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The automatic generation control (AGC) system is temporally situated between economic dispatch and synchronous generator dynamics, and its primary role is to regulate frequency within and tie-line flows between control areas. Given appropriate choice of participation factors (feed-forward controller gains that govern the disaggregation of the area-level power requirement to individual generators), the AGC can be engineered to nudge system dynamics toward a steady-state operating point corresponding to economic optimality. This paper establishes necessary and sufficient conditions under which a widely accepted choice of participation factors guarantees the alignment of steady-state synchronous generator outputs with a global minimum of a prototypical economic dispatch problem. In so doing, it resolves several ambiguities and formalizes technical assumptions governing the role of the standard AGC architecture in the context of economic dispatch and steady-state operation. Numerical case studies tailored to a modified version of the New England 39-bus 10-machine test system validate the theoretical results. [ABSTRACT FROM AUTHOR]

Power flow formulated with a distributed slack bus involves modeling the active-power output of each generator with three elements: a nominal injection modulated by a fraction of the net-load imbalance allocated via a participation factor. This setup acknowledges generator dynamics and system operations, but it has long been plagued by ambiguous and inconsistent interpretations of its constituent elemental quantities. In this paper, we establish that, with the: i) nominal active-power injections set to be the economic dispatch setpoints, ii) participation factors fixed to be the ones used in automatic generation control, and iii) net-load imbalance considered to be the total load and loss unaccounted in economic dispatch, the power flow solution best matches results from a simulation unto steady state of the system differential algebraic equation (DAE) model. Numerical case studies tailored to the New England test system validate the analysis by demonstrating that solutions obtained from a distributed slack formulation offer lower errors (with respect to DAE-model simulations) compared to the exhaustive set of all single slack bus choices. [ABSTRACT FROM AUTHOR]

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]