A review on mathematical models of electric vehicle for energy management and grid integration studies

Electric Vehicle (EV) users are always concerned about the vehicle's mileage, available electric range, availability of the nearest charging station, power processing capabilities, slot availability at the station, tariff rates, type of charger, response by the aggregator or the independent system operator, etc. For efficient EV grid integration and power exchange, an appropriate mathematical framework in terms of the aforementioned must be constructed. Framing and building an acceptable and efficient mathematical model is extremely tough due to the intricacies of real-world difficulties involved with EV integration and charging station infrastructure. Depending on the target function, mathematical models might be single-objective or multi-objective, but they will always attempt to reduce EV operating costs (maximizing profit) and grid load capacity. The correctness of any model's output is influenced by deep limitations and advanced mathematical modeling methodologies. This article provides an extensive examination on numerous mathematical models proposed by researchers to lower operating costs, energy consumption, CO2 emissions, frequency deviation, and EV trip distance, among other things. The deterministic and probabilistic mathematical models discussed in this paper highlight excellent results such as an average 30 % reduction in operation cost, a faster (at least 10s earlier) settling time thus enhancing stability, an average 10 % reduction in CO2 emission, an average 20 % reduction in energy consumption, an average 5 % reduction in fuel cost, and zero frequency deviation, etc. The review also provides actual insights into various EV models, their objectives, background, validation and test setup, and relative constraints, emphasizing their limitations and benefits.