A Dynamical Systems Approach to Modeling and Analysis of Transactive Energy Coordination

Abstract

Under transactive (market-based) coordination, a population of distributed energy resources (DERs), such as thermostatically controlled loads (TCLs) and storage devices, bid into an energy market. Consequently, a certain level of demand will be cleared based on the operating conditions of the grid. This paper analyzes the influence of various factors, such as price signals, feeder limits, and user-defined bid functions and preferences, on the aggregate energy usage of DERs. We identify cases that can lead to load synchronization, undesirable power oscillations and highly volatile prices. To address these issues, the paper develops an aggregate model of DERs under transactive coordination. A set of Markov transition equations have been developed over discrete ranges (referred to as "bins") of price levels and their associated DER operating states. A detailed investigation of the performance of this aggregate model is presented. With reformulation of the transition equations, the bin model has been incorporated into a model predictive control setting using both mixed integer programming and quadratic programming. A case study shows that a population of TCLs can be managed economically while avoiding congestion in a distribution grid. Simulations also demonstrate that power oscillations arising from synchronization of TCLs can be effectively avoided.

An integrated transmission and distribution test system for evaluation of transactive energy designs

“…Although a careful study of TES design in relation to power spiking is beyond the scope of the current paper, we note that some research on this important topic has already been conducted. For example, Nazir and Hiskens [45] demonstrate that unintended oscillations in aggregate power usage can arise from a number of different factors, including bid function formulations, distribution feeder capacity limits, and the timing of price signals. In particular, Nazir and Hiskens [45] stress the role of lock-out conditions during which customers require uninterrupted power supply.…”

“…8 Centrally-managed TES designs can in turn be divided into two basic types, direct and iterative. In direct forms, referred to in [8] as one-time information exchange-based designs, an aggregator sets the terms of trade in each market period directly following the receipt of bids from GERs; see, for example, [45]. In iterative forms, referred to in [8] as iterative information exchange-based designs, an aggregator sets the terms of trade in each market period only after multiple information exchanges have taken place between the aggregator and GER participants.…”

“…Although a careful investigation of bid-function formulation in relation to TES design performance is outside the scope of our current study, we note that much work on this important topic is currently under way [45][46][47][48]. In general, different bid-function formulations will lead to different messages (functions) that need to be exchanged among agents.…”

Optimal and Resilient Coordination of Virtual Batteries in Distribution Feeders

“…where P set,r refers to the set-point provided by the optimal set-point dispatcher about every minute, K r is a proportional controller that is further adjusted by a factor K adj,r (as defined in (18), see below). The net VB power, p b,r , (computed from (6)) is injected into the "Feeder" block (which represents the feeder with nodal active power injections as input and its head node active power as output) at the respective location.…”

“…Some of these schemes focus on broadcasting prices directly to devices. However, with large-scale participation of DERs, transactive energy is susceptible to harmful load synchronization effects, power oscillations, and volatile prices, as shown in [18]. Other grid-aware approaches include optimization-based methods to account for AC network constraints [19], where VB control is achieved by solving an optimization problem based on AC network models and tracking a Karush-Kuhn-Tucker (KKT) point that satisfies the KKT optimality conditions.…”