Big-Data Framework for Electric Vehicle Range Estimation

Big-Data Framework for Electric Range Estimation * Habiballah Rahimi-Eichi*, Mo-Yuen Chow* Department of Electrical and Computer Engineering, North Carolina State University, NC, USA Emails: hrahimi@ncsuedu, chow@ncsuedu Abstract Range anxiety is a major contributor in low penetration of electric vehicles into the transportation market Although several methods have been developed to estimate the remaining charge of the battery, the remaining driving range is a parameter that is related to different standard, historical, and real-time data Most of the existing range estimation approaches are established on an overly simplified model that relies on a limited collection of data However, the sensitivity and reliability of the range estimation algorithm changes under different environmental and operating conditions; and it is necessary to have a structure that is able to consider all data related to the range estimation In this paper, we propose a bigdata based range estimation framework that is able to collect different data with various structures from numerous resources; organize and analyze the data, and incorporate them in the range estimation algorithm MATLAB/SIMULINK code is demonstrated to read real-time and historical data from different web databases and calculate the remaining driving range Keywords Electric, Driving range estimation, Remaining charge estimation, Big-Data Analytics I INTRODUCTION Electric s (EVs) are now financially within reach of many American families, yet their adoption rate remains low in the US (338 % of new cars were EVs in 2012) Industry research has uncovered that the anxiety felt by many drivers about the remaining driving range their vehicle can run before the next charge is a major contributing factor to this low adoption rate [1] This anxiety is mainly because the current technologies cannot accurately estimate the remaining driving range of EVs Existing EV remaining range estimation technologies mainly rely on limited collection of data While some methods put more emphasis on electrochemical behavior of the battery [2], there are others that focus on identifying different driving patterns [3, 4] Moreover, there are some other approaches that consider more GPS-based and manufacturers-provided data with a simplified EV power train model [5] Finally, some techniques consider up to nine factors to estimate the driving range of the EV [6] However, the sensitivity and reliability of the range estimation algorithm changes under different environmental and operating conditions; and it is necessary to have a structure that is able to consider all data related to the range estimation To accurately estimate the driving range of the EVs, our Big Data based range estimation uses adaptive estimation models along with Big Data Analytics In this paper, we propose an effective and robust framework to discover and analyze the factors that are important in estimation of the driving range This framework helps with qualitative demonstration of the relationships between the Range Estimation results and the available data, as well as quantitative evaluation of the relativeness, importance and required precision of different data types to accomplish the estimation The rest of this paper is organized as follows: section II introduces the big data concept especially related to the range estimation technique; section III describes the range estimation data framework In section IV, a MATLAB/SIMULINK-based example of the big data range estimation framework is presented; and section V concludes the paper and explains the future work II BIG DATA CONCEPT AND RANGE ESTIMATION The amount of data collected in Electric s has been growing fast because we have many more sensors, higher bandwidth communication systems, and cheaper memory to monitor and measure real-time driving range related data and store the data on the vehicles, in connected clouds, etc This massive amount of data can have different levels of accuracy, resolutions, and relevance in unstructured ways Big Data technologies have been emerging to address huge, diverse and unstructured data to substantially improve the overall system performance With proper use of Big Data concepts and techniques, the remaining driving range estimation of the vehicle can be substantially improved As described earlier, many available, yet unstructured and growing data exist to provide much better estimates of the vehicle driving range Different data has been collected from the battery in-situ measurements, state of charge (SOC) estimation, battery manufacturers and models, EV manufacturers and models, driving history, GPS location tracking of the EV, traffic report, weather center, etc However, some of these factors are more important than others when trying to provide an accurate estimate of range This assorted data can be categorized into standard, historical, and real-time data While the standard data is associated with deterministic non-updating phenomena, the 1

