[Paper Review] Smart Routing of Electric Vehicles for Load Balancing in Smart Grids

S. Rasoul Etesami, Walid Saad+2 more|arXiv (Cornell University)|May 10, 2017

Electric Vehicles and Infrastructure37 references7 citations

TL;DR

This paper proposes a distributed game-theoretic framework for smart routing of electric vehicles (EVs) in smart grids to balance electricity load while accounting for traffic congestion and charging station waiting times. Using noncooperative game theory, it proves the existence of a pure-strategy Nash equilibrium with a price of anarchy bounded by the ratio of ground load variance to the number of EVs, ensuring near-optimal system efficiency even under selfish behavior.

ABSTRACT

Electric vehicles (EVs) are expected to be a major component of the smart grid. The rapid proliferation of EVs will introduce an unprecedented load on the existing electric grid due to the charging/discharging behavior of the EVs, thus motivating the need for novel approaches for routing EVs across the grid. In this paper, a novel gametheoretic framework for smart routing of EVs within the smart grid is proposed. The goal of this framework is to balance the electricity load across the grid while taking into account the traffic congestion and the waiting time at charging stations. The EV routing problem is formulated as a noncooperative game. For this game, it is shown that selfish behavior of EVs will result in a pure-strategy Nash equilibrium with the price of anarchy upper bounded by the variance of the ground load induced by the residential, industrial, or commercial users. Moreover, the results are extended to capture the stochastic nature of induced ground load as well as the subjective behavior of the owners of EVs as captured by using notions from the behavioral framework of prospect theory. Simulation results provide new insights on more efficient energy pricing at charging stations and under more realistic grid conditions.

Motivation & Objective

• To address the challenge of load imbalance in smart grids caused by the uncoordinated charging of rapidly proliferating electric vehicles (EVs).
• To design a distributed control mechanism that enables EVs to self-optimally route to charging stations while minimizing travel and waiting costs.
• To incorporate real-world factors such as traffic congestion, variable ground load, and behavioral decision-making in EV owners.
• To quantify system efficiency under selfish routing using the price of anarchy and social cost metrics.
• To extend the model to stochastic ground loads and subjective EV behavior using prospect theory.

Proposed method

• Formulates the EV routing problem as a repeated noncooperative game where each EV minimizes its individual cost function, including travel, waiting, and charging costs.
• Introduces a potential function to prove the existence of a pure-strategy Nash equilibrium (NE) in the game.
• Derives an upper bound on the price of anarchy (PoA) as the ratio of the variance of the ground load to the total number of EVs.
• Extends the model to stochastic ground loads by incorporating random variables into the cost function and analyzing system performance under uncertainty.
• Applies prospect theory (PT) to model risk-sensitive behavior of EV owners, using parameters from behavioral studies to simulate subjective valuation of costs and benefits.
• Employs simulation-based evaluation to compare pricing schemes (quadratic vs. exponential) under different EV population sizes and behavioral profiles.

Experimental results

Research questions

• RQ1 What is the efficiency loss due to selfish routing of EVs in a smart grid, and can it be bounded?
• RQ2 How does the system performance degrade under selfish behavior, and what is the theoretical limit of inefficiency?
• RQ3 Can a distributed, game-theoretic approach achieve load balancing while respecting traffic and charging constraints?
• RQ4 How do behavioral biases in EV owners—such as risk aversion or overestimation of delays—affect system efficiency and pricing design?
• RQ5 Which energy pricing strategy (quadratic or exponential) performs better under realistic, heterogeneous EV behavior and stochastic loads?

Key findings

• The price of anarchy (PoA) is upper bounded by the ratio of the variance of the ground load to the total number of EVs, implying near-optimal system efficiency for large EV populations.
• Any achieved pure-strategy Nash equilibrium significantly improves load balancing across the grid, with the potential for even tighter bounds on social cost.
• For risk-neutral EVs (parameter set C), the system achieves the best load balance and lowest PoA, indicating that behavioral biases degrade system performance.
• Simulation results show that quadratic pricing is more effective for large numbers of EVs, while exponential pricing performs better when EV numbers are small.
• EVs with subjective valuations (groups D and E in prospect theory) cause the worst system outcomes, necessitating tailored pricing mechanisms to correct for behavioral inefficiencies.
• The framework maintains stability and efficiency under stochastic ground loads, with the potential function approach ensuring convergence to equilibrium despite uncertainty.