ROBOETHICS-CCS345 ETHICS AND ARTIFICIAL INTELLIGENCE.ppt
Investigating Time-of-Use as a Factor in Dynamic Wireless Charging Infrastructure Planning for Battery Electric Buses
1. Investigating Time-of-Use as a Factor in
Dynamic Wireless Charging Infrastructure
Planning for Battery Electric Buses
Chris Carey
1
New York University
Urban Transport and Logistics Systems – Fall 2021
2. Growing in adoption:
47% of global city bus fleet by 20251
Significant down-time charging:
Larger battery size requires longer
charging time
Battery Electric Buses (BEBs) Background
Photo: MTA
1Bloomberg New Energy Finance
2
3. Online Electric Vehicle (OLEV):
First commercialized by KAIST (2009)
Zero down-time potential:
BEBs charge while in motion over
charging lane
Higher initial cost:
Power inverters + power cables
Lane length vs. battery size:
Cost tradeoff
Dynamic Wireless Charging (DWC) Background
Photo: AFP
3
4. What are the optimal charging infrastructure locations and battery sizes for a given
vehicle route?
Ko and Jang (2013): First formalization:
Objective: Minimize cost → Battery cost + Transmitter cost + Cable cost
Decision Variables: Battery sizes, transitter & cable locations
Given: # of BEBs, per-unit costs, route speed profile, route slope profile
Constraints: Minimum battery level, maximum cable length, etc.
Model: Continuous Mixed Integer Nonlinear Programming (MINP)
Approach: Particle Swarm Optimization (PSO) solution
Single-Route Planning Literature Review
4
5. Jang et al. (2015): Segmentized
decision variable to enable Mixed
Integer Programming (MIP) model
solved with CPLEX
Segmentation Literature Review
5
6. Multi-route planning considers overlapping routes
Hwang, Jang, Ko, and Lee (2017): Continuous Meta-heuristic model (PSO)
Lee and Jang (2017): Segmentized Mixed Integer Programming (MIP) model
solved with CPLEX and genetic algorithms (GA)
Multi-Route Planning Literature Review
Lee & Jang (2017)
6
7. How to account for uncertainty introduced by traffic congestion?
Liu, Song, and He (2017):
● Deterministic network-based MIP model solved with CPLEX
Liu and Song (2017):
● Set-based Robust Optimization (RO) approach for parameter uncertainty
● Selected over Stochastic Programming (SP) for tractability
● Used deterministic speed profiles and calculated costs at varying
uncertainty levels
Network Model & Robust Planning Literature Review
7
8. Consider the phased conversion of the existing NYC bus
network to DWC BEBs.
Goal: Most cost-effective rollout.
Previous models can support this analysis, but they need to
account for the time of day.
Phased Conversion Problem
8
9. Time-of-Use Problem
Energy supply costs
vary by time of day
Route speed profiles
vary by time of day
Con Edison Residential
Summer Rates (¢/kWh)
23.84
12am-8am 8am-12am
1.68
M15 Local Weekday
(Downtown Branch)
9
10. Does the optimal multi-route charging infrastructure micro-
allocation solution change when energy supply cost and vehicle
speed profile vary by time of day?