historical data is related to the stochastic behavioraldependent trends The real-time data are deterministic or stochastic data that need to be updated in real-time Here we use a three-day trip planning to a nearby site for our vacation to illustrate the proposed framework concept The planning needs a combination and synchronization of different types of data: Standard data: Eg the schedule of different tours and activities such as parachuting, skydiving, etc from the websites, the normal driving time to the destination from GPS or Google Map, or the climatic conditions such as hurricane season Historical Data: Eg Recent Mile per Gallon (MPG) of the car to schedule the refueling stops on the road, the reviews from the people who have planned a similar trip or visited the area from review websites such as tripadvisorcom, the reviews of the restaurants and hotels for dining and accommodation from websites such as yelpcom, etc Real-time Data: Eg a traffic jam caused by an accident, a sudden rain, an urgent issue that needs to be resolved before departure, etc Therefore, we always use a combination of standard, historical and real-time data to plan and adjust our plans Based on the good reviews on a restaurant (historical data), we choose the close-to-lunch tours (standard data) near that restaurant If a sudden rain or sickness happens (real-time data) we compromise the activities with less priority, eg from skydiving to watching a movie (the priority of the activities is based on the historical and standard data) Similarly, the range estimation needs the incorporation and synchronization of all standard, real-time and historical data For example, assume that we drive a Tesla Model S (with LiCoO2 battery pack) in California We plan to make a trip from Sacramento to San Jose (around 120 miles) on a winter morning Our Big Data-based range estimation system will give the driving range prediction based on the following data: Standard Data: Eg the standard test data that provides the specification (eg capacity degradation) of the LiCoO2 battery from NASA; the regular route to San Jose from GPS; the winter climatic condition of northern California from Wikipedia, the nominal All Electric Range (AER) of Model S from Tesla, etc Historical Data: Eg the average of the past energy consumptions of the vehicle, the battery misuse history (eg operation under extreme temperatures, high humidity, high charging/discharging rate, deep cycles, etc) that could cause a lasting effect on the performance of the battery logged in the vehicle computer, the morning traffic pattern for the route in the last months from the California Department of Transportation, etc Real-time Data: Eg a traffic jam on the highway due to accidents, weather changes like sudden rain during the trip, rerouting due to the highway shutdown, etc The driving range estimation is based on these three forms of data Usually, the standard and historical data provides an initial prediction of the driving range; and the real-time data updates the estimation during the driving However, under different conditions, some data are more relevant than others for the range estimation This data can be historical, standard, or real-time depending on different situations The big data analytics helps us identify the relevant data and discover its correlation to the remaining driving range estimation III RANGE ESTIMATION DATA FRAMEWORK All the standard, historical and real-time data related to the range estimation are available from different resources, including the electric vehicle, battery management system, traffic report, GPS center, etc with different structures, accuracies, sampling rates, and communication standards Therefore, we develop a range estimation data framework to collect different data from various resources, analyze them, and include them as parameters and models in the range estimation algorithm This framework has the ability to be implemented in big data computing structures such as Hadoop [7] Figure 1 shows an example of the range estimation framework block diagram with five data collecting nodes including route, weather, driving behavior, vehicle, and battery nodes These nodes collect the range estimation related data from different resources Then the electric vehicle model along with the battery model is utilized to estimate the driving range based on the stored data The following subsections explain the components of this block diagram Data Collection Nodes Google Map Route and Terrain Distance, Terrain, location Temperature, wind Speed Wunderground com Weather Driver History Driving Behavior Electric Model Parameters Manufacturer Modeling Battery Model Parameters Battery Manufacturer Power Consumption Battery Modeling Battery Simulator (SimBattery) Driving Range Figure 1 Range estimation framework block diagram A Route information Route information including the driving distance, the road terrain, speed limit, and the traffic data is one of the most important components to estimate the driving range This information can be categorized as standard data in the case of the distance, road terrain and speed limit, as well as real-time data in the case of live traffic data, and historical data in case of typical traffic data The route data (point-topoint longitude-latitude path) as well as the speed limit and traffic data are easily available through the Google map website Moreover, the Google website encourages developing free Application Programming Interfaces (APIs) 2

