A Scalable Virtual Zonal Aggregation Framework for EV Charging Coordination and Transformer Overload Prevention in Residential Distribution Networks

Abstract

The accelerating adoption of electric vehicles (EVs) is transforming residential electricity demand in ways that traditional low-voltage distribution networks were never designed to accommodate. Coincident, uncoordinated EV charging produces large, synchronised load peaks that regularly push residential distribution transformers beyond their thermal ratings — accelerating insulation aging, threatening voltage stability, and increasing the risk of unplanned outages. Existing coordination frameworks address this challenge imperfectly. Centralised approaches operated by a Distribution System Operator require direct control of customer assets and face prohibitive computational burdens at scale. Decentralised peer-to-peer schemes preserve customer autonomy but provide no mechanism to enforce a binding physical capacity constraint at the transformer level. Neither paradigm offers a market-compatible mechanism that simultaneously protects the transformer, reduces customer electricity costs, and sustains the coordinating intermediary without external subsidy. This thesis introduces a Virtual Zonal Aggregation (VZA) framework designed to fill that gap. The architecture partitions a distribution feeder into virtual zones, each administered by a cloud-hosted Virtual Zonal Aggregator (VZA) that coordinates one or more Virtual Transformers — software digital twins of physical distribution transformers — within its zone. The VZA sets day-ahead retail price signals derived from wholesale market prices and iteratively refines them; each Virtual Transformer enforces its own transformer's thermal capacity limit by aggregating the load profiles of its downstream customers and detecting overloaded hours. Customer Home Energy Management Systems (HEMS) respond to these signals by solving individual cost-minimisation problems and returning updated load profiles. No direct load control is imposed; customers retain full autonomy over their EV charging decisions. When the aggregated load in a zone exceeds a transformer's thermal limit, the Virtual Transformer reports the overload to the VZA, which initiates an iterative price-update loop — increasing prices in overloaded hours and reducing them in underloaded ones — until the load profile becomes feasible. The framework is validated through a simulation case study on a 15-customer residential feeder served by a single distribution transformer, using real Hourly Ontario Energy Price (HOEP) wholesale data and seasonal baseload profiles derived from 18 months of anonymised smart-meter data provided by Toronto Hydro. Under the Ontario Time-of-Use (TOU) baseline (Scenario A), uncoordinated EV charging causes transformer overloads in both winter and summer. The VZA framework (Scenario B) eliminates all overloads in 6 iterations (winter) and 15 iterations (summer) through iterative price-signal updates, while simultaneously delivering a 43.4% reduction in community net electricity cost in winter and a 58.3% reduction in summer — with every individual customer benefiting. The Virtual Zonal Aggregator sustains a daily profit of $10.15 (winter) and $11.87 (summer), confirming economic viability without external subsidy or direct load curtailment. The scalability and safety of the framework beyond the single-zone case study are established through seven formal results derived for standard IEEE radial distribution test feeders and presented in Chapter 3. A zone independence proposition proves that in any radial network each Virtual Transformer's overload sub-problem is fully decoupled from every other zone by Kirchhoff's current law, so the multi-zone coordination problem decomposes into N independent parallel sub-problems. A voltage stability proposition proves that enforcing the per-transformer kW ceiling simultaneously guarantees an analytical lower bound on all bus voltages satisfying the ANSI C84.1 Range A service requirement (≥ 0.95 p.u.), validated numerically on the IEEE 33-bus feeder via linearised DistFlow under standard unity-PF EV and bounded-reactive-load assumptions. A zone feasibility proposition derives a necessary and sufficient condition — relating the transformer's 24-hour load headroom to the zone's aggregate EV energy demand — under which an overload-free schedule is guaranteed to exist. A finite convergence proposition proves that the iterative price-update algorithm eliminates all overloads in a finite number of iterations; a network-wide corollary extends this to N parallel zones. A system non-disruption proposition establishes that the algorithm is operationally conservative at every intermediate iteration: it preserves each customer's full daily energy requirement, reduces total transformer overload monotonically at each step, and keeps retail prices within operator-set bounds throughout. Beyond these qualitative guarantees, a geometric overload reduction theorem sharpens the convergence result to a quantitative rate: the total overload energy contracts geometrically by factor (1 − c) per iteration, where the contraction constant c ∈ (0, 1) is derived entirely from physical system parameters and algorithm design choices, giving an explicit closed-form iteration bound K*. A counter-intuitive implication is that larger zones converge at least as fast as smaller ones, because aggregate EV flexibility grows with zone size while the transformer limit is fixed. A horizontal scalability theorem proves that adding zones to the network does not increase the iteration count for any existing zone and that total wall-clock time scales as O(K* · Mmax), independent of the number of zones. Together, these results place the single-zone empirical study on a rigorous quantitative theoretical footing and guarantee that the architecture composes to networks of arbitrary size at no additional algorithmic cost.