## Quantifying the Benefits of Extending Electric Vehicle Charging Deadlines with Solar Generation

Imagine a parking lot that was powered by solar panels, where you could leave your electric vehicle to charge during the workday. If you specify that you will be driving home at say, 4 PM, the parking lot would ensure that your car is charged fully by that deadline.

If all cars in the parking lot have strict deadlines however, it might not be possible to charge all cars fully by the time their owners return. Instead, how much would it help if you added an hour’s leeway to your charging deadline? For example, “I will return home sometime between 4 PM and 5 PM” versus “I will return at 4 PM exactly”. If someone returns closer to 4 PM there is a bigger chance their car won’t be fully charged, whereas if they return closer to 5 PM there is a greater chance the car will be charged. If people are more flexible with their charging deadline, the parking lot is able to charge all the cars to a fuller capacity.

In this paper, we optimized when to charge each car, and how much to charge each car over a day to meet flexible and strict charging deadlines. The paper can be accessed here:

O. Ardakanian, C. Rosenberg and, S. Keshav, Quantifying the Benefits of Extending Electric Vehicle Charging Deadlines with Solar Generation, Proc. IEEE Smart Grid Communications, November 2014.

## How Similar is the Usage of Electric Cars and Electric Bicycles?

**Problem
**There is a lot of data-driven research being released on EVs. However, a lot of this research is based on

*assumptions*of EV usage rather than actual data, because buying a fleet of EVs in order to collect its data is very expensive. Also, there isn’t an abundance of public data on EV usage available to researchers.

**Solution
**Our idea was to model EVs using eBike data. This would be a much cheaper solution than purchasing an entire fleet of vehicles. In this study, we analyzed 70GB of usage data from eBikes, as well as data logged from pure EVs and hybrids to determine whether eBike usage could model EV usage.

**Evaluation
**We found that EVs actually

*cannot*be modelled using eBike data, because they are used differently. This includes the time of charging, the state of charge when charging begins, duration of charging, destinations, and trip durations. Moreover, the distribution of months of operation and trip lengths differ at a fundamental level.

**Access the paper here
**C5. Simon Dominik Fink and Lukasz Golab and Srinivasan Keshav and Hermann de Meer. (

**2017**). How Similar is the Usage of Electric Cars and Electric Bicycles?. ACM eEnergy EVSys Workshop, (334–340)

## The return on investment for taxi companies transitioning to electric vehicles: San Francisco

**Problem
**What would be the return on investment of transitioning a taxi company’s fleet to electric vehicles?

**Solution
**We built a Bayesian model to calculate the return on investment when switching to electric vehicles. The model can be configured with several input parameters, including the type of vehicle to be tested, electricity and gasoline prices, and roadside charging/battery switching infrastructure assumptions.

**Evaluation
**We evaluated our model using location data collected from over 500 Yellow Cab San Francisco (YCSF) taxis. Using prices at the time of the study, 2014, we found that transitioning YCSF’s fleet to battery electric vehicles and hybrid vehicles was indeed profitable. Moreover, given that gasoline prices in San Francisco were only 5.4% higher than the rest of the US, but electricity prices were 75% higher, taxi companies with similar mobility patterns in other cities were likely to profit more than YCSF. Generally, when gas prices rise above a certain level, EVs will give a better return on investment.

We’d like to note that at the time of this study, we made the assumption that there would be battery swapping stations set up around San Francisco to allow EVs to recharge immediately (see: Better Place). As part of our study, we determined that the optimal place to put these swapping stations would be at the airport, where longer taxi trips would likely drain the battery of an EV. Unfortunately, the infrastructure for these stations was never realized.

**Access the paper here
**J20. T Carpenter*, AR Curtis*, S Keshav. (

**2014**). The return on investment for taxi companies transitioning to electric vehicles. Transportation. 41(4)

## Sizing vehicle and bikeshare pools

**Sizing Finite-Population Vehicle Pools
**Range anxiety, or the fear that a battery will run out before reaching a destination, is a factor that prevents customers from buying electric cars. Solutions like battery switching, adding more charging outlets, and larger batteries have been proposed, but in 2014 BMW offered a simpler solution: what if when a dealership sells an electric car, they automatically “subscribe” the buyer to a program that allows them to borrow gasoline cars for longer trips? That is, whenever an EV car owner needs to make a longer trip that will outlast the car’s battery range, they can come to the dealership, trade in a subscription coupon for a gasoline car, and rent out that gasoline car free of charge that day.

The question then becomes: how many gasoline cars does a dealership need to reserve for this program? In this study, we analyzed four different methods of sizing this vehicle pool, one of which doesn’t need any prior data or training. The following paper describes these methods in detail.

J16. Tommy Carpenter and Srinivasan Keshav and Johnny Wong. (2014). Sizing Finite-Population Vehicle Pools. IEEE Trans. Intelligent Transportation Systems. PP(99)

**Bikeshare Pool Sizing for Bike-And-Ride Multimodal Transit
**In shared bike-and-ride systems, commuters can ride a shared bicycle from home to a public transportation station, drop the bicycle off in a pool, take public transportation, pick up another bicycle from a pool at their destination stop, then ride to their final destination. So, how many bicycles would be needed at each transportation stop? A naive solution would be to have two bicycles for each commuter, one at the stop they board public transportation, and one at the stop they get off. The caveat is that this would be prohibitively expensive. So, what would be the

*smallest*number of bikes that should be available at each public transportation station for this to work?