that use the Google map information and provide additional information For example, the elevation API provides the terrain of the road using the longitude and latitude of the routing points Note that what the Google map website shows to the driver is the decision points on the route In the other words, the website displays the points at which the driver needs to make decisions such as turn right/left, merge, or switch the road, rather than overwhelming the driver with so many inbetween points that are not necessary However, these inbetween points are necessary for accurate route terrain calculation The good news is that the latitude and longitude information of detailed in-between data points on the driving route is already available on the website although not displayed This data is available in a polyline data format ; and we use googlepolylinedecoder, which is an open source MATLAB code, to extract the latitudelongitude information of the route points B Weather Data The weather data mainly falls into the category of the real-time data Although the historical data helps to predict the weather in the near future, the accurate prediction is performed by analyzing the satellite images Therefore, the weather prediction is a well-established expertise that we can just use the results to make the range estimation more accurate There are several webpages that present accurate weather reports and prediction results According to the main idea of this big data framework, we write a code to locate the information, extract the parameters that are important to the range estimation algorithm, and integrate them into the range estimation algorithm We use Wundergroundcom, a website that provides the information regarding temperature, wind speed and wind direction at the given longitudes and latitudes While the temperature is used to adjust the battery parameters based on the temperature effect analysis, the wind speed and direction gives the velocity of the wind in the opposite direction of the vehicle to calculate the aerodynamic power consumption of the vehicle C Driving Behavior Data The driving behavior is the most challenging data to obtain, because it is tied to the human behavior; and can be related to all historical, standard, and real-time data Although the historical data could be available for each driver by recording the speed and location in the vehicle s GPS, the access to this type of data is not easy due to the privacy and security issues Moreover, different background and daily events can significantly influence the driving behavior and make the real-time data deviated from the historical data Several approaches have been suggested so far to model the drivers behavior based on the experimental data There are standard driving cycle tests available from the United States Environmental Protection Agency [8] that gives the driving speeds at different trips These data provide the standard driving speeds at typical highways and urban areas at different conditions The actual driving behavior can be different from these standard data For example, some studies have categorized different driving behaviors into aggressive, normal and slow drivers depending on the individual history of the driver Each of those categories is assigned a weight to approximate the vehicles speed based on the standard data or the road speed limit The same approach has been used by categorizing the trips into short, medium and long distance trips and assigning standard driving behaviors to each category Also, some data-driven approaches [9, 10] have been proposed that consider the historical driving speed of different drivers on a route or highway; and use Fuzzy Logic or Markov Chain techniques to predict the speed of the vehicle on the road These methods have been used extensively in transportation area However, incorporating these approaches is beyond the scope of this paper, and will be pursued in our future work In this paper, we use the distance and predicted time data of the google map to approximate the average speed of the driver among decision points D Electrical Modeling Data To calculate the power consumption of an electric vehicle at different speeds, accelerations, as well as road and weather conditions, we consider a widely-used model [11] to represent the power that needs to be provided by the vehicle's battery to propel the vehicle Accordingly, we consider a vehicle along a slope as demonstrated in Figure 2 with all the forces applied to the vehicle as a free body diagram Figure 2 Free body diagram of an electric vehicle along a slope Table 1 Power Consumption Parameters Description Parameter v a m vw Velocity of the vehicle (m/s) Acceleration of the vehicle (m/s2) α μ ρ A Cd Slope of the road (rad) mass (kg) Velocity of the wind in the opposite direction (m/s) Friction coefficient Density of the fluid (air) (kg/m3) Cross section of the car (m2) Drag coefficient 3

