). In general, this model provides a good basis for JU Solar team to further develop into a model optimized for their solar cars for racing purposes. A weakness of this model is that its resource heavy. For instance, a simulation run on a Xeon E5-1620 v2 @ 3.7 GHz takes around 1 minute and 20 seconds, and around 50 seconds on a Ryzen 9 3900X @ 4.2 GHz, so this model might not be optimal for live scenarios unless adequate hardware is used. Another weakness of this model is that it is optimized for a long-term strategy with no regard of emptying the battery on the last day to get the best placement as possible.

6 Conclusions and further research

6.1 Conclusions This research has developed a model for JU solar team that is a good basis for developing a racing strategy for solar car racing at the WSC. In the problem statement it is explained that having a driving strategy is important to aid in racing scenarios because of the unpredictability of the sun. With the help of simulations this paper can conclude that developing a driving strategy is key to optimize power consumption to up the mean speed of the solar car and get a better placement in the competition. Other solar car teams as mentioned in 3.1.3 focus on finding optimal speeds in the WSC race, in this research power consumption has been a focus and optimal speeds has then become the by-product. Future solar team building a driving strategy can get inspired by the findings of this research, biggest thing being the BDR or (C rating) of 8-9% (0.08-0.09C). This research recommends when sun irradiation is lower, as compared to the 2017 race (see Appendix H), where only 400 to 800 W/m2 of sunlight was available some days, to aim for a BDR 8% and when the sun irradiation is ideal i.e., 800 W/m2 and up (see Appendix G), having a BDR of 9%. As mentioned previously the model does not take the short-term strategy in the end of the race into account when it is essential to finish the race as quickly as possible with near zero or zero SOC. The research has no concrete results on the last part of the race strategy, but conclusions can be made that adjustments are necessary e.g., increase the BDR in the model for the later stages of the race to be able to finish earlier with near zero or zero SOC. In short, this paper recommends following a simple procedure, to keep the BDR on 9% if the sun irradiation stays above 800 W/m2 and lower the BDR to 8% if irradiation goes below 800 W/m Adjustments to increase the BDR for the end of the race is also recommended for optimal driving strategy.

6.1.1 Practical implications The practical implications of the result of this study are, first the practical change of driving strategy JU Solar team is going to have by applying this model to future race in WSC or in other solar car races. The second is the possibility of use in commercial solar cars where long-term strategies can be used for finding optimal mean speeds.

6.1.2 Scientific implication Since this model in its current form is optimized for general solar car driving, this model and the results presented in this paper might aid further scientific research and driving strategies for commercial solar cars.

Furthermore, JU Solar team has never released studies in this area, so this might inspire further research from both JU Solar team and competitors to also release more research in this area.

6.2 Further research Further research can be done, by for instance, adding additional datasets like weather data, where e.g., wind speed can be used to calculate the power consumption. More accurate sun data, such as local shading from buildings, clouds and foliage may be used to improve the accuracy of the battery charging form the solar panel. Live data can be gathered during race events to further improve accuracy and hence, the driving strategy planning. The topographical data is only used for downhill slopes because of time constraints, the utility of the topographical data can be expanded. Because in a real-life scenario an uphill takes more energy than on a flat surface. The thesis has shown that hill anticipation is relevant for hills and can be used to further develop the model. The model might be optimized to make it less resource intensive, thus making it work better in live scenarios. As mentioned previously the model could be improved to give better optimal strategy at the end of the race when being conservative with energy is not needed.

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8 Appendixes

Solar panel area 4 m2

퐶푑퐴 0,106

Solar panel efficiency 19.2%

Weight 186 kg

Wheels 4

Battery capacity 5300 Wh

Battery voltage 118V

Average speed in race 59.7km/h

Table 3. car properties of Solveig (2017) (Cars - JU Solar Team - Jönköping University, 2021)

Solar panel area 6 m2

퐶푑퐴 0,126

Solar panel efficiency 18.3%

Weight 237 kg

Wheels 4

Battery capacity 4000 Wh

Battery voltage 96V

Average speed in race 66 km/h

Table 4. car properties of Solbritt (2015) (Cars - JU Solar Team - Jönköping University, 2021)

Solar panel area 6 m2

퐶푑퐴 0,097

Solar panel efficiency 17.5%

Weight 190 kg

Wheels 4

Battery capacity 4000 Wh

Battery voltage 96V

Average speed in race No finish

Table 5. car properties of Magic (2013) (Cars - JU Solar Team - Jönköping University, 2021)

Appendx A. Simulation results for Solveig (2017)

Appendix B Simulation results for Solbritt (2015)

Appendix C Simulation results for Magic (2013)

Appendix D Simulation results for Axelent (2017 race conditions)

Appendix E Simulation results for Axelent (2015 race conditions)

Appendix F Simulation results for Axelent (2013 race conditions)

Appendix G. Solar irradiation (GHI) during the 2019 race

Appendix H. Solar irradiation (GHI) during the 2017 race

Appendix I. Solar irradiation (GHI) during the 2015 race

Appendix J. Solar irradiation (GHI) during the 2013 race