# Optimal multi-period dispatch of distributed energy resources in unbalanced distribution feeders

## TL;DR

This paper presents an efficient algorithm for multi-period optimal dispatch of energy storage in unbalanced distribution feeders with high solar PV, ensuring AC feasibility and near-optimal solutions within a minute.

## Contribution

It introduces a convex SOCP-based dispatch method combined with NLP refinement to handle unbalanced feeders and prevent simultaneous charging and discharging of batteries.

## Key findings

- Achieves AC-feasible, near-optimal dispatch solutions.
- Solves within a minute for large test feeders.
- Effectively manages high solar PV variability.

## Abstract

This paper develops an efficient algorithm for the multi-period optimal dispatch of deterministic inverter-interfaced energy storage in an unbalanced distribution feeder with significant solar PV penetration. The three-phase, non-convex loss-minimization problem is formulated as a convex second order cone program (SOCP) for the dispatch of batteries in a receding-horizon fashion in order to counter against the variable renewable net-load generation. The solution of the SOCP is used to initialize a nonlinear program (NLP) in order to ensure a physically realizable solution. The phenomenon of simultaneous charging and discharging of batteries is rigorously analyzed and conditions are derived that guarantee it is avoided. Simulation scenarios are implemented with GridLab-D for the IEEE-13 and IEEE-123node test feeders and illustrate not only AC feasibility of the solution, but also near-optimal performance and solve-times within a minute.