1 Distributed Optimization-based Electric Vehicle Charging and Discharging in Unbalanced Distribution Grids Nanduni I. Nimalsiri, Elizabeth L. Ratnam, Senior Member, IEEE, David B. Smith, Member, IEEE, Chathurika P. Mediwaththe, Member, IEEE, and Saman K. Halgamuge Fellow, IEEE Abstract—The worldwide proliferation of Electric Vehicles (EVs) is accelerating the need for distributed optimization ap- proaches that are both scalable and computationally efficient, to enable coordinated EV charging and discharging. This pa- per proposes a distributed optimization-based algorithm called Dis-Net-EVCD for network-aware EV charging and discharging in unbalanced distribution grids, incorporating grid voltage con- straints and EV customer economics. The Alternating Direction Method of Multipliers (ADMM) underpins the development of our Dis-Net-EVCD algorithm, wherein EVs determine their charge-discharge profiles locally via peer-to-peer communication. A receding horizon implementation of Dis-Net-EVCD supports near-real-time EV charging and discharging, while accommodat- ing unexpected EV arrivals and departures. Numerical simula- tions carried out on the IEEE 13 node test feeder demonstrate that EV customers implementing Dis-Net-EVCD yield a total op- erational cost reduction of 78% compared to uncoordinated EV charging, while improving grid voltage regulation services and satisfying EV charge requirements ahead of departure. Moreover, in simulation, Dis-Net-EVCD is shown to be approximately 60 times computationally faster than its centralized counterpart. Index Terms—Distributed optimization, electric vehicles, un- balanced distribution grids, vehicle-to-grid, voltage regulation. I. I NTRODUCTION Energy systems across the globe are transitioning to ac- commodate a dramatic uptake of Electric Vehicles (EVs), supporting a significant reduction in carbon emissions from the transportation sector [1]. EV proliferation increases grid congestion, especially when EV charging coincides with un- derlying peak load periods. Grid congestion potentially lowers supply voltages in distribution circuits to below steady-state operating limits. To enable EV proliferation without exacer- bating periods of grid congestion that potentially drive costly distribution infrastructure expansion, coordinated approaches to EV charging and discharging are required [2]. Approaches to coordinate EV charging and discharging for the regulation of system voltages in distribution grids in- clude centralized approaches [2–6] and distributed approaches [7–16]. Compared to centralized approaches, distributed ap- proaches are scalable and offer opportunities for fast comput- ing, while empowering EV customers in the decision-making process. However, the distributed approaches in [7–16] require a central coordinator (e.g., an aggregator) through which all communication is transmitted — limiting opportunities to reduce communication-based single point of failures. The authors are with the Australian National University, Aus- tralia (e-mail: nanduni.nimalsiri, elizabeth.ratnam, chathurika.mediwaththe, saman.halgamuge@anu.edu.au; david.smith@data61.csiro.au). N. I. Nimalsiri and D. B. Smith are also with Data61, CSIRO, Australia. S. K. Halgamuge is also with the University of Melbourne, Australia. The studies in [7, 8] propose distributed EV charging schemes based on the shrunken primal-dual subgradient algo- rithm to fill the load-curve valley while operating within com- pliant steady-state voltage constraints. Alternating Direction Method of Multipliers (ADMM)-based distributed EV charg- ing schemes are proposed in [9–11] to avoid system voltages dropping below the permissible limits. Other distributed EV charging schemes focused on reducing voltage fluctuations in a distribution grid include droop control [12], game theory [13] and multi-agent system modelling [14]. While the aforemen- tioned literature is limited to EV charge-only operations, the distributed approaches in [15, 16] incorporate Vehicle-to-Grid (V2G) operation to further improve voltage regulation. In practice, three-phase distribution grids are typically un- balanced in both load and impedance across phases, especially when designed with single phase and two phase laterals. With the exception of [10], the distributed EV charging schemes in [7–16] incorporate single-phase representations of three- phase distribution grids. However, single-phase representations of the power flow equations cannot capture the steady-state voltage variability across phases in an unbalanced distribution grid. Interestingly, the distributed EV charging scheme in [10] minimizes power supply costs subject to regulating unbalanced steady-state voltages. Similar to [10], we seek to develop a distributed approach that yields minimal costs for EV charging while regulating quasi-steady-state voltages across phases. Beyond [10], we seek to include V2G operations and remove the requirement for a central coordinator — reducing the risk of communication-based single point of failures. In this paper, we propose an algorithm for Dis tributed and Net work-aware EV C harging and D ischarging, referred to as Dis-Net-EVCD. Specifically, Dis-Net-EVCD minimizes EV customer operational costs while maintaining the voltages in an unbalanced distribution grid within prescribed quasi-steady- state limits. We consider EV customer operational costs associ- ated with: (1) purchasing (or otherwise being compensated for delivering) electricity on a Time-of-Use (ToU) net-metering tariff; and (2) battery degradation due to frequent charging and discharging. Dis-Net-EVCD also accommodates individ- ual EV preferences and battery constraints, including EV charge-discharge rate limits, EV battery state-of-health thresh- olds, and customer-specified charging requirements. Central to Dis-Net-EVCD is the Dual Consensus - ADMM (DC- ADMM [17]) decomposition method, in which a centralized optimization problem is decomposed into a set of tractable subproblems that are solved by EVs in parallel by exchanging information with neighboring EVs. The contributions of this paper are summarized as follows: