# Convex inner approximation of the feeder hosting capacity limits on dispatchable demand

## TL;DR

This paper introduces a convex inner approximation method for distribution feeders that ensures feasible operation of dispatchable demand by accurately modeling voltage constraints considering both real and reactive power.

## Contribution

It proposes a novel convex inner approximation technique that guarantees feasible voltage levels in distribution networks considering real and reactive power effects.

## Key findings

- The method improves the feasibility of OPF models in resistive distribution networks.
- Validation on IEEE test networks confirms the effectiveness of the approach.
- The approach ensures dispatchable resources operate within feasible voltage limits.

## Abstract

This paper presents a method to obtain a convex inner approximation that aims to improve the feasibility of optimal power flow (OPF) models in distribution feeders. For a resistive distribution network, both real and reactive power effect the node voltages and this makes it necessary to consider both when formulating the OPF problem. Inaccuracy in linearized OPF models may lead to under and over voltages when dispatching flexible demand, at scale, in response to whole-sale market or grid conditions. In order to guarantee feasibility, this paper obtains an inner convex set in which the dispatchable resources can operate, based on their real and reactive power capabilities, that guarantees network voltages to be feasible. Test simulations are conducted on a standard IEEE distribution test network to validate the approach.