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This paper outlines a procedure to design power–frequency droop slopes for distributed energy resources (DERs) installed in distribution networks to optimally participate in primary frequency response. In particular, the droop slopes are engineered such that DERs respond in proportion to their power ratings and they are not unfairly penalized in power provisioning based on their location in the distribution network. The main contribution of our approach is that a guaranteed level of frequency regulation can be obtained at the feeder head, while ensuring that the outputs of individual DERs conform to some well-defined notion of fairness. The approach we adopt leverages an optimization-based perspective and suitable linearizations of the power-flow equations to embed notions of fairness and information regarding the physics of the power flows within the distribution network into the droop slopes. Time-domain simulations from a differential algebraic equation model of the 39-bus New England test-case system augmented with three instances of the IEEE 37-node distribution network with frequency-sensitive DERs are provided to validate our approach. [ABSTRACT FROM PUBLISHER]

This paper develops a real-time algorithmic framework for aggregations of distributed energy resources (DERs) in distribution networks to provide regulation services in response to transmission-level requests. Leveraging online primal-dual-type methods for time-varying optimization problems and suitable linearizations of the nonlinear AC power-flow equations, this work establishes a system-theoretic foundation to realize the vision of distribution-level virtual power plants. The optimization framework controls the output powers of dispatchable DERs such that, in aggregate, they respond to automatic generation control and/or regulation-services commands. This is achieved while concurrently regulating voltages within the feeder and maximizing customers’ and utility's performance objectives. Convergence and tracking capabilities are analytically established under suitable modeling assumptions. Simulations are provided to validate the proposed approach. [ABSTRACT FROM AUTHOR]