Coordinated aggregation of a large population of thermostatically controlled loads (TCLs) presents a great potential to provide various ancillary services to the grid. One of the key challenges of integrating TCLs into system level operation and control is developing a simple and portable model to accurately capture their aggregate flexibility. In this paper, we propose a geometric approach to model the aggregate flexibility of TCLs. We show that the set of admissible power profiles of an individual TCL is a polytope, and their aggregate flexibility is the Minkowski sum of the individual polytopes. In order to represent their aggregate flexibility in an intuitive way and achieve a tractable approximation, we develop optimization-based algorithms to approximate the polytopes by the homothets of a given convex set. As a special application, this set is chosen as a \emph{virtual battery model} and the corresponding optimal approximations are solved efficiently by equivalent linear programming problems. Numerical results show that our algorithms yield significant improvement in characterizing the aggregate flexibility over existing modeling methods. We also conduct case studies to demonstrate the efficacy of our approaches by coordinating TCLs to track a frequency regulation signal from the Pennsylvania-New Jersey-Maryland (PJM) Interconnection.
We consider the problem of determining the optimal aggregate power consumption of a population of thermostatically controlled loads. This is motivated by the problem of synthesizing the demand response for a load serving entity (LSE) serving a population of such customers. We show how the LSE can opportunistically design the aggregate reference consumption to minimize its energy procurement cost, given day-ahead price, load and ambient temperature forecasts, while respecting each individual load's comfort range constraints. The resulting synthesis problem is shown to be amenable to optimal con…
Thermostatically-controlled-loads (TCLs) have been regarded as a good candidate for maintaining the power system reliability by providing operating reserve. The short-term reliability evaluation of power systems, which is essential for power system operators in decision making to secure the system real time balancing, calls for the accurate modelling of operating reserve provided by TCLs. However, the particular characteristics of TCLs make their dynamic response different from the traditional generating units, resulting in difficulties to accurately represent the reliability of operating rese…
Considering the potential of thermostatically controlled loads (TCLs) to provide flexibility in demand response or load control, a semi-Markov model (SMM) for the ON/OFF controlled TCL is developed in this paper. This model makes full use of the adjustment flexibility of TCLs when the control period is long and maintains the diversity of switch state in the cluster. This model also can satisfy user comfort and protect user privacy. Then, this paper adopts the cyber-physical system (CPS) to realize the coupling of the discrete control process and the continuous physical process. Finally, the pr…
A significant portion of electricity consumed worldwide is used to power thermostatically controlled loads (TCLs) such as air conditioners, refrigerators, and water heaters. Because the short-term timing of operation of such systems is inconsequential as long as their long-run average power consumption is maintained, they are increasingly used in demand response (DR) programs to balance supply and demand on the power grid. Here, we present an \textit{ab initio} phase model for general TCLs, and use the concept to develop a continuous oscillator model of a TCL and compute its phase response to …
This chapter presents the development and the analysis of a scheme for aggregate power tracking control of heterogeneous populations of thermostatically controlled loads (TCLs) based on partial differential equations (PDEs) control theory and techniques. By employing a thermostat--based deadband control with forced switching in the operation of individual TCLs, the aggregated dynamics of TCL populations are governed by a pair of Fokker--Planck equations coupled via the actions located both on the boundaries and in the domain. The technique of input-output feedback linearization is used for the…
This paper addresses the modeling and control of heterogeneous populations of thermostatically controlled loads (TCLs) operated by model predictive control (MPC) schemes at level of each TCL. It is shown that the dynamics of such TCLs populations can be described by a pair of Fokker-Planck equations coupled via the actions in the domain. The technique of input-output feedback linearization is used in the design of aggregate power control, which leads to a nonlinear system in closed loop. Well-posedness analysis is carried out to validate the developed control scheme. The closed-loop stability …
Aggregation of a large number of responsive loads presents great power flexibility for demand response. An effective control and coordination scheme of flexible loads requires an accurate and tractable model that captures their aggregate flexibility. This paper proposes a novel approach to extract the aggregate flexibility of deferrable loads with heterogeneous parameters using polytopic projection approximation. First, an exact characterization of their aggregate flexibility is derived analytically, which in general contains exponentially many inequality constraints with respect to the number…
We consider the problem of planning the aggregate energy consumption for a set of thermostatically controlled loads for demand response, accounting price forecast trajectory and thermal comfort constraints. We address this as a continuous-time optimal control problem, and analytically characterize the structure of its solution in the general case. In the special case when the price forecast is monotone and the loads have equal dynamics, we show that it is possible to determine the solution in an explicit form. Taking this fact into account, we handle the non-monotone price case by considering …
The flexibility of active ($p$) and reactive power ($q$) consumption in distributed energy resources (DERs) can be represented as a (potentially non-convex) set of points in the $p$-$q$ plane. Modeling of the aggregated flexibility in a heterogeneous ensemble of DERs as a Minkowski sum (M-sum) is computationally intractable even for moderately sized populations. In this article, we propose a scalable method of computing the M-sum of the flexibility domains of a heterogeneous ensemble of DERs, which are allowed to be non-convex, non-compact. In particular, the proposed algorithm computes a guar…
Increasing integration of distributed energy resources (DERs) within distribution feeders provides unprecedented flexibility at the distribution-transmission interconnection. To exploit this flexibility and to use the capacity potential of aggregate DERs, feasible substation power injection trajectories need to be efficiently characterized. This paper provides an ellipsoidal inner approximation of the set of feasible power injection trajectories at the substation such that for any point in the set, there exists a feasible disaggregation strategy of DERs for any load uncertainty realization. Th…
Aggregators have emerged as crucial tools for the coordination of distributed, controllable loads. To be used effectively, an aggregator must be able to communicate the available flexibility of the loads they control, as known as the aggregate flexibility to a system operator. However, most of existing aggregate flexibility measures often are slow-timescale estimations and much less attention has been paid to real-time coordination between an aggregator and an operator. In this paper, we consider solving an online optimization in a closed-loop system and present a design of real-time aggregate…
In recent years, electric vehicle (EV) charging stations have witnessed a rapid growth. However, effective management of charging stations is challenging due to individual EV owners' privacy concerns, competing interests of different stations, and the coupling distribution network constraints. To cope with this challenge, this paper proposes a two-stage scheme. In the first stage, the aggregate EV power flexibility region is derived by solving an optimization problem. We prove that any trajectory within the obtained region corresponds to at least one feasible EV dispatch strategy. By submittin…
Unlocking Deep Demand Flexibility via Dynamic Signals
National Laboratory of the Rockies（落基山国家实验室）；Stanford Graduate School of Business（斯坦福大学商学院）；Eaton Research Labs（伊顿研究实验室）；Trellis Climate at Prime（Prime旗下的Trellis气候项目）
Optimal Ensemble Control of Loads in Distribution Grids with Network Constraints
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Tandon School of Engineering, New York University（纽约大学坦登工程学院）
With the increased share of Distributed Generation (DG) and Demand Responsive (DR) loads in the power systems, new approaches based on the game theory framework have been proposed to tackle the problem of coordination of Price Responsive Devices (PRD). The PRDs are modeled as self-benefiting players who try to optimize their consumption based on the price. In this paper, for the first time, a new algorithm based on the Dantzig-Wolfe (DW) Decomposition method to solve the coordination problem of self-benefiting PRDs in a distributed fashion has been proposed. By utilizing the distributed nature…
