With the recently increasing adoption of transactive energy markets, the role of a load aggregator is becoming increasingly important. Among the many tasks of an aggregator, the task of managing the electricity consumption among a group of grid-interactive efficient buildings according to the demand on the grid is taken up. Specifically, the task of allocating a certain amount of power among the participating customers while respecting their preferences and comfort is considered. Modeling this as an aggregate flexibility, the virtual battery conditions that are employed to verify the feasibility of a candidate power profile are derived. A feasible power profile, when allocated, satisfies specified comfort bands. To determine the ideal power requirement of the loads, the model-free control method is employed. The feasible power profile is allocated by embedding the customers’ preferences through weights, posing the power constraint as a hyperplane, and employing a weighted projection from the ideal power requirements onto the constraint plane to solve the considered task. The proposed method is computationally efficient and scalable to any number of heterogeneous thermostatically controlled loads in buildings.