Transportation systems are undergoing a major transition with the integration of electric vehicles (EVs). However, due to increase in battery energy and charger power ratings, potential adverse effects on the distribution grid is a crucial issue to be addressed. Large voltage drops at charging nodes will deteriorate the quality of power service and cause unfair utilization of grid capacity among EV users. Safe and efficient operation of the grid along with a fast, convenient, and fair charging strategy is an important research problem. In this paper, we adapt the additive increase multiplicative decrease (AIMD) algorithm used in the Internet congestion control to EV charging using only local node measurements. We analyze the relationship between distance and grid voltage, and show how to extract this information from local measurements. Then, we present a detailed analysis to understand the relationship between distance and charging power in a distribution network to better address the fairness in the proposed AIMD EV charging algorithm. Results show that localized information at charging node voltages include important signature information on grid congestion and can be used to implement AIMD control for EV charging.