ηg r G I ηm T ω kc ki kw C The gear system efficiency Radius of the wheel (m) Gear ratio moment of inertia of the rotor s motor efficiency Torque (Nm) Angular speed (rad/s) Figure 3 Power transition block diagram in the electric vehicle Copper losses coefficient Iron losses coefficient Windage loss coefficient Constant losses In this figure, the traction force of the vehicle provided by the drivetrain is the interaction of different forces: (1) Defining all vehicle parameters in Table 1, where the friction and gravity forces are: ( ), (2) sin( ), (3) the aerodynamic force, a function of the relative speed of the vehicle v and the wind vw, is calculated as: ( ), (4) (5) and the acceleration force is a combination of the linear and rotational acceleration: Therefore, the traction power of the vehicle can be calculated as: (6) Obtaining the motor angular speed from:, The applied torque to the motor can be calculated as: The efficiency of the motor at this speed and torque is: The input power to the motor is: E Battery Modeling Data Depending on the required accuracy and the application, different types of models have been developed for the battery Among those models, the RC-equivalent circuit is an effective one to represent the battery s dynamics for battery energy management purposes The following subsections describe some of the battery s characteristics that are considered in the electric vehicle s battery model 1) Linear Model with Internal Resistance A typical rechargeable battery can be modeled by a large capacitor that stores and releases electrical energy during charging and discharging cycles As in any electrochemical process, these charging/discharging cycles encounter a small resistance due to the electrolyte and the inter-phase resistance This small resistance is modeled as an internal resistor, R0, in series with the battery capacitor Q in Figure 4 Since the value of R0 changes with the battery State of Charge (SOC), the ambient temperature, and the aging effect of the battery, online parameters identification technique is used to estimate the internal resistance of the battery from the battery terminal current and voltage (7) (8) (9) (10) Another power consumption load inside the vehicle is the ancillary power including air conditioner, battery management system, light and audio systems: (11) Thus, the power that needs to be provided by the battery power is: (12) Figure 3 demonstrates the power transmission in electric vehicles from battery to the wheels with considering all previously mentioned power consumptions Figure 4 Battery model with relaxation effect, internal resistance, and VOC-SOC function 2) Relaxation Effect The relaxation effect is another basic characteristic of the battery that appears during and after the charging and discharging cycles This effect represents the slow convergence of the battery s terminal voltage to its equilibrium after hours of relaxation following charging/discharging and is modeled by series-connected parallel RC circuits The number of RC groups used is a trade-off between accuracy and complexity While Chen, et al, [12] recommended two RC groups as the optimal model, there are several references [13] stating that one RC group structure can provide results that are accurate enough for applications such as electric vehicles 3) VOC-SOC Relationship Despite the common assumptions about a simple linear 4

model for the battery, the static relationship between the open circuit voltage (VOC) and the SOC of the battery is intrinsically nonlinear This nonlinear relationship is the function of electrochemical characteristic of the battery cell; and is obtained from experimental tests on the battery cell The VOC-SOC curve is usually provided by the battery cell manufacturer, or obtained from experimental results 4) Cycling and temperature Effect The parameters of the battery are subject to change due to different conditions of temperature and ageing (calendar time and cycling) The effect of temperature and cycling on those parameters are available as standard data for different chemistries and battery types Those data along with statistical analysis to apply uncertainty factors including partial charge/discharge and temperature fluctuations, helps predicting the battery parameters variations during a medium to long trip In this paper, we just consider the temperature effect on the internal resistance of the battery to keep the simplicity of the demonstration 5) Battery SOC and SOH The SOC and SOH of the vehicle s battery at the time of the prediction are crucial for the range estimation algorithm The SOC provides the remaining charge of the battery compared to the full capacity, and SOH provides the ability of the battery to handle the chare/discharge cycles during the trip For accurate estimation of the remaining charge at the time of the range estimation, we have developed a parameters/soc/soh co-estimation algorithm [14-16] that accurately estimates the SOC and full capacity of the battery based on a model with updating parameters IV PROTOTYPE AND RESULTS To demonstrate the big-data-based range estimation concept as a prototype, we have developed a MATLAB/SIMULINK code that is able to search for the range estimation-related data including route, weather, driving behavior, electric vehicle, and battery data from different resources The interface of the code is a Graphical Figure 5 Big-data based range estimation GUI front page User Interface (GUI) in MATLAB that is in a prototyping stage As described earlier, each part of the code can be considered as a data collection and analysis node that can be implemented in a distributed computing structure Moreover, in our implementation the processing and incorporating the data into the range estimation algorithm is performed on the same PC as the data collecting process although it can be distributed among different processors to increase the computing speed A GUI has been designed so that the user is able to verify the features of the data-driven based range estimation approach Figure 5 shows the front page of the designed GUI In this page, the users enter the departure and destination cities of the trip inside the Origin and Destination boxes Pressing the Get Route Data button, a MATLAB function starts running This function acts as the Route and weather data collecting nodes in Figure 1 Figure 6 shows part of the code in this function that starts with the origin and destination points, and uses a Google map API called Direction to provide the latitude, longitude and the predicted arrival time at the turning points of the route from the origin to the destination With the distance and duration data, the normal driving speed between two points can be approximated assuming average speed between turning points Although assuming the average speed between route points is a practical solution to the intrinsically stochastic driving behavior, the road grades in shorter travel distances can be obtained in more details compared to the route points As explained in section III-A, the googlepolylinedecoder() which is an open source MATLAB function, is used to convert the polyline ASCII code of the Google map data into the latitude and longitude of the in-between points google_searchstrcat('http://mapsgoogleapis com/maps/api/directions/xml?origin',origin,' &destination',destination,'&sensorfalse'); DOMnodexmlread(google_search); xmlwrite('tempxml',domnode); s xml2struct('tempxml'); n_speednumel(sdirectionsresponserouteleg step); distance_speedzeros(1,n_speed); duration_speedzeros(1,n_speed); for i1:n_speed duration_speed(i) str2num(sdirectionsresponseroutelegst ep{1,i}durationvaluetext); distance_speed(i) str2num(sdirectionsresponseroutelegst ep{1,i}distancevaluetext); end speeddistance_speed/duration_speed; currentroute sdirectionsresponserouteoverview_polylinep ointstext; [route_lat,route_lon] googlepolylinedecoder(currentroute,0); Figure 6 Code for extracting route, speed and polyline data 5

Afterwards, as demonstrated in the Figure 7 code, the Elevation API is utilized to provide the altitude (elevation) of all available points The road grade is a direct function of the relative altitude of the consecutive points along the route google_searchstrcat('http://mapsgoogle apiscom/maps/api/elevation/xml?location s',num2str(route_lat(i)),',',num2str(ro ute_lon(i)),'&sensorfalse'); DOMnodexmlread(google_search); xmlwrite('tempxml',domnode); s xml2struct('tempxml'); elev_route(i)str2num(selevationrespons eresultelevationtext); Figure 7 Code for extracting road grade data After obtaining the route and terrain information, the latitude and longitude data is used along with the wui API which collects the real-time weather data from the Wundergroundcom website The MATLAB code to extract the weather data is demonstrated in Figure 8 This data contains the temperature, wind speed, and wind direction information The temperature data is used in our battery simulator, called SimBattery, to adjust the internal resistance and the full capacity of the battery As explained in sections III-B and III-D, the wind speed and wind direction is used to calculate the wind velocity in the opposite direction of the vehicle; and adjust the aerodynamic power consumption Other data collecting nodes, regarding different vehicles, driving behaviors and battery chemistries can be added to the MATLAB function Those nodes would be able to incorporate different standard, historical and real-time data, and increase the accuracy of modeling and range estimation For demonstration purposes, we use data regarding Tesla Roadster model [17] and lithium polymer battery Moreover, we consider average speed with constant acceleration and deceleration at way points to model the driving behavior google_search2strcat('http://apiwunder groundcom/auto/wui/geo/wxcurrentobxml/i ndexxml?query',num2str(route_lat(i)),',',num2str(route_lon(i))); xmlwrite('temp1xml', xmlread(google_search2)); s1 xml2struct('temp1xml'); T_route(i)str2num(s1current_observatio ntemp_ftext); wdeg_route(i)str2num(s1current_observa tionwind_degreestext); wmph_route(i)str2num(s1current_observa tionwind_mphtext); Figure 8 Weather data collection code Following the mentioned considerations about the driving speed, battery, and vehicle, the vehicle power consumption is calculated using equations 1-11 in section III-D This task starts with pressing the Range Estimation button on the GUI, or the Range Estimation/Weather button to include weather data Afterwards as demonstrated in Figure 9, the battery power is obtained from equation 12 An average model for a DC/DC converter is developed to calculate the input current of the battery from the power Figure 10 shows the battery model called SimBattery developed in SIMULINK to represent the dynamic RC equivalent model of the battery that was described in section III-E As explained earlier, this model is an RC equivalent circuit with adjusting internal resistance based on the reported temperature The relationship between the internal resistance and the temperature (in oc) has been obtained from experimental results on the battery cell as follows: ( ) 006438 (13) Figure 9, battery, and range estimation data analysis block diagram Figure 10 Simbatterybattery model simulator with DC/DC convertor The SimBattery is executed by pressing the SimBattery button on the GUI; and provides the battery voltage and SOC In this case study, the initial SOC at the beginning of the trip is the SOC value estimated in the last usage of the battery (eg, yesterday from work to home), which can be different from the actual SOC now due to already changes due to change of operating conditions (eg, different temperature, relaxation) When the trip starts, the current SOC is estimated in real-time by feeding in-situ voltage and current of the battery to the parameters/soc/soh co-estimation algorithm Moreover, the algorithm provides the updates of the battery parameters based on the real-time and historical data Figure 11 shows the predicted consumed power, as well as the battery current, voltage and SOC for a short 12 miles trip from Cary, NC to Raleigh, NC Figure 11(d) shows that for a 12mile drive the SOC drops for 5% It means that this driver is able to drive for 12 16192 miles with 80% SOC at similar 6

conditions Although in this figure the data has been plotted versus time, it is also available versus distance; and leads to the range that the vehicle can go before the battery goes out of charge analyses, based on the standard, historical and real-time data and development to enhance range estimation accuracy and robustness ACKNOWLEDGMENT The authors would like to thank Advanced Diagnosis, Automation, and Control (ADAC) lab for all fruitful group discussions and feedbacks This project is financially supported by Samsung Advanced Institute of Technology (SAIT) REFERENCES (a) [1] [2] [3] [4] (b) [5] [6] [7] [8] (c) [9] [10] [11] [12] (d) Figure 11 The simulated (a)battery power (b)battery current (c) battrey voltage (d) battery SOC for range estimation V CONCLUSION AND FUTURE WORK A big-data analytics-based framework was introduced to estimate the remaining driving range of electric vehicles This framework collects different standard, historical, and real-time data from different resources It then analyzes and compiles them as a part of the range estimation algorithm An example of the framework was introduced; and the data collecting and processing trend was explained A MATLAB/SIMULINK version of an example framework was implemented to demonstrate the feasibility of the approach Future works will include various in-depth [13] [14] [15] [16] [17] R A Daziano, "Conditional-logit Bayes estimators for consumer valuation of electric vehicle driving range," Resource and Energy Economics, vol 35, pp 429-450, 2013 M Ceraolo and G Pede, "Techniques for estimating the residual range of an electric vehicle," Vehicular Technology, IEEE Transactions on, vol 50, pp 109-115, 2001 Hai Yu, Finn Tseng, and R McGee, "Driving pattern identification for EV range estimation," Electric Conference (IEVC), 2012 IEEE International, pp 1-7, 2012 H He, C Sun, and X Zhang, "A Method for Identification of Driving Patterns in Hybrid Electric s Based on a LVQ Neural Network," Energies, vol 5, pp 3363-3380, 2012 J G Hayes, R P R de Oliveira, S Vaughan, and M G Egan, "Simplified electric vehicle power train models and range estimation," Power and Propulsion Conference (VPPC), 2011 IEEE, pp 1-5, 2011 Yuhe Zhang, Wenjia Wang, Y Kobayashi, and K Shirai, "Remaining driving range estimation of electric vehicle," Electric Conference (IEVC), 2012 IEEE International, pp 1-7, 2012 Apache Hadoop [Online] Available: http://hadoopapacheorg/ Dynamometer Driving Schedule: United States Environmental Protection Agency [Online] Available: http://wwwepagov/nvfel/testing/dynamometerhtm L Bor Yann and M Dubarry, "From driving cycle analysis to understanding battery performance in real-life electric hybrid vehicle operation," Journal of Power Sources, vol 174, pp 7688, 2007 Tae-Kyung Lee, B Adornato, and Z S Filipi, "Synthesis of Real-World Driving Cycles and Their Use for Estimating PHEV Energy Consumption and Charging Opportunities: Case Study for Midwest/US," Vehicular Technology, IEEE Transactions on, vol 60, pp 4153-4163, 2011 J Larminie and J Lowry, Electric Technology Explained 2nd ed: John Wiley & Sons, 2012 M Chen and G A Rincon-Mora, "Accurate electrical battery model capable of predicting runtime and I-V performance," Energy Conversion, IEEE Transactions on, vol 21, pp 504511, 2006 M A Roscher and D U Sauer, "Dynamic electric behavior and open-circuit-voltage modeling of LiFePO4-based lithium ion secondary batteries," Journal of Power Sources, vol 196, pp 331-336, 2011 H Rahimi-Eichi, F Baronti, and M Chow, "Online Adaptive Parameters Identification and State of Charge Co-Estimation for Lithium-Polymer Battery Cells," Industrial Electronics, IEEE Transactions on, 2013 H Rahimi-Eichi and Mo-Yuen Chow, "Adaptive online battery parameters/soc/capacity co-estimation," Transportation Electrification Conference and Expo (ITEC), 2013 IEEE, pp 16, 2013 H Rahimi-Eichi, U Ojha, F Baronti, and M Chow, "Battery Management System: An Overview of Its Application in the Smart Grid and Electric s," Industrial Electronics Magazine, IEEE, vol 7, pp 4-16, 2013 J Straubel Roadster Efficiency and Range [Online] Available: http://wwwteslamotorscom/blog/roadster-efficiency-and-range 7