It turns out that the mathematical problem for sizing these bikeshares has the same structure as the mathematical problem for sizing vehicle pools, which was described above. By using this method, we were able to reduce the number of bicycles in each pool by between 39% to 75%, compared to having two bikes per commuter.

J6. G. Tang and S. Keshav and L. Golab and K. Wui. (2018). Bikeshare Pool Sizing for Bike-And-Ride Multimodal Transit. IEEE Transactions on Intelligent Transportation Systems.

## Range prediction for electric bicycles

**Problem
**

Range anxiety is a significant reason why people are hesitant to buy e-bikes – they’re afraid of running out of battery in the middle of a ride, with no place to recharge. It doesn’t help that e-bikes often don’t have a gauge that shows how much distance is left in a bike battery. Instead, most e-bikes have a display that reveals battery voltage—though we can all agree that it’s difficult to determine the remaining range on an e-bike from this number.

Although e-bike manufacturers do publish the maximum range of their models, we found that this number isn’t accurate for all riders, since some people ride more aggressively than others.

**Solution
**Using data from a fleet of 31 sensor-equipped e-bikes used in the University of Waterloo WeBike project, combined with OpenStreetMap data, we evaluated two range prediction methods for e-bikes. The first model is a simple one, since it just takes into account the average battery usage from past trips. The second model is a more complex linear regression model that considers the characteristics of the anticipated route (such as off-road percentage, the number of stop signs, and the number of traffic lights), as well as battery temperature.

**Evaluation
**

We found that the more complex linear regression model didn’t perform much better than the simpler one. Using real trip data, our predictions using the simple model were usually within a 10% of the actual remaining range at the end of the trip.

These results should be of interest to e-bike manufacturers because the simple model we tested, which gave promising results, can be implemented as a simple on-board prediction technique. Since most e-bikes have an odometer built in, making this odometer data accessible and adding the ability to measure battery voltage and current are the only main additions needed to implement our technique inexpensively.

L. Gebhard, L. Golab. S. Keshav, and H. de Meer, “Range prediction for electric bicycles,” Proc. *ACM e-Energy 2016.*

## Control of Electric Vehicle Charging

**Problem
**Electric vehicles (EVs) pose a challenge to the electrical grid in two ways.

- First, large-scale introductions of EVs pose a
**significant load to the grid.**An EV can be charged with a load of up to 19.2kW (with Level 2 chargers), whereas a typical North American home has an average load of 1kW – this means a single EV could impose a load as large as that imposed by nearly twenty average homes. - Secondly,
**the load posed by an EV is variable by time and location**: its load on a grid will unpredictably disappear when it is being driven. It might then charge at a different location, re-appearing at a different part of the electricity distribution network.

**Solution
**Since a typical EV charger is located within 3km of the nearest substation, the transmission delay between any charger and its connected substation is less than 1ms. As such, we can design a distributed control algorithm that adjusts the charging rate of an EV every few milliseconds, in response to the load being placed on the overall distribution system. For example, if an EV is charging at a rate that affects the reliability of the grid, its charging rate can be decreased.

Three papers were written on this subject. The first paper introduces the problem and describes how the congestion control problem for a grid distribution system is similar to the congestion control problem in the Internet.

- O. Ardakanian, C. Rosenberg, and S. Keshav. Real Time Distributed Congestion Control for Electrical Vehicle Charging (invited paper), ACM SIGMETRICS Performance Evaluation Review 40.3 (2012): 38-42.

By using a mathematical framework originally developed for rate control in the Internet (TCP), each EV charger in the grid can independently update its charging rate, while ensuring that the overall load on the grid stays at an ideal level, the allocated rates for each charger are proportionally fair, and that these allocations are optimal. The second paper in this series focuses on a static network scenario, in which the non-EV load is constant, and a fixed number of EVs are connected to chargers.

- O. Ardakanian, C. Rosenberg, and S. Keshav. Distributed Control of Electric Vehicle Charging, Proc. ACM e-Energy, May 2013.
**Winner of Best Paper Award.**

The third paper goes into detail about the dynamic network scenario, which involves variable home loads and number of plugged-in EVs. Since the dynamic network scenario can be decomposed into a series of static intervals, the static control algorithm described above can be extended to be used in a dynamic network.

- O. Ardakanian, S. Keshav, C. Rosenberg. Real-Time Distributed Control for Smart Electric Vehicle Chargers: From a Static to a Dynamic Study, IEEE Transactions on Smart Grid, vol.5, no.5, pp. 2295-2305, Sept. 2014.

**Evaluation
**We show that in a test setting, only 70 EVs could be fully charged without control, whereas up to around 700 EVs can be fully charged using our control algorithm. This work was further extended to integrate EV charging control with control of distributed storage, while accounting for distributed solar generation. Details can be found here: O. Ardakanian, S. Keshav, C. Rosenberg, “Integration of Renewable Generation and Elastic Loads into Distribution Grids,”

*Springer*, 2016.