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 flexibility feedback, termed the maximum entropy feedback (MEF). In addition to deriving analytic properties of the MEF, combining learning and control, we show that it can be approximated using reinforcement learning and used as a penalty term in a novel control algorithm -- the penalized predictive control (PPC), which modifies vanilla model predictive control (MPC). The benefits of our scheme are (1). Efficient Communication. An operator running PPC does not need to know the exact states and constraints of the loads, but only the MEF. (2). Fast Computation. The PPC often has much less number of variables than an MPC formulation. (3). Lower Costs. We show that under certain regularity assumptions, the PPC is optimal. We illustrate the efficacy of the PPC using a dataset from an adaptive electric vehicle charging network and show that PPC outperforms classical MPC.
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…
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…
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 polyt…
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…
Tube-enhanced multi-stage nonlinear model predictive control is a robust control scheme that can handle a wide range of uncertainties with reduced conservatism and manageable computational complexity. In this paper, we elaborate on the flexibility of the approach from an application point of view. We discuss the path to making design decisions to implement the novel scheme systematically. We illustrate the critical steps in the design and implementation of the scheme for an industrial example.
Optimal scheduling of deferrable electrical loads can reshape the aggregated load profile to achieve higher operational efficiency and reliability. This paper studies deferrable load scheduling under demand charge that imposes a penalty on the peak consumption over a billing period. Such a terminal cost poses challenges in real-time dispatch when demand forecasts are inaccurate. A block model-predictive control approach is proposed by breaking demand charge into a sequence of stage costs. The problem of charging electric vehicles is used to illustrate the efficacy of the proposed approach. Num…
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）
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 …
Most literature surrounding optimal bidding strategies for aggregators in European day-ahead market (DAM) considers only hourly orders. While other order types (e.g., block orders) may better represent the temporal characteristics of certain sources of flexibility (e.g., behind-the-meter flexibility), the increased combinations from these orders make it hard to develop a tractable optimization formulation. Thus, our aim in this paper is to develop a tractable optimal offering strategy for flexibility aggregators in the European DAM (a.k.a. Elspot) considering these orders. Towards this, we emp…
