Electric Vehicle Fleet and Charging Infrastructure Planning

Sushil Varma

Ph.D. Student

ISyE, Georgia Tech

(yes, that is me)

Francisco Castro

Assistant Professor

Anderson School of Management, UCLA

Siva Theja Maguluri

Associate Professor

ISyE, Georgia Tech

Academic Job Market

Looking for faculty positions

Motivation to Study Electric Vehicles

Motivation

Technological Advancements

• Efficiency of electric vehicles (EVs) has improved making them a feasible option
• Tesla and Rivian are the leaders with Ford, GM and Volkswagen joining as well

Government Backing (incentivize production and adoption of EVs)

• Inflation Reduction Act
• Executive order N-79-20 in CA: by 2035, the state will ban sales of new gasoline cars

Climate Change Awareness

• Several ride-sharing companies are going electric
• User preferences are changing

Technological Advancements

Government Backing

Climate Change Awareness

We study a Transportation System with EVs

We study a Transportation System with EVs

EVs distributed in Space

We study a Transportation System with EVs

Charging Stations distributed in Space

EVs distributed in Space

We study a Transportation System with EVs

Charging Stations distributed in Space

EVs distributed in Space

Customers arrive uniformly at random in space

We study a Transportation System with EVs

Charging Stations distributed in Space

EVs distributed in Space

Customers arrive uniformly at random in space

System Operator’s Decisions:

• Which EV to dispatch (based on location and state of charger)?

We study a Transportation System with EVs

Charging Stations distributed in Space

EVs distributed in Space

Customers arrive uniformly at random in space

System Operator’s Decisions:

• Which EV to dispatch (based on location and state of charger)?

We study a Transportation System with EVs

Charging Stations distributed in Space

EVs distributed in Space

Customers arrive uniformly at random in space

System Operator’s Decisions:

• Which EV to dispatch (based on location and state of charger)?

EV pickup and drives to customer’s destination

We study a Transportation System with EVs

Charging Stations distributed in Space

EVs distributed in Space

Customers arrive uniformly at random in space

System Operator’s Decisions:

• Which EV to dispatch (based on location and state of charger)?

EV pickup and drives to customer’s destination

EV loses state of charge (SoC) in the process

We study a Transportation System with EVs

Charging Stations distributed in Space

EVs distributed in Space

Customers arrive uniformly at random in space

System Operator’s Decisions:

• Which EV to dispatch (based on location and state of charger)?

EV pickup and drives to customer’s destination

EV loses state of charge (SoC) in the process

• When to send to charge? For how long?

We study a Transportation System with EVs

Charging Stations distributed in Space

EVs distributed in Space

Customers arrive uniformly at random in space

System Operator’s Decisions:

• Which EV to dispatch (based on location and state of charger)?

EV pickup and drives to customer’s destination

EV loses state of charge (SoC) in the process

• When to send to charge? For how long?

EV drives to the charger and then starts charging

Charging Stations distributed in Space

EVs distributed in Space

Customers arrive uniformly at random in space

System Operator’s Decisions:

• Which EV to dispatch (based on location and state of charger)?

EV pickup and drives to customer’s destination

EV loses state of charge (SoC) in the process

• When to send to charge? For how long?

EV drives to the charger and then starts charging

EV gains state of charge (SoC)

We study a Transportation System with EVs

Infrastructure Planning Question

Related Literature on Infrastructure Planning

Larger buffer due to pickup times (spatial effects)

Spatial EV System: Differences and Challenges

Preview of the talk

Infrastructure Planning Prescription

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Trade-off between fleet size, number of chargers, and battery pack size

Near-Optimal Dispatching

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Power-of-d Vehicles Dispatch Policy is near-optimal

Overview of the Model followed by the following 2 results

Model

Model

Abstracting out the spatial component

• We model pickup times and drive-to-charger times using average quantities

The state space involves SoC and state of all EVs (idle/charging/driving)

Universal Lower Bound

Tight Upper Bound

Formulate a system of ODEs - tracks the evolution of the state of system

Generic ODEs satisfied by any policy

Detailed ODEs for Power-of-d Dispatch

Useful bounds on the Fixed Point

Fixed point translates into bounds on fleet size and number of chargers

Existence, Uniqueness, and Characterization of Fixed Point

Universal Lower Bound

Tight Upper Bound

Formulate a system of ODEs - tracks the evolution of the state of system

Generic ODEs satisfied by any policy

Detailed ODEs for Power-of-d Vehicles Dispatch

Useful bounds on the Fixed Point

Fixed point translates into bounds on fleet size and number of chargers

Infrastructure Planning Prescription

Infrastructure Planning Prescription

Takeaways

Takeaways

Takeaways

Takeaways

Takeaways

Takeaways

Pareto Frontier: Characterizes the trade-off between fleet size and charger density

Takeaways

Partially charged EVs help!

