Aggregation and Control of Populations of Thermostatically Controlled Loads by Formal Abstractions

This work discusses a two-step procedure, based on formal abstractions, to generate a finite-space stochastic dynamical model as an aggregation of the continuous temperature dynamics of a homogeneous population of Thermostatically Controlled Loads (TCL). The temperature of a single TCL is described by a stochastic difference equation and the TCL status (ON, OFF) by a deterministic switching mechanism. The procedure is formal as it allows the exact quantification of the error introduced by the abstraction -- as such it builds and improves on a known, earlier approximation technique in the literature. Further, the contribution discusses the extension to the case of a heterogeneous population of TCL by means of two approaches resulting in the notion of approximate abstractions. It moreover investigates the problem of global (population-level) regulation and load balancing for the case of TCL that are dependent on a control input. The procedure is tested on a case study and benchmarked against the mentioned alternative approach in the literature.Comment: 40 pages, 21 figures; the paper generalizes the result of conference publication: S. Esmaeil Zadeh Soudjani and A. Abate, "Aggregation of Thermostatically Controlled Loads by Formal Abstractions," Proceedings of the European Control Conference 2013, pp. 4232-4237. version 2: added references for section

COHORT: Coordination of Heterogeneous Thermostatically Controlled Loads for Demand Flexibility

Demand flexibility is increasingly important for power grids. Careful coordination of thermostatically controlled loads (TCLs) can modulate energy demand, decrease operating costs, and increase grid resiliency. We propose a novel distributed control framework for the Coordination Of HeterOgeneous Residential Thermostatically controlled loads (COHORT). COHORT is a practical, scalable, and versatile solution that coordinates a population of TCLs to jointly optimize a grid-level objective, while satisfying each TCL's end-use requirements and operational constraints. To achieve that, we decompose the grid-scale problem into subproblems and coordinate their solutions to find the global optimum using the alternating direction method of multipliers (ADMM). The TCLs' local problems are distributed to and computed in parallel at each TCL, making COHORT highly scalable and privacy-preserving. While each TCL poses combinatorial and non-convex constraints, we characterize these constraints as a convex set through relaxation, thereby making COHORT computationally viable over long planning horizons. After coordination, each TCL is responsible for its own control and tracks the agreed-upon power trajectory with its preferred strategy. In this work, we translate continuous power back to discrete on/off actuation, using pulse width modulation. COHORT is generalizable to a wide range of grid objectives, which we demonstrate through three distinct use cases: generation following, minimizing ramping, and peak load curtailment. In a notable experiment, we validated our approach through a hardware-in-the-loop simulation, including a real-world air conditioner (AC) controlled via a smart thermostat, and simulated instances of ACs modeled after real-world data traces. During the 15-day experimental period, COHORT reduced daily peak loads by an average of 12.5% and maintained comfortable temperatures.Comment: Accepted to ACM BuildSys 2020; 10 page

Robust Engineering of Dynamic Structures in Complex Networks

Populations of nearly identical dynamical systems are ubiquitous in natural and engineered systems, in which each unit plays a crucial role in determining the functioning of the ensemble. Robust and optimal control of such large collections of dynamical units remains a grand challenge, especially, when these units interact and form a complex network. Motivated by compelling practical problems in power systems, neural engineering and quantum control, where individual units often have to work in tandem to achieve a desired dynamic behavior, e.g., maintaining synchronization of generators in a power grid or conveying information in a neuronal network; in this dissertation, we focus on developing novel analytical tools and optimal control policies for large-scale ensembles and networks. To this end, we first formulate and solve an optimal tracking control problem for bilinear systems. We developed an iterative algorithm that synthesizes the optimal control input by solving a sequence of state-dependent differential equations that characterize the optimal solution. This iterative scheme is then extended to treat isolated population or networked systems. We demonstrate the robustness and versatility of the iterative control algorithm through diverse applications from different fields, involving nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI), electrochemistry, neuroscience, and neural engineering. For example, we design synchronization controls for optimal manipulation of spatiotemporal spike patterns in neuron ensembles. Such a task plays an important role in neural systems. Furthermore, we show that the formation of such spatiotemporal patterns is restricted when the network of neurons is only partially controllable. In neural circuitry, for instance, loss of controllability could imply loss of neural functions. In addition, we employ the phase reduction theory to leverage the development of novel control paradigms for cyclic deferrable loads, e.g., air conditioners, that are used to support grid stability through demand response (DR) programs. More importantly, we introduce novel theoretical tools for evaluating DR capacity and bandwidth. We also study pinning control of complex networks, where we establish a control-theoretic approach to identifying the most influential nodes in both undirected and directed complex networks. Such pinning strategies have extensive practical implications, e.g., identifying the most influential spreaders in epidemic and social networks, and lead to the discovery of degenerate networks, where the most influential node relocates depending on the coupling strength. This phenomenon had not been discovered until our recent study