Using distributed energy resources (DERs), such as thermostatically controlled loads (TCLs), electric vehicles (EVs), and energy storage systems (ESSs) as a way to manage demand has been known for decades. A demand management scheme that explicitly considers the individual DER's local quality of service (QoS) is known as demand dispatch. Packetized energy management (PEM) is a demand dispatch paradigm that borrows packet-based concepts from wireless communications to dynamically manage fleets of DER at-scale and in realtime via small, discrete fixed-duration/fixed-power energy packets. PEM addresses QoS in a bottom-up fashion by having a coordinator authorize/deny incoming requests from DERs to consume energy packets. This manuscript extends prior work on modeling a large-scale population (i.e., macro-model) of homogeneous TCLs and ESSs operating under the PEM paradigm. In particular, we extend the macro-model methodology to include deferrable loads (DLs), such as EVs, together with analysis of QoS guarantees. Comparisons between an agent-based (micro-model) simulation and the proposed macro-model are presented to validate modeling accuracy and QoS guarantees.

The purpose of this paper is to address the problem of physical realizability for $n$-level quantum systems. We provide necessary and sufficient conditions for quantum stochastic differential equations that ensure the existence of physical parameters characterizing the unitary evolution required by the laws of quantum mechanics. Also, these conditions guarantee the preservation of the commutation and anticommutation relations of the underlying Lie algebra $su(n)$.