Efficient Desynchronization of Thermostatically Controlled Loads

This paper considers demand side management in smart power grid systems containing significant numbers of thermostatically controlled loads such as air conditioning systems, heat pumps, etc. Recent studies have shown that the overall power consumption of such systems can be regulated up and down centrally by broadcasting small setpoint change commands without significantly impacting consumer comfort. However, sudden simultaneous setpoint changes induce undesirable power consumption oscillations due to sudden synchronization of the on/off cycles of the individual units. In this paper, we present a novel algorithm for counter-acting these unwanted oscillations, which requires neither central management of the individual units nor communication between units. We present a formal proof of convergence of homogeneous populations to desynchronized status, as well as simulations that indicate that the algorithm is able to effectively dampen power consumption oscillations for both homogeneous and heterogeneous populations of thermostatically controlled loads.Comment: 6 pages, 8 Figure

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

Super-relaxation of space-time-quantized ensemble of energy loads to curtail their synchronization after demand response perturbation

Ensembles of thermostatically controlled loads (TCL) provide a significant demand response reserve for the system operator to balance power grids. However, this also results in the parasitic synchronization of individual devices within the ensemble leading to long post-demand-response oscillations in the integrated energy consumption of the ensemble. The synchronization is eventually destructed by fluctuations, thus leading to the (pre-demand response) steady state; however, this natural desynchronization, or relaxation to a statistically steady state, is too long. A resolution of this problem consists in measuring the ensemble's instantaneous consumption and using it as a feedback to stochastic switching of the ensemble's devices between on- and off- states. A simplified continuous-time model showed that carefully tuned nonlinear feedback results in a fast (super-) relaxation of the ensemble energy consumption. Since both state information and control signals are discrete, the actual TCL devices operation is space-time quantized, and this must be considered for realistic TCL ensemble modelling. Here, assuming that states are characterized by indoor temperature (quantifying comfort) and air conditioner regime (on, off), we construct a discrete model based on the probabilistic description of state transitions. We demonstrate that super-relaxation holds in such a more realistic setting, and that while it is stable against randomness in the stochastic matrix of the quantized model, it remains sensitive to the time discretization scheme. Aiming to achieve a balance between super-relaxation and customer's comfort, we analyze the dependence of super-relaxation on details of the space-time quantization, and provide a simple analytical criterion to avoid undesirable oscillations in consumption

Optimal Demand Response Schemes for Renewable Integration using Thermal Inertial Loads

We consider a smart microgrid environment where renewable power sources like wind generators are available to service the thermal inertial load along with conventional non-renewable energy sources. The flexibility in power consumption of thermal inertial loads, like air-conditioners can be used towards absorbing the fluctuations in intermittently available renewable power sources. Several optimization schemes can be used towards this goal. We discuss and analyze some of these optimization models. An optimization model which promotes renewable consumption by penalizing non-renewable consumption, but does not account for variations in the load requirements, lead to an optimal solution in which all the loads’ temperatures behave in a lockstep fashion. That is, the power is allocated in such a fashion that all the temperatures are brought to a common value and they are kept the same after that time, resulting in synchronization among all the loads. We show that under a model which additionally penalizes the comfort range violation, the optimal solution is in fact of a de-synchronizing nature, where the temperatures are intentionally kept apart to avoid power surges resulting from simultaneous comfort violation across many loads. In the sequel, we additionally take into account several other factors, such as the privacy requirements from the users of loads, architectural simplicity, and tractability of the solution. We propose a demand response architecture where no information from the end-user is required to be transferred in order to optimally co-ordinate their power consumption. We propose a simple threshold value based policy which is architecturally simple, computationally inexpensive, and achieves optimal staggering among loads to smooth the variations in non-renewable power requirements. We show that it is possible to compute the optimal solution in a number of scenarios, and give a heuristic approach to approximate the optimal solution for the scenarios where information such as cooling/heating rates, etc. is not available