Differential Game Theory in Electric Vehicle Charging Optimization

Differential Game Theory is a strong way to solve the hard optimization problems that come up when charging electric vehicles (EVs) in smart grids. This method takes into account the strategic exchanges between many parties, such as EV users, charging station operators, and grid operators, each of whom has their own goals. In this study, we look at how differential game theory can be used to find the best charging plans for electric vehicles. Our goal is to lower total energy costs, make the grid less crowded, and get more energy from green sources. We take into account how power prices change, the different types of green energy that are available, and how EVs move around by modeling the charging process as a difference game. The game-theoretic method lets you come up with plans where each player maximizes their own reward while taking into account what other players do. To find the best price methods for different situations, such as peak and off-peak hours, different amounts of green energy usage, and different pricing plans, we use Nash equilibrium solutions. Our findings show that differential game theory can successfully balance the different needs of parties, which can lead to EV charging systems that work better and last longer. Furthermore, the suggested way not only makes smart grids work better, but it also helps lower carbon emissions by supporting the use of clean energy. In addition, this method helps us understand how to create reward systems that match individuals' goals with world improvement goals. This makes it possible for EV charging strategies to work together better. This study shows that differential game theory could be a very useful tool in the development of smart and environmentally friendly transportation systems.