Modeling charging choices of BEV owners using stated preference data

Transcription

1 EVS28 KINTEX, Korea, May 3-6, 2015 Modeling charging choices of BEV owners using stated preference data Yuan Wen 1, Don MacKenzie 1, David Keith 2 1 Civil & Environmental Engineering, University of Washington Box , Seattle WA , USA 2 Sloan School of Management, Massachusetts Institute of Technology 77 Massachusetts Ave, Room E62-441, Cambridge MA 02139, USA Corresponding Author: Don MacKenzie dwhm@uw.edu

2 Context I. This study aims at explaining charging choice made by BEV drivers. II. We developed models of BEV use and charging that use information about travel plans and charging situations to predict whether or not a BEV driver charges when given the opportunity. III. We use data from a web-based stated preference survey. Respondents were presented with different situations characterized by charging price, charger power, dwell time, current electric range remaining in battery, distance to home and distance to next charging opportunity. Socio-demographic information were also collected. IV. We assume that the importance of attributes are different across individuals, meaning that different people will behave differently even under the same circumstances. V. Three statistical approaches were investigated: binary logit model, mixed logit model and latent class logit model. Parameter estimates are presented, along with a discussion of goodness of fit. 2

3 Introduction: Reasons to investigate the charging behavior of PEVs I. Charging behavior affects the energy security and environmental benefits of PEVs 1. Petroleum displacement [1] 2. Reduce GHG emissions, criteria pollutant emissions and displace emissions to less densely populated areas [2-4] II. Charging behavior affects the demands on the electric grid 1. Small increase in uncontrolled charging may have substantial impact on marginal electricity costs [5] III. However, the realization of these benefits depend crucially on the fraction of miles driven that are powered by electricity 1. For BEVs, petroleum displacement hinges on the fraction of travel days that can be satisfied by a BEV. [6-7] 2. For PHEVs, petroleum displacement is based on the charge-depleting range and the distance between two charging events. [8] 3

4 Introduction: Actual charging pattern of BEV I. In general, drivers are cost sensitive and strongly prefer to low cost EV charging. [9] II. Longer charging duration time at public charging station will decrease of preference of charging.[9] III. Charging choice is heterogeneous across drivers.[9] 4

5 Introduction: Prior work on choice modeling I. Limited research on quantitative models of charging choice Dependent Variable Independent Variables Data Source Method Ref. Charge or not at the end of trip SOC, dwell time, day & time, location, last trip Instrumented premarket Prius PHEVs in U.S. Binary mixed logit [1] Charging location Cost, charging duration, trip purpose, time of day SP survey of Australian PEV owners Multinomial mixed logit [9] Timing of charging & trip adaptation SOC, price, trip purpose, distance, dwell time SP survey of UK car drivers (mostly non- PEV) Multinomial logit [10] SOC at start of mid-trip fastcharge events Charging station density, region, battery size, daily trips & VMT, speed, HVAC Instrumented PEVs ( km range) in Japan Stochastic frontier modeling [11] 5

6 Price Data: Web-based stated preference survey I. We identified several factors relevant to decision 1. Price 2. Charger power 3. Dwell time 4. Remaining travel distance to home 5. Current electric range remaining in battery 6. Distance to next charging opportunity II. Attributes level: Charger power Dwell time Distance to home Current range $0.5/h, $1/h, $1.5/h, $2/h, $5/h 1.9kw, 6.6kw, 50kw 0.25h, 0.5h, 1h, 2h, 4h, 8h 2mi,5mi,10mi, 20mi, 30mi, 50mi 3mi~70mi Distance to next charging opportunity 2mi,5mi,10mi, 20mi, 30mi, 50mi 6

7 Data: Web-based state preference survey III. We used a fractional factorial experimental design. A set of 8 scenarios was given to each respondent in the survey, with each scenario characterized by the variables on the preceding slide. Respondents were asked whether or not they would charge if they encountered this situation in their EV. IV. Subjects were members of the Electric Auto Association (EAA) and were contacted through their local EAA chapters. We also collect some social-demographic information of each respondents. V. A total of 417 respondents participated in the survey with 410 complete sets of responses. Thus, the total complete observations in this dataset are 410 8=

