A Fast Distributed Algorithm for Large-Scale Demand Response Aggregation

Abstract

Abstract-A major challenge to implementing residential demand response is that of aligning the objectives of many households, each of which aims to minimize its payments and maximize its comfort level, while balancing this with the objectives of an aggregator that aims to minimize the cost of electricity purchased in a pooled wholesale market. This paper presents a fast distributed algorithm for aggregating a large number of households with a mixture of discrete and continuous energy levels. A distinctive feature of the method in this paper is that the nonconvex DR problem is decomposed in terms of households as opposed to devices, which allows incorporating more intricate couplings between energy storage devices, appliances and distributed energy resources. The proposed method is a fast distributed algorithm applied to the double smoothed dual function of the adopted DR model. The method is tested on systems with up to 2560 households, each with 10 devices on average. The proposed algorithm is designed to terminate in 60 iterations irrespective of system size, which can be ideal for an online version of this problem. Moreover, numerical results show that with minimal parameter tuning, the algorithm exhibits a very similar convergence behavior throughout the studied systems and converges to near-optimal solutions, which corroborates its scalability.

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“…Some of (centralized) deterministic algorithms, e.g., [18], rely on (commercial) solvers which may not be scalable to very large systems to meet the requirement of realtime control. b) Controlling Devices with Dynamics: Controllable devices with dynamics are usually handled in two ways: control based on heuristic or engineering intuition, see, e.g., [19] that controls TCLs based on temperature status; and optimizationbased control that can integrate specific objective functions and constraints, see, e.g., [20] that considers device dynamics but does not involve discrete variables, [21] that considers device dynamics and discrete decision variables but employs commercial solvers, [22], [23] that solve OPF over various devices with dynamics but consider equality constraints only, and [24], [25] that formulate mixed-integer linear programs which cannot be applied to solving more general problems with convex cost functions. c) Market-Based/Demand-Response Design: Existing literature on market-based and demand-response problem formulation mostly focuses on demand/supply balancing, without considering network structure, see, e.g., [3]- [6], [20], [21], [26].…”

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