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Under transactive (market-based) coordination, a population of distributedenergy resources (DERs), such as thermostatically controlled loads (TCLs) andstorage devices, bid into an energy market. Consequently, a certain level ofdemand will be cleared based on the operating conditions of the grid. Thispaper analyzes the influence of various factors, such as price signals, feederlimits, and user-defined bid functions and preferences, on the aggregate energyusage of DERs. We identify cases that can lead to load synchronization,undesirable power oscillations and highly volatile prices. To address theseissues, the paper develops an aggregate model of DERs under transactivecoordination. A set of Markov transition equations have been developed overdiscrete ranges (referred to as "bins") of price levels and their associatedDER operating states. A detailed investigation of the performance of thisaggregate model is presented. With reformulation of the transition equations,the bin model has been incorporated into a model predictive control settingusing both mixed integer programming and quadratic programming. A case studyshows that a population of TCLs can be managed economically while avoidingcongestion in a distribution grid. Simulations also demonstrate that poweroscillations arising from synchronization of TCLs can be effectively avoided.

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