8 Data: Information about the respondents I. The survey are answered by a sample of PEV drivers recruited through their membership in the Electric Auto Association (EAA). II. Several advantages using EAA members as subjects 1. EAA members are highly interested in the technology and willing to participate in the study, even without tangible compensation 2. Many of the members have owned PEVs for longer than other uses, so there s less risk that their charging choice is shaped by a lack of familiarity with the technology 3. EAA chapters spread all over the U.S., providing high geographic diversity 8

9 Data: Summary of socio-demographic information Age Gender % Female 12% % Male 88% % Household Size % 1 10% Education 2 41% Less than Bachelor's Degree 29% 3 23% Bachelor's Degree 40% 4+ 26% Master's Degree 19% Electricity price at home Doctor's Degree 6% $0.06/kwh~$0.08/kwh 25% Professional Degree 6% $0.09/kwh~$0.11/kwh 46% Income $0.12/kwh~$0.14/kwh 14% less than $59,999 12% $0.15/kwh~$0.17/kwh 6% $60,000-$99,999 19% $0.18/kwh~$0.20/kwh 3% $100,000-$119,999 17% $0.21/kwh~$0.23/kwh 2% $120,000-$139,999 10% $0.24/kwh+ 4% $140, % 9

10 Data: Derive new interaction variables I. Previous work only included related variables linearly in the utility function (i.e. price, dwell time, etc.), however did not consider how they would interact II. We derived some new interaction terms based on the information we collected in the survey. The variables are given below. 1. Range charged at this station = min {power dwell time, (max range- current range)} 2. Enough to next charger = 0, if current range distance to next charging opportunity>0 =1, if current range distance to next charging opportunity<=0 3. Cost at this stop = price dwell time 4. Additional cost at home = Cost at home (charge here) Cost at home (no charge here) 10

11 Data: Derive new interaction variables 4. (continue with last page) Cost at home = range to be charged at home (mi) energy consumption (kwh/mi) electricity price at home ($/kwh) If not charged at this station: range to be charged at home = min{max range, (max range - current range + distance to home )} If charged at this station: range to be charged at home = min{max range, (max range-current range - range charged at this station+ distance to home)} 11

12 Method: Binary logit model P(Charge it ) = ev it 1 + e V it!!" =!!" +!!" =!!"! +!!" X it = characteristics of choice situation t faced by individual i Dwell time Price Range charged Charger power Distance to next charging opportunity Cost at this stop Electric range remaining in Battery Additional cost at home Enough to next charger Distance to home today β = fixed coefficients ε it = independent, identically distributed random error term (Gumbel distribution) 12

13 Step 1: Economically rational model I. We start with a very economically rational model of charging choices from a purely rational view of the charging utility: how much energy I get vs. how much I pay, also allowing that if I NEED to charge to finish my travel, I may behave differently. II. The results of binary logit model are given below: Variable Estimate Std. error t Pr(>t) (Intercept) *** Cost at this stop *** Additional cost at home Range charged *** Enough to next charger *** Model summary statistics Log-likelihood: AIC: BIC:

14 Step 2: Allow for some departures from pure rationality I. Then we included more variables in the choice model. Variable Estimate Std. error t Pr(>t) (Intercept) *** Price *** Cost at this stop Additional cost at home Dwell time: >30min *** Charger power (baseline: 1.9kw) 6.6kw *** 50kw *** Range charged Remaining distance to home *** Range remaining in battery *** Enough to next charger Distance to next charging opportunity Model summary statistics Log-likelihood: AIC:4137 BIC:

