# Smart Electric Vehicle Charging via Adjustable Real-Time Charging Rates
## 1 Introduction
Users can create their own charging patterns, which can be based on a priced or non-priced electric scheme [40; 41]. These profiles are sent to a centralized operating controller that updates the demand load, adding the newly constructed PEV charging pattern [42; 43]. Unfortunately, there is not a guarantee that the overall structure of the demand load will be optimal when using this approach [28; 44; 45]. [PERSON] et al. [19] introduced a valley-filling algorithm that generates a near-ideal solution, but it produces significant harmful transformer overload and overheating. [PERSON] et al. [46] expand this strategy by using Modified Timeslot Rejection (MTR) to reduce stress on transformers. The MTR protocol uses forecasted data to determine the optimal times to charge vehicles and establishes vehicle charging patterns based on this information. When a vehicle plugs into the network, the algorithm assesses the forecasted baseload and determines the optimal time for the vehicle to charge using the grid valley-filling algorithm by [PERSON] et al. [19]. After the profile is created, the algorithm verifies that the profile does  
Figure 1: Cumulative PEV sales in the U.S. from 2011 to 2020.  
not violate any of the recommended temperature and loading limits in the IEEE C57.91 standard [47]. If the profile does exceed any transformer operating limits, the profile is adjusted to minimize stress on the transformer. The algorithm then updates the charging profile for the vehicle and sends it to the grid operator to update the projected demand load. The process is then repeated for the following vehicle that plugs in. MTR performs well when the forecasted and actual baseloads are extremely similar; however, its functionality decreases significantly when the predicted and actual baseloads deviate. In reality, demand varies from day to day. While historical data may provide a relative sense of what to expect, it can never be exact, especially given the dramatic rise in PEVs and BEVs nationally. Algorithms that are more robust to these changes without requiring costly additional optimization are needed. As technology evolves, the need for an algorithm that can adjust for variation will intensify as the number and power demand of devices connecting to the grid will continue to increase [48]. These changes will lead to more frequent and larger fluctuations in baseloads, making an algorithm that can adjust for variation valuable. Additionally, MTR only optimizes transformer loads that violate the operating limits. If all transformer loads were assessed, not only when operating boundaries are violated, transformer life can be extended further as loss of transformer life is directly related to the load transformers observe. Focusing on local distribution transformers is important because a single PEV home-charger can draw as much as 11.5 kW, enabling a few simultaneously charging PEVs during an early summer evening to dramatically degrade transformer lifespan [33; 49]. [PERSON] et al. show that extreme uncontrolled charging conditions can increase the loss of life percentage for transformers by over 2000% in as little as 24 h [15]. Furthermore, residential transformers should be monitored more heavily, as they are the component most susceptible to damage from uncontrolled damage within the U.S. power system [50]. This work presents Adjustable Real-Time Valley Filling (ARVF), a practical valley-filling strategy that determines its solutions in real time. ARVF extends the analysis of MTR by [PERSON] et al. [46], focusing on improving PEV charging at the local power distribution level and minimizing excess damage to distribution transformers, a rationale from [PERSON]. [PERSON] et al. [50]. The objectives of this study are (1) to create a robust strategy that can adjust to significant unforeseen variations in the forecasted baseload and (2) to investigate and determine the amount of variation in the baseload that causes algorithms such as [PERSON] et al. [19] and [PERSON] et al.