Time-of-Use Problem
10
12. power transmitter or
charging lane at
end point
Charging Infrastructure Model
Constraints: Charging lanes must be adjacent to power transmitters or other charging lanes
power transmitter or
charging lane at
starting point
every power transmitter
placed along a route must be
adjacent to a charging lane
belonging to that route
set of bus routes
node sequence of
route K
set of all nodes
12
13. Energy Supply and Consumption Model
Equation: The cumulative net energy usage to reach node m
Constraints: Battery cannot exceed or fall below min/max threshold
Limitations: Bus driving over charging lane must charge; fixed battery size
energy supplied
energy consumed
set of daily time
intervals
battery capacity
13
14. Energy Supply and Consumption
energy supplied
energy consumed
constant rate × length of edge constant rate × duration along edge
14
17. Speed profiles:
Road segment speeds were
derived from expected bus stop
arrival times through linear
interpolation
Future work could use observed
bus stop arrival times from GTFS
dynamic data
Bus Route Speed Profiles Data
stop_id
stop_name
stop_lat
stop_lon
trip_id
arrival_time
stop_id
stop_sequence
stops stop_times
Row: Bus stop Row: Bus trip
GTFS Static Data Tables
17
18. Model Verification Results
changes in power
transmitter cost
low medium high
18
power transmitter
charging lane
Model parameters
were modified to
verify expected
responses
19. Model Verification Results
changes in battery
capacity (proportional to
route energy supply
potential)
19
Model parameters
were modified to
verify expected
responses
low medium high
power transmitter
charging lane
20. Model Verification Results
changes in difference
between daytime and
nighttime energy supply
cost
20
Model parameters
were modified to
verify expected
responses
low medium high
power transmitter
charging lane
21. Model Verification Results
21
low medium high 12am-8am 8am-4pm 4pm-12am
power transmitter
charging lane
slower speed
faster speed
changes in difference between daytime and
nighttime energy supply cost
route speed profile by time-of-day
22. Model Validation Results
22
no cost difference cost difference
difference between constant
and variable energy supply cost
Model parameters were
substituted with real-world
estimates
power transmitter
charging lane
23. Discussion
Possible Explanations for Near-Identical Solutions:
● Differences in Scale
○ Savings in energy supply cost did not offset installation costs
● Model simplification
○ Fixed battery sizes and power consumption rates
● Additional Cost Tradeoff
○ Cheaper nighttime energy
○ Faster nighttime speeds
● Network simplification
○ Exclusion of express routes and bus lanes
○ No overlapping routes
23
Hinweis der Redaktion
A larger model of nine bus routes was then explored and model constants were substituted with real-world estimates for installation and operation costs. However, differences between the solutions produced by the model which accounted for or ignored route speed and energy supply cost variations by time of day were negligible. While there were minor variations in charging lane placements, the differences were too small to be attributed to time-of-day cost variation.
Other fixed constants were modified such as the battery size and operation duration, but produced little difference in results. For further experimentation, a mixed bus fleet was considered where whether to operate a route was introduced as a binary decision variable as well, without an observed difference in results as well.
The model presented in this paper exhibited expected behavior under experimental scenarios, including responsiveness to variations in energy supply cost based on time of day. However, when applied to the real-world use case of the Manhattan bus network, the accumulated cost variation attributed to differences in energy supply cost by time of day did not prove substantial enough to affect the optimal charging lane infrastructure placement.
This could be explained by differences in scale. The difference between daytime and nighttime energy supply cost might not have exceeded the difference in charging lane installation cost, even over extended time periods. Or the cost tradeoff between faster night-time speeds and cheaper nighttime energy costs may have cancelled out. One thing that I wasn’t able to accomplish for this project was a thorough sensitivity analysis since I couldn’t find a solution difference to base it around.
Even the simplified model had a lot of moving parts and what remains uninvestigated is the extent to which model simplification impacted observed results. While optimal solution differences were not observed in this particular paper, these differences may still be observed in other scenarios and models. This project did not investigate overlapping routes or express routes utilizing bus lanes with reduced variations between daytime and nighttime speeds, where energy supply cost variation might be the sole factor.
While I only produced a simplified model which didn’t result in differences in time-of-day energy supply costs in real-world scenarios, this suggests that models do not need to account for this in real-world planning. This means simpler models, leading to more computationally efficient solution derivations which are still accurate. However, time-of-day could still be a factor in the planning of a phased rollout of a mixed bus fleet, which was not investigated in this project.
Lastly, this project was limited by the lack of a proper road network representation of the Manhattan bus network, which if developed could support multiple network-based modeling problems merged with GTFS data.