15 Interpretation: Step 1 & 2 I. Including these new variables help improve the model fit. 1. Lower AIC and BIC values, higher log-likelihood. II. The results in table 2 demonstrated that in fact some of other factors matter, even though they shouldn t if the person were only motivated by minimizing cost and finishing their travel day. 1. The significant coefficients for variables: price, dwell time, charger power, distance to home and remaining range in the battery. III. In fact, when we include charger power and dwell time in the step 2, the range charged variable turns to nonsignificant, indicating that people seem to react charger power and dwell time more than to the range charged here. IV. However, this finding leads us to test whether some people are more sensitive to range charged and some people are more sensitive to charger power and dwell time. Thus, in the next step, we want to consider the heterogeneity in our model 15

16 Step 3: Consider the heterogeneity Mixed logit model P(Charge it ) = ev it 1 + e V it U it = V it + ε it = X it β + Z it b i + ε it X it, Z it = characteristics of choice situation t faced by individual i β = fixed coefficients b i = individual-specific coefficients (normally distributed with mean 0, b i ~ N(0,σ 2 )) Ø This is the only difference from binary logit model ε it = independent, identically distributed random error term (Gumbel distribution) R package lme4 are used to estimate the model [13] 16

17 Results: Mixed logit model Variable Fixed effects (β) Random effects (σ) (Intercept) * *** Price *** Cost at this stop ** *** Additional cost at home *** Dwell time: >30min *** *** Charger power 6.6kw *** *** 50kw *** *** Range charged Distance to home today *** *** Range remaining in battery *** Enough to next charger *** Distance to next charging opportunity Model summary statistics Log-likelihood: AIC: BIC:

18 Step 3: Consider the heterogeneity Latent class model P[choice exp(α j + βqx j i, t, class = q] = J(i) = exp(α j + β I. Assuming that each individual belongs to a set of Q classes and for each class q,estimate different coefficients. II. Models heterogeneity differently than mixed logit model 1. It approximates the underlying continuous distribution with a discrete one. [12] III. The appropriate number of classes are determined by the goodness of fit. I. We estimated one- to nine-class models with the same model specification in step 2. The AIC values indicates that the six-class model is the best model (AIC is lowest for this model among these nine models). IV. R package flexmix is used to estimate the model [14] j 1 itj q ) x itj )!! 18

19 Results: latent class model Variable Class1 Class2 Class3 Class4 Class5 Class6 Size of class (410 respondents total) (Intercept) * * Price *** *** *** *** * *** Cost at this stop *** * Additional cost at home * Dwell time: >30min ** * * Charger power 6.6kw ** ** * *** 50kw *** *** * ** *** Range charged * Range remaining in battery *** *** *** *** *** *** Distance to home today ** ** *** *** * Have enough charge to reach next charger * Distance to next charging opportunity *** ** Summary of model statistics Log-likelihood: AIC: BIC:

20 Interpretation: Step 3 I. Obvious heterogeneity is observed across classes 1. How much I pay? 1) In general, all classes are sensitive to price. 2) Class 4 & 6 are also sensitive to the cost at this stop 3) Some classes sensitive to additional cost at home. Positive coefficient indicates that people in class 5 are more likely to charge at this station while they have to pay more to charge at home (!) 2. How much energy I get? 1) All classes except class 5 show a strong preference for charging when level 2 or 3 charging is available. Class 6 shows a strong preference for level 3 over level 2. 2) When dwell time is longer than 30 minutes, Class 1, 4 & 6 are more likely to charge at this stop. 3) No class is sensitive to range charged, indicating that people actually react charger power and dwell time more than the actual amount of range they can get during a session. 3. If I need to charge to finish my travel 1) All classes are more likely to charge as available range in the battery decreases. 2) Class 5 is much less likely to charge when they have enough range to reach the next charging opportunity. 3) Class 3 & 4 are more likely to charge when they are a long way from the next charging opportunity. 20

