Recently it has been shown that an aggregation of Thermostatically Controlled Loads (TCLs) can be utilized to provide fast regulating reserve service for power grids and the behavior of the aggregation can be captured by a stochastic battery with dissipation. In this paper, we address two practical issues associated with the proposed battery model. First, we address clustering of a heterogeneous collection and show that by finding the optimal dissipation parameter for a given collection, one can divide these units into few clusters and improve the overall battery model. Second, we analytically characterize the impact of imposing a no-short-cycling requirement on TCLs as constraints on the ramping rate of the regulation signal. We support our theorems by providing simulation results.
TCL have been recently considered for providing load following and regulation services to the grid @cite_4 @cite_0 @cite_24 @cite_7 @cite_17 @cite_20 . In particular, it has been recently shown that the aggregate flexibility offered by a collection of TCL can be succinctly modeled as a stochastic battery with dissipation @cite_10 @cite_2 . The power limits and energy capacity of this battery model can be calculated in terms of TCL model parameters and exogenous variables such as ambient temperature and user-specified set-points. Simple battery models are also considered in @cite_0 @cite_20 . Clustering and no-short-cycling of TCL have been reported in @cite_15 @cite_9 .
@cite_4 @cite_7 @cite_9 @cite_0 @cite_24 @cite_2 @cite_15 @cite_10 @cite_20 @cite_17
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The thermal storage potential of Thermostatically Controlled Loads (TCLs) is a tremendous flexible resource for providing various ancillary services to the grid. In this work, we study aggregate modeling, characterization, and control of TCLs for frequency regulation service provision. We propose a generalized battery model for aggregating flexibility of a collection of TCLs. A theoretical characterization of the aggregate power limits and energy capacity of TCLs is provided. Moreover, we propose a priority-stack-based control strategy to manipulate the power consumption of TCLs for frequency regulation, while preventing short cycling on the units. Numerical experiments are provided to show the accuracy of the proposed model and the efficacy of the developed control method. As the penetration of intermittent energy sources grows substantially, loads will be required to play an increasingly important role in compensating the fast time-scale fluctuations in generated power. Recent numerical modeling of thermostatically controlled loads (TCLs) has demonstrated that such load following is feasible, but analytical models that satisfactorily quantify the aggregate power consumption of a group of TCLs are desired to enable controller design. We develop such a model for the aggregate power response of a homogeneous population of TCLs to uniform variation of all TCL setpoints. A linearized model of the response is derived, and a linear quadratic regulator (LQR) has been designed. Using the TCL setpoint as the control input, the LQR enables aggregate power to track reference signals that exhibit step, ramp and sinusoidal variations. Although much of the work assumes a homogeneous population of TCLs with deterministic dynamics, we also propose a method for probing the dynamics of systems where load characteristics are not well known. Thermostatically controlled loads (TCLs), such as refrigerators, air conditioners, and electric water heaters, can be aggregated and used to deliver power systems services. The effectiveness of control strategies depends on the level of infrastructure and communications. This paper explores the use of TCLs for load following when measured state information is not available in real time. We use Markov Chain models to describe the temperature state evolution of populations of TCLs, and Kalman filtering techniques for both state estimation and joint parameter state estimation. We find power tracking RMS errors in the range of 2-16 of the aggregate steady state power consumption of the TCL population. Results depend upon the information available for system identification, state estimation, and control. If high precision tracking is not required, TCLs may not need to be metered to provide state information to the central controller in real time or at all. We consider the capacity of an energy harvesting communication channel with a finite-sized battery. As an abstraction of this problem, we consider a system where energy arrives at the encoder in multiples of a fixed quantity, and the physical layer is modeled accordingly as a finite discrete alphabet channel based on this fixed quantity. Further, for tractability, we consider the case of binary energy arrivals into a unit-capacity battery over a noiseless binary channel. Viewing the available energy as state, this is a state-dependent channel with causal state information available only at the transmitter. Further, the state is correlated over time and the channel inputs modify the future states. We show that this channel is equivalent to an additive geometric-noise timing channel with causal information of the noise available at the transmitter. We provide a single-letter capacity expression involving an auxiliary random variable, and evaluate this expression with certain auxiliary random variable selection, which resembles noise concentration and lattice-type coding in the timing channel. We evaluate the achievable rates by the proposed auxiliary selection and extend our results to noiseless ternary channels.