EV v/s non-EV System

Takeaways

Pareto Frontier: Characterizes the trade-off between fleet size and charger density

Staffing for

non-EV system

EVs driving with customers/to chargers are unavailable

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EVs driving with customers/to chargers are unavailable

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EVs driving with customers/to chargers are unavailable

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Pick the one with the highest SoC among them

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Needs to be picked carefully!

What I did not talk about

Simulations

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Verifies the theoretical results and provides further insights

Time-Varying Arrivals

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Phase Transition from EV-like to non-EV-like behavior

Takeaways

Backup Slides

Validating the Scaling Results

Provides Empirical validation of the Theory

We simulate a real-life spatial system without any simplifying assumptions

Power of d v/s Closest Available Dispatch

• Wild Goose Chase results in large pickup times for CAD
• Po2 and CD actively drop customers to maintain stable SoC
• Large pickup times induce low SoC, implying inefficient system operation
• The workload served under CAD is much smaller than Po2 and even CD

Time-Varying Arrival Rate

Incoming Workload

EV Driving

EV Charging

Takeaways

Infrastructure Planning

• Finite charging time increases the first-order term
• Partially charged EVs reduce the second-order term
• The trade-off with # of chargers and pack size: the reduction in the second order term depends on the charger density and battery pack size

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Dispatching Policy

• The closest dispatch does not work
• Power-of-d works – takes into account the trade-off between load balancing and pickup times
• Motivated by load balancing literature but the value of d needs to be optimized

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Practical Insights

• d = 2 or 3 is a good rule of thumb
• To scale up the system, both fleet size and # of chargers needs to be increased simultaneously
• Phase transition from EV-like behavior to non-EV-like behavior in the presence of time-varying arrivals

Model

For lower bound, coarse tracking of states is sufficient

Model

For lower bound, coarse tracking of states is sufficient

Model

For lower bound, coarse tracking of states is sufficient

Universal Lower Bound

Average time EV spends driving to serve a customer:

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Universal Lower Bound

Average time EV spends driving to serve a customer:

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Universal Lower Bound

Average time EV spends driving to serve a customer:

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Trip Time

Pickup Time

Universal Lower Bound

Average time EV spends driving to serve a customer:

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Trip Time

Pickup Time

Universal Lower Bound

Average time EV spends driving to serve a customer:

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Trip Time

Universal Lower Bound

Average time EV spends driving to serve a customer:

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Trip Time

Fleet size requirement

Proof Idea

Step 1: Abstract out the spatial component

Proof Idea

Step 1: Abstract out the spatial component

Proof Idea

Step 1: Abstract out the spatial component

Step 2A: Define state space

Proof Idea

Step 1: Abstract out the spatial component

Step 2A: Define state space

Proof Idea

Step 1: Abstract out the spatial component

Step 2A: Define state space

Proof Idea

Step 1: Abstract out the spatial component

Step 2A: Define state space

Proof Idea

Step 1: Abstract out the spatial component

Step 2A: Define state space

Proof Idea

Step 1: Abstract out the spatial component

Step 2A: Define state space

Step 2B: Define transitions under Power-of-d

Pickup and Drive to Charger Times

Verifies the spatial abstraction

Trade-off: Fleet size, pack size and # of chargers

Power of d v/s Closest Available Dispatch

• Wild Goose Chase results in large pickup times for CAD
• Po2 and CD actively drop customers to maintain stable SoC
• Large pickup times induce low SoC, implying inefficient system operation
• The workload served under CAD is much smaller than Po2 and even CD

Questions?

CREDITS: This presentation template was created by Slidesgo, and includes icons by Flaticon, and infographics & images by Freepik

Paper available at

https://sites.google.com/view/sushil-varma/home

and

https://arxiv.org/pdf/2306.10178.pdf

Bonus Slides

Time dependent arrival rate?

Our results kick in the regime where

• the peaks are flatter and the valleys shorter
• Battery pack size is small

Mainly due to charging required during peaks

Flatter peaks can be encountered coz

• Surge Pricing
• Use the fleet for other applications in tandem (Ride and Eats)

Charging during peaks can be beneficial

• Flatten the load on the grid

How significant is the reduction in the second order term?

Frequent Charging Sessions?

Global Stability Justification

CAD is operating inefficiently as it tries to serve all customers

This results in high pickup times

Which reduces the SoC to the minimum

With no partially charged EV advantage, it reinforces the pickup times to be high

Po2 and CD preemptively drops customers to maintain a stable non-zero SoC

Further comparisons with natural policies

Further comparisons with natural policies

CD: Closest Dispatch

CAD: Closest Available Dispatch

Po2: Power of 2

How to compute 90% fleet size?

Trade-offs observed in simulations?