Hierarchical, Grid-Aware, and Economically Optimal Coordination of Distributed Energy Resources in Realistic Distribution Systems.

Renewable portfolio standards are targeting high levels of variable solar photovoltaics (PV) in electric distribution systems, which makes reliability more challenging to maintain for distribution system operators (DSOs). Distributed energy resources (DERs), including smart, connected appliances and PV inverters, represent responsive grid resources that can provide flexibility to support the DSO in actively managing their networks to facilitate reliability under extreme levels of solar PV. This flexibility can also be used to optimize system operations with respect to economic signals from wholesale energy and ancillary service markets. Here, we present a novel hierarchical scheme that actively controls behind-the-meter DERs to reliably manage each unbalanced distribution feeder and exploits the available flexibility to ensure reliable operation and economically optimizes the entire distribution network. Each layer of the scheme employs advanced optimization methods at different timescales to ensure that the system operates within both grid and device limits. The hierarchy is validated in a large-scale realistic simulation based on data from the industry. Simulation results show that coordination of flexibility improves both system reliability and economics, and enables greater penetration of solar PV. Discussion is also provided on the practical viability of the required communications and controls to implement the presented scheme within a large DSO.

Long signaling cascades tend to attenuate retroactivity.

Signaling pathways consisting of phosphorylation/dephosphorylation cycles with no explicit feedback allow signals to propagate not only from upstream to downstream but also from downstream to upstream due to retroactivity at the interconnection between phosphorylation/dephosphorylation cycles. However, the extent to which a downstream perturbation can propagate upstream in a signaling cascade and the parameters that affect this propagation are presently unknown. Here, we determine the downstream-to-upstream steady-state gain at each stage of the signaling cascade as a function of the cascade parameters. This gain can be made smaller than 1 (attenuation) by sufficiently fast kinase rates compared to the phosphatase rates and/or by sufficiently large Michaelis-Menten constants and sufficiently low amounts of total stage protein. Numerical studies performed on sets of biologically relevant parameters indicated that ∼50% of these parameters could give rise to amplification of the downstream perturbation at some stage in a three-stage cascade. In an n-stage cascade, the percentage of parameters that lead to an overall attenuation from the last stage to the first stage monotonically increases with the cascade length n and reaches 100% for cascades of length at least 6.