# Stochastic Optimal Power Flow in Distribution Grids under Uncertainty from State Estimation

## TL;DR

This paper addresses the challenge of maintaining voltage levels in distribution grids with uncertain state estimation by formulating a stochastic optimal power flow problem, proposing a tractable solution, and demonstrating its effectiveness through case studies.

## Contribution

It introduces a novel stochastic optimal power flow formulation that accounts for state estimation uncertainty and provides a practical, less conservative solution method for distribution grids.

## Key findings

- The proposed method effectively maintains voltage within limits under uncertainty.
- Ignoring estimation uncertainty can cause voltage violations.
- The approach outperforms deterministic methods in uncertain conditions.

## Abstract

The increasing amount of controllable generation and consumption in distribution grids poses a severe challenge in keeping voltage values within admissible ranges. Existing approaches have considered different optimal power flow formulations to regulate distributed generation and other controllable elements. Nevertheless, distribution grids are characterized by an insufficient number of sensors, and state estimation algorithms are required to monitor the grid status. We consider in this paper the combined problem of optimal power flow under state estimation, where the estimation uncertainty results into stochastic constraints for the voltage magnitude levels instead of deterministic ones. To solve the given problem efficiently and to bypass the lack of load measurements, we use a linear approximation of the power flow equations. Moreover, we derive a transformation of the stochastic constraints to make them tractable without being too conservative. A case study shows the success of our approach at keeping voltage within limits, and also shows how ignoring the uncertainty in the estimation can lead to voltage level violations.