21 Interpretation: Step 3 II. Latent class results are consistent with the random effects coefficients in mixed logit model. 1. For example, we observed people in different class consider cost at this stop and additional cost at home differently and the corresponding random effects in mixed logit model are significant. III. An example of charging probability under certain condition using the results from latent class model. Variable CASE1 CASE2 Price ($/hour) $1.50 $5.00 Cost at this stop ($) $1.50 $20.00 Additional cost at home ($) ($0.56) ($1.85) Dwell time: >30min Yes Yes Charger power (kw) Range charged (mi) Range remaining in battery (mi) Distance to home today (mi) Enough to next charger Yes Yes Distance to next charging opportunity (mi) Average Probability Charging Probability CASE1 CASE 2 21

22 Conclusion: I. Main observations from this study are: 1. Generally, drivers are sensitive to the charging price, cost at this stop; some certain group of people are sensitive to additional cost at home. 2. Higher power charging is attractive. 3. When drivers dwell time is longer than 30 minutes, they are more likely to charge. 4. With longer distance to home or next charging opportunity, people are more likely to charge. 5. In general, when state of charger is higher, drivers are less likely to charge. If current SOC will not reach the next charger, people prefer to charge. 6. Charging behavior across individuals or groups is heterogeneous. II. Latent class model provides better fit than mixed logit model and binary logit model. 1. The lowest AIC score and highest log-likelihood. 22

23 References 1. Zoepf, S., MacKenzie, D., Keith, D., & Chernicoff, W. Charging Choices and Fuel Displacement in a Large-Scale Plug-in Hybrid Electric Vehicle Demonstration. Transportation Research Record: Journal of the Transportation Research Board, No. 2385, pp (2013) 2. Ji, S., Cherry, C. R., Bechle, M.J., Wu, Y., & Marshall, J. D. (2012). Electric vehicles in China: emissions and health impacts. Environmental science & technology, 46(4), Peterson, S. B., Whitacre, J. F., & Apt, J. (2011). Net air emissions from electric vehicles: the effect of carbon price and charging strategies. Environmental science & technology, 45(5), Michalek, J. J., Chester, M., Jaramillo, P., Samaras, C., Shiau, C. S. N., & Lave, L. B. (2011). Valuation of plug-in vehicle life-cycle air emissions and oil displacement benefits. Proceedings of the National Academy of Sciences, 108(40), Wang, L., Lin, A., & Chen, Y. (2010). Potential impact of recharging plug in hybrid electric vehicles on locational marginal prices. Naval Research Logistics (NRL), 57(8), Pearre, N.S., Kempton, W., Guensler, R. and Elango, V.V. (2011) Electric vehicles: How much range is required for a day s driving?, Transportation Research Part C, 2011, 19, pp Dong, J., & Lin, Z. (2014). Stochastic Modeling of Battery Electric Vehicle Driver Behavior: The Impact of Charging Infrastructure Deployment on BEV Feasibility. TRB Paper No Presented at Transportation Research Board 93rd Annual Meeting. January, Shiau, C. S. N., Samaras, C., Hauffe, R., & Michalek, J. J. (2009). Impact of battery weight and charging patterns on the economic and environmental benefits of plug-in hybrid vehicles. Energy Policy, 37(7),

24 References 9. Jabeen, F., Olaru, D., Smith, B., Braunl, T., & Speidel, S. (2013, October). Electric vehicle battery charging behaviour: findings from a driver survey. In Australasian Transport Research Forum (ATRF), 36th, 2013, Brisbane, Queensland, Australia. 10. Daina, N. (2013). Electric vehicle market: stated value of the charging operation. Universities Transport Study Group. Oxford. January, Sun, X., Yamamoto, T., and Morikawa, T. (2014). The timing of mid-trip electric vehicle charging. TRB Paper No Presented at Transportation Research Board 93 rd Annual Meeting. January, Greene, William H., and David A. Hensher. "A latent class model for discrete choice analysis: contrasts with mixed logit." Transportation Research Part B: Methodological 37.8 (2003): Bates, D., Maechler, M., Bolker, B. and Walker, S. (2014). _lme4: Linear mixed-effects models using Eigen and S4_. R package version Leisch, F.. FlexMix: A general framework for finite mixture models and latent class regression in R. Journal of Statistical Software, 11(8), 1-18,