# Smart Electric Vehicle Charging via Adjustable Real-Time Charging Rates
## 1 Introduction  
As cities expand and populations increase, the amount of available fossil fuels decreases and air quality laws are made stricter [1]. Thus, Zero-Emission Vehicles (ZEV) become a more appealing answer to future transportation problems [2, 3, 4]. California has initiated measures to encourage the adoption of ZEVs, to have at least 5 million ZEVs on the road by 2030 to reduce emissions from transportation sources [5]. Battery electric vehicles (BEVs), fuel cell electric vehicles (FCEVs), and plug-in electric vehicles (PEVs) are the three types of ZEVs [6]. Since 2011, almost two million PEVs have been sold, with California accounting for nearly one-third of all sales, shown in Figure 1[7, 8, 9]. However, increased PEV adoption will lead to disturbances in the electric grid because of power demands exceeding the grid's initial design conditions [10, 11, 12, 13, 14]. The increased electric demand from PEV charging can easily double or even triple a household's energy demand [15, 16]. Furthermore, the load from multiple charging PEVs can shorten transformer life and necessitate repairs and replacements of parts earlier than expected [15, 17]. These concerns led to the development of \"smart charging\" protocols [18]. These strategies allow PEV adoption to expand and manage electric grid levels within safe limits, reducing the need for utility investments to renovate the distribution network to accommodate larger demand loads [19, 20, 21, 22]. Without smart charging protocols, vehicles immediately begin charging when plugged in, regardless of the time or demand, which is referred to as \"uncontrolled charging\" [23]. By shifting charging to the late evenings and early mornings, a practice known as \"valley filling\" is used to control PEV charging [19, 24, 25]. This technique charges vehicles when the grid's energy demand is low, lessening the impact of the extra load caused by charging PEVs. Multiple charging control systems have been created to regulate PEV charging, with decentralized and centralized control being the most common [26, 27]. Centralized smart charging methods rely on a central operating controller to manage charging patterns for customers [28; 29; 30; 31; 32]. The controller lowers the demand load by estimating the ideal charging profile for each PEV based on the customer's requested charge, residence duration, and vehicle plug-in time, as well as the predicted load [1; 28; 33; 34; 35; 36]. Several centralized charging methods that incorporate fuzzy logic have been produced. [PERSON] et al. [35] developed a centralized method employing maximum sensitivity selection (MSS) optimization and fuzzy logic to optimize the algorithm. [PERSON] et al. [37] improved on [PERSON] et al. [35] and provided two solutions for reducing energy generation costs and grid losses while increasing electricity delivered to automobiles. Fuzzy logic is used by [PERSON] et al. [37] to improve the effectiveness of the genetic algorithm and discrete particle swarm optimization used in the study. However, this approach is not very practical because vehicles cannot input a plug-out time. In another study, [PERSON] et al. [38] implement fuzzy logic controllers in PEV charging stations at distribution substations. The controller that is applied to PEV charging stations regulates the amount of power each station receives. The controller installed in the substation monitors the total amount of power consumed by all the charging stations connected to it. This protocol demonstrates that it can peak-shape, load flatten, and valley-fill charging profiles; however, this strategy relies on vehicle-to-grid (V2G) technology. Unfortunately, [PERSON] et al. [39] show that V2G technology accelerates wear and the frequency that PEVs need battery replacements. Several developed decentralized valley-filling algorithms [15; 19; 28; 40] have gained interest due to their ability to allow PEVs to establish individual charging patterns.