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  1. We consider radial distribution networks hosting Distributed Energy Resources (DERs), including Solar Photo­voltaic (PV) and storage-like loads, such as Electric Vehicles (EVs). We employ short-run dynamic Distribution Locational Marginal Costs (DLMCs) of real and reactive power to co­optimize distribution network and DER schedules. Striking a balance between centralized control and distributed self­dispatch, we present a novel hierarchical decomposition ap­proach that is based on centralized AC Optimal Power Flow (OPF) interacting with DER self-dispatch that adapts to real and reactive power DLMCs. The proposed approach is designed to be highly scalable for massive DER Grid integration with high model fidelity incorporating rigorous network component dynamics and costs and reffecting them in DLMCs. We illustrate the use of an Enhanced AC OPF to discover spatiotemporally varying DLMCs enabling optimal Grid-DER coordination in­corporating congestion and asset (transformer) degradation. We employ an actual distribution feeder to exemplify the use of DLMCs as financial incentives conveying sufficient information to optimize Distribution Network and DER (PV and EV) operation, and we discuss the applicability and tractability of the proposed approach, while modeling the full complexity of spatiotemporal DER capabilities and preferences.
  2. The Holomorphic Embedding Load flow Method (HELM) employs complex analysis to solve the load flow problem. It guarantees finding the correct solution when it exists, and identifying when a solution does not exist. The method, however, is usually computationally less efficient than the traditional Newton-Raphson algorithm, which is generally considered to be a slow method in distribution networks. In this paper, we present two HELM modifications that exploit the radial and weakly meshed topology of distribution networks and significantly reduce computation time relative to the original HELM implementation. We also present comparisons with several popular load flow algorithms applied to various test distribution networks.
  3. We consider decentralized scheduling of Distributed Energy Resources (DERs) in a day-ahead market that clears energy and reserves offered by both centralized generators and DERs. Recognizing the difficulty of scheduling transmission network connected generators together with distribution feeder connected DERs that have complex intertemporal preferences and dynamics, we propose a tractable distributed algorithm where DERs self-schedule based on granular Distribution Locational Marginal Prices (DLMPs) derived from LMPs augmented by distribution network costs. For the resulting iterative DER self-scheduling process, we examine the opportunity of DERs to engage in strategic behavior depending on whether DERs do or do not have access to detailed distribution feeder information. Although the proposed distributed algorithm is tractable on detailed real-life network models, we utilize a simplified T&D network model to derive instructive analytical and numerical results on the impact of strategic DER behavior on social welfare loss, and the distribution of costs and benefits to various market participants.