Cornell engineers have come up with a solution to a tricky problem: where to install charging stations for electric vehicles so they’re convenient for drivers and profitable for investors.

Without abundant and well-placed charging stations, consumers will purchase fewer electric vehicles. Without enough electric vehicle owners, publicly available charging stations won’t be profitable; that means there will be fewer of them.

“Improving charging-station infrastructure is essentially the chicken-and-the-egg problem,” said co-author Oliver Gao, the Howard Simpson 1942 Professor of Civil and Environmental Engineering at Cornell Engineering.

The research team found that in urban settings, installing an equal mix of two different kinds of stations – one that charges at a medium speed and another that charges more quickly – and distributing them strategically increases the chances that drivers will use them. And that in turn improves the profitability for investors by 50% to 100%, compared to current random placement strategies.

The research, “Bayesian Optimization for Battery Electric Vehicle Charging Station Placement by Agent-Based Demand Simulation,” published Aug. 9 in Applied Energy.

“Placing publicly available charging stations around cities sounds like a simple thing, but mathematically, it’s actually very hard,” said lead author Yeuchen Sophia Liu, Ph.D. ’22, an operations researcher in Gao’s laboratory.

That’s because simple models don’t allow for the complexity of thousands of possible driver decisions, Liu said, not to mention factors like traffic and road characteristics.

So the team reached back six decades to use Bayesian optimization, a mathematics strategy that uses past attempts at optimization to inform each subsequent attempt. That results in a much faster and productive analysis. It has become popular in machine learning algorithms.

“The Bayesian optimization model algorithm allows us to simulate millions of individual behaviors, while at the same time, find answers efficiently and quickly,” Liu said.

The team set up an algorithm that used Bayesian optimization to analyze data from the Atlanta region, home to about 6 million people. They studied the behavior of 30,000 vehicles on more than 113,000 simulated trips, forecasting a variety of commuter traffic patterns.

The algorithm found an optimal placement using only 2% of the runtime of existing benchmark methods. “This enables the use of the algorithm on a more complex, real-world scale,” Liu said.

The team found that medium speed “level-2” commercial charging stations and direct-current, fast-charging “DCFC” stations serve different needs. Drivers who park for 20 minutes – while running into a grocery store, for example – are likely to choose fast charging spots. But if someone is going to work and parking for several hours, the driver will likely select the level-2 station.

In addition, a sensitivity analysis demonstrated that factors such as the size of the battery electric vehicle market, charging preferences and charging price have significant impacts on the optimal placement and profitability of an electric vehicle charging infrastructure project.

The findings have important implications, Liu said. In the U.S., according to the paper, eight states have adopted California’s Zero Emission Vehicle program mandate to have at least 3.3 million zero-emission light-duty vehicles – replacing carbon combustion engine cars – on the road by 2025.

“Economically strategic placement of charging stations could play a pivotal role in accelerating the transition to zero-emission vehicles,” Liu said.

In addition to Liu and Gao, co-authors are Mohammad Tayarani, a visiting scientist in Gao’s lab, and Fengqi You, the Roxanne E. and Michael J. Zak Professor in Energy Systems Engineering in Cornell Engineering. The work was funded by a grant from the U.S. Department of Transportation. 

Gao and You are senior faculty fellows at the Cornell Atkinson Center for Sustainability.