Measuring Range Anxiety: the Substitution-Emergency-Detour (SED) Method
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World Electric Vehicle Journal Vol. 5 - ISSN 2032-6653 - © 2012 WEVA Page 0008 EVS26 Los Angeles, California, May 6-9, 2012 Measuring Range Anxiety: the Substitution-Emergency-Detour (SED) Method Zhenhong Lin Oak Ridge National Laboratory, 2360 Cherahala Boulevard, Knoxville, TN 37932, USA Abstract Range anxiety has been widely recognized as a critical barrier for battery electric vehicles (BEV), but its measurement method is lacking. Such a knowledge gap makes it difficult to analyse the competiveness of and the demand for BEVs. This study develops the Substitution-Emergency-Detour (SED) method to measure the range anxiety cost, and conducts sensitivity analysis of range anxiety cost with respect to nine factors. It is found that the most effective ways to reduce range anxiety are reducing driving intensity, increasing the vehicle range, extending the vehicle range with better charging infrastructure. Better household vehicle flexibility and less range uncertainty can also significantly reduce range anxiety. The SED method and the numerical results are expected to contribute to better understanding of the range anxiety barrier and the BEV demand. Keywords: EV (electric vehicle), range, market 1 Introduction 2 Concept and Formulation Range anxiety has been widely recognized as a The SED method is based on the notion that range critical barrier for battery electric vehicles anxiety can be theoretically compensated with no- (BEV), but has yet to be properly measured [1]- cost, hassle-free vehicle substitution, emergency [3]. This makes it difficult to analyse the roadside service (ERS), and detours to access competiveness of and the demand for BEVs. A public chargers. In reality, these activities cost good method to measure range anxiety could measurable money, time and inconvenience, thus allow an improved understanding of market providing a framework to formulate the range barriers, optimization of the BEV range, and anxiety cost as a function of value of time, exploration of solutions to reduce range anxiety. household vehicle ownership, charging infrastructure coverage and driving patterns. This study develops the Substitution-Emergency- Detour (SED) method to monetize the range anxiety. The concept of the SED method is explained in the next section, followed by some ∑ ( ) numerical examples that illustrate how the method can be used and how range anxiety cost Figure 1: the Substitution-Emergency-Detour method can be sensitive to the chosen 9 factors. EVS26 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium 1 World Electric Vehicle Journal Vol. 5 - ISSN 2032-6653 - © 2012 WEVA Page 0009 For further formulation, 4 random variables are When xe< Re, the driver would operate the BEV, considered—the expected daily driving distance hoping the uncertain actual daily distance (x) not (xe), the unexpected deviation (xd) of actual daily to exceed the uncertain actual vehicle range (r). distance (x) from xe, the unexpected deviation But once the BEV leaves home, the actual daily (rd) of the actual vehicle range (r or rr, explained distance (x) may deviate from xe due to unplanned later) from the expected vehicle range (Re), the errands or other reasons, and the actual vehicle probability (Pe) of using emergency roadside range (r) may also deviate from Re as caused by service as opposed to detouring to the nearest on-road speeds, use of air conditioner, congestion, charging station under the condition that the and other reasons. These situations result in the actual vehicle range is less than the actual daily possibility (Ped) of the actual daily distance distance. When no detour is taken, the actual exceeding the actual vehicle range (i.e. x>r) and vehicle range (r) is the sum of the expected the need to either call for emergency roadside vehicle range (Re) and the unexpected range services or detour to a public charger. Such deviation (rd). When a detour is taken, the actual possibility is expressed in the equation (8), where vehicle range (rr) will include an additional g(x) and h(r) are the probability density function of extended range (Rb) resulting from the detour x and r, respectively. and recharge. This detour-extended range (R ) is b (7) a function of the BEV range (R ), the detour 0 ( ) ( ) ( ) recharge ratio (E ) and the wasted range (L) in ∫ ∫ ∫ b reaching and returning from the charger (5). The expected vehicle range (Re) is the product of the BEV range (R0) and the expected extension ratio Let E0 and D0 respectively be the cost of one (E) that reflects the regular charging activities roadside service and one detour for recharging. anticipated by the driver. The relationships Between these two options, the probability (Pe) of among these variables are illustrated in the calling for roadside services can be expressed as a equations (1)—(5), with lowercase letters function, as in the equation (8), of E0, D0 and the representing random variables and uppercase price coefficient (β) that reflects the choice letters representing deterministic variables or elasticity. constant parameters. (8) (1) (2) The annual cost of emergency roadside services (E) and detour charging (D) can be expressed in the (3) equation (9) and (10). (4) (9) (5) ( ) (10) Logically, a vehicle substitution occurs when the expected daily distance exceeds the expected vehicle range (i.e. xe> Re). The cost of obtaining 3 Example and using a substitution vehicle (S0) could be as low as the daily depreciation of another vehicle To apply the SED method established by the in the household and as high as a daily rate of a equation (1)—(10), a Base example is created rental vehicle plus fees of home delivery. based on the following assumptions. Therefore, the annual substitution cost (S) can be The cost of one roadside service (E ) is assumed to expressed in the equation (6), where f(xe) is the 0 be $62 for each service call, based on rates of fuel probability density function of xe. delivery services by rental car companies [4]. (6) ∫ ( ) The cost per detour for recharging (D0) depends on the availability of public chargers, time value and charging time. It is estimated to be $63 based on EVS26 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium 2 World Electric Vehicle Journal Vol. 5 - ISSN 2032-6653 - © 2012 WEVA Page 0010 the assumptions of the wage rate at $21/hour, the 4 Sensitivity Analysis BEV range at 100 miles, the detour charging ratio at 100%, the charging availability at 0.5% Sensitivity of the range anxiety cost is analysed (equivalent percentage of existing gasoline with respect to the following 9 factors, each stations), and the charging power at 60 kW. changed by 50% up and down. Vehicle Substitution Cost ($/each) The price coefficient (β) is assumed to be -0.325, Emergency Roadside Service Cost ($/each) based on the assumption of price elasticity at -10. Value of Time ($/hour) Daily VMT Mode (miles) The probability density function f(xe) is assumed Annual VMT (miles) to be a Gamma distribution where the driver Vehicle Range (miles) drives 16000 miles per year and most frequently Expected Extension Ratio (100%) 20 miles per day. The form of distribution has Range St.D. (miles) been adopted for plug-in electric vehicle analysis Charger Availability (100%) [5][6] and validated with real-world travel data [7]. The probability density function g(x) is 4.1 Vehicle Substitution Cost assumed to be a Gamma distribution with its Vehicle substitution cost indicates the easiness to mean at x and its standard deviation at 2.5% of e obtain a backup vehicle when the expected daily x . The probability density function h(r) is e distance exceeds the expected vehicle range. It assumed to be a Gamma distribution with its depends on household vehicle flexibility and can mean at R and its standard deviation at 20 miles, e range from $15 to $50, where the lower bound based on real-world BEV data. Figure 2 shows reflects the cost of using an easily available vehicle the distribution of x and r and the distribution of e in the household by considering vehicle x on the days when x =70 miles. The overlap e depreciation and the upper bound reflects the cost between the distributions of x (subject to x =70) e of a delivered rental vehicle. As shown in Figure 3, and r indicates the chance of the actual daily the vehicle substitution cost only affects the distance exceeding the actual vehicle range, even Substitution component of range anxiety. Higher though the expected daily distance (70 miles) is vehicle substitution cost leads to higher range much below the expected vehicle range (100 anxiety cost. High-income consumers are more miles). likely to have high vehicle ownership and thus better vehicle flexibility. Because of this, they may perceive less range anxiety. However, they may have higher value of time and perceive a higher cost for detour recharges. Figure 2: Variation of daily distance and range Both the detour recharge ratio (Eb) and the expected extension ratio (E) are assumed to be 100%, meaning that the driver can use up to 100% of the BEV range each day and extend the BEV range by another 100% when detouring to Figure 3: Range anxiety sensitivity to vehicle recharge. substitution cost Based on the Base assumptions above, the range 4.2 Emergency Roadside Service Cost cost is estimated to be $1309/year, 53% of which is for vehicle substitution, 28% for emergency The ERS cost rate indicates the penalty each time a roadside service, and 19% for detour charging. BEV is out of range on the road and the driver EVS26 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium 3 World Electric Vehicle Journal Vol. 5 - ISSN 2032-6653 - © 2012 WEVA Page 0011 calls for ERS.