A K-Additive Fuzzy Logic Approach for Optimizing FCS Sizing and Enhanced User Satisfaction

Efficient network management plays a pivotal role in the Internet of Vehicles (IoVs), emphasizing the need for the proper consideration of fast-charging station (FCS) allocation and sizing. Insufficient attention to these aspects when integrating FCSs into the distribution network can result in detrimental effects on the power grid. This may manifest in increased power loss, voltage instability, and imbalances in demand and supply. Therefore, ensuring optimal FCS allocation and sizing is critical to prevent potential negative repercussions on the power grid within the context of IoVs [19]. While predictions of electric vehicle (EV) charging behavior and waiting time for charging can encompass various categories, this study specifically focuses on minimizing the delay that occurs by waiting in the queue and at the charging station and finding the optimal number of charging stations. Other charging behaviors, such as forecasting whether the EVs will be charged the following day [20], identifying the use of fast charging [21], predicting the time to the next plug [22], charge profile prediction [18], charging speed prediction [19], and forecasting charging capacity and daily charging times [23], offer valuable insights. However, from a cost and user satisfaction point of view, the more significant focus lies in finding the number of charging stations that can serve the EVs without causing too much delay. Figure 1a,b presents detailed statistics on introducing EVs into the global market in different countries and the retail price, respectively [24]. Nations worldwide are implementing comparable government initiatives to boost the development and manufacture of electric vehicles (EVs) and to ensure the stability of their supply chains for essential minerals necessary for EV production. While we have only highlighted the efforts of China, Europe, and the US for brevity, many other countries around the world are developing their own financial programs to promote EV initiatives. The growth of electric vehicle (EV) sales in China has been driven by supportive policies and low retail prices. In 2022, the average price of small EVs in China was under USD 10,000, much lower than in Europe and the US, where it exceeded USD 30,000. The top-selling EVs in China, like the Wuling Mini BEV and BYD’s Dolphin, were priced below USD 16,000, indicating strong demand for compact models. Chinese automakers focus on cost reduction and smaller, more affordable models, benefiting from lower costs and supply-chain integration. In contrast, Western automakers prioritize larger, luxury EVs, offering a better range but limiting options for mass-market consumers. Different evolutionary algorithms [25,26,27,28,29] have been proposed for EV systems; however, very few have used fuzzy logic to predict the number of charging stations as well as the average waiting time of EV users. Frendo et al. [30] employed support vector machines (SVM) to predict the arrival and departure times of electric vehicle (EV) commuters on a university campus. Utilizing historical arrival and departure times along with temporal features such as week, day, and hour, the reported mean absolute percentage error (MAPE) stood at 2.9% and 3.7% for arrival and departure times, respectively. Ref. [31] employed ensemble machine-learning techniques, incorporating SVM, random forest (RF), and a diffusion-based kernel density estimator (DKDE) for predicting session length and energy consumption. The training data involved historical charging records from two distinct datasets—one public and the other residential. The ensemble model outperformed individual models in both predictions, with reported symmetric mean absolute percentage errors (SMAPEs) of 10.4% for the duration and 7.5% for consumption. In the literature, many studies have been proposed for minimizing waiting time and predicting the optimal sizing and location of charging stations where machine-learning algorithms are incorporated; however, this study is the first to address the waiting time and sizing of charging stations based on fuzzy logic in EVs. In [32], the authors introduced a multi-objective optimization approach to determine the optimal location and size of fast-charging stations (FCSs) near Bangi City, Malaysia. This method considers factors such as the Google Maps API, road traffic density, and harmonic power flow. The optimization problem is formulated to minimize various costs, with the primary objective being to reduce the total expenditure. In [33], the authors developed a mixed-integer programming model to address the best charging station location and to maximize the number of people who can complete round-trip itineraries. In [34], the authors proposed an optimization cost model for locating and sizing charging stations for electric vehicles. The model considers the number of EVs and uses the Analytic Hierarchy Process (AHP) to assign weights to candidate locations. The model incorporates constraints like the distance between the substation and candidate locations and the installation cost of charging stations. As can be observed, most of the studies in the literature focus on solving the sizing problem of charging stations; however, important factors related to users’ waiting times and the queuing model of the charging stations are not well focused on. Hence, this paper adopts the M/M/c queuing model for the charging stations and determines the optimal number of charging stations, which is crucial from the EV user’s perspective, by applying the K-additive fuzzy logic algorithm to predict the average waiting time and the optimal